On the mathematical modelling of tumor-induced angiogenesis
An angiogenic system is taken as an example of extremely complex ones in the field of Life Sciences, from both analytical and computational points of view, due to the strong coupling between the kinetic parameters of the relevant branching -growth -anastomosis stochastic processes of the capillary n...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017004 |
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| author | Luis L. Bonilla Vincenzo Capasso Mariano Alvaro Manuel Carretero Filippo Terragni |
| author_facet | Luis L. Bonilla Vincenzo Capasso Mariano Alvaro Manuel Carretero Filippo Terragni |
| author_sort | Luis L. Bonilla |
| collection | DOAJ |
| description | An angiogenic system is taken as an example of extremely complex ones in the field of Life Sciences, from both analytical and computational points of view, due to the strong coupling between the kinetic parameters of the relevant branching -growth -anastomosis stochastic processes of the capillary network, at the microscale, and the family of interacting underlying biochemical fields, at the macroscale. To reduce this complexity, for a conceptual stochastic model we have explored how to take advantage of the system intrinsic multiscale structure: one might describe the stochastic dynamics of the cells at the vessel tip at their natural microscale, whereas the dynamics of the underlying fields is given by a deterministic mean field approximation obtained by an averaging at a suitable mesoscale. But the outcomes of relevant numerical simulations show that the proposed model, in presence of anastomosis, is not self-averaging, so that the 'propagation of chaos' assumption cannot be applied to obtain a deterministic mean field approximation. On the other hand we have shown that ensemble averages over many realizations of the stochastic system may better correspond to a deterministic reaction-diffusion system. |
| format | Article |
| id | doaj-art-1aafa4f3c03a48869a6b65117867fac3 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-1aafa4f3c03a48869a6b65117867fac32025-01-24T02:39:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-01-01141456610.3934/mbe.2017004On the mathematical modelling of tumor-induced angiogenesisLuis L. Bonilla0Vincenzo Capasso1Mariano Alvaro2Manuel Carretero3Filippo Terragni4G. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos Ⅲ de Madrid, 28911 Leganés, SpainADAMSS, Universitá degli Studi di Milano, 20133 MILANO, ItalyG. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos Ⅲ de Madrid, 28911 Leganés, SpainG. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos Ⅲ de Madrid, 28911 Leganés, SpainG. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos Ⅲ de Madrid, 28911 Leganés, SpainAn angiogenic system is taken as an example of extremely complex ones in the field of Life Sciences, from both analytical and computational points of view, due to the strong coupling between the kinetic parameters of the relevant branching -growth -anastomosis stochastic processes of the capillary network, at the microscale, and the family of interacting underlying biochemical fields, at the macroscale. To reduce this complexity, for a conceptual stochastic model we have explored how to take advantage of the system intrinsic multiscale structure: one might describe the stochastic dynamics of the cells at the vessel tip at their natural microscale, whereas the dynamics of the underlying fields is given by a deterministic mean field approximation obtained by an averaging at a suitable mesoscale. But the outcomes of relevant numerical simulations show that the proposed model, in presence of anastomosis, is not self-averaging, so that the 'propagation of chaos' assumption cannot be applied to obtain a deterministic mean field approximation. On the other hand we have shown that ensemble averages over many realizations of the stochastic system may better correspond to a deterministic reaction-diffusion system.https://www.aimspress.com/article/doi/10.3934/mbe.2017004angiogenesisstochastic differential equationsbirth and death processesgrowth processesmean field approximationhybrid modelspropagation of chaosensemble average |
| spellingShingle | Luis L. Bonilla Vincenzo Capasso Mariano Alvaro Manuel Carretero Filippo Terragni On the mathematical modelling of tumor-induced angiogenesis Mathematical Biosciences and Engineering angiogenesis stochastic differential equations birth and death processes growth processes mean field approximation hybrid models propagation of chaos ensemble average |
| title | On the mathematical modelling of tumor-induced angiogenesis |
| title_full | On the mathematical modelling of tumor-induced angiogenesis |
| title_fullStr | On the mathematical modelling of tumor-induced angiogenesis |
| title_full_unstemmed | On the mathematical modelling of tumor-induced angiogenesis |
| title_short | On the mathematical modelling of tumor-induced angiogenesis |
| title_sort | on the mathematical modelling of tumor induced angiogenesis |
| topic | angiogenesis stochastic differential equations birth and death processes growth processes mean field approximation hybrid models propagation of chaos ensemble average |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017004 |
| work_keys_str_mv | AT luislbonilla onthemathematicalmodellingoftumorinducedangiogenesis AT vincenzocapasso onthemathematicalmodellingoftumorinducedangiogenesis AT marianoalvaro onthemathematicalmodellingoftumorinducedangiogenesis AT manuelcarretero onthemathematicalmodellingoftumorinducedangiogenesis AT filippoterragni onthemathematicalmodellingoftumorinducedangiogenesis |