Corroboration of mechanoregulatory algorithms for tissue differentiation during fracture healing: comparison with in vivo results

Several mechanoregulation algorithms proposed to control tissue differentiation during bone healing have been shown to accurately predict temporal and spatial tissue distributions during normal fracture healing. As these algorithms are different in nature and biophysical parameters, it raises the question of which reflects the actual mechanobiological processes the best. The aim of this study was to resolve this issue by corroborating the mechanoregulatory algorithms with more extensive in vivo bone healing data from animal experiments. A poroelastic three-dimensional finite element model of an ovine tibia with a 2.4 mm gap and external callus was used to simulate the course of tissue differentiation during fracture healing in an adaptive model. The mechanical conditions applied were similar to those used experimentally, with axial compression or torsional rotation as two distinct cases. Histological data at 4 and 8 weeks, and weekly radiographs, were used for comparison. By applying new mechanical conditions, torsional rotation, the predictions of the algorithms were distinguished successfully. In torsion, the algorithms regulated by strain and hydrostatic pressure failed to predict healing and bone formation as seen in experimental data. The algorithm regulated by deviatoric strain and fluid velocity predicted bridging and healing in torsion, as observed in vivo. The predictions of the algorithm regulated by deviatoric strain alone did not agree with in vivo data. None of the algorithms predicted patterns of healing entirely similar to those observed experimentally for both loading modes. However, patterns predicted by the algorithm based on deviatoric strain and fluid velocity was closest to experimental results. It was the only algorithm able to predict healing with torsional loading as seen in vivo.