Download Structural Meso-Scale Bone Remodelling of the Pelvis

P. Patel
1
Structural Meso-Scale Bone Remodelling of the Pelvis
P. Patel, A.T.M. Phillips
Department of Civil and Environmental Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UK
July 2012
Artical Info
Abstract
Keywords:
Pelvis
Finite element
Bone remodelling
Adaption
Simulation
Biomechanics
Structures
Mechanostat
Meso-scale musculosketal models have successfulyl predicted trabecular and cortical
structures for bones. This modelling technique would be of great importance if successfully applied to the pelvis, by providing invaluable bone remodelling information
for different system changes.
The model consists of one pelvic innominate with the mesh obtained from a CT scan of
R
. The forces applied to the pelvis (from muscle and joint reaction
a pelvic Sawbones
forces) were extracted from an OpenSim model, only providing information on lower
limb muscles. Meso-scale modelling was used to ensure computational efficiency while
retaining accuracy.
The final product successfully modelled trabecular structure adaptation between different load cases and pelvic fracture positions within the pubic ramus. However, a
greater understanding into the importance of including upper body muscles and all
pelvic components was found due to inaccurate representation of the cortical shell.
1
Introduction
An accurate, efficient and comprehensive computation musculoskeletal model would be of great importance in orthopaedics. Such a model would increase the understanding of bone remodelling and
lay the foundations for enhancing the knowledge of
the musculoskeletal reaction to system changes.
The pelvis is formed from the sacrum, the coccyx and a large irregular bone structure linking the
trunk and lower limbs (Davies & Coupland, 1967).
The right and left innominates of the pelvis are
united posteriorly by the sacrum, through sacroiliac joints, and anteriorly, by the pubic symphysis
(Drake et al., 2010).
The structural purposes of the pelvis are to
transmit forces from the upper body to the lower
limbs, absorb motion forces from the lower limbs
and to support and protect the abdominal viscera
(Palastanga & Soames, 2012). This load path is
completed by the upper body force being transferred across the sacro-iliac joint, through the pelvis
to the acetabulum and finally into the lower leg
(during a standing position) (Kingston, 2001; Dalstra & Huiskes, 1995).
Loading on weight bearing bones is normally assumed to be dominated by body weight, but the
greatest loads on weight bearing bones are applied
from muscles due to gravitational and lever-arm
effects (Inman, 1947; English & Kilvington, 1979;
Afoke et al., 1980; Currey, 1984; Kannus et al.,
1996). It is therefore essential to include muscle
forces for an accurate in vivo model.
Ligaments provide the vital connections between bone structures, allowing the transfer of
forces across joints while maintaining the body0 s
structure. Therefore to produce a realistic in vivo
model, ligaments will need to be included.
The structural composition of load bearing
bones consists of outer and inner material types,
known as the cortical and trabecular bone respectively, forming a sandwich structure (Jacob et al.,
1976). The trabecular bone is formed of multiple struts of isotropic stiffness, resulting in a bone
structure with porosity varying spatially (Phillips,
2010). This structure is orientated to resist the
principal strains which can consist of orthogonal
axes (Martinón-Torres, 2003). For the cortical shell
of the pelvis, the thickness has been observed to
vary between 0.44 and 4mm by Anderson et al.
(2005a).
Pelvic injuries are not uncommon, with 3 to 8%
of all skeletal injuries relating to pelvic fractures
(Gillespie, 2009). Additionally, the most common
fractures of the pelvis occur at the superior pubic
ramus and ischiopubic ramus, bearing a 6.3 to 8%
10 year survival rate (van Dijk et al., 2010). Thus,
the pelvic model will be validated against this type
of weakness in the lower pelvic parts.
The aim of this project is to develop a computation model to accurately predict the bone architecture of the pelvis, justify structural features and
aid the global objective of building a full musculoskeletal model. To achieve this, the model would
involve mechanostat bone remodelling for different
load cases on the pelvis (Frost, 2003). Computational efficiency will be ensured by the use of mesoscale modelling, allowing a compromise in accuracy
for a reduction in computational power (Phillips,
P. Patel
2010).
2
2.1
Model
Geometric definition
The pelvic mesh was obtained from Dr. Andrew
Phillips with the process for the formation given
below.
The first step in the process for creating the
pelvic mesh consisted of CT scanning a large fourth
R
generation Sawbones
composite pelvis (#3405),
c and
from which the data was processed in Mimics
c
then modified by a MATLAB script. The script
altered the mesh to include three noded triangular
cortical shell elements (consisting of 0.1mm thickness) by using the surface element faces and nodes.
The internal trabecular structure of the model was
created by generating truss elements (with circular
cross-sections and initial radii of 0.1mm) from each
of the internal nodes to the 16 closest neighbours.
This resulted in a minimum node connectivity of 16,
231576 trabecular truss elements and 12448 cortical
shell elements.
2.2
Material properties
The material properties for cortical and trabecular
bone have been observed to vary from the longitudinal to traverse axis, with ranges of 16 to 20 GPa
(van Rietbergen et al., 1995) and 1 to 20GPa (Rho
et al., 1998; Helgason et al., 2008) for cortical and
trabecular bone respectively. The anisotropic nature of trabecular bone occurs due to the spatial
distribution of trabeculae when looking in a continuum persective. Conversely, it has been observed
by Dalstra et al. (1993) that the pelvic trabecular
bone can be considered as isotropic at meso-scale
because the anisotropic nature was not deemed significant.
In conclusion, from nanoindentation by Turner
et al. (1999) (assuming the bone materials are elastically isotropic) values of 18,000Nmm−2 and 0.3
will be assigned as the Young’s modulus and Poisson’s ratio respectively.
Ligaments of the pelvis consist of 90% collegen
fibres, of which Sydney (2005) observed to have a
Youngs modulus of 1000 N mm−2 and Poissons ration of 0.3. The properties set for muscle elements
were chosen to be very low to allow muscle elements
to distort and be redirected towards the muscle line
of action, as will be discussed in Section 2.5.
The material properties applied to the model are
shown in Table 2.
2.3
2
Boundary conditions
Spring elements will be neglected in the model due
to the increased time for pre-processing. Therefore
fixed displacement boundary conditions in all three
directions have been applied to the Lumbosacral
joint, fixed displacement in the z direction at the
pubis symphysis joint and force boundary conditions applied in the form of both muscle and joint
reaction loads. Only the z direction was restricted
for the pubis symphysis joint to represent the left
pelvic innominate interaction.
For the boundary conditions applied to the
Lumbosacral joint, a sacrum was required in the
model.
2.4
Load cases
The three most common activities of walking, going up stairs and sit to stand will be included in
the model. For all the activities, ten frames were
extracted from the total elapsed time of each activity, incorporating the joint reaction and muscle
forces. These selected frames were applied to the
c steps simultaneously.
model as ABAQUS
2.5
Muscles and ligaments
A total of 18 lower body muscles and 6 ligaments
have been included in the pelvic model. The muscle lines of action and attachments were extracted
from OpenSim by the use of motion files and a lower
limb muscleskeletal model (provided by Luca Modenese). To distribute the force vector over a muscle
attachment area, truss elements (with no compression properties) connected to the attachment area
and converged to a single point. Truss elements
were used instead of spring elements and the convergence point was taken as 100mm perpendicular
from the surface.
Both the coordinate position of the convergence
point and muscle element material properties were
important because as force vectors change with
each step, the truss elements should distort towards
the vector direction, like muscle fibres. Distortion
would be aided by low muscle element stiffness (Table 2), while the amout of distortion required can
be reduced with the correct convergence point.
2.6
Mechanostat parameters
Mechanostat is the concept of bone remodelling
used within the model by where bone resorption
and modelling occur within seperated microstrain
ranges (Figure 1 and Table 1).
P. Patel
3
number of effective trabecular elements being less
than 0.1%. If the model had not converged, a new
model input file was created, and therefore rerun,
else termination of the iterative process would occur.
Figure 1: Mechanostat adopted values of the relevant zones(Phillips, 2012)
Table 1: Mechanostat model values
Remodelling
Bone apposition
Lazy zone
Bone resorption
Dead zone
2.7
Microstrain values
1500 - 25000
1000 - 1500
250 - 1000
0 - 250
Iterative process
The first step of the iteration process was to load
c and
the initial model input file into MATLAB
c
run ABAQUS
will no GUI. Strain data was
next extracted from the output ODB file by a
PythonTM script. This strain data was used by
c , according to the Mechanostat apMATLAB
proach and parameters (Table 1), to assign new
cortical thicknesses and trabeculae radii (Equations
(1) and (2)) to a new model.
Ti+1
= Ti ti
(1)
Ai+1
Ai ti
(2)
=
Where T is the cortical shell thickness, A is the
cross-sectional area of the trabecular truss element,
i is the current element strain and t is the target
strain (1250µ).
Convergence of the model occured when the selfsimilarity of both the cortical and trabecular elements were greater than 99% and the change in
3
Results
To validate the trabecular structure within the
pelvic model, CT scans or scientific papers were required. Up to current day there are very few papers dealing with pelvic trabecular structure, resulting in validation difficulties, but making the
pelvic model all the more important.
From one of the few human ilium scans found,
the main trabecular structure is present between
the acetabulum and sacroiliac joint. This is shown
within the pelvic model (Figure 2) and provides reassurance of trabecular structure re-orientating to
resist principal strains. The scan also shows an area
of low trabecular structure within the supra-ilium,
which is presently modelled.
The cortical thickness model used for validation
was obtained from Clarke (2011). The thickness
was calculated from CT scan based information proc and MATLAB
c (using
cessed through Mimics
the same method as Anderson et al. (2005b)).
From comparison between the validation and
meso-scale pelvic models, there are several differences (Figure 3). The cortical structure formed at
the ischial tuberosity, superior and inferior of the ischial spine and ischiopubic ramus are approximately
half as thick on the validation model. The mesoscale model lacks structure mainly at the inferior
gluteal surface and iliac crest. A greater structure
has been predicted inferior to the sciatic notch by
the meso-scale model in comparison to an underestimate superior to the notch. Cortical thickness
from the sacroiliac joint to the inferior iliac fossa
has been overestimated, followed by an underestimate from this point to the superior pubic ramus.
Table 2: Material properties
Material
Cortical Bone
Trabecular Bone
Sacrum
Ligaments
Muscle
Cartilage
Youngs modulus (E ) (N mm−2 )
1.8×104
1.8×104
1.8×104
1×103
10
10
Poissons ratio (ν)
0.3
0.3
0.3
0.3
0.3
0.3
Note: Any elements in the model with no tension or compression properties have to be overlayed
c.
with an element of very low stiffness for processing in ABAQUS
P. Patel
It seems as if the high cortical thickness inferior
to the sacroiliac joint is spread down to the superior
pubic ramus.
The most common pelvic fractures occured at
the superior pubic and ischiopubic ramus. Within
Figure 4, a clear absense of trabecular structure is
present at the ischiopubic ramus and inferior pubic
ramus with an interuption of the structure at the
superior pubic ramus.
By combining both the trabecular and cortical
structure information, the possible fracture positions can be identified. The superior pubic and ischiopubic ramus have thin average cortical shells,
an absence of trabecular structure and thin widths,
leading to weak overall structures (Figures 4 and
5). Hence, from the pelvic model, the regions most
probable for the fractures to occur would be the
superior pubic and ischiopubic ramus.
4
Summary
One of the purposes of the model was to observe the difference in structure between a person
who undertakes all activities and one which rarely
uses stairs. But from structural comparison little
change was observed. This could be due to sit to
stand and climbing up stairs requiring the similar
muscle groups and applying similar joint reaction
forces, hence forces would use the existing structures formed by the previous load case.
When looking within the pelvic fracture region,
both the trabecular and cortical structure showed
points of weakness coinciding with the pubic ramus fracture positions. Due to the time constraint,
this analysis was only undertaken for the final complex load case, but comparison with other load cases
would be of interest.
During validation of the trabecular and cortical
2.1: 13-256 TS.
2.2: 19-256 TS.
4
structures, the cortical shell was observed to have
a structural presence in similar areas but majority of thickness values were over or underestimates.
The trabecular structure responded to different load
cases but the lack of validation material has reduced
the confidence of the trabecular validation.
Within every model there are limitations which
provide incentives for improvements. From the
OpenSim model, only the lower limb muscles were
present and therefore the only muscles included.
Any muscles attaching to membranes on the pelvis
in addition to the pelvic floor have also been neglected. The representation of activities involved
taking ten equally spaced load values from each activity, which could inaccurately represent the activity by missing peak loads. Muscle attachments
to the pelvic model have been represented as circular shapes of varying size and has resulted in noncircular muscle attachment areas not being represented. The muscle attachment truss system used
within the model relied on the convergence node position and truss elements to allow a significant distortion. This convergence node position was based
on the walking load case and thus if another load
case vector was very different from walking, the
pelvis could be falsely loaded. The pubic symphysis joint was not accurately represented, as the inferior pelvic joint should restrict movement in all
direction and allow small movements. This can be
achieved by including the second half of the pelvis.
5
Achievements
Within this pelvic model there have been several
strides of success towards the end goal, starting
with providing the foundations for further improvements on pelvic model and remaining computationally efficient.
2.3: 13-256 TS.
2.4: 19-256 TS.
Figure 2: Trabecular structure for all activities. Medial view(2.1 - 2.2) and lateral view (2.3 - 2.4). TS:
Trabecular sections.
P. Patel
5
STH
(Avg: 75%)
+4.000e+00
+3.703e+00
+3.407e+00
+3.110e+00
+2.813e+00
+2.517e+00
+2.220e+00
+1.923e+00
+1.627e+00
+1.330e+00
+1.033e+00
+7.367e−01
+4.400e−01
3.1: Legend.
3.2: Medial View.
3.3: Posterior View.
3.4: Laterial View.
3.5: Anterior View.
3.7: Medial View.
3.8: Posterior View.
3.9: Laterial View.
3.10: Anterior View.
STH
+4.913e+00
+4.000e+00
+3.703e+00
+3.407e+00
+3.110e+00
+2.813e+00
+2.517e+00
+2.220e+00
+1.923e+00
+1.627e+00
+1.330e+00
+1.033e+00
+7.367e−01
+4.400e−01
+8.000e−06
3.6: Legend.
Figure 3: Comparison of pelvic model cortical thickness for all activities (Figures 3.1 - 3.5) and validation
model (Figures 3.6 - 3.10) (Clarke, 2011) .
4.1: 7-256 TS.
4.2: 13-256 TS.
4.3: 19-256 TS.
Figure 4: Medial view of walking, stairs and sit to stand load case. Pubis and ischium pelvic parts (?? 4.3) trabecular structure. TS: Trabecular sections.
STH
(Avg: 75%)
+4.000e+00
+3.703e+00
+3.407e+00
+3.110e+00
+2.813e+00
+2.517e+00
+2.220e+00
+1.923e+00
+1.627e+00
+1.330e+00
+1.033e+00
+7.367e−01
+4.400e−01
5.1: Legend.
5.2: Medial view.
5.3: Lateral view.
Figure 5: Cortical shell thickness for walking, climbing stairs and sit to stand load case.
P. Patel
6
Another achievement included successfully mod- Frost, H. M. 2003 Bone’s mechanostat: a 2003 update. The
anatomical record. Part A, Discoveries in molecular, celelling the trabecular structure adaptation between
lular, and evolutionary biology, 275(2), 1081–101. (doi:
different load cases, predicting pelvic fractures and
10.1002/ar.a.10119)
assisting in justification of particular structural features. In addition to these, a greater understanding Gillespie, P. 2009 Pelvic fracture. Surgery (Oxford), 27(7),
292–296. (doi:10.1016/j.mpsur.2009.04.014)
into the importance of including upper body muscles and all pelvic components was formed.
Helgason, B., Perilli, E., Schileo, E., Taddei, F.,
Acknowledgements
Brynjólfsson, S. & Viceconti, M. 2008 Mathematical relationships between bone density and mechanical properties: a literature review. Clinical biomechanics (Bristol,
Avon), 23(2), 135–46. (doi:10.1016/j.clinbiomech.2007.08.
024)
I would like to thank my project supervisor, Dr.
Andrew Phillips for his guidance, availability and Inman, V. 1947 Functional aspects of the abductor muscles
advice throughout the project.
of the hip. The Journal of Bone and Joint Surgery, 29(3).
My thanks also to Diogo Miguel Geraldes for his
c and Luca Modenese for his
help with ABAQUS
help with the muscle data.
Jacob, H. A. C., Huggler, A. H., Dietschi, C. & Schreiber,
A. 1976 Mechanical function of subchondral bone as experimentally determined on the acetabulum of the human
pelvis. Journal of Biomechanics.
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