Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour
In this paper, we develop a mathematical model to describe interactions between tumour cells and a compliant blood vessel that supplies oxygen to the region. We assume that, in addition to proliferating, the tumour cells die through apoptosis and necrosis. We also assume that pressure differences wi...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2001
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| _version_ | 1797054705433575424 |
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| author | Breward, C Byrne, H Lewis, C |
| author_facet | Breward, C Byrne, H Lewis, C |
| author_sort | Breward, C |
| collection | OXFORD |
| description | In this paper, we develop a mathematical model to describe interactions between tumour cells and a compliant blood vessel that supplies oxygen to the region. We assume that, in addition to proliferating, the tumour cells die through apoptosis and necrosis. We also assume that pressure differences within the tumour mass, caused by spatial variations in proliferation and degradation, cause cell motion. We couple the behaviour of the blood vessel into the model for the oxygen tension. The model equations track the evolution of the densities of live and dead cells, the oxygen tension within the tumour, the live and dead cell speeds, the pressure and the width of the blood vessel. We present explicit solutions to the model for certain parameter regimes, and then solve the model numerically for more general parameter regimes. We show how the resulting steady-state behaviour varies as the key model parameters are changed. Finally, we discuss the biological implications of our work. |
| first_indexed | 2024-03-06T19:00:58Z |
| format | Journal article |
| id | oxford-uuid:1383b5d8-72d9-44c6-8668-306a285eec00 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:00:58Z |
| publishDate | 2001 |
| record_format | dspace |
| spelling | oxford-uuid:1383b5d8-72d9-44c6-8668-306a285eec002022-03-26T10:14:15ZModelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumourJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1383b5d8-72d9-44c6-8668-306a285eec00EnglishSymplectic Elements at Oxford2001Breward, CByrne, HLewis, CIn this paper, we develop a mathematical model to describe interactions between tumour cells and a compliant blood vessel that supplies oxygen to the region. We assume that, in addition to proliferating, the tumour cells die through apoptosis and necrosis. We also assume that pressure differences within the tumour mass, caused by spatial variations in proliferation and degradation, cause cell motion. We couple the behaviour of the blood vessel into the model for the oxygen tension. The model equations track the evolution of the densities of live and dead cells, the oxygen tension within the tumour, the live and dead cell speeds, the pressure and the width of the blood vessel. We present explicit solutions to the model for certain parameter regimes, and then solve the model numerically for more general parameter regimes. We show how the resulting steady-state behaviour varies as the key model parameters are changed. Finally, we discuss the biological implications of our work. |
| spellingShingle | Breward, C Byrne, H Lewis, C Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour |
| title | Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour |
| title_full | Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour |
| title_fullStr | Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour |
| title_full_unstemmed | Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour |
| title_short | Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour |
| title_sort | modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour |
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