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arXiv · 2006.10477

Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network

Marvin Fritz·Prashant K. Jha·Tobias Köppl·J. Tinsley Oden·Barbara Wohlmuth
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Abstract

In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy's law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D-1D coupled model. We show some mathematical results on the existence of weak solutions. Furthermore, simulation results are presented illustrating the evolution of tumors and the effects of ECM erosion.

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Marvin Fritz, Prashant K. Jha, Tobias Köppl, J. Tinsley Oden, Barbara Wohlmuth. 2021-03-23. Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network. https://doi.org/10.1016/j.nonrwa.2021.103331

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