The effect of domain growth on spatial correlations
Mathematical models describing cell movement and proliferation are important research tools for the understanding of many biological processes. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations between agent locations in a continuum appr...
| Những tác giả chính: | , , |
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| Định dạng: | Journal article |
| Được phát hành: |
Elsevier
2016
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| _version_ | 1826283404485722112 |
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| author | Ross, R Yates, C Baker, R |
| author_facet | Ross, R Yates, C Baker, R |
| author_sort | Ross, R |
| collection | OXFORD |
| description | Mathematical models describing cell movement and proliferation are important research tools for the understanding of many biological processes. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations between agent locations in a continuum approximation of a one-dimensional lattice-based model of cell motility and proliferation. This is important as the inclusion of spatial correlations in continuum models of cell motility and proliferation without domain growth has previously been shown to be essential for their accuracy in certain scenarios. We include the effect of spatial correlations by deriving a system of ordinary differential equations that describe the expected evolution of individual and pair density functions for agents on a growing domain. We then demonstrate how to simplify this system of ordinary differential equations by using an appropriate approximation. This simplification allows domain growth to be included in models describing the evolution of spatial correlations between agents in a tractable manner. |
| first_indexed | 2024-03-07T00:58:24Z |
| format | Journal article |
| id | oxford-uuid:88df9225-9bdc-4acb-a26d-ce54d8977e7f |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:58:24Z |
| publishDate | 2016 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:88df9225-9bdc-4acb-a26d-ce54d8977e7f2022-03-26T22:20:33ZThe effect of domain growth on spatial correlationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:88df9225-9bdc-4acb-a26d-ce54d8977e7fSymplectic Elements at OxfordElsevier2016Ross, RYates, CBaker, RMathematical models describing cell movement and proliferation are important research tools for the understanding of many biological processes. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations between agent locations in a continuum approximation of a one-dimensional lattice-based model of cell motility and proliferation. This is important as the inclusion of spatial correlations in continuum models of cell motility and proliferation without domain growth has previously been shown to be essential for their accuracy in certain scenarios. We include the effect of spatial correlations by deriving a system of ordinary differential equations that describe the expected evolution of individual and pair density functions for agents on a growing domain. We then demonstrate how to simplify this system of ordinary differential equations by using an appropriate approximation. This simplification allows domain growth to be included in models describing the evolution of spatial correlations between agents in a tractable manner. |
| spellingShingle | Ross, R Yates, C Baker, R The effect of domain growth on spatial correlations |
| title | The effect of domain growth on spatial correlations |
| title_full | The effect of domain growth on spatial correlations |
| title_fullStr | The effect of domain growth on spatial correlations |
| title_full_unstemmed | The effect of domain growth on spatial correlations |
| title_short | The effect of domain growth on spatial correlations |
| title_sort | effect of domain growth on spatial correlations |
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