The application of the homogenisation method to the numerical modelling of cancellous bone

Master Thesis


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University of Cape Town

This thesis reports on an investigation into the viability of developing idealised numerical models of cancellous bone in order to make reasonable predictions about its macro- and microstructural mechanical behaviour using the homogenisation method. In total joint replacement, cancellous bone (the soft porous bone which lies below the articular surfaces at weight-bearing joints) provides the medium for the transfer of loads from the artificial component, or prosthesis to the hard, outer cortical bone. Although total joint replacement is usually a successful operation - providing relief from pain and often considerably improved joint function - loosening of the metal components remains a major obstacle to the long-term success of these operations. In the ongoing work to develop joints which are less susceptible to loosening, it has become necessary to study the micromechanics of cancellous bone in order to predict its response to the changing stress environments brought about by the inserted prostheses. Biomechanical engineers have used finite element analysis extensively in the analysis of reconstructed joints. However, owing to the prohibitively high computational costs associated with the microstructural modelling of cancellous bone, it is generally modelled simply as a homogeneous, isotropic material. It is not possible to accurately predict the mechanical response of cancellous bone to various implant conditions under this simplistic modelling assumption. Thus, alternative methods are being sought which will allow for more realistic modelling of cancellous bone. The homogenisation method is one such alternative. This method makes it possible to uncouple the analysis of some problem involving a composite material into an apparent global analysis and a local microstructural analysis. The apparent material properties of the periodically repeating composite microstructure are calculated, taking into account the structural heterogeneities of the composite. These properties are then used in the global analysis where the composite is treated as a continuum. The apparent global-level results are subsequently postprocessed to obtain the microstructural behaviour in any local regions of interest. The main aim of this research project was to investigate the applicability of the homogenisation method to the modelling of cancellous bone. The first part of this work involved an extensive literature study on the architecture and micromechanics of cancellous bone to investigate whether cancellous bone can indeed be modelled as an idealised composite material with a periodically repeating microstructure. The outcome of this investigation revealed that the structure and behaviour of cancellous bone is highly variable - depending on the patient, anatomic location and the level of density. However, certain regions of cancellous bone do have typical repeating architectures which have a major influence on the apparent mechanical behaviour of the bone. Thus it has been concluded that these specific regions of cancellous bone can be modelled by idealised structures, provided the observed microstructures and predominant deformations modes are well characterised in the models.

Includes bibliographical references (pages 75-78).