Computational Mechanobiology in Cartilage and Bone Tissue Engineering: From Cell Phenotype to Tissue Structure - Computational Modeling in Tissue Engineering - page 335

Uniaxial and biaxial cyclic stretching of cells by 3 and 10% at 0.1, 1.0 and
10.0 Hz were simulated using the Deshpande model in Wei et al. [ 114 ]. Corre-
sponding to experimental observations the model predicted stress-fibre alignment
perpendicular to the stretch direction and its dependence on the stretch magnitude,
the amount of lateral contraction and the frequency. Isotropic stress-fibre archi-
tectures were predicted in the biaxially stretched cells. An earlier model [ 113 ] had
investigated cytoskeletal reorganisation in response to cyclic loading by assuming
acting filament remodelling in response to normal strain and filament disassembly
when their strain energies reach certain levels below or above their basal attach-
ment values. While that model was capable of predicting experimentally observed
alignment patterns, it is incapable of reproducing frequency dependent effects.
This is rooted in the purely elastic (i.e. scleronomous) approach taken that
neglected transient biochemical signals. While the model by Deshpande and
coworkers [ 27 , 28 ] represents a three dimensional finite strain constitutive
framework suitable for finite element implementation, this early model was based
on two in-plane normal strains and assumed linear elastic actin filaments [ 113 ].
Arrays of flexible micro posts have been used to measure forces exerted by the
cells onto a substrate and their distribution within the cell. Due to the dynamic
nature of the cells the interpretation of the results and the extraction of meaningful
parameters has proven difficult. McGarry et al. [ 75 ] simulated smooth muscle
cells, mesenchymal stem cells and fibroblasts on different beds of micro posts
using the model by Deshpande and coworkers [ 27 , 28 ]. Certain model parameters
such as the maximum tensile stress of a fibre bundle were cell type dependent
which has been attributed to the expression of different isoforms of actin and
myosin among those cell types and potentially presents meaningful parameters for
the interpretation of cell type dependent experimental results. For a single cell
type, namely smooth muscle cells, the model could predict a number of experi-
mental observations with the same set of parameters: ''(i) the scaling of the force
exerted by the cells with the number of posts; (ii) actin distributions within the
cells, including the rings of actin around the micro-posts; (iii) the curvature of the
cell boundaries between the posts; and (iv) the higher post forces towards the cell
periphery'' [ 75 ]. The experimental and computed actin stress-fibre architecture of
a cell on a micropost array is depicted in Fig. 1 .
Motivated by observations of fibroblast alignment with directions of tensile
strain, cell locomotion along rigidity gradients towards areas of higher stiffness or
tensile strain and enhanced cell spreading and cytoskeletal organisation with
increasing substrate stiffness, Bischofs and Schwarz [ 6 ] developed a model based
on the idea that cells have a preference for large effective stiffnesses in their local
environment which drives their positioning and orientation. Linear elasticity
continuum theory was adopted to model the ECM in order to keep the presented
calculations feasible. Cells pull on the ECM with their contractile machinery to
extract mechanical information that encompasses the effects of both rigidity and
prestrain in the substrate. In order to capture this behaviour, mechanical work was
chosen as the fundamental stimulus of the mechanoregulation algorithm. By
pulling on the ECM cells build up a force at a focal adhesion site that in