Many reaction-diffusion models produce traveling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumor growth. These partial differential equation models have since been adapted to describe the interactions between cells and extracellular matrix (ECM), using a variety of different underlying assumptions. In this work, we derive a system of reaction-diffusion equations, with cross-species density-dependent diffusion, by coarse-graining an agent-based, volume-filling model of cell invasion into ECM. We study the resulting traveling wave solutions both numerically and analytically across various parameter regimes. Subsequently, we perform a systematic comparison between the behaviors observed in this model and those predicted by simpler models in the literature that do not take into account volume-filling effects in the same way. Our study justifies the use of some of these simpler, more analytically tractable models in reproducing the qualitative properties of the solutions in some parameter regimes, but it also reveals some interesting properties arising from the introduction of cell and ECM volume-filling effects, where standard model simplifications might not be appropriate.

Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons / Crossley, Rm; Maini, Pk; Lorenzi, T; Baker, Re. - In: STUDIES IN APPLIED MATHEMATICS. - ISSN 0022-2526. - 151:4(2023), pp. 1471-1497. [10.1111/sapm.12635]

Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons

Lorenzi, T;
2023

Abstract

Many reaction-diffusion models produce traveling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumor growth. These partial differential equation models have since been adapted to describe the interactions between cells and extracellular matrix (ECM), using a variety of different underlying assumptions. In this work, we derive a system of reaction-diffusion equations, with cross-species density-dependent diffusion, by coarse-graining an agent-based, volume-filling model of cell invasion into ECM. We study the resulting traveling wave solutions both numerically and analytically across various parameter regimes. Subsequently, we perform a systematic comparison between the behaviors observed in this model and those predicted by simpler models in the literature that do not take into account volume-filling effects in the same way. Our study justifies the use of some of these simpler, more analytically tractable models in reproducing the qualitative properties of the solutions in some parameter regimes, but it also reveals some interesting properties arising from the introduction of cell and ECM volume-filling effects, where standard model simplifications might not be appropriate.
File in questo prodotto:
File Dimensione Formato  
Crossleyetal_StudApplMath2023.pdf

accesso aperto

Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Creative commons
Dimensione 1.67 MB
Formato Adobe PDF
1.67 MB Adobe PDF Visualizza/Apri
2302.11345.pdf

accesso aperto

Tipologia: 1. Preprint / submitted version [pre- review]
Licenza: Pubblico - Tutti i diritti riservati
Dimensione 1.24 MB
Formato Adobe PDF
1.24 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2984435