Related papers: Study on Multicellular Systems Using a Phase Field…
We consider a cellular monolayer, described using a vertex-based model, for which cells form a spatially disordered array of convex polygons that tile the plane. Equilibrium cell configurations are assumed to minimize a global energy…
We consider a phase field crystal modeling approach for binary mixtures of interacting active and passive particles. The approach allows to describe generic properties for such systems within a continuum model. We validate the approach by…
Cell-cell adhesion is an inherently nonlocal phenomenon. Numerous partial differential equation models with nonlocal term have been recently presented to describe this phenomenon, yet the mathematical properties of nonlocal adhesion model…
We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction-diffusion equations with singular diffusion forced by a…
Animal morphogenesis often involves significant shape changes of epithelial tissue sheets. Great progress has been made in understanding the underlying cellular driving forces and their coordination through biomechanical feedback loops.…
This work aims at providing a mathematical and numerical framework for the analysis on the effects of pulsed electric fields on biological media. Biological tissues and cell suspensions are described as having a heteregeneous permittivity…
We propose a one-dimensional model of a string decorated with adhesion molecules (stickers) to mimic multicomponent membranes in restricted geometries. The string is bounded by two parallel walls and it interacts with one of them by short…
This chapter summarizes several approaches combining theory, simulation and experiment that aim for a better understanding of phenomena in lipid bilayers and membrane protein systems, covering topics such as lipid rafts, membrane mediated…
In many biological processes heterogeneity within cell populations is an important issue. In this work we consider populations where the behavior of every single cell can be described by a system of ordinary differential equations.…
As motivated by studies of cellular motility driven by spatiotemporal chemotactic gradients in microdevices, we develop a framework for constructing approximate analytical solutions for the location, speed and cellular densities for cell…
We demonstrate how concepts of statistical mechanics of interacting particles can have important implications in the choice of interaction potentials to model qualitative properties of cell aggregates in theoretical biology. We illustrate…
The processes taking place inside the living cell are now understood to the point where predictive computational models can be used to gain detailed understanding of important biological phenomena. A key challenge is to extrapolate this…
This paper considers membranes of globular structure in the framework of the cell model technique. Coupled micropolar and Brinkman-type equations are used to model the flow of micropolar fluid through a spherical cell, consisting of solid…
Multicellular tissues are the building blocks of many biological systems and organs. These tissues are not static, but dynamically change over time. Even if the overall structure remains the same there is a turnover of cells within the…
A novel mechanism for cell differentiation is proposed, based on the dynamic clustering in a globally coupled chaotic system. A simple model with metabolic reaction, active transport of chemicals from media, and cell division is found to…
The mechanics of crawling cells on a substrate is investigated by using a minimal model that satisfies the force-free condition. A cell is described by two subcellular elements connected by a linear actuator that changes the length of the…
We develop and analyse a discrete, one-dimensional model of cell motility which incorporates the effects of volume filling, cell-to-cell adhesion and chemotaxis. The formal continuum limit of the model is a nonlinear generalisation of the…
We present a 2-dimensional cellular automaton model for the simulation of pedestrian dynamics. The model is extremely efficient and allows simulations of large crowds faster than real time since it includes only nearest-neighbour…
We study closed liquid membranes that segregate into three phases due to differences in the chemical and physical properties of its components. The shape and in-plane membrane arrangement of the phases are coupled through phase-specific…
A phase field approach is proposed to model the chemotaxis of Dictyostelium discoideum. In this framework, motion is controlled by active forces as determined by the Meinhardt model of chemical dynamics which is used to simulate directional…