Modeling tumor growth with variable mass and angiogenesis-driven perfusion through a 3D-1D coupled framework

TL;DR

This paper introduces a coupled 3D-1D modeling framework for simulating tumor growth and angiogenesis-driven perfusion, integrating tissue and vascular network dynamics through optimization and hybrid tip-tracking methods.

Contribution

It presents a novel numerical approach combining PDE-based tissue modeling with hybrid capillary growth simulation, enabling detailed analysis of tumor-vascular interactions.

Findings

Vascular development critically influences tissue perfusion and tumor progression.

Sensitivity analysis identifies key parameters affecting system behavior.

The framework effectively simulates tumor growth and angiogenesis dynamics.

Abstract

Tumor growth beyond a critical size relies on the development of a functional vascular network, which ensures adequate oxygen and nutrient supply. In this work, we present a modeling framework based on an optimization-based 3D-1D coupling strategy to simulate perfusion in a tumoral tissue with growing mass, interacting with a dynamically evolving capillary network. The tumor is described as a multiphase system including tumor cells and interstitial fluid, governed by a non-linear PDE system for cell volume fraction, pressure, oxygen, and VEGF, and discretized via finite elements. Capillary growth is tackled using a continuous-discrete hybrid tip-tracking approach. The vascular geometry is updated over time according to angiogenic signals, and coupled to the tissue model through a constrained optimization formulation that enforces fluid and nutrient exchange via interface variables. A sensitivity analysis using the Morris elementary effect method identifies key parameters influencing system behavior. Results highlight the critical role of vascular development in regulating tissue perfusion and tumor progression. Overall, the proposed numerical approach provides a versatile tool for investigating tumor-vascular interactions and can support further quantitative analysis of angiogenesis and tumor perfusion dynamics.