Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons
Many reaction–diffusion models produce traveling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumor growth. These partial differential equation models have since been adapted to describe the interactions between cells and extracellular...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Wiley
2023
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| _version_ | 1797111898135592960 |
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| author | Crossley, RM Maini, PK Lorenzi, T Baker, RE |
| author_facet | Crossley, RM Maini, PK Lorenzi, T Baker, RE |
| author_sort | Crossley, RM |
| collection | OXFORD |
| description | Many reaction–diffusion models produce traveling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumor growth. These partial differential equation models have since been adapted to describe the interactions between cells and extracellular matrix (ECM), using a variety of different underlying assumptions. In this work, we derive a system of reaction–diffusion equations, with cross-species density-dependent diffusion, by coarse-graining an agent-based, volume-filling model of cell invasion into ECM. We study the resulting traveling wave solutions both numerically and analytically across various parameter regimes. Subsequently, we perform a systematic comparison between the behaviors observed in this model and those predicted by simpler models in the literature that do not take into account volume-filling effects in the same way. Our study justifies the use of some of these simpler, more analytically tractable models in reproducing the qualitative properties of the solutions in some parameter regimes, but it also reveals some interesting properties arising from the introduction of cell and ECM volume-filling effects, where standard model simplifications might not be appropriate. |
| first_indexed | 2024-03-07T08:15:22Z |
| format | Journal article |
| id | oxford-uuid:3dc4f01a-a9c6-4644-9f6c-1f8b57fd2129 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:15:22Z |
| publishDate | 2023 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:3dc4f01a-a9c6-4644-9f6c-1f8b57fd21292024-01-05T08:04:07ZTraveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisonsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3dc4f01a-a9c6-4644-9f6c-1f8b57fd2129EnglishSymplectic ElementsWiley2023Crossley, RMMaini, PKLorenzi, TBaker, REMany reaction–diffusion models produce traveling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumor growth. These partial differential equation models have since been adapted to describe the interactions between cells and extracellular matrix (ECM), using a variety of different underlying assumptions. In this work, we derive a system of reaction–diffusion equations, with cross-species density-dependent diffusion, by coarse-graining an agent-based, volume-filling model of cell invasion into ECM. We study the resulting traveling wave solutions both numerically and analytically across various parameter regimes. Subsequently, we perform a systematic comparison between the behaviors observed in this model and those predicted by simpler models in the literature that do not take into account volume-filling effects in the same way. Our study justifies the use of some of these simpler, more analytically tractable models in reproducing the qualitative properties of the solutions in some parameter regimes, but it also reveals some interesting properties arising from the introduction of cell and ECM volume-filling effects, where standard model simplifications might not be appropriate. |
| spellingShingle | Crossley, RM Maini, PK Lorenzi, T Baker, RE Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons |
| title | Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons |
| title_full | Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons |
| title_fullStr | Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons |
| title_full_unstemmed | Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons |
| title_short | Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons |
| title_sort | traveling waves in a coarse grained model of volume filling cell invasion simulations and comparisons |
| work_keys_str_mv | AT crossleyrm travelingwavesinacoarsegrainedmodelofvolumefillingcellinvasionsimulationsandcomparisons AT mainipk travelingwavesinacoarsegrainedmodelofvolumefillingcellinvasionsimulationsandcomparisons AT lorenzit travelingwavesinacoarsegrainedmodelofvolumefillingcellinvasionsimulationsandcomparisons AT bakerre travelingwavesinacoarsegrainedmodelofvolumefillingcellinvasionsimulationsandcomparisons |