Predictive modelling of the form and development of bone fracture healing
Comiskey, Damien (2010) Predictive modelling of the form and development of bone fracture healing. PhD thesis, Dublin City University.
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It is the contention of this study that the rate and formation of bone healing can be modelled mathematically and computationally, respectively, based on mechanical stimuli induced by the relative motion between bone fragments. To argue this case, the following hypotheses are tested; 1) the relationship between temporal rate of bone healing, measured in terms of callus stiffening per week, and the percentage of interfragmentary strain, can be described mathematically, and 2) the spatial distribution of callus tissue around a fracture can be modelled computationally based on compressive principal strains experienced by the immature healing tissues caused by interfragmentary motions.
To test the first hypothesis, a comparative analysis of empirical relationships between rate of healing and level of mechanical stimulus found in the literature was conducted. Based on this, a mathematical phenomenological model was derived. To test the second hypothesis, the finite element method was employed to determine how bone-fixator position, fracture geometry, loading and the consequent strains experienced by the healing tissues, influence callus formation. An algorithm was proposed which iteratively removed lowly strained soft tissue from a large domain at the fracture site, thus producing a more efficient callus formation. The premise of this algorithm was based on the adage that ‘form follows function’, and a callus will inevitably strive to remodel itself to the point where greatest mechanical efficiency is achieved.
The results of the comparative literature review and the proposed mathematical model revealed a positive correlation between the rate of callus stiffening and the initially applied interfragmentary strain. The results of computational models showed direct agreement with experimental findings and clinical observations which reinforces the hypothesis that compressive principal strains are the dominant driving force behind callus formation. Furthermore, it was shown that the proximity of a unilateral fixator to the fractured bone has a greater influence over asymmetric callus formation than the physical presence of the fixator itself. Finally, the implications of the proposed strategies show potential in pre-clinical testing of fixation devices and configurations, which was demonstrated using simulated comparisons with clinical case studies of healing bones under unilateral fixation.
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