Phenomenological computational models of tissue regeneration and bone healing have been only partially successful in predicting experimental observations. This may be a result of simplistic modeling of cellular activity. Furthermore, phenomenological models are limited when considering the effects of combined physical and biological interventions. In this study, a new model of cell and tissue differentiation, using a more mechanistic approach, is presented and applied to fracture repair. The model directly couples cellular mechanisms to mechanical stimulation during bone healing and is based on the belief that the cells act as transducers during tissue regeneration. In the model, the cells within the matrix proliferate, differentiate, migrate, and produce extracellular matrix, all at cell-phenotype specific rates, based on the mechanical stimulation they experience. The model is assembled from coupled partial differentiation equations, which are solved using a newly developed finite element formulation. The evolution of four cell types, i.e. mesenchymal stem cells, fibroblasts, chondrocytes and osteoblasts, and the production of extracellular matrices of fibrous tissue, cartilage and bone are calculated. The material properties of the tissues are iteratively updated based on actual amounts of extracellular matrix in material elements at progressive time points. A two-dimensional finite element model of a long bone osteotomy was used to evaluate the model's potential. The additional value of the presented model and the importance of including cell-phenotype specific activities when modeling tissue differentiation and bone healing, were demonstrated by comparing the predictions with phenomenological models. The model's capacity was established by showing that it can correctly predict several aspects of bone healing, including cell and tissue distributions during normal fracture healing. Furthermore, it was able to predict experimentally established alterations due to excessive mechanical stimulation, periosteal stripping and impaired effects of cartilage remodeling.
Isaksson, H. E., Donkelaar, van, C. C., Huiskes, R., & Ito, K. (2008). A mechano-regulatory bone-healing model incorporating cell-phenotype specific activity. Journal of Theoretical Biology, 252(2), 230-246. https://doi.org/10.1016/j.jtbi.2008.01.030