Computational Mechanobiology in Cartilage and Bone Tissue Engineering: From Cell Phenotype to Tissue Structure - Computational Modeling in Tissue Engineering - page 333

stress or strain generating mechanisms, the lack of such constitutive models is
particularly problematic for the elucidation of relevant signalling cascades [ 53 ].
Cellular rheology is therefore a very active field of research where phenomena
unknown from traditional engineering materials play a role, e.g. the ability of the
''material'' to perform work via ATP hydrolysis. While classical equilibrium
materials exhibit thermal fluctuations, the cell presents a nonequilibrium material
with additional actively driven fluctuations [ 69 ]. For a recent review on me-
chanosensing, candidate signalling mechanisms and their relation to cell rheology
see the article by Janmey and McCulloch [ 53 ].
Most tissue cells are anchorage dependent, probe their environment by actively
pulling on it and respond with cytoskeletal (re)organisation and rearrangement of
focal adhesion complexes [ 29 ]. Apart from this anchorage dependent behaviour of
differentiated cells, mesenchymal stem cells (MSCs) have recently been shown to
differentiate into neurons, myoblasts and osteoblasts depending on the stiffness of
the substrate onto which they adhere [ 31 ]. This differentiation mechanism was
shown to be dependent on nonmuscle myosin II and is hence linked to the active
contractility of the cells [ 31 ]. In contrast to the response to external forces relying
on outside-in signalling pathways, sensitivity to passive properties of the extra-
cellular space requires a two-step inside-out outside-in mechanism [ 29 ]. Cell
contraction and stress-fibre formation are thus fundamental aspects of both the
behaviour of differentiated cells and stem cell differentiation itself and are of direct
relevance for tissue engineering applications. In this review we chose to highlight
a class of models that incorporates some of the active mechanisms described above
and appears useful in the investigation of cell-ECM or cell-substrate interactions.
Understanding these interactions is important not only for explaining fundamental
cell functions, cell remodelling and cell differentiation, but also for the design of
biomaterials that support cells and are used in pharmacology, cell culture and
tissue engineering.
2.2 Modelling the Environmentally Regulated Dynamics
of the Cytoskeleton
Early models of cell contraction relied on static discrete sets of stress-fibres [ 77 ]or
classical continuum modelling strategies such as thermoelasticity [ 83 ], neglecting
the dynamic and anisotropic nature of the cell. Deshpande et al. [ 27 ] developed a
continuum model that incorporates ''three key biochemical processes: (i) an
activation signal that triggers actin polymerization and myosin phosphorylation,
(ii) the tension-dependent assembly of the actin and myosin into stress fibres, and
(iii) the cross-bridge cycling between the actin and the myosin filaments that
generates the tension.'' The finite strain constitutive model for the cell was
developed based on the homogenisation of the activation and deformation
behaviour of a single cellular stress fibre. It has been shown to capture the scaling