Mechanobiological Modelling of Angiogenesis: Impact on Tissue Engineering and Bone Regeneration - Computational Modeling in Tissue Engineering - page 381

Fig. 5 Distribution of oxygen (top left), MDGF (top right), capillary (bottom left) and fibroblasts
(bottom right) in a quarter of the whole domain after one day
mechanoregulation theories [ 49 , 101 ]. To incorporate the cellular scale with a
more realistic approach, a lattice based formulation is being developed by the
authors and is explained next.
A two-dimensional lattice based model is simulated to predict the outcome of
the distraction osteogenesis process. At the macroscopic scale a poroelastic
analysis is performed to compute the mechanical stimulus within the distracted
gap. An axisymmetric finite element model of a sheep tibia has been established.
The macroscopic scale of the model includes the bone marrow, the cortical bone,
the periosteum, the nail and the distracted gap [ 14 , 102 ]. The distracted gap, is
treated with a lattice-based approach and therefore each macrocopic element is
modelled at the cellular scale with a regular cartesian grid. The different cells
(chondrocytes, osteoblasts, mesenchymal stem cells, fibroblats and dead cells) are
constrained to move on this grid and their evolution is assumed to depend on
different migration, proliferation and differentiation rules [ 49 , 102 ]. Cell migration
and proliferation were modelled as random-walk processes following the random