Computational Methods in the Modeling of Scaffolds for Tissue Engineering - Computational Modeling in Tissue Engineering - page 111

studies illustrate how for different scaffold microstructure designs, different
effective stiffnesses and permeabilities are computed [ 6 , 14 ]. However, the
importance of this method lies in the ability to maximize the permeability for cell
migration and mass transport, always taking care to maintain the effective elastic
properties similar to that of the natural tissue [ 24 ].
Homogenization is a powerful mathematical technique and can be applied in
tissue engineering to optimize the process inside the scaffold. The study proposed
by Shipley et al. [ 25 ] used this theory to optimize the oxygen, glucose and lactate
transport through the maximum value of diffusion, consumption and production
with optimal choice of cell density. So select the most favorable scaffold structure
and the preference of perfuse direction.

4 Simulating Fluid Flow Within Porous Scaffolds

4.1 Computing Fluid Stimuli on the Scaffold Pores

In tissue engineering bioreactors are usually used as systems to provide the
dynamic environment to the cells. The stimuli can be obtained from the scaffold
surface deformations or from the fluid flow inside the pores. Mass transport within
the pores is related with the cell seeding and with the possible response of the cells
to the stimuli. Perfusion bioreactors are systems extensively used in tissue engi-
neering, due to the capacity to lead to a uniform distribution of fluid over the
scaffold [ 26 - 28 ]. Micro pore shapes in the scaffold have a higher influence in flow
profile. Generally, the flow is simulated using computational fluid dynamic (CFD)
method. In the specific case of direct perfuse flow, a laminar and Newtonian flow
are simulated, computed by the Navier-Stokes equation (Eq. 6 ) and the continuity
equation (Eq. 7 ), where u and r p are the fluid velocity and pressure gradient
respectively.

qu r u ¼r p þ g r 2 u ð 6 Þ

r u ¼ 0 ð 7 Þ

In Fig. 6 results of CFD for irregular pores morphologies [ 13 ] and regular
morphologies [ 5 ] are presented. Irregular morphology models were developed
from the micro-CT images and the fluid volume inside the pore was modeled
(Fig. 6 a). The scaffold material property in itself was not accounted for in these
studies, only the pore morphological characteristics influenced the results. Milan
et al. [ 13 ] obtained a non homogeneous distribution of fluid flow due to the
irregular interconnection between the pores. For an inlet velocity of 100 lm/s, the
highest velocities (150-780 lm/s) were found in the center of the scaffold pores
whereas the lowest velocities (0-50 lm/s) were found close to the pore walls
(Fig. 6 a).