Mechanobiological Modelling of Angiogenesis: Impact on Tissue Engineering and Bone Regeneration - Computational Modeling in Tissue Engineering - page 376

Recently, Checa and Prendergast [ 21 ] have proposed a lattice-based
mechanobiological model for tissue differentiation and blood vessel growth to
determine the influence of cell seeding on vascular network development and
tissue growth inside a regular-structured bone scaffold under different loading
conditions. They combined the mechanoregulation theory proposed by Prendergast
et al. [ 101 ] with a stochastic model for cell migration and proliferation based on a
random walk theory [ 97 ].
3.2.2 Cellular Potts Models
The Glazier-Graner-Hogeweg model, also known as the cellular potts model
(CPM) is a discrete lattice Monte Carlo model developed by Glazier and Graner
and is based on an energy minimization principle [ 47 ]. Therefore, in these models
migration occurs in those directions that minimize a local energy function [ 82 ] and
the aggregation/interaction between cells is defined by cell-cell contact energies
[ 4 ]. CPM have been used to model vasculogenesis by Merks et al. [ 79 - 81 ] and
angiogenesis by Bauer et al. [ 7 ] and Merks et al. [ 81 ]. Bauer et al. [ 7 ] described
the first cell-based model of tumor-induced angiogenesis. At the cellular level, the
model uses the cellular Potts model and describes endothelial cell migration,
growth, division, cellular adhesion, and the evolving structure of the stroma.
Merks et al. [ 81 ] proposed a CPM that simulated both vasculogenesis and angi-
ogenesis with a single biophysical mechanism.
3.2.3 Agent-Based Models
In contrast to previous models, agent based models go beyond the lattice-based
space representation and aim to incorporate information of the shape and size of
the cells [ 84 ]. Stokes and Lauffenburger [ 116 ] have based their modelling of
angiogenesis on stochastic differential equations accounting for chemotaxis and
random motion with an agent based model (lattice-free). They were able to model
tip cell migration by imposing rules for branching and anastomosis. However,
other important features such as the interaction of cells and the ECM and the brush
border effect were not taken into account.
Wood et al. [ 123 ] developed an agent field model to simulate the angiogenic
vascular network formation. The model consists of an inhomogeneous population
Markov chain where transition probabilities vary according to the state of the gel
matrix field.
3.2.4 Cell Force-Based Models
These models normally use individual cells as basic units, each of which is
characterized by its location and orientation, its state of stress, and the active