Travelling waves in a free boundary mechanobiological model of an epithelial tissue
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse travelling wave solutions with negative, zero, and positive wavespee...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2020
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| _version_ | 1797081386971037696 |
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| author | Murphy, RJ Buenzli, PR Baker, RE Simpson, MJ |
| author_facet | Murphy, RJ Buenzli, PR Baker, RE Simpson, MJ |
| author_sort | Murphy, RJ |
| collection | OXFORD |
| description | We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse travelling wave solutions with negative, zero, and positive wavespeeds. Unlike classical travelling wave solutions of reaction–diffusion equations, the travelling wave solutions that we explore have a well-defined front and are not associated with a heteroclinic orbit in the phase plane. We find leading order expressions for both the wavespeed and the density at the free boundary. Interestingly, whether the travelling wave solution invades or retreats depends only on whether the carrying capacity density corresponds to cells being in compression or extension. |
| first_indexed | 2024-03-07T01:13:46Z |
| format | Journal article |
| id | oxford-uuid:8df01d91-6e6c-4da1-94d6-f263e1516776 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:13:46Z |
| publishDate | 2020 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:8df01d91-6e6c-4da1-94d6-f263e15167762022-03-26T22:54:21ZTravelling waves in a free boundary mechanobiological model of an epithelial tissueJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8df01d91-6e6c-4da1-94d6-f263e1516776EnglishSymplectic ElementsElsevier2020Murphy, RJBuenzli, PRBaker, RESimpson, MJWe consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse travelling wave solutions with negative, zero, and positive wavespeeds. Unlike classical travelling wave solutions of reaction–diffusion equations, the travelling wave solutions that we explore have a well-defined front and are not associated with a heteroclinic orbit in the phase plane. We find leading order expressions for both the wavespeed and the density at the free boundary. Interestingly, whether the travelling wave solution invades or retreats depends only on whether the carrying capacity density corresponds to cells being in compression or extension. |
| spellingShingle | Murphy, RJ Buenzli, PR Baker, RE Simpson, MJ Travelling waves in a free boundary mechanobiological model of an epithelial tissue |
| title | Travelling waves in a free boundary mechanobiological model of an epithelial tissue |
| title_full | Travelling waves in a free boundary mechanobiological model of an epithelial tissue |
| title_fullStr | Travelling waves in a free boundary mechanobiological model of an epithelial tissue |
| title_full_unstemmed | Travelling waves in a free boundary mechanobiological model of an epithelial tissue |
| title_short | Travelling waves in a free boundary mechanobiological model of an epithelial tissue |
| title_sort | travelling waves in a free boundary mechanobiological model of an epithelial tissue |
| work_keys_str_mv | AT murphyrj travellingwavesinafreeboundarymechanobiologicalmodelofanepithelialtissue AT buenzlipr travellingwavesinafreeboundarymechanobiologicalmodelofanepithelialtissue AT bakerre travellingwavesinafreeboundarymechanobiologicalmodelofanepithelialtissue AT simpsonmj travellingwavesinafreeboundarymechanobiologicalmodelofanepithelialtissue |