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Structural Modelling of the Musculoskeletal System
1.1
Introduction
This area of research is motivated by the desire to produce a more efficient framework for modelling the musculoskeletal system. It is striking
that the early works of Culmann and von Meyer focused on the structure of the skeletal system. Recent micro-scale continuum finite element
models have the potential to represent this structure but are incredibly computationally demanding. While macro-scale continuum models are
significantly more efficient they are limited to the extent that they can represent the structural characteristics of the skeletal system.
Continuum models may have gained prominence due to the ease of comparison to CT and micro-CT studies. However in the context of bone
modelling and remodelling a structural mechanics as opposed to solid mechanics approach can further elucidate the behavioural characteristics of
the skeletal system. Meso-scale and macro-scale structural models of the skeletal system have the potential to be both computationally efficient
as well as providing behavioural information complimentary to that found using continuum models.
While the structural approach has obvious application to the skeletal system it is recognised that the soft tissues of the musculoskeletal system
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also have clear structural layouts associated with them. It is therefore proposed that methods similar to those outlined here for representation
of the skeletal system will also find application in describing the soft tissues of the musculoskeletal system.
Macro-scale modelling of the skeletal system operates on the cross-sectional level of bones. In this way the skeletal system can be represented
as a series of beam elements with appropriate cross-sectional properties. Solution times for this type of structural system are extremely low. It
offers an ideal way of combining structural and static optimisation modelling. Meso-scale modelling operates between micro and macro-scale
continuum modelling. The structure of trabecular and cortical bone is modelled using strut, beam and shell elements. However these elements
are not required to be at the same scale as identifiable structural components in bone. Solution times for this type of structural system are
relatively low, while the developed models offer true structural representations of the skeletal system.
The development of an structural optimisation derived model of the femur is discussed to illustrate the concept of meso-scale structural
modelling of the skeletal system.
1.2
Meso-scale structural model of the femur
Full details of the femur model are given in:
• Phillips, ATM, /Structural Optimisation: Biomechanics of the Femur/.
Invited paper accepted for publication in Engineering and Computational Mechanics
The mesh for the iterative model of the femur was assembled based on a CT scan of a Sawbones composite femur. Mimics was used to
create a tetrahedral mesh from the CT data. This mesh was adapted using MATLAB to create the initial structural model. Nodes and element
faces on the surface of the mesh were used to generate a shell mesh representing cortical bone. Surface and internal nodes were used to generate
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a strut mesh representing trabecular bone. Each node was connected to its nearest sixteen neighbours, providing a range of directionalities for
the strut elements. In the original structural model shell and strut elements were assigned uniform thicknesses and radii. All elements were
assigned identical isotropic elastic material properties.
The developed model was subjected to a simplified load case representative of the maximum hip joint contact force during normal walking.
Fixed boundary conditions were applied at the condyles and loads were applied representing the contact force at the hip joint, the abductor
muscles and the iliotibial band. The radii of the strut elements and the thicknesses of the shell elements were updated over a number of
iterations until convergence was achieved based on attaining a target strain in each of the elements. This was done based on the axial strain
in the strut elements, and the absolute maximum principal strain in the shell elements. The iterative process was controlled using MATLAB;
Abaqus/Standard was used as the finite element solver and a Python script was used to extract strain results for processing. Through this
approach a structural optimisation derived meso-scale model of the femur was arrived at for a single load case.
The figure below shows a coronal slice of the proximal femur in the original and converged model states, as well as at selected iterations.
It is observed that the structure of the converged state of the model resembles a coronal slice taken from the proximal femur shown below.
A 3D view of the internal structure in the proximal femur for the converged state is shown in the anaglyph shown below.
Additional 3D representations of the converged model are available from the structural modelling of the musculoskeletal system project page.
Further work is now being undertaken to combine the structural modelling approach with the free boundary condition modelling approach.
Combined structural and static optimisation models are also being investigated. While the basic meso-scale structural femur model presented
here has a number of limitations it is clear that structural modelling of the musculoskeletal system has significant potential and studies are
ongoing investigating its application, in particular in the fields of blast and fracture biomechanics.
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(a)
(b)
(c)
(d)
Figure 1: 5mm slice through the proximal femur for the (a) original, (b) 1st, (c) 5th and (d) converged iterations. Trabecular bone size
and greyscale value is scaled based on the crosssectional area; cortical bone size is scaled based on the thickness.
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Figure 2: Coronal slice from the proximal femur.
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Figure 3: Anaglyph of the internal structure of the proximal femur for the converged state (requires red-cyan glasses).
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1.3
Downloads
The following files related to this project are available for download from the structural modelling of the musculoskeletal system project page:
• Text file of node numbers and coordinates
• Text file of tetrahedral elements for the original solid mesh
• Text file of surface shell elements for the structural mesh
This work by Imperial College London, Structural Biomechanics : http://www.imperial.ac.uk/structuralbiomechanics
is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
As more advanced structural models are developed and published these will be made available using a Creative Commons license through
the Structural Biomechanics website.
Contact: Andrew Phillips ([email protected])
Structural Biomechanics ([email protected])
c MMXI Imperial College London
Structural Biomechanics, Skempton Building, London SW7 2AZ
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