Multiscale modelling, analysis and simulation of cancer invasion mediated by bound and soluble enzymes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909790039441408 |
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| author | Ptashnyk, Mariya Venkataraman, Chandrasekhar |
| author_facet | Ptashnyk, Mariya Venkataraman, Chandrasekhar |
| contents | We formulate a cell-scale model for the degradation of the extra-cellular matrix by membrane-bound and soluble matrix degrading enzymes produced by cancer cells. Based on the microscopic model and using tools from the theory of homogenisation we propose a macroscopic model for cancer cell invasion into the extra-cellular matrix mediated by bound and soluble matrix degrading enzymes. For suitable and biologically relevant initial data we prove the macroscopic model is well-posed. We propose a finite element method for the numerical approximation of the macroscopic model and report on simulation results illustrating the role of the bound and soluble enzymes in cancer invasion processes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_12413 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiscale modelling, analysis and simulation of cancer invasion mediated by bound and soluble enzymes Ptashnyk, Mariya Venkataraman, Chandrasekhar Analysis of PDEs 35Kxx, 92Bxx, 65M60 We formulate a cell-scale model for the degradation of the extra-cellular matrix by membrane-bound and soluble matrix degrading enzymes produced by cancer cells. Based on the microscopic model and using tools from the theory of homogenisation we propose a macroscopic model for cancer cell invasion into the extra-cellular matrix mediated by bound and soluble matrix degrading enzymes. For suitable and biologically relevant initial data we prove the macroscopic model is well-posed. We propose a finite element method for the numerical approximation of the macroscopic model and report on simulation results illustrating the role of the bound and soluble enzymes in cancer invasion processes. |
| title | Multiscale modelling, analysis and simulation of cancer invasion mediated by bound and soluble enzymes |
| topic | Analysis of PDEs 35Kxx, 92Bxx, 65M60 |
| url | https://arxiv.org/abs/2509.12413 |