Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network |
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Institution: | Departamento de Métodos Matemáticos e de Representación, Universidade da Coruña, Campus de A Coruña, 15071, A Coruña, Spain |
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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. |
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Keywords: | Tumor growth 3D–1D coupled blood flow models ECM degradation Existence of weak solutions Energy inequality Galerkin method |
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