Multi-Organ Modeling of Respiratory Motion

Multi-Organ Modeling of Respiratory Motion - ETH E

DISS. ETH NO. 22217
Multi-Organ Respiratory Motion Modeling
A dissertation submitted to
ETH ZURICH
for the degree of
Doctor of Sciences (Dr. sc. ETH Zürich)
presented by
Golnoosh Samei
M. Sc. in computer science
born September 19, 1985
citizen of Iran
accepted on the recommendation of
Prof. Dr. Gábor Székely, ETH Zürich, examiner
Prof. Dr. Horst Karl Hahn, Fraunhofer MEVIS, Bremen, co-examiner
Dr. Christine Tanner, ETH Zürich, co-examiner
2014
Abstract
The work presented in this thesis aims at improving the applicability of Magnetic Resonance guided High Intensity Focused Ultrasound (MRgHIFU) for abdominal organs with
a focus on the liver. MRgHIFU is an emerging and promising minimally-invasive therapy for tumour treatment. Unfortunately, its application in abdominal organs such as the
liver has remained limited due to two major problems, namely respiratory motion and the
presence of ribs along the beam path.
A model-based method to automatically detect ribs in MR images is presented. This
method combines a geometric ribcage model with an appearance model of ribs in MRI.
The geometric model, which is built from a rib cage population obtained from CT data,
describes the centerline of the 4 ribs which enclose the liver, using 6 parameters for each
rib. For a given MR image, these parameters are found such that the resulting rib cage
best fits the image according to a previously learned MR appearance model.
Moreover, a registration method for tracking the respiratory motion of ribs in 4DMR images is proposed. Based on the kinematics of ribs, this method constrains the space of possible rigid transformations for each rib to an anatomically plausible subset. Evaluations
of the results demonstrated good accuracy and suitability for creating motion models.
To model the motion of the liver during therapy, a non-parametric method is introduced
which is capable of modeling a non-homogeneous population. This model was able to
predict the motion of liver points from partial observations and outperforms existing methods by 10%. Finally, a subject-specific and a population-based joint rib-liver model were
created which could compensate for 60% and 40% of the respiratory motion of the ribs,
respectively.
Zusammenfassung
Das Ziel der in dieser Dissertation vorgestellten Studien ist die Verbesserung der Anwendung von magnetresonanzgesteuertem hochintensivem fokussiertem Ultraschall (Magnetic Resonance guided High Intensity Focused Ultrasound, MRgHIFU) auf Bauchorgane,
insbesondere die Leber. MRgHIFU ist eine vielversprechende, sich noch entwickelnde
Krebstherapie der minimal-invasiven Chirurgie. Ihre Anwendung auf Bauchorgane wie
die Leber war bisher allerdings von zwei Problemen behindert, nämlich der Atembewegung und der Abschattung der Organe durch die Rippen.
Zunächst führen wir eine modellbasierte Methode zur automatischen Erkennung von Rippen in MR Bildern ein. Diese Methode vereint ein geometrisches Modell des Brustkorbes mit einem Erscheinungsmodell der Rippen in MR Bildern. Das geometrische Modell
wurde aus CT Daten von Brustkörben gewonnen und beschreibt mit sechs Parametern die
Mittellinie derjenigen vier Rippen, die die Leber einschliessen. Diese Parameter werden
für jedes gegebene MR Bild so bestimmt, dass der resultierende Brustkorb am Besten,
bezüglich des Erscheinungsmodelles, zu dem Bild passt.
Desweiteren stellen wir eine Methode zur Bildregistrierung vor, die die Bewegung der
Rippen während des Atmens quantifiziert. Ausgehend von der Kinematik der Rippen bestimmt diese Methode für jede Rippe die Menge aller für sie realistischen Bewegungen im
Raum aller möglichen euklidischen (starren) Transformationen. Die Resultate bezeugen
hohe Genauigkeit und Eignung der Methode zum Erstellen von Bewegungsmodellen.
Schliesslich beschreiben wir eine Methode für die statistische Vorhersage der Bewegung
der Leber während der Therapie, die auch auf inhomogene Datensätze einer Bevölkerung
angewendet werden kann. Die Methode bestimmt die Bewegung der ganzen Leber anhand
weniger Teilbeobachtungen und erreicht dabei eine um 10% höhere Genauigkeit als alle
bisherigen Modelle. Zuletzt erstellen wir aus all diesen Resultaten patientenspezifische
und bevölkerungsbasierte Modelle zur simultanen Beschreibung von Rippen und Leber.
Ausgehend von Teilbeobachtungen der Leber, können diese Modelle 60% respektive 40%
der Atembewegung der Rippen kompensieren.
Acknowledgements
This thesis would not have been possible without the help of so many people and I would
like to extend my sincere gratitude to all of them.
First and foremost, I would like to thank my advisor, Prof. Dr. Gábor Székely who
provided me with the opportunity and freedom to explore this exciting field of research. I
would also like to thank my supervisor, Dr. Christine Tanner who supported me greatly,
gave me independence and taught me how to persevere in research.
I am very grateful to Prof. Dr. Bjoern Menze and Prof. Dr. Orcun Goksel for interesting
discussions and their help and support with my research.
I greatly appreciate the help of Prof. Dr. Sebastian Kozerke and Dr. Johannes Schmidt in
the data acquisition.
I would like to thank all my colleagues at CVL (former BIWI), especially my officemates,
Danfeng, Valeria and Angela, for the friendly and productive atmosphere and the countless constructive discussions. I am especially grateful to my friends, Sarah, Hossein and
Asal who were always there for me through all the ups and downs.
I would also like to acknowledge the grant no 270186 from the EU’s Seventh Framework
Programme which funded my research at Computer Vision Laboratory.
Lastly, I would like to thank my family, Maman, Baba and Soorena, without whose unconditional love, sacrifices and support throughout my education, I would not be the person
I am. And to Martin, thanks for your unlimited understanding, patience and encouragement.
Contents
1 Introduction
1.1 MRgHIFU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Current State of MRgHIFU for Liver Treatment . . . . . . .
1.2 Organization of the Thesis and Contributions . . . . . . . . . . . .
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2 Management of Respiratory Motion in Abdominal Organs during Extracorporeal Therapies
2.1 Respiratory Induced Motion of Abdominal Organs and its Effects
on Therapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Effects of Abdominal Respiratory Motion on Therapy . . . .
2.2 Methods for Measuring and Monitoring Respiratory Motion . . . .
2.2.1 Pre-therapy Imaging Methods and Motion Observations . .
2.2.2 Intra-therapy Indirect Monitoring . . . . . . . . . . . . . . .
2.2.3 Intra-therapy Direct Monitoring . . . . . . . . . . . . . . . .
2.3 Organ Motion Management Techniques . . . . . . . . . . . . . . .
2.3.1 Motion Restriction . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Breath-hold . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Gating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Real-time Motion Compensation or Tracking . . . . . . . . .
2.3.5 Motion Management in MR guided HIFU . . . . . . . . . . .
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3 Rib Segmentation in Magnetic Resonance Images
3.1 Introduction . . . . . . . . . . . . . . . . . . . . .
3.2 Related Work . . . . . . . . . . . . . . . . . . . .
3.2.1 Rib Segmentation in Chest Radiographs .
3.2.2 Ribs Segmentation in Chest CT . . . . . .
3.2.3 Rib Segmentation in MRI . . . . . . . . .
3.3 Materials . . . . . . . . . . . . . . . . . . . . . .
3.4 Ribcage Statistical Shape Model . . . . . . . . .
3.4.1 Ribcage Model . . . . . . . . . . . . . . .
3.4.2 Preprocessing steps . . . . . . . . . . . .
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5
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C ONTENTS
3.5
3.6
3.7
3.8
3.4.3 Points Correspondence . .
3.4.4 Ribs Orientation . . . . . .
3.4.5 Rib Shape Model . . . . . .
3.4.6 Ribcage Parameters . . . .
Rib Appearance Model . . . . . . .
3.5.1 Ground Truth . . . . . . . .
3.5.2 Random Forest Classifiers
Ribcage Fitting . . . . . . . . . . .
3.6.1 Cost Function . . . . . . . .
3.6.2 Optimization Strategy . . .
Experiments and Results . . . . .
3.7.1 Error Measures . . . . . . .
Discussion and Conclusion . . . .
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4 Rib Registration in Magnetic Resonance Images
4.1 Introduction . . . . . . . . . . . . . . . . . . . .
4.2 Ribcage Anatomy and Kinematics . . . . . . .
4.2.1 Ribcage Anatomy . . . . . . . . . . . .
4.2.2 Ribs Kinematics . . . . . . . . . . . . .
4.3 Rib Registration Method . . . . . . . . . . . . .
4.3.1 Transformation Model . . . . . . . . . .
4.3.2 Similarity Measure . . . . . . . . . . . .
4.3.3 Optimization Method . . . . . . . . . . .
4.4 Experiments and Results . . . . . . . . . . . .
4.4.1 Breath-hold Images . . . . . . . . . . .
4.4.2 4DMR Images . . . . . . . . . . . . . .
4.5 Discussion and Conclusion . . . . . . . . . . .
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5 Motion Modeling of Liver and Ribs
5.1 Introduction . . . . . . . . . . . . . . . . . . . .
5.2 Review of Statistical Motion Models . . . . . .
5.2.1 Principle Component Analysis . . . . .
5.2.2 Patient-specific models . . . . . . . . .
5.2.3 Population models . . . . . . . . . . . .
5.3 Predicting Liver Motion Using Exemplar Models
5.3.1 Liver Motion Data . . . . . . . . . . . .
5.3.2 Motion Model Concept . . . . . . . . . .
5.3.3 Subject-specific PCA Modeling . . . . .
5.3.4 Population PCA Modeling . . . . . . . .
5.3.5 Exemplars Modeling . . . . . . . . . . .
5.3.6 Experiments and Results . . . . . . . .
5.3.7 Discussion and Conclusion . . . . . . .
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C ONTENTS
5.4 Joint Modeling of the Respiratory Motion of Liver and Ribs . . . . .
5.4.1 Ribs and Liver Motion Model . . . . . . . . . . . . . . . . .
5.4.2 Conclusion and Discussion . . . . . . . . . . . . . . . . . .
6 Summary and Outlook
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List of Abbreviations
2D
2 dimensional
3D
3 dimensional
4D
4 dimensional
ABC
active breathing control
AP
anterior-posterior
BH
bucket handle
CC
cranio-caudal
COM
center of mass
CT
computed tomography
DIBH
deep inspiration breath-hold
EE
end-exhalation
EI
end-inhalation
FEM
finite element model
FUS
focused ultrasound
GT
ground truth
GTV
gross tumour volume
HIFU
high intensity focused ultrasound
IMRT
intensity modulated radiation therapy
IS
inferior-superior
KL
Kullback-Leibler
K-PCA
kernel principal component analysis
LR
left-right
MI
mutual information
ML
medial-lateral
mm
millimeter
MR(I)
magnetic resonance (image)
MRF
Markov random field
MRgHIFU magnetic resonance guided high intensity focused ultrasound
LIST OF ABBREVIATIONS
NCC
PC(A)
PDM
PH
PTV
RF
RT
SSD
US
USgHIFU
normalized cross correlation
principal component (analysis)
point distribution model
pump handle
planning target volume
random forest
radiotherapy
sum of squared differences
ultrasound
ultrasound guided high intensity focused ultrasound
viii
1
Introduction
Magnetic resonance guided high intensity focused ultrasound (MRgHIFU) is an emerging and promising extracorporeal therapy to ablate malignant tissues. This method has
already been granted approval for treating uterine fibroid tissue (Food and Administration
[a]) and for pain palliation of metastatic bone cancer (Food and Administration [b]) by the
Federal Drug Administration (FDA) in the USA. However, application of this method for
abdominal organs such as the liver, remains a challenge due to multiple reasons. Firstly,
the ribs which lie on the beam path absorb and reflect the ultrasound energy. This has an
important effect on reducing the efficacy of the therapy at the target, as well as leading to
energy deposit on the neighbouring tissues such as skin, causing them to burn (Kennedy
et al. [2002]). Secondly, the respiratory motion of the target organ as well as the organs
and structures on the beam path can have adverse effects on HIFU therapy. On the one
hand, these motions hinder the delivery of the necessary therapeutic dose to the target. On
the other hand, they expose healthy neighbouring tissues to harmful heat deposit.
The works presented in this thesis aim to overcome the issues mentioned above. In the
next section, an overview of the MRgHIFU therapy is given. In Sec. 1.2, the contributions
of the author and the organization of the thesis are described.
1.1
MRgHIFU
The effects of thermal energy on living cells has been well studied (Miller and Ziskin
[1989]). At temperatures higher than 45◦ C evidences of cell damage become visible,
and at 60◦ C one second of exposure is sufficient to cause cell death. A high intensity
ultrasound beam which is brought to a focus can increase the temperature at the target site
to over 80◦ C within a few seconds (Ter et al. [1991], Hill and Ter Haar [1995]).
Even though high intensity focused ultrasound (HIFU) is not a new technology and its
effect on causing coagulative necrosis of tissues was known for decades (Lynn et al.
[1942], Fry et al. [1955], Wells et al. [1963]), its applicability remained limited for a
1.1. MR G HIFU
2
long time due to a lack of targeting capability. The use of real-time ultrasound imaging
to guide the HIFU therapy (USgHIFU) paved the way for its routine clinical application
(Gelet et al. [1995], NAKAMURA et al. [1997], Wu et al. [2005]). MR imaging was also
proposed for guiding the HIFU therapy (Cline et al. [1992]), which in addition to excellent
target visualisation, has the advantage of providing continuous 2D temperature mapping
using the proton resonance frequency shift technique (Poorter et al. [1995], Ishihara et al.
[1995], de Senneville et al. [2007]) or pulse sequences monitoring changes in relaxation
time (Dickinson et al. [1985], Stepanow et al. [1993], Cline et al. [1994], Schwarzbauer
et al. [1995]). This enabled real-time monitoring of thermal effects at the target zone
as well as the surrounding tissues during the therapy. Therapeutic systems have been
designed based on this concept (Dick and Gedroyc [2010]) and used in ablating tissues
in static organs such as fibroids in uterus (Stewart et al. [2006], Rabinovici et al. [2007]),
and tumours in brain (Ram et al. [2006]). Unfortunately, the application of these systems
in abdominal organs has been limited. This is mainly due to their respiratory motion,
but also to the presence of ribcage which limits the available acoustic window. In the
next section, we explain these challenges and describe the limited clinical trials aiming at
performing MRgHIFU on abdominal organs.
1.1.1
Current State of MRgHIFU for Liver Treatment
Due to the limitations mentioned in the previous section, MRgHIFU is still not being
routinely performed for treatment of tumours in abdominal organs. Even though there
have been some reports about clinical trials of USgHIFU for the treatment of liver tumours
(Kennedy et al. [2004], Illing et al. [2005], Okada et al. [2006]), only one describes the
use of MRgHIFU for this purpose (Anzidei et al. [2014]).
Currently, MRgHIFU procedures (e.g. for treating fibroids in uterus) are performed
on a modified MR table equipped with an MR compatible high power ultrasound (US)
transducer (Ellis et al. [2013]). While initial basic US devices consisted of a single element transducer which was mechanically moved to ablate multiple sites (Hynynen et al.
[1996]), more advanced multiple element phased array transducers have been developed
whose focal point could be steered electronically (Daum and Hynynen [1999]). The patient is positioned on the table and a pelvic MR coil is placed around the region of interest.
Initially, planning images are acquired and the region of interest and the risk structures, including the bowels, ribs and skin, are delineated on them (Ellis et al. [2013]). Each single
HIFU exposure, a so called sonication, creates a small ablated region whose size varies
according to the transducer characteristics, but is generally in the range of 1-3 mm and
8-15 mm in the transverse plane and along the beam axis, respectively (Kennedy [2005]).
For treatment of common abdominal tumours, larger volumes of cells must be ablated.
Therefore, a number of sonications are performed, whose energy, location and number
are usually computed by the accompanying software of the MRgHIFU system, but can be
altered by the radiologist as necessary during the treatment (Ellis et al. [2013]).
1.2. O RGANIZATION OF THE T HESIS AND C ONTRIBUTIONS
3
As mentioned earlier, motion of the organs during free breathing is a major obstacle for
HIFU in abdominal organs and current approaches to mitigate its effects are sub-optimal.
For example, Okada et al. [2006] reported on the use of USgHIFU for treating a single
patient with liver tumour during voluntary breath-holds. This was done with the help
of coaching the patient and giving feedback through the use of respiratory monitoring
devices. However, the procedure took 120 minutes for a relatively small (15 mm in diameter) tumour. Illing et al. [2005] were also able to ablate liver tumours with a median
diameter of 33 mm using USgHIFU during the same amount of time (2 hours) relying
on a technique called single lung ventilation. This technique, which consists of intubating patients under general anaesthesia and ventilating the lung contralateral to the target
organ, was also used by Ritchie et al. [2010] for treating tumours in the kidney using USgHIFU. Anzidei et al. [2014] used a mechanical ventilator controlled by the MRgHIFU
system which temporarily halts the patient’s respiration (apnea) during sonication. Both
latter techniques, namely single lung ventilation and mechanically induced apnea, were
performed under general anaesthesia. Yet, general anaesthesia can lead to complications,
especially due to the relatively long therapy time. It is evident that such invasive approaches for respiratory motion management undermine the advantages of MRgHIFU. In
the next section, we outline the contributions of this thesis in overcoming some of the
major obstacles for safe and effective MRgHIFU in abdominal organs.
1.2
Organization of the Thesis and Contributions
As described in Sec. 1.1, respiratory motion of abdominal organs creates serious challenges for the application of HIFU to these organs. In Chapter 2 we review the stateof-the-art methods to manage respiratory motion of abdominal organs in extracorporeal
therapies. Accurate knowledge of the target organ motion, as well as structures on the
beam path, are crucial for overcoming these limits. However, currently, no imaging device is fast enough to allow real-time acquisition and quantification of the 3D motion of
the abdominal organs. Hence, partial observations need to be complemented by prior
knowledge about the expected 3D motion. To that end, the main goal of this thesis was
to construct a joint respiratory motion model of abdominal organs, in particular, the liver,
and the ribs enclosing them.
The presence of ribs on the beam path necessitates their delineation as risk structures
during therapy planning. This can be tedious and difficult given the poor visibility of
ribs in MR images. In Chapter 3, we propose a method to semi-automatically detect
the ribs enclosing the liver in MR images. This method takes advantage of the accuracy
of CT in imaging the ribs to build a geometric ribcage model and combines it with an
appearance model of the ribs and their neighbouring structures in MRIs to reconstruct
realistic centerlines. This method achieves a mean error of 2.5 mm, making it currently
1.2. O RGANIZATION OF THE T HESIS AND C ONTRIBUTIONS
4
the only one suitable for clinical application. The work described in this chapter was
presented in (Samei et al. [2014b]) and (Samei et al. [2014a]).
To gain information about the respiratory motion of the ribcage and its correlation with
that of the liver, one needs to track the ribs in 4DMRIs. In addition to being the imaging
modality in MRgHIFU, MR has the advantage that long acquisitions can be performed
without any known adverse effects on the volunteers. In Chapter 4 we propose an intramodality 3D rib registration method, which conserves the shape and length of ribs, and
imposes realistic constraints on their motions based on our geometric ribcage model. It
achieved a mean registration accuracy of 1.06 mm for 4DMRIs with 5 mm slice thickness.
Parts of the results and methods presented in this Chapter first appeared in (Samei et al.
[2014a]).
In Chapter 5, we first give a review on statistical motion models for abdominal organs
which is based on our survey paper (Tanner et al. [2012]). Then we describe our proposed
population respiratory motion model based on motion exemplars. Most approaches in
statistical respiration modeling either build a subject-specific model which is only suitable
for that individual subject or create a population model by assuming a coherent population
with a relatively simple distribution and, therefore, often fail to account for a significant
amount of the variation between the breathing pattern among different subjects. To bridge
this gap, we propose a more flexible method based on exemplar models, which is able
to cope with heterogeneous population data and can be better adapted to a previously
unseen subject. We show that, in contrary to principal component analysis based models,
our method is capable of effectively utilizing complementary information provided by
increasing number of examples taken from a population. This method achieved for the
liver 10% error reduction in comparison to a model assuming a coherent population. This
work was originally published in (Samei et al. [2012]). Finally we investigated joint
liver and rib models, where the rib motion is predicted from partial observations of liver
motion. We first constructed a subject-specific joint motion model for points inside the
liver and on the ribs centerline. The subject-specific model, which is trained on data from
20 respiratory cycle, can compensate 60% of the motion of the ribs on average. Then we
devised a population model and showed that it has the potential to reduce the motion of
the ribs by 40% without the need for subject specific motion data.
Finally in Chapter 6, we conclude this thesis by summarizing the contributions and discussing potential future research directions based on the experience and outcomes of the
presented work.
2
Management of Respiratory Motion in
Abdominal Organs during
Extracorporeal Therapies
Extracorporeal tumour therapy techniques are attractive as they obviate the need for more
invasive surgical procedures. The goal of these therapies is to cause cell change with the
aim of ultimate cell death in target sites such as tumours, using devices positioned outside of the body (extracorporeal devices). Currently, there are two major extracorporeal
technologies to treat tumours in the abdominal organs namely, radiotherapy (RT), and
high intensity focused ultrasound (HIFU) therapy. Radiotherapy includes subcategories
of photon therapy and particle therapy, which itself includes, proton, electron, and ion
beam therapy. All of these therapies are adversely affected by tumor and organ motion
during therapy (intrafraction motion). While dose delivery using these modern techniques
can nowadays be performed with submillimeter precision, intrafraction motion can cause
significant geometric and dosimetric uncertainties. Therefore, for an effective and safe
procedure, it is necessary to understand and mitigate the effect of these motions. In the
case of abdominal organs, the causes of intra-therapy motion vary and might include
respiration, cardiac pulsation, muscle fatigue, and digestion. In this study we focus on
respiratory motion of the abdominal organs, which also has the largest contribution to the
intrafraction motion.
There are already a number of reviews for management of respiratory motion, namely,
Langen and Jones [2001] and Keall et al. [2006] for radiotherapy, Mundt and Roeske
[2005] and Guckenberger et al. [2012] for intensity modulated radiation therapy (IMRT,
which is an advanced form of RT and suffers more than conventional RT from respiratory
motion), Rietzel and Bert [2010] for proton beam therapy and Bert and Rietzel [2012]
for ion beam therapy. Most recently, Muller et al. [2013] reviewed the methods used
in clinical settings for the management of respiratory motion during HIFU treatment of
abdominal tumours.
2.1. R ESPIRATORY I NDUCED M OTION OF A BDOMINAL O RGANS AND ITS E FFECTS ON
T HERAPY
6
Even though different therapy methods are affected by the respiration in slightly different ways, and each has specific management requirements, they all face similar challenges. Therefore, management techniques which have been developed for one therapy
can often be slightly modified and applied to another therapy. In what follows we try
to unify these different techniques and give classifications for their components such as,
pretherapy imaging of respiratory movements, respiration monitoring and management
techniques. Finally we will highlight the specific methods developed for HIFU therapy.
2.1
Respiratory Induced Motion of Abdominal Organs
and its Effects on Therapy
Respiration is vital for providing the human body with oxygen. The task of respiration is
to get oxygen-rich air from outside the body into the lungs (inhalation) and to return carbon dioxide rich air from the lungs to the outside (exhalation). During inhalation, lungs
expand and are filled with the outside air, and during exhalation lungs contract causing
the air to be forced out. These deformations are caused mainly by the diaphragm and the
muscles between the ribs (intercostal muscles). The diaphragm is the principal muscle
of inhalation. It contracts during inhalation causing the abdomen to move inferiorly and
anteriorly, and the thoracic cavity to expand and draw air inside the lungs. Due to this
relationship between the diaphragm, abdomen and inhalation, abdomen surface motion is
considered an important indicator of respiratory phase. However, intercostal muscles also
play a role in inhalation by elevating the ribs causing them to move superiorly and anteriorly (Wade [1954]), effectively increasing the volume of the thoracic cavity. The varying
proportion of the contributions of these muscles to respiration, creates a complicated motion which is difficult to explain solely by the motion of the diaphragm. Strategies to
observe respiratory motion are described in Sec. 2.2.
Inside the abdominal cavity, organs such as liver, kidney and pancreas undergo a complex
mixture of motion and deformation during respiration. Early studies of these movements
in radiology, focused on their range and magnitude rather than describing their 3D motion and deformation. Scintillation cameras (Weiss et al. [1972], Harauz and Bronskill
[1979]), ultrasound (Suramo et al. [1983], Davies et al. [1994]), and fluoroscopic images
(Kubo and Hill [1996]) were among the first to quantify the abdominal organs’ respiratory
motion magnitude. Fluoroscopic images have also been used to track the diaphragm (Ford
et al. [2002]; Dawson et al. [2001]). However these studies were limited by the 2D nature
of the fluoroscopic images, having ambiguities in the 3D position and displacement of the
organs.
The options of the researchers were limited to, either ultrafast (cine) 2D imaging (CT or
MR) during free breathing (Bussels et al. [2003]; Shimizu et al. [1999]), or multiple 3D
images (CT or MR) acquired at breath-holds at different respiratory states. This limited
2.1. R ESPIRATORY I NDUCED M OTION OF A BDOMINAL O RGANS
7
the study to 2D or unrealistic 3D measurements (Shimizu et al. [1999]; Bussels et al.
[2003]), or inaccurate 3D motion patterns due to the acquisition of images at different
states under breath-hold rather than free breathing. However, tracking the 3D position of
tumours was made possible by means of a few, mostly 3, implanted radiopaque markers and two fluoroscopic imaging units (Shirato et al. [2000]). This led to interesting
observations such as the existence of motion hysteresis, where different paths are taken
during inhalation and exhalation, for points in the abdominal organs (Seppenwoolde et
al. [2002]). With the advent of 4D CT (Pan et al. [2004]), and 4DMR (Von Siebenthal
et al. [2007a]) imaging techniques, the study of 3D deformation and movement of not
only single individual markers but the entire volume of the organ during free breathing
became possible. More details regarding imaging and quantifying respiratory motion will
be provided in Sec. 2.2
Having a good understanding of the deformation and motion of the organs during respiration has made it possible to estimate the effects of breathing on dose delivery in therapy
Bortfeld et al. [2002]. In the following section, we review the publications that studied
these effects.
2.1.1
Effects of Abdominal Respiratory Motion on Therapy
During extracorporeal therapies (e.g., RT and HIFU), the applicator (e.g., linear accelerator, or HIFU transducer) stays outside of the patient’s body and therefore the target of
the beam is susceptible to organ’s motion. The effects of the respiratory motion on the
treatment depend to a great extent on the specific therapy technology. For example, in
static field radiotherapy treatments, the intrafraction organ motion only effects the boundaries of the target volume and causes a smooth dose gradient (Engelsman et al. [2005];
Guckenberger et al. [2009]), whereas in dynamic IMRT and pencil beam proton therapy
the motion of the target can have interplay effects resulting in dose heterogeneity (Bert
and Rietzel [2012]). Generally, the movement of the organ leads to a spread of the applied
dose (photon, particle or thermal dose), which leads to two major problems.
The first problem with such a spread is the loss of efficacy of the treatment. HIFU is
mostly affected by an underdose of thermal energy because the accumulation of temperature is compromised as a result of perfusion of heat in the target organ. It has been shown
that thermal dose, does not have a linear relationship with exposure time (Sapareto and
Dewey [1984]). This means that a slight reduction of temperature at the focal point might
lead to a drastic reduction of thermal dose deposit. Indeed, Auboiroux et al. [2012a]
reported that a small motion of 10 mm (in the lower range of the motion amplitude in abdominal organs due to respiration ), resulted in a temperature elevation reduction of factor
1.37. Unsuccessful HIFU application due to underdose have been reported in treatment
of the liver by Allen et al. [2002] and the kidney by Ritchie et al. [2010].
2.2. M ETHODS FOR M EASURING AND M ONITORING R ESPIRATORY M OTION
8
The second problem caused by the dose spread is its effect on surrounding healthy tissue,
posing an injury risk to sensitive structures and organs. Cedric et al. [1998] investigated
the effects of intrafraction organ motion on the delivery of dynamic IMRT. Due to the
dynamic feature of this therapy, the organ motion can have interplay effects with the dose
delivery and cause over and underdosed regions, also called ”hot” and ”cold” spots. They
performed numerical analysis to calculate the received beam intensity by each point in the
target and concluded that for a set of clinically realistic motion parameters, the received
beam intensity at the target can be greater than the intended dose. In HIFU therapy, Jung
et al. [2011] studied the complications of 113 patients treated at St. Marys Hospital,
Korea in an interval of 5 years. They reported that all of the patients who underwent
treatment for tumours in their liver or pancreas, experienced at least one side effect of rib,
subcutaneous fat layer and vertebral necrosis. This highlights the importance of careful
planning and taking into account the effects of beams on the neighbouring tissues.
Moreover, a specific problem that respiratory motion poses to MRgHIFU is its interference with thermal imaging. However, several methods have been proposed to tackle this
problem and have achieved acceptable results (Ehman and Felmlee [1989]; Foo and King
[1999]; Vigen et al. [2003]).
In conclusion, for an effective and safe therapy, the motion of the abdominal organs during
respiration has to be taken into account during planning and an appropriate management
technique needs to be employed. In the next section, we explore the methods for measuring and monitoring this motion.
2.2
Methods for Measuring and Monitoring Respiratory
Motion
The methods for observing respiratory motion can be classified in several different ways.
We chose to categorise them according to the therapy phase, namely methods for pretherapy planning, and intra-therapy monitoring.
In pre-therapy planning, the goal is to measure the extent and if possible the path of
the motion of the tumour and its neighbouring tissues. Since therapy is performed after
this prior analysis, there is no need for these methods to be real-time. This allows for
retrospective processing of the data and capturing more details. The proposed and applied
pre-therapy imaging methods are detailed in section 2.2.1.
During therapy, it is important to know the position of the target in real-time at all time,
or at least when the beam is on. The intra-therapy real-time monitoring, can consist in
direct tracking of the target region, or an indirect surrogate respiratory signal which has
an acceptable correlation with the target. These methods will be discussed in Sec. 2.2.3
and Sec. 2.2.2, respectively.
2.2. M ETHODS FOR M EASURING AND M ONITORING R ESPIRATORY M OTION
2.2.1
9
Pre-therapy Imaging Methods and Motion Observations
Gamma Cameras : Early studies by Weiss et al. [1972] and Harauz and Bronskill [1979]
used scintillation camera after administration of Tc-99 to quantify the range of the respirator movement of the liver and reported under normal and deep breathing, motion ranges
of respectively, 8 ± 2 mm (11 ± 3 mm), and 12 (14) mm in standing (supine) positions.
Ultrasound : In an early study by Suramo et al. [1983], ultrasound was employed for
studying the organ motion in 50 patients. A mean peak-to-peak movement of 25 mm
(range 10-40 mm), and 55 mm (range 30-80 mm) was reported for the liver in the craniocaudal (CC) direction during normal and deep breathing respectively. Davies et al. [1994]
also used ultrasound to quantify the respiratory motion of upper abdominal organs in 9
patients. They reported a mean peak-to-peak movement of 10 mm (range 5-17 mm), and
37 mm (range 25-57 mm) for the liver in the CC direction during normal and deep breathing respectively. The motion in the anteroposterior (AP) direction was reported to be less
than 2 mm by Serago et al. [2002].
CT : Balter et al. [1996] performed CT scans on 9 patients during breath-hold at normal
inspiration and exhalation levels. An average movement of 17 mm were reported for the
liver.
4D CT or respiration-correlated CT is a technique where fast 2D CT images are acquired
at all respiration states with a simultaneous recording of a respiratory signal, which is
most of the time an external abdominal marker. A sufficient number of CT images are
collected and sorted according to their respiratory phase (normally 10 phases are distinguished) (Pan et al. [2004]; Ford et al. [2003]; Vedam et al. [2003a]; Low et al. [2003]).
Brandner et al. [2006] performed 4D CT in 13 patients to quantify the respiratory induced
motion in the liver, spleen, and kidneys. They reported 13 mm average displacement for
the liver in the CC direction. Beddar et al. [2007] also acquired 4D CT to investigate the
correlation between the motions of an external marker and internal fiducials implanted
in the liver for 8 patients. They observed a CC movement in the range of 7.5-17.5 mm
for the internal gold fiducials. They conclude that there is a good correlation between
internal fiducial motion and external marker motion. Xi et al. [2009] calculated the 3D
movement of diaphragm and abdominal organs of 13 patients using 4D CT. They reported
a 10.1 ± 3.9 mm movement in CC direction for the liver with great inter-patient variations.
The CC movement of the liver correlated well with the diaphragmatic movement. Hallman et al. [2012] acquired 4D CT using an external abdominal marker for 18 patients
under normal breathing. The contours were drawn in a single phase by a radiation oncologist and then propagated using deformable registration. The center of mass of the
segmented volume and its motion was computed. A motion of 9.7 ± 5 (range 3-18 mm)
was observed in the CC direction. Their conclusion was to perform the therapy at the end
of respiration cycle as there was a higher correlation between the motion of the external
maker and the tumour.
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10
MRI : Shimizu et al. [1999] used a 2D MR sequence with 1 second acquisition time for
imaging a spherical liver tumour in a patient under normal breathing. They acquired 20
sagittal images followed by 20 coronal images on the planes across the tumour center in
a time span of 1 minute. They reported a mean tumour border displacement of 21 mm,
8 mm, and 9 mm in CC, AP, and mediolateral (ML) directions, respectively. They noted
that these measurements are not accurate 3D measurements of the center of the tumour,
but rather 2D measurements of the tumour border. Bussels et al. [2003] studied the respiratory motion of 3 abdominal organs, namely, pancreas, liver and kidneys in 12 subjects
using 2D dynamic MR imaging in coronal and sagittal planes. The organ displacement
was computed by manually delineating the organs in each slice, and computing its center
of mass (COM). The displacement of the COM of the liver was 24.4 ± 16.4 (17.5 ± 6.7),
13.2 ± 6.9 and 9.0 ± 3.5 in CC direction in coronal (sagittal) slices, ML direction in coronal slices and AP direction in sagittal slices, respectively. The discrepancy in CC measurements in coronal and sagittal slices were related to the different COMs in these 2D
slices. Kokuryo et al. [2007] used 2D sagittal MR slices to track vessels and structures
within the liver. Assuming there is no out-of-plane motion for these vessels, and by computing the COM of these structures they were able to compute the translation, rotation,
and deformation of the tissue in sagittal slices. The reported average displacement of
the vessels’ COM in sagittal slices was 19.6 ± 3.6 (3.1 ± 1.4) mm in CC (AP) direction.
Deformation was defined as the absolute difference of the distances between the COM of
arbitrary pairs of vessels, and was 3.7 ± 1.1 (3.0 ± 1.2) mm in CC (AP) direction. Kirilova et al. [2008] performed kV fluoroscopy followed by T2-weighted single shot fast
spin echo MR imaging in three orthogonal planes during free breathing in 36 patients
to quantify the movements of tumours in the liver. They observed an average tumour
displacement of 15.5 mm (range, 6.9-35.4 mm), 10 mm (range, 3.7-21.6 mm) and 7.5 mm
(range, 3.8-14.8 mm) in CC, AP, and ML directions, respectively. They also noted that
the fluoroscopic CC diaphragm motion did not correlate well with the tumour motion.
Due to the acquisition of three consecutive images in three different orientations with a
one slice/s temporal resolution, there can be ambiguity in the real 3D movement of the
tumours. Indeed they noted a difference in the tumour motion in AP direction on axial
versus sagittal slices.
Von Siebenthal et al. [2007a] proposed a method to reconstruct 4DMR images based
on interleaving 2D sagittal navigator slices, and retrospective sorting of 2D sagittal slices.
They used this technique to image 12 volunteers over long periods of time (40-75 minutes)
under free breathing. They extracted dense deformation fields for livers from these data
using non-rigid registration. In addition to the respiratory motion of the organs, they
observed a mean displacement of 5 mm in the position of points inside the liver at endexhalation (so called drift motion).
2.2. M ETHODS FOR M EASURING AND M ONITORING R ESPIRATORY M OTION
2.2.2
11
Intra-therapy Indirect Monitoring
Even though pre-therapy techniques for measuring the respiratory motion can provide
useful information, it is still crucial to monitor this motion during therapy. Moreover,
intra-therapy monitoring methods need to provide this information in real-time, which is
difficult to achieve for direct observations of large target regions. On the one hand, the
respiratory motion is an approximately periodic motion, and hence, could be assigned
phase and amplitude, without expecting them to be identical in different cycles. On the
other hand, it could be assumed that there is a correlation between the phase and amplitude
of the respiration and the respiratory motion of organs. Therefore, there has been several
works for monitoring the respiratory motion of the organs indirectly from respiratory
surrogate signals, which will be discussed in this section.
Depending on the therapy mode, either the exact position of the target region has to be
known during the entire therapy, or only at pre-determined respiratory states. In the former case, motion of the target region and the surrogate signal are acquired simultaneously
prior to therapy and their correlation is established. In the course of therapy, only the surrogate signal is acquired and the position of the tumour is predicted accordingly (Vedam
et al. [2004]; Beddar et al. [2007]). In other cases, the position of the organ at a specific
respiratory phase is obtained through imaging the patient at that respiratory phase. Later,
the phase of respiration is determined using the surrogate signal, and the therapeutic beam
is turned on only during the pre-determined phase (this method is called gating and will
be discussed in details in Sec. 2.3.3).
There has been works to evaluate the correlation of the external surrogate signals and the
organ or tumour motion (Vedam et al. [2004], Gierga et al. [2005], Yan et al. [2006],
Beddar et al. [2007]). They report that the best correlation occurs during end exhalation
and that even though a good level of correlation is observed, care should be taken and
perfect correlation is not guaranteed (Beddar et al. [2007]). Moreover, Chen et al. [2001]
noticed phase differences between the motion of the tumour and that of external markers.
External surrogate signals
Most real-time direct monitoring systems are either invasive or expose patients to additional radiation or both, as will be discussed in Sec. 2.2.3. To reduce the exposure of the
patients to extra dose due to radiographic imaging, and to avoid the invasive implanting
of markers in the patients body, external surrogate signals have been proposed. These include spirometry, nasal temperature sensors, abdominal pressure belts, and thorax surface
optic imaging.
Spirometry : The oldest respiratory signal acquisition method is spirometry. It consists in
measuring the air flow from and to the lungs. The patient breathes through a mouthpiece
which is connected to the spirometer device (Kubo and Hill [1996], Zhang et al. [2003]).
2.2. M ETHODS FOR M EASURING AND M ONITORING R ESPIRATORY M OTION
12
Nasal Temperature Sensors : Ehman et al. [1984] built two devices for acquiring a respiratory signal based on the difference in temperature of the inhaled and exhaled air. Kubo
and Hill [1996] also used a device that reacted to the temperature difference and placed
it near the nostrils. They reported feasibility of the device and good patient comfort.
However, there has not been any recent reports on the use of nasal temperature sensors.
Optical Imaging of Thorax Surface : Generally speaking, methods that rely on observing the surface position of the thorax for obtaining a respiratory surrogate signal either
scan the entire skin surface, or place a number of markers on the thorax. In the former methods, different imaging techniques such as laser (Tada et al. [1998]) and stereo
infrared cameras (Vedam et al. [2003b], Park et al. [2011]) have been employed. An
example of the latter methods is a commercially available system (Varian RPM System)
which has been used by many groups e.g. Kubo et al. [2000]; Beddar et al. [2007]. This
system consists of a small plastic block with a pair of reflective markers that can be placed
on the thorax (chest or abdomen). These markers are imaged with a charge-coupled device (CCD) camera using infrared light produced by light-emitting diodes. The images
are processed by a software, the block position is tracked and a 1D respiratory signal is
produced.
Mechanical Detectors on Abdomen Surface : The use of respiratory pressure belts
which measure the amount of tension exerted to the belt through extension during breathing has also been reported Kubo et al. [2000]. A more advanced and commercially available product is the Anzai pressure-sensitive belt (Anzai Medical Co, Japan).
Electromagnetic Position Sensor : Recently, Yang et al. [2014] used an electromagnetic
position sensor to measure the motion of the abdominal skin. The main component of
this motion was computed using principal component analysis and was used as a 1D
respiratory signal.
All of the aforementioned methods have the limitation that they track only the external
surface of the thorax. Some of these methods such as the optical systems and the electromagnetic sensor do so very accurately as opposed to pressure belts which have the
additional disadvantage of physically interfering with the abdominal motion. In the next
section, we describe how internally tracked surrogate signals are obtained.
Internal surrogate signals
To obtain higher correlation with the tumour motion, internal surrogate signals are obtained through tracking structures inside the abdomen. Since the diaphragm is the most
important muscle for respiration, many studies have tracked the diaphragm as a surrogate
for respiratory movement of organs (Ford et al. [2002],Wein et al. [2008], Rijkhorst et al.
[2011]).
Tracking the Diaphragm using Fluoroscopy : Fluoroscopy can be used without markers
to provide an indirect respiratory signal. To that end, the lung-liver interface which is
2.2. M ETHODS FOR M EASURING AND M ONITORING R ESPIRATORY M OTION
13
visible in X-ray images is detected and its motion is tracked. Mageras et al. [2001]; Ford
et al. [2002]; Vedam et al. [2003b]. Berbeco et al. [2005] exploited the differences of the
radiological pathlength in different respiratory states and the associated brightening and
darkening of the fluoroscopic intensities.Kirilova et al. [2008] also used AP fluoroscopy
to locate the diaphragm and track its motion in the CC direction. These methods have the
disadvantage of exposing the patient to radiation by fluoroscopy.
Tracking Diaphragm using US : Diagnostic US could be used to track the diaphragm
without irradiating patients. Wein et al. [2008] employed a 2D ultrasound transducer in
combination with a position sensor attached to the patient’s skin. Rijkhorst et al. [2011],
also used US to track the diaphragm. However, since the diaphragm is a mainly axial
surface without additional image features, only its CC translational movements could be
tracked. This might not be enough to predict the more complex deformations of abdominal organs.
MR Navigator Echoes were introduced by Ehman and Felmlee [1989] to measure organ
shift. Navigators are partial image data, which are acquired interleaved with the intraoperative images and are processed to track motion. The navigators are designed for
a small region at the liver-lung interface to track the CC translational movement of the
diaphragm and are used to correct for respiratory motion in MR imaging (Taylor et al.
[1997]). de Zwart et al. [2001] also employed navigator echoes to track the diaphragm
under the assumption of rigid motion. Köhler et al. [2011] designed a spectrally sensitive MR navigator to be placed on the moving organ for correcting MR thermometry
acquisitions. They report interference of the fat-selective navigator acquisition with the
water-selective thermometry acquisitions. They could track motion at a maximum of 9 Hz
which might not be sufficient. While the applicability of navigator echoes in thermal MR
imaging for rigid motions has been established, its applicability for nonrigid motions such
as respiratory motion of the liver needs further investigations.
2.2.3
Intra-therapy Direct Monitoring
Even though the indirect methods of tracking external signals have shown acceptable correlation with the internal movement of the tumour for gating (to be discussed in Sec. 2.3.3),
there has been reports of phase lags and poor correlations (Chen et al. [2001]). This
questions their applicability for more accurate compensation methods (see Sec. 2.3.4).
The gold-standard in tracking the tumour for directly observing its motion in real-time is
through tracking implanted fiducial markers inside the organ around the tumour. Three
different types of markers have been introduced, namely radiopaque markers to be used
with fluoroscopy, electromagnetic markers, and positron emission markers.
Tracking Radiopaque Markers with Fluoroscopy is a technique which is by far the
most popular, accurate and reliable method to monitor tumour motion during respiration. Radiopaque markers, which are opaque to X-rays or similar radiation and hence
2.2. M ETHODS FOR M EASURING AND M ONITORING R ESPIRATORY M OTION
14
well visible in the radiography images, are usually made of gold and have a size in the
range of 3 mm. They are placed inside the patient’s body near the target area. During
therapy, fluoroscopic images are acquired and the markers are tracked in real-time. Since
the markers are placed very close to the target, their motion can be considered identical
to tumours motion. To be able to recover rotation and deformation in addition to translation, more than one maker is placed. However, they have the disadvantage that their
implanting procedure is invasive with the associated risks such as infection and complications. Moreover, they can move in the organ between planning and therapy (Murphy
[2004]). The use of fluoroscopy, has the additional disadvantage of exposing the patient
to extra radiation dose. Shirato et al. [2000] used this method for tracking the organs for
conformal lung radiotherapy. They used dual fluoroscopes to achieve 3D localization of
the implanted marker at a rate of 30 frames per second. They continued employing this
technique in their consecutive studies (Shirato et al. [2003, 2004b]). Gierga et al. [2004]
studied 7 patients with abdominal tumours for quantifying of their respiratory motion and
its impact on IMRT.
Electromagnetic markers : Even though the tracking system of radiopaque markers with
fluoroscopy is very accurate and reliable, imaging dose is a major concern with the skinsurface dose caused by the fluoroscope of a commercial system (Mitsubishi/Hokkaido
RTRT) estimated as much as 1,200 mGy/h (Shirato et al. [2004a]). To avoid the excessive
exposure of patients to radiation dose, Balter et al. [2005] developed a system based on
implanted electromagnetic transponders (beacons) and a source array for their real-time
localization. They achieved submillimeter accuracy in experiments with a dynamic phantom with speeds of up to 30 mm/s. This system was commercialized under the name ”Calypso 4D Localization System” (Calypso Medical Technologies, Seattle, WA). Sawant et
al. [2009] used a modified version of the Calypso system in combination with a dynamic
multileaf collimator to quantify the accuracy in tracking and irradiating the tumours. The
modification consisted of increasing the frequency of the updates of the transponder positions to 25 Hz to achieve real-time monitoring. They reported an accuracy of below 2 mm
in tracking the respiratory motion trace in a phantom.
Willoughby et al. [2006] reported the first use of this system in vivo. They implanted
the transponders in the prostates of 20 patients without complications. Further, they conducted experiments in 11 patients and showed that the localization accuracy is within
2 mm of that of radiopaque markers. Even though this study reports successful implantation of Calypso markers in prostate, their relatively large size (8.5 mm and 1.8 mm for Calypso markers in comparison to 3 mm and 0.8 mm for gold radiopaque markers in length
and diameter, respectively) limits their application in lungs tumours, where there has already been reports of complication due to implantation of markers (Whyte et al. [2003],
Shah et al. [2013]). As an example, Shah et al. [2013] investigated the potentials of implanting the Calypso markers inside lungs to track tumours. They report difficulties in
implanting the markers in 3 out of 7 patients and for the other patients problems with
2.3. O RGAN M OTION M ANAGEMENT T ECHNIQUES
15
keeping the transponder stable. Moreover, one of the patients developed marker related
complication.
Positron Emission Markers: Xu et al. [2006] proposed the use of positron emission
markers as an alternative to both radiopaque markers and electromagnetic transponders.
They adapted an already available method of tracking a single particle labeled with a
positron emission source developed by Parker et al. [2002] to the problem of providing
real-time position information of tumours. They proposed implanting radiopaque markers filled with a low activity (110MBq ) positron emission source, which they named
peTrack, and detecting the annihilation radiation from these sources using position sensitive gamma detectors mounted on the linear accelerator gantry. The advantages of their
technique is the low dose exposure for normal tissue, and the small size of the implanted
markers (diameter of 0.8 mm). Churchill et al. [2009] and Chamberland et al. [2011]
further evaluated this method and achieved accuracy below 2 mm in tracking respiratory
motion in phantoms. However, there is no report about the application of this technique
to humans.
2.3
Organ Motion Management Techniques
There are several approaches to management of the respiratory motion, whose choice
depends on the specific therapy and application (e.g. tumour site). After evaluating the
range of the respiratory motion, it might even be decided not to take any action against it
and instead, incorporate the range of the motion into the planning and increase the margin
of gross tumour volume (GTV) so that the planning target volume (PTV) covers the organ
even if it moves (Mageras et al. [1996]). Other studies have shown that under specific
conditions of therapy, respiratory motion has an averaging affect and does not have to be
compensated (Bortfeld et al. [2002]; Guckenberger et al. [2009]). However, most of the
time this is not the case. Below, we will first review the general methods of respiratory
motion management which are more or less common to all major extracorporeal therapies.
Later we will review the specific methods that have been developed for HIFU therapy.
2.3.1
Motion Restriction
Abdominal Pressure
One of the most direct approaches to respiratory motion management is to physically
constrain it. Blomgren et al. [1995] developed a device to constrain the motion of the
diaphragm due to breathing by exerting pressure on the abdomen. They succeeded in
reducing the motion of the diaphragm to 10 mm. Wunderink et al. [2008] investigated
2.3. O RGAN M OTION M ANAGEMENT T ECHNIQUES
16
the efficacy of abdominal compression on the reduction of respiratory motion in liver tumours. They studied patients who had undergone radiotherapy and already had three gold
markers around the tumour. They used fluoroscopic imaging to track the motion of the
tumour using the gold implants. They reported a reduction in median free-breathing excursion of 62% and 38% in CC and AP directions, respectively, and an increase of 15%
in the ML direction. They also reported a median residual excursion of 4.1 mm, 2.4 mm
and 1.8 mm in the CC, AP and ML directions, respectively. They concluded that abdominal compression can effectively reduce the liver tumour motion, and that the compression
levels established at planing are reliably applicable during treatment. However, 4.1 mm
of motion is still too high for most recent accurate therapies.
Single-lung ventilation
This method consists in obstructing the air path of one of the lungs invasively. The patient
can still breath through the free lung. The obstruction of air into the lung, will restrict
its expansion and hence the motion of the organs inferior to it. This method has been
used with HIFU therapy under general anaesthesia by Illing et al. [2005] and Ritchie et
al. [2010]. In other procedures, such as radiotherapy, where general anaesthesia is not
performed, this technique can not be applied.
High-Frequency Jet Ventilation
High-frequency jet ventilation is a relatively new technique in which very low tidal movements of the lung are used to decrease the associated respiratory movement Hildebrand et
al. [1984]. This technique has been successfully used to decrease the respiratory motion
in kidneys and uterus during lithotripsy Cormack et al. [2007]. Biro et al. [2009] report
its successful application during radiofrequency ablation of liver tumours in one patient
where the amplitude of the CC motion of the patient’s liver was reduced by 75% from
20 mm to 5 mm. However, this technique is also invasive, requiring intubating the trachea
of patients under anaesthesia and moreover, motions in the range of 5 mm might still be
too high for some therapies.
2.3.2
Breath-hold
Breath-hold is a technique where the respiratory motion of the organs is temporarily
stopped through voluntarily or externally suspending the patient’s respiration. Holding
the breath has been a common method for a long time in radiological image acquisition
to reduce organ motion related blurring (Brailsford [1947]). For extracorporeal therapies
(Radiotherapy, HIFU), treatment is performed during the breath-holds. Breath-hold methods are typically applied at end-inhalation (e.g. Wong et al. [1999]; Mah et al. [2000]),
2.3. O RGAN M OTION M ANAGEMENT T ECHNIQUES
17
at end-exhalation (e.g. Dawson et al. [2001]), or sometimes using case-specific regimes
(e.g. Ford et al. [2002]). Even though it might appear to be a relatively simple method,
in practice factors such as the ability of the patients to hold their breath, the depth of the
breath and comfort might prove challenging. This becomes a major issue in cases where
the patient has pulmonary problems. Moreover, the reproducibility of the breath-hold is
very important. This is the case especially when the therapy planning is also done on a
single breath-hold image.
Voluntary Breath-hold
In its technically least involved form, breath-hold is done by the patient voluntarily (Murphy et al. [2002]). The patient is asked to hold their breath during either the end-inhalation,
deep inspiration breath-hold (DIBH), or end-exhalation state. For therapies on lung,
breathing at the largest possible lung volume (DIBH), has been reported to yield the
best results by some authors Mundt and Roeske [2005]. Firstly, DIBH is expected to
be more reproducible (Mundt and Roeske [2005]). Secondly, larger lung volume means
less density of tissue and therefore less irradiation exposure to surrounding healthy tissues. Lastly, for some patients there will be more separation of the target site and critical
structures (Paoli et al. [1999]; Rosenzweig et al. [2000]). The preference of DIBH over
end-exhalation breath-hold has, however, been disputed by Giraud et al. [2006], reporting
insufficient dose delivery to the target volume.
Often, the patient receives coaching or feedback for respiration. In an early experiment,
Suramo et al. [1983] placed a bar above the patient’s abdomen to guide the patients to
hold their breath when the abdomen reaches the bar during inspiration. More advanced
methods, measure the respiratory depth of the patient through a spirometer. The nose
is usually closed using a clip and the patient breathes through a mouthpiece connected
to the spirometer. The lung volume trace can be shown to the patient directly, or to the
clinicians who will guide the patient accordingly (Mundt and Roeske [2005]). The use of
audio-visual biofeedback has also been reported by researchers (e.g. Kini et al. [2003];
Okada et al. [2006]) to help regulating respiration and enhance reproducibility. Park et al.
[2011] proposed a quasi-breath-hold technique, where the audio-visual biofeedback was
used to lengthen the end-exhalation phase of the respiration.
Active Breath-hold
Although simple to implement, voluntary breath-hold has certain problems. First, the patients might not be able to hold their breath at the designated depth, or have difficulties in
doing so consistently due to fatigue, causing premature termination of the therapy session.
To overcome these issues, active breathing control (ABC) which consists in temporarily immobilizing the patient’s breathing through a dedicated apparatus, was proposed by
2.3. O RGAN M OTION M ANAGEMENT T ECHNIQUES
18
Wong et al. [1999] and further evaluated for its application in Hodgkins disease patients
by Stromberg et al. [2000]. They employed a commercially available ventilator, which
had 2 flow monitors and 2 valves for the two directions of air flow. They connected the
valves and the monitors to a computer which could also operate the ventilator. At a certain respiratory phase, determined by the lung volume and flow direction, the command
to close the valves was sent to the ventilator, causing breath-hold. The patient was trained
beforehand by being shown a real-time display of the changing lung volumes along with
the desired level for the breath-hold. The patient would be notified when the valves will
be closed. ABC was performed on 12 patients to examine their acceptance of the procedure showing that all the patients were able to tolerate it. They tested their method by
acquiring spiral CT scans from 5 patients and observed no scan artifacts associated with
normal breathing. The organ motion in 3D was captured by acquiring CT scans with ABC
at different phases of respiration. Dawson et al. [2001] used this system for the first time
in a clinical study. They successfully immobilised and treated liver tumours during radiotherapy in 8 patients. Most recently, controlled deep inspiration was performed under
general anaesthesia to treat liver tumours using MRgHIFU by Anzidei et al. [2014].
2.3.3
Gating
Instead of holding the respiration at a certain phase, in gating the patient breathes freely.
The respiration is monitored and the therapy beam is turned on only during certain respiratory states. Gating is a very effective method to reduce the safety margin. It has been
used in almost all radiotherapy techniques including IMRT (Mundt and Roeske [2005])
and particle therapy (Rietzel and Bert [2010]; Bert and Rietzel [2012]). The advantage of
a gating system is that the patient can continue breathing freely, which is especially beneficial for patients with respiratory problems. Instead of keeping the target site at a certain
position, the treatment occurs only when the target is at an appropriate position. The main
idea of gating is to have therapeutic beam on only when the target is in a predefined gating
window during its repetitive motion. This window could be defined based on the phase of
the respiratory motion or the physical position of the target. This necessitates knowledge
of the motion of the target volume during the therapy. This information can be obtained
directly, or indirectly using respiratory monitoring devices. Different monitoring methods
have been discussed in Sec. 2.2.
Generally, in gating for radiotherapy it is only necessary to know if the tumour (and
other structures in the beam path for HIFU and proton therapy) are at the same position
as accounted for in planning. Therefore, in most cases a respiratory surrogate signal
which has an acceptable correlation with the tumour motion is chosen. The application of
external surrogate signals, such as optic imaging of abdomen surface (Tada et al. [1998]
Ford et al. [2002] Wagman et al. [2003]) has been reported for gating. More accurate
surrogate signals using direct tumour tracking methods such as radiopaque markers with
fluoroscopy (Shirato et al. [2004b]) have also been employed.
2.3. O RGAN M OTION M ANAGEMENT T ECHNIQUES
2.3.4
19
Real-time Motion Compensation or Tracking
In gating, the therapy beam is on at most during 30% of the duty cycle of the beam
(Mageras et al. [2004] Wagman et al. [2003] Bert and Rietzel [2012] Guckenberger et
al. [2012]). The effective tumour ablation time being even shorter, 10%, if the hysteresis
of the respiratory motion is taken into account (Seppenwoolde et al. [2002]). This is
undesirable as it leads to lengthy treatments. For HIFU this is especially impractical
as the treatment pauses cause temperature reductions which prevent head accumulation
and hence delivery of the required thermal dose (Muller et al. [2013]). Rijkhorst et al.
[2011] described simulation of HIFU experiments using realistic liver motion data, where
gating would not result in ablation of the target volume, whereas motion compensation
would yield almost the same result as absence of motion. Breath-hold techniques also
suffer from short duty cycles, leading to lengthy and inefficient therapy sessions with the
additional issue of causing patient discomfort.
In tracking, or motion compensation, the position of the target volume is determined
in real-time and the therapeutic beam (RT, HIFU) is steered to follow the target during
the entire respiratory cycle. In theory this is the ideal form of respiration management,
decreasing the dose and therapy time, leading to a more efficient and effective therapy.
However, there are two major challenges, real-time tracking of the target region, and realtime steering of the beam. The latter is outside of the scope of this work, but recent
advances have made it possible for both radiotherapy (Sawant et al. [2008]) and HIFU
(Auboiroux et al. [2012b]).
In radiotherapy, most of the proposed methods for real-time tracking involve direct monitoring of the tumour using internal fiducial markers and fluoroscopy or electromagnetic
transponders (Sawant et al. [2009]; Krauss et al. [2011]) in ex vivo experiments. The use
of external markers have also been proposed (Sawant et al. [2008]).
2.3.5
Motion Management in MR guided HIFU
A motion management technique, specific to the use of US in HIFU, was proposed by
Pernot et al. [2004]. Their method is based on speckle tracking in ultrasound to correct
the organ motion in real-time. They emit a pulse echo sequence by a subset of the transducers of the phased array HIFU system. Next, they compute the 1D cross-correlation
of the backscattered signals acquired at two different time points. Finally they compute
a 3D motion vector through triangulation. Marquet et al. [2011] tested this method in
anaesthetized pigs and showed very accurate sonications on the target. However, the pigs
were ventilated which meant controlled air inhalation and breathing rhythm. Results of
tests on animals were promising but the applicability of the method for humans under free
breathing conditions remains to be validated.
2.4. C ONCLUSION
2.4
20
Conclusion
Respiratory motion of abdominal organs compromises an effective and safe treatment in
all extracorporeal therapies. The motion of the organs, causes a blurring of the therapy
dose in motion direction and might hamper the delivery of sufficient dose to the target
region. Moreover, this motion poses a risk to healthy tissues and critical neighbouring
structures. While larger PTVs to account for the respiratory motion in conventional radiotherapy might have been adequate, latest techniques which allow precise targeting such
as IMRT, proton therapy, and HIFU require appropriate management of the respiratory
motion.
We discussed the proposed and applied management techniques including, motion restriction, breath-hold, gating and tracking. Motion restriction methods such as abdominal
pressure, single-lung ventilation and high-frequency jet ventilation either cause discomfort (abdominal pressure) or are invasive (general anaesthesia for the latter two). Moreover, they are not able to completely restrict the respiratory motion. Breath-hold and
gating methods have been successfully applied for patient treatment. However, they both
have a short duty cycle (≈30%), which leads to lengthy treatment sessions. This problem is significant in HIFU therapy, where pauses in thermal dose delivery hinder heat
accumulation, leading to ineffective tumour ablation. Therefore, motion tracking and
compensation methods have been proposed to tackle these issues. Currently, methods
for directly observing the tumour motion require implantation of markers (radiopaque,
magnetic transponders, or proton emission). This would detract from the merits of noninvasive methods. Indirect methods, which predict the respiratory motion of the target
site based on surrogate respiratory signals, could be performed non-invasively. For a successful motion prediction, accurate models which correlate the motion of surrogate sites
to targets sites on abdominal organs are required. In the following chapters, we discuss
statistical motion models and our contributions in creating accurate respiratory motion
models for the liver and ribs.
3
Rib Segmentation in Magnetic
Resonance Images
3.1
Introduction
Ribs pose an important challenge to an effective and safe HIFU therapy on on abdominal
organs such as the liver, which can be attributed to two of their properties. One the
one hand, they absorb the ultrasound beams which might cause damage to themselves
and the surrounding tissues such as skin. On the other hand, they aberrate the beams
and prevent them from focusing on the target tissue and hence undermine an effective
therapy (Kennedy et al. [2002]). Cao et al. [2012] studied the effects of the ribcage
on HIFU sonication and reported that the presence of a ribcage phantom reduced the
maximum temperature at the focus by approximately 60-70% and the maximum pressure
at the focal zone by 50%. Quesson et al. [2010] addressed this issue and proposed a
method to avoid ribs by deactivating ultrasound transducer elements that emit through the
ribs. They analysed ex vivo and in vivo temperature data during sonication with their
proposed technique, and reported that the temperature near the ribs was reduced and no
loss of heat efficiency occurred. Their results are encouraging and show that avoiding the
ribs in MR guided HIFU (MRgHIFU) is possible, provided that the position of the ribs
is known. In their experiments, the knowledge of the ribs position is obtained through
manual segmentation of the ribs on the MR images which could be tedious and difficult
in clinician practice. Hence, considering the imaging modality in MRgHIFU, it would be
highly desirable to detect ribs automatically in MR images. Acquisition of pre-therapy
CT images might be possible, but being able to avoid it is valuable as it poses some
undesirable health risks (Brenner and Hall [2007]). In the case of already available CT
images, the segmented ribs in CT still have to be positioned in an MR image in the therapy
planning step.
However, due to the scarcity of mobile protons which can be excited in bones, one cannot
observe ribs entirely and accurately in MR. Dense bones appear mostly as signal voids
in MR images, while neighbouring tissues such as vessels and muscles show relatively
3.2. R ELATED W ORK
22
good visibility. This contrast could be used to locate the ribs. However, as a result of
variation of tissue intensity in different MR acquisitions, an intensity profile for ribs cannot be robustly defined as is done in CT images for example by Klinder et al. [2007].
Moreover, the relatively low signal to noise ratio of MR images as well as low resolution
lead to unreliable local, low level features. The fact that there are no strong local cues
for a bottom-up segmentation of ribs, in addition to the fact that ribs cannot assume any
arbitrary shape, call for incorporation of prior knowledge of the ribcage into the detection
process. We opted to use statistical shape models to gain this prior knowledge as they
have been successfully used in many applications in medical imaging and for which there
is a rich body of literature. An extensive review on this subject is given by Heimann and
Meinzer [2009].
To build ribcage shape models we turned our attention to the suitable modality for imaging
bones, namely CT. We performed semi-automatic segmentation of ribs to ensure accurate
individual segmentations. The details of constructing the statistical ribcage shape model
are explained in Sec. 3.4. To be able to find the shape model parameters for a given MR
image, we created an appearance model of ribs in MR images. This provided us with a
measure to estimate the fitness of a candidate ribcage for a given MR image. We employed
machine learning tools, namely random forest classifiers (Breiman [2001]), to build a
robust appearance model based on manual segmentations of ribs in a set of training MR
images. The details of building this appearance model are explained in Sec. 3.5. Finally
to find the parameters of the statistical shape model, which provide the maximum fitness
according to the MR rib appearance model, we had to solve an optimization problem. The
technique which was employed is explained in Sec. 3.6.
Before going into the details of our method, we give an overview of the rib detection and
segmentation efforts in three modalities, namely radiographs, CT and MRI, in the next
section.
3.2
Related Work
The detection and segmentation of ribs in MRI have hardly been investigated. Recently,
there has been an increase of interest in the subject due to its application in MRgHIFU
(Noorda et al. [2013]; Polonen and Schubert [2013]). Nevertheless, detecting and modeling ribs in other modalities have been extensively studied. Therefore we will first give
a summary of these efforts in chest radiographs, and chest computed tomography (CT)
images. Finally we will review the proposed methods for rib segmentation in MRI.
3.2. R ELATED W ORK
3.2.1
23
Rib Segmentation in Chest Radiographs
In radiographs, the segmentation methods consist of the following two general steps.
First, rib candidates are found locally through edge detectors. Second, these edges are
grouped together to form a geometric object such as a parabola or ellipse (Ballard [1978];
de Souza [1983]; Sanada et al. [1991]; Yue et al. [1995]; Vogelsang et al. [1998]). An example is the work of Vogelsang et al. [1998], where a method is proposed to detect ribs in
chest radiographs in order to remove them for better lung pathology visibility. The projections of ribs onto the radiographs are described as parabolas whose edges are found using
template matching. Each rib is modelled by 4 parabolas to describe the borders of the
ventral and dorsal parts of the rib. Edges are found by maximizing the normalized cross
correlation of the image with a set of predefined edge templates. Finally, a generalized
Hough transform for finding parabolas in the image is preformed. Van Ginneken et al.
[2001] gives a review on segmentation of ribs in radiographs, and concludes that almost
all reviewed methods fail to take into account the correlation between ribs or do so in
an adhoc manner. The exception is their own work (Van Ginneken and ter Haar Romeny
[2000]), which seems to be the first attempt at trying to model the ribcage shape and fitting
it to the radiograph.
3.2.2
Ribs Segmentation in Chest CT
More advanced methods are proposed for rib detection in CT. One of the first attempts is
that of Weese et al. [2001], where they introduce shape constrained deformable models
by combining active shape models (Cootes et al. [1995]) with an elastically deformable
model (McInerney and Terzopoulos [1996]). The external energy of the deformable models framework is defined in such a way that the detected surface points attract the segmentation mesh. The internal energy is based on the statistical shape model such that
deviation from statistically probable instances of the mesh are penalized. This approach
was chosen to increase flexibility in comparison to an active shape model.
Shen et al. [2004] propose a centerline tracing algorithm based on the assumption that
the surface normals of the ribs are perpendicular to the direction of the ribs’ centerline.
Around a starting point, local edges are extracted by means of convolving the image
region with 3D edge template masks and then applying non maximum suppression. Principal component analysis is performed on the 3D normal direction of these edges, and the
eigenvector with the smallest eigenvalue is obtained and considered as the rib’s centerline
direction. A recursive equation is introduced for points on the centerline, deriving a new
point on the centerline from moving stepwise in the direction of the centerline from an
already traced point. Starting from the new point, 20 equally spaced search directions
towards the exterior of the rib, are defined. The most suitable edges along each direction
are found by dynamic programming, and the local direction of the centerline at this point
is computed in the same way as for the starting point. The starting points for this tracing
3.2. R ELATED W ORK
24
algorithm are found rather heuristically by applying a suitable threshold to a sagittal slice
close to the medial plane which does not include the spine and sternum. Such a tracing
algorithm might stop prematurely if the local structures are not found sequentially as the
result of a local noisy region. They do not provide any quantitative evaluation of their
algorithm, but the one depicted example shows an early termination for one of the ribs.
Staal et al. [2004, 2007], employ a similar bottom-up framework for detection and segmentation of ribs in CT images. The general steps are as follows. First, local relevant
structures of interest are detected. Next, the local structures are filtered and grouped
together to form what they call primitives. Finally, the primitives are used as seeds to
initialize a seeded region growing. In more details, they propose detecting elongated 1D
structures, called ridge voxels, by eigen-decomposition of the Hessian matrix of the intensity around image points and selecting the eigenvectors with the smallest eigenvalues.
Next, similar ridge voxels are grouped to form line elements. Then a k-nearest neighborhood classifier is used to distinguish between the rib versus non-rib line elements. Finally,
the line elements are grouped together in a similar fashion as joining ridge voxels. Since
local structures, 1D ridges, are searched in the entire image, this method is less affected
by local noisy regions. However, the correct grouping and classification might fail, which
leads to shorter ribs or ribs reaching into the spine as discussed in their results.
Shi et al. [2007] automatically find the ribs’ joints to the vertebrae and use them as a
starting point for their tracing algorithm. This is done by first automatically finding the
extent of the bony region attached to the spine in each axial slice, and defining the bone
span of that slice as the absolute value of the most lateral ML coordinate of a bony voxel
which is connected to the spine. In the next step, the rib joints are identified as the peaks
in the plot of bone span versus IS coordinate. Starting from these joints, they trace the
ribs by moving a cube with a step size of half the size of the cube along the rib in the
direction which has not been tracked. An EM algorithm is employed to find a mixture of
3 Gaussians (bones, soft-tissue, background) in the intensity histogram from the cube’s
voxels. Finally the voxels belonging to the Gaussian with the highest intensity are classified as bone voxels and added to the rib. In their tracing algorithm, they directly trace
the entire rib, as opposed to its centerline. This tracing algorithm is also susceptible to
the local noisy region problem, and since no evaluation of rib detection is provided, its
performance cannot be judged.
Klinder et al. [2007] overcame the tracing problem by combining a top-down and a
bottom-up approach, using high level and low level cues for segmenting ribs in CT. For
the top-down approach, they constructed a template ribcage based on the mean of interactively segmented ribcages of a population of subjects, and found a deformation of this
mean model to best fit it to a new given CT image. Their first step in fitting a ribcage to
a new image is global model positioning. In the bottom-up approach they found local rib
segments. To that end, they fit a cylinder to the thorax, and determined a typical intensity
profile for the rib segment of a ray that starts from the center of this cylinder and passes
through ribs. For each axial slice, this intensity profile was searched along 180 rays uni-
3.2. R ELATED W ORK
25
formly sampled in the 2π range, and candidate rib segments were collected. Heuristics
were employed to rib candidates, such as grouping those which have a similar distance
to the center of the cylinder. Finally, these grouped candidates were registered with the
template ribcage centerlines using a generalized iterative closest points algorithm (ICP)
which allowed an affine transformation at each iteration. After this initial registration,
the template was registered to the rib candidate lines using a thin-plate spline approximation. Since this method constructs a mean model of the population without considering
the variations between the subjects, the permitted deformations from the mean model to a
new ribcage do not have to necessarily lead to valid ribcage configurations. However, the
results for 16 datasets suggest that this is not a problem. The reason could be that due to
the meaningful intensities in CT, the rib candidates obtained through matching rib intensity profiles are sufficiently accurate in displaying the underlying geometry. Even though
successful in detecting ribs in CT, this method might not be applicable to MR images,
where a typical intensity profile can not be reliably defined for ribs.
Wu et al. [2012] also use both high level and low level cues to fit a ribcage to a new
CT image. First, the appearance of ribs in CT is learnt through using Haar-like features
(Papageorgiou et al. [1998]), and a pyramid of probabilistic boosting trees with Adaboost
classifiers. Next, a probability map is created for the given image, where each voxel
value represents the probability that this voxel belongs to ribs’ centerlines. A template
is created by manual segmentation of one ribcage, and a transformation of the template
that maximizes the sum of the probability of the voxels in the transformed template is
found. In order to overcome the variability in the ribcage shapes, they divide each rib into
4 segments and perform a rigid registration for each segment individually. Further, they
employ a Markov random field (MRF) model to ensure pairwise smoothness of transformation parameters of these segments. As a final step, they use the outputs of the previous
steps as an initialisation for an active contour model in order to get a refined smooth segmentation. The use of one ribcage as a template seems to be too restrictive. Indeed, the
authors propose breaking up the template, to introduce more flexibility into the framework. However, this causes individual segments to be registered to different ribs. As a
remedy for this problem, they use MRFs, which, as shown in the results, do not guarantee a smooth centerline either. Therefore, the active contour method had to be applied to
obtain a final smooth result. This makes the process computationally intensive and difficult to reimplement due to the use of many steps which all require tuning of individual
parameters.
Among the many proposed rib detection methods in CT, the methods of Staal et al. [2007],
Klinder et al. [2007] and Wu et al. [2012] seem to be the most promising ones with the
most convincing results. Klinder et al. [2007] report 0.36 mm (11.43 mm) mean (max)
error on 16 datasets. Staal et al. [2007] provide a qualitative evaluation and report 9.9%,
7.4%, and 2.5% of the detected ribs reached into the spine, were too short, and were too
long, respectively. Wu et al. [2012] report the Hausdorff distance between the extracted
rib centerlines and the ground truth. For ribs 3 to 10 this error was 1.2 mm. Staal et
3.2. R ELATED W ORK
26
al. [2007] do not use any model, and employ grouping of primitives and region growing
to obtain full ribcage segmentation. Klinder et al. [2007] and Wu et al. [2012] both
use a single template ribcage to deform it into the ribcage in a new image. The former
used a mean model from a population, while the latter used a single subject’s ribcage.
Klinder et al. [2007] use ICP with global affine transformation to register ribs from the
template to the new image, followed by a thin-plate spline transformation to match the
extracted centerlines. Wu et al. [2012] divide the template into segments and register them
to the candidate centerlines with rigid transformation using MRFs to ensure a smooth
transition between segments. None of these methods model the population variations of
the ribcages, and therefore, have to use adhoc strategies for transformation of the template
to a new ribcage. While in high quality CT images, this might only affect the efficiency
of these methods, in lower quality CT images, cases with pathology or MRI, more robust
methods that define valid deformations of the mean template are required.
3.2.3
Rib Segmentation in MRI
There have been relatively few attempts at segmenting ribs in MRI. A major reason for
this might be the unsuitability of this modality for depicting small bony structures such
as ribs. However, due to the emergence of MR guided therapies, where the available
modality during the therapy is MR and also the risk associated with CT imaging, there
is an increasing interest in detection and segmentation of ribs in MR images. In what
follows, we discuss the two methods proposed so far. The slice thickness in both cases is
2mm, and the detection is performed on breath-hold full thorax images.
In the work of Polonen and Schubert [2013], the three coordinates of a rib centerline
are each approximated by a second order polynomial in the arc-length parameter. The
fitness of a candidate rib point is measured by cross correlation of a pre-defined rib crosssection template with the patch around that candidate point. Starting from a manually
selected initial point, the rib centerline is tracked by finding the optimal parameters of the
polynomials and fixing the length of the rib. The polynomial parameters are determined
through numerical optimization of the sum of the fitness measure of the points on the rib
centerline. Eventually the rib is reconstructed by fitting ellipses to the cross sections of
the extracted centerline. It is not clear if a single pre-defined rib cross-section template
would be appropriate for the entire length of the ribs since the appearance of the ribs and
their surrounding tissues vary along their length. Moreover, the length of the ribs have
to be known for optimization. This can be difficult to determine in advance, as it varies
across different ribs and over the population. To overcome this problem, they suggest
to rely on the fitness measure to determine the length of the ribs. However, the tracking
algorithm might terminate prematurely if the visibility of the ribs in a region along the
rib is poor. Unfortunately, the performance of the method cannot be judged based on the
limited evaluation (a mean error of 1.32 mm in segmenting 5 ribs of a single volunteer).
3.3. M ATERIALS
27
Noorda et al. [2013] follow the general steps proposed by Staal et al. [2007] with modifications to better adapt them to MRI. In the first step, a vesselness filter is applied in 3D
to find elongated structures. Next, the exterior of the ribcage is identified through fuzzy
clustering and morphological operations, and projected onto a 2D surface. A ridgeness
filter is applied to the resulting 2D image to find the center of the identified elongated
structures. A cost measure is assigned to each projected voxel based on the outcome of
the ridgness filter. Dynamic programming is used to find the centerline of the first 7 ribs
with the highest response to the ridgeness filter. The detection is aimed at the first 7 ribs,
which is not sufficient for the declared goal which is MRgHIFU of abdominal organs
such as liver. Moreover, given the low signal to noise ratio of MRI for bones, it is unlikely
that plausible ribcages are reliably achieved with this purely bottom-up and data-driven
approach. This is confirmed by the results from 5 volunteers, which are noisy, contain
local false-positives, and show confusion between ribs.
3.3
Materials
We used two abdominal image collections, a CT and an MR dataset, which will be described next.
CT Dataset contains high resolution CT images of end-inspiration (EI) breath-holds.
The images were acquired from 20 healthy volunteers, with a resolution of 1.37 × 1.37 ×
1 mm3 , in the anterior-posterior (AP), left-right (LR), and inferior-superior (IS) direction,
respectively. The images were acquired and used in accordance with the local institutional
review board regulations and were made available to us by the authors of Donner et al.
[2013].
MR Dataset consists of free-breathing 4DMRIs obtained from 29 healthy volunteers (14
female, 15 male, average age 31, range 17-75) according to the method proposed by
Von Siebenthal et al. [2007a].
The first 12 set of 4DMIs (subjects 1 to 12) were obtained by the authors of Von Siebenthal
et al. [2007a] using balanced Steady State Free Precession sequence, SENSE factor 1.7
and halfscan (flip angle 70◦ , TR=3.1 ms). The MR imaging instrument was an 1.5T
Philips Achieva whole body MR system (Philips Medical Systems, Best, NL) and the
images were acquired using a 4 channel cardiac array coil. These image had a spatial
resolution of (1.33 × 1.33 × 4 mm3 in AP, IS, LR direction) and a temporal resolution of
2.6-2.8 Hz and covered the right liver lobe.
We acquired further 17 datasets based on the same MR protocol and using the same MR
system as Von Siebenthal et al. [2007a]. The study was approved by the local institutional
review board and all volunteers provided informed consent. In our first 10 acquisitions
(subjects 13 to 22) we used a 6 channel cardiac array coil. For the last 7 acquisitions
3.4. R IBCAGE S TATISTICAL S HAPE M ODEL
28
(subjects 23 to 29) we used a 32 channel cardiac array coil. The signal to noise ratio of the
latter 7 were markedly better. The sessions were on average 2 hours, including volunteer
positioning, system setup and acquisition of 5 blocks of 10 minutes with 5 minute pauses
in between. These 29 datasets contain between 200 to 900 respiratory cycles. In addition
to the 4DMR images, for subjects 24 o 29, we acquired breath-hold 3DMR images in
end-inhalation (EI), and end-expiration (EE) with 2.5 mm slice thickness and using the
same acquisition parameters as for the 4DMRIs. Eventually, we had to discard 3 out of
29 4DMRI datasets. One of the volunteers (subject 18) interrupted the imaging process
due to discomfort. Two other volunteers (subject 25 and 28) had considerable movement
during acquisition such that an acceptable 4DMRI reconstruction was not possible. Also,
the breath-hold images of subject 25 (EI and EE) and subject 23 (only EI) had to be
discarded due to severe artefacts.
As the first 12 datasets were acquired for studying the motion of the right liver lobe, they
did not always include the ribs’ joints to the vertebrae. Therefore, for our rib detection
experiments we used the datasets 13 to 29.
3.4
Ribcage Statistical Shape Model
The review on existing rib segmentation methods showed the need for incorporating topdown information about the expected ribcage shape and variation into the segmentation
method. In this section, we explain how we modelled the ribcage shape and variation
using statistical shape models. Statistical shape models are powerful tools in medical
imaging. They are used widely in segmentation and analysis of structures in medical
images (Heimann and Meinzer [2009]). While there is variation in the methodology of
creating shape models, there are general steps which are common to most method. The
first step is selecting a representation for the structure, which in most cases is a point
distribution model (PDM) (Cootes and Taylor [1992]). Other representations such as mreps which is based on the objects’ medial line (Pizer et al. [2003]) and spherical harmonic
(SPHARM) which is a decomposition of the object geometry into surface bases (Kelemen
et al. [1999]), have also been proposed. The second step is establishing correspondence
between the representations of the structure across different subjects in the population. In
the case of PDM, this means finding correspondence between the points. Finally statistical
analysis is performed on the population with the aim of extracting the mean structure and
the principal modes of variation. Most often, principal component analysis (PCA) is the
method of choice. PCA has the advantage that it is fast, intuitive, easy to implement and
has a strong dimensionality reduction power. The underlying assumption in performing
PCA is that the data have a Gaussian distribution, which is not necessarily true in many
practical cases. Kendall [1984] defines shape as ”what is left when the differences which
can be attributed to translations, rotations, and dilatations have been quotiented out”, and
shows that such a shape space forms a Riemannian manifold. Extensions to PCA have
3.4. R IBCAGE S TATISTICAL S HAPE M ODEL
29
been proposed to circumvent its linearity assumption such as principal geodesic analysis
by Fletcher et al. [2004] and kernel PCA by Schölkopf et al. [1997]. However, in practice,
PCA provides results with sufficient accuracy for applications such as dimensionality
reduction (van der Maaten et al. [2009]) and statistical shape modeling (Heimann and
Meinzer [2009]). Next we will explain how these different steps were performed for
constructing a ribcage model.
3.4.1
Ribcage Model
A naive way to create a statistical ribcage model would be to create a PDM of all points
from the surfaces of the ribs as was done by Dworzak et al. [2010]. The first problem
with such an approach is that, while smaller Euclidean distance of points on the same
rib correctly implies a higher correlation between them, this does not necessarily hold
for nearby points on different ribs. A more suitable approach would be to describe a
ribcage as an articulated object with several parts, each having a number of attributes.
This approach increases model flexibility by dividing the ribcage model into several, independently modeled parts which are simpler and exhibit less variation in comparison to
a single ribcage PDM. We take this approach and model the relationship between individual parts separately. Our proposed ribcage model consists of ribs each having shape,
length, and orientation attributes, where the shape of a rib was determined by creating a
PCA model from the PDM of the rib and using the principal component (PC) coefficients
as shape attributes. Finally, the correlation between the different attributes of ribs in a
ribcage were computed. In what follows each of these steps will be explained in more
details.
3.4.2
Preprocessing steps
The ribs were semi-automatically segmented in the CT images by using a simple region
growing algorithm in the 3D Slicer software (Fedorov et al. [2012]), and manual selection
of seeds on the ribs (see Fig. 3.1). The outcome was a binary volume consisting of all the
ribs and the vertebral column. Next, the ribs were manually separated from the vertebral
column by removing all the voxels on a sagittal plane placed at their joints. Finally, a
triangulated mesh was created for each rib using the ModelMaker module of the 3D Slicer
software, which implements the marching cube algorithm (Lorensen and Cline [1987] ).
Since the rib meshes were noisy, we formed a point cloud from their vertices, and computed their centerlines as follows. First, an ellipse was fit to the entire point cloud of a rib.
Then subdividing planes were created from the center of this ellipse and perpendicular
to its plane at every 2 degrees. The centerline positions were obtained by computing the
center of mass of the points lying between two neighboring subdividing planes. Next, the
30
3.4. R IBCAGE S TATISTICAL S HAPE M ODEL
(a)
(b)
(c)
Figure 3.1: The preprocessing steps for extracting the rib centerlines are demonstrated in
this scheme. In step (a) a number of manual landmarks (shown as red dots) are placed on
bony parts of the ribcage, which are used as seeds in the region growing method. In step
(b) the segmented ribs are manually separated from the vertebrae. In step (c) the centerlines of the ribs enclosing the liver are computed from the vertices of the segmentation
meshes.
centerlines were smoothed by a 0.1 mm moving average filter and parameterized according to their arc length.
3.4.3
Points Correspondence
Since ribs do not have a complicated shape, we opted to use three landmarks that divide
the ribs into two segments. The first landmark was the rib’s joint to the vertebra, the
second landmark was the most anterior point at the rib’s transition from bone to cartilage,
and the third point was an anatomically defined point, called angle point, which was
located in each rib as the most posterior point in the world coordinate system. The world
coordinate system was defined as x: A→P, y: I→S, z: L→R. The angle point was used
to divide the ribs into two segments. Each segment was equally subdivided into a fixed
number of points (in total 100 points per rib) to establish inter-subject correspondence of
the ribs.
3.4.4
Ribs Orientation
For each rib its natural coordinate system was found by applying PCA on the position
vectors of its points. Considering the general extent of ribs, the x-, y- and z-axis of
the natural coordinate system of a rib was defined by the first, third, and second PCs,
3.5. R IB A PPEARANCE M ODEL
31
respectively. A 3D rotation from the natural coordinate system to the world coordinate
system of each rib was computed. To obtain the correct orientation, we ensured that after
the rotation, the middle rib point was more lateral than the end points of the rib and that
the first point was the most medial and the most superior point.
3.4.5
Rib Shape Model
Our ribcage model, rc, consists of the right ribs number 7 to 10 which enclose the liver
(r7 , r8 , r9 and r10 ). All ribs were normalized to have equal length and the 3D position
vectors of all the 100 points of a rib were concatenated to form a 300 dimensional vector.
The resulting vectors for r7 to r10 of all subjects formed a population of 80 ribs in total. By
performing PCA on these vectors, we captured the high correlation between the elements
of these vectors, with the first 2 PCs covering 96% of the variation. Hence, we chose our
shape parameters to be the projection of the 300D vector of each rib onto these 2 PCs.
3.4.6
Ribcage Parameters
Each rib is defined by its shape, length and orientation. For detection we had to find all
of these attributes which consist of 6 parameters, namely 2 shape parameters introduced
in Sec. 3.4.5, 3 Euler angles and 1 length value. The attributes of each rib are highly
correlated with each other and with those of other ribs in the ribcage. We built a statistical population model of these attributes to find the principle modes of variation of the
geometry of ribcages. Moreover, such a model would allow us to generate anatomically
plausible ribs using a few parameters.
To model the correlation between these parameters for all the ribs, we performed another
PCA on 20 instances of the resulting 24D vectors, with 6 PCs capturing 96% of the
population variation.
This allowed us to generate, rc, consisting of the centerlines r7 , r8 , r9 and r10 , approximately by 6 parameters h = [h1 ..h6 ]. However, due to the relatively small training dataset,
the population model might not capture the whole variability. Therefore, we reintroduced
some local flexibility in the final steps of fitting to further adjust the generated ribcage
to the given MR image. These local modifications included rotation and translation, and
their parameters are represented by δ. This will be discussed in details in Sec. 3.6.2 under
Optimization Strategy.
3.5
Rib Appearance Model
In the previous section we defined the parameter vector h, which represents a ribcage. To
find the optimal parameters for a given MR image, we need to also define a cost measure
3.5. R IB A PPEARANCE M ODEL
32
of a ribcage with respect to a given MR image. Our employed cost measure is based on the
likelihood of a given image location belonging to the centerline of a rib. This likelihood
is referred to as ribness hereafter. We created an MR appearance model to compute the
ribness of a point from its intensity and that of its neighbourhood in MR images. To that
end, we used random forest classifiers (Breiman [2001]) trained on MRI sagittal patches
(See Sec. 3.5.2). To train our random forest classifiers we needed ground truth for rib
centerlines, which we explain next.
3.5.1
Ground Truth
In order to create the MRI appearance model of the ribs, as well as to evaluate our rib
detection method, we had to establish a ground truth for the rib centerlines. However,
due to low visibility of bones, reliable selection of rib points on all sagittal slices was not
possible. As a result, the selected points were sparse and did not lie on a smooth curve.
Therefore, we connected the selected points with line segments and resampled these lines
with 0.01 mm spacing and performed an initial smoothing by moving averages with a span
of 0.05 mm. Next, we interpolated these points, using cubic B-splines and parameterized
the centerlines by arc-length with the first point being the rib’s joint to the vertebra, and
the last one being the most anterior point. Finally, the centerlines were smoothed once
again using moving averages with a span of 0.4 mm.
Finally, the natural coordinate system and parameterizations of ribs were computed in the
same manner as they were done on ribs in CT images in Sec 3.4.5, and Sec 3.4.4.
3.5.2
Random Forest Classifiers
In a first attempt to train our random forest (RF) classifiers, we used feature vectors which
were based merely on image intensities. An appearance model built in this way, was sensitive to intensity range changes. Moreover, slight changes in the structures (such as the
size of the rib cross sections), would result in very dissimilar features, necessitating a
large training dataset to learn all the variations. To overcome these shortcoming, we used
more robust features namely Fp = (Fp1 ...Fp6 ), with 6 channels for a point p = [px , py , pz ],
as in Dantone et al. [2012]. These channels were comprised of raw intensity values, normalized intensity values, Canny [1986] and Sobel [1990] edge detector responses, outputs
of morphological operators (erosion and dilation) on the intensity, and the response of a
Gabor filter bank with eight different rotations and four different phase shifts. We define
N (I, p, w) as a square neighbourhood with width 2w around point p as follows:
N (I, p, w) (i,j) = I(px + i, py + j, pz )
i, j ∈ {−w, .., w}
(3.1)
33
3.6. R IBCAGE F ITTING
with I(x, y, z) the interpolated MR intensity at position [x, y, z]. Each Fp was constructed
from N (I, p, w). The choice of sagittal patches instead of 3D subvolumes for creating our
features was motivated by the relatively high in-plane resolution (1.33 mm) in comparison
to the slice thickness (5 mm) of the images in our dataset. Our evaluations suggested that
features built on these 2D patches were sufficiently discriminative and hence, the cost
of computing 3D features could be spared (see Table 3.1). We assumed that the ribness
probability of a point p conditioned on a patch N (I, p, 15) around it, is independent
of
the rest of the image
I and therefore obtained the conditional probability, P p|I ≈
P (p|N I, p, w) . In addition we used RF thresholds on comparison features Dantone et
al. [2012], rather than on the original features.
We trained our RF classifiers on positive features, FpR , around points on the manually determined rib centerlines, pR , and negative features, FpN , around randomly selected points
pN , with a distance of more than 10 mm from all pR . To obtain more discriminative classifiers, we trained 4 RFs for regions along the ribs with different appearances on sagittal
slices. The first one (C1) was built for the points that had an AP distance of 5 mm from
the angle point. The second one (C2), was trained on the points within an LR distance of
5 mm (slice thickness) from the most lateral rib point. The third and fourth classifiers (C3,
C4) were trained on the points between the angle point and the most lateral rib points, and
the remaining points, respectively (see Fig. 3.2i).
3.6
Ribcage Fitting
The parameter vector h defined in Sec. 3.4.6 is used to represent a ribcage rc, and for rib
fitting we need to determine values for h such that the reconstructed ribs of ribcage, rch ,
are located on the rib centerlines in the given MR image. Therefore, we need a fitness
measure of rib fitting (i.e. a method to estimate the likelihood of a given image location
belonging to the centerline of a rib, which is referred to as ribness hereafter, and a cost
function for a set of generated ribs based on these likelihoods), and a strategy to find the
optimal set of ribs according to the cost function.
3.6.1
Cost Function
We define our cost function, C(r, I) based on the conditional negative log-likelihood of
the parameters h, given the MR image I. Initially we used the following cost function:
C(h, I) = −
X X
r∈rch p∈r
log P p|N (I, p, w) ,
34
3.6. R IBCAGE F ITTING
where rch is the ribcage associated with parameters h. This definition resulted in a cost
measure which sharply increased with distance to rib centers, making it very hard to optimize. An ideal cost measure for efficient solving of our optimization problem should
be increasing with the distance to rib centers with a smooth gradient. Therefore we employed a cost function that incorporates the ribness evidence from the neighbouring voxels
by spatially smoothing the RF log-likelihood with a Gaussian kernel:
C(h, I, σ, δ) = −
X X X
r∈rch,δ p∈r
log P q|N (I, q, w) · Gσ (q − p),
(3.2)
3σ
q∈Sp
where Gσ is a Gaussian kernel with variance σ 2 , Sp3σ is a spherical neighbourhood around
p with radius 3σ, and δ is the vector of parameters for local modifications of ribs (discussed in Sec. 3.6.2), and rch,δ is the ribcage computed from parameters h, and δ.
3.6.2
Optimization Strategy
To position a generated centerline in the image, we rely on two manual inputs. Firstly,
the location of a point close to the rib’s joint to the vertebral disc is manually selected,
which we call the manual landmark. This point defines the position of one of the first rib
points (exactly which one is determined during optimization). Secondly, we computed the
bounding box of the ribcage from the ground truth centerlines, and rejected any solution
which exceeded this bounding box.
Optimization was based on grid search and a multi-resolution approach. At the first step,
we draw hypotheses of ribcage parameters, h, from a uniform grid on the interior of
a 6D hyper-ellipsoid which covers 95% of the multidimensional Gaussian distribution
associated with the PCA model. The√grid spacing was 1/5 of the standard deviation
of the first principal component, i.e. λ1 /5, where λ1 is the largest eigenvalue of our
PCA ribcage model. This grid spacing was determined heuristically as it was observed
that finer grids would not decrease the cost measure of the optimal solution, and coarser
grids would not result in the optimal solution. To introduce more flexibility into the
model, further hypotheses were created in two ways; by uniformly changing the proposed
orientation for all ribs within ±20o in steps of 5o , and by changing the positioning of the
ribs through assigning the manual landmark to one of the first points up to the angle point.
Then the cost function C(h, I, 5) was calculated for all hypotheses in the bounding box
and the k = 5 best results were kept. In the following steps, σ and the rotation range were
divided by 3 and the rib orientations and the starting point were modified. Finally, after 3
iterations we selected the modified hypothesis with the lowest cost.
35
3.7. E XPERIMENTS AND R ESULTS
Classifiers
C1
C2
C3
C4
mean
mean
0.93
0.89
0.89
0.87
0.89
std. dev.
0.05
0.04
0.06
0.09
0.07
min
0.80
0.78
0.75
0.53
0.72
Table 3.1: Statistics of the accuracy of the RF classifier in discriminating rib from non-rib
patches
3.7
Experiments and Results
We performed our experiments either on an end-exhalation (EE) image from the 4DMR
images (subjects 13 to 22), or a breath-hold EE 3DMR image (subjects 23-29). First,
we assessed the performance of RF classifiers in discriminating rib versus non-rib 2D
patches. The statistics of their accuracy over the 15 leave-one-subject-out experiments
are summarized in Table 3.1. The mean accuracy of 0.89 suggests that RFs in combination with the utilized features, which are based on 2D sagittal patches, have a high
discriminative power for detecting rib vs nonrib points.
To evaluate our detection method we first established ground truth rib centerlines from
manually selected points (see Sec. 3.5.1). Next, we determined error measures, which
will be explained in Sec. 3.7.1. Since we used the same MR dataset for building the appearance models as for evaluating our method, we performed leave-one-out experiments.
An example result is shown in Fig. 3.2. A small distance between the ground truth and
the detected centerlines can be observed. Moreover, the falsely assigned high probability
of the RF classifier to the intercostal space (Fig. 3.2b, 3.2f) and the liver (Fig. 3.2d, 3.2g)
demonstrates the importance of the constraints from the ribcage model.
3.7.1
Error Measures
We report three error measures, namely the 3D location accuracy (DistanceError), the
accuracy in detecting the whole rib (LengthError), and the clinically relevant error (OutOfPlaneError). DistanceError was defined as the closest Euclidean distance between a
point on the detected centerline and the ground truth. LengthError denotes the difference
in length of the detected centerline and the ground truth centerlines. DistanceError and
LengthError are 3D errors, while only the 2D error projected onto the ribcage surface
matters clinically when deciding which elements of the FUS transducer should be active
for treatments through the ribcage (Gao et al. [2012]). Hence, we define OutOfPlaneError
as the projection of the DistanceError on the z axis of the rib’s ground truth natural coordinate system. See Table 3.2 for statistics of the results. It can be observed that on average
36
3.8. D ISCUSSION AND C ONCLUSION
Subj.
13
14
15
16
17
19
20
21
22
23
24
26
27
28
29
mean
OutOfPlaneError
mean ± std (95 %)
0.64 ± 0.51 ( 1.64 )
1.04 ± 0.93 ( 2.60 )
1.03 ± 1.20 ( 3.08 )
0.97 ± 1.19 ( 3.53 )
1.37 ± 1.37 ( 4.14 )
1.50 ± 1.34 ( 4.55 )
1.67 ± 2.13 ( 6.62 )
1.02 ± 1.24 ( 3.86 )
1.34 ± 1.61 ( 5.14 )
1.87 ± 3.16 ( 8.85 )
0.93 ± 0.97 ( 3.06 )
1.37 ± 1.37 ( 4.15 )
0.99 ± 1.00 ( 3.20 )
1.29 ± 1.08 ( 3.56 )
1.03 ± 0.92 ( 3.04 )
1.20 ± 1.48 ( 4.09 )
DistanceError
mean ± std (95 %)
1.66 ± 0.91 ( 3.36 )
2.27 ± 1.38 ( 5.05 )
2.08 ± 1.23 ( 3.86 )
2.80 ± 1.60 ( 5.85 )
2.31 ± 1.53 ( 5.36 )
3.15 ± 1.66 ( 6.33 )
2.74 ± 2.08 ( 7.38 )
2.22 ± 1.40 ( 5.18 )
2.40 ± 1.65 ( 5.74 )
3.58 ± 3.09 ( 9.87 )
2.65 ± 1.98 ( 7.30 )
2.63 ± 1.81 ( 5.71 )
2.10 ± 1.41 ( 4.80 )
2.64 ± 1.55 ( 5.66 )
2.27 ± 1.01 ( 4.20 )
2.49 ± 1.73 ( 5.67 )
LengthError
mean ± std (95 %)
14.70 ± 7.98 ( 24.66 )
13.70 ± 12.03 ( 29.86 )
9.52 ± 8.45 ( 19.52 )
25.38 ± 7.29 ( 30.91 )
23.22 ± 7.74 ( 31.20 )
11.00 ± 9.65 ( 19.78 )
16.49 ± 12.49 ( 27.93 )
7.45 ± 5.29 ( 13.49 )
7.54 ± 9.44 ( 18.40 )
37.88 ± 4.56 ( 41.76 )
21.12 ± 4.77 ( 26.49 )
7.07 ± 5.14 ( 12.46 )
9.95 ± 4.89 ( 16.44 )
7.95 ± 8.58 ( 20.57 )
9.78 ± 7.78 ( 20.35 )
14.87 ± 11.09 ( 35.09 )
Table 3.2: Statistics of rib detection error measures in mm per subject.
we have achieved 2.49 mm DistanceError. The relevant clinical error, OutOfPlaneError,
is on average 1.2 mm.
3.8
Discussion and Conclusion
In this study we have shown that, despite their poor visibility, ribs can be detected in
MRI by taking advantage of the accuracy of CT images in observing the ribs. This was
achieved by learning a ribcage model from CT and combining it with a powerful MR
appearance model.
The intercostal distance is on average 20 mm (Dewhurst et al. [2012], Helm et al. [2013]).
Considering a safety margin equal to the average 95% error on each side of the detected
centerlines, it can be observed that there would still be on average 12 mm space left between two adjacent ribs to safely emit HIFU rays as proposed by Quesson et al. [2010].
However, the current implementation is rather slow. Future work will be focused on
improving the efficiency and implementation of our algorithm to achieve faster detection.
One approach would be to build a regression RF to predict the distance of points to rib
centerlines, which would give the cost measure C(h, I, σ) directly without the need for
convolution.
3.8. D ISCUSSION AND C ONCLUSION
37
Another area where the current implementation of our rib segmentation method could
be improved is in optimization. The proposed cost measure is highly nonconvex in the
model parameters, and gradient-based optimization methods were not appropriate. These
methods either got trapped at local minima or did not converge. To overcome this problem in our current implementation, we first evaluated a large number of initial hypothesis
and then searched in the vicinity of the 5 best hypotheses for the final optimal hypothesis.
More advanced population-based stochastic optimization algorithms, which do not depend on the gradient, such as particle swarm optimization (Kennedy [2010]), which will
be discussed in the next chapter, could achieve the same results more efficiently.
Despite the low mean error along the ribs (2.48 mm), the anterior part of the detected
ribs were on average 14 mm shorter than the ground truth. This was partly caused by the
difficulty in manually distinguishing cartilage from the bony structures in MRI, resulting
in the manually selected MR landmarks reaching into cartilage, whereas the geometric
model from CT did not include them. Obtaining a dataset of MR and CT of the same
subjects, will provide a better ground truth for evaluating our method. We believe that our
method would be more accurate by including the cartilage in both ribcage and appearance
models.
38
3.8. D ISCUSSION AND C ONCLUSION
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Figure 3.2: (a-d) The detected (yellow) and ground truth (red) centerlines on 4 sagittal
slices. (e-h) The probability heat map of the same slices obtained from classifiers (e) C1
(posterior), (f) C3 (posterior-to-lateral), (g) C2 (lateral) and (h) C4 (anterior). (i) The
corresponding regions of the classifiers are illustrated on an axial view of the rib.
4
Rib Registration in Magnetic
Resonance Images
4.1
Introduction
As mentioned in the previous chapters, ribs pose a challenge to a successful HIFU therapy.
In Chapter 3, we proposed a method to detect ribs in MR images. Yet, detecting the ribs
in a single MRI during planning is not sufficient as ribs also undergo respiratory motion.
Therefore, it is important to study the motion of ribs, evaluate its range under different
breathing conditions and be able to predict it using surrogate respiratory signals.
The detection framework introduced in Chapter 3 can be straightforwardly used for rib
tracking by detecting them in every frame, using the result in the previous frame as initialization with constraints to conserve the length and shape of the ribs. However, this
would be computationally intensive and would not exploit the fact that the appearance of
ribs remain relatively constant in a series of consecutive images. Therefore, to achieve
a faster method, we employed intensity based registration after the first detection step.
Registration of ribs in MRI means tracking the ribs’ position in each image in a series of
consecutive 3DMR images, also called 4DMRIs, to extract the motion of the ribcage.
The gold standard modality for imaging ribs is CT. Yet 4DCT can only capture the average motion of a breathing cycle due to dose restrictions (see Sec. 2.2.1), while we were
interested in the relationship between the movement of the ribs and the liver over multiple respiratory cycles, which include the natural variations of free-breathing. The 4DCT
images obviously did not allow this. Hence, we employed 4DMR images acquired using
the method of Von Siebenthal et al. [2007a].
However, as discussed in the previous chapter, detecting the ribs in MR images is a difficult task, and rib registration is also challenging for the same reasons. Similar to the
detection task, we tackled this challenge with prior knowledge including the anatomy and
kinematics of the ribcage. The advantages of incorporating rib anatomy and kinematics
into our method are twofold. First, we constrain our problem and hence, can solve it more
4.2. R IBCAGE A NATOMY AND K INEMATICS
40
efficiently. Second, by constraining our registration to biomechanically valid settings, we
avoid obtaining implausible or incorrect motions due to noise.
Next, we will first review the literature on ribs anatomy and kinematics in Sec. 4.2. Then,
we explain the registration problem and the proposed method in Sec. 4.3. Finally, we give
details of our experiments and results in Sec. 4.4
4.2
4.2.1
Ribcage Anatomy and Kinematics
Ribcage Anatomy
The human thorax contains the ribcage, the spine and the thorax cavity. The spine consists
of vertebrae with vertebral discs between them. The ribcage consists of 12 pairs of right
and left ribs, numbered 1 to 12 from superior to inferior. The ribs are connected to the
vertebrae at the posterior and to the sternum at the anterior end. The vertebral column
consists of 33 vertebrae, of which the 12 vertebrae connected to the ribs are called thoracic
vertebrae and correspondingly to the ribs are numbered 1 to 12. A typical vertebra and
the thoracic vertebrae are illustrated in Fig. 4.1.
Each rib has two extremities, the anterior or sternal extremity, and the posterior or vertebral extremity. The part in between is called the body or the shaft. The region around
the vertebral extremity consists of 3 subregions: head, neck and tubercle as illustrated in
Fig. 4.2. The angle, is the point where there is a marked change of curvature and from
which the rib can be divided into two parts each lying approximately on a different plane.
The part of the rib body from the angle to the head points in medial direction, changes
little in SI direction and is relatively linear, while the part from the angle to the anterior
extremity has a more convex shape and points towards inferior (Gray [2000]).
Ribs number 2 to 9 are each connected to two adjacent vertebrae, the vertebra with the
same number and the vertebra superior to it. Ribs number 1, 10, 11, and 12 are each only
connected to the vertebra with the same number (Gray [2000]). Ribs number 1 to 10 are
connected to the sternum at the anterior side of the ribcage and are classified into true and
false ribs based on the type of their connection to the sternum. True ribs, which consist
of ribs number 1 to 7, are connected to the sternum directly through their own cartilage.
False ribs, consisting of ribs number 8 to 12 are either indirectly connected to the sternum
through the cartilage of rib number 7, or not connected at all. Ribs number 8 to 10 which
are indirectly connected to the sternum are different from true ribs as they are less strictly
bound to the sternum allowing them to move moderately freer than true ribs. Ribs number
11 and 12, which are not connected to the sternum, move more freely than the rest of the
ribs and are also called floating ribs for the same reason (Gray [2000]).
The head is at the posterior extremity of the rib and consists of either one facet (ribs 1,
10, 11 and 12) or two demifacets separated by an axial edge, which is called interarticular
41
4.2. R IBCAGE A NATOMY AND K INEMATICS
(a)
(b)
Figure 4.1: Sagittal views of (a) a typical vertebra and (b) the thoracic vertebrae. Images
are courtesy of Gray’s Anatomy, (Gray [2000])
crest (See Fig. 4.2b). Each of these demifacets connects the rib to one of the two adjacent
vertebrae (See Fig. 4.1a). The tubercle lies on the neck of the rib and has an articular and
a non-articular part, which are illustrated in Fig. 4.2a and Fig. 4.2b. The articular part of
the tubercle is connected to the rib’s own vertebra at a location called transverse process.
This is a small, concave surface, as depicted in Fig. 4.1a, and allows some sliding and
gliding for the rib. Therefore, at the posterior, the ribs are connected to the spine at 3
joints for ribs 2 to 9, and two joints for ribs 1 and 10 and one joint for ribs 11 and 12
(Gray [2000]).
In conclusion, among the ribs that enclose the liver and are of interest to us, ribs 7 to 9
are connected to the vertebral column at 3 different joints constraining their articulation
but allowing some degree of rotation. Rib number 7 is connected to the sternum directly
further constraining its rotation. Rib number 10 is only connected at two joints, and
therefore can move more freely.
4.2.2
Ribs Kinematics
The kinematics of ribs are naturally affected by their anatomy. The articulation of the ribs
happen at three joints; the costovertebral joints with its own vertebra and the vertebra on
top, and at the costotransverse joint which connects the tubercle of the rib to the transverse
process of its own vertebra.
Since the anterior extremities of the ribs do not have significant lateral movement, it has
been shown that the ribs’ rotation should necessarily be around an axis normal to the
midplane (the sagittal plane in the middle of the body) (Saumarez [1986]). Moreover,
42
4.2. R IBCAGE A NATOMY AND K INEMATICS
(a)
(b)
Figure 4.2: (a) Axial view of a right rib in superior to inferior direction. Head, neck,
angle and the body of the rib are marked. (b) Coronal view of a left rib from the back.
Images are courtesy of Gray’s Anatomy, ( Gray [2000])
the ligaments that connect the rib to the vertebrae are such that only slight gliding in the
craniocaudal orientation is possible. This means that the movement of the ribs occurs
primarily through a rotation around the axis that connects the costovertebral joints with
the costotransverse joint (De Troyer et al. [2005]). In their seminal work, Wilson et al.
[1987] studied the geometry and respiratory movement of human ribs using CT of EI
and EE of 2 volunteers. They selected points on the ribs in CT images, fit a plane to the
selected points for each rib and computed the rotation of the planes of the ribs from EE to
EI. The rotation of the ribs as described previously was decomposed into two rotations: a
rotation around the ML axis, called pump handle rotation, followed by a rotation around
AP axis, called bucket handle rotation. They reported a decrease in the angles of these
rotations from superior to inferior ribs (3 to 7). They also reported a small rotation around
the IS axis. They reported these angles for EI and EE respiratory phases of two subjects.
However, their study did not provide any trajectory or motion data for ribs at intermediary
respiratory phases.
To analyse the movement of the ribs, researchers have relied mostly on simulation and
mechanical models with finite element modelling (e.g. Andriacchi et al. [1974], Saadé et
al. [2010], Villard et al. [2009], Villard et al. [2011], and Vaziri et al. [2010]). For example, Vaziri et al. [2010] constructed a 3D finite element model of ribcage movement to
study the effects of different elements in the respiratory system on the bucket handle motion of human ribs. They concluded that their method needs external validation regarding
the uncertainties of their theoretical models. Yet, there has been relatively little work on
4.3. R IB R EGISTRATION M ETHOD
43
validating these model through in vivo observations of rib movements during breathing,
and efforts in this direction have been limited to cadavers or animals (e.g. DiMarco et al.
[1990], Loring [1992] and De Troyer et al. [2005]). Moreover, details on the amplitude of
rib movement and its relationship to the movement of other organs have not been studied.
Hence, we employed our registration method based on general kinematics of the ribs, and
set out to investigate the details of rib motion during respiration.
4.3
Rib Registration Method
Image registration is the process of determining the spatial correspondence between regions of two images. For this purpose, a spatial transformation is found that brings the
region of interest in the first image, also called source image, into alignment with the region of interest in the second image, or target image. The criterion to judge the quality of
this matching includes the similarity measure, which is a function of the corresponding
intensities or features. Furthermore, the matching criterion may include spatial regularization terms to penalize unrealistic transformations. Generally speaking, image registration consists of finding the optimal transformation based on the matching criterion.
Registration methods are ubiquitous in all areas of image processing, and can be categorized in different ways based on their applications, see reviews by Maintz and Viergever
[1998], Zitova and Flusser [2003], Hill et al. [2001], and Sotiras et al. [2013]. In medical
image processing, the registration frameworks have mainly three components, the transformation model, the matching criterion, and an optimization method to find the optimal
transformation based on the matching criterion.
Similarity measures are based either directly on the intensity of regions to be matched, or
on features extracted from these regions. Feature-based similarity measures are generally
robust towards intensity variations (observed in different modalities in medical images,
and different lighting conditions in optical images), and have been exploited in many
fields of image processing such as computer vision. Feature-based methods are computationally more efficient, as the matching criterion has to be computed for a relatively
small set of features in comparison to every pixel (in 2D images) or voxel (in 3D images)
in the region of interest. In medical imaging, even though successful applications have
been reported (Shen and Davatzikos [2002], Urschler et al. [2006]), they remain generally
less popular. This can be due to the fact that, as a result of relatively low resolution, low
signal to noise ratio, and the existence of artifacts in medical images, accurate extraction
of reliable features, which is crucial for a feature-based registration, is a difficult task.
Intensity-based registrations, on the other hand, are computationally more intensive, but
also more robust in most practical medical imaging applications. To be invariant towards
intensity changes across different images, these methods use similarity measures that consist of functions of the intensity of pixels or voxels in the regions of interest. The most
popular intensity-based similarity measures are sum of squared differences (SSD), nor-
4.3. R IB R EGISTRATION M ETHOD
44
malized cross correlation (NCC), and mutual information (MI). Each of these similarity
measures have assumptions regarding the corresponding intensities in source and target
regions of interest. For example, SSD assumes that the intensities differ only by Gaussian noise, NCC assumes a linear correlation between intensities and MI assumes there
is a statistical relationship between the intensities. The choice of the similarity measure
depends upon practical considerations, such as the resolution, signal to noise ratio, and
modality of the images. For example, in intermodality registrations where only a statistical relationship between the corresponding intensities is expected, often MI is utilized.
The transformation model is determined based on the motion and properties of the objects
in the image. The transformations are, generally speaking, divided into two categories of
rigid vs. non-rigid transformation. Rigid transformations are suitable for rigid objects
whose movements are restricted to rotation and translation. Non-rigid transformations
constitute a large family of mappings and are suitable for describing the motion of deformable and non-rigid objects such as soft-tissue organs. Under perfect conditions, a
more flexible transformation model should result in the correct transformation. However,
in almost all practical applications, in the presence of noise, an excessively flexible model
will result in fitting the model to noise and artefacts rather than finding the true underlying
transformation. Moreover, too many degrees of freedom make the task of optimization
difficult and in some cases intractable. Therefore, the choice of an appropriate transformation model with adequate degrees of freedom is crucial for a successful registration.
Optimization in image registration is the task of finding the transformation that results
in the highest matching score between the target image and the transformed source image. The choice of a suitable optimization method depends both on the transformation
model and the matching criterion. If small changes in the parameters of the transformation model do not result in large and abrupt changes of the matching criterion, (i.e.
there exists a smooth gradient for the matching function in transformation parameters),
gradient-descent based techniques can be efficient and reliable. In contrast, if these conditions are not met, or if the matching criterion is highly non-convex in transformation
parameters, a gradient-descent based method might not converge or be trapped at local
optima. In that case, population-based and stochastic optimization methods can be used
at the cost of increasing computation time.
Next, we explain how we determined each of these components to solve the problem of
registration of ribs in MR images.
4.3.1
Transformation Model
Based on the kinematics of ribs and the ribcage model developed in Chapter 3, we defined a suitable ribcage transformation model. A global rigid registration of the image
volume cannot capture the individually different rotations of the ribs around their joints
to the vertebral column. An unconstrained non-rigid registration would also introduce too
45
4.3. R IB R EGISTRATION M ETHOD
many degrees of freedom to the problem. As seen in Sec. 4.2.2, the motion of each rib
consists primarily of a rotation either around an axis which connects its joints (ribs 2-10),
or around its single joint (ribs 1, 11 and 12). Therefore, the transformation of k ribs of
a ribcage can be modelled by a piecewise rigid transformation, consisting of k centered
rotations with 6k parameters (3 parameters for rotation and 3 parameters for the center of
rotation for each rib). In theory, the center, c, of rotation R for a rib, is its head which
remains stationary during respiration. However, since there is uncertainty about the accurate positioning of this point, we also permitted a displacement, ∆c for the center of
rotation, hence the 6 parameters per rib of our transformation.
4.3.2
Similarity Measure
Our matching criterion will only be based on an image similarity measure, since the employed transformation model is expected to sufficiently regularize the solution. NCC is
a common metric in MR image registration to measure the similarity of two image regions. It has the advantage of being robust against linear intensity changes, and being
fast to compute and simple to implement. In image processing NCC between two image
regions, I and J with equal size of n voxels, is defined as:
1 X I(x, y, z) − I¯ J(x, y, z) − J¯
,
N CC(I, J) =
n x,y,z
σI σJ
(4.1)
where, x, y, and z are coordinates of the corresponding voxels in both images, and I¯
and σI are the mean value and standard deviation of the voxel intensities in I. We used
NCC in two different ways. As a first attempt, we slightly modified the rib segmentation
framework introduced in Chapter 3 to adapt it to the registration problem. That is, we
changed the cost term for each point on the rib in Equ. 3.2 from the negative log-likelihood
of ribness from the MR appearance model to NCC of the corresponding patches, and
only allowed a centered rotation per rib. In details, for each point p on the rib r in the
reference image Iref we computed the negative NCC of its local sagittal 2D patch of size
2w × 2w (N (Iref , p, w) introduced in 3.1) and its transformed counterpart for image It
under transformation φr ,
c(Iref , It , r, φr ) = −
X
N CC N (Iref , p, w), N (It , φr (p), w) .
(4.2)
p∈r
We used this metric, which we call 2D NCC, to find the transformation between two
breath-hold images. However, since the NCC has to be computed for each pair of patches,
this can be very slow. The reason is that, there is a considerable overlap in N (Iref , p, w) of
consecutive points on a rib. Therefore, in the second attempt, we computed the NCC of the
46
4.3. R IB R EGISTRATION M ETHOD
entire 3D rib region in the following manner. According to literature (Mohr et al. [2007]),
ribs 7, 8 and 9 have a cross-section width of 7.4 ±1.7 mm, 6.5 ±2.1 mm and 6.6 ±1.9 mm
and a cross-section height of 12.8 ±2.8 mm,13.1 ±3.6 mm and 12.3 ±3.8 mm, in their native coordinate systems, respectively. Therefore, for each rib, r, we built a rib mask, Mr0 ,
in the rib’s native coordinate system in the form of tubes around the extracted centerline
with semi-elliptical cross-sections based on the reported measurements, as follows:
(
Mr0 (qx , qy , qz ) =
1
0
2
x)
if ∃p = [px py pz ] ∈ r, ( (qx −p
+
w2
otherwise,
(qy −py )2
h2
+
(qz −pz )2
)
w2
≤1
(4.3)
for all voxel positions q = [qx qy qz ] of Iref in the rib’s native coordinate system with
h and w being the height and width of the tube, respectively. Finally, the mask Mr , was
obtained by bringing Mr0 into the world coordinate system. Fig. 4.3 illustrates a mask
constructed as described for a right number 9 rib. Note that, the neighbouring voxels of
a rib centerline in the IS direction, which lie in the intercostal space, undergo a similar
motion. However, the neighbouring voxels in the AP, or ML direction, can reach into the
abdominal cavity, in which case they have a different motion. Hence, we applied a very
conservative w = 5 mm to ensure we do not include any lung or liver structures into our
mask. In contrast, we applied a larger h = 14 mm than the reported mean rib height to
include the edge features on the borders between the ribs and the intercostal muscles. The
mentioned values for h and w were used for all ribs (7-10), and for all subjects. NCC
of the mask region, M , in image, Iref , with the corresponding region in image J under
transformation φ, is then defined as follows:
1 X I(p) − I¯M J(φ(p)) − J¯M,φ
,
N CC(I, J, M, φ) =
n p∈M
σIM σJM,φ
(4.4)
where, I¯M , J¯M,φ , σIM and σJM,φ are the mean and standard deviation values of the corresponding regions. The new NCC similarity measure, s(.), for a rib with centerline r at
the reference image, Iref , undergoing the transformation φ at the target image, It was as
follows:
s(Iref , It , r, φ) = N CC Iref , It , Mr , φ .
4.3.3
(4.5)
Optimization Method
With the similarity measure and the allowed transformations being determined, what remains is to find the optimal transformation with parameters inside the acceptable parameter space, that gives the highest similarity measure. Initial experiments with gradient
47
4.3. R IB R EGISTRATION M ETHOD
based optimizers resulted in convergence problems or high errors. It is known that gradient descent methods are sensitive to initialization, and are not suitable for our highly
nonconvex optimization problem. We believe that these factors contributed to the poor
performance of gradient descent based methods in our application. Therefore, we employed particle swarm optimization introduced by Kennedy and Eberhart [1995], which
belongs to the category of population-based optimization algorithms, which are known
for overcoming such problems.
Particle Swarm Optimization
Particle swarm optimization is a biologically inspired stochastic algorithm with belongs
to the category of population-based metaheuristic optimization algorithms. It is inspired
by the movement of individuals in flocks of birds which is assumed to be influenced both
by the other birds’ and the bird’s own movement. In terms of optimizing a multivariate
function over a d-dimensional parameters space, particles are defined as points with a
position x and velocity v in this d-dimensional parameter space, that move around to find
the optimal function value. A particle swarm consists of a set of particles with a certain
topology that defines how the particles are connected. The particles that are connected
influence the future velocity of each other and will be referred to as neighbouring particles.
At each time step t the position and velocity of the particles are defined by two equations
(Kennedy [2010]). The position xt+1
(i,d) of a particle with index i, along the dimension d, at
time step t + 1 is given by the following equation:
(t+1)
xi,d
(t)
(t+1)
= xi,d + vi,d .
(4.6)
(t+1)
The velocity vi,d of particle i at time step t + 1 along dimension d is given by the
following equation:
(t+1)
vi,d
(t)
(t)
(t)
= α vi,d + U (0, β1 ) pi,d − xi,d + U (0, β2 ) pg,d − xi,d ,
(4.7)
where α, β1 and β2 are constants, U (0, β) is a uniform random number generator with
mean value 0 and range β, pi is the best position that particle i has previously encountered,
and pg is the best position among all neighbouring particles of i. The constant β = β1 =
β2 is called acceleration constant, and the constant α represents the inertia weight. We
used the values α = 0.7298 and β = 1.5, proposed by Clerc and Kennedy [2002].
We used the ITK implementation (Johnson et al. [2013]) of this algorithm for finding the
optimal 6 parameters of our centered rigid transformation for each rib. This implementation utilizes a global neighborhood (i.e. all particles are connected), and clamps the
position of particles to the valid range after each iteration.
4.4. E XPERIMENTS AND R ESULTS
4.4
48
Experiments and Results
First, we applied our registration algorithms to breath-hold images at EE and EI, as these
have greater motion ranges. From the experience gained, we selected the most promising
registration approach and applied it to the 4DMR images.
In one set of experiments, we evaluated the error of the entire procedure including detection of the ribs and the subsequent registration for the breath-hold image pairs. In the rest
of the experiments, including those with 4DMR images, we used the ground truth centerlines to create the masks. This allowed us to evaluate the performance of the registration
individually. We used the transformation model described in Sec. 4.3.1, and the particle swarm optimizer described in Sec. 4.3.3. The automatically detected and the ground
truth centerline of a rib r in image I will be referred to as CI,r and GI,r respectively. We
assessed the following 4 similarity measures:
• RF: uses ribness (computed through RF classifiers as described in Sec 3.5) of voxels
of rotated rib centerlines to compute the cost of a rotation.
• 2D NCC: computes the NCC of the sagittal patches around CEEref ,r in the reference
EE image (EEref ) and their corresponding patches in the target image according to
Equ. 4.2.
• NCC with masks: computes the NCC of the 3D regions defined by the mask,
Mr , around CEEref ,r and the corresponding region in the target image according
to Equ. 4.4.
• NCC with GT masks: is the same as NCC with masks with the difference that the
mask is constructed around the ground truth (GT) centerlines GEEref ,r .
The registration was performed either between a pair of breath hold EE and EI images,
or between a reference end-exhalation (EE) image and a target image both of which are
from the 4DMR images. The output of the registration for a rib r consisted of a centered
rotation φr (.) (a center of rotation and a rotation matrix). We applied this transformation
to CEEref ,r , and computed the error measures described in Sec. 3.7.1 between the ground
truth centerlines of the target image GIt ,r and φr (GEEref ,r ), the transformed ground truth
centerlines in IEEref . Since the rib length does not change, LengthError remains the same
as for detection and hence it was not computed. We summarized the results by the mean,
standard deviation and 95th percentile of the distribution created by pooling all results per
subject (4 ribs with 100 rib points each) or over all subjects.
In the following, we describe these experiments and their results.
4.4. E XPERIMENTS AND R ESULTS
Sbj
24
26
27
28
29
mean
49
Respiratory motion
Out Of Plane Motion
3D Motion
mean ± std (95%) mm mean ± std (95%) mm
1.23 ± 1.39 (3.91) 3.76 ± 2.92 (9.47)
1.02 ± 1.01 (3.20) 5.48 ± 4.16 (12.67)
1.72 ± 1.86 (5.36) 8.42 ± 5.57 (17.50)
2.28 ± 1.81 (7.16) 5.90 ± 3.75 (12.40)
2.36 ± 2.42 (8.24) 9.16 ± 5.93 (18.78)
1.75 ± 1.86 (5.58) 6.69 ± 5.05 (16.65)
Table 4.1: Summary of ribs’ motion statistics (4 ribs, 100 points each) from EE to EI
breath-holds. The 3D motion refers to the Euclidean displacement, while out of plane
motion denotes the projection of this displacement on the normal of the ribs’ planes.
4.4.1
Breath-hold Images
The mean magnitude of respiratory motion over the 100 rib points, between the EE and
EI breath hold images, for the studied subjects is presented in Table 4.1. Since the ribs
are anchored at the posterior extremity, the 95th percentile of the movement is due to the
most anterior points. It can be observed that during a deep inhalation, the displacement
of these anterior points is on average 16.4 mm and can be as large as 18.8 mm for one
subject.
The mean DistanceError (defined in Sec. 3.7.1) is slightly increasing from random forest
(Table 4.2), to 2D NCC (Table 4.3), to NCC with masks (Table 4.4). However, the computation time also decreases substantially from RF to 2D NCC and further to NCC with
masks.
Note that the DistanceError of NCC also includes the detection error, as the registration
is initialized with the detected and not the ground truth centerline. Therefore, to evaluate
the performance of our NCC registration algorithm independent of the detection errors,
we performed experiments in which we created masks using the ground truth centerlines,
referred to as GT masks hereafter. The results of NCC with the GT masks are presented
in Table 4.5. These are substantially better than the results including the detection errors.
By comparing these registration results with the respiratory motion (Table 4.1), it can be
observed that the error stays approximately the same (≈2 mm), even though the motion
varies from subject to subject (e.g. 4.1 mm for subject 11 versus 9.7 mm for subject 15).
Given that the resolution of these images is 1.33 × 1.33 × 2.5 mm in IS, AP, and ML
direction, we believe that it will be very hard to reduce these errors much further.
50
4.4. E XPERIMENTS AND R ESULTS
Sbj
24
26
27
28
29
mean
RF
OutOfPlaneError
mean ± std (95%) mm
1.02 ± 0.98 (3.02)
0.91 ± 0.96 (4.19)
1.32 ± 1.23 (3.82)
1.24 ± 1.21 (3.76)
1.19 ± 1.06 (3.92)
1.14 ± 1.08 (3.81)
DistanceError
mean ± std (95%) mm
3.33 ± 2.58 (9.65)
2.21 ± 1.08 (4.37)
2.84 ± 3.43 (9.61)
2.85 ± 1.45 (5.47)
2.56 ± 2.01 (6.01)
2.72 ± 2.26 (5.90)
Table 4.2: Statistics of rib registration error using random forests (RF) in mm.
Sbj
24
26
27
28
29
mean
2D NCC
OutOfPlaneError
DistanceError
mean ± std (95%) mm mean ± std (95%) mm
1.04 ± 0.96 (3.41) 4.60 ± 2.20 (7.89)
0.73 ± 0.65 (2.10) 2.14 ± 1.11 (4.23)
0.81 ± 0.77 (2.43) 2.47 ± 1.16 (4.30)
1.65 ± 1.53 (5.17) 2.98 ± 1.32 (5.06)
1.78 ± 1.71 (4.51) 3.54 ± 2.35 (8.62)
1.20 ± 1.28 (3.90) 3.07 ± 1.87 (6.81)
Table 4.3: Statistics of the combined error in rib detection and registration in mm.
Sbj
24
26
27
28
29
mean
NCC with Masks
OutOfPlaneError
DistanceError
mean ± std (95%) mm mean ± std (95%) mm
2.03 ± 1.83 (5.55) 4.82 ± 3.14 (11.93)
1.47 ± 1.64 (3.87) 2.75 ± 2.67 (7.01)
1.50 ± 1.43 (5.06) 2.82 ± 1.74 (6.02)
1.36 ± 1.54 (2.99) 3.52 ± 1.75 (6.71)
1.80 ± 1.38 (4.3)
3.70 ± 1.54 (5.89)
1.63 ± 1.57 (5.29) 3.52 ± 2.43 (10.21)
Table 4.4: Statistics of the combined error in rib detection and registration in mm.
4.4. E XPERIMENTS AND R ESULTS
Sbj
24
26
27
28
29
mean
51
NCC with GT Masks
OutOfPlaneError
DistanceError
mean ± std (95%) mm mean ± std (95%) mm
0.74 ± 0.72 (1.57) 1.82± 1.53 (4.98)
0.97 ± 1.70 (5.32) 1.85± 2.04 (7.38)
1.32 ± 1.26 (3.95) 2.25± 1.63 (5.12)
1.25 ± 2.02 (1.22) 2.40± 0.97 (3.68)
1.17 ± 1.12 (3.42) 2.27± 1.30 (4.26)
1.09 ± 1.43 (4.98) 2.11 ± 1.52 (6.78)
Table 4.5: Statistics of rib registration error in mm.
4.4.2
4DMR Images
The previous section showed the advantage of using GT masks for the registration to
support accurate motion extraction. As the correction of detected ribs can be achieved
relatively easily and fast (by for example identification of a few points for determining a
better rotation), we believe that this effort is worth spending. Hence, we assess here the
performance of the registration which uses GT masks.
Rib Points Displacement
On 4DMR images, the amplitude of the respiratory motion of rib points for breathing
under rest conditions were on average 1 mm (see Table 4.8). Since it is difficult to evaluate
small displacements in the range of image resolution (1.33×1.33× 5mm), we evaluated
the registration on deep end-inhalation (EI) images in the following manner.
1. For all EIc images of the cycles c ∈ 1, ..., 100, we extracted mEIc , the magnitude of
the motion of the most anterior rib point after registering EIc to the reference EE
image IEEref .
2. Next, we determined the distribution of the m over the EIc images.
3. Among EIc , we selected those whose mEIc were larger than the 95th percentile of
this distribution (5 EI image per subject).
To generate the ground truth centerlines for these selected EI images, we propagated GEEc ,r
to these new images using the following scheme. In each EI image, instead of densely
selecting points as was done in Sec. 3.5.1, only a limited number of points were placed on
a rib r. GEEref ,r was moved rigidly to fit these points based on the iterative closest point
algorithm. We refer to the resulting ground truth centerlines for rib r in an EIc image as
∗
GEI
.
c ,r
4.5. D ISCUSSION AND C ONCLUSION
Sbj
1
2
3
4
5
6
7
8
mean
52
NCC with GT Masks in Free-breathing
OutOfPlaneError
DistanceError
mean ± std (95%) mm mean ± std (95%) mm
0.59 ± 0.52 (1.70) 1.21 ± 0.67 (2.35)
0.42 ± 0.39 (1.25) 1.14 ± 0.68 (2.53)
0.42 ± 0.37 (1.29) 0.84 ± 0.43 (1.68)
0.57 ± 0.52 (1.47) 1.01 ± 0.53 (1.82)
0.36 ± 0.43 (1.35) 0.77 ± 0.49 (1.58)
0.98 ± 0.79 (2.58) 1.65 ± 0.92 (3.06))
0.36 ± 0.28 (0.77) 0.75 ± 0.41 (1.38)
0.36 ± 0.28 (0.93) 0.56 ± 0.32 (1.22)
0.53 ± 0.52 (1.56) 1.06 ± 0.69 (2.46)
Table 4.6: Statistics of rib registration error for selected deep inhalations in mm.
∗
The errors were computed between GEI
, and the results of the registration, T (GEEref ,r ).
c ,r
Due to the time-consuming process of registration of images of 100 respiratory cycles
and its validation, only the initial results of the experiments on the first 8 subjects in
our dataset are presented. The errors for these 8 subjects are shown in Table 4.6. For
∗
comparison, the motion between GEEc ,r and GEI
are shown in Table 4.7. The statistics
c ,r
of the displacements of all rib points for all 8 subjects computed using the registration
method are summarized in Table 4.8.
Rotation Angles
Furthermore, the bucket handle (BH) and pump handle (PH) angles as described by Wilson et al. [1987] were computed. To that end, a rotation R was decomposed as follows:
R = RM L RAP RIS ,
where the angles of the ribs’ rotation around the ML and AP axes of the ribs native
coordinate system, are the PH and BH angles.
The change of the Euler angles of rotation over time for an exemplar subject is illustrated
in Figs. 4.4 and 4.5. It can be observed that the pump handle angle is on average the
largest among the three angles.
4.5
Discussion and Conclusion
We have proposed a constrained locally rigid registration for the ribs based on our ribcage
model. We implemented three registration schemes using the RF and -NCC cost measure
53
4.5. D ISCUSSION AND C ONCLUSION
Sbj
1
2
3
4
5
6
7
8
mean
Respiratory Motion of Selected Deep Inhalations
Out of Plane Motion
3D Motion
mean ± std (95%) mm mean ± std (95%) mm
1.18 ± 0.48 (2.02) 4.11 ± 1.24 (5.65)
0.89 ± 0.79 (2.29) 2.64 ± 1.16 (4.85)
0.54 ± 0.42 (1.52) 1.61 ± 1.11 (3.64)
1.11 ± 1.02 (2.92) 1.94 ± 1.13 (3.56)
0.51 ± 0.56 (1.91) 1.41 ± 1.04 (3.12)
2.16 ± 1.68 (5.15) 4.31 ± 2.13 (7.09)
0.64 ± 0.66 (2.09) 1.61 ± 1.00 (3.20)
0.72 ± 0.82 (2.74) 1.93 ± 1.52 (4.66)
1.01 ± 1.00 (2.85) 2.71 ± 1.75 (5.85)
Table 4.7: Summary of ribs’ motion statistics (4 ribs, 100 points each) from EE to
selected deep inhalations. The 3D motion refers to the Euclidean displacement, while out
of plane motion denotes the projection of this displacement on the normal of the ribs’
planes.
Sbj
Respiratory motion
mean ± std (95%)
1
2
3
4
5
6
7
8
mean
1.55 ±
0.94 ±
1.03 ±
1.74 ±
1.26 ±
1.37 ±
0.80 ±
1.02 ±
1.10 ±
1
2
3
4
5
6
7
8
mean
1.31 ±
0.59 ±
0.65 ±
1.19 ±
0.92 ±
1.65 ±
0.65 ±
0.99 ±
0.99 ±
rib 7
1.63
0.81
0.45
1.14
1.27
1.64
0.59
0.92
1.48
rib 9
1.47
0.73
0.64
0.91
1.06
1.66
0.72
1.04
1.21
(5.09)
(2.72)
(1.84)
(3.73)
(3.95)
(5.27)
(2.15)
(3.01)
(4.15)
1.43 ±
0.81 ±
0.78 ±
1.31 ±
0.83 ±
1.63 ±
0.70 ±
1.07 ±
1.08 ±
(4.50)
(2.25)
(2.19)
(2.85)
(3.39)
(5.45)
(2.37)
(3.42)
(3.69)
1.22 ±
0.93 ±
0.81 ±
0.80 ±
0.84 ±
1.70 ±
0.58 ±
1.03 ±
0.91 ±
rib 8
1.54
0.83
0.64
0.99
0.81
1.77
0.78
0.99
1.22
rib 10
1.24
0.90
0.58
0.90
0.84
1.86
0.72
1.10
1.13
(4.57)
(2.67)
(2.18)
(2.86)
(2.53)
(5.74)
(2.46)
(3.21)
(3.62)
(3.77)
(2.65)
(1.77)
(2.94)
(2.73)
(5.79)
(2.35)
(3.63)
(3.44)
Table 4.8: Rib respiratory motion during free breathing. The DistanceError statistics over
all four ribs are 1.02 ± 1.27 (3.74) mm.
4.5. D ISCUSSION AND C ONCLUSION
54
for local patches or for the tube shaped rib mask. We achieved a registration accuracy of
1.06 mm and 2.11 mm for 4DMRIs and breath-hold 3DMRIs respectively.
Furthermore, we applied our registration algorithm to 4DMR images of subjects under
free breathing during rest. We extracted the bucket handle and pump handle angles described in the literature. Our results confirm the theoretical kinematics described for the
ribs.
Our motivation for registration of ribs in MR images was its application in modeling their
respiratory motion during HIFU therapy. However, our proposed method can also be a
useful tool for studying the long-term relationship between the motion of respiratory organs such as the diaphragm and intercostal muscles during free-breathing, as was pursued,
for example by Gilbert et al. [1981].
55
4.5. D ISCUSSION AND C ONCLUSION
(a)
(b)
(c)
(d)
(e)
(f)
Figure 4.3: (a-c) Overlay of the M mask constructed for a right number 9 rib on 3 sagittal
slices, (d-e) a coronal and an axial slice. (f) 3D view of the same M mask.
4.5. D ISCUSSION AND C ONCLUSION
56
Figure 4.4: The three Euler angles of rotation (PH: pump handle, IS: inferior-superior,
BH: bucket handle) for a subject during 100 cycles of free breathing. End-inhalation
states are marked with red asterisks. Angles in degrees for ribs 7 (top) and 8 (bottom) are
displayed.
4.5. D ISCUSSION AND C ONCLUSION
57
Figure 4.5: The three Euler angles of rotation (PH: pump handle, IS: inferior-superior,
BH: bucket handle) for a subject during 100 cycles of free breathing. End-inhalation
states are marked with red asterisks. Angles in degrees for ribs 9 (top) and 10 (bottom)
are displayed.
5
Motion Modeling of Liver and Ribs
5.1
Introduction
As discussed in Chapter 2, for an effective therapy using the tracking method to compensate the respiratory movement, it is important to have accurate information about the position of the target organ during therapy. Moreover, acquisition of reliable 3D images with
acceptable quality in real-time is not possible yet. Advanced invasive tracking technologies such as fluoroscopic images with radiopaque markers, electromagnetic markers, or
noninvasive tracking technologies such as HIFU speckle tracking (Marquet et al. [2011])
have been proposed. These methods are capable of tracking the target in real-time. However, these methods provide no information about the motion of organs in the beam path.
This information is especially important in HIFU to avoid collateral damage (Jung et al.
[2011]).
Predicting 3D organ motion in the abdomen in real-time has been made possible through
constructing 4D motion models, that is 3D motion of organs in time. These models learn
the correlation between the motion of points tracked inside the organs or markers outside
of the organ and the 3D motion of the entire organ. In this chapter, we first review 4D
motion models in Sec. 5.2. Next, we describe our proposed exemplar 4D motion models
in Sec. 5.3. Finally, in Sec. 5.4, we present a joint motion model of liver and ribs based on
the registration results of Chapter 4.
5.2
Review of Statistical Motion Models
There is an extensive body of work dedicated to modeling 4D motion in abdominal organs. These works follow two general approaches. Either, a biomechanical model is created based on the physical characteristics of tissues, or a statistical model is built based on
registration of 4D images (MR or CT). Biomechanical models are mostly used for simulation purposes (Eom et al. [2010]). These models are usually not suitable for predicting
5.2. R EVIEW OF S TATISTICAL M OTION M ODELS
59
the position of the target sites during therapy. Below, we give a review of the literature
(published until 2012) on statistical 4D motion models which is the focus of this chapter.
Statistical models use prior observations to learn the relationship between surrogates
and the organ motion. The observations are gathered for either a certain patient (see
Sec. 5.2.2) or for a population (see Sec. 5.2.3). The statistical motion models thus fall
into two categories, the so called subject-specific models which are built from the data
acquired through a planning session (Blackall et al. [2006], Zhang et al. [2007], Liu et al.
[2010a]), and population models which are created by gathering data from different subjects (Von Siebenthal et al. [2007b], He et al. [2010], Nguyen et al. [2009], Klinder et al.
[2010], Ehrhardt et al. [2011], Preiswerk et al. [2011]). The most commonly employed
method for the characterization of the underlying variability is principal component analysis (PCA), which we summarize in the following.
5.2.1
Principle Component Analysis
We assume that N points describe the position of an organ at T time instances. The
3D position and the displacement vector of the ith point at time t are denoted as pit =
[pit,x , pit,y , pit,z ] and dji = [dji,x , dji,y , dji,z ] respectively. The 3D coordinates and displacement
vectors of all N points at time t are collected in single vectors and are referred to as
N T
2
T
1
Pt = [p1t , p2t , . . . , pN
t ] and Dt = [dt , dt , . . . , dt ] respectively. To keep the
definitions general, we introduce Ut as the vector containing all the observed data of
the organ at time t. This vector may be replaced by Dt , Pt , or a combination of these
vectors and the surrogate vector st . As a next step, we compute the corresponding centered
PT
vectors by Ũt = Ut − Ū, where Ū =
t=1 Ut /T . All data is then collected in the
matrix Ũ = [Ũ1 , Ũ2 , . . . , ŨT ] (size 3N × T for Dt , Pt ) and the covariance matrix
ΣŨ = ŨŨT is determined. Then the eigenvalue decomposition of ΣŨ is calculated:
P CA
ΣŨ = EΛET , where E = [e1 , e2 , ..., e3N ] is composed of the eigenvectors ej of ΣŨ ,
which are the principal components of Ũ, and Λ has the corresponding eigenvalues λj on
its diagonal. Often T < 3N and therefore only T − 1 nonzero eigenvalues exist. In this
P CA
case, the eigenvectors are calculated by ŨT Ũ = XLXT and E = ψ(ŨX), where ψ(A)
denotes normalization of the columns of matrix A. The eigenvalues are proportional to the
variance of the data covered by the corresponding eigenvector. Eigenvectors can therefore
be sorted according to this variance. Efficient dimensionality reduction is then achieved
by discarding eigenvectors which correspond to lower eigenvalues. A full reconstruction
is given by
Ũ = EW,
(5.1)
where the weight matrix W = [wi,t ]3N ×T is derived by W = ET Ũ. For dimensionality
reduction, the subset of eigenvectors associated with the K highest eigenvalues Ê =
[e1 , e2 , ..., eK ] is employed, and the projection into the reduced PCA space is calculated
5.2. R EVIEW OF S TATISTICAL M OTION M ODELS
60
by the pseudo-inverse Ŵ = (ÊT Ê)−1 ÊT Ũ. The resulting Û = ÊŴ approximates Ũ in
the minimum least squares sense.
During therapy, only partial information of Ũ (e.g. some surrogate) is usually available
at time t. By partitioning Ũt into unknown positions P̃t and known surrogate s̃t , we can
rewrite Equ. 5.1 as P̂t = Êp Ŵt and ŝt = Ês Ŵt , where Êp and Ês are the corresponding
partitions of Ê. In order to estimate P̂t , one has to first to determine Ŵt from the latter
equation. Using the least squares method and knowing that Ês is of size Ks × K, with
Ks < K, we utilize its right pseudo-inverse, which results in
−1
−1
ŝt ,
P̂t = Êp Ês T Ês ÊTs
ŝt .
(5.2)
Ŵt = ÊTs Ês ÊTs
This provides the vector P̂t with the smallest Euclidean norm given the measurements.
However, in order to find the most probable vector we have to take into account the
variance along the principal axes. Hug et al. [2000] address this issue by minimizing
the Mahalanobis distance kŝt − Ês Ŵt km to determine Ŵt
−1
ŝt ,
Ŵt = ΛÊTs Ês ΛÊTs
5.2.2
−1
P̂t = Êp ΛÊTs Ês ΛÊTs
ŝt .
(5.3)
Patient-specific models
Zhang et al. [2007] used respiratory correlated CT scans to build 4D lung images based
on the method of Ford et al. [2003]. The SI-position at the top of the diaphragm at time
t and t − 3 was chosen as surrogate (st = [st , st−3 ]T ). A diffusion-based registration
method minimizing the sum of squared intensity differences was used to determine the
displacement fields. The data vector Ut was constructed by concatenating the coordinates
of all points Pt and the surrogate signals st . After PCA, a decomposition as described in
Sec. 5.2.1 was performed resulting in P̃t = Ep Wt and s̃t = Es Wt . The latter equation
could be solved for Wt by a pseudo-inverse as in Equ. 5.3. Instead, the authors preferred
to reduce the number of eigenvectors to the number of surrogates such that Ês is invertible. The relation between Pt and st is then given by Pt = Êp Ê−1
s st . In comparison to
Equ. 5.3, this does not lead to an approximation of the surrogate values, but limits the
model to include at most as many eigenvectors as surrogate signals. For evaluation, the
Gross Tumor Volume (GTV) in the EE state was transformed by the model to the other
breathing phases. Performance was quantified by comparing the centroids of the transformed GTV and the manually delineated GTV. The mean discrepancy of centroids for
the intra-session experiment was less than 1 mm in LR and AP direction and about 2 mm
in the SI direction. The inter-fraction mean error were 1.1 ± 0.6 mm (LR), 1.8 ± 1.0 mm
(AP) and 1.6 ± 1.3 mm (SI).
Liu et al. [2009] built a patient-specific motion model using respiratory correlated 4D
CT images of the lung. The shape of the lung was employed as surrogate signal. Dense
5.2. R EVIEW OF S TATISTICAL M OTION M ODELS
61
displacement fields, between each respiratory state and the reference frame at EE, were
computed using symmetric, diffeomorphic image registration. The lung volumes were automatically segmented from the 4D CT images. Correspondence between surface points
in different phases was established by deforming an initial surface by a diffusion process along the surface normal direction until fitting the individual segmentation. In their
later work (Liu et al. [2010b]), shape correspondences were group-wise optimized using a
method where surface points samples are modeled as sets of dynamic particles whose position is subject to entropy minimization. PCA was independently performed on the centered surface points P̃ and the centered displacement fields D̃, resulting in P̃ = EP WP
and D̃ = ED WD . P̃ and D̃ were then connected by assuming a linear relationship between them in PCA space, i.e. W̃D = W̃P M. The matrix M was calculated by using
−1
a pseudo-inverse, i.e. M = (W̃PT W̃P ) W̃PT W̃D . For a given P̃t , WPt is determined
by WPt = (ÊP T ÊP )−1 ÊP T P̃t , and then the learned linear relationship is used to get
W̃Dt = W̃Pt M and D̃t = ED WDt . In their later work (Liu et al. [2010b]), the correlation between P and the corresponding D was maximized by Canonical Correlation
Analysis (CCA). The model reduced the mean GTV surface distances to the manual delineation from about 2.1 mm to 1.5 mm for two patients (Liu et al. [2009]). Employing
the CCA improved the average Center of Gravity (COG) error of the tumor from about
4.5 mm to 2 mm for 5 patients (Liu et al. [2010b]). Both studies used 2-5 eigenvectors
to cover 90% of the total variation. The lung surface was a better surrogate than the diaphragm position (≈1.8 mm vs. ≈1.4 mm) (Liu et al. [2010b]). However it remains
unclear how the lung surface can be extracted during therapy.
King et al. [2012] compared the predictive power of a patient-specific functional (average
cycle, 2nd-order polynomial as proposed by Blackall et al. [2006] and McClelland et al.
[2011]) and a patient-specific statistical motion model (PCA as proposed by Zhang et
al. [2007]) for the lung. Two types of surrogates were tested, namely a 1D navigator
signal extracted from an image region at the dome of the right hemi-diaphragm and a
2D navigator MRI simulated from the 3D MRI. Prediction using the 2D navigator was
based on finding the model parameters which maximized the image similarity between the
2D navigator MRI and the deformed reference image in the overlap region. Respiratory
motion for 3 types of breathing (normal, quick and deep) was captured for 10 volunteers
using fast 3D MRIs (≈700 ms) over a period of 70-100 s. Evaluation was based on the
lung surface distance after automatic segmentations, as the poor signal-to-noise ratio of
the 3D MRIs did not allow for any landmark based assessment. Best results were achieved
with the PCA model using 5 components and 2D MRI navigators, reducing the surface
distance from 7.12 mm to 2.75 mm on average. The functional model provided an average
performance of 2.83 mm and 2.93 mm for 2D and 1D navigators, respectively. Similar
performance was achieved for a PCA model with only 2 components and 2D navigators
(2.90 mm). Worst was the patient-specific PCA model using 1D navigators (4.63 mm).
5.2. R EVIEW OF S TATISTICAL M OTION M ODELS
5.2.3
62
Population models
Von Siebenthal et al. [2007b] observed the long term (≈1 hour) motion of the liver for
12 healthy volunteers using 4D MRIs (Von Siebenthal et al. [2007a]) and created a population model which captured the additional motion (drift of the EE position) occurring
besides the quasi-periodic respiratory motion. For each breathing cycle, the image with
the most superior liver position was selected as EE image. Normalized cross-correlation
and a B-Spline deformation model was employed for registering the EE images of a volunteer. Inter-subject correspondence was established by manual selection of 4 prominent
liver landmarks on sagittal slices of a selected EE image, interpolation by B-splines, regular subdivision of the resulting coarse segmentation and mesh refinement to a manual fine
segmentation. PCA was performed on 200 EE liver positions per volunteer. The position
of individual nodes were employed as surrogate and the position of all other nodes were
predicted using Equ. (5.3). The capability of individual nodes as surrogates was tested
following the method of Hug et al. [2000]. The average drift motion was 4.3 mm. This
was reduced to 1.5 mm when using the best surrogate and to 1.1 mm when using the 3
best surrogate positions.
Ehrhardt et al. [2011] built a population mean motion model for 17 lung cancer patients
during free-breathing using CT images. The motion model was generated in 3 steps.
Firstly, the subject-specific motion for patient q was estimated by registering the 3D images at time t 6= r (Iq,i ) to a reference image (Iq,r at EI) using a nonlinear, diffeomorphic,
intensity-based registration method. The resulting transformation ϕq,t maps Piq,r to Piq,t .
Secondly, an average image of the lung for the reference state (I¯r ) was iteratively generated. Registration of Iq,r to I¯r provides transformation ψq , which maps Piq,r to PiI,r
¯ .
Thirdly, a population mean motion model was created by mapping all subject-specific
motion models ϕq,t to the average image space using ϕ̃q,t = ψq ◦ ϕq,t ◦ ψq−1 and calculating the Log-Euclidean mean at time t (denoted as ϕ̄t ) from all mapped transformations
ϕ̃q,t . This assumes that transformation ψq is also applicable to Piq,t6=r , which does not necessarily hold. To predict patient-specific respiratory motion, the mean motion model was
adapted to a specific patient q. First the transformation ψq was determined by registration
of Iq,r to I¯r . Then the mean motion model ϕ̄t was mapped to the space of patient q by
ϕ̂q,t = ψq−1 ◦ ϕ̄t ◦ ψq . Finally the amplitude of the respiratory motion was adapted using
a scaling factor λ to the velocity field of ϕ̂q,t , where λ was set to achieve the observed
change in lung air volume (from EE and EI CT images). The mean absolute distance
of manually selected landmarks between EI and EE was 6.8±5.4 mm. Model prediction
reduced this to 3.3±1.6 mm for 13 lungs with intact motion and to 4.0±2.0 mm for 7
lungs with impaired motion (due to large tumors or other diseases). The mean absolute
tumor motion between EI and EE improved from 6.9±6.1 mm to 4.0±2.0 mm by model
prediction.
Klinder et al. [2008, 2009] used breath-hold CT images at EI and EE of 7 lung cancer patients. In their later work (Klinder et al. [2009]), 10 phases from free-breathing
5.2. R EVIEW OF S TATISTICAL M OTION M ODELS
63
4D CT lung images from 36 patients were studied. A surface-based tracking technique
including internal pseudo landmarks was employed for registration and the position of
the diaphragm or the ribcage were chosen as surrogates. A general lung surface mesh
was adapted to all patients and was propagated from inhale to exhale for each patient.
Points inside the general surface mesh were sampled on a Cartesian grid. Thin-platesplines interpolation of the surface node displacements was employed for getting dense
displacement fields and warping the points inside the lung. PCA analysis was performed
on the displacement vectors for all vertices of the general mesh. The displacements came
either from 1 patient over all session (intra-patient model) or from all patients for 1 session (inter-patient model). Adapting the model to a specific patient when knowing a
sparse motion field s̃t was formulated as a maximum likelihood problem with conditional
probability p(P̃t |s̃t ), where P̃t denotes the unknown dense motion field. The data and
covariance matrix were partitioned as follows:
ΣP ΣPs
P̃
Ũ =
,
ΣŨ =
.
(5.4)
ΣsP Σs
s̃
The maximum likelihood estimate is then calculated by P̃i = ΣPs Σs −1 s̃i . When the
dimensions of s is higher than the observations, then Σs is likely to be not invertible.
Therefore some regularization was applied by replacing Σs by Σs + γI, where γ is a
positive, small constant. In their later work (Klinder et al. [2010]), regularization was
achieved by using a reduced set of eigenvectors after PCA on Σs . The mean lung motion
observed by Klinder et al. [2008] was 9.8 mm. This was reduced to 2.8 (3.7) mm for the
intra- (inter-) patient model when knowing the diaphragm and rib-cage position. Using
the 7 best landmarks, as determined by the procedure described by Hug et al. [2000],
led to higher errors (3.0 (4.8) mm). Klinder et al. [2009] achieved a reduction of the
average lung motion between EE and EI from 11.2 mm to 3.4 (4.2) mm for intra- (inter-)
patient prediction based on the diaphragm information. Recently the authors compared
4 definitions for U (2 shape-based, 2 displacement-based) for the intra-patient models
(Klinder et al. [2010]). Displacements were either directly used or parameterized by
the 3 complex Fourier coefficients corresponding to the lowest temporal frequencies. The
results showed that the displacement-vector methods outperform the shape-based methods
and that using the displacement vectors directly gave slightly better results.
Nguyen et al. [2009] analyzed EE and EI breath-hold and free-breathing CT images of
13 patients. A population liver model was built by translating all EE liver segmentations
to the same center of mass (COM) location, combining all binary liver masks by a logical
OR operation and generating a FEM mesh from this combined mask. The model was then
rigidly aligned (based on the masks’ principle directions) and deformed (using the FEM as
proposed by Brock et al. [2005]) to match the surface of a particular EE liver. The model
was further translated and deformed to the shape of the EI liver for the same patient. The
population motion model was then created by computing the mean displacement for each
of its nodes. During therapy, two narrow rectangular bands (called navigator channels
5.2. R EVIEW OF S TATISTICAL M OTION M ODELS
64
N C1 and N C2 ) were manually placed on the SI and AP edge of the EE liver respectively.
Next, the corresponding locations of N Cm for the EI liver were automatically determined
and the 1D shift (∂N Cm ) computed. Subsequently,
h thedisplacement
of agiven
i node
∂ N C1
∂N C2
was calculated by ∂(x0 , y0 , z0 ) = ∆(x0 , y0 , z0 ) ∆N C (1 − k) + ∆N C k , where
1
2
∆(x0 , y0 , z0 ) denotes the displacement of this node predicted by the model, ∆N Cm refers
to the predicted displacement of N Cm and k stands for the distance of the node to the
superior, right and anterior liver edge relative to the liver size. The absolute mean motion
of the liver model was 12.4 mm (SI), 8.4 mm (AP) and 1.2 mm (LR). Prediction resulted
in an absolute mean error of 1.4 mm (SI), 1.3 mm (AP) and 2.1 mm (LR) for the tumor
COM.
He et al. [2010] employed Kernel PCA (K-PCA) proposed by Kim et al. [2005] to construct a population motion model of the lung surface points from 4D CT images of 30
patients. First, the 4D images of each patient were registered to the EE image. Then, a
deformable registration (Xue et al. [2010]) was carried out to transform the EE image of
each patient and the motion vectors to the template space (one selected case). Finally,
K-PCA was applied to the displacement vectors to build the motion model. Ridge regression, using the least squares support vector machine, was employed to predict the motion
of the lung surface points from the surrogate signal (artificial fiducials on the chest/belly
surface from 4D CT). This method is similar to that Liu et al. [2009] (see Sec. 5.2.2) in
terms of using regression after PCA. Unfortunately, the benefit of K-PCA over PCA was
not assessed. The average lung motion over all phases was 4.78 mm. The mean distance
between the predicted and the segmented lung surface was 1.63 mm.
Preiswerk et al. [2011] extended the method of Von Siebenthal et al. [2007b] to include
the full respiratory motion instead of only the drift of the EE position. The PCA model
was based on respiratory cycles from the beginning, middle and end of the acquisition
session. In the prediction phase, they follow the Bayesian approach of Blanz and Vetter [2002]. This is equivalent to the method of Hug et al. [2000] except for relaxing the
assumption that the measured surrogate is accurate, i.e. allowing for noise in the measurements. They minimized a cost function with two terms: C = kŝt − Ês Ŵt k2m + ηkŴt k2m .
The first term consists of the squared Mahalanobis distance between the measurements
(ŝt ) and their corresponding elements in the reconstructed vector (Ês Ŵt ). The second
term is the squared Mahalanobis distance of the reconstruction to the mean model. The
weighting η is used to balance between matching the observations and the prior probability of the model. Using 3 surrogate markers, an average error of 1.2 mm was achieved for
12 subjects for predictions over 12 minutes.
Arnold et al. [2011] combined a patient-specific respiratory motion model and a populationbased drift model (Von Siebenthal et al. [2007b]) to provide spatial and temporal predictions of the liver motion. A database, containing the registered data (3D displacements)
from 7-13 min of 4D MRI observations and their 1D surrogate signal from tracking the
diaphragm position in the images, served as patient-specific model. Prediction was then
5.3. P REDICTING L IVER M OTION U SING E XEMPLAR M ODELS
65
based on finding the most similar surrogate sequence to the current one in the database
and selecting the 3D displacement field associated with the next time step. Incorporation
of the drift model (Von Siebenthal et al. [2007b]) was based on tracking the motion on 2D
MR navigators acquired after every 60 s at EE. The mean error for data from 12 volunteers
and sequences of 75-200 full respiratory breathing cycles for predictions of ≈300 ms into
the future reduced from 4.7 mm to 1.1 mm for the full model and to 1.6 mm without the
drift model.
The reviewed methods are summarized in Table 5.1.
5.3
Predicting Liver Motion Using Exemplar Models
In the previous section we reviewed patient-specific and population-based statistical motion models. The former has the advantage that the model captures the specific motion
patterns of an individual subject. However, any inter-session changes in the organ motion
are difficult to account for in this approach. Moreover, building subject-specific models
could be time consuming and expensive.
Population models are designed to overcome these shortcomings. However, these models
assume a coherent population (e.g. one Gaussian distribution modeled by PCA), which
is unlikely to hold as the variations in the motion patterns of different subjects is usually more complex. He et al. [2010] used kernel PCA with least-square support vector
machines to model the non-linear statistics of respiratory motion. However, they did not
specifically address the issue of population sub-classes. Even though their model is more
powerful than PCA, the tuning of the parameters of the kernel function as well as the
support vector algorithm is a time consuming and cumbersome process and might have to
be repeated for each new dataset.
To address these issues, we propose the use of exemplar models as a non-parametric
method for adapting the population model to an individual subject during therapy, based
on the individual breathing patterns observed via the surrogate. To that end, we have
created submodels by PCA analysis for individual subjects. The final model is a linear
mixture of these exemplar models. Even though the use of most similar samples has
been previously proposed in other fields such as atlas-based segmentations Ramus et al.
[2010], to the best of our knowledge this is the first attempt to build an individualized
breathing model from observations over a population by taking advantage of similarities
in the respiratory motion of different subjects.
5.3.1
Liver Motion Data
We employed intensity-based non-rigid registration (Rueckert et al. [1999]) to quantify
the motion of the liver observed during 4D MRI acquisition. In order to establish inter-
5.3. P REDICTING L IVER M OTION U SING E XEMPLAR M ODELS
66
subject correspondences, a number of anatomically and biomechanically corresponding
points were chosen manually for each subject. By performing a cubic interpolation between these landmarks, the positions of 290 corresponding points in the liver were obtained (Von Siebenthal et al. [2007b]).
In this study we used the position of three of these points as our surrogates and assumed
that they can be tracked during therapy. These surrogates include a point on the diaphragm, the entrance point of the portal vein into the liver, and a point in the center
of the liver defined by vessel features. We also considered the case where the liver motion
of a subject can be observed for 3-5 minutes immediately prior to therapy for creating
a subject-specific respiratory model. We refer to these data, which typically consist of
27-84 respiratory cycles, as the pre-therapy data.
The notations used in this chapter have been already introduced in Sec. 5.2.1. In summary,
the liver position is described by N points, pit , where i = 1...N , and t = 1...T . The liver
position vector pt at time t, is built from concatenating the pit vectors. The motion of the
liver at time t is defined by ∆pt = pt − pref with pref being the reference exhale vector
constructed using the available exhale image(s) during the pre-therapy stage.
The exhale state texh in each cycle is defined as the local minima of the SI component
of the mean motion trajectory of the observed points (i.e. surrogates). Motivated by the
work of Von Siebenthal et al. [2007b], we decompose the generic motion vector ∆pt into
respiratory ∆presp,t and drift ∆pdrif t,t components:
∆pt = ∆presp,t + ∆pdrif t,t = (pt − ptexh ) + (ptexh − pref ) ,
where ptexh is the position of the points at the most recent exhale state. The same decomposition is done for the surrogate signal during therapy, with each component of the
surrogate being used to predict the respective component of the motion vector.
5.3.2
Motion Model Concept
PCA has been successfully employed in the literature for modeling the subject-specific
respiratory motion of abdominal organs (Zhang et al. [2007], Liu et al. [2010a]) and the
underlying reason of its effectiveness for this purpose has theoretically been explained
(Li et al. [2011]). Yet, PCA’s suitability for modeling a population of subjects is not as
well justified. Indeed, variations in anatomy and breathing regimes between individual
subjects are likely to lead to different motion patterns that are not well approximated by a
single Gaussian distribution.
In this work we propose to distinguish between different patterns of breathing motion
within a population. On the one hand, effective clustering of the motion vectors for such
5.3. P REDICTING L IVER M OTION U SING E XEMPLAR M ODELS
67
Figure 5.1: This scheme illustrates the different steps of our proposed exemplar method
for motion prediction during therapy.
high dimensional data is not easily attained. On the other hand, it is reasonable to assume that motion vectors originating from an individual subject acquired during a single
session demonstrate similar breathing patterns. Therefore, instead of finding different
patterns of breathing motion by means of clustering, we turn to a classification method
called instance-based learning (Aha et al. [1991]) , which has been effectively exploited
in computer vision and machine learning (Chum and Zisserman [2007], Belongie et al.
[2002]).
In particular, our method is based on the distance-weighted k-nearest neighbor algorithm
(Dudani [1976]). We have assumed that different examples of breathing patterns exist
in the population and each of them is represented by at least one subject in the dataset.
Hence, we built our exemplar models by fitting a PCA model to the motion vectors of each
individual subject. During therapy, the prediction is realized as a weighted combination of
the predictions of all the exemplar models, where the weights are based on the similarity
of the surrogate and the corresponding model. The different steps of our proposed method
are illustrated in Figure 5.1.
5.3.3
Subject-specific PCA Modeling
Assuming that the 3N dimensional motion vectors ∆pt , t = 1..T , with T being the number of time steps, belong to a 3N dimensional Gaussian distribution ∆pt ∼ N (µ, Σ), our
task is to find the most probable vector ∆p̂t , given a subset of its elements, namely the
surrogate vector st . To create the motion model, the observed vectors ∆pt are decomposed into the surrogate st and the motion vector of the rest of the points which we wish
to predict (rt ), as ∆pTt = sTt , rTt .
68
5.3. P REDICTING L IVER M OTION U SING E XEMPLAR M ODELS
The same decomposition into correspondingcomponentsis done for their mean µT =
T T Σss Σsr
. It is known that if the distriµs , µr , and their covariance matrix Σ =
Σrs Σrr
bution of the ∆pt vectors is Gaussian, then the conditional distribution (∆pt |st ) is also a
Gaussian distribution of the form
(∆pt |st ) ∼ N (µ +
Σss
Σrs
−1
Σss (st − µs ), Σ −
Σss
Σrs
Σss
−1
Σss
) .
Σrs
(5.5)
Therefore, the most probable vector ∆p̂t given st , is the mean of the above conditional
distribution.
As the points on the liver are connected, it is expected that their displacement vectors
display a high correlation. Therefore, to find the principal components of the ∆pt vectors,
Eig
we perform Eigenvalue decomposition on their covariance matrix, Σ = EΛET , where
E is composed of the eigenvectors of Σ, and Λ has the corresponding eigenvalues on its
diagonal. By breaking up
ET = ETs , ETr into two submatrices, each consisting of the rows corresponding to s
and r, we find the most probable vector ∆p̂t given st in terms of eigenvectors as:
−1
∆p̂t = µ + EΛETs (Es ΛETs ) (st − µs ) .
(5.6)
This derivation is equivalent to Equ. 5.3.
5.3.4
Population PCA Modeling
Given a dataset with J subjects, where each subject j = 1..J, has Tj observations of
the same N points, a PCA population model is built similar to Sec. 5.3.3, by using the
observations from all included subjects j. Index t then denotes the observation index and
P
ranges from 1 to j Tj . The rest of the algorithm is the same as the subject-specific
algorithm.
5.3.5
Exemplars Modeling
To create a population model using exemplars, we build a PCA model M j from each
subject j as described in Sec. 5.3.3. To predict ∆pt , for a new subject, given st at time
step t, we obtain the motion vector predictions ∆p̂jt of all M j models through equation
5.6. To combine these predictions in a distance-weighted k-nearest-neighbor approach
(Dudani [1976]), we have to estimate the dissimilarity of each of the exemplar models to
69
5.3. P REDICTING L IVER M OTION U SING E XEMPLAR M ODELS
the current observation. We base this dissimilarity on the squared Mahalanobis distance
between the surrogate st and the corresponding components of an individual model M j :
−1
d(st , M j ) = (st − µjs )T (Σjss ) (st − µjs ) .
(5.7)
Consequently, the exemplar weight, wtj , which provides the contribution of the prediction
of model M j at time t to the final prediction, is computed from the inverse of the above
distance:
1/(d(st , M j ) + η)
wtj = PJ
,
k
k=1 1/(d(st , M ) + η)
(5.8)
where η is a small positive number introduced to avoid numerical instability. Finally, the
motion vector, ∆p̂t , is formed from a weighted sum of the ∆p̂jt vectors:
∆p̂t =
J
X
wtj ∆p̂jt .
(5.9)
j=1
5.3.6
Experiments and Results
The prediction error of the model at each point pit was defined by the Euclidean distance
between the predicted motion (∆p̂it ) and the motion obtained from the non-rigid registration result (∆pit ), ie. Eti = k∆p̂it − ∆pit k. For each subject j, the error distribution was
summarized by its mean mEj , standard deviation sEj and maximum xEj . Moreover,
their corresponding mean value over all subjects j are denoted by mE, sE and xE. e.g.
1
mEj = /Tj N
Tj N
X
X
t=1 i=1
Eti
1
mE = /J
J
X
mEj .
(5.10)
j=1
The number of points in the liver of each subject was 290 and the number of time steps Tj
varied between 3300 and 6700. The prediction accuracy of the population models were
evaluated based on leave-one-out experiments. We used 3 of the points as our surrogates
and predicted the positions of the remaining N = 287 points in the livers. No temporal
prediction was performed.
Statistical significance at the α=0.001 level of the difference in the mean of mEj over all
subjects of two methods was tested by bootstrapping (Efron and Tibshirani [1993]). For
this, prediction results were resampled with replacement 5000 times and the difference in
the mean error was calculated. The probability of equal results was based on the fraction
of differences which were zero or negative.
5.3. P REDICTING L IVER M OTION U SING E XEMPLAR M ODELS
70
In this study, we performed two sets of experiments to evaluate two aspects of our proposed method, namely its prediction accuracy and its learning capability. In the following
we will explain each set of experiments in more details.
Prediction Accuracy Experiments
To fully investigate the contribution of individual steps of our framework to the prediction
accuracy, we conducted 7 experiments, with different combinations of the type of motion vectors {drift, respiration and generic = drift + respiration} and the type of motion
model {exemplar models, subject-specific PCA and population PCA}. PCA and exemplar models of drift and respiratory motion were built by replacing ∆pt with ∆pdrif t,t and
∆presp,t vectors, respectively, in the calculations of Sec. 5.3.3 and 5.3.5. Subject-specific
PCA models were based on the pre-therapy data from the same subject. Since no substantial drift could be observed during the pre-therapy stage, no subject-specific drift motion
models were created.
Learning Capacity Experiments
To test the ability of our proposed method to fully utilize the information provided by an
increasing number of samples used for model building, we performed the following experiment. After excluding the subject to be tested, we randomly picked n ∈ {1, 2 . . . 11}
subjects from the population, and built a PCA and an exemplar drift model. Next, we
used these models to predict the drift of the left-out subject. The same procedure was
carried out for all the subjects and the mean error over all of them, εn , was computed.
We repeated this experiment 7 times for each number n and computed the mean and the
standard deviation of εn over all 7 repetitions.
Results
Table 5.2 lists the statistics of the motion magnitude for the individual subjects. The
results of the prediction accuracy experiments, using the generic motion models and the
experiments using the separated motion models are summarized in Tables 5.3 and 5.4,
respectively. These results suggest that,
• Exemplar models outperform the PCA models in all of the experiments (G3 vs G2,
S2 vs S1, and S4 vs S3).
• Separation of drift and respiratory motion lowers the error only when the respiratory
component is modeled by a subject-specific model (S3 and S4 have lower errors
than G2 and G3, but S1 and S2 have higher errors than G2 and G3 respectively).
5.3. P REDICTING L IVER M OTION U SING E XEMPLAR M ODELS
71
• The best results are achieved by modeling the drift component using exemplar models and the respiratory component by a subject-specific model (S4).
• The use of exemplar models improves the lowest error achieved by PCA model by
10% (compare experiments S3 and S4).
Figure 5.2 shows a comparison of the drift prediction in experiments S3 and S4 for the
individual subjects. It can be observed that the exemplar method provided a lower mean
and maximum error than the PCA method for each subjects. The difference in mean
prediction error of S4 and S3 was also statistically significant (p < 0.001). No other
significance tests were performed.
The results of the learning capacity experiments are depicted in Figure 5.3. The PCA
model shows no substantial improvement when incorporating more than 5 subjects. In
contrast, the exemplar model continues to improve as the number of considered subjects
increases.
5.3.7
Discussion and Conclusion
Discussion
Using Kullback-Leibler(KL) divergence as a distance measure between distributions, we
observed that subjects 12 and 7 have the largest and the smallest sum of distances from the
other subjects in the population. Also, the highest and lowest amounts of improvement
using exemplar models are associated with subjects 12 and 7 respectively. This can be
due to the fact that by fitting one PCA model to a population, the model captures the
average motion pattern, performing poorly on uncommon subjects. The exemplar model
is, however, more robust towards such outliers in motion patterns.
The most important advantage of exemplar models is their learning capacity. The trend
seen in Figure 5.3 suggests that exemplar models are more capable of using complementary information from a new subject and incorporating it into their models.
Furthermore, the exemplar method is incremental in the sense that adding new subjects
to the model can be performed without re-calculating already considered cases. This attribute reduces the computational time and, together with the improved learning capacity
of the approach, allows for step-by-step incorporation of cases where insufficient prediction is observed.
Conclusion
In this study, we addressed the problem of modeling and predicting two independent types
of liver motion namely respiratory and drift motion in the presence of different breathing
5.4. J OINT M ODELING OF THE R ESPIRATORY M OTION OF L IVER AND R IBS
(a)
72
(b)
Figure 5.2: Comparison of the performance of PCA and exemplar drift population models, showing (a) the mean and (b) the maximum error in predicting the drift of each point
in the liver of the left-out subjects.
patterns among subjects. We proposed a method to generate an adaptable population
model based on 4D motion fields obtained from 4DMR images of 12 subjects.
Exemplar models were built for classes of the population represented by the individual
subjects. Using a linear combination of the prediction of these exemplar models, the
respiratory motion of a new subject was predicted, such that the most similar exemplar
models have the highest influence.
We have explored different modeling methods for respiration and drift motion using PCA
and exemplar models and concluded that a subject-specific PCA respiratory motion model
based on pre-therapy data, combined with an exemplar population model for the drift
achieve the lowest mean error. Finally, it was shown that the exemplar models have a
higher learning capacity.
5.4
Joint Modeling of the Respiratory Motion of Liver
and Ribs
The extraction of the respiratory motion of the ribs has been described in Chapter 4. The
next step is to study the relationship between the motion of the ribs and the liver during
respiration. Initially, we computed the correlation between the mean motion magnitude of
the surrogate liver points introduced in Sec. 5.3.1, and the motion magnitude of the most
anterior point of each rib for the 8 subjects studied in Chapter 4, (see Table 5.5). Motivated
by the high correlation between points in the liver and ribs, we created a subject-specific
and a population liver-rib motion model, which will be explained in the next section.
5.4. J OINT M ODELING OF THE R ESPIRATORY M OTION OF L IVER AND R IBS
73
Figure 5.3: Mean error of drift prediction over all subjects as a function of the size of the
population using PCA and exemplar population models. The error bars show the standard
deviation of the mean error from the 7 repetitions.
5.4.1
Ribs and Liver Motion Model
Subject-Specific Ribs-Liver Respiratory Motion Model
To find the relationship between the respiratory motion of the ribs and the liver, we created
a combined PCA model from the motion vector of the liver points, and the motion vector
of the rib points as described in Sec. 5.3.3. For each patient, we created a patient-specific
model from the data of the first 20 breathing cycles (which roughly amount to 1 minute of
free breathing). We used this model and the 3 liver surrogates to predict the motion of the
rib points for the remaining cycles (80 cycles). The results of the prediction in terms of
the DistanceError (described in Sec. 3.7.1) are presented in Table 5.6, which correspond
to the 3D motions summarized in Table 4.8. It can be observed that the patient-specific
models are able to compensate for 60% of the respiratory motion on average.
Population Model of Ribs-Liver Respiratory Motion
To create a population model, we had to bring the data of different subjects into correspondence. Note that the points’ positions on the ribs were already in correspondence due
to the way the ground truth centerlines were created (see Sec. 3.5.1). However, to build a
population model, we needed to also find corresponding motion directions. While Euler
angles provide a general parametrisation of the corresponding rotational degrees of freedom, they are not suitable for population models, because differences in the first two Euler
rotations render the subsequent Euler rotations incomparable (for example, different first
Euler rotations geometrically correspond to different axes of rotation for the second and
5.4. J OINT M ODELING OF THE R ESPIRATORY M OTION OF L IVER AND R IBS
74
third Euler rotations). However, while we allowed for three Euler rotations per rib during
registration, only two rotations are reported in literature (bucket and pump handle), which
indicates the existence of a preferred axis (Wilson et al. [1987]). A closer study of the
anatomy suggests that the ribs are actually much more constrained and the hypothesis is
that the main motion is only a rotation around the axis from the head to the articular part
of the tubercle (see Figs. 4.2a and 4.2b). If the hypothesis is true, this would be the most
suitable axis for defining inter-patient respiratory motion. Hence, we first investigated if
this observation holds by extracting the main rotation axis and analyzing how well this
axis describes the extracted rib motion. Note that, unfortunately, the image resolution and
visibility of ribs in MRI do not allow for defining this axis purely from a single image, as
the anatomical landmarks are hard to determine. Therefore, this axis was computed for
each rib from the rotation matrices of all registration results (1200 rotation matrices on
average), as follows. If we denote each of the rotations by Rt , and their axis of rotation
by ν, we have: ∀t = 1, . . . , T :
Rt ν = ν
(Rt − I)ν = 0,
(5.11)
where I is the 3 × 3 identity matrix. In the absence of noise, under the hypothesis, solving
the above equation for each of the rotations Rt of a specific rib, would result in the same
ν. However, in practice one needs to find a ν that minimizes kRt − Ik for all t. To that
end, we stacked the Rt − I matrices to form a 3T × 3 matrix and performed singular
value decomposition on this matrix. The main axis of rotation ν was obtained as the right
singular vector corresponding to the least singular value. Together with the other right
singular vectors, it forms a frame which we will refer to as the “natural rotation frame”.
Next, all rotation matrices Rt of a rib were decomposed according to these extracted
singular vectors. That is, the Euler angles of the rotation in the natural rotation frame
were computed and it was observed that the first angle, in contrast to the other two angles,
had a high correlation with the mean of the motion magnitudes of the liver surrogates (see
Table 5.7). Therefore, we constructed a PCA rib-liver model similar to Sec. 5.3.3 from
concatenation of the motion vectors of the 3 liver surrogates and the angle of rotation
around ν for all time points t and included subjects. To validate the performance of
this linear model, we performed leave-one-out experiments where a rib-liver model was
created based on 7 subjects, and the rotation angle around ν was predicted for the leftout-subject based on its liver surrogate vector. The rotation matrices were reconstructed
based on the predicted rotation angle and the computed rotation axis ν. Finally, these
rotation matrices were applied to the rib centerlines of the reference EE image and the
DistanceError to the registration result was computed for all the points on the ribs (see
Table 5.8). Comparing these results to the 3D motion of the rib points (Table 4.8), it can
be observed that the population model is able to compensate 40% of the total motion on
average. This is 20% less than the patient-specific model, and requires the identification
5.4. J OINT M ODELING OF THE R ESPIRATORY M OTION OF L IVER AND R IBS
75
of the axis of rotation. However, this model has the advantage that it could be built without
the need for the patient’s own motion data if the axis of rotation can be identified purely
based on the anatomy.
5.4.2
Conclusion and Discussion
In this section, we analysed the respiratory motion of the ribs during free-breathing. We
showed that there is, as expected, a high correlation between the motion of ribs and
the liver during respiration. We built subject-specific and population-based PCA models which could predict the motion of the ribs using liver surrogate signals with a mean
accuracy of 0.4 mm and 0.6 mm, respectively. Even though the average motion of all rib
points over the entire time series is 1.02 mm, over deep inhalations this number increases
to respectively, 2.71 mm and 5.85 mm for all points and for the anterior points, which
have the largest movement (95%). Therefore, predicting the rib motion is necessary during free breathing, even though the need for compensating it might arise only during deep
inhalations.
Recalling the anatomy of ribs from Sec. 4.2, we know that the motion of ribs consists
of a centered rotation around a fixed point (head of ribs). Moreover, for ribs 7 to 9, the
axis of these rotations remains fixed during the entire respiration, since these ribs are
connected to the vertebrae at two points. Even though, two rotations, called pump handle
and bucket handle, have been employed for describing the respiratory motion of ribs in
the literature (Wilson et al. [1987]), these two are in fact referring to the decomposition
of the rotation around a main axis, into two rotations around two axes of the rib’s native
coordinate system.
We extracted this main axis through analysing the matrices of rotations over 100 breathing cycles. However, according to the literature on rib anatomy, this main axis should
also be identifiable without motion data as the axis that connects the head of the rib to its
articular tubercle (see Sec. 4.2 and Fig. 4.2). We believe that finding this axis automatically from the extracted rib centerlines is possible but needs further investigations. One
approach would be to identify the axis of rotation on the mean shape model described in
Sec. 3.4.5. By fitting the shape model to the ground truth, the axis of rotation would then
automatically be identifiable on the fitted rib model. That would enable our population
rib-liver model to predict the motion of the ribs of a new subject from a single 3DMR
image and surrogate liver signals without the need for acquiring 4DMRI training data.
Moreover, we showed that if a short sequence of 4DMR images of the patient could be
acquired, more accurate patient-specific models could be created, which can compensate
for 60% of the ribs’ motion.
lung
liver
lung
liver
liver
Klinder et al. [2009]
Nguyen et al. [2009]
He et al. [2010]
Preiswerk et al. [2011]
Arnold et al. [2011]
K-PCA
mean
motion
EE/EI
bh/fb
CT
4DCT
AP &
SI
navigator
fiducials
from 4DCT
3 points
diaphragm
2D MRI
1 point
3 points
lung
volume
diaphragm
diaphragm
s(t) &
s(t-3)
lung
surface
2D MRI
Surrogate3
12.4
8.4
1.2
4.8
6.8
4.8
11.2
4.3
2.1
4.5
7.1
Mean Motion
(mm)
1.5
1.1
3.5
2.8
3.4
4.2
1.4
1.3
2.1
1.6
1.1±0.6
1.8±1.0
1.6±1.3
1.5
2.0
2.7
Mean Error
(mm)
EE/EI
4 phases
interF
interS
SI
AP
LR
drift
SD
LR interF
AP interF
SI interF
Comment4
PCA
fb 4DMRI
1.2
20 min
patient-specific
fb 4DMRI
4.7
1.1
75-200
+ drift PCA
cycles
PCA: Principle Component Analysis, K-PCA: Kernel PCA
CT: Computer Tomography, MRI: Magnetic Resonance Imaging, RPM: Varian Real-time Position Management
EE: End-Exhalation, EI: End-Inhalation, fb: free-breathing, bh: breathhold
AP: Anterior-Posterior, SI: Superior-Inferior, LR: Left-Right
toM: tested against Model, intra: intra-patient model, interF: inter-Fraction model, SD: Surface Distance, interS: inter-Subject model
12
12
30
13
4DCT
fb
4DMRI
4DCT
4DCT
(RPM)
fb 4DMRI
4DCT
(RPM)
Image2
Type
Table 5.1: Summary of 4D respiratory motion models listing the modeled organ, the number of evaluated subjects (#S), the model
type, the image type to create the model, the surrogate measure, the mean motion and the mean prediction error.
4
3
2
2
1
10
lung
Ehrhardt et al. [2011]
36
PCA
12
mean
motion
PCA
PCA
PCA
PCA
2
5
10
4
Patient-specific statistical models
Zhang et al. [2007]
lung
Model1
Type
Liu et al. [2009]
lung
Liu et al. [2010b]
King et al. [2012]
lung
Population-based statistical models
Von Siebenthal et al. [2007b]
liver
#S
Organ
Reference
5.4. J OINT M ODELING OF THE R ESPIRATORY M OTION OF L IVER AND R IBS
76
5.4. J OINT M ODELING OF THE R ESPIRATORY M OTION OF L IVER AND R IBS
# Amplitude of motion
mean ± std (max)
1 5.76 ± 3.47 (20.93)
2 3.10 ± 1.73 (17.26)
3 3.13 ± 1.65 (11.51)
4 3.25 ± 2.09 (16.68)
# Amplitude of motion
mean ± std (max)
5 3.40 ± 2.05 (19.49)
6 5.96 ± 3.42 (19.71)
7 2.76 ± 1.71 (11.21)
8 3.99 ± 2.28 (18.40)
77
# Amplitude of motion
mean ± std (max)
9 3.91 ± 2.09 (14.29)
10 7.28 ± 3.61 (21.15)
11 3.58 ± 2.13 (16.75)
12 4.37 ± 2.42 (18.02)
Table 5.2: Statistics of the motion amplitude of the liver points (k∆pit k) for all subjects
in mm. The average value of mean, standard deviation (std) and maximum (max) over all
subjects was 4.21 mm, 2.39 mm and 17.12 mm, respectively.
Generic Motion Models
G1
G2
G3
Subject-Specific Model
PCA Population Model
Exemplar Population Model
Mean (in mm) over
all subjects j of
mEj sEj xEj
1.18 0.99 8.45
1.08 0.82 8.12
1.02 0.70 8.07
Table 5.3: Performance of the models without separating drift and respiratory motions in
leave-one-out tests.
Separated Motion Models
S1
S2
S3
S4
Drift Model
PCA Population
Exemplar Population
PCA Population
Exemplar Population
Respiration Model
PCA Population
Exemplar Population
Subject-Specific
Subject-Specific
Mean (in mm) over
all subjects j of
mEj sEj xEj
1.16 0.84 9.02
1.05 0.79 8.26
0.97 0.77 8.65
0.87 0.67 7.99
Table 5.4: Performance of separated drift and respiratory models in leave-one-out tests.
Subjects
1
2
3
4
5
6
7
8
Correlation of Respiratory
Motion in Liver and Ribs
in Individual Subjects
Rib 7 Rib 8 Rib 9 Rib 10
0.96 0.96 0.98
0.93
0.92 0.91 0.91
0.95
0.85 0.94 0.97
0.95
0.95 0.95 0.96
0.92
0.94 0.89 0.94
0.93
0.96 0.92 0.94
0.97
0.95 0.91 0.89
0.88
0.92 0.97 0.97
0.94
Table 5.5: Correlation coefficient between the respiratory motion magnitude of the most
anterior point of ribs 7 to 10, and the mean motion magnitude of the surrogate liver points.
5.4. J OINT M ODELING OF THE R ESPIRATORY M OTION OF L IVER AND R IBS
Sbj
1
2
3
4
5
6
7
8
mean
1
2
3
4
5
6
7
8
mean
78
Patient-Specific Model Prediction Error
mean ± std (95%) mm
Rib 7
Rib 8
0.69 ± 0.49 (1.68) 0.49 ± 0.45 (1.68)
0.30 ± 0.21 (0.66) 0.27 ± 0.22 (0.69)
0.24 ± 0.20 (0.61) 0.29 ± 0.23 (0.76)
0.46 ± 0.40 (1.26) 0.39 ± 0.39 (1.08)
0.90 ± 1.39 (2.97) 0.29 ± 0.24 (0.81)
0.59 ± 0.47 (1.47) 0.62 ± 0.51 (1.63)
0.52 ± 0.44 (1.42) 0.22 ± 0.21 (0.66)
0.25 ± 0.20 (0.62) 0.17 ± 0.14 (0.43)
0.57 ± 0.74 (1.64) 0.35 ± 0.36 (1.06)
Rib 9
Rib 10
0.36 ± 0.30 (1.06) 0.50 ± 0.26 (0.98)
0.16 ± 0.15 (0.41) 0.22 ± 0.23 (0.66)
0.40 ± 0.30 (0.95) 0.37 ± 0.32 (0.88)
0.35 ± 0.31 (0.90) 0.24 ± 0.20 (0.58)
0.22 ± 0.18 (0.57) 0.19 ± 0.16 (0.51)
0.67 ± 0.52 (1.70) 0.53 ± 0.39 (1.33)
0.26 ± 0.24 (0.76) 0.37 ± 0.34 (1.10)
0.17 ± 0.13 (0.43) 0.29 ± 0.17 (0.61)
0.30 ± 0.31 (0.93) 0.34 ± 0.29 (0.89)
Table 5.6: Prediction results of ribs’ respiratory motion during free breathing using a
patient-specific model from the first 20 cycles tested on the remaining 80 cycles. The
DistanceError statistics over all four ribs is 0.42 ± 0.57 (1.23) mm.
Angle
1
2
3
Correlation of Respiratory
Motion in Liver and Ribs
over the Population
Rib 7 Rib 8 Rib 9 Rib 10
0.80 0.86 0.82
0.81
-0.01 -0.05 -0.15
0.10
-0.07 -0.07 -0.25
-0.19
Table 5.7: Correlation coefficient between the 3 Euler angles of respiratory motion around
the axes of the natural rotation frame for ribs 7 to 10, and the mean motion magnitude of
the surrogate liver points.
5.4. J OINT M ODELING OF THE R ESPIRATORY M OTION OF L IVER AND R IBS
Sbj
1
3
4
5
6
7
8
mean
1
3
4
5
6
7
8
mean
79
Population Model Prediction Error
mean ± std (95%)
Rib 7
Rib 8
0.93 ± 0.78 (2.38) 0.65 ± 0.48 (1.58)
0.39 ± 0.35 (1.09) 0.43 ± 0.28 (0.97)
0.46 ± 0.43 (1.15) 0.43 ± 0.40 (1.09)
1.56 ± 2.09 (3.50) 0.73 ± 0.48 (1.54)
1.86 ± 1.57 (5.27) 0.98 ± 0.75 (2.45)
0.77 ± 0.55 (1.92) 0.36 ± 0.32 (0.94)
0.32 ± 0.29 (0.84) 0.31 ± 0.28 (0.88)
0.77 ± 0.88 (2.38) 0.56 ± 0.49 (1.49)
Rib 9
Rib 10
0.69 ± 0.48 (1.56) 0.59 ± 0.42 (1.40)
0.44 ± 0.31 (1.06) 0.42 ± 0.35 (1.15)
0.63 ± 0.51 (1.61) 0.66 ± 0.55 (1.69)
0.46 ± 0.37 (1.14) 0.67 ± 0.45 (1.40)
0.91 ± 0.76 (2.45) 1.07 ± 0.79 (2.63)
0.33 ± 0.30 (0.93) 0.48 ± 0.41 (1.30)
0.35 ± 0.39 (1.21) 0.45 ± 0.42 (1.37)
0.55 ± 0.49 (1.46) 0.61 ± 0.51 (1.56)
Table 5.8: Prediction results of ribs’ respiratory motion during free breathing using a
population model and a predetermined axis of rotation. The DistanceError statistics over
all four ribs is 0.62 ± 0.63 (1.71) mm.
6
Summary and Outlook
In this thesis we proposed methods to improve the applicability of MRgHIFU to the treatment of liver tumors. Most of the results also seem suitable to be utilized in other scenarios. We have evaluated and discussed the individual methods at the end of each chapter.
Here, we summarize the conclusions and give an outlook on possible future research in
these areas.
In Chapter 2, we discussed the respiratory motion and its effects on different extracorporeal therapies. We also reviewed the techniques which have been proposed to mitigate
the respiratory motion effects. The most relevant methods include breath-hold, gating
and motion compensation through tracking. Breath-hold and gating methods have generally short (≈ 30%) duty cycles, which can lead to lengthy treatment sessions. In HIFU,
the pauses between sonications might prevent heat accumulation and hinder an effective
therapy. Motion tracking methods are the ideal form of respiratory motion management,
allowing free breathing for patients and continuous sonications. However, they require
accurate information about the position of the target organ as well as of the organs in the
beam path. This can be achieved non-invasively through the use of real-time surrogate
signals and a motion model which can predict the motion of the organs of interest from
the surrogate signals based on prior information.
In Chapter 3, we introduced a model-based method which made detecting ribs in MR
images possible, in spite of poor visibility and low signal to noise ratio. The proposed
method achieved an average Euclidean error of 2.49 mm in 3D and an average clinically
relevant error of 1.20 mm. The latter corresponds to the error along the normal of the
rib’s plane and is important because it defines the safe acoustic window for the HIFU
transducer. We argued in Sec. 3.8 that these results are clinically suitable. Even though
our method was built for the 4 right ribs which enclose the liver, it can straightforwardly
be extended to the entire ribcage. Also, we expect automated detection of ribs in MR
images to have applications apart from MRgHIFU. For example, routine screening of patients with bone cancer, such as multiple myeloma, can be achieved with MR imaging,
which does not have the side effects of CT. Automatic detection of ribs can help create
unfolded rib cage visualizations, which facilitate diagnosis (as done in CT, for example by
81
Ramakrishnan and Alvino [2011]). Currently our rib detection method requires manual
input for positioning the ribs. This step could be done automatically, by incorporating the
distance between the ribs into the ribcage model. Vertebral disks, which have been identified in MR images successfully, can also be used to guide the automatic rib detection.
Our initial experiments in this regard have been promising, but the results were not yet as
accurate as when utilizing manual landmarks. One can also go in the opposite direction
and allow more user interaction. For example, in a clinical scenario where more accuracy
is required, an interactive system could be built where the rib detection results could be
refined based on multiple points placed on arbitrary regions in the ribs. The cost term
could be altered to include a term for penalizing the distance between these input points
and the detected rib centerlines. Another area where our rib detection method could be
improved is the optimization strategy. Stochastic methods have proven to be very powerful for problems which do not have a smooth gradient, an example of which was shown
in Chapter 4. Utilizing such approaches for finding the optimal ribcage parameters would
make the current method faster and more efficient.
In Chapter 4 we proposed a ribcage specific registration method. Our method was able to
extract the respiratory motion of the ribs in the presence of noise, partial volume effects
and motion artefacts in 4DMR images with a mean accuracy of 1.06 mm. Our transformation consisted of 6 parameters, 3 rotation angles, and 3 coordinates of the center
of rotation. We optimized these 6 parameters individually for each image. However, it
is evident that the center of rotation should remain the same over the whole image sequence, after having accounted for patient motion. Therefore, one way to improve the
current method would be to optimize the center of rotation jointly for consecutive images.
The proposed registration, in conjunction with the devised detection method, enables the
analysis of rib motion patterns during free breathing as captured on long MR sequences,
which was previously not possible.
In Chapter 5, we reviewed statistical motion models and described the two current approaches, namely subject-specific and population-based methods. The subject-specific
methods are able to extract the specific motion patterns of an individual. However, they
are time-consuming and expensive to build. Population models are created based on a
large number of subjects and aim to model their common motion patterns. The challenge in creating these models is to find a suitable correspondence between the subjects.
Moreover, by assuming a coherent population, variations across different individuals are
neglected. We proposed an exemplar model, which is a non-parametric method and has
the ability to adapt the population model to an individual subject during therapy, based
on the individual breathing patterns observed via the surrogate. This adaptation provided
higher learning capabilities and improved prediction performances by 10%.
Finally, we created patient-specific and population models for predicting the motion of the
ribs using the same liver surrogates. The patient-specific and population model were able
to compensate for 60% and 40% of the motion of the ribs, respectively. We also showed
that a rotation around the main axis can approximate the respiratory motion of the ribs.
82
We extracted this axis by analysing the rotation matrices obtained through registration.
The literature suggests that this axis should be identifiable from the anatomy of the ribs.
Yet, performing this automatically requires further investigations.
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List of Publications
Journal Publications
1. Christine Tanner, Dirk Boye, Golnoosh Samei, and Gabor Szekely, “Review on 4d
models for organ motion compensation,” Critical Reviews in Biomedical Engineering, vol. 40, no. 2, 2012.
Refereed Conference Proceedings
1. Golnoosh Samei, Christine Tanner, and Gabor Székely, “Predicting liver motion
using exemplar models,” in Abdominal Imaging. Computational and Clinical Applications, pp. 147–157. Springer Berlin Heidelberg, 2012.
2. Golnoosh Samei, Christine Tanner, and Gábor Székely, “Advantage of a patientspecific respiratory motion model for the liver,” .
3. Golnoosh Samei, Grzegorz Chlebus, Gabor Székely, and Christine Tanner, “Adaptive confidence regions of motion predictions from population exemplar models,”
in Abdominal Imaging. Computation and Clinical Applications, pp. 231–240.
Springer Berlin Heidelberg, 2013.
4. Dirk Boye, Golnoosh Samei, Johannes Schmidt, Gabor Székely, and Christine Tanner, “Population based modeling of respiratory lung motion and prediction from
partial information,” in SPIE Medical Imaging. International Society for Optics
and Photonics, 2013, pp. 86690U–86690U.
5. Golnoosh Samei, Christine Tanner, and Gábor Székely, “Rib detection in MR images using shape priors and appearance models,” in Biomedical Imaging (ISBI),
2014 IEEE 10th International Symposium on.
6. Golnoosh Samei, Christine Tanner, and Gabor Székely, “Detection and registration
of ribs in MRI using geometric and appearance models,” in MICCAI 2014.
Curriculum Vitae
Personal Data
Name
Golnoosh Samei
Date of birth 19th December 1985
Place of birth Tehran, Iran
Citizenship
Iranian
Education
2011 – 2014 ETH Zurich, Computer Vision Laboratory, Switzerland
Doctoral studies
2008 – 2011 ETH Zurich, Switzerland
Studies of Electrical Engineering and Information
Technology
Graduation with the degree M. Sc.
2003 – 2008 Sharif University of Technology, Tehran, Iran
Graduation with the degree B. Sc.
Work Experience
2011 – 2014 ETH Zurich, Computer Vision Laboratory, Switzerland
Teaching and research assistant
2011 – 2011 Disney Research Lab, Zurich, Switzerland
Internship
2008 – 2011 ETH Zurich, Computer Vision and Geometry Laboratory
Switzerland
Research assistant, and master thesis
2007 – 2007 KTH Stockholm, CVAP Laboratory, Sweden
Internship

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