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Comparative analysis of angiogenesis models: MATLAB data files

Cite this dataset

Martinson, William (2021). Comparative analysis of angiogenesis models: MATLAB data files [Dataset]. Dryad.


This data set contains the MATLAB files that were used to generate figures located in the article "Comparative analysis of angiogenesis models" (J. Math. Biol, in press). The article's abstract may be found below. 

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, 2017). 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.


These data were produced and processed using MATLAB 2018b (Mathworks), using codes "ABM_2D_Model.m" and "Larger_Domain_Angiogenesis_Models.m" listed at Partial differential equations were solved using the method of lines (Sciesser, 1991, The numerical method of lines: Integration of partial differential equations). For further details on the equations and rules used to simulate the models, we refer to the article by Martinson et al. (in press, J. Math. Biol., DOI: 10.1007/s00285-021-01570-w).

Usage notes

Please see the attached README file (MARTINSON_DATASET_MATLAB_CAAM_README.txt) for further details on how the data in the collection were generated, information on the files contained in this dataset, and descriptions of the meanings of the variables and parameter values contained within the dataset.


Keasbey Memorial Foundation

Mathematical Institute, University of Oxford