Modeling and simulation of vascular tumors embedded in evolving capillary networks

TL;DR

This paper introduces a comprehensive 3D-1D coupled model for simulating vascular tumor growth within evolving capillary networks, incorporating angiogenesis, extracellular matrix erosion, and fluid flow dynamics for realistic tumor progression analysis.

Contribution

The work presents a novel integrated model combining tumor growth, vascular network evolution, and fluid flow, capturing stochastic angiogenesis and tumor development in a unified framework.

Findings

Model successfully simulates satellite tumor formation.

Demonstrates the impact of angiogenesis on tumor growth.

Shows flexibility and applicability across various scenarios.

Abstract

In this work, we present a coupled 3D-1D model of solid tumor growth within a dynamically changing vascular network to facilitate realistic simulations of angiogenesis. Additionally, the model includes erosion of the extracellular matrix, interstitial flow, and coupled flow in blood 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 factors (TAFs); blood vessels grow towards the increasing TAFs concentrations. This process is not deterministic, allowing random growth of blood vessels and, therefore, due to the coupling of nutrients in tissue and vessels, makes the growth of tumors stochastic. 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.