Multiphysics Computational Modeling in Cartilage Tissue Engineering - Computational Modeling in Tissue Engineering - page 259

1 Introduction
A basic concept in the design of ex vivo tissue reconstruction is to provide a proper
biophysical microenvironment to cells [ 38 ]. In cartilage regeneration (Fig. 1 ),
mechanical stimulation is being extensively evaluated as a tool to modulate extra-
cellular matrix (ECM) synthesis, coherently with the evidence that mechanical
forces play an important role in cartilage homeostasis in vivo [ 14 ]. Mechanobiology
models of engineered cartilage are currently addressed at optimizing the applied
mechanical stimuli, by combining different stimuli, for example flow perfusion with
cyclic pressurization (Fig. 2 )[ 25 , 26 , 42 , 46 ], as a means to better mimic the complex
biophysical environment of chondrocytes within native cartilage.
To gain a better insight into the quantitative relationship between the applied
culture conditions and cartilage growth, advanced computational models are
currently applied to interpret the results from bioreactor studies. These attempts to
calculate and control the balance of mass transport and mechanical stresses exerted
on cells, have proven useful in capturing a rough understanding of the conditions
favoring the development of engineered cartilage [ 36 , 37 , 39 , 40 , 42 , 26 , 44 ].
In mechanobiology models of engineered cartilage, comparison between the
experimental findings and the computational results enable the local field variables
to be correlated with specific cell responses. Only from the mastering of the
complex biological phenomena (cell metabolism and proliferation, substrate
degradation and remodeling of the ECM) that take place during the in vitro
culturing process, one can control key aspects of tissue maturation.
2 Tissue Engineering: A Multiphysics/Multiscale Problem
Bioreactors for tissue culture are complex multiphase systems composed of a
scaffold portion, a culture medium and a growing biomass. For their rational
design, it is thus strongly required to have a quantitative understanding of the
interplay between geometry, interstitial flow field, nutrient mass transfer and
cellular behavior (proliferation, migration, biosynthetic activity). These variegated
phenomena encompass a wide range of embedded scales.
Figure 3 shows five distinct scales at which (at least) the considered problem
can be modeled, namely:
- Macroscale: it is the scale at which the perfused scaffold is treated as a con-
tinuum and at which the Bioengineer sets the control parameters (inlet velocity,
pressure drop). Its characteristic length is of the order of a few millimeters.
- Mesoscale: it is the scale corresponding to a collection of a few functional
sub-units (shortly, unit cells) of the scaffold. Its characteristic length spans from
tens of microns to millimeters.
- Microscale: it is the scale of the single unit cell of the polymeric scaffold, of the
order of 100 microns.