Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models
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Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models Sonja Mathias1 · Adrien Coulier1 · Anass Bouchnita1,2 Andreas Hellander1
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Received: 18 March 2020 / Accepted: 21 September 2020 / Published online: 6 October 2020 © The Author(s) 2020
Abstract Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter, there are multiple choices that could potentially affect both the biological behaviour captured, and the robustness and efficiency of simulation. For example, available open-source software implementations of centre-based models rely on different force functions for their default behaviour and it is not straightforward for a modeller to know if these are interchangeable. Our study addresses this problem and contributes to the understanding of the potential and limitations of three popular force functions from a numerical perspective. We show empirically that choosing the force parameters such that the relaxation time for two cells after cell division is consistent between different force functions results in good agreement of the population radius of a two-dimensional monolayer relaxing mechanically after intense cell proliferation. Furthermore, we report that numerical stability is not sufficient to prevent unphysical cell trajectories following cell division, and consequently, that too large time steps can cause geometrical differences at the population level. Keywords Cell-based model · Force function · Numerical method · Monolayer growth
This work has received funding from the Swedish Research Council under Grant 2015-03964 and from the eSSENCE strategic initiatives on eScience. The computations were performed on resources provided by SNIC through the Uppsala Multidisciplinary Centre for Advanced Computational Science (UPPMAX) under Project SNIC 2019/8-227. Extended author information available on the last page of the article
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1 Introduction Discrete cell-based models are becoming increasingly popular for simulating tissue mechanics. In contrast to continuum models that average over the cell density, cell-based models represent each cell individually. Therefore, they readily allow for incorporating cellular events such as cell division, cell differentiation or cell death, as well as cell heterogeneity across a population. As a result, these models have been used to probe biological questions of how the interplay of individual cell behaviour affects population-level measures (e.g. (Meineke et al. 2001; Li and Lowengrub 2014; Kursawe et al. 2015; Atwell et al. 2015)). There are different kinds of cell-based models that can be divided into two general categories. The first category, so-called on-lattice models, restricts the move
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