On a mathematical model of bone marrow metastatic niche
We propose a mathematical model to describe tumor cells movement towards a metastasis location into the bone marrow considering the influence of chemotaxis inhibition due to the action of a drug. The model considers the evolution of the signaling molecules CXCL-12 secreted by osteoblasts (bone cells...
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| Format: | Article |
| Language: | English |
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AIMS Press
2016-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017019 |
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| _version_ | 1832590067646857216 |
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| author | Ana Isabel Muñoz J. Ignacio Tello |
| author_facet | Ana Isabel Muñoz J. Ignacio Tello |
| author_sort | Ana Isabel Muñoz |
| collection | DOAJ |
| description | We propose a mathematical model to describe tumor cells movement towards a metastasis location into the bone marrow considering the influence of chemotaxis inhibition due to the action of a drug. The model considers the evolution of the signaling molecules CXCL-12 secreted by osteoblasts (bone cells responsible of the mineralization of the bone) and PTHrP (secreted by tumor cells) which activates osteoblast growth. The model consists of a coupled system of second order PDEs describing the evolution of CXCL-12 and PTHrP, an ODE of logistic type to model the Osteoblasts density and an extra equation for each cancer cell. We also simulate the system to illustrate the qualitative behavior of the solutions. The numerical method of resolution is also presented in detail. |
| format | Article |
| id | doaj-art-98ac8be9131a49ef83f800a8d14af3f4 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-98ac8be9131a49ef83f800a8d14af3f42025-01-24T02:39:32ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-12-0114128930410.3934/mbe.2017019On a mathematical model of bone marrow metastatic nicheAna Isabel Muñoz0J. Ignacio Tello1Departamento de Matemática Aplicada, Ciencia e Ingeniería de Materiales y Tecnología Electrónica, ESCET, Universidad Rey Juan Carlos, E28933, Móstoles, Madrid, SpainDepto. Matemática Aplicada a las T.I.C. ETSI Sistemas Informáticos, Universidad Politécnica de Madrid. Madrid 28031, SpainWe propose a mathematical model to describe tumor cells movement towards a metastasis location into the bone marrow considering the influence of chemotaxis inhibition due to the action of a drug. The model considers the evolution of the signaling molecules CXCL-12 secreted by osteoblasts (bone cells responsible of the mineralization of the bone) and PTHrP (secreted by tumor cells) which activates osteoblast growth. The model consists of a coupled system of second order PDEs describing the evolution of CXCL-12 and PTHrP, an ODE of logistic type to model the Osteoblasts density and an extra equation for each cancer cell. We also simulate the system to illustrate the qualitative behavior of the solutions. The numerical method of resolution is also presented in detail.https://www.aimspress.com/article/doi/10.3934/mbe.2017019mathematical modeling of cancerhematopoietic nicheosteoblastcxcl-12pthrpfem |
| spellingShingle | Ana Isabel Muñoz J. Ignacio Tello On a mathematical model of bone marrow metastatic niche Mathematical Biosciences and Engineering mathematical modeling of cancer hematopoietic niche osteoblast cxcl-12 pthrp fem |
| title | On a mathematical model of bone marrow metastatic niche |
| title_full | On a mathematical model of bone marrow metastatic niche |
| title_fullStr | On a mathematical model of bone marrow metastatic niche |
| title_full_unstemmed | On a mathematical model of bone marrow metastatic niche |
| title_short | On a mathematical model of bone marrow metastatic niche |
| title_sort | on a mathematical model of bone marrow metastatic niche |
| topic | mathematical modeling of cancer hematopoietic niche osteoblast cxcl-12 pthrp fem |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017019 |
| work_keys_str_mv | AT anaisabelmunoz onamathematicalmodelofbonemarrowmetastaticniche AT jignaciotello onamathematicalmodelofbonemarrowmetastaticniche |