In Vivo, In Vitro, In Silico: Computational Tools for Product and Process Design in Tissue Engineering - Computational Modeling in Tissue Engineering - page 8

drawback of these models is that they are not based on knowledge of the system and
as such are difficult to interpret in a biological way. At the other end of the spectrum,
there are mechanistic models (white box) that are knowledge based and as a result
often (much) more complex than data-based models. A hybrid (grey box) approach
has been developed that combines the advantages of both the dynamic data-based
modelling approach and the mechanistic modelling approach into a so called data-
based mechanistic (DBM) modelling approach [ 43 ]. DBM models can be developed
in different ways, but one commonly used approach is to start from available
mechanistic models that then will be reduced in complexity by applying sensitivity
analysis and principal component approaches (e.g. [ 44 , 45 ]). Parameters of the
reduced order model structure can be estimated in a time varying way by using e.g. a
recursive instrumental variable estimation method using data from dynamic exper-
iments with the bioreactor system to be controlled.
Mechanistic (white box) models of in vitro bioreactor processes have been
repeatedly proposed in the literature. O'Dea et al. [ 46 ] provide an overview of the
models that use continuum modelling techniques to investigate how the different
underlying processes interact to produce functional tissues for implantation in cell-
seeded porous scaffolds. They aim to demonstrate how a combination of mathematical
modelling, analysis and in silico computation, undertaken in collaboration with
experimental studies, may lead to significant advances in the understanding of the
fundamental processes regulating biological tissue growth and the optimal design of in
vitro methods for generating replacement tissues that are fully functional. Raimondi
et al. [ 47 ] discuss, also for cell-seeded porous scaffolds, the need for and the advances
in the use of multiphysics and multiscale mathematical models. They describe various
possible approaches to couple biomass growth, medium flow and mass transport in a
single model. Furthermore they discuss recent advances in scientific computing
techniques that are needed to implement these multiscale/multiphysics models as well
as new tools that can be used to experimentally validate the computational results.
Besides the control of the bioreactor process, the design of the bioreactor set-up
itself can play a major role obtaining the desired results. Bjork et al. [ 48 ] use
computational models focusing on the dissolved oxygen transport to design bio-
reactor set-ups for engineered vascular tissues that improve transport, particularly
by perfusion of medium through the interstitial space by transmural flow. Their
computational models, supported by empirical data, specifically investigated
designs that would eliminate nutrient gradients evident during static culture
methods, in order to develop more uniform engineered vascular tissues which
would lead to improved mechanical properties of the resulting construct.
3.3 Computational Tools for the Study of the In Vivo Process
Although according to the developmental engineering concept [ 4 - 8 ], the estab-
lishment of robust modular tissue intermediates in vitro should lead to the desired
high-quality outcome in vivo, the effect of the in vivo environment is an important