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A Novel Method for Simulating the Extracellular Matrix in Models of Tumour Growth

A novel hybrid continuum-discrete model to simulate tumour growth on a cellular scale is proposed. The lattice-based spatiotemporal model consists of reaction-diffusion equations that describe interactions between cancer cells and their microenvironment. The fundamental ingredients that are typicall...

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Autores principales: Toma, Alina, Mang, Andreas, Schuetz, Tina A., Becker, Stefan, Buzug, Thorsten M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2012
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3420324/
https://www.ncbi.nlm.nih.gov/pubmed/22919426
http://dx.doi.org/10.1155/2012/109019
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author Toma, Alina
Mang, Andreas
Schuetz, Tina A.
Becker, Stefan
Buzug, Thorsten M.
author_facet Toma, Alina
Mang, Andreas
Schuetz, Tina A.
Becker, Stefan
Buzug, Thorsten M.
author_sort Toma, Alina
collection PubMed
description A novel hybrid continuum-discrete model to simulate tumour growth on a cellular scale is proposed. The lattice-based spatiotemporal model consists of reaction-diffusion equations that describe interactions between cancer cells and their microenvironment. The fundamental ingredients that are typically considered are the nutrient concentration, the extracellular matrix (ECM), and matrix degrading enzymes (MDEs). The in vivo processes are very complex and occur on different levels. This in turn leads to huge computational costs. The main contribution of the present work is therefore to describe the processes on the basis of simplified mathematical approaches, which, at the same time, depict realistic results to understand the biological processes. In this work, we discuss if we have to simulate the MDE or if the degraded matrix can be estimated directly with respect to the cancer cell distribution. Additionally, we compare the results for modelling tumour growth using the common and our simplified approach, thereby demonstrating the advantages of the proposed method. Therefore, we introduce variations of the positioning of the nutrient delivering blood vessels and use different initializations of the ECM. We conclude that the novel method, which does not explicitly model the matrix degrading enzymes, provides means for a straightforward and fast implementation for modelling tumour growth.
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spelling pubmed-34203242012-08-23 A Novel Method for Simulating the Extracellular Matrix in Models of Tumour Growth Toma, Alina Mang, Andreas Schuetz, Tina A. Becker, Stefan Buzug, Thorsten M. Comput Math Methods Med Research Article A novel hybrid continuum-discrete model to simulate tumour growth on a cellular scale is proposed. The lattice-based spatiotemporal model consists of reaction-diffusion equations that describe interactions between cancer cells and their microenvironment. The fundamental ingredients that are typically considered are the nutrient concentration, the extracellular matrix (ECM), and matrix degrading enzymes (MDEs). The in vivo processes are very complex and occur on different levels. This in turn leads to huge computational costs. The main contribution of the present work is therefore to describe the processes on the basis of simplified mathematical approaches, which, at the same time, depict realistic results to understand the biological processes. In this work, we discuss if we have to simulate the MDE or if the degraded matrix can be estimated directly with respect to the cancer cell distribution. Additionally, we compare the results for modelling tumour growth using the common and our simplified approach, thereby demonstrating the advantages of the proposed method. Therefore, we introduce variations of the positioning of the nutrient delivering blood vessels and use different initializations of the ECM. We conclude that the novel method, which does not explicitly model the matrix degrading enzymes, provides means for a straightforward and fast implementation for modelling tumour growth. Hindawi Publishing Corporation 2012 2012-08-07 /pmc/articles/PMC3420324/ /pubmed/22919426 http://dx.doi.org/10.1155/2012/109019 Text en Copyright © 2012 Alina Toma et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Toma, Alina
Mang, Andreas
Schuetz, Tina A.
Becker, Stefan
Buzug, Thorsten M.
A Novel Method for Simulating the Extracellular Matrix in Models of Tumour Growth
title A Novel Method for Simulating the Extracellular Matrix in Models of Tumour Growth
title_full A Novel Method for Simulating the Extracellular Matrix in Models of Tumour Growth
title_fullStr A Novel Method for Simulating the Extracellular Matrix in Models of Tumour Growth
title_full_unstemmed A Novel Method for Simulating the Extracellular Matrix in Models of Tumour Growth
title_short A Novel Method for Simulating the Extracellular Matrix in Models of Tumour Growth
title_sort novel method for simulating the extracellular matrix in models of tumour growth
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3420324/
https://www.ncbi.nlm.nih.gov/pubmed/22919426
http://dx.doi.org/10.1155/2012/109019
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