Computational analysis of the effect of physical
activity on the changes in femoral bone density in
prepubertal children
Pieter-Jan Hendrikus Alexander Terryn
Thesis to obtain the Master of Science Degree in
Biomedical Engineering
Supervisors:
Professor Paulo Rui Alves Fernandes
Professor Maria de Fátima Baptista
Examination Committee
Chairperson:
Supervisor:
Faculty of Movement Specialist:
Member of the Committee:
Professor Luís Humberto Viseu Melo
Professor Paulo Rui Alves Fernandes
Professor Filipa Oliveira da Silva João
Professor João Orlando Marques Gameiro Folgado
June 2015
ii
Acknowledgements
“In order for man to succeed in life, God provided him with two means, education and
physical activity. Not separately, one for the soul and the other for the body, but for the
two together. With these means, man can attain perfection.” - Plato
Although I do not want to judge this quote in the literal sense, it is a metaphoric summary of this master thesis and of my educational career in general. Studying ’Ancient
Greek-Mathematics’ in secondary school, Plato was part of my personal education as
counterpart to the exact sciences. When I started university, I did not know what to
expect of the engineering world, full of science and mathematics. When I finished my
bachelor in Mechanical engineering, I enrolled into the master of Biomedical engineering
to find more practical applications of engineering. The master thesis, being the final
step in my academic education, is the scientific research to the physical activity Plato
mentioned.
I am very grateful to have the opportunity to write a master thesis in international
context. Many thanks go to my supervisor, professor Paulo Fernandes. His enthusiasm
for the field of study encouraged me to start and finish this master thesis. A special
word goes to Carlos, a post-doc member of the research team. For every practical
problem, he has a solution. If the matter was urgent, he even sacrificed spare time
for help. Without professor Filipa João of the Faculty of Human kinetics, I wouldn’t
have crucial experimental data and useful advice. Also Professor Clarke (University of
Southamptom), professor Brys (KULeuven) and many others are thanked for their help
in the search for CT data.
Writing a master thesis is a process with a lot of ups and downs. I want to thank my
direct environment for their patience and support: international friends I met during
my exchange, my Belgian friends and of course my family. Special thanks go to Sebastiaan, Mike and Charlotte, respectively for help in the lay-out, proofreading and mental
boosting.
Finally, I want to thank both my parents in particular. As this writing is a mile-stone
in my educational career, now is the time to say the unspoken ’thank you’. These words
account in many ways: help in practical issues, having entertaining or wise conversations, giving me the financial support and to give me a free and careless educational
career.
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Abstract
Human bone health, and osteoporosis in particular, are a highly topical research. A
causal and positive effect of physical activity on bone mineral density is supported by a
bunch of clinical-based research studies. Moreover, actual research suggests long-term
benefits of childhood physical activity to the prevention of osteoporosis in adulthood.
Complementary to the clinical-based study is the computational analysis, based on a
bone remodeling model. Although many different remodeling models are developed by
several research groups, very little research is done in the application of computational
remodeling in children. The current study is performed in this gap and consists of two
major parts. First, a model is developed to represent the femoral bone of a prepubertal child. A finite element with assigned material properties based on Computed
Tomography scans is created and verified. The musculosketal loads are obtained from
experimental kinematic data by the Faculty of Human Kinetics. Gait, stance, run and
countermovement jump as performed by prepubertal children are represented by superposition of crucial timeframes in the activity cycle. The effect of physical activity on
bone mineral density in prepubertal children is investigated with the Lisbon bone remodeling model. An optimal value of model parameters k and m is investigated, which
take into account the inter-subject variability. A value of k = 0.0025 and m = 4 are
considered as best to represent the prepubertal population. In the second part of the research, the effect of additional physical activity on bone mineral density is investigated.
It is concluded that results of the computational model are in agreement with clinical
results. Spending more time in physical activity, high-intensive activity in particular,
the bone mineral density increases. It is stated that an initial increase in activity time
leads to a greater increase in bone mass compared to a further increase in activity time.
Further, the results suggest that physical activity decreases the risk for typical (osteoporotic) femoral fractures, as suggested by former research. In the region of the femoral
neck, this happens by the periosteal apposition of bone: a relative increase in density of
the outer shell. In the trochanteric region, the fracture risk is decreased by an increased
bone mineral density.
Keywords
Bone mineral density - Finite element modeling - Prepubertal children - Bone remodeling
- Lisbon model - Physical activity - Subject specific modeling
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Contents
1 Introduction
1
2 Background
2.1 Osteoporosis . . . . . . . . . . . . . . . . . . . .
2.2 Biology . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Macroscopic bone . . . . . . . . . . . . .
2.2.2 Microscopic bone . . . . . . . . . . . . . .
2.2.3 Bone growth . . . . . . . . . . . . . . . .
2.2.4 Bone modeling . . . . . . . . . . . . . . .
2.2.5 Bone remodeling . . . . . . . . . . . . . .
2.2.6 Balance between processes/bone turnover
2.2.7 Mechanical controls . . . . . . . . . . . .
2.3 Physical activity . . . . . . . . . . . . . . . . . .
2.3.1 Kind of stimulus . . . . . . . . . . . . . .
2.4 Optimal age . . . . . . . . . . . . . . . . . . . . .
2.4.1 Peak bone mass . . . . . . . . . . . . . . .
2.4.2 Window of opportunity . . . . . . . . . .
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3 Methods
3.1 Bone density . . . . . . . . . . . . . . . . . . . . . .
3.1.1 BMC, aBMD and vBMD . . . . . . . . . . .
3.1.2 Conversion between BMC, aBMD and vBMD
3.2 Lisbon model . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Microscale: the unit cell . . . . . . . . . . . .
3.2.2 Macroscale: bone tissue . . . . . . . . . . . .
3.2.3 Elastic properties: coupling of scales . . . . .
3.2.4 Optimisation . . . . . . . . . . . . . . . . . .
3.3 Subject specificity . . . . . . . . . . . . . . . . . . .
3.3.1 Finite element model . . . . . . . . . . . . . .
3.3.2 Material Assignment . . . . . . . . . . . . . .
3.3.3 Constraints . . . . . . . . . . . . . . . . . . .
3.3.4 Musculoskeletal loading . . . . . . . . . . . .
3.3.5 Hip contact force . . . . . . . . . . . . . . . .
3.4 Parameters of the remodeling model . . . . . . . . .
3.4.1 General . . . . . . . . . . . . . . . . . . . . .
3.4.2 K and m . . . . . . . . . . . . . . . . . . . .
3.4.3 Load weights αp . . . . . . . . . . . . . . . .
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3.5
Physical Activity . . . . .
3.5.1 Reference group .
3.5.2 Regions of interest
3.5.3 Intervention . . . .
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4 Results and discussion
4.1 Creation of femoral model of prepubertal child . . . .
4.1.1 Bone density: clinical versus computational . .
4.1.2 Remodeling model applied on children . . . . .
4.1.3 Subject specificity . . . . . . . . . . . . . . . .
4.1.4 Parameters of the remodeling model . . . . . .
4.1.5 Limitations . . . . . . . . . . . . . . . . . . . .
4.2 Change in density . . . . . . . . . . . . . . . . . . . .
4.2.1 Influence of physical activity . . . . . . . . . .
4.2.2 Additional time per day spent physical activity
4.2.3 Difference between trabecular and cortical bone
4.2.4 Particular regions of interest . . . . . . . . . .
4.3 Daily-life application . . . . . . . . . . . . . . . . . . .
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5 Conclusion
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62
viii
List of Figures
2.1
Conceptual graphs of bone mass as a function of age. A, In normal individuals, bone mass increases during childhood and adolescence, peaks
in young adulthood, and then decreases in later adulthood. B, An intervention as physical activity (solid box) during childhood to increase bone
mass acquisition is assumed to have a persistent effect on bone mass
throughout life. Adopted from Stagi [36] . . . . . . . . . . . . . . . . . .
3.1
3.2
3.3
Femoral neck and geometric properties . . . . . . . . . . . . . . . . . . .
Material model for bone. Adopted from Fernandes et al. [59] . . . . . .
Upper: Maximum nodal displacement plotted for different number of
nodes. Fit with a power series. Lower: Change in maximum displacement
with respect to the number of nodes of the model. . . . . . . . . . . . .
3.4 Upper: Maximum nodal Von Mises stress plotted for different number of
nodes. Fit with a power series. Lower: Change in maximum Von Mises
stress with respect to the number of nodes. . . . . . . . . . . . . . . . .
3.5 Upper: Total strain energy for the model plotted for different number of
nodes. Fit with a power series. Lower: Change in total strain energy
with respect to the number of nodes. . . . . . . . . . . . . . . . . . . . .
3.6 Histogram of the grayvalues, plotting the frequency of appareance of the
grayvalues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 The model with assigned materials based on a linear relationship with
grayvalues. Rainbow spectrum, blue corresponds with low grayvalue, red
with high grayvalue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 Histogram of the discretized densities, plotting the frequency of appareance of the densities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 Investigated constraints. (a) Three nodes fully constrained (b) All nodes
constrained in the axial direction. Two nodes constrained in medial/lateral
direction and two nodes constrained in posterior/anterior direction (circled). (c) All nodes fully constrained . . . . . . . . . . . . . . . . . . .
3.10 Stress distributions at bottom for different constraints: (a) Three nodes
fully constrained (b) All nodes constrained in the axial direction. Two
nodes constrained in medial/lateral direction and two nodes constrained
in posterior/anterior direction (circled). (c) All nodes fully constrained
3.11 Muscles taken into account in the remodeling model. . . . . . . . . . . .
3.12 A typical gaitcycle and important timeframes. Heel-Contact (HC), Maximal Weight Acceptance (MWA), Midstance (MS), Push-Off (PO) and
Toe-Off (TO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
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3.13 The experimental gaitcycle with vertical component of ground reaction
forces plotted with respect to time. . . . . . . . . . . . . . . . . . . . . .
3.14 A typical runcycle. Two peaks are noticed: the impact peak and the
active peak. Adopted from [81] . . . . . . . . . . . . . . . . . . . . . . .
3.15 Runcycle of the studied subject. The impact peak is not clearly visible.
Vertical component of ground reaction force plotted versus time. . . . .
3.16 Hip contact forces plotted versus time during the runcycle. The impact
peak could be localized. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.17 Jump activity cycle. Vertical component of ground reaction force plotted
versus time. Also the activity ’stance’ could be substracted. . . . . . . .
3.18 A sphere (grey) is wrapped and fitted in the femoral head (red). . . . .
3.19 For a given muscle path, the anatomical (yellow dot) and the effective
(green dot) femoral attachments are represented, together with the associated muscle direction (red arrow). Adopted from Modenese [83]. . . .
3.20 Coupled surface with point of attachment of the concentrated load(yellow
cross). The coupling distributes the load over the surface. . . . . . . . .
3.21 Point of peak load for the different types of Physical Activity . . . . . .
3.22 Definition of the spherical angle in the hip joint. Adapted from Bombelli
[94] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.23 The spherical area measured in the CT-images. . . . . . . . . . . . . . .
3.24 Stress distributions at the femoral head due to hip contact force. Rainbowspectrum red (highest) to blue (lowest) stress. . . . . . . . . . . . .
3.25 Stress distributions at the femoral head due to hip contact force. Rainbowspectrum red (highest) to blue (lowest) stress. . . . . . . . . . . . .
3.26 Weight distribution of a linear and a cubic weighting scheme. The cubic polynomial give higher weights to the points closer to the pole and
smaller weights to the points further from the pole compared to the linear
decreasing weights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.27 Femoral head with load distribution in a cubic distributed coupled surface.
3.28 Definition of seven ROI as proposed by Prevrhal [103]. Figure adopted
from Vahdati [104]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.29 The regions of interest selected on the finite element model. . . . . . . .
4.1
4.2
4.3
4.4
4.5
X-ray images used for the qualitative analysis of material assignment
and geometry. (a) Virtual X-ray of the created model (b) X-ray of nonpathological subject. Adopted from Pennstatemedicine [110]. . . . . . .
The correlation between simulated densities with different k and m and
the real densities of the CT scan. Left subplot shows different values for
m ranging from 1 to 7 with respect to k fixed on the X-axis. . . . . . . .
The average error (average between absolute and relative error) between
simulated densities with different k and m and the real densities of the
CT scan. Left subplot shows different values for m ranging from 1 to
7 with respect to k fixed on the X-axis. Right subplot shows different
values for k ranging from 10x10−5 to 500x10−5 with m fixed on the x-axis.
Simulated data of density with respect to additional time spent in physical
activity per day. Reference group 1 performs additional high-intensive
activity. Intervention group 2 performs additional walking. The reference
group does not perform additional activity. . . . . . . . . . . . . . . . .
Change in bone density for additional time spent in physical activity. . .
x
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4.6
4.7
4.8
Bone mineral density at the integral femoral neck and at the superior,
inferior, anterior and posterior femoral neck subregions according to additional time spent in (a) ordinary and supplementary (b) low-, (c) moderateand (d) high-impact physical activity, relatively to the reference regime.
Adapted from Machado [117]. . . . . . . . . . . . . . . . . . . . . . . . .
Upper: ratio of trabecular bone to cortical bone. Lower: change in ratio
with respect to increased activity. Figures for intervention group 1 . . .
Upper: ratio of central to neck ROI. Lower: change in ratio with respect
to increased activity. The indicates periosteal apposition. . . . . . . . .
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xii
List of Tables
3.1
3.2
3.3
3.4
4.1
Types of physical activity, the selected timeframes and the label of the
timeframe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results of the analysis to determine parameters k and m. Difference
with the mean and standard deviation of the CT scan, the correlation
coefficient, the RMS of the absolute error, the RMS of the relative error
and a weighted average of the absolute end relative error are given. The
combination k = 0.0025 and m = 4 is selected. . . . . . . . . . . . . . .
Time spent on physical activity and rest with the corresponding calculated BMD of the femoral neck. . . . . . . . . . . . . . . . . . . . . . . .
Summary of the physical activity of each group. Parameter x increments
from 0 to 9 to represent additional time per day spent on the respective
activity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Starting densities in the different regions of interest as measured on the
created model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
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51
xiv
Abbreviations
aBMD Areal Bone Mineral Density
BW Body Weight
BMC Bone Mineral Content
BMD Bone Mineral Density
CENTRAL Central region of interest
CIRCROI Circular region of interest
CT Computed Tomography
DEXA Dual Energy Radiograph Absorptiometry
DOF Degrees of Freedom
GV Grayvalue
PF Proximal Femur
FN Femoral Neck
FE Finite Element
FEM Finite Element Method
NECK Femoral Neck
HCF Hip Contact Force
PA Physical Activity
pQCT Peripheral Quantitative Computed Tomography
pyvXRAY Python Virtual Xray
ROI Region Of Interest
SD Standard Deviation
STL Standard Triangulation File
TOT FEM Total Proximal Femur
WARD Ward’s triangle
xv
xvi
Chapter 1
Introduction
A highly topical research theme in medical science nowadays is the disease Osteroporosis.
As people grow older compared to the past, the optimal condition of the human body
is expected to be maintained for a longer period of time. As drugs are not yet able
to prevent osteoporosis, the best solution for maintaining bone health is prevention by
physical activity. As the femur is the bone which is most vulnerable to osteoporosis,
this bone is investigated.
The effect of physical activity on bone health is extensively investigated based on clinical
results [1]. Despite the great benefits of these studies, they are limited to a time scale
(often several month between two measurements) and to existing medical equipment
to measure density (rarely volumetric bone density). A computational analysis gives a
complementary view to obtain more complete data.
Several definitions of bone density with different units are disorderly used in literature
[2]: bone mineral content, areal bone mineral density and volumetric bone mineral
density . Definitions and explanation of these are summarized. Further, some techniques
to convert one definition into another are presented briefly.
To explain and predict clinical data, one tries to catch biological reality into a model.
In this study, the Lisbon model is used to predict the bone remodeling. The model is
based on Wolff’s law and describes biology on both the scale of the bone unit cell and the
scale of the bone tissue. The scales are coupled by the theory of homogenization. The
change in density is captured by optimization of the design variable based on principles
of topology optimization.
This study is aimed at a population of prepubertal children, because of the so called
’window of opportunity’ around this growth phase. Therefore, a subject specific model
representing the femoral bone in the aimed population needs to be created.
First, a geometric model of the femur is made based on computed tomography scans.
The geometry is meshed to obtain a finite element model. In this way, a discretization
of the bone is realized. Convergence tests are performed to ensure that the effect of the
discretization is negligible on the outcome of the results.
The CT scans provides besides information about the geometry also information about
the densities of the model, stored as grayvalues. A relation between grayvalue and
1
the bone material is presented. This information is computed for each element. An
algorithm is implemented to interpolate this information to nodes.
A model needs to be constrained. The impact of the constraints on the outcome is tried
to be as realistic as possible with some experiments.
Besides the modeling of the femoral bone, the loads on the bone also need to be modeled.
The musculoskeletal loading makes use of experimental data obtained by a team of the
Faculty of Human Kinetics (University of Lisbon). The experimental data consist of
musculoskeletal loading of the lower limbs on a subject of the aimed population. They
include different types of physical activity as gait, stance, run and jump. The useful
information for the model is extracted of the data by analysation. Further, the musculoskeletal loading data are converted to match with the finite element model.
The remodeling model has several parameters which needs to be defined and adjusted
for the aimed population. Tests are performed to set those parameters.
Finally, the change in femoral bone density of prepubertal children is investigated with
respect to increasing physical activity. A reference group is defined as the average nonactive child which performs hardly high intensive physical activity. Two intervention
groups are defined to compare with the reference group. The first intervention group
performs more high-intensive activity compared to the reference group. The amount of
time spent on high-intensive activity is gradually increased with 10 minute increments.
The second intervention group spends the same time on additional physical activity
as the first intervention group, but performing gait instead of high-intensive activity.
Seven regions of interest of the proximal femur are defined to investigate. Each region
has several important characteristics.
Besides the creation of a subject specific model for the aimed population, four main
objectives are studied. First, the difference between intervention groups compared to
the reference group. The effect of spending more time doing physical activity on bone
mineral density is investigated. Also the difference between both intervention groups is
examined. This points out the difference between walking or vigorous activity on bone
density. Secondly, it is studied how the density changes spending additional time in
physical activity. In other words, the impact of an additional time increment on the
density. Thirdly, the effect of physical activity on both trabecular and cortical bone
is examined. Fourthly, some crucial region of interests are inspected with changing
physical activity.
As mentioned before, this study is complementary to other research based on clinical
data. The outcome of this research could lead to a better understanding of bone health
or osteoporosis in particular. Underpinned advice about physical activity could be
given to children with a high potential risk for developing osteoporosis. Or, by better
understanding of the disease, this study could help in the research for more effective
drugs. Which does not take away the importance of phsysical activity...
2
Chapter 2
Background
2.1
Osteoporosis
Osteoporosis is a musculoskeletal disease characterized by reduced bone mineral density
(BMD) and increased risk of fragility fractures. Moreover, it is a silent disease with no
symptoms until a fracture occurs. Osteoporotic fractures result in significant mortality
and morbidity and lead to considerable societal costs, including direct medical costs and
indirect costs resulting from reduced quality of life, disability, and death[3].
According to the International Osteoporosis Foundation [4], 27.5 million people in the
European Union are estimated to have osteoporosis. Due to changes in population
demographics this number will rise from 27.5 million in 2010 to 33.9 million in 2025,
to an increase of 23%. In 2010, the number of deaths in the EU causally related to
osteoporotic fractures was estimated at 43000.
This increasing number of people who are suffering from it, has economic repercussions,
which are generated during treatment and rehabilitation. The annual direct economic
burden in the European Union of new and prior fragility fractures is 37 billion euro.
These costs of fragility fractures are expected to increase by 25% from 2010 to 2025. In
fact, the costs derived from bone fracture as a consequence of this disease are higher
than those produced by breast cancer and prostate cancer [5].
The International Osteoporosis Foundation (2014), with the aim of avoiding this social
and economic repercussion, proposed that prevention is the best method to fight against
this disease. In this view, it is necessary to understand the underlying concepts of
osteoporosis and in general, the concepts of reduced bone mineral density.
2.2
2.2.1
Biology
Macroscopic bone
In the normal, mature human skeleton bones are composed of two types of tissue:
3
• A hard outer layer called cortical (compact) bone, which is strong, dense and
tough.
• A spongy inner layer called trabecular (cancellous) bone. This network of trabeculae is lighter and less dense than compact bone.
Most bones consist of a mixture of outer cortical bone and inner trabecular bone, enabling the optimal compromise between strength and weight [6]. The adult human
skeleton is composed of 80% cortical bone and 20% trabecular bone overall. Different
bones and skeletal sites within bones have different ratios of cortical to trabecular bone.
The femur head for example is composed of cortical to trabecular bone in a ratio of
50:50 [7]. Although macroscopically and microscopically different, the two forms are
identical in their chemical composition.
Cortical bone, which comprises 80% of the skeleton, is dense and compact. The turnover
rate (cfr. Infra) is slow compared to trabecular bone: 2%-3% [8]. The major part of
the cortical bone is calcified and its function is to provide mechanical strength and
protection, but it can also participate in metabolic responses, particularly when there is
severe or prolonged mineral deficit [9]. The structural unit of the compact bone is the
osteon. This unit consisting of layers is oriented along the long axis of bone and gives
compact bone anisotropic mechanical characteristics to withstand bending, torsion and
compression. Furthermore, cortical bone has a very low porosity.
Trabecular bone represents 20% of the skeletal mass but 80% of the bone surface. It
is found inside the long bones. Trabecular bone is less dense, more elastic, and has
a much higher turnover rate than cortical bone exhibiting a major metabolic function
[9]. Spongy, cancellous or trabecular bone comprises a network of fine, interlacing small
beams. these are enclosed cavities that contain either hematopoietic or fatty marrow.
The physical arrangement of broad plates connected by thin struts provides for maximum support but with a minimum of material. This explains why trabecular bone
has a higher porosity compared to cortical bone. The trabecular struts have adopted
a preferential alignment along the direction of principal mechanical forces: trabecular
bone is an anisotropic material as well.
2.2.2
Microscopic bone
Bone is a porous and mineralized structure. It is a visco-elastic composite biomaterial
consisting of cells (10%) held within a matrix (90%). The matrix contains both inorganic
and organic components [10]. Three types of cells present in bone are of particular
interest: osteoblasts, osteoclasts and osteocytes, which are respectively responsible for
the production, resorption and maintenance of bone [11].
• Osteoclasts are bone-resorbing cells, as they break down bone. They are large,
multinucleate cells that form through the fusion of precursor cells. Unlike osteoblasts, which are related to fibroblasts and other connective tissue cells, osteoclasts are descended from mesenchymal stem cells in the bone marrow that also
give rise to monocytes.
• Osteoblasts are bone forming cells and originate from undifferentiated mesenchymal stem cells as well. Their major function is to create organic matrix. They
4
can be stimulated to proliferate and differentiate as osteocytes, when entrapped
in mineralized matrix.
• Osteocytes are bone cells. They produce collagen and other substances that make
up the bone extracellular matrix. Osteocytes are found enclosed in bone. Furthermore, they are the mechanosensive cells of bone and play a crucial role in
functional adaptation of bone [12].
2.2.3
Bone growth
Bone growth is the initial formation of bone. It consists of the activity of osteoblast only.
Bone growth starts early in fetal life and goes on until the end of somatic growth.
For the creation of bone tissue, there are two mechanisms: endochondral ossification and
intramembranous ossification. Intramembranous ossification occurs in the formation of
flat bones such as those in the skull. Since this mechanism is not relevant for the femur,
it will not be covered further here. Endochondral ossification occurs in embryonic long
(e.g.: the femur) bone, the growth plate (physis) of immature bones, and in fracture
healing.
In endochondral ossification, undifferentiated mesenchymal cells secrete a cartilage like
matrix, after which they differentiate into chondrocytes. The matrix gets calcified and
the chondrocytes undergo apoptosis. Now, blood vessels grow into cavities within the
matrix which bring osteoclasts and osteoblasts to the area. Osteoblasts then use the
calcified matrix as a support structure to lay down osteoid, which forms the bone trabeculae. Osteoclasts break down the calcified matrix (spongy bone) to create the medullary
cavity, which contains bone marrow. In essence, a cartilage matrix is replaced by bone
[10][11].
2.2.4
Bone modeling
Bone modeling occurs mainly during birth to adulthood and is responsible for gain in
skeletal mass and changes in skeletal form. Unlike bone growth, there is activity in both
the osteoblasts and osteoclasts. However, this osteoblastic formation and osteoclastic
resorption process are uncoupled. The bone resorption and bone formation occur on
separate surfaces [7].
Modeling is the process that naturally tends to correct bone deformities. The outcome
is some change in the design of a trabecular network or a cortical shell. During growth,
modeling can determine bone growth in length as well as morphological changes in the
cross sections of the bone. Modeling decreases with age but never disappears completely.
To summarize, one can say that modeling influences the bone architecture: It consists
in macroscopic changes of the shape of skeletal segments. [13]
2.2.5
Bone remodeling
Remodeling of bone begins early in fetal life, and once the skeleton is fully formed in
young adults almost all of the metabolic activity is in this form. Unlike bone modeling,
5
the resorption activity of osteoclasts and the bone formation of the osteoblasts are
coupled. They occur on the same surface, but with temporal sequence.
The remodeling is a continuous process of replacing bone for maintaining normal calcium
levels in the body and to maintain bone strength. The outcome of the process is the
replacement of a small amount of the pre-existing bone by a comparable, a larger or a
smaller piece of new bone. It serves to prevent and remove fatigue-related micro damage
and allows adaptation of the bone mass and structure. It makes adjustment of bone
architecture possible to meet changing mechanical needs [9]. But during the process,
the general shape of the bones is maintained through their course of growth.
The underlying metabolic process involves the removal of mineralized bone by osteoclasts
followed by the formation of bone matrix through the osteoblasts that subsequently
become mineralized. The remodeling cycle consists of three consecutive phases. First
is the resorption phase, during which osteoclasts digest old bone. Next is the reversal
phase, when the resorption process ends and the osteoclasts are replaced by osteoblasts.
The last step is the formation phase. Osteoblasts lay down new bone, starting with
the creation of a matrix of collagen called osteoid. The osteoblasts then mineralize this
matrix to form the new bone. Then, the resorbed bone is replaced [9].
To summarize, one can say that remodeling influences the bone structure: It consists in
microscopic changes of the composition of skeletal segments on the same surface.
2.2.6
Balance between processes/bone turnover
Bone turnover is the absolute amount of the bone mass balances resulting from bone
formation and destruction [14].
During childhood, both bone modeling (formation and shaping) and bone remodeling
(replacing or renewing) occurs, whereas in young and middle adulthood bone remodeling
is the predominant process to maintain skeletal integrity [6]. However, remodeling is also
very important during periods of growth, puberty and adolescence, when the majority
of adult bone mass is laid down [10]. Since bone modeling and remodeling often occur
simultaneously, distinctions between them are not always apparent.
As a person enters old age, osteoclastic (resorption) activity tends to exceed osteoblastic
(formation) activity [15]. This imbalance in the regulation of bone remodeling’s two subprocesses, results in many metabolic bone diseases, such as osteoporosis.
2.2.7
Mechanical controls
The number and activity of osteoclasts and osteoblasts are determined by a multitude
of factors, such as genetics, hormones and cytokines and nutritional status. However,
this discussion is beyond the scope of this text. Other determining factors are locally
produced signaling molecules under the influence of mechanical stimuli [16]. While
genetics outlines the general shape, length, and architecture, changes in mechanical
environment elicit adaptive responses [17].
The cells responsible for sensing the physical stimuli derived from mechanical forces
exerted on bones are the osteocytes, which comprise over 90% of the bone cells [16].
6
“These cells are old, differentiated osteoblasts occupying the lacunar space surrounded
by the bone matrix. They possess cytoplasmic dendrites that form a canalicular network, through which osteocytes and the bone surface communicate. Mechanical loading
stimulates several physical signals as tissue strain, fluid shear, and fluid pore pressure,
which induce osteocyte activation [18]. The unique ability to translate mechanical stimulus to biochemical activity may be related to the fact that the osteocyte is the only cell
in bone that expresses sclerostin, which is a secreted protein that inhibits the canonical wnt-signaling pathway. It inhibits osteoblastic and stimulates osteoclastic activity.
Hence, when osteocytes secrete more sclerostin, the production of new bone slows down.
Consequently, in bones that are subjected to mechanical stimuli and physical loads, osteocytes secrete less sclerostin. Diminished sclerostin levels allow heightened osteoblast
activity, which permits the production of additional bone in areas that are under stress”
[19]. In short, osteocytes have a mechanosensing role that is dependent upon the intensity, the frequency and the duration of strain [20].
A classic clinical example of the stimulating effect of mechanical stimuli on bone mass
is the response of bone to physical extremes: astronauts enduring microgravity lose up
to 2% of hip bone density each month, whereas professional tennis players possess up to
35% more bone in the dominant arm than the arm that tosses the ball into the air [21].
In general, disuse and unloading of the skeleton promotes reduced bone mass, whereas
loading promotes increased bone mass.
2.3
Physical activity
As discussed supra, mechanical loading promotes increased bone mass. The most obvious way of applying this mechanical loading on bones is through exercise and physical
activity. In other words, exercise means forcing bones to bear more weight than they
are used to.
Physical activity is an umbrella term defined as any bodily movement produced by
skeletal muscles that result in energy expenditure above the basal level. The selectable
parameters of physical activity are frequency, intensity, time, and type, of which each
has an effect on the health outcome [22]. Studies suggest that the type of physical
activity carried out is by far the most important dimension that affects bone, since each
type of physical activity stimulates the bone differently [23].
2.3.1
Kind of stimulus
Physical activities that are dynamic and odd in nature, high in magnitude and rate,
and short in duration are the most effective in increasing bone mass and changing
its structure. Examples of these activities include jumping, hopping, and tumbling
[24].
Threshold
Frost [25] theorized that above a certain threshold of mechanical use, where the bone
is exposed to higher than normal mechanical loads, bone formation occurs to increase
7
bone strength. Conversely, if mechanical strain remains below a certain threshold, bone
is resorbed, and excess mass is removed [26].
The potential of physical activity to place great enough strains on bone to cause reshaping depends on the intensity of the load, the rate at which the load is applied, the
duration of the loading bout, and the novelty of the load [27]. In addition to habitual
physical activity, the threshold appears to vary between individuals (and also bone sites)
according to maturity, sex, and perhaps race/ethnicity.
Weight bearing or impact?
The physical activity can consist of weight bearing or impact exercises. In weightbearing exercise, the majority of the peak loads exerted on bone are muscle forces. On
the other hand, in impact exercise, the gravitational and ground reaction force is the
major component of the peak load. Some examples of weight-bearing exercises include
weight training, walking, hiking, jogging, climbing stairs, tennis, and dancing. Examples
of exercises that are not weight-bearing include swimming and bicycling.
Total bone mineral content is more strongly associated with muscle mass than with fat
mass or total body mass, supporting that muscle forces are closely interrelated with bone
mass. As muscle forces are generated during impact or non-impact exercise, it is difficult
to separate the effects of gravity alone from muscle forces on bone mass. Experiments
have demonstrated that the majority of the forces generated within the femur during
walking are the result of muscle forces and much less the result of weight bearing [18].
However, the best exercise for bones is the weight-bearing kind, which forces muscles to
work against gravity.
Dynamic/time varying?
The load must be dynamic (time varying) to initiate an anabolic response. Large static
loads are known to induce bone loss similar to that which occurs through disuse [21].
Moreover, the load must be cyclical including rest periods to avoid desensitization of
the osteocytes [28].
Magnitude
Even the most strenuous activity will generate peaks of only 0.3% strain in loaded
bones. Even extremely-low-magnitude bone strains, three orders of magnitude below
peak strains generated during strenuous activity, can be anabolic to bone when induced
at high frequencies, in essence mimicking the spectral content of muscle contractibility
[21]. Bone architecture and mass are influenced by the applied tension peak, whereas
the bone formation rate is modulated by the stimulus frequency [29].
8
2.4
2.4.1
Optimal age
Peak bone mass
An important marker of skeletal health is peak bone mass (PBM). According to the
world health organization, PBM is the bone mineral density during the stable period
following growth and accrual of bone mass and prior to subsequent bone loss. In other
words, at the point of peak bone mass, the bones are denser than they ever have been or
ever will be in the future. Although the bones may have finished growing in size many
years before the peak point, they have never stopped developing internally. The point of
peak bone mass is indicated in figure 2.1A. In general terms, peak bone mass occurs by
the end of the second or early in the third decade of life, which holds for both genders
[30]. After peak bone mass is achieved, there is a slow but progressive decline in bone
mass until a theoretical fracture threshold is reached.
A widely accepted element is that that the amount of peak bone mass achieved during
adolescence and young adulthood is a strong predictor of osteoporosis risk in later life
[31][32][33][34]. This is also indicated by statistical projections [35] and confirmed by
meta-analysis of different studies in this domain [1]. The higher the peak bone mass
achieved in young adult age, the more one can ‘afford’ to lose bone mass in old age
without suffering from osteoporosis or getting a fracture. A low peak bone mass will
lead to a higher risk of osteoporosis. On the other hand, a high peak bone mass will
provide a larger reserve for old age, reducing or delaying a person’s risk of becoming
osteoporotic. This could be seen in figure 2.1B. The increment in bone mass during
childhood could have a persistent effect for decades. Therefore, the acquisition of an
optimal bone mass is an essential factor in reducing the future risk of osteoporosis and
fractures.
Figure 2.1: Conceptual graphs of bone mass as a function of age. A, In normal individuals, bone mass increases during childhood and adolescence, peaks in young adulthood,
and then decreases in later adulthood. B, An intervention as physical activity (solid
box) during childhood to increase bone mass acquisition is assumed to have a persistent
effect on bone mass throughout life. Adopted from Stagi [36]
Genetic factors account for 50 to 85% of the variance in peak bone mass [37]. Because
heredity does not determine all of the variance, environmental modifications might make
a substantial impact on peak bone mass. This finding suggests that the remainder may
be targeted by interventions as physical activity.
9
Several studies tried to quantify the benefits of maximizing PBM. Based on a mathematical model using several experimental variables to predict the relative influences of
peak bone mass and age related bone loss on the development of osteoporosis, it was
calculated that a 10% increase in peak bone mass would delay the onset of osteoporosis
by 13 years [35]. In figure 2.1B, this corresponds with changing the offset of the peak
bone mass. In comparison, a 10% reduction in age related bone loss would only delay
the onset of osteoporosis by 2 years [38]. In the same figure, the corresponding effect is
the change of the slope of the declining curve.
The importance of maximizing PBM has also been quantified from the risk determination of experiencing an osteoporotic fracture in adulthood. From the results of epidemiological studies [39], it is possible to predict that a 10% increase (about one standard
deviation) in population PBM would reduce fracture risk for women after menopause by
as much as 50% [38]. Another study of Clark et al. estimated an 89% increase in adult
fracture risk per standard deviation decrease in bone mass during childhood [40].
Thus, this theoretical analysis indicates that peak bone mass could be the most important factor for the prevention of osteoporosis and bone loss related fractures later in
life.
2.4.2
Window of opportunity
In the previous section is explained the importance of peak bone mass on bone health
in later life. However, it is hard to stick an age on the most opportune moment of
intervention, i.e. physical activity. An important remark is that the relation between
chronological age and physical development could only be discussed in general terms.
Each individual has a different growth curve. The Tanner scale [41] provides a good
correlation between age and physical measurements of development, based on external
primary and secondary sex characteristics. However, it is uncommon that for the creation of a dataset including children, the Tanner stage is included. The combination
of chronological age, length and weight, combined with population averages of these
parameters, gives already a good indication of the maturity of the individual.
Baxter-Jones et al. have demonstrated that the accumulation of bone mass and its
persistence in adulthood are favored by doing sport or physical activity at early ages,
between 8 and 15 years [42]. According to Vicente-Rodriguez et al., the effect of physical
exercise is larger when it the intervention is done before puberty [43]. In a review of
prior relevant research Macdonald et al. [44] confirm the fact that the growing skeleton
has a greater capacity to adapt to loads associated with weight-bearing exercise than
the mature skeleton. These findings suggest that the years of childhood and adolescence
represent an opportune period during which bone adapts particularly efficiently to such
loading: a ‘window of opportunity’.
The benefits are quantified in a systematic review of randomized and nonrandomized
exercise trials in youth. It suggests that gains in bone mass due to physical activity
range between 0.9% and 5.5% in pre- and early puberty and are considerably smaller
after puberty (between 0.3% and 1.9%) [45]. The accumulation of bone mass gives
rise to stronger bones. In female racquet-sport athletes, side-to-side differences in bone
strength of the mid-humerus were 14% greater in women who began their training
prior to, or at, menarche (‘young starters’) compared with women who began training
10
after menarche (‘old starters’) . This quantification provides further support for the
window of opportunity occurring during pre- and early puberty when the skeleton is
most responsive to loading [46].
Based on evidence presented thus far, the benefits associated with early exposure to
physical activity may be explained by elements such as the decreasing responsiveness of
bone to mechanical stimuli with age [47]. It is during the adolescence stage of growth
that bone is building up most rapidly and is most sensitive to the osteogenic effects of
physical activity [48]. Specifically during the pre pubertal and early pubertal years, the
outer surface of bone, the periosteum, is covered with a greater proportion of active
osteoblasts [49]. This may explain the fact that bone formation is more rapidly initiated
with mechanical stimulation, which occurs during physical activity [24].
Together, these findings strengthen the notion that maximizing bone health during
childhood growth, especially during (pre)pubertal years, may represent an important
strategy in the prevention of osteoporosis and fractures during ageing.
11
Chapter 3
Methods
As concluded in the previous chapter, the age and mainly the maturity of the subject
are crucial parameters when investigating the evolution of the bone density. The aimed
population in this research is a pre-pubertal male child, 130 centimeter tall and a mass
of 30 kilogram. To generate subject-specific computational models of femoral bone
remodeling for this target population, one must acquire and discretized geometry for
the model, assign subject-specific loading, select appropriate parameters and choose
a bone remodeling algorithm. Each aspect of model development and simulation is
discussed in the subsequent sections.
3.1
3.1.1
Bone density
BMC, aBMD and vBMD
The bone mineral content (BMC) is a measure of the amount of calcium and other
minerals in a segment of bone. A higher mineral content indicates a higher bone density
and strength and it is used to detect osteoporosis [50]. The unit of BMC is mass
(g).
BMC is often measured using dual-energy X-ray absorptiometry (DEXA). The attenuation of two X-rays with different energy levels is measured. The BMC can be calculated
from the absorption of each beam by bone.
To obtain density information, the BMC is adjusted for the projected area of the region scanned, which is measured by the machine. In this way, the areal bone mineral
density (aBMD) is calculated. However, because DEXA is a two-dimensional imaging
technology and does not measure depth of bone, it systematically overestimates density
for taller children compared with their peers [51]. The unit of aBMD is mass per area
(g/cm2 ).
To provide true measure of density, volumetric bone mineral density (vBMD) is defined.
Other modalities than X-ray should be used to define to measure vBMD. A computed
12
tomography scan provides the necessary depth information. Or, a relatively new advancement in bone imaging is peripheral quantitative computed tomography (pQCT).
It provides three dimensional images of distal bone locations such as the lower arm and
lower leg [24]. The unit of vBMD is mass per volume (g/cm3 ).
From now on, when mentioning bone mineral density (BMD), there is referred to true
bone mineral density or volumetric bone mineral density.
3.1.2
Conversion between BMC, aBMD and vBMD
In clinical practice, BMC and aBMD are used. This study is aimed at calculating
differences in vBMD. To be able to compare the different measures of density, two
techniques are used.
Calculate BMC from vBMD
From the finite element model, virtual X-ray image could be created with tools as
pyvXRAY [52]. The images are generated by creating a bounding box around the 3D
model of the femur and meshing this box. Next, the density is projected from the 3D
model to the bounding box mesh. The two dimensional density information is obtained
by summation of the values along each coordinate direction of the box. These images
can then be analysed with software to measure BMC or aBMD.
Density images of the finite element model shown in this study are created by this
technique. However, since a major advantage of this research is the three-dimensional
density information, another technique is preferred to express densities
Calculate vBMD from BMC and BMD
In literature concerning the density of the femur, a region of interest which is very often
reported is the femoral neck. As a majority of the research is based on clinical data
measured by DEXA, BMC and aBMD are reported instead of vBMD.
Figure 3.1: Femoral neck and geometric properties
13
Lu et al [53] proposed a method to calculate the vBMD from the BMC for the femoral
neck. It is assumed that this region approximates a cylinder, so vBMD can be calulated
as:
vBM D =
BM C
!2
D
π
·h
2
(3.1)
With r the radius of the femoral neck and h the height of the femoral neck as shown
in figure 3.1. h is depending on the manufacturer’s scanner default. For DEXA scans
made by a hologic scanner, this value equals 1.512cm [54]. The radius r is depending on
the size of the scanned femur and is rarely reported in research. However, if both aBMD
BM C
The
and BMC are reported, the radius could be estimated: aBM D is defined as
A
area A is measured by the scanner and is the area of the projected femoral neck in the
direction of the X-rays.
aBM D =
BM C
BM C
= Rh
A
2 0 f (x)dx
(3.2)
With the X-axis defined as the axis of the femoral neck and f (x) the curve of the femoral
neck. As scanners report area A and height h, an approximation could be made of the
value f (c) with c a point between 0 and h. Now: A = 2·f (c)·h. Value f (c) is considered
as the average radius of the femoral neck and approximates r. Given this information,
the vBMD could be calculated as:
vBM Da =
BM C
=
!2
D
π
·h
π
2
BM C
BM C
2 · h · aBM D
=
!2
4 · aBM D2 · h
π · BM C
(3.3)
·h
As the average radius of the femoral neck is estimated, another technique is experimented to have a better estimation of the femoral neck volume. It is assumed that the
femoral neck is symmetric around its axis. Or, in other words, that the unknown depth
information d = 2 · raverage could be estimated. In this way:
A=
BM C
aBM D
(3.4)
A
h
(3.5)
d=
vBM Db =
BM C
BM C
=
=
A·d
A
A
h
14
BM C · h
aBM D2 · h
!2 =
BM C
BM C
aBM D
(3.6)
Experiments calculating the vBMD using both techniques are done for research which
repots BMC, aBMD and vBMD. The first technique (vBM Da ) reports higher densities
than the second technique (vBM Db ) since it is a factor 4/π larger. The calculated
vBM Da differ less than 2.5% with reported vBMD. This rather indicates that the
reported vBMD is calculated under the assumption of a cylindrical femoral neck than
prooving the accuracy of the formula. By knowledge of the author, no studies report
BMC and aBMD by a DEXA scan and vBMD by a three-dimensional technique. No
verification could be performed.
As the cylindrical assumption and vBM Da provide a good approximation of the true
geometry according to Sievanen [55], the relation between BMC, aBMD and vBMD for
the femoral neck is used.
3.2
Lisbon model
Many mathematical models of bone remodeling are proposed. Usually these models
assume bone to be a linear elastic material and consider changes in bone density as a
function of a local mechanical stimulus as strain, stress or strain energy density. The
Lisbon model, introduced by Fernades et al [56] is based on maintaining a homeostatic
state of stress/strain/strain energy [57].
Julius Wolff proposed his law of bone transformation, from which follows that the trabecular structure of cancellous bone adapts functionally to the loading environment [58].
The Lisbon remodeling model makes use of this law. It assumes that bone is able to
adapt itself in order to attain the stiffest structure for a given set of loads, while taking
into account biological cost parameters that controls total bone mass. The model relies
on the coupling of two scales, the micro (trabeculae) and macro (bone).
3.2.1
Microscale: the unit cell
The closed unit cell forms the essence of the model and is considered as a cubic with a
prismatic hole. The dimensions of the hole are given by the parameters a1 , a2 and a3 .
Further, an orientation of the unit cell is given by the Euler angles θ = [θ1 θ2 θ3 ]. This is
depicted in figure 3.2. The relative density of the unit cell is stated as µ = 1 − a1 a2 a3 .
With a periodic repetition of this unit cell, the material model is obtained. Consequently,
bone is characterized at each point by a periodic microstructure, where the geometric
cell parameters define the relative density and orthotropy level, and by a well defined
orientation.
3.2.2
Macroscale: bone tissue
On a macroscale, there are two types of tissue, which are biologically identical. The
difference is in how the microstructure is arranged. Trabecular bone is naturally porous
with a variable density, while cortical bone is denser. Assuming that trabecular bone
has same material properties as cortical bone, the remodeling model can predict the
macroscopic type of bone tissue based on the microscale. Cortical bone corresponds
with high relative densities µ and is considered as the base material. Lower relative
15
Figure 3.2: Material model for bone. Adopted from Fernandes et al. [59]
densities are considered as trabecular bone. Since density is a continuous function, a
threshold could distinguish the tissues. However, setting a threshold is according to the
author not useful and behind the scope of this text.
3.2.3
Elastic properties: coupling of scales
Both scales are coupled by the theory of homogenization [60], which is a rigorous mathematical theory which makes the bone model computationally treatable. It is assumed
that the apparent material properties of the base material are a periodic repetition of
the microstructure. A homogeneous base material is obtained in the limit of a microscopic cell size reduced to zero. For a more detailed description of the mathematics, one
is encouraged to read the original papers [56] [61].
3.2.4
Optimisation
The elastic properties are optimized as a minimization of the structural compliance
(i.e. the inverse of the structural stiffness) with respect to the design parameters (a
and θ). The obtained stiffest is considered as the mechanical advantage. However, the
structural stiffness cannot change infinite and is constrained. This is the metabolic cost
of bone apposition. It takes into account several biological factors such as age, disease
or hormonal status. The optimization problem is in fact a tradeoff between mechanical
advantage and a metabolic cost.
The optimal conditions could be stated with respect to each of the two model parameters (a and θ), regarding the optimal density and the optimal orientation of the bone
elements. The goal of this work is to investigate the change in bone distribution; the
strength of it is disregarded. For this reason, no optimization with respect to θ is per16
formed. The analytical problem is solved with the Lagrangian method. In optimal
condition, the remodeling law is stated as:
NC
X
P =1
!
H
∂E
∂µm
ijkl
αp
ekl (up )ei j(up ) − k
=0
∂a
∂a
(3.7)
The first term is the mechanical advantage, constricted to the metabolic cost represented
by the second term. E are the homogenized elastic properties. Components of the strain
fields eij en ekl are dependent of the set of displacement fields up. The mechanical
advantage (first term) is the sum over the p loading conditions. Each loading condition
has a weigh αp . The metabolic cost is dependent of the change of relative density µ.
k and m are parameters dependent on the individual (cfr. infra). Model parameter a
is considered constant within each finite element. Calculation of the optimal condition
independently for each element occurs in different steps. Iteration over steps 2 to 4
occurs.
1. An initial density is assumed
2. Homogenised elastic properties (E) for given density pattern.
3. Displacement (u) to the applied loads in a finite element approximation
4. New density pattern
3.3
Subject specificity
3.3.1
Finite element model
Kerner et al. [62] suggested that prediction of subject-specific bone remodeling processes
requires modeling of the subject-specific geometry of the femur. The use of individualized FE models is now customary when analyzing the bone remodeling processes.
The geometry of the proximal femur is created based on medical scans. To be able
to do a correct segmentation of the bone mass, a CT scan is needed. Use of other
modalities like MRI or DXA will lead to a very inaccurate geometry. Moreover, it is
not possible to subtract an adequate density pattern with the latter. The advantages
of using CT images could be explained by the higher radiation dose (3 mSv). On the
other hand, the higher radiation dose implies a higher risk, especially for children [63].
For this reason, radiologists are very reluctant to use CT modalities. The CT images
used in this research are from the University hospital Southampton (United Kingdom)
and University hospital Leuven (Belgium).
The subject of the CT scans is a male of 7 years old, 128 centimeters tall and has a
mass of 31 kilogram. The pathology, a tumor in the upper leg does not affect the bone
mass. Moreover, the tumor is distally located, while the proximal femur is the research
objective.
The data are acquired using Siemens SOMATOM Definition Flash computed tomography scan. The scan has a slice thickness of 1 mm in the axial direction. A pixel
size of 0.346 mm is automatically computed accounting the present image resolution
17
which equals 512 x 512 pixels. The DICOM images generated during the CT scan are
processed using Mimics software (Materialise, Leuven). Mimics uses 2D cross-sectional
medical images to construct 3D models, which can then be directly used for creating
the finite element model. This process is done in several steps.
Segmentation of CT images
The first step of converting anatomical data from images to 3D models is segmentation.
During this process, the structure of interest is indicated in the sliced image data.
Accurate segmentation is important in order to extract meaningful information from
images.
Thresholding is used to separate the bone from the other tissue in the scan. Pixels
with similar grayvalues (GV) and therefore also similar material densities, are grouped
together to create a mask. A lower limit of 1325 GV is used. This is slightly higher
than the predefined value of the software of 1250 GV to separate bone. Since compact
bone is the material with the highest density of the scan, no upper limit is used.
The result of the thresholding is a mask collecting all pixels with grayvalues above the
selected limit. Besides the pixels belonging to the femoral bone, also other pixels are
included such as the elements of the pelvic bone and floating pixels. The Region Growing
tool is used to split the segmentation into separate objects, each consisting of connected
points.
To fill internal gaps of the mask, the cavity fill function is used. However, the tool is
in this case not able to get rid of all internal holes, so some other operations are used.
Polylines are computed for the mask. The calculated polylines are the high resolution
segmentation contours identical to how they will be calculated to create the 3D object.
Hence, the quality of the segmentation will not be affected by this operation. By filling
every polyline, a mask without cavities is created.
Manual editing is done to eliminate noisy pixels and artefacts. In order not to adapt
contours in such a way that they violate the entity of the scan, the LiveWire tool is
used. Points lying at the boundaries of an object are indicated. Based on this information, the mask is edit following the exact object contours according to the gradient
magnitude.
From the final pixel mask, a 3D voxel mask is calculated using custom settings. Grayvalue interpolation uses the interpolation of grayvalues in the axial direction to expand
the image in the third dimension. It has the advantage over contour interpolation that
it takes into account the partial Volume effect. It gives a lot of detail and the dimensions
are correct [64]. This method could only be used because the slice thickness and the
slice distance are equal. A last feature used to create an optimal geometry is the shell
reduction, tom remove small inclusions and keeping only the largest shell.
Surface Mesh
The created 3D model is separately divided into triangular elements and nodes with 3Matic software (Materialise NV, Leuven) to generate a Standard Triangulation Language
(STL) file. To increase and optimize the quality of triangles, the STL file is remeshed.
18
The process for remeshing is divided in three big steps: smoothing the model, reducing
the number of triangles, and optimizing quality of the triangles.
First smoothing is performed to remove sharp edges to avoid unwanted stress risers in
finite element analysis. Also noise and the amount of detail of the femur are reduced
by conservatively smoothening it without compromising the faithfulness of the model.
A 1st order Laplacian is used with a smooth factor of 0.75. Compensation is used to
counteract shrinking that might occur as a result of the smoothing algorithm.
The created model contains a large number of triangular elements with different sizes.
To increase the calculation speed during analysis, the triangles are reduced. If during the
reducing process, two triangles are replaced by one triangle, the position might change
a bit. By selecting a maximum deviation allowed between the original surface and the
new one, the geometrical error is controlled. A rule of thumb is to use 1/8 of the pixel
size to maintain accuracy between scanner data and models. The scan resolution is 0.35
m, so the geometrical error is set to 0.044. The default flip threshold angle of 15 is
kept.
To improve the quality of the model, they are also resized and reshaped with the auto
remesh function. The shape measure Height/Base is selected as indication of the quality.
The value is set to 0.3, since triangles with a lower quality than this, will not import
into FEA packages [64]. The allowed geometrical error for auto remesh, is also set
to 0.044. The mesh still consists of group of small triangles. These are removed by
using the quality preserving reduce triangles operation with the same setting as the first
reduction operation. The result of the previous steps is an optimized surface mesh. This
is exported as a point cloud file, with the output format ASCII. In this file, the surface
is represented by X, Y and Z coordinates of the nodes.
Solid
The next step is to create a solid from the point cloud. This is realized with Solidworks
software, in particular with the Scan to 3D module. First, the Mesh Prep Wizard
prepares and cleans up point cloud files. The wizard reproduces the mesh feature as
created with 3-Matic, from which the solid model will be created. In this operation,
all the parameters are kept to the maximum quality value to keep the original mesh
properties. Afterwards, the Surface Wizard tool is used to automatically create the 3D
CAD geometry. This automatic creation is suggested for anatomical shapes [65]. Due
to smoothing, the bottom of the femur is rounded and not flat anymore. If boundary
conditions are applied at this section, it leads to stress concentrations. For this reason,
1 mm of the distal part is cut. This results in a flat bottom surface. The final geometry
consists of 1136 faces, which is exported as a parasolid file.
Mesh
The final step in the creation of a subject-specific finite element model of the proximal
femur is the creation of a volume mesh. This is realized in finite element software
Abaqus. This is done in three steps: selecting the type of elements, creating seeds and
finally meshing the whole instance. Various elements are available in the FE libraries,
19
with specific characteristics: first-order or second-order, full or reduced integration and
hexahedral or tetrahedral shaped elements.
Linear interpolation (first-order) elements are usually overly stiff. They could be used
in general cases in combination with a fine mesh. Moreover, they suffer less from mesh
distortion, which could lead to inaccurate deformations. That is the reason that linear
elements are preferred in deformation simulations. Quadratic interpolation (secondorder) elements provide higher accuracy than linear elements for smooth problems that
do not involve severe element distortions. Nevertheless, these advantages are at the
cost of an increased computational complexity. According to Ramos [66] for proximal
femur meshes with the same number of elements, the results between first- and second
order tetrahedral meshes did not produce significantly different results. The use of use
of tetrahedral quadratic elements in the simulation of the proximal femur is therefore
questionable, increasing unnecessary computational effort.
The default approach is using of tetrahedral elements. Tetrahedral elements are geometrically versatile. It is very convenient to mesh a complex shape with triangles or
tetrahedral. Consequently tetrahedral meshing can be more easily automated, so it has
been the approach of choice to date in anatomical finite element modeling [67]. According to the study of Ramos [66] for the simplified proximal femur, tetrahedral first-order
elements allowed results more closely to theoretical ones. On the other hand, hexahedral second-order elements seemed to be more stable and less influenced to the degree
of refinement of the mesh.
Continuum 3 dimensional 4 node elements (C3D4) are chosen because of lower computational expenses and the automated approach. Nevertheless, C3D8R elements would
also have been a good choice.
The use of C3D4 (but also C3D8R) has another advantage. The remodeling algorithm
used, defines integration points to compute the simulations. (cfr. supra) Variables of an
element as strain or density are considered to be in this integration point. Using C3D4
elements, the integration point is the same point as the centroid of the element. This
avoids unnecessary interpolation.
Several models with different mesh refinements need to be created to select an optimal
mesh. At each model, seeds are automatically placed over the whole instance based
on an approximate edge length. Small geometric features should also be represented
adequately, so a denser mesh is needed in these regions. With a non-uniform mesh, this
could be realized without the need to increase the global mesh size and the computational effort. Seeds are created denser at curvatures with the curvature control function.
Finally, the meshes are created from the seeded instances.
Convergence test
The choice for C3D4 elements is at the condition of an adequate refined mesh. To
ensure accurate results, mesh convergence tests are performed. The numerical solution
provided by the finite element model will tend toward a unique value as the mesh
density is increased. But, the computer resources required increase as well with the
mesh refinement. The mesh is said to be converged when further mesh refinement
produces a negligible change in the solution.
20
The convergence tests are performed for a simplified loading condition. The greatest
load of the simulation is approximately 3000N and occurs as a hip contact force during
counter movement jump. This load is applied in combination with the non-displacement
in three dimensions boundary condition at the bottom of the femur (cfr. infra).
Convergence is checked using three different solution variables. Maximum displacement,
maximum Von Mises stress and total strain energy. The resulting data points are plotted
and a two-term power series given by y = a + bxc is fit through the data points.
To quantify the convergence, the derivative of the fitted function is calculated with
respect to number of nodes. This function measures the sensitivity to change of the
inspected variable (displacement, stress or energy) determined by the independent variable ‘number of nodes’. If the instantaneous rate of change is less than 1 percent, the
change is negligible and the solution is considered converged.
The maximum displacement of the nodes of the model with respect to the number of
nodes is plot in figure 3.3. It could be noticed that the variable converges. The immediate
change in displacement is always less than 1 percent for the considered number of nodes,
so no criterion for the number of nodes arises for this variable.
Figure 3.3: Upper: Maximum nodal displacement plotted for different number of nodes.
Fit with a power series. Lower: Change in maximum displacement with respect to the
number of nodes of the model.
In figure 3.4, the maximum Von Mises stress of the model is plotted with respect to
the number of nodes. The power series does not smoothly capture the data and some
oscillations at the start are noticed. A possible explanation is the type of elements
used. The element exhibits slow convergence with mesh refinement [68]. Where C3D4
elements are good in capturing displacements, the element type is less stable in capturing
stress, which explains the oscillation. However, the fitted curve is clearly converging.
The instantaneous change of the curve is less than 1 percent if the number of nodes is
greater than 10065.
21
Figure 3.4: Upper: Maximum nodal Von Mises stress plotted for different number of
nodes. Fit with a power series. Lower: Change in maximum Von Mises stress with
respect to the number of nodes.
The maximum displacement and stress values are local measures, meaning that this value
occurs at a local point, and does not apply over a large region. Better is to use variables
related to the whole model, as the total strain energy [69]. Strain energy is the energy
stored by the model undergoing deformation and defined as U = 21 V σ where σ is stress,
is strain and V is volume. So, it takes both the displacement and the stress variable
into account. The total strain energy of the whole model is plotted versus the number
of nodes in figure 3.5. The fitted curve shows convergence. The instantaneous change
of the curve is less than 1 percent if the number of nodes is greater than 27129.
22
Figure 3.5: Upper: Total strain energy for the model plotted for different number of
nodes. Fit with a power series. Lower: Change in total strain energy with respect to
the number of nodes.
As a conclusion of the convergence tests, a mesh refinement of 28732 nodes is sufficient
to ensure that the solutions from the finite element negligible difference with the exact
numerical solution. The final FE model has an approximate average edge length of
1.25mm. It consists of 28732 nodes and 145051 elements. Since each node has three
degrees of freedom, the whole model consists of 86196 degrees of freedom.
3.3.2
Material Assignment
Material properties
The CT images consist of grayvalues, which is the attenuation of the X-ray by the tissue.
This means, that it is also a measure of the density of each voxel. A relationship between
gray scale and material density is created. The histogram of the grayvalues is depicted
in figure 3.6.
Figure 3.6: Histogram of the grayvalues, plotting the frequency of appareance of the
grayvalues.
23
To assign the material properties to the model, the finite element meshes are imported
into Mimics again and densities are assigned by relating the grayvalues from the CTimage to apparent bone mineral density. Gupta et al.[70] describes a linear relationship
in the grayvalues and density using air and compact bone as reference bone. However,
it is more accurate to assume a linear relation within the bone and pick reference points
inside the bone, similar to Bitsakos et al. [71]. The first reference point to calibrate the
curve is the grayvalue of trabecular bone with lowest measured density. A grayvalue
of 1133 is measured and corresponds with highly porotic trabecular bone which has a
minimal density of 0.1g/cm3 [72] [73]. The second point was the CT gray value of dense
cortical bone. The grayvalue measured in the cortical layer of the femoral shaft equals
approximately 2813. In children, the density of compact bone is lower than adults and
changes with age. Högler [74] describes the change of cortical bone density and age based
on clinical data. For the the subject of the images, the apparent density is 1.01 g/cm3 .
The apparent density at any point in the bone was obtained by linear interpolation of
CT gray values and given by the following relationship:
µ = −0.5137 + 0.0005467GV
(3.8)
Ideally, the size of the mesh elements would have an average edge length similar to the
CT in-plane resolution. Each pixel in the scan would correspond approximately with one
element of the model, allowing for accurate representation of bone material properties.
In this case the average edge length should be around 0.35 mm, which corresponds
with a mesh of more than 200000 nodes. Regarding the computational effort, this is
not advantageous. The material properties are calculated from interpolated grayvalues
instead of the real values. This results in a blurring of the cortical bone, with a lower
density and a thicker border.
Figure 3.7: The model with assigned materials based on a linear relationship with
grayvalues. Rainbow spectrum, blue corresponds with low grayvalue, red with high
grayvalue.
The range of apparent densities is not continuous, but discretized. A continuous range
is practically not possible and would also be not meaningful, since the grayvalues are
also a discretized set of values. The apparent densities in the model range from 0, 01
g/cm3 to 1.18 g/cm3 and are divided in 132 equally spaced intervals. The histogram of
the assigned materials is showed in figure 3.8. The extreme lower and upper values are
24
biologically less realistic since they correlate with respectively non-bone and bone which
is more dense than is expected in children. Moreover, these extreme values are assigned
to only a couple of elements. These low values occur in the model in circular patterns
around the femur head and the greater trochanter as depicted in figure 3.7. Besides,
they appear only at a very thin layer at the outside of the model. It can be concluded
that they are a consequence to some inaccuracies of the mask due to smoothing and
interpolation in the axial direction. All pixels with densities above 1.1 g/cm3 and under
0.05 g/cm3 together make less than 2.5% of total pixels. On the basis of frequency of
appearing, the elements outside these limits are probably an error of the scan modality
or the linear interpolation curve. To preserve real-to-nature results, a lower limit of
0.056 is set and an upper limit of 1.1 g/cm3 . Values outside these limits are set to the
respectively minimal or maximal value. This correction occurs for 2.5 % of the elements.
The resulting number of equally spaced intervals is reduced to 100 and are depicted in
figure 3.8.
Figure 3.8: Histogram of the discretized densities, plotting the frequency of appareance
of the densities.
As an intrinsic property of the Lisbon Remodeling model, it is assumed that trabecular
bone tissue has the mechanical properties of compact bone. The base material, which is
the true mineralized tissue with a relative density of 1, is assigned a Young’s modulus of
20 GPa and a Poisson’s ratio of 0.3 [75]. For lower relative densities, the bone material
is considered to be linear elastic.
Elements to nodes
The material properties as calculated in the previous section are assigned to elements.
However, in this study, an optimisation for elements is prefered. The material properties
should be interpolated from the elements to the nodes. The density of each node is defined as a weighted average of the surrounding elements with the volume of the elements
as weights. The relation between nodes and elements is defined as follows:
Pn
µinode
=
j
j
j=1 (µelement · Velement )
Pn
j
j=1 (Velement )
(3.9)
With µ the density at node i or element j, n the number of elements adjacent to node
i and V the undeformed elemental volume.
25
3.3.3
Constraints
Constraints vary between studies and are a whole object of study [76]. Common methods
include constraining of the whole femur in at least six degrees of freedom constrained
by two or three nodes in the mid-diaphysis. In that case, each node is constrained in
maximal three degrees of freedom: the three displacement directions.
(a)
(b)
(c)
Figure 3.9: Investigated constraints. (a) Three nodes fully constrained (b) All nodes
constrained in the axial direction. Two nodes constrained in medial/lateral direction
and two nodes constrained in posterior/anterior direction (circled). (c) All nodes fully
constrained
Some experiments are performed with the simplified loading condition as described in the
section ‘convergence tests’. Only the highest load is applied, the hip contact force. This
loading is combined with three different constraints. First, only three nodes are fully
constrained. The second set-up consists of all nodes of the ground surface constrained
in the axial direction. The movement of two nodes is constrained in the medial/lateral
direction and the movement of two other nodes is constrained in the posterior/anterior
direction. In the last set up all nodes of the ground surface are fully constrained in three
directions. The constraints are showed in figure 3.9.
Running the analysis with three different constraints, results in three different stress
distributions of the bottom surface which are shown in figure 3.10. In the first two
setups with only two nodes constrained in a direction, a higher stress is noticed around
these nodes. These stresses are physiologically unrealistic. The point of splitting the
femur in a proximal and distal part is arbitrary chosen. There is no biological reason to
assume higher stresses at these points.
In this study, all 115 nodes at the distal end of the model are constrained with a nondisplacement condition in three dimensions. The number of degrees of freedom of the
model reduces from 86 196 to 85 851.
3.3.4
Musculoskeletal loading
Results of several studies suggest that the loading configuration of the FE model does
play an important role in the outcome of the remodeling simulation [71]. A description
of the physiological muscle loading that is as complete as possible is included, based on
experimental values.
26
(a)
(b)
(c)
Figure 3.10: Stress distributions at bottom for different constraints: (a) Three nodes
fully constrained (b) All nodes constrained in the axial direction. Two nodes constrained
in medial/lateral direction and two nodes constrained in posterior/anterior direction
(circled). (c) All nodes fully constrained
Experimental data
Experimental data of muscle and reaction forces are calculated by Professor Filipa João
of the Faculty of Human Kinetics, University of Lisbon. In the experiments participates
a typically developing male subject of the aimed population, as described in the introduction of section ‘methods’. The subject is 9 years old, 131 centimeters tall and has a
mass of 26 kilogram. 3D gait analysis, recording kinematics and ground reaction forces
are performed to provide the input experimental data for the musculoskeletal model.
During subject performing physical activity, reflective markers track the motion of the
subject with Qualysis Track Manager software while two force plates (Kistler) measure
the ground contact force. The motion analysis includes the extraction of the motion and
tracking file to prepare as input for OpenSim. This is is done with the MatLab toolbox
MOtoNMS v2.1 which is freely available online.
The musculoskeletal model OpenSim v3.2 presented by Delp et al [77], is used in the
calculation of kinematics and inverse dynamics. The generic model is the gait 2392
computer model of the human musculoskeletal system. Based on the markers and the
measured properties of the subject, the generic model with normal bone geometry is
scaled. Joint moments are calculated with the inverse dynamics tool in OpenSim, based
on the respective ground reaction forces and gait kinematics. The inverse dynamics
algorithm calculates only the muscle forces to realize the movement of the model. However, the greatest part of the muscle forces is exerted in compressing the bones. So,
a static optimization algorithm in OpenSim is used to estimate the underlying muscle
forces required to balance the joint moments, while minimizing the global amount of
muscle activation.
To calculate the resultant joint loads, the JointReaction algorithm in OpenSim is used.
The algorithm calculates the joint forces and moments transferred between consecutive
bodies as a result of all loads acting on the model. The resultant joint load consists of
the joint moments and the compressive force which represents the sum of contact forces
between the consecutive bodies articular surfaces and all ligament forces crossing the
joint. So, the joint load is only an internal load carried by the structure of the joint
[78].
27
Muscle activation patterns of 92 actuators are computed over one cycle of activity. Although the loading conditions aimed at are as close to the physiological case as possible,
only the relevant muscles are taken into account into the calculations. Three criterions
are used to select if the muscles are relevant: The muscles need to cross the hip joint,
attach at the proximal half of the femur in OpenSim software and have a minimal magnitude in at least one of the used loading configurations of 2.5% of the bodyweight (which
equals 8 N). The muscles used in the calculations are depicted in figure 3.11 and are the
following: Gluteus Minimus 1, Gluteus Minimus 2, Gluteus Minimus 3, Gluteus Medius
1, Gluteus Medius 2, Gluteus Medius 3, Gluteus Maximus 1, Gluteus Maximus 2, Iliascus, Psoas, Quadratus Femoris, Gemellus, Piriformis, Pectineus and Adductor Brevis.
Muscles which satisfy the first and second criterions but have a negligible magnitude
are the Gluteus Maximus 3 and the Adductor Magnus. An overview of the magnitudes
of the muscle forces is attached in Appendix A. All muscle forces have intensities very
similar to what is reported in other studies involving prepubertal children [79].
Figure 3.11: Muscles taken into account in the remodeling model.
During the experiments, three types of physical activities are performed: gait, countermovement jumps and running. To obtain a representation of the complete activity
cycle, physiological loading is approximated with a superposition of different loading
cases.
The first type of physical activity consists of walking barefoot at a self-selected speed.
Three phases of the gait cycle are selected as loading cases. Specifically, the loading of
the femur at 10%, 30% and 45% of the gait cycle are crucial timeframes, according to
Bitsakos [71]. These timeframes match respectively with the maximal weight acceptance,
midstance and push-off and are indicated in figure 3.12. They match with the peaks of
the ground reaction force and the minimum in between. The experimental data of the
ground reaction forces are plotted in figure 3.13 with the selected timeframes marked
by a grey line.
The second type of physical activity is running. It should be mentioned that due to a
lack of experimental information another subject with similar characteristics (34 kg and
143 cm) is observed than during the other types of physical activities used in this study.
Muscle strength in the lower limb could be scaled with following scaling law proposed
and proven to give accurate results by Correa [80]:
scaled
generic
Fmax
= Fmax
·
28
M scaled lscaled
·
M generic lgeneric
(3.10)
Figure 3.12: A typical gaitcycle and important timeframes. Heel-Contact (HC), Maximal Weight Acceptance (MWA), Midstance (MS), Push-Off (PO) and Toe-Off (TO)
Figure 3.13: The experimental gaitcycle with vertical component of ground reaction
forces plotted with respect to time.
l is the scaled muscle tendon length and M the total body mass. This equation can
be simplified by assuming, that muscle tendon length is proportional to body length.
Invoking this assumption gives the following relation, which is used to scale the muscle
force for this subject with L body length:
scaled
generic
Fmax
= Fmax
·
M scaled Lscaled
·
M generic Lgeneric
(3.11)
The hip contact force is depending on the scaled muscle strength, but also on the
bodyweight. For this reason, the HCF is scaled with the relation:
scaled
generic
HCFmax
= HCFmax
·(
M scaled 2 Lscaled
) · generic
M generic
L
(3.12)
A typical evolution of the ground reaction force during the activity cycle is plotted in
figure 3.14. Two peaks could be noticed. The first is the impact peak and results from
the collision of the body with the ground. The second peak is called the active peak and is
related to the active response of the musculoskeletal system to the experienced collision.
29
Figure 3.14: A typical runcycle. Two peaks are noticed: the impact peak and the active
peak. Adopted from [81]
These peaks are important characteristics of the activity cycle [82] and since they both
have a maximal magnitude, but are different in direction, they are also important for
the bone remodeling. The ground reaction force of the experimental data is plotted in
figure 3.15. Here, the impact peak is not clearly visible. This might be due to the poor
time resolution of the data of the ground reaction force. The timeframe of the impact
peak could be localized by looking at the hip contact forces in figure 3.16. A maximal
hip contact force indicates the impact peak.
Figure 3.15: Runcycle of the studied subject. The impact peak is not clearly visible.
Vertical component of ground reaction force plotted versus time.
30
Figure 3.16: Hip contact forces plotted versus time during the runcycle. The impact
peak could be localized.
Activity
Gait
Stance
Jump
Run
Label
gait1
gait2
gait3
stance
jump1
jump2
run1
run2
run3
Timeframe
Maximal Weight acceptance
Midstance
Push-off
Balanced standing
Take off
Landing
Impact peak
Active peak
Push-off
Table 3.1: Types of physical activity, the selected timeframes and the label of the
timeframe.
After the loading of the muscles during the active peak, there is still a long phase until
toe-off where the body gets propelled. To have a more complete representation of the
activity cycle, a third timeframe is selected during this push-off phase. This timeframe is
selected exactly in between the active peak and toe-off. The direction of the hip contact
force is different than during the two selected peaks: the Z and X component of the HCF
are approximately constant, while the Y component is significantly smaller. The HCF
of the impact peak (run 1), is of the same order as the impact of the countermovement
jump (jump 2). The HCF during muscle loading before toe-off (run 3) is of comparable
magnitude to the HCF during the muscle loading before toe-off of jumping (jump 1).
This indicates that the scaling law is a good approximation.
A third type of physical activity is the countermovement jump. Two moments in activity
cycle are selected to use as loading condition: one during take-off and one during landing,
both at the greatest magnitude of ground reaction force as could be seen in figure 3.17. In
the same experimental set as the countermovement jump, a last type of physical activity
could be noticed: stance. The selected timeframe is selected during a constant ground
31
reaction force and also indicated in figure 3.17 as the first marked timeframe.
Figure 3.17: Jump activity cycle. Vertical component of ground reaction force plotted
versus time. Also the activity ’stance’ could be substracted.
All types of physical activity and the according timeframes are listed in table 3.1.
Match coordinate system
In the musculoskeletal model used, OpenSim, the global model coordinate system is fixed
with axes defined as follow: X-axis pointing anterior, Y- axis pointing superior and Zaxis pointing lateral. This is defined as CSOS . The software with which the model is
created with, Mimics, uses a different coordinate system. In mimics, the axes are defined
as: X-axis pointing lateral, Y-axis pointing posterior and Z-axis pointing superior. This
defined as CSF E . Moreover, the scale of both types of software is different: OpenSim
is defined in meter and Mimics uses millimeters. This is the first match that should be
made: between CSOS and CSF E
In OpenSim, different CS are defined. The first type is the global CS, fixed to the ground
and independent of movement of the model. This is defined as CSglobal(OS) . The second
type is a local reference frame attached to a body (e.g. femur or pelvis). This CS moves
is fixed with respect to the body. With respect to the global CS, it is dependent on
the movement of the model. It is defined as CSf emur(OS) . The two transformations are
summarized as follows:
CSglobal(OS) → CSf emur(OS) → CSF E
(3.13)
The first transformation results in data expressed in the reference frame attached to the
femur. OpenSim is able to do this transformation with internal calculations. For this
reason, only the results will be presented.
For the second transformation, the following technique is applied. First, the hip joint
center needs to be determined. This is done by wrapping a sphere around and fitting
it to the femur ball as shown in figure 3.18. The center of the sphere is defined as
32
Figure 3.18: A sphere (grey) is wrapped and fitted in the femoral head (red).
a reference point. This reference point is the origin of CSf emur(OS) . A translation
matches the origins. As mentioned before, the orientation of the axis in OpenSim and
finite element model is different. A rotation is applied. Further, the scale is changed.
The coordinates expressed in CSf emur(OS) are transformed into CSF E by the following
transformation matrix.

0
0


−1
0
−1
0
0
1
0.0624

0
0.01744 


0 −0.1415
0
0
(3.14)
1
This corresponds with a rotation of π/2 radials around the Y-axis and a rotation of
−π/2 around the X-axis to match the directions of both coordinate systems. Then,
the points are translated over a distance of (−0.020, −0.01744, −0.1415)m to match the
origins. Finally, the coordinates are multiplied by 1000 to match the scale.
Line of action
The line of action of the muscles forces is calculated as the connection of two points.
The start and end point are extracted of OpenSim. The coordinates are converted to
CSF E with the procedure described in ‘matching coordinate system’.
However, some muscles do not act in a straight line. They wrap around the bone and
make a curvature before they attach at the distal bone. In other words, there is a
difference in the anatomical and the effective attachment, as shown in figure 3.19. In
this study, three muscles have such an ‘effective attachment’: the Glut Max, Iliacus
and Psoas. But, these concerning muscles have no rigid fixation (ligamented) to the
bone at the position of ’effective attachment’. The muscle is just wrapped around the
bone or has a via point, so it is irrelevant for the bone remodeling model. However, it
influences the line of action, the direction of the load. In this situation the vector is
calculated with the anatomical attachment as start point and the effective attachment
as end point.
The method of morphing the femur as described in the next section is not used to define
the muscle line of action. This method could be used to match coordinates lying on the
femoral surface. However, transformation of the end points would introduce a significant
33
Figure 3.19: For a given muscle path, the anatomical (yellow dot) and the effective
(green dot) femoral attachments are represented, together with the associated muscle
direction (red arrow). Adopted from Modenese [83].
error. After all, these direction points are located on another bone than the femur, so
morphing would be senseless.
Morphing femur
The OpenSim musculoskeletal model is scaled based on body measurements of the concerning subject and affine transform scaling. Such schemes are good assumptions when
more accurate measurements are not available. This more simple approach accepts the
oversimplification of the isometric model, that all people are geometrically similar. But
the geometry is especially important in the target group of pre pubertal children, since
the bone does not have the full grown geometry yet. A CT scan of a subject of the
aimed population is possessed. A natural next step is to improve the precision of the
extracted data of the model by utilizing the available medical images. These contain
more detailed information about the bone shape and local deformities that cannot be
mimicked by the anthropometric scaling.
Specialised software exists to deal with this problem and match the bone shape of a
standard and a subject-specific model. Some experiments and trials are performed with
this software. No satisfactory results are obtained, due to the fact that the subject
specific proximal half of the femur is tried to match with a full femur standard model.
An alternative algorithm is developed.
A set of 6 source landmarks, i.e. on the OpenSim model, is created. The only available
known landmarks at the OpenSim model are those of the muscle attachments. So 6 of
the 15 muscles included attaching at different sides of the femur are selected: Gluteus
Minimus 1, Gluteus Maximus 1, Iliacus, Gemelus, Quadratus Femoris and Piriformis.
34
The corresponding spots are indicated on the target femur, i.e. the finite element model.
This is done manually making use of paper [84] and 3D [85] anatomy atlases and bony
landmarks extracted of the medical images.
The algorithm builds a transformation that fits iteratively the set of source and target
landmarks in a least-squares manner. The implementation of the algorithm is done in
Matlab and makes use of the matlabfunction iteratively closest point (ICP) implemented
by Jakob Wilm [86]. The algorithm constructs a linear transform in a rigid-body manner
(orthogonal rotation of unscaled object and translation). There are 3 degrees of freedom
associated with translation and 3 degrees of freedom associated with rotation.
Essentially, the performed procedure in the algorithm is as follows: for each landmark in
the source set, estimate a combination of rotation and translation using a mean squared
error cost function that will align best each source landmark to its target. Transform
the source landmarks using the constructed transformation. Iterate by revising the
transformation needed to minimize the distance from the source to the target landmark.
The resulting transformation matrix is:
0.997
0.0378
0.0624
−18.52
0.0358


0.0636
0.0999
0.0328
0.0305
0.998
6.88 


−2.94 
0
0

0

(3.15)
1
After the transformation, each point is projected onto the surface of the finite element
model via a normal weighted closest point matching.
Muscle Attachment
The next step is to attach muscles to the bone. To mimick physiological loading conditions, a muscle attachment area is defined. However, there is a great inter subject
variability considering the muscle allocation. Standard deviations, as a percentage of
the mean, are about 70% for attachment area [87]. On the other hand, applying a concentrated loading at the point attachment of the muscle line of action would result in
physiological unrealistic stress distributions.
The muscle attachment point is defined as the location of the mechanical centroid of
muscle lines of action. The coordinates are obtained as follows. First, the anatomical
attachment (cfr. figure 3.11) is extracted from OpenSim. This point is multiplied by
the transformationmatrix of the section ‘match coordinate system’. Afterwards, this
attachment point is multiplied by the transformationmatrix of section ‘morph femur’
to match shapes. The result is the attachment point expressed in CSF E . The area of
muscle attachment is defined with a manual procedure based on previously measured
physiological muscle attachment areas [84][88]. The attachment areas are depicted in
figure. The coordinates of the muscle attachment point and the areas are listed in
appendix A, including the steps of the calculations.
To distribute the load over the muscle area, the nodes of the selected surface are coupled.
This is done in the software Abaqus, which is used to calculate the remodeling of the
finite element model. These settings are similar to those of the specialized software for
35
this purpose. The surface-based coupling, couples the motion of a collection of nodes
on a surface to the motion of a reference point. The distributing coupling is used, so
that the motion of the surface nodes is constrained to the translation and rotation of
the reference point.
There are several ways to distribute the applied load over the coupled surface. Important
to take into account is that the remodeling model is configured to optimize the simulation
for nodes. This avoids a checkerboard pattern of densities. Therefore it is more accurate
to distribute the load over the nodes instead of the elements, since interpolation between
nodes and elements in the remodeling model is avoided.
A coupling in Abaqus is always defined as a coupling between nodes or recalculated
to a coupling between nodes [68]. If a coupling between elements is defined, Abaqus
calculates default weight factors for the elements (cfr. infra). If elements would be
coupled in Abaqus without any weight factor, the constraint is dependent of the mesh.
In a perfect uniform mesh, the coupling would be equally distributed over the elements.
In a non-uniform mesh as in this finite element model, the coupling is depending on the
element area. Loading distributed through a coupling dependent on mesh refinement
is physiological not realistic, so the coupling is related to nodes. A verification of the
default distrusting weight factors is done by Abaqus [89].
The muscle attachment surfaces are defined as an area, created as a collection of element
faces to represent the physiological case as close as possible (as depicted before in figure
3.19). To deal with this problem, Abaqus has an elegant method to distribute the
load uniformly over the nodes of the coupled element-based surface. A default weight
distribution is assigned to the coupled elements based on the tributary surface area at
each coupling node. Through this weight distribution, a load is distributed over the
uniformly constrained nodes of the surface, which is advantageous for the remodeling
model.
The loads of the experimental data are applied as a concentrated load at the calculated
point of attachment. The constraint distributes loads such that the resultants of the
forces (and moments) at the coupling nodes are equivalent to the forces and moments
at the reference node. An example of a coupled surface and the concentrated load is
showed in figure 3.20.
3.3.5
Hip contact force
The hip contact force (HCF) is the greatest load applied on the proximal femur since
this joint transfers the entire bodyweight to the leg. This makes accurate loading conditions especially important. The hip contact force is calculated as well with the inverse
dynamics analysis and the static optimization in OpenSim, as explained in the section
‘experimental data’ of the musculoskeletal loading chapter.
Point of peak load
The experimental data represents the HCF as a vector with magnitude and direction.
The point at the proximal femur where this load is applied needs to be calculated. This
is done by approximating the femur ball as a sphere. From the center of a sphere, a
36
Figure 3.20: Coupled surface with point of attachment of the concentrated load(yellow
cross). The coupling distributes the load over the surface.
vector is assumed with the same direction as the HCF. The intersection of the sphere
and the vector is calculated. However, since the sphere is only an approximation of the
femoral ball, this intersection point is not on the surface. The point is projected onto the
surface triangles via a normal-weighted closest point matching. This point represents
the peak load. This point of peak load is depending on physical activity. For every
timeframe of the activity cycle another point is calculated. The points of peak load are
summarized in Appendix C.
According to [90], the location of the peak pressure was found at the anterior–superior
aspect of the lateral roof where the cartilage thickness is greatest. This is in accordance
with the defined point of peak load as seen in figure 3.21.
Figure 3.21: Point of peak load for the different types of Physical Activity
Contact area
The HCF is distributed over the contact surface between hip and the femoral ball.
The area of this surface has been the topic of a considerable debate. In fact, contact
areas during a typical gait cycle have been predicted to range from 304mm2 to 2265mm2
[91][92]. Thus, this relatively large range, with the maximum reported contact area three
times larger than the minimum, suggests high variability among hip morphologies.
37
The potential area of contact is depending on anatomical parameters. An approximation
could be made based on measurements of the medical images. The weight bearing area is
related to several parameters, including the spherical sector angle [93], which is depicted
in figure [94]. The femoral head is considered as a sphere, in which a spherical sector
is defined by this angle. The cap of this sector is in contact with the pelvic bone and
defines the potential area of contact.
Figure 3.22: Definition of the spherical angle in the hip joint. Adapted from Bombelli
[94]
The spherical sector angle is determined in Mimics software by thresholding the maximum distance between both contact surfaces. The maximal distance as a condition for
contact is measured as 7.71 mm, which corresponds to a sphere with a diameter of 44.34
mm. The spherical angle in the coronal plane (upper left view of figure) is as 49.14
degrees. The area of the cap of the spherical sector is defined as 2π · r2 · (1 − cos(α)) with
α the spherical sector angle and r the radius of the sphere. The area as measured in
the coronal plane is 1068mm2 . The spherical angle in the sagital view is 70.98 degrees,
which corresponds to a cap surface of 2082 mm. Different angles in the two different
views means that the real shape is not a cap, but an irregular surface. The potential
contact area is calculated as an average of the two caps, which equals 1575mm2 .
Figure 3.23: The spherical area measured in the CT-images.
The contact area changes during movement. The contact area calculated in the previous
38
paragraph is the potential contact area. This is the area of the acetabular surface which
makes contact with the femoral ball during a type of physical activity. Only a portion
of the potential contact area is involved in each activity. Yoshida [90] calculated which
portion of the potential area is used. For walking, 79% of the total area is used. This
number is equal for fast walking or running. In this study, the final contact area for
walking and running is 1244mm2 . The timeframes of the activity cycle used involve
bending of the knees. Knee bending corresponds with 52% of the potential contact area
is used. This corresponds with a contact area of 819mm2 .
Load distribution
(a) Adopted from [91]
(b) Adopted from [90]
Figure 3.24: Stress distributions at the femoral head due to hip contact force. Rainbowspectrum red (highest) to blue (lowest) stress.
The contact force on this surface is chosen pointing towards the hip joint center. The
load could be applied onto the selected area in several ways. Since a force acts on a
surface, a natural reflex would be to apply the load as a pressure. However, a pressure
has no direction and works normal to each element surface. The femoral ball is not a
perfect sphere, so a summation of all forces on the elements would result in a different
direction than the direction of the experimental data. An alternative to pressure is the
use of a surface traction. Forces are transmitted between elements in contact. Although
this would be a good option, this introduces new assumptions. A surface traction is
expressed in units of stress (Pascal), while the load of the experimental data is given as
a force (unit: Newton). To calculate the surface traction, the force could be divided by
the total area. This makes the load on each element dependent on the element surface
area again. The option chosen in this research study makes use of the distributing
surface-based coupling of elements.
According to research with finite element models [90] [91], the amplitude of the distributed contact force diminishes in amplitude away from the pole. Also in vitro study
[95], reports on the distribution of the hip contact pressure in the loaded femoral head
using a pressure sensitive film in five cadaver hips. This study demonstrated that peak
pressures in the femoral head increases towards the peak load in all of the specimens.
Typical hip contact distributions of healthy subjects during gait are depicted in figure
3.24.
Experiments are performed with different coupling constraints. Weights are given to the
coupled nodes to diminish their relative importance away from the peak load. The first
weighting scheme is a linear decreasing weight distribution. The second is a quadratic
polynomial weight distribution. Results of these experiments are shown in figure 3.25.
39
(a) Linear decreasing weight distribution
(b) Quadratic weight distribution
Figure 3.25: Stress distributions at the femoral head due to hip contact force. Rainbowspectrum red (highest) to blue (lowest) stress.
The linear distribution is visually a quite good in accordance with the results of other
studies presented in figure. However, the peak load should have a higher weight to
increase the load at this point. Therefore, a cubic polynomial distribution with monotonically decreasing weight distribution is used which applies more weight to the points
close to the peak load and less to the outer points compared to the linear distribution,
as seen in figure 3.26. The cubic polynomial is given by:
wi = 1 − 3
ri
ro
!2
+2
ri
ro
!3
(3.16)
With wi the weight factor at location i, ri the distance at point i from the pole and ro
the maximal distance from the pole. The results of this stress distribution are plotted
on the femoral head is plotted in figure 3.27. This load distribution is qualitatively the
most similar to Yoshida and Russell 3.24 and is selected to use.
Figure 3.26: Weight distribution of a linear and a cubic weighting scheme. The cubic
polynomial give higher weights to the points closer to the pole and smaller weights to
the points further from the pole compared to the linear decreasing weights.
40
Figure 3.27: Femoral head with load distribution in a cubic distributed coupled surface.
3.4
Parameters of the remodeling model
To run the remodeling model, several parameters characteristic for the Lisbon remodeling model need to be adjusted. The mathematical and physiological meaning of these
parameters is explained in the section ‘Remodeling model’. The selected values are
discussed in this section.
3.4.1
General
One of the parameters is the number of iterations the model is run before convergence
could be estimated. To quantify the change, the objective function is monitored. When
the maximal change of the objective function is less than 0.1%, the iteration processed is
stopped. However, to obtain comparable results, all simulations concerning one investigated topic have the same number of iterations equal to that of the slowest convergence.
Another parameter which indicates the progression of the evolution is the change in
volume with respect to the previous iteration. Again, a maximal change of 0.1% is
accepted.
The iterations are performed with a fixed step s. Machado [96] performed a parametric
study to assess the sensitivity to the step length. According to the results, a small
step length (order 10−2 )leads to a slower convergence compared to a large step length
(order 101 ) but with a smoother evolution to the result. More iterations and therefore
more computational expenses are required to obtain the result. An intermediate step
length of 1 is chosen. Using the intermediate value, the need for a check of convergence
based on the objective function and change in volume is even strengthened. The limited
bone turnover rated, defined by parameter ζ is left at the default value of 0.25. This
maximum change in bone structure in a time step also indicates the need for a sufficient
number of iterations.
The model is selected to optimize with respect to the nodes. Parameters related to the
elements are assumed to be concentrated in the centroid of the element. The initial
bone density is established as the real density pattern as extracted from medical images
(cfr. ‘Materials’), unless stated differently (cfr ‘K and m’).
The optimization problem consists of two separated objectives, regarding the optimal
41
density and the optimal orientation of the bone elements. The goal of this work is to
investigate the change in bone distribution; the strength of it is disregarded. So, the
algorithm is run for optimal density only.
3.4.2
K and m
Even in the presence of identical loading environment the remodeling response may differ
from individual to individual. The model is calibrated to this inter individual biological
variability by means of the parameters k and m. Their major importance on the outcome
of the remodeling model explains the need for the following investigation.
The remodeling model is run under the impression of a non-active subject. This means
that the relative amount of weight bearing physical activity consists only of walking. No
intensive activities as running or walking are included. A uniform initial density equal
to the median of the range of real densities extracted from the medical scans. This
impartial value is selected to allow each element to change to lower or higher densities
with minimal cost. The algorithm is run for different parameters k and m. The resulting
density pattern of each combination of k and m is compared to the real densities of the
medical scan. The best match between the densities indicates an optimal combination
of parameters k and m for the subject.
Investigated values of parameter k are 0.00010, 0.00025, 0.00050, 0.00075, 0.00100,
0.000125, 0.00150, 0.00200, 0.00500 and 0.01000. Each parameter k is combined with
parameter m equaling the natural numbers ranging from 1 to 7. In total, 70 different combinations are inquired. The comparison between the real density values (scan)
and the calculated values (model) is based on a statistical analysis, similar to Quental
et al [97]. Five quantitative parameters are taken into account, complemented with a
qualitative visual inspection.
First of all, the mean and standard deviation of each simulation are calculated. To
investigate the connection between the densities, a correlation coefficient is included in
the analysis, given by:
Pn
¯ )
(µi − µsim
¯ )(µiCT − µCT
rsim/CT = pPn i=1i sim
P
n
¯ )2 i=1 (µiCT − µCT
¯ )2
i=1 (µsim − µsim
(3.17)
With µsim and µCT the density of node i of respectively the simulations and the CT scan,
µ̄ the mean density and n the number of nodes. The difference between corresponding
densities is expressed in absolute terms as:
∆µa = µisim − µiCT (3.18)
To take into account the whole model, the quadratic square of the sample is calculated.
To give more importance to the lower densities, a relative difference criterion as follows
is considered:
µi − µi sim
CT ∆µr = µiCT
42
(3.19)
Again, the root mean square of the relative difference takes into account the whole
sample. To objectivise a tradeoff between absolute and relative difference, Quental [97]
suggests to calculate an average error. This is done by normalizing the rms of the relative
and absolute errors with respect to the maximum value appearing in all simulations with
different k and m. The analysis is implemented in Matlab. The results are listed in table
3.2 and discussed in the chapter ’Results and Discussion’. The combination k = 0.0025
and m = 4 is considered as the best.
3.4.3
Load weights αp
αp is the load weight factor and indicates the relative frequency of each type of physical
activity. The sum of all αp is defined as α. Since it is a relative measure, the maximum
value of α is 1. For each type of physical activity, different loading conditions at several
timeframes of the activity cycle contribute to the total loading. As explained in the
section ‘musculoskeletal loading’, a superposition of the diverse load cases represents
the mechanical loading during the whole cycle. Each timeframe is thoroughly selected,
so it is estimated that the contribution of each timeframe is equally important. E.g. run
1, run 2 and run 3 always have an equal weight).
This definition based on the relative frequency is abstract and for that reason hard to
compare with other studies. For this reason, this parameter is redefined. First the total
time spent in physical activity of prepubertal children per day is defined. It is all activity
that influences (even slightly) bone density, including light (stance), moderate (walking)
and vigorous (run and jump) activity [98][99]. Time spent in sedentary activity (sitting,
lying) is not taken into account, because of the irrelevance for positive changes in bone
density. So, α is the sum of all activity that influences bone density. Rest (sedentary
activity) is defined as 1 − α, In this way, the relative frequency of physical activity and
rest sum to 1.
According to the study of Konstabel et al [100], European prepubertal boys spend
on average 368 light activity and 48 minutes moderate to vigourous activity. This is
slightly higher than numbers reported by Ridgers et al[101]. For this study, 400 minutes
per day spend on physical activity is estimated. This amount of time corresponds to
α = 1. Now a value of αp per minute can be defined: each minute spend in activity
equals αp = 1/400 = 0.0025min−1 . In this way, time is related to a parameter of the
remodeling model.
The total time α, could be devided over several types of physical activity as mentioned
before. It is also possible that the subject is less active than the average and spends for
example only 300 minutes in physical activity, which equals α = 300min·0.0025min− 1 =
0.75. In this case, rest equals 1 − α = 0.25 or 100 minutes. So, the sum of rest and
physical activity is always 400 minutes or α = 1.
43
K
m
CT-scan
∆mean
∆SD
Corr Coef
RMS err
RMS err
Av err
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.00010
0.00010
0.00010
0.00010
0.00010
0.00010
0.00010
1
2
3
4
5
6
7
0.2008
0.2008
0.2003
0.2007
0.2015
0.2024
0.2034
0.0769
0.0769
0.0774
0.0783
0.0793
0.0802
0.0809
0.5780
0.5780
0.5805
0.5812
0.5809
0.5800
0.5788
0.2546
0.2546
0.2540
0.2543
0.2549
0.2557
0.2566
0.5793
0.5793
0.5779
0.5785
0.5801
0.5821
0.5840
0.4919
0.4919
0.4906
0.4912
0.4925
0.4941
0.4958
0.00050
0.00050
0.00050
0.00050
0.00050
0.00050
0.00050
1
2
3
4
5
6
7
0.1728
0.1593
0.1596
0.1641
0.1695
0.1747
0.1794
0.0560
0.0504
0.0565
0.0638
0.0701
0.0751
0.0789
0.5997
0.6154
0.6267
0.6322
0.6336
0.6324
0.6297
0.2321
0.2209
0.2192
0.2215
0.2253
0.2294
0.2333
0.5259
0.4992
0.4958
0.5020
0.5116
0.5216
0.5311
0.4473
0.4250
0.4220
0.4270
0.4347
0.4430
0.4509
0.00100
0.00100
0.00100
0.00100
0.00100
0.00100
0.00100
1
2
3
4
5
6
7
0.1205
0.1025
0.1105
0.1227
0.1345
0.1449
0.1538
0.0039
0.0089
0.0296
0.0469
0.0600
0.0696
0.0768
0.5902
0.6272
0.6488
0.6598
0.6650
0.6665
0.6653
0.2099
0.1917
0.1869
0.1902
0.1966
0.2037
0.2105
0.4669
0.4212
0.4132
0.4246
0.4424
0.4610
0.4783
0.4002
0.3629
0.3550
0.3633
0.3773
0.3922
0.4063
0.00250
0.00250
0.00250
0.00250
0.00250
0.00250
0.00250
1
2
3
4
5
6
7
0.0193
0.0232
0.0051
0.0343
0.0598
0.0812
0.0990
0.0942
0.0510
0.0085
0.0231
0.0461
0.0630
0.0755
0.6264
0.6469
0.6564
0.6666
0.6760
0.6835
0.6886
0.2241
0.1898
0.1628
0.1526
0.1543
0.1619
0.1714
0.4554
0.3648
0.3111
0.3047
0.3243
0.3529
0.3821
0.4057
0.3332
0.2849
0.2736
0.2847
0.3050
0.3272
0.00500
0.00500
0.00500
0.00500
0.00500
2
3
4
5
6
0.1305
0.0872
0.0457
0.0099
0.0203
0.0631
0.0135
0.0213
0.0465
0.0651
0.6159
0.6180
0.6261
0.6382
0.6518
0.2420
0.1946
0.1643
0.1498
0.1469
0.4214
0.3231
0.2752
0.2686
0.2865
0.4029
0.3161
0.2681
0.2533
0.2599
0.01000
0.01000
0.01000
0.01000
0.01000
2
3
4
5
6
0.2168
0.1717
0.1160
0.0780
0.0331
0.0389
0.0031
0.0254
0.0563
0.0780
0.5651
0.5826
0.4577
0.6038
0.6189
0.2950
0.2443
0.2207
0.1728
0.1543
0.4921
0.3862
0.3262
0.2650
0.2573
0.4803
0.3872
0.3384
0.2697
0.2512
Table 3.2: Results of the analysis to determine parameters k and m. Difference with
the mean and standard deviation of the CT scan, the correlation coefficient, the RMS of
the absolute error, the RMS of the relative error and a weighted average of the absolute
end relative error are given. The combination k = 0.0025 and m = 4 is selected.
44
3.5
3.5.1
Physical Activity
Reference group
To determine a change in density due to physical activity, a reference group is created.
The reference group performs only the baseline level of physical activity. It is the activity
of an average non-active child. This non-active child does not spend supplementary time
doing sports and the time of physical activity is spent walking, standing and sedentary
activity. This child is the reference group. It is assumed that as much time walking is
spend as standing. Within each gait, the weight is as discussed before equally distributed
over the 3 timeframes. In modeling terms, this means that αgait1 + αgait2 + αgait3 =
αstance . With gait1, gait2, and gait3 the three selected timeframes of the gait cycle.
The weight factors αp for the reference group are defined as follows:
Several simulations are run with different total amount of activity α, with α = αgait1 +
αgait2 + αgait3 + αstance . In every simulation, only the total time on activity is changed
(α). So, there is only one degree of freedom. Simulations with three different values of
α are performed with α in line of expectations. The resulting BMD could be compared
with literature to define the activity of the reference group. Since the system has only
one degree of freedom, only one region is measured to compare with literature. The
BMD of the a crucial proximal femur region is selected, the femoral neck. The results
are listed in table 3.3.
α
0.6
PA [min]
240
0.7
280
0.8
320
Type of PA [min]
Walking: 120
Standing: 120
Walking: 140
Standing: 140
Walking: 160
Standing: 160
Rest [min]
160
BMD NECK [g/cm3 ]
0.396
120
0.408
80
0.413
Table 3.3: Time spent on physical activity and rest with the corresponding calculated
BMD of the femoral neck.
In literature, several studies report slightly different values of BMC and aBMD of the
femoral neck depending on physical activity in prepubertal children. Nogueira et al [102]
did a meta-analyis of 15 important studies and assigned a quality score on a scale from
1 to 20 reflecting the lowest risk of bias. From the 15 reported studies, the studiy of
Fuchs et al. is considered the best with a quality score of 20 out of 20. Moreover, it
includes prepubertal children(7-10 years, tanner stage 1) of both genders and reported
both BMC and aBMD for the femoral neck (to be able to calculate BMD). Measurements
are done with a HOLOGIC QDR-4500 scanner, so h = 1.512cm to calculate the BMD
(cfr supra, ’BMC, aBMD and vMBD’). The resulting femoral neck BMC and aBMD are
respectively 1.84g and 0.61/cm2 . On the assumption of a cylindral femoral neck, the
density equals 0.393g/cm3 This is most similar to a physical activity time of 240 min or
α = 0.6. This is selected as the amount baseline activity or reference group.
45
3.5.2
Regions of interest
Several regions of interest (ROI) are selected to investigate the change in bone density.
Four standard ROIs and three additional ROIs (total of seven ROIs) are selected as
proposed by Prevrhal et al [103] and shown in figure 3.28.
Figure 3.28: Definition of seven ROI as proposed by Prevrhal [103]. Figure adopted
from Vahdati [104].
The additional defined ROI have the advantage to be able to differentiate changes in
trabecular and cortical bone density at the proximal femur. The four standard ROIs are:
total proximal femur (TOT FEM), trochanteric (TROCH), WARD’s triangle (WARD)
and femoral neck (NECK) ROI (figure 3.28) left). The three additional ROIs are defined as follows: a central ROI focusing on trabecular-rich region in the femoral neck
(CENTRAL), another region focusing on trabecular bone and consisting of the largest
circle that can fit inside the femoral proximal metaphysis without touching the endocortical walls of the superior and inferior cortical aspects (CIRCROI), and a third ROI for
weight-bearing cortical bone (CORTROI) that was defined as a horizontal rectangular
box crossing the femoral shaft below the lesser trochanter [103] (figure 3.28 right).
In clinical practice, the ROI are used to measure densities from an X-ray image, which
has no depth information. The ROI are expanded to the 3D finite element model by
selecting the regions on the projection in the posterior direction of the model. Hence,
the regions are defined on an X-ray which is obtained by a posterior/anterior projection
of the femur. The selection of the ROI on the model is shown in figure 3.29.
3.5.3
Intervention
Besides the reference group, an intervention group is defined to study the change in
BMD of the proximal femur with respect to physical activity.
The intervention group performs the same baseline activity as the reference group, which
consists of 120 walking and 120 stance. Instead of spending 160 minutes non-weight
bearing activity (rest), the intervention groups performs gradually more high-intensive
physical activity. The additional amount of activity is gradually increased with steps
of 10 minutes. Each additional 10 minutes consists of 5 minutes running and 5 minutes
46
(a) CENTRAL
(e) TOTFEM
(b) CIRCROI
(c) CORTROI
(f) TROCH
(d) NECK
(g) WARD
Figure 3.29: The regions of interest selected on the finite element model.
performing counter-jumps. Hence, a prepubertal child performs physical activity doing
sports or running playing an active game. The activity is a combination of running,
start and stop, jumping, climbing, hopping and much more. Therefore, activity is
defined as the superposition of the five selected timeframes during run and jump (cfr
section ’experimental data’.
Further, a second intervention group is defined performing also the baseline activity
as the reference group. Above this amount of activity, additional time is spent walking instead of the combination of jump and run. In this way, the difference between
additional high-intensive physical activity (jump and run) compared to additional gait
activity (walking) is investigated. The activity of the reference group, intervention group
1 and intervention group 2 is summarized in table 3.4.
Reference group
Intervention group 1
Intervention group 2
Walking [min]
120
120
120 + 10x
Stance [min]
120
120
120
Jump [min]
0
5x
0
Run [min]
0
5x
0
Table 3.4: Summary of the physical activity of each group. Parameter x increments
from 0 to 9 to represent additional time per day spent on the respective activity.
47
Chapter 4
Results and discussion
The thesis consisted of two main goals: the creation of a femoral model of a prepubertal
child and investigating the changes in density with respect to physical activity.
4.1
Creation of femoral model of prepubertal child
The model is created as described in the chapter ’methods’. The implementation of
each step required a final decision of the previous one. Hence, results and explanation
of intermediate steps of the model are already mentioned in the chapter ’methods’.
However, some proceedings need some additional discussion.
4.1.1
Bone density: clinical versus computational
In clinical practice, BMC and aBMD are often used. Both expressions are size dependent. This has several disadvantages compared to vBMD, for research with children in
particular, since they are not full-grown. If 2 people with identical vBMD are compared,
the shorter person will have a lower BMD than the taller one [105].
A higher BMC or aBMD in an intervention compared to the control group may be due
to growth in size rather than an increase in the amount of bone in the bone (vBMD). On
the other hand, an increase in volumetric BMD may be achieved by increasing cortical
thickness, trabecular number, thickness, or the true density of these structures.
In computational models, volumetric density could be used. The fact that vBMD is
independent of size has also the advantage that it is less dependent from the region
determined by scanner. Different manufacturers using other standards of ROI. Moreover,
the manual or automated selection of the ROI is less critical, due to the elimination of
size.
These advantages in three-dimensional densities, come with the cost of three-dimensional
detector modalities, which implies a higher radiation dose. This is even more important for paediatric examinations because children are more vulnerable to radiation than
adults. These techniques deliver average doses to patients of 3 mSv. It will only be used
48
for diagnostics and rarely for research [106]. Radiation doses associated with dual-energy
X-ray absorptiometry are very low. These facts confirm that the use of three-dimensional
scanning modalities are indispensable for the creation of the model.
4.1.2
Remodeling model applied on children
The femoral bone of children is not yet fully developed and might differ for this reason
from mature bone tissue in two important ways: the way it reacts on mechanical stimuli
and the composition of the tissue.
In immature bone, the remodeling responds differently to mechanical stress. The relation
between mechanical stress and epiphyseal bone growth is given by the Huetere-Volkmann
law. It states that compression (increased stress) at the growth plate reduces bone
growth and to a lesser extent, distraction (tension or decreased stress) at the growth
plate increases it [10]. However, growth responds to sustained load, but bone remodeling
responds primarily to transient loading [107]. Intuitively it could be explained that if
bone growth responded to transient forces, then active children would achieve different
stature than their less active peers.
The Lisbon remodeling model calculates the equilibrium equation as a summation of the
different load cases. In this point of view, loads are not sustained but transient. This fact
could be stated more generally that it accounts for all types of physical activity.
An important characteristic of the Lisbon model is that it is a phenomenological model.
It is in the first place a rigorous mathematical theory which describes observed changes
of density. The link with the biological background is defined in a second place. This
has the benefit that the model does not distinguish mature or immature bone. After
all, in children’s bone three processes are active: growth, modeling and remodeling. A
phenomenological model is able to deal with all three processes at once, since there is
no relationship between biology and modelship. For this reason, the phenomenological
model is probably the best approach of remodeling the prepubertal bone. Moreover, the
classic phenomenological remodeling approach is considered as the gold standard for the
simulation of bone remodeling [57].
Further, the Lisbon model has the variable cost parameters k and m. These parameters define the cost of bone maintenance and therefore, control the total amount of
bone mass. They depend on several biological factors such as gender, age, hormonal
status and disease. In this way, the model captures the possible age or growth related
differences.
A result of increased physical activity, might be a geometrical adapatation of the bone
[34], which may occur more readily in children. This change is not taken into account
by the remodeling model, as it analyses change in densities for a fixed geometry.
As a conclusion, it is stated that there is no reason to assume a worse performance of the
remodeling model for immature compared to mature bone. A verification of the model
for mature bone is done by Santos [108]. Results of DEXA examinations are compared
quantitatively with computational model results. The results evidence the predictive
ability of the computation model in esimation of femoral neck bone mineral content. It
is concluded that the remodeling model has very suitable characteristics for use in this
research.
49
4.1.3
Subject specificity
Geometry and material
From major importance is the subject specificity of the model. The geometry is created
based on the CT scans with standard segmentation protocols as described by Materialise
in the Mimics reference guide [64]. For the adult femur, there exists a standardized model
created in order to compare similar studies [109]. There does not exist a counterpart for
children. On one hand, this confirms the uniqueness of this study. On the other hand,
this makes a quantitative evaluation of the created geometry very hard. A qualitative
evaluation is done by comparing a virtual X-ray of the model with a DEXA scan of
clinical practice (figure 4.1).
(a)
(b)
Figure 4.1: X-ray images used for the qualitative analysis of material assignment and
geometry. (a) Virtual X-ray of the created model (b) X-ray of non-pathological subject.
Adopted from Pennstatemedicine [110].
Materials are assigned to the model by relating the grayvalues to densities. This is done
under the assumption of linear relation between both. This method is applied before by
Gupta [70] and Bitsakos [71]. Again, the results are verified qualitatively by comparing
the X-rays of figure 4.1.The cortical shell on the femoral shaft is clearly visible on both
the images. Moreover, a dark area of low density is noticed in the trochanteric region. A
possible critique is the apparent circular line around the femoral head, which is possible
an inaccuracy of the segmentation. Because no region of interest is focussing on the
femoral head, this is only a minor concern.
A quantitative analysis could be done based on the characteristics of the selected ROIs.
Table 4.1 lists the densities at the ROI measured from the model. These values only
report a starting pattern and is not yet the reference group, since no baseline activity
50
is applied yet.
ROI
CENTRAL
CIRCROI
CORTROI
NECK
TOT FEM
TROCH
WARD
Density [g/cm3 ]
0.283
0.258
0.526
0.304
0.324
0.231
0.260
Table 4.1: Starting densities in the different regions of interest as measured on the
created model.
Ward triangle refers to a radiolucent area between principle compressive, secondary
compressive and primary tensile trabeculae in the neck of femur. It is per defintion an
area of diminished density. The value is indeed lower than the other ROI except for the
CIRCROI and the TROCH. However, the CIRCROI is defined as the largest circle that
can fit inside the femoral proximal methaphysis without touching the endocortical walls.
As this region together with CENTRAL is focussing on the trabecular rich regions, the
low values are explained. Further, the trochanteric region is also lower than the average
due to the amount of porotic trabecular bone. CORTROI on the other hand, focuses on
the weight bearing cortical bone. As this region includes the femoral shaft, the density
is high. Finally, it is mentioned that the definition of TOT FEM is rather arbitrary. As
the box would have been selected a bit lower, it includes more cortical shaft and the
density increases. However, this region is a good reference for the average density of the
proximal femur.
It can be concluded that the relative densities of the different ROI are correct representation. Speaking in absolute terms, the densities of trabecular and cortical bone
are calibrated with values of peer-reviewed research. Moreover, the amount of baseline
activity of the reference group is defined as the activity which establishes a femoral neck
density equal to the value found in literature.
Finite elements
The performance of the created finite element model is checked by convergence tests
(cfr. supra). However, it is decided to optimize for nodes instead of elements. Further,
elements are represented by integration points. In case of C3D4 elements, the integration
points equal the centroids of the elements.
Running the model for nodes has the advantage that it does not create a checkerboard
density pattern. In this case, adjacent remodeled elements are either saturated (high
density) or resorbed (low densities) [111]. This effect is eliminated by a node-based
approach.
When the remodeling model is run at the nodes, the densities are interpolated to the
integration points, just like the displacement field. Consequently, small differences are
51
expected in the average density using the densities at the nodes or at the integration
points.
To verify the used formula and the MatLab implementation, the average density of the
CT scans is calculated for the proximal femur and the proximal neck, using on the one
hand of the given elemental densities and on the other hand of the calculated nodal
densities. The relative difference of the results for the proximal femur and the femoral
neck are respectively 1.83% and 1.96%. Taking into account that these densities are
only the starting densities for simulations, the difference is considered negligible.
Musculoskeletal loading
Large number of finite element analyses of the proximal femur rely on a simplified set of
muscle and joint contact loads to represent the boundary conditions of the model. Very
often standard generic hip loading conditions are applied in FE simulations, derived from
measurements with instrumented implants [112], the subject-specific gait kinematics
strongly influence the hip joint loading. After all, in the context of bone remodeling
analysis, muscle loading affects directly the spatial distribution of the remodeling signal
[71].
Several studies present sensitivity analysis on the effect of different muscle loading configurations on the outcome of the bone remodeling simulation. Bitsakos [71] suggests
that the loading configuration of the FE model does play an important role in the
outcome of the remodelling simulation. Also Vahdati [104], highlights the importance
of subject-specific musculoskeletal loading on the analysis of the bone remodeling and
prediction of bone density distribution in the proximal femur.
The fact that musculoskeletal loads of children have a different order than for adults,
emphasizes the use of a complete muscle set. This study includes 15 muscle lines of
actions, which are almost all muscles arriving on the proximal femur. Only muscles
which load was not higher than 2.5% in any of the loadcases are excluded as their
contribution is considered negligble. As boundary condition, the whole bottom part of
the femur is constrained in three directions. Speirs [76] suggests to constrain the distal
condyles. As this constraint is not possible for the proximal femur model, some tests are
performed to avoid unreal stresses. Further, the maximal displacement of the femoral
head is less than 1.65 mm. This is still within the physiological deflection range of 2
mm [76].
4.1.4
Parameters of the remodeling model
K and m
As parameters k and m determine the intersubject variability, an accurate selection of
these parameters is important. In particular, because this is the way how the Lisbon
model is set to remodel bone of children.
Tests are performed by starting with a uniform density, the average of the real densities.
Then, the remodeling model is run for different parameters. The resulting density
pattern is compared with the real density pattern of the CT scans. Results of the
52
statistical analysis to investigate parameter k and m are listed in table 3.2. To have
a better view on the trade-offs made, the results are also presented in bar charts. It
is not possible to define which parameter k or m is most important. Parameter k
corresponds to the metabolic cost of bone apposition and is of major importance since
it strongly influences the total bonemass. Parameterm on the other hand also influences
the total bonemass, but the main role is to control the density distribution. So, to see
the evolution of m within a fixed k and vice versa, two plots are given for each statistical
test. Tendencies are discussed with one parameter kept fixed. The left subplots depict
the trends over a changing m. Right subplots give the trends with respect to a changing
k. Test results for k greater than 0.005 are not plotted. These statistical results are
considered as generally poor and tendencies seem to be random.
The correlation coefficients are depicted figure 4.2. They all show a moderate to good
correlation between 0.4 and 0.7. In the left subplot, the tendency for varying parameter
m with respect to one value of parameter k could be analyzed. As m goes from 1 to 7
(different colored bars), the correlation gets better. This evolution is bigger for greater
values of k. In the right subplot, the evolution of parameter k within a fixed parameter
m could be inspected. It is seen that the correlation gets better for increasing k, with
a maximum around k = 200 × 10−5 . Then, the correlation declines. Based on these
findings, values of parameters k = 200 × 10−5 and m = 5 would be selected. However,
the difference with other combinations is very small.
Figure 4.2: The correlation between simulated densities with different k and m and the
real densities of the CT scan. Left subplot shows different values for m ranging from 1
to 7 with respect to k fixed on the X-axis.
The average error, as seen in figure 4.3 takes into account both the relative and the
absolute error equally weighted. Combination k = 25 · 10−5 m = 6 is considered as
an outlier with an error in the simulation. Within one value of k, the variation shows
a parabolic tendency (opened up) with a minimum around m = 3 (left subplot). A
lower error could be noticed in the right subplot for high values of parameter k. This
tendency flattens and even reverses sometimes around k = 250. Based on the average
error, values of parameters k = 500 and m = 5 are considered best. Again, combinations with parameters selected slightly different result in approximately equally good
solutions.
In general, it is noticed that a low value of k leads to a lower importance of parameter
m. For the smallest values of k, there is almost no difference in results for changing m.
Vice versa, for the greatest values of k, the outcome changes significantly with m. This
53
Figure 4.3: The average error (average between absolute and relative error) between
simulated densities with different k and m and the real densities of the CT scan. Left
subplot shows different values for m ranging from 1 to 7 with respect to k fixed on the
X-axis. Right subplot shows different values for k ranging from 10x10−5 to 500x10−5
with m fixed on the x-axis.
is explained by looking at the term which represents the cost of bone in the remodeling
dµm
. Parameter k scales the change in density. For very small values of k,
model: –k ·
da
the change in density gets negligible.
A trade-off between all tendencies should be made. Parameters k = 0.0025 and m = 4
is considered best, especially because it has only a very small difference with the meand
(∆mean = 0.034) and standard deviation (∆SD = 0.0231). For the chosen value of
parameters k and m, a correlation coefficient of 0.666 is obtained. The average error,
which is a relative value, is 0.274. All the tested statistical parameters give in general
better results compared to Sharma [113] et al or Quental [97], who did similar analyses
for the scapula. This could be explained by the simpler density destribution of the femur
compared to the scapula.
4.1.5
Limitations
Despite the try to underpin each assumption, there are some limitations or potential
errors in the model.
First of all, geometric adaptations, which may occur more readily in children, are not
taken into account. On the other hand, the geometric adaptation is especially important
when one would investigate the gain in strength due to physical activity. According
to Petit [114], the geometrical adaptation may also be overlooked in classical DEXA
studies.
Only a few time frames in each activity cycle are used to represent the load cases in this
study. Moreover, only one cycle is taken into account into the calculations. Human gait,
even within one subject, varies a lot. This one cycle is not necessarily representative
for the average gait cycle of the subject and the loads that act on the femur. By
selecting very carefully the timeframes taken into account, this potential error is tried
to minimize.
Further, the musculoskeletal data and the CT images are from different subjects. Al54
though they have very similar characteristics (sex, age, height and weight), there will
be some slight intersubject variability. However, in this study there is no access to both
kinematic data of movement analysis and CT scans from the same subject.
More general, it is a limitation that only one subject is investigated to represent the
average prepubertal child. As no standardized model of the prepubertal femur exist
similar to the one created by Viceconti [109], this was the best solution. This is mainly
a disadvantage when the results of this study would be compared with a similar study,
but a different finite element model.
Finally, considering the hormonal and genetic factors, even an accurate and representative set of muscle and joint forces, might still give bone densities that deviate from the
in vivo values. Factors that are not directly related to the mechanically induced bone
remodeling, such as genetic predetermination, hormonal and central control of bone
remodeling could skew the bone density predictions [104].
4.2
4.2.1
Change in density
Influence of physical activity
Children are one of the most active groups of population. As discussed in the chapter
’background’, they have greater befits of additional amount of physical activity. So, it
is expected that an additional amount of physical activity leads to a greater increase in
bone mineral density compared to adults.
The results of the analysis are plotted in figure 4.4. The simulated data for intervention
group 1 (increased high-intensive activity), intervention group 2 (increased time spent
walking) are marked with a cross. Each data point represents the density of the ROI
with respect to the additional amount of time per day spent on physical activity. The
data are fitted with a smooth curve, to accentuate the tendency. The curve which
represents the data best is a two term power function (y = a + bxc ). Further, also
the density of the reference group (only performing the baseline amount of activity) is
plotted. Since the reference group does not perform any additional activity above the
baseline activity, the curve is flat. The subplots of figure 4.4 represent the densities of
the different region of interest.
Janz [115] performed observational studies examining self-selected physical activity levels
and bone outcomes. The study convincingly show that children who participate in
higher levels of physical activity have greater bone mass accrual compared to less active
children. Many other studies based on clinical data have similar conclusions. Behringer
et al [1] performed a meta-analysis of a majority of the research in this field of study.
The results of this meta-analysis conclude that weight-bearing activity alongside high
calcium intake provide a practical, relevant method to significantly improve BMC in
prepubertal children, justifying the application of this exercise form as an osteoporosis
prophylaxis in this stage of maturity.
The results of the remodeling model simulations, as seen in figure 4.4, show a clear
ascending tendency with increased physical activity of both reference group 1 and reference group 2. This corresponds to the conclusions of clinical based research. This
55
(a) Central region
(b) Circular region
(c) Cortical region
(d) Neck region
(e) Total proximal femur
(f) Trochanter
(g) Ward’s triangle
Figure 4.4: Simulated data of density with respect to additional time spent in physical
activity per day. Reference group 1 performs additional high-intensive activity. Intervention group 2 performs additional walking. The reference group does not perform
additional activity.
56
tendency is noticed for all defined ROI. It could be stated that the proximal femur as a
whole has benefits with increased physical activity.
In a study of Sardinha et al [116] the relationship between intensity and duration of
physical activity is analyzed. Their results suggest that the intensity of physical activity
needs to be vigorous to influence bone strength of the femoral neck. Children may need
to accumulate 25 minutes of vigorous intensity per day to improve their bone strength
by changing bone mass and/or geometry.
Comparing the findings of Sardinha et al with the computational results of this study,
the findings are similar. The computational results have the advantage of acting on
a smaller time scale. In this way, it is possible to nuance the findings of Sardinha.
Bone mass acrual is noticed for both moderate (walking) and vigorous or high-intensity
activity. However, the change in density with time spent in walking is much smaller
than performing vigorous activity. Sardinha suggests that 25 minutes of activity are
needed to improve remarkable benefits. The computational results show an effect on
bone mass for each additional minute spent in physical activity. It is not known if the
initial density accrual are not remarkable in clinical practice or that the initial density
accrual is a bias of the remodeling model.
Finally, these results are also compared with the study of Machado [117]. The research
investigated the effect of different weight-bearing PA types in the adaptation of the
femoral neck by analysing regional differences in bone mineral density at the integral
and its subregions. Moreover, the research makes use of the same remodeling model.
Machado predicted also gains in density of the femoral neck. The offset and the change
in density are different. This could be explained by a different population of the study,
which implicates a different cost function, a different load regime, different geometry
and different starting density pattern.
As a conclusion, it is stated that the computational results agree with the clinical-based
research. Spending more time in physical activity per day, the bone mineral density
increases. This accounts for all investigated regions of interest. The effect of highintensive activity is noticeable higher than the effect of walking. But, compared to
the clinical-based research, the computational results reveal more accurate information
about the way how it changes and is able to differ between several regions of interest.
Therefore, these advantages are investigated more closely in the next sections.
4.2.2
Additional time per day spent physical activity
From the previous section, it is seen that spending more time in physical activity per
day increases the bone density. Another objective of the study is to investigate how
the density changes spending additional time in physical activity. In other words, the
impact of an additional time increment on the density.
From figure 4.4 it is seen that the fitted function is an increasing function. But, the
increase becomes smaller when more time is spent in physical activity. This fact is
verified by checking the derivative. The plot of figure 4.5 shows he derivative of the
fitted function for intervention group 1 and 2 of the total proximal femur. The function
indicates the immediate change in bone density with respect to changing time. Al ROI
show the same tendency, but for convenience only the total proximal femur is plot.
57
Figure 4.5: Change in bone density for additional time spent in physical activity.
The change in density is a decreasing function. This implicates that more bone mass
is gained in with an initial increase in physical activity time. In other words, the bone
seems to have some resistance for adding more bone mineral content with increasing
activity time. The derivative function seems to be convergent, so after a large amount
of additional activity time bone changes linearly with time. This could be explained
intuitively based on biological knowledge. As the tissue tends to be less porotic, or
more mineral content is added, the additional mineral content comes with an increased
metabolic cost.
Looking at figure 4.5 at the derivative for intervention group 2, a rather flat curve is
noticed. Indeed, the fitted function in figure 4.4 looks linear. Spending additional time
per day walking results in a proportional increase of bone and activity time.
Although no derivatives are plotted, the results of Machado [117] seem to have the same
tendency. As seen in figure 4.6, ordinary activity and low impact exercise have a linear
effect on bone mineral density. This is similar to the result of intervention group 2 in
this study. Odd impact or high impact activity lead to a high initial increase in bone
density with respect to time. These is similar to the result of intervention group 2. In
this research, this tendency is shown for all investigated ROI.
As a conclusion, it is stated that an initial activity time increment leads to a greater
increase in bone mass compared to another time increment. This only accounts for
high-intensive activity and not for the gait cycle. Results suggest that low porotic bone
has a higher resistance for added mineral content compared to high porotic bone. The
latter is investigated further in the next chapter.
4.2.3
Difference between trabecular and cortical bone
In the previous section it is suggested that low porotic bone has a higher resistance for
added mineral content compared to high porotic bone. If this hypothese is true, the
trabecular bone would have a higher benefit of increased physical activity than cortical
bone.
The central ROI and the circular ROI are selected as containing a high amount of
trabecular bone. On the other hand, the cortical ROI is selected as a region with a high
58
Figure 4.6: Bone mineral density at the integral femoral neck and at the superior,
inferior, anterior and posterior femoral neck subregions according to additional time
spent in (a) ordinary and supplementary (b) low-, (c) moderate- and (d) high-impact
physical activity, relatively to the reference regime. Adapted from Machado [117].
amount of cortical bone. To investigate the change in trabecular to cortical bone, the
following ratio is defined:
(CEN T RAL + CIRCROI)/2
T rabecularbone
=
Corticalbone
CORT ROI
(4.1)
The result of the remodeling analysis for this ratio are plotted in figure 4.7. The ratio of
trabecular bone to cortical bone grows with additional time spent on physical activity.
But, if we look at the derivative of the ratio, the change in ratio is a decreasing function.
This means that the trabecular gets less dens compared to the cortical bone, which is
not expected. A possible explanation of this is the difference in region of the femur. The
cortical region is located in the femoral shaft. The tubercular ROI are located in the
femoral neck or close to the trochanter. For this reason, they will perceive a different
load configuration. It is possible to make a judgement on the region of interest, but
there is no direct correlation with the type of tissue they represent.
No conclusion is made about the ratio between trabecular and cortical bone.
4.2.4
Particular regions of interest
Some regions of interest are especially important since they are more vulnerable to
fractures than others. Two types of fractures are frequently noticed: a fracture of the
femoral neck and a fracture in the trochanteric region. Some research suggests that these
two types of fractures reveal dissimilar etiologies. Trochanteric fractures are associated
59
Figure 4.7: Upper: ratio of trabecular bone to cortical bone. Lower: change in ratio
with respect to increased activity. Figures for intervention group 1
with bone fragility or reduced bone mineral density and femoral neck fractures are
determined by femoral geometry [118].
Neck ROI
As important as the amount of bone that is accrued during childhood is the manner
in which newly acquired bone is distributed. After all, the distribution influences bone
structure and strength. Since bone is lost from the endosteal surface during adulthood,
exercise-induced increases to the periosteum are likely to help maintain the bone’s resistance to fracture with age. According to Gunter [47], this periosteal apposition is the
predominant effect in response to increased physical activity during growth, particularly
in pre- and early puberty. This apposition is particular important in the femoral neck,
since this region is often associated with (osteoporotic) fractures. To verify this, the
following ratio is defined:
P eriostealapposition =
Central
N eck
(4.2)
As all defined ROI have an increasing density, the ratio is increasing as seen in figure
4.8. The lower subplot shows the derivative of the fitted function. This is a decreasing
function. This implicates that central region grows less fast than the neck region. This
is exactly the principle of periosteal apposition. This mechanism leads to an improved
mechanical strength of the femoral neck without a change in total amount of bone
mass. This is in agreement with the suggested ethiology of the fracture. With periosteal
apposition, the relative geometry of the neck changes and the region is able to withstand
higher loads.
It can be concluded that periosteal apposition in the femoral neck increases with increased time spent in physical activity.
60
Figure 4.8: Upper: ratio of central to neck ROI. Lower: change in ratio with respect to
increased activity. The indicates periosteal apposition.
Trochanter ROI
The second type of frequently noticed fracture is in the trochanteric region. The reason
for this type of fractures is a decreased bone mineral density. Or, the other way around,
an increased trochanteric density leads to a lower fracture risk. As seen in figure 4.4, the
bone mineral density of the trochanteric ROI increases with additional activity. Hence,
it reduces the fracture risk.
It is concluded that physical activity decreases the risk for typical (osteoporotic) femoral
fractures. In the region of the femoral neck, this happens by the periosteal apposition:
a relative increase in density of the outer shell. In the trochanteric region, the fracture
risk is decreased by an increased bone mineral density.
4.3
Daily-life application
Current world health recommendations recommend bone enhancing physical activities
for children three days a week as part of a 60 minute per day physical activity recommendation. The current study underpinnes this recommendations and indicates the
benefits of an inital increase in physical activity.
It is surrealistic and useless to prescribe an exercise program for each child. However, for
high-risk individuals, the outcomes of the study could be used for bone health recommendations by medical doctors. This could be the case for prepubertal children belonging
to one of the following high-risk groups: Individuals receiving longterm glucocorticoid
therapy as it sometimes associated with the inhibition of bone formation. Individuals
with hyperparathyroidism as the horomonal secretion increases bone resorption. Individuals with obesity as it is associated with decreased osteoblast differentiation and
bone formation.
In general, this study presents support regarding the amount of physical activity is
needed to obtain bone-health benefits in children.
61
Chapter 5
Conclusion
The thesis consisted of two major parts. The first consisted in constructing a subjectspecific model representative for prepubertal children. The second part consisted in
using the model in a bone remodeling simulation to investigate density changes with
respect to physical activity.
First, a finite element model is created and verified based. This is done segmenting the
bony part in CT-images, to represent the true geometry of the femur of a prepubertal
child. To the author’s knowledge, it is the first created model used for research purposes
in this field. As useful CT-scans are very scarce and the search was hard, acquiring
these data is also considered as an achievement of this study. Next, material densities
are assigned by calibrating grayvalues for trabecular and cortical bone. To avoid a
checkerbord density pattern, the material properties are interpolated to nodes with
elemental volumes as weights.
Musculoskeletal and hip contact loads are gathered by kinematic analysis by the Faculty
of Human Kinetics. Prepubertal children performed physical activity as gait, stance,
jump and run. The inclusion of experimental subject-specific data is innovative, as often
generic hip and muscle loads are used. Instead of using only the highest loads to represent
the musculoskeletal loading, a superposition of different timeframes of the activity cycle
is adopted. Therefore, crucial timeframes in each activity cycle are selected. The final
model is evaluated in a qualitative and quantitative way.
As it is the first time that the remodeling model is adopted for children, some model
parameters needed to be selected. The cost parameter is the most important since it
reflects the inter-subject variability. Based on statistical results, the best combination
for prepubertal children was k = 0.0025 and m = 4.
To study the changes in density, three groups are created. The reference group performs
only a baseline amount of activity. This activity is defined as the activity which establishes a femoral neck density equal to the value found in literature. Two intervention
groups are defined which spend additional time in physical activity above the baseline
amount. The additional physical activity consisted of increments of 5 minutes jumping
and 5 minutes run. This combination of run and jump represents children’s activity,
which includes many different movements running, hopping, climbing, jumping etc. The
second reference group spends the additional activity time walking.
62
From the density analysis, some conclusions are made. First, it is stated that the
computational results agree with the clinical-based research. Spending more time in
physical activity per day, the bone mineral density increases. This accounts for all
investigated regions of interest. The effect of high-intensive activity is remarkable higher
than the effect of walking.
It is stated that an initial activity time increment leads to a greater increase in bone mass
compared to a second time increment. This only accounts for high-intensive activity and
not for the gait cycle. Results suggest also that low porotic bone has a higher resistance
for added mineral content compared to high porotic bone.
Further, the results suggest that physical activity decreases the risk for typical (osteoporotic) femoral fractures. In the region of the femoral neck, this happens by the
periosteal apposition of bone: a relative increase in density of the outer shell. In the
trochanteric region, the fracture risk is decreased by an increased bone mineral density.
The results of this thesis could be taken into account into governmental health recommendation. For individuals with a high-risk for bone health disorders, a more detailed
training program could be made. And, most important, it is a base for other research
in this field. After all, the current study offers some additions to the existing bone
remodeling simulations, for prepubertal children in particular.
63
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