Continuum Modelling of In Vitro Tissue Engineering: A Review - Computational Modeling in Tissue Engineering - page 245

For example, Lemon and coworkers specialise the modelling framework to
consider two fluid phases (cells and culture medium being modelled by a viscous
fluid and an inviscid fluid, respectively) contained within a rigid porous scaffold,
employing the resulting model to investigate proliferation, aggregation, dispersal
and travelling wave behaviour of a population motile cells within an artificial
scaffold. In Lemon et al. ( 2006 ), linear stability analysis was employed to deter-
mine how aggregative or dispersive behaviour depends upon the model parame-
ters; in Lemon and King ( 2007b ), by considering travelling wave solutions, taking
distinguished limits of certain model parameters (such as the viscous drag between
the cell and scaffold phases) and obtaining numerical solutions in one spatial
dimension it was shown that this model displays a wide range of travelling wave
behaviour. Notably, both backward and forward-travelling waves may exist, an
unusual feature of models for tissue growth. By introducing a generic passive
solute whose spatio-temporal dynamics are governed by an advection-reaction-
diffusion equation, the influence of nutrient limitations on tissue growth was
considered in Lemon and King ( 2007a ). In addition, different initial cell seeding
strategies were studied, and spatial heterogeneity of the scaffold was accommo-
dated in a limited sense by prescribing a scaffold density distribution which is
constant except near the periphery where it tapers to zero. Numerical simulation
(in one spatial dimension), as well as simplifying asymptotic limits, indicate
preferential tissue growth near the scaffold's periphery due to nutrient depletion by
the cells; reduction of cell-scaffold drag ameliorates this feature.
These models reveal that scaffold properties (drag and porosity) are key
determining factors affecting the expansion of the cell population to colonise the
scaffold, and provides a methodology with which to determine model parameter
regimes in which the cell population is able to colonise uniformly the scaffold.
In the above studies by Lemon and coworkers, attention was restricted to a single
cell phase, which was assumed to proliferate at a constant rate (or at a rate pro-
portional to the local nutrient concentration). O'Dea et al. ( 2008 , 2010 ) employed
the general multiphase formulation ( 1 ), ( 2 ), ( 6 ) and ( 7 ) to investigate the ability of
different mechanical stimuli to influence tissue construct growth. By suitable
specification of the mass transfer rates S i (and employing viscous constitutive
assumptions for both the cell and culture medium phases), progression between
three different cell phenotypes was considered: (i) proliferative, (ii) ECM-depos-
iting and (iii) apoptotic. Guided by experimental studies (Roelofsen et al. 1995 ;
Klein-Nulend et al. 1995a ; You et al. 2000 ; Bakker et al. 2004b ; Han et al. 2004 ;
Yourek et al. 2004 ), simple functional forms were proposed to model phenotypic
changes in response to cell density (reflecting contact inhibition), and culture
medium pressure and shear stress (reflecting the accepted influences of these
stimuli on bone tissue growth). This approach was also exploited in the study of
Shakeel et al. ( 2011 ), described above. Numerical simulations presented in O'Dea
et al. ( 2010 ) indicated that the mechanical stimuli to which the cells respond can
alter significantly the composition and morphology of the resulting tissue construct.
This suggests that, in real applications, the histology of engineered tissue constructs