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A hybrid approach to multi-scale modelling of cancer
In this paper, we review multi-scale models of solid tumour growth and discuss a middle-out
framework that tracks individual cells. By focusing on the cellular dynamics of a healthy …
framework that tracks individual cells. By focusing on the cellular dynamics of a healthy …
Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results
In this paper we present an overview of agent-based models that are used to simulate
mechanical and physiological phenomena in cells and tissues, and we discuss underlying …
mechanical and physiological phenomena in cells and tissues, and we discuss underlying …
Modelling collective cell migration: neural crest as a model paradigm
A huge variety of mathematical models have been used to investigate collective cell
migration. The aim of this brief review is twofold: to present a number of modelling …
migration. The aim of this brief review is twofold: to present a number of modelling …
Excluded-volume effects in the diffusion of hard spheres
Excluded-volume effects can play an important role in determining transport properties in
diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two …
diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two …
From a discrete to a continuum model of cell dynamics in one dimension
Multiscale modeling is emerging as one of the key challenges in mathematical biology.
However, the recent rapid increase in the number of modeling methodologies being used to …
However, the recent rapid increase in the number of modeling methodologies being used to …
Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient flow structure
We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-
linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known …
linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known …
Building macroscale models from microscale probabilistic models: a general probabilistic approach for nonlinear diffusion and multispecies phenomena
A discrete agent-based model on a periodic lattice of arbitrary dimension is considered.
Agents move to nearest-neighbor sites by a motility mechanism accounting for general …
Agents move to nearest-neighbor sites by a motility mechanism accounting for general …
Dynamic cluster field modeling of collective chemotaxis
Collective migration of eukaryotic cells is often guided by chemotaxis, and is critical in
several biological processes, such as cancer metastasis, wound healing, and …
several biological processes, such as cancer metastasis, wound healing, and …
A continuum approximation to an off-lattice individual-cell based model of cell migration and adhesion
Cell–cell adhesion plays a key role in the collective migration of cells and in determining
correlations in the relative cell positions and velocities. Recently, it was demonstrated that off …
correlations in the relative cell positions and velocities. Recently, it was demonstrated that off …
[HTML][HTML] A computational model for early cell spreading, migration, and competing taxis
Cell motility represents one of the most fundamental functions in life such as organ
development or tissue regeneration and diseases such as cancer. Here, we derived a …
development or tissue regeneration and diseases such as cancer. Here, we derived a …