MODELLING DIAPHRAGM KINEMATICS FOR 3D
SIMULATION LIVER ACCESS
Bello F, Villard P-F and MD Reyes
Dept. of Biosurgery and Surgical Technology
Imperial College London
10th Floor QEQM, St Mary's Hospital
Praed Street, London W2 1NY, UK
i.
PROJECT AIM
Understanding the behaviour of the diaphragm muscle in order to develop a model
that simulates with accuracy its movement and the role that it plays on liver
displacement.
ii.
METHODS
Research on previous work about diaphragm physiology was focused on its
anatomical, histological and mechanical components. The data obtained was analysed
and compared to determine viability and validity for its use. Based primarily on the
work presented in [2-4] we obtained the main physiological components involved in
displacement of the diaphragm and studied how each one of them determines the
excursion and the vectors towards which the diaphragm will move. Once all the data
was obtained and analysed, we organized it in order to apply it to the previously
generated model shown in Fig 1.1.1 by the non-rigid registration technique. Non-rigid
registration is a process for determining the correspondence of features between
images collected at different times or using different imaging modalities. The
correspondences can be used to change the appearance, by rotating, translating,
stretching etc., of one image so it more closely resembles another so the pair can be
directly compared, combined or analyzed as is further explained in [8].
Fig. 1.1.1 Results of displacement obtained by non-rigid registration of a set of 2 CT
Scans in 2 different stages of the breathing cycle.
Fig. 1.1.2 Model of a Diaphragm obtained by non-rigid registration of the same CT
scans in figure 1.1.1
Before discussing how the vectors and displacement measures of the diaphragm
were defined, we will make a brief review of respiratory kinematics focusing in the
anatomy of the diaphragm and the role it plays in lung volume capacities and intraabdominal content distribution.
RESPIRATORY KINEMATICS
The diaphragm is the primary muscle of respiration. It is a narrow, dome-shaped
sheet of muscle that, in mechanics, would be called a membrane because of its
properties of flexure after an external load is applied. When this membrane contracts,
as it happens in the inhaling process, it pushes downward and spreads out, increasing
the vertical dimension of the chest cavity and driving up abdominal pressure. This
increase in pressure drives the abdominal contents (i.e. the liver) down and out,
which, as a consequence, increases the transverse diameter of the chest cavity.
Contraction, when used referring to the muscular system, implies the generation of
tension by muscle fibers commanded by motor neurons. The product of muscle
thickness and stress paralleling the fiber bundles gives the tension in the diaphragm
and the contraction, as a product of this tension, would follow the trajectory from its
fiber’s origin to its insertions.
The muscular fibers may be grouped according to their origins and insertions into
three parts; sternal, costal, and vertebral. The sternal part arises by two fleshy slips
from the back of the xiphoid process; the costal part from the inner surfaces of the
cartilages and adjacent portions of the lower six ribs on each side; and the vertebral
part from the aponeurosic arches, named the arcuate ligaments (lumbocostal arches),
and from the lumbar vertebrae by two pillars or crura (Fig.1.2) [6].
Fig. 1.2 In this figure, in an axial view from below the muscle fibers inserting into a
Central Tendon can be observed. The crura attached to the lumbar vertebrae.
The diaphragm muscle attaches in the chest wall (CW) and the fibers radiate
inwards inserting into a Central Tendon (CT). The zone of apposition is that part of
the diaphragm that is apposed an inner aspect of the rib cage. The pericardium is
attached to the CT on its upper surface; the circumferential part is muscular. During
inspiration, the lowest ribs are fixed; and from these and the crura the muscular fibers
contract and draw downwards and forwards the central tendon with the attached
pericardium. In this movement the, curvature of the diaphragm is scarcely altered, the
dome moving downwards nearly parallel to its original position and pushing before it
the abdominal viscera. The descent of the abdominal viscera is permitted by the
extensibility of the abdominal wall, but the limit of this is soon reached. The central
tendon, applied to the abdominal viscera, then becomes a fixed point for the action of
the Diaphragm, the effect of which is to elevate the lower ribs and through them to
push forwards the body of the sternum and the upper ribs. The right cupola of the
diaphragm, lying on the liver, has a greater resistance to overcome than the left, which
lies over the stomach, but to compensate for this, the right crus and the fibers of the
right side generally are stronger than those on the left.
During quiet expiration, the diaphragm passively relaxes and returns to its
equilibrium position moving around a centimeter or two up and down, average of 1.5
and 1.7 standing and supine respectively [7]. During exercise, it can move more than 10
cm
Once the anatomy is understood, we’ll discuss lung volumes and their influence on
diaphragm displacement in order to understand how certain measures were assigned and
calculated.
Lung Volumes
The total air content in the lung can be classified as volumes and these can be
further divided into capacities as can be observed in Fig. 1.3. The basic lung volumes are
Tidal Volume (TV), which is the gas inspired or expired with each breath in quiet
breathing. The Inspiratory Reserve Volume (IRV) is the additional air that can be
inspired from the end of a normal Inspiration. The Expiratory Reserve Volume (ERV) is
the additional air that can be expired from the end of a normal expiration and the
Residual Volume (RV) is the air remaining after maximal expiration. Lung can be
deducted from these. For example, Total Lung Capacity (TLC) is the sum of RV + IRV
+ ERV + RV.
Vital capacity (VC) is the sum of inspiratory reserve volume plus tidal volume plus
expiratory reserve volume (VC= IRV+TV +ERV), the Functional Residual Capacity
(FRC) is the air remaining in the lung at the end of a normal expiration FRC= RV +
ERV. And finally, Inspiratory Capacity (IC) is the maximum volume of air that can be
inspired from an expiratory position (TV + IRV), this capacity is of less clinical
significance than the others but, for the aim of this project, it is important to understand
how the excursion at some points of the breathing cycle was claculated.
Fig. 1.3 Illustration of lung volumes and capacities [9].
MECHANICAL IMPLICATIONS FOR THE DETERMINATION OF
VECTORS AND DISPLACEMENT OF THE MODEL DIAPHRAGM
In [4] the shape at different lung volumes of a diaphragm was obtained after a 3D
reconstruction of MRI obtained images. They studied 4 healthy subjects at 4 different
volumes (VLS) in the supine position. This approach allowed the assessment of the
diaphragm excursion in its different planes also offered the possibility of quantitative
estimations of changes in the total diaphragm surface, area of apposition and area of
the diaphragm dome. The interslice gap was of 0.8 mm, flip angle of 90o, and the
thickness of the slices 8.0 mm. The procedure was carried out at the following VLS
and capacities in the following sequence: RV, FRC, FRC plus one half of inspiratory
capacity and TLC. The data observed in fig. 2.1 describes the excursion of the
diaphragm at the different VLS and Capacities [4]. The measurements observed are
comparable on the ones in other sources, therefore we can confidently base on [4] the
displacement applied to our model. In Fig. 2.1 we can observe the average diaphragm
silhouettes at the 4 different lung volumes mentioned above. A. left midsagittal plane,
B: midcoronal plane and C. right midsagittal plane. The solid circles show the
costophrenic angles.
Fig 2.1 Diaphragm silhouettes at the 4 different lung volume. A. left midsagittal plane, B:
midcoronal plane and C. right midsagittal plane.
In A and C we can observe that the posterior zone doesn’t show a significant
displacement, while the anterior apposition zone moves forward and upward along the
costophrenic angles in function of the contraction of the fibers of the diaphragm
muscle, meaning that the ribacage will also move in function of that contraction at the
end on the inhalation and going to the former state at the end of the exhalation. We
can observe as well that the right diaphragmatic dome has a relative lesser
displacement compared with the left dome, but this can be due to the surrounding
anatomy, primarily the liver . Meaning the right dome is normally higher than the left
one, and the displacement required to achieve the same height is less.
The lateral displacement of the diaphragm, as shown in C is of much lesser
extent compared with the front and upward excursion, but not of less significance for
modelling the diaphragm kinematics. Finally, as stated in the discussion of diaphragm
anatomy, the displacement upward and downward of the diaphragm happens in a
parallel manner at the central tendon and leaflets areas that are extensions of the
central tendon to each side of the diaphragm (see fig. 1.2). This information is of great
importance for the assignment of vectors and displacements on the model, as well as
the function of each component
The action of the diaphragm is complex and the details of its shape and
displacement depend on its attachments and surrounding structures.
iii.
DISCUSSION
For the development of the model of the diaphragm and its motion three main
aspects have been taken into account: anatomy, excursion displacement and its
vectors. The anatomy, described previously, is of interest to infer the physiological
components that will help to determine the motion of the diaphragm, for example,
when we know where and how the muscle bundles origin and insert, we can assign
the muscle stretching extension and, if that is the case, leave the apposition zone
motionless.
The knowledge that the vertebral part of the diaphragm originates from the
arcuate ligaments and crura, both aponeurosic tissue, lead us to the inference that it is
a fixed point, as well as the central tendon, but with the difference that the former will
not show displacement, while the latter will displace upwards and downwads (Z-axis)
in function of the fiber bundles surrounding it; but, being the one that carries the heart
in a much lesser extent than the right and left leaflets.
As inferred from Fig. 2.1, the average excursion of the diaphragm on the Z-axis
is of 17 mm on a supine position, which has been validated by other sources [2,4,10].
For the other axes however, X-axis corresponding to lateral and Y-axis for front and
back, the displacements, even when parallel to the origin, are not comparable to the
displacement of the dome. We applied the measures obtained in [4] to designate the
displacement, combined with the information obtained at the anatomy review and
applied to the vectors and lines of tensions described in [3] and Fig 3.1, 3.2 and 3.3.
Fig. 3.1 We can observe the directions of lines
of tension from centers of hemidiaphragm
domes to zone of apposition. The lines of
tension do not proyect, except in narrow
isthmus, between spine and xiphoid process.
Therefore, tension in one hemidiaphragm is
not well transmitted to the other side
maintaining its relative independent, but
coordinated movement. The blank area,
corresponds to the fixed point, the Central
Tendon.
Fig. 3.2 Diagram of the interaction between
tension in medial crural fibers in sagittal plane
and tension in transverse direction over
domes. Tension across the saddle in medial
crura (open arrows), like tension in a laundry
line, can make the saddle act as an anchor for
fibers pulling laterally and upward over domes
(solid arrows)
Fig 3.3. Vector of tension exerted by the diaphragm on the lower margin of the ribcage. Shaded
area, zone of apposition (fixed area) with dashed line at its upper boundary.
As mentioned previously, we obtained excursion and displacement vectors to
apply to the model generated using Non-rigid registration (Fig 3.4). From this model
we had the nodes or coordinates which will be then be assigned with displacements in
function of X, Y and Z vectors.
Fig 3.4 Diaphragm model generated by non-rigid registration expressed in
“displacement nodes”
The nodes of this model can be presented in tabular format as shown on Table
3.1. With this database we created a model that can be manipulated and generated a
full grind in order to determine anatomical landmarks with more accuracy Fig 3.5.
Table 3.1 Model display on an data source worksheet
The anatomical landmarks and the coordinates of Fig 3.5 were then matched in
order to create a new data source to which Displacement Vectors and Excursion in
function of X, Y and Z (Table 3.2) could be assigned.
Fig 3.5 Matching the model created based on our data source worksheet and the
anatomical Pattern.
Final results determined 16 zones or anatomical landmarks for Displacement and
Excursion assignment (see fig 3.6):
1.
2.
3.
4.
5.
6.
7.
8.
Anterior Apposition Zone
Left Apposition Zone
Right Apposition Zone
Crura
Central Tendon
Left Crus
Right Crus
Left Tendon
9.
10.
11.
12.
13.
14.
15.
16.
Right Tendon
Anterior Left Muscle
Anterior Right Muscle
Anterior Central Muscle
Posterior Central Muscle
Posterior Right Muscle
Posterior Left Muscle
Posterior Apposition Zone
A brief analysis of the anatomy and histology took place for each Landmark
and the displacements were calculated. The results are illustrated on fig 3.6.
Fig 3.6 Diaphragm Divided in zones for the assignment of Displacement Vectors and
excursions as a function of anatomical, histological and phsysiological components.
Anterior Apposition Zone: Even when considered as a fixed point, due to the lack of
intrinsic motion and inability to full stretching being formed of aponeurosic tissue, it
moves upfront as a consequence of the muscle fiber bundles attached to it, generating
a pulling force along with the ribcage to the front.
Left Crus and Right Crus: Sharing the same properties as the Anterior Apposition
zone, but presenting a slight displacement to the Left and Right correspondingly
following the extension of the ribs attached.
Crura: Being also aponeurosic and completely attached to the spine it becomes a
fixed point on every direction.
Central Tendon: Being the insertion for the fibers radiating inwards from the CW
and attached to the pericardium on its upper surface, it becomes a Fixed point mainly
in the X and Y directions; showing displacement only in Z axis in function of the
muscle stretching around it.
Left and Right Tendons of Leaflets: Share the same histological properties as the
Central Tendon. They have an excursion in X, Y and Z axis as a result of the muscle
fiber applying a pulling force on them in the direction of the muscle insertions on the
CW.
Muscles (Anterior, Posterior; Left and Right): Tissue specialized in stretching in
every direction as a product of the energy applied to the fibers. The direction
assigned for the model mainly corresponds to their given names.
Posterior Apposition Zone: Being a continuum of the Crura, spreading to the left
and righ following the ribs, it shares the same histological properties and becomes a
fixed point, differentiating from the Anterior apposition zone by the fact that these
ribs are not affected by the pulling force of the diaphragm and show no real intrinsic
or extrinsic displacement.
iv. RESULTS
The displacement vectors were assigned and ordered to a complete set of 5 405
nodes as follow (table 4.1).
Table 4.1 Table only showing the assigned displacements and vectors to 20 of the 5
405 total nodes.
Finally, the vectors displacement were “translated” and applied to the original
model on which the real displacement could be later visualized in a more global
manner (fig 4.1).
Fig 4.1 Graphic showing the movement of the diaphragm with colours corresponding
to the amplitud of the displacements
A summary of the displacements assigned to each zone can is described in the
following tables:
Description by Zones
ZONE
AXIS
X
MIN
DISPLACEMENT
MAX
DISPLACEMENT
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
-1
1
-0,004
0,31
0,55
MIN
DISPLACEMENT
MAX
DISPLACEMENT
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
4,5
5
4,77
0,033
0,18
MIN
DISPLACEMENT
MAX
DISPLACEMENT
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
5
6
5,28
0,1
0,32
MIN
DISPLACEMENT
MAX
DISPLACEMENT
X
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
-1
-1,7
-1,8
0,01
0,11
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Y
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0,1
2
1,17
0,23
0,48
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Z
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0,1
3
0,55
0,51
0,71
Y
AP
ZONE
Z
AP
ZONE
LEFT
AP
ZONE
RIGHT
POST AP
ZONE
CENTRAL
TENDON
MIN
DISPLACEMENT
1,7
MAX
DISPLACEMENT
2
MIN
DISPLACEMENT
0,1
MAX
DISPLACEMENT
2
MIN
DISPLACEMENT
MAX
DISPLACEMENT
X
AVERAGE
DISPLACEMENT
1,89
Y
AVERAGE
DISPLACEMENT
0,54
Z
AVERAGE
DISPLACEMENT
0
3
0,51
MIN
DISPLACEMENT
0
MAX
DISPLACEMENT
0
MIN
DISPLACEMENT
0
MAX
DISPLACEMENT
0,25
MIN
DISPLACEMENT
0
MAX
DISPLACEMENT
0,35
X
AVERAGE
DISPLACEMENT
0
Y
AVERAGE
DISPLACEMENT
0,16
Z
AVERAGE
DISPLACEMENT
0,13
VARIABILITY
0,014
STANDARD
DEVIATION
0,12
VARIABILITY
0,33
STANDARD
DEVIATION
0,57
VARIABILITY
STANDARD
DEVIATION
0,39
0,63
VARIABILITY
0
STANDARD
DEVIATION
0
VARIABILITY
0,01
STANDARD
DEVIATION
0,11
VARIABILITY
0,02
STANDARD
DEVIATION
0,13
X
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
1,25
-0,05
0,33
0,57
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Y
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0,25
2
1,02
0,44
0,66
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Z
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
10
14,5
12,56
2,53
1,59
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0
0
0
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0
0
0
MIN
DISPLACEMENT
MAX
DISPLACEMENT
-1,25
X
MIN
DISPLACEMENT
MAX
DISPLACEMENT
0
0
Y
CRURA
MIN
DISPLACEMENT
MAX
DISPLACEMENT
0
0
Z
MIN
DISPLACEMENT
MAX
DISPLACEMENT
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0
2
0,16
0,14
0,37
LEFT
CRUS
RIGHT
CRUS
LEFT
TENDON
RIGHT
TENDON
MIN
DISPLACEMENT
MAX
DISPLACEMENT
X
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
-1,5
0
-0,59
0,36
0,6
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Y
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0
0
0
0
0
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Z
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0
1,5
0,27
0,24
0,49
MIN
DISPLACEMENT
MAX
DISPLACEMENT
X
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0
1,5
0,38
0,12
0,35
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Y
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0
0
0
0
0
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Z
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
1,5
1,5
0,49
0,47
0,68
MIN
DISPLACEMENT
MAX
DISPLACEMENT
X
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
-2
1,4
-1,7
0,05
0,22
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Y
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0
2
0,53
0,24
0,49
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Z
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
13
15
14,22
0,35
0,59
MIN
DISPLACEMENT
MAX
DISPLACEMENT
X
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
1,4
2
1,78
0,03
0,19
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Y
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0
2
0,63
0,2
0,44
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Z
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
13,2
16
15,37
0,87
0,93
RIGHT
ANTERIOR
MUSCLE
LEFT
ANTERIOR
MUSCLE
ANTERIOR
CENTRAL
MUSCLE
POSTERIOR
CENTRAL
MUSCLE
X
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
1,5
1,19
0,02
0,14
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Y
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
2,4
3,5
2,79
0,12
0,34
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Z
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
3
15
9,55
15,27
3,91
MIN
DISPLACEMENT
MAX
DISPLACEMENT
X
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
-1,5
-1,1
-1,35
0,02
0,15
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Y
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0,1
1
0,63
0,16
0,4
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Z
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0,75
2
1,54
0,27
0,52
MIN
DISPLACEMENT
MAX
DISPLACEMENT
X
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
-1
1
-0,03
0,16
0,41
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Y
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
2,2
5
4,16
0,72
0,85
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Z
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
6
14,5
9,2
7,31
2,7
MIN
DISPLACEMENT
MAX
DISPLACEMENT
1
MIN
DISPLACEMENT
MAX
DISPLACEMENT
X
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
-1,6
1,6
0,21
1,6
1,28
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Y
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0,25
0,6
0,52
0,02
0,11
MIN
DISPLACEMENT
MAX
DISPLACEMENT
Z
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
10
14,5
10,41
0,94
0,97
X
RIGHT
POSTERIOR
MUSCLE
MIN
DISPLACEMENT
MAX
DISPLACEMENT
0,7
1,4
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0,97
0,08
0,28
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0,81
0,28
0,53
Y
MIN
DISPLACEMENT
MAX
DISPLACEMENT
0,3
1,8
Z
MIN
DISPLACEMENT
MAX
DISPLACEMENT
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
5
14
8,2
5,69
2,38
MIN
DISPLACEMENT
MAX
DISPLACEMENT
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
-1,3
-0,2
0,61
0,15
0,39
MIN
DISPLACEMENT
MAX
DISPLACEMENT
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
0,5
1,8
1,01
0,2
0,45
X
LEFT
POSTERIOR
MUSCLE
Y
Z
MIN
DISPLACEMENT
MAX
DISPLACEMENT
AVERAGE
DISPLACEMENT
VARIABILITY
STANDARD
DEVIATION
4
14
8,03
5,62
2,37
Further research should be done to prove the feasibility of this methodology and
standardization of this displacement.
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