Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour Cells
The goal of this paper is to construct a new algorithm for the numerical simulations of the evolution of tumour invasion and metastasis. By means of mathematical model equations and their numerical solutions we investigate how cancer cells can produce and secrete matrix degradative enzymes, degrade...
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Hindawi Limited
2011-01-01
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| Series: | Computational and Mathematical Methods in Medicine |
| Online Access: | http://dx.doi.org/10.1155/2011/452320 |
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doaj-37aa28f3f467474ea0bd84586b03fd5c2020-11-24T23:37:45ZengHindawi LimitedComputational and Mathematical Methods in Medicine1748-670X1748-67182011-01-01201110.1155/2011/452320452320Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour CellsM. Kolev0B. Zubik-Kowal1Department of Mathematics and Computer Science, University of Warmia and Mazury, Zolnierska 14, 10-561, Olsztyn, PolandDepartment of Mathematics, Boise State University, 1910 University Drive, Boise, ID 83725, USAThe goal of this paper is to construct a new algorithm for the numerical simulations of the evolution of tumour invasion and metastasis. By means of mathematical model equations and their numerical solutions we investigate how cancer cells can produce and secrete matrix degradative enzymes, degrade extracellular matrix, and invade due to diffusion and haptotactic migration. For the numerical simulations of the interactions between the tumour cells and the surrounding tissue, we apply numerical approximations, which are spectrally accurate and based on small amounts of grid-points. Our numerical experiments illustrate the metastatic ability of tumour cells.http://dx.doi.org/10.1155/2011/452320 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. Kolev B. Zubik-Kowal |
| spellingShingle |
M. Kolev B. Zubik-Kowal Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour Cells Computational and Mathematical Methods in Medicine |
| author_facet |
M. Kolev B. Zubik-Kowal |
| author_sort |
M. Kolev |
| title |
Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour Cells |
| title_short |
Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour Cells |
| title_full |
Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour Cells |
| title_fullStr |
Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour Cells |
| title_full_unstemmed |
Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour Cells |
| title_sort |
numerical solutions for a model of tissue invasion and migration of tumour cells |
| publisher |
Hindawi Limited |
| series |
Computational and Mathematical Methods in Medicine |
| issn |
1748-670X 1748-6718 |
| publishDate |
2011-01-01 |
| description |
The goal of this paper is to construct a new algorithm for the numerical simulations of the evolution of tumour invasion and metastasis.
By means of mathematical model equations and their numerical solutions we investigate how cancer cells can produce and secrete matrix
degradative enzymes, degrade extracellular matrix, and invade due to diffusion and haptotactic migration. For the numerical simulations
of the interactions between the tumour cells and the surrounding tissue, we apply numerical approximations, which are spectrally accurate
and based on small amounts of grid-points. Our numerical experiments illustrate the metastatic ability of tumour cells. |
| url |
http://dx.doi.org/10.1155/2011/452320 |
| work_keys_str_mv |
AT mkolev numericalsolutionsforamodeloftissueinvasionandmigrationoftumourcells AT bzubikkowal numericalsolutionsforamodeloftissueinvasionandmigrationoftumourcells |
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1725519307882889216 |