ArticlePloS one2015
Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.
Article in PloS one, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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Who cites it
6 citing papers in PubMed.
- Multiscale Asymptotic Analysis Reveals How Cell Growth and Subcellular Compartments Affect Tissue-Scale Hormone Transport.Bulletin of mathematical biology · 2023Article
- Size matters: tissue size as a marker for a transition between reaction-diffusion regimes in spatio-temporal distribution of morphogens.Royal Society open science · 2022Article
- Article
- Incorporating domain growth into hybrid methods for reaction-diffusion systems.Journal of the Royal Society, Interface · 2021Article
- Modelling collective cell migration: neural crest as a model paradigm.Journal of mathematical biology · 2020Article
- Exact Solutions of Coupled Multispecies Linear Reaction-Diffusion Equations on a Uniformly Growing Domain.PloS one · 2015Article
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1 author.
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Abstract
Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0<x<L(t), where L(t) is the length of the growing domain. Comparing our exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).
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