Computational Methods in the Modeling of Scaffolds for Tissue Engineering - Computational Modeling in Tissue Engineering - page 116

Fig. 10 a Lattice generated
from granulation element
geometry. b possible cell
locations when migrating
properties (typical initial tissue that fill wounds). Each lattice is considered a
region of space for both the cell and extracellular matrix (Fig. 10 ).
The lattice model has been used as an alternative to simulate cell proliferation
and migration. The proliferation of a cell is initially assumed (in 3D) to be sur-
rounded by six possible locations. First a new position is randomly selected from
the surrounding locations (including its original position). In turn one of the
remaining neighboring positions is then chosen for the daughter cell to occupy. In
the event that the chosen location is already occupied, another position is chosen
again at random. This process continues until either the simulation ends or all
lattice positions are occupied. Recognizing that migration is a more rapid process,
a new location for a migrating cell is chosen per iteration of the proliferation
process. A lattice point can be occupied by a mesenchymal cell (MSC), a fibro-
blast, a chondrocyte, an osteoblast or an endothelial cell. The sequence of endo-
thelial cells and the vessel growth direction, growth length and branching are
defined through the lattice formulation as probabilistic functions.
The lattice concept was applied in tissue engineering by Byrne et al. [ 39 ]
(Fig. 11 ). They studied the effect of important design properties such as scaffold
porosity, degradation rate and scaffold mechanical properties, on the tissue for-
mation process inside a regular structured bone scaffold. Initially the scaffold was
assumed to be filled with granulation tissue and 1% of lattice points, chosen at
random, were ''seeded'' with mesenchymal stem cells. Over time, the scaffold
dissolved at a rate of 0.5% per iteration of the simulation, leaving space for the
developing tissue. In this study, they were able to identify optimal scaffold
properties that would lead to the highest amount of bone formation.
Studies of angiogenesis during tissue differentiation were performed by Checa
and Prendergast [ 40 ] using the lattice model. The angiogenesis model was applied
to a simplified scaffold for bone tissue engineering and the number of cells initially
seeded into the scaffold was related to the rate of vascularization and the pene-
tration of the vascular network. They showed that the initial cell seeding condi-
tions had a significant effect on the vascularization of the scaffold.
In order to simulate also the angiogenesis phenomenon in CaP cement, Sandino
et al. [ 41 ] applied the lattice approach in a scaffold with irregular morphology
(Fig. 12 ). For the magnitudes of mechanical strain studied (0.5 and 1% of total