Multiphysics Computational Modeling in Cartilage Tissue Engineering - Computational Modeling in Tissue Engineering - page 264

actual fluid velocities in the scaffold, which are impossible to measure. This
problem has been dealt with by using detailed pore-scale computational fluid-
dynamic (CFD) simulations of fluid and chemical transport in tissue-engineering
scaffolds populated with living cells [ 1 , 10 , 11 , 31 , 47 ]. In these models, the same
set of equations is solved as in the above cited model, but considering only a few
unit cells. This allows to obtain a much higher scale resolution and to represent the
real local scaffold empty/filled structure. These simulations are able to capture
flow, pressure and concentration fields resolved at the microscopic level. In par-
ticular, it is shown how the scaffold micro architecture influences the hydrody-
namic shears imposed on cells within constructs. Calculations of nutrient flow
indicate that inappropriately designed dynamic culture environments lead to
regions of nutrient concentration insufficient to maintain cell viability. These
studies provide a foundation for exploring the effects of dynamic flow on cell
function and provide an important insight into the design and optimization of 3D
scaffolds suitable in bioreactors for in vitro tissue engineering.
4 Coupled Models of Biomass Growth, Medium Flow
and Mass Transport
A consistent mathematical description of tissue regeneration requires to provide a
model of biomass growth, as indicated in Eq. ( 4 ). This is a very complex problem,
involving several biophysical variables. Experimental observations and measure-
ments [ 32 ] suggest that after seeding, cells undergo (i) a first period (5-7 days) of
rapid proliferation, (ii) a second period (2-4 weeks) in which they start to signifi-
cantly secrete the typical highly hydrated extracellular matrix (ECM), comprising
proteoglycan monomers assembled with glycosaminoglycans (GAGs) anchored to
hyaluronic acid chains, type II collagen and a small amount of other types of
collagen. To our knowledge, there are no comprehensive models of (i), and (ii) in this
application field, rather, only partial descriptions of (i) or (ii) have been developed.
4.1 Cell Population Dynamics
Computational tools known under the name of multicellular simulations can be used
to model cell population dynamics. In these approaches, simple rules based on cell
automata are adopted to describe cell behavior and the emergent trend of the cell
populations is observed and analyzed. In particular, biased random walk techniques
have found widespread use in biological applications like the simulation of angio-
genesis [ 30 ] and, recently, have been applied to simulate cell populations that
migrate, collide, and proliferate to build a tissue inside a 3D scaffold [ 7 ].
Simulation results show that the speed of cell locomotion modulates the rates
of tissue regeneration by controlling the effect of contact inhibition and that the