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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...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Hindawi Publishing Corporation
2012
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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. |
format | Online Article Text |
id | pubmed-3420324 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2012 |
publisher | Hindawi Publishing Corporation |
record_format | MEDLINE/PubMed |
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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