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Travelling-Wave and Asymptotic Analysis of a Multiphase Moving Boundary Model for Engineered Tissue Growth

Jepson, Jacob M.; Fadai, Nabil T.; O’Dea, Reuben D.

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Authors

Jacob M. Jepson

NABIL FADAI NABIL.FADAI@NOTTINGHAM.AC.UK
Assistant Professor



Abstract

We 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.

Citation

Jepson, J. M., Fadai, N. T., & O’Dea, R. D. (2022). Travelling-Wave and Asymptotic Analysis of a Multiphase Moving Boundary Model for Engineered Tissue Growth. Bulletin of Mathematical Biology, 84(8), Article 87. https://doi.org/10.1007/s11538-022-01044-0

Journal Article Type Article
Acceptance Date Jun 15, 2022
Online Publication Date Jul 12, 2022
Publication Date Aug 1, 2022
Deposit Date Jun 21, 2022
Publicly Available Date Jul 13, 2023
Journal Bulletin of Mathematical Biology
Print ISSN 0092-8240
Electronic ISSN 1522-9602
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 84
Issue 8
Article Number 87
DOI https://doi.org/10.1007/s11538-022-01044-0
Public URL https://nottingham-repository.worktribe.com/output/8630048
Publisher URL https://link.springer.com/article/10.1007/s11538-022-01044-0

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