Is callus formation optimised for fracture stability? A computational study

Aims Fractures that are not rigidly fixed heal via the formation of a fibro-cartilaginous callus, which is progressively converted to bone. We examine the hypothesis that callus morphology is optimal to achieve a defined limiting stiffness of the bone-callus construct. We demonstrate the use of this principle in designing the starting geometry for iterative computational models of the fracture healing process. Methods For a given fracture geometry, optimal callus dimensions are determined by iteratively increasing the callus size until a defined stiffness is attained, as determined by finite element (FE) analysis of the bone-callus construct. This process is performed using various canonical shapes and material properties for the callus. The optimal morphologies thus predicted are compared to typical histological and radiological observations. The impact of callus morphology on the outcomes of an iterative FE model of fracture healing is investigated using experimental and "optimal" callus dimensions. This model is similar to those published previously, and plots the maturation of tissues in the callus until bony union. We analyse the predicted healing outcomes when optimal, sub-optimal and supra-optimal calluses are used as initial states, by evaluating against existing experimental data. Results Using an FE modelling scheme and comparing its results with typical histology, we establish that callus initially forms an optimally-determined morphology. Secondly, we illustrate the impact of sub-optimal and supra-optimal calluses on the outcomes of an evolutionary FE model, to establish the efficacy of employing optimal callus dimensions in computational models of fracture healing. Conclusions Defining principles for optimal callus morphology provides a feasible starting point for computational models of fracture healing. This may be useful in avoiding modelling artefacts when early-stage experimental data is insufficient. Such models may provide new insights into how different fracture stabilisation methods manipulate the healing process.