Mechanical Analysis of Cancellous Bone Architecture

Joint replacement surgery (arthroplasty) dramatically alters the localised mechanical environment of the surrounding bone compared to the original skeletal structure. Stress concentrations with concomitant stress shielding can occur in the bone leading to osteolysis (bone resorption) resulting in periprosthetic fractures. The current gold standard methodology to analyse the stresses surrounding an arthroplasty is to use finite element analysis adopting classical elastic elements to represent the cortical and trabecular bone. Such a material description may be insufficient to fully capture the resulting stress environment following arthroplasty.

Load bearing materials are often assumed to be homogeneous continua at all scales. This assumption is central to the classical theory of elasticity. However, materials such as trabecular bone are actually heterogeneous; they have a distinctly observable microstructure. Continuum theories like classical elasticity are of limited use in predicting their behaviour when the scale of the microstructure tends towards the overall dimensions. However, other theories such as micropolar (also known as Cosserat) elasticity, whilst still regarding the material as a continuum, are able to predict their behaviour because they acknowledge the heterogeneity through additional mechanical properties. For some time, cortical bone has been known to possess such micropolar behaviour and more recently trabecular bone has also been identified as possessing these qualities. Among the fascinating and unexpected consequences arising from this theory are the predicted reduction in stress concentration around holes and other defects and, critically, the increase in stress concentration around rigid inclusions, i.e. prosthetic implants.

Riches_fig.1

 
 
 
 
 
 
 

A contour plot of the Von Mises stresses in trabecular bone under 0.1% compressive strain in the x-direction.

 
 
 
 
 
 
 
 
 

Building on a recent project on cortical bone, we propose a virtual-experimental approach to develop a full micropolar description of trabecular bone. To do this, a human distal femur will be scanned in high resolution using a micro-CT (mCT) machine and from this scan, the 3D network of trabeculae will be segmented. The micropolar parameters of trabecular bone will be determined by analysing, using computational FE analysis, the size effect during virtual bending and torsional experiments. The segmented mCT image of the distal femur will be repeatedly sampled at different sizes, but maintaining aspect ratio, and subjected to pure bending. The size effect changes in stiffness behaviour will then be determined.

This programme of research will provide fundamental understanding of bone mechanics. This work is essential to improve our understanding of the stress concentrations in the vicinity of implants, and will ultimately result in the development of implants that are less susceptible to aseptic loosening and periprosthetic fracture. As such it is of interest to orthopaedic implant industry.

For more information about the project contact Carl Muscat (carl.muscat [at] strath [dot] ac [dot] uk), Dr Marcus Wheel (marcus.wheel [at] strath [dot] ac [dot] uk), Lecturer at the Department of Mechanical and Aerospace Engineering or Dr Philip Riches () Senior Lecturer at the Department of Biomedical Engineering at the University of Strathclyde.

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