Parameter identification problems in the modelling of cell motility

Croft, Wayne, Elliott, Charles M, Ladds, Graham, Stinner, Björn, Venkataraman, Chandrasekhar and Weston, Cathryn (2015) Parameter identification problems in the modelling of cell motility. Journal of Mathematical Biology, 71 (2). pp. 399-436. ISSN 0303-6812

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We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference between the computed and observed data are proposed and the parameter identification problem is formulated as a minimisation problem of nonlinear least squares type. A Levenberg–Marquardt based optimisation method is applied to the solution of the minimisation problem and the details of the implementation are discussed. A number of numerical experiments are presented which illustrate the robustness of the algorithm to parameter identification in the presence of large deformations and noisy data and parameter identification in three dimensional models of cell motility. An application to experimental data is also presented in which we seek to identify parameters in a model for the monopolar growth of fission yeast cells using experimental imaging data. Our numerical tests allow us to compare the method with the two different formulations of the objective functional and we conclude that the results with both objective functionals seem to agree.

Item Type: Article
Keywords: Parameter identification; Cell motility; Geometric evolution law; Reaction-diffusion system; Fission yeast; 92C17; 65K10; 53C44; 35K57
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Chandrasekhar Venkataraman
Date Deposited: 20 Oct 2014 12:59
Last Modified: 07 Mar 2017 11:06

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