A Mechanobiological Model for Tissue Differentiation that Includes Angiogenesis: A Lattice-Based Modeling Approach

Abstract

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.

A computational model to explore the role of angiogenic impairment on endochondral ossification during fracture healing

“…Angiogenesis was modelled using a lattice based approach whereby the elements of the FE model was discretised into a sequence of lattice points, each of which represented a potential cell space ( Figure 1B) (Checa and Prendergast, 2009). Each lattice point had a diameter of 10 µm which corresponded with an overall lattice density of 1 x 10 6 lattice points/mm 3 .…”

“…Vessels were also able to branch should the vessel length exceed a certain value (L min ). The probability of branching then increased linearly until the vessel reached the maximum allowable length (L max ) at which point the probability of branching occurring was 1 (Checa and Prendergast 2009). Vessels grew at a constant rate (V growth ) and could grow into any neighbouring lattice point provided that it was empty.…”

“…The migration and proliferation of MSCs, osteoblasts (OBs), adipocytes (ABs), chondrocytes (CCs), hypertrophic chondrocytes (HCs) and fibroblasts (FBs) was also modelled using the lattice approach (Pérez and Prendergast, 2007;Checa and Prendergast, 2009). The migration of cells was implemented using random walk theory where a cell attempted to randomly move into any of its neighbouring lattice points (Pérez and Prendergast, 2007).…”

“…In-silico models of MSC differentiation have long been used to better understand how environmental factors, and in particular mechanical cues, regulate tissue differentiation during fracture healing (Burke and Kelly, 2012;Burke et al, 2013;Checa and Prendergast, 2009;Isaksson et al, 2008;Alierta et al, 2014). We have previously used such computational models to provide support for the hypothesis that stem cell fate during fracture healing is governed by the local oxygen concentration and stiffness of the surrounding substrate (Burke and Kelly, 2012;Burke et al, 2013Burke et al, , 2014.…”

Mechano-regulation of mesenchymal stem cell differentiation and collagen organisation during skeletal tissue repair

“…The intrinsic viscoelasticity of the involved soft tissues was neglected. We furthermore did not model angiogenesis (Geris et al, 2006;Checa and Prendergast, 2009b) because the developing neoarthrosis and not bone formation was the focus of interest. Stem cell dispersal as a combination of proliferation and migration was implemented as a simple diffusive process without accounting for cell death or the biochemical environment (such as growth factors, e.g.…”