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.

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
• 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