A probabilistic-based approach for computational simulation of bone fracture healing

It is widely known that bone fracture healing is affected by mechanical factors such as fracture geometry, fixation configuration and post-operative weight bearing loading. However, there are several uncertainties associated with the magnitude of the mechanical factors affecting bone healing as it is challenging to adjust and control them in clinical practice. The current bone fracture healing investigations mainly adopt a deterministic approach for identifying the optimal mechanical conditions for a favourable bone healing outcome. However, a probabilistic approach should be used in the analysis to incorporate such uncertainties for prediction of bone healing.

In this study we developed a probabilistic-based computational model to predict the probability of delayed healing or non-union under different fracture treatment mechanical conditions for fractures stabilised by locking plates.

The results show that there is a strong positive linear correlation between the mechanical stimulations (S) in the fracture gap and the magnitude of weight bearing, the bone-plate distance (BPD) and the plate working length (WL), whereas the fracture gap size has a highly negative and nonlinear correlation with S. While the results show that fracture mechanical microenvironment is more sensitive to the uncertainties in WL compared to BPD, the uncertainty associated with the magnitude of WL is very low and can be resulted from implant manufacturing tolerance. However, there is a high uncertainty associated with the magnitude of BPD as it cannot be accurately adjusted during the surgery. The results show that the tissue differentiation at the far cortex of fracture gap is more sensitive to the variation of BPD compared with that at the near cortex. The probability of delayed healing (fibrous tissue formation) at far cortex is increased from 0% to 40% when coefficient of variation (COV) of BPD rises from 0.1 to 0.9 (for average BPD = 2 mm, WL = 65 mm, fracture gap size = 3 mm and Weight bearing = 150 N). Further, both near and far cortex of fracture site are sensitive to the variation in weight bearing loading.

The developed probabilistic model may lead to useful guidelines that could help orthopaedic surgeons identify how reliable a specific fracture treatment strategy is.