title: Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches.
abstract: Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations are a popular tool for modelling such phenomena deterministically, but it is often necessary to use stochastic models to accurately capture the behaviour of a system, especially when the number of diffusing particles is low. The stochastic models we consider in this paper are 'compartment-based': the domain is discretized into compartments, and particles can jump between these compartments. Volume-excluding effects (crowding) can be incorporated by blocking movement with some probability. Recent work has established the connection between fine- and coarse-grained models incorporating volume exclusion, but only for uniform lattices. In this paper, we consider non-uniform, hybrid lattices that incorporate both fine- and coarse-grained regions, and present two different approaches to describe the interface of the regions. We test both techniques in a range of scenarios to establish their accuracy, benchmarking against fine-grained models, and show that the hybrid models developed in this paper can be significantly faster to simulate than the fine-grained models in certain situations and are at least as fast otherwise.
authors.affiliation: Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK paul.taylor@maths.ox.ac.uk.
authors.forename: P R
authors.initials: PR
authors.lastname: Taylor
authors.affiliation: Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK.
authors.forename: R E
authors.initials: RE
authors.lastname: Baker
authors.affiliation: Mathematical Sciences, Queensland University of Technology, G.P.O. Box 2434, Brisbane 4001, Australia.
authors.forename: M J
authors.initials: MJ
authors.lastname: Simpson
authors.affiliation: Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK.
authors.forename: C A
authors.initials: CA
authors.lastname: Yates
mesh_terms: D008962:Models, Theoretical; D013269:Stochastic Processes
keywords: compartment-based modelling; diffusion; hybrid modelling; volume exclusion