Comparative analysis of continuum angiogenesis models

Although discrete approaches are increasingly employed to model biological phenomena, it remains unclear how complex, population-level behaviours in such frameworks arise from the rules used to represent interactions between individuals. Discrete-to-continuum approaches, which are used to derive sys...

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Egile Nagusiak: Martinson, WD, Byrne, HM, Ninomiya, H, Maini, PK
Formatua: Journal article
Hizkuntza:English
Argitaratua: Springer 2021
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author Martinson, WD
Byrne, HM
Ninomiya, H
Maini, PK
author_facet Martinson, WD
Byrne, HM
Ninomiya, H
Maini, PK
author_sort Martinson, WD
collection OXFORD
description Although discrete approaches are increasingly employed to model biological phenomena, it remains unclear how complex, population-level behaviours in such frameworks arise from the rules used to represent interactions between individuals. Discrete-to-continuum approaches, which are used to derive systems of coarse-grained equations describing the mean-field dynamics of a microscopic model, can provide insight into such emergent behaviour. Coarse-grained models often contain nonlinear terms that depend on the microscopic rules of the discrete framework, however, and such nonlinearities can make a model difficult to mathematically analyse. By contrast, models developed using phenomenological approaches are typically easier to investigate but have a more obscure connection to the underlying microscopic system. To our knowledge, there has been little work done to compare solutions of phenomenological and coarse-grained models. Here we address this problem in the context of angiogenesis (the creation of new blood vessels from existing vasculature). We compare asymptotic solutions of a classical, phenomenological “snail-trail” model for angiogenesis to solutions of a nonlinear system of partial differential equations (PDEs) derived via a systematic coarse-graining procedure (Pillay et al. in Phys Rev E 95(1):012410, 2017. https://doi.org/10.1103/PhysRevE.95.012410). For distinguished parameter regimes corresponding to chemotaxis-dominated cell movement and low branching rates, both continuum models reduce at leading order to identical PDEs within the domain interior. Numerical and analytical results confirm that pointwise differences between solutions to the two continuum models are small if these conditions hold, and demonstrate how perturbation methods can be used to determine when a phenomenological model provides a good approximation to a more detailed coarse-grained system for the same biological process.
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spelling oxford-uuid:5719ce67-a757-448e-9f93-f7e9c03a0f452022-03-26T16:54:38ZComparative analysis of continuum angiogenesis modelsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:5719ce67-a757-448e-9f93-f7e9c03a0f45EnglishSymplectic ElementsSpringer2021Martinson, WDByrne, HMNinomiya, HMaini, PKAlthough discrete approaches are increasingly employed to model biological phenomena, it remains unclear how complex, population-level behaviours in such frameworks arise from the rules used to represent interactions between individuals. Discrete-to-continuum approaches, which are used to derive systems of coarse-grained equations describing the mean-field dynamics of a microscopic model, can provide insight into such emergent behaviour. Coarse-grained models often contain nonlinear terms that depend on the microscopic rules of the discrete framework, however, and such nonlinearities can make a model difficult to mathematically analyse. By contrast, models developed using phenomenological approaches are typically easier to investigate but have a more obscure connection to the underlying microscopic system. To our knowledge, there has been little work done to compare solutions of phenomenological and coarse-grained models. Here we address this problem in the context of angiogenesis (the creation of new blood vessels from existing vasculature). We compare asymptotic solutions of a classical, phenomenological “snail-trail” model for angiogenesis to solutions of a nonlinear system of partial differential equations (PDEs) derived via a systematic coarse-graining procedure (Pillay et al. in Phys Rev E 95(1):012410, 2017. https://doi.org/10.1103/PhysRevE.95.012410). For distinguished parameter regimes corresponding to chemotaxis-dominated cell movement and low branching rates, both continuum models reduce at leading order to identical PDEs within the domain interior. Numerical and analytical results confirm that pointwise differences between solutions to the two continuum models are small if these conditions hold, and demonstrate how perturbation methods can be used to determine when a phenomenological model provides a good approximation to a more detailed coarse-grained system for the same biological process.
spellingShingle Martinson, WD
Byrne, HM
Ninomiya, H
Maini, PK
Comparative analysis of continuum angiogenesis models
title Comparative analysis of continuum angiogenesis models
title_full Comparative analysis of continuum angiogenesis models
title_fullStr Comparative analysis of continuum angiogenesis models
title_full_unstemmed Comparative analysis of continuum angiogenesis models
title_short Comparative analysis of continuum angiogenesis models
title_sort comparative analysis of continuum angiogenesis models
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AT byrnehm comparativeanalysisofcontinuumangiogenesismodels
AT ninomiyah comparativeanalysisofcontinuumangiogenesismodels
AT mainipk comparativeanalysisofcontinuumangiogenesismodels