Stochastic Model of Tumor-induced Angiogenesis: Ensemble Averages and Deterministic Equations

TL;DR

This paper connects a stochastic model of tumor-induced angiogenesis with its deterministic counterpart, demonstrating that ensemble averages match the deterministic equations and fitting key parameters for consistency.

Contribution

It provides a detailed analysis showing how ensemble averages of a stochastic angiogenesis model correspond to deterministic equations, including parameter fitting.

Findings

Ensemble averages match deterministic equations.

Fitted anastomosis rate coefficient for consistent vessel tip evolution.

Validated the stochastic model against deterministic descriptions.

Abstract

A recent conceptual model of tumor-driven angiogenesis including branching, elongation, and anastomosis of blood vessels captures some of the intrinsic multiscale structures of this complex system, yet allowing to extract a deterministic integro-partial differential description of the vessel tip density [Phys. Rev. E 90, 062716 (2014)]. Here we solve the stochastic model, show that ensemble averages over many realizations correspond to the deterministic equations, and fit the anastomosis rate coefficient so that the total number of vessel tips evolves similarly in the deterministic and ensemble averaged stochastic descriptions.