Random-walk models of cell dispersal included in mechanobiological simulations of tissue differentiation

Computational models have shown that biophysical stimuli can be correlated with observed patterns of tissue differentiation, and simulations have been performed that predict the time course of tissue differentiation in, for example, long bone fracture healing. Some simulations have used a diffusion model to simulate the migration and proliferation of cells with the differentiating tissue. However, despite the convenience of the diffusion model, diffusion is not the mechanism of cell dispersal: cells disperse by crawling or proliferation, or are transported in a moving fluid. In this paper, a random-walk model (i.e., a stochastic model), with and without a preferred direction, is studied as an approach to simulate cell proliferation/migration in differentiating tissues and it is compared with the diffusion model. A simulation of tissue differentiation of gap tissue in a two-dimensional model of a bone/implant interface was performed to demonstrate the differences between diffusion vs. random walk with a preferred direction. Results of diffusion and random-walk models are similar with respect to the change in the stiffness of the gap tissue but rather different results are obtained regarding tissue patterning in the differentiating tissues; the diffusion approach predicted continuous patterns of tissue differentiation whereas the random-walk model showed a more discontinuous pattern-histological results are not available that can unequivocally establish which is most similar to experimental observation. Comparing isotropic to anisotropic random walk (preferred direction of proliferation and cell migration), a more rapid reduction of the relative displacement between implant and bone is predicted. In conclusion, we have shown how random-walk models of cell dispersal and proliferation can be implemented, and shown where differences between them exist. Further study of the random-walk model is warranted, given the importance of cell seeding and cell dispersal/proliferation in many mechanobiological problems.