Continuum Modelling of In Vitro Tissue Engineering: A Review - Computational Modeling in Tissue Engineering - page 238

authors have considered similar approaches, using either Brinkman (Lawrence
et al. 2008 ; Devarapalli et al. 2009 ) or Darcy constitutive laws Cioffi et al. ( 2008 )
to model flow through the porous scaffold.
In addition to the above macroscale approach, there are two alternative ways to
incorporate scaffold topology into the models. In the first, imaging techniques are
used to provide detailed information about the pore scale geometry, which in turn
provides a realistic computational domain within which to simulate the governing
model equations. As an example, Cioffi et al. ( 2006 ) reconstructed the scaffold
micro-geometry from l-CT images acquired from a sample of the actual scaffold.
The steady-state Navier-Stokes equations through the domain were solved using
the commercial CFD software ANSYS FLUENT, which enabled quantification of
the flow field and fluid shear stresses acting on the internal walls of the matrix in a
tissue engineered construct subject to direct perfusion of culture medium within a
bioreactor. A second approach is to idealise the micro-scale geometry. Boschetti
et al. ( 2006 ) used a simplification of the geometry of a polymeric scaffold obtained
by particulate leaching. A micro-domain of the scaffold was idealised as 27 sub-
units arranged in a honey-comb pattern. Each sub-unit was obtained by subtracting
a solid sphere from a concentric solid cube. The aim was to predict how the shear
stress experienced by the cells depends on physical quantities such as scaffold
porosity, pore size, and the imposed flow rate. By solving the Navier-Stokes
equations in this complex domain, subject to appropriate boundary conditions
(such as no-slip), it was possible to determine the exact nature of the flow prop-
erties. In Cioffi et al. ( 2006 ), the results of the simulations using the exact detailed
scaffold architecture were compared with that from a simplified micro-scale model
(Raimondi et al. 2004 ). A key finding is that, within the parameter regime con-
sidered (low Reynolds number flow and interconnected pores), the micro-geom-
etry of the scaffold did not affect significantly the median shear stress acting on the
inner scaffold walls. Hence, for the scaffolds considered in Cioffi et al. ( 2006 ), it is
not necessary to build a detailed model for each new scaffold geometry, when a
simple estimation of the median, mode and mean shear stress is required. The use
of 3D geometrical models simplifies the scaffold geometry and reduces signifi-
cantly the cost of the computation. Cioffi et al. ( 2008 ) considered a combined
macro-scale/microscale computational approach to quantify oxygen transport and
flow-mediated shear stress experienced by cells cultured in three-dimensional
scaffolds in perfusion bioreactor systems. The macro-scale model consisted of
Darcy equations for flow in the porous scaffold and an advection-reaction-
diffusion equation for nutrient transport. The micro-scale approach was based on
l-CT reconstruction of the scaffold geometry. While both modelling approaches
predicted similar average oxygen levels at different depths, the l-CT model
captured the micro-scale variations associated with the scaffold architecture. Thus,
the choice of modelling approach for the scaffold geometry should be motivated by
the required model outputs—if estimations of average shear stress and oxygen
concentration are of interest, a simplified modelling approach can be taken,
whereas if precise details of the spatial distribution of shear stress and oxygen