Numerical Analysis of the Vertex Models for Simulating Grain Boundary Networks

Torres, Claudio E.; Emelianenko, Maria; Golovaty, Dmitry; Kinderlehrer, David; Ta’asan, Shlomo

doi:10.1137/140999232

Cited by 15 publications

(26 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A careful choice of time steps and cell rearrangement threshold is crucial since an incorrect choice may lead to failure of the simulation algorithm. For vertex models designed to simulate polycrystalline materials an adaptive time-stepping scheme has been developed that resolves the exact time at which the end points of a short edge meet, and a T1 transition is performed whenever this happens [18]. More work is required to understand how rates of T1 transitions differ if different conditions for rearrangement are implemented, such as the shortening of an edge to a given threshold or the shrinking edge of an edge to a point.…”

Section: Discussionmentioning

confidence: 99%

“…Vertex models were originally developed to study inorganic structures, such as foams [16] and grain boundaries [17,18], where surface tension and pressure drive dynamics. They have since been modified to study epithelial tissues [19][20][21][22], one of the major tissue types in animals.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of vertex models of grain boundaries, the authors of [18] proposed an adaptive time-stepping algorithm to accurately resolve vertex rearrangements without the need of ad-hoc rearrangement thresholds and provide a numerical analysis of the simulation algorithm. However, vertex models in that context only consider energy terms that are linear in each grain-grain (or cell-cell) interface length, whereas the energy terms in vertex models of biological cells typically depend non-linearly on cell areas and perimeters.…”

Section: Introductionmentioning

confidence: 99%

“…Importantly, previous studies such as [18] do not analyse to what extent changes in hidden model parameters, such as parameters of numerical approximation, like the size of the time step, or non-physical model parameters, such as length thresholds for cell rearrangement, can influence vertex configurations and other summary statistics. Here, we analyse a force-propagation implementation of vertex models [48,49] as applied to a widely studied system in developmental biology, the larval wing disc of the fruit fly Drosophila [3,4,25].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Impact of implementation choices on quantitative predictions of cell-based computational models

Kursawe

Baker

Fletcher

2016

Preprint

View full text Add to dashboard Cite

'Cell-based' models provide a powerful computational tool for studying the mechanisms underlying the growth and dynamics of biological tissues in health and disease. An increasing amount of quantitative data with cellular resolution has paved the way for the quantitative parameterisation and validation of such models. However, the numerical implementation of cell-based models remains challenging, and little work has been done to understand to what extent implementation choices may influence model predictions. Here, we consider the numerical implementation of a popular class of cell-based models called vertex models, which are often used to study epithelial tissues. In two-dimensional vertex models, a tissue is approximated as a tessellation of polygons and the vertices of these polygons move due to mechanical forces originating from the cells. Such models have been used extensively to study the mechanical regulation of tissue topology in the literature. Here, we analyse how the model predictions may be affected by numerical parameters, such as the size of the time step, and non-physical model parameters, such as length thresholds for cell rearrangement. We find that vertex positions and summary statistics are sensitive to several of these implementation parameters. For example, the predicted tissue size decreases with decreasing cell cycle durations, and cell rearrangement may be suppressed by large time steps. These findings are counter-intuitive and illustrate that model predictions need to be thoroughly analysed and implementation details carefully considered when applying cell-based computational models in a quantitative setting.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Impact of implementation choices on quantitative predictions of cell-based computational models

Kursawe

Baker

Fletcher

2016

Preprint

View full text Add to dashboard Cite

show abstract

“…In order to investigate how the structure and time evolution of misorientation distribution functions depend on the grain boundary energy anisotropy and set of laws governing the dynamics at a microscopic scale, it is possible to conduct numerical experiments via well-known large-scale simulation approaches. In particular, these are Monte Carlo methods [10][11][12][13][14], phase field models [12,17,18,25], curvature-driven grain growth models [19][20][21], level set methods [23,24], vertex models [26][27][28], etc. An alternative way is to develop kinetic models which are based on differential equations and, therefore, can be more computationally efficient, while focusing only on a restricted amount of essential characteristics.…”

Section: Introductionmentioning

confidence: 99%

A kinetic approach to modeling general-texture evolution in two-dimensional polycrystalline grain growth

Yegorov

Emelianenko

2016

Computational Materials Science

Self Cite

View full text Add to dashboard Cite

Important statistical descriptors of grain boundary networks are misorientation distribution functions (often referred to as grain boundary character distributions), which show relative measures of interfaces with given misorientation parameters. This paper is aimed at extending the Boltzmann-type kinetic modeling framework developed in the previous work [1] to the two-dimensional case of general textures with no restrictions on possible grain orientations, but under the assumption that the grain boundary energy density depends only on the disorientation variable. In order to avoid an enormous computational complexity of treating the general-texture case, the kinetic model for polycrystalline grain growth is constructed from the very beginning in a specific discretized form with respect to the disorientation variable. A significant aspect of the developed approach is that its formulation requires a collection of a priori distributions which describe possible disorientations of grain boundaries connected in a triple junction. A separate numerical algorithm for approximating such distributions is proposed as applied to cubic crystal lattices. The numerical results obtained by the constructed model are in good agreement with the corresponding large-scale simulation results from the related literature.

show abstract