Abstract
AbstractWe derive a multiphase, moving boundary model to represent the development of tissue in vitro in a porous tissue engineering scaffold. We consider a cell, extra-cellular liquid and a rigid scaffold phase, and adopt Darcy’s law to relate the velocity of the cell and liquid phases to their respective pressures. Cell–cell and cell–scaffold interactions which can drive cellular motion are accounted for by utilising relevant constitutive assumptions for the pressure in the cell phase. We reduce the model to a nonlinear reaction–diffusion equation for the cell phase, coupled to a moving boundary condition for the tissue edge, the diffusivity being dependent on the cell and scaffold volume fractions, cell and liquid viscosities and parameters that relate to cellular motion. Numerical simulations reveal that the reduced model admits three regimes for the evolution of the tissue edge at large time: linear, logarithmic and stationary. Employing travelling-wave and asymptotic analysis, we characterise these regimes in terms of parameters related to cellular production and motion. The results of our investigation allow us to suggest optimal values for the governing parameters, so as to stimulate tissue growth in an engineering scaffold.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,General Agricultural and Biological Sciences,Pharmacology,General Environmental Science,General Biochemistry, Genetics and Molecular Biology,General Mathematics,Immunology,General Neuroscience
Cited by
3 articles.
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