A mechanobiological model for tissue differentiation that includes angiogenesis: a lattice-based modeling approach

Mechanobiological models have previously been used to predict the time course of the tissue differentiation process, with the local mechanical environment as the regulator of cell activity. However, since the supply of oxygen and nutrients to cells is also a regulator of cell differentiation and oxygen diffusion is limited to few hundred micrometers from capillaries, the morphology of the new vascular network may also play a critical role in the process. In this paper, a computational model for tissue differentiation based on the local mechanical environment and the local vascularity is presented. A regular lattice is used to simulate cell activity (migration, proliferation, differentiation, apoptosis, and angiogenesis). The algorithm for capillary network formation includes mechanoregulation of vessel growth. A simulation of tissue differentiation in a bone/implant gap under shear was performed. The model predicts capillary networks similar to those found in experimental studies and heterogeneous patterns of tissue differentiation, which are influenced by the morphology of the capillary network. Higher mechanical loads caused slower vascular development and delayed bone tissue formations.