Phase Field Models of the Growth of Tumors Embedded in an Evolving Vascular Network: Dynamic 1D-3D Models of Angiogenesis

Abstract

In this talk, we present a coupled 3D-1D model of tumor growth within a dynamically changing vascular network to facilitate realistic simulations of angiogenesis. Additionally, the model includes ECM erosion, interstitial flow, and coupled flow in vessels and tissue. We employ continuum mixture theory with stochastic Cahn–Hilliard type phase-field models of tumor growth. The interstitial flow is governed by a mesoscale version of Darcy’s law. The flow in the blood vessels is controlled by Poiseuille flow, and Starling’s law is applied to model the mass transfer in and out of blood vessels. The evolution of the network of blood vessels is orchestrated by the concentration of the tumor angiogenesis factor (TAF) by growing towards increasing TAF concentration. The process is not deterministic, allowing random growth of blood vessels and, therefore, due to the coupling of nutrients in tissue and vessels, stochastic tumor growth. We demonstrate the performance of the model by applying it to a variety of scenarios. Numerical experiments illustrate the flexibility of the model and its ability to generate satellite tumors. Simulations of the effects of angiogenesis on tumor growth are presented as well as sample-independent features of cancer. This is joint work with Dr. J. T. Oden at the University of Texas at Austin, M. Fritz, Dr. T. Köppl, A. Wagner, and Dr. B. Wohlmuth at the Technical University of Munich. The work of PKJ and JTO was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Mathematical Multifaceted Integrated Capability Centers (MMICCS), under Award Number DE-SC0019303.