# Stochastic model of tumor-induced angiogenesis: Ensemble averages and deterministic equations.

@article{Terragni2016StochasticMO, title={Stochastic model of tumor-induced angiogenesis: Ensemble averages and deterministic equations.}, author={Filippo Terragni and Manuel Carretero and Vincenzo Capasso and Luis L. Bonilla}, journal={Physical review. E}, year={2016}, volume={93 2}, pages={ 022413 } }

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 one 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…

## 18 Citations

### On the mathematical modelling of tumor-induced angiogenesis.

- PhysicsMathematical biosciences and engineering : MBE
- 2017

The outcomes of relevant numerical simulations show that the proposed model, in presence of anastomosis, is not self-averaging, so that the ``propagation of chaos" assumption cannot be applied to obtain a deterministic mean field approximation.

### Stochastic Models of Blood Vessel Growth

- BiologyStochastic Dynamics Out of Equilibrium
- 2019

A hybrid mesoscale tip cell model involves stochastic branching, fusion and extension of active vessel tip cells with reaction-diffusion growth factor fields and adopts the form of an advancing soliton that can be characterized by ordinary differential equations for its position, velocity and a size parameter.

### The statistical theory of the angiogenesis equations

- Mathematics
- 2022

Angiogenesis is a multiscale process by which a primary blood vessel issues secondary vessel sprouts that reach regions lacking oxygen. Angiogenesis can be a natural process of organ growth and…

### Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis

- BiologyEntropy
- 2017

This work shows the delaying effect of haptotaxis on the advance of the angiogenic vessel network by direct numerical simulations of the stochastic process and by a study of the soliton motion.

### Integrodifference master equation describing actively growing blood vessels in angiogenesis

- Physics
- 2020

This system models tumor-induced angiogenesis, the process of formation of blood vessels induced by a growth factor released by a tumor, by tracking the density of active tips, calculated as an ensemble average over many realizations of the stochastic process.

### Solitonlike attractor for blood vessel tip density in angiogenesis.

- PhysicsPhysical review. E
- 2016

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.

### A convergent numerical scheme for integrodifferential kinetic models of angiogenesis

- PhysicsJ. Comput. Phys.
- 2018

### The Mathematical modeling of Cancer growth and angiogenesis by an individual based interacting system.

- BiologyJournal of theoretical biology
- 2023

### Notch signaling and taxis mechanims regulate early stage angiogenesis: A mathematical and computational model

- BiologybioRxiv
- 2019

A mathematical model of early stage angiogenesis is presented that permits to explore the relative importance of mechanical, chemical and cellular cues in vessel growth and unravels the regulating role of Jagged, Notch and Delta dynamics in vascular cells.

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