Soliton-like attractor for blood vessel tip density in angiogenesis

TL;DR

This paper derives and analyzes a soliton-like model for blood vessel tip density in angiogenesis, showing how it adapts to different conditions and can be used to predict vessel network responses.

Contribution

It introduces a soliton collective coordinate framework for modeling vessel tip density, linking stochastic simulations with deterministic soliton solutions.

Findings

Soliton-like profiles accurately represent vessel tip density.

Maximum tip density locations follow the soliton peak.

Model can predict vessel network responses to parameter changes.

Abstract

Recently, numerical simulations of a stochastic model have shown that the density of vessel tips in tumor induced angiogenesis adopts a soliton-like profile [Sci. Rep. 6, 31296 (2016)]. In this work, we derive and solve the equations for the soliton collective coordinates that indicate how the soliton adapts its shape and velocity to varying chemotaxis and diffusion. The vessel tip density can be reconstructed from the soliton formulas. While the stochastic model exhibits large fluctuations, we show that the location of the maximum vessel tip density for different replicas follows closely the soliton peak position calculated either by ensemble averages or by solving an alternative deterministic description of the density. The simple soliton collective coordinate equations may also be used to ascertain the response of the vessel network to changes in the parameters and thus to control it.