Related papers: Mathematical Modelings for Angiogenesis - A Cellul…
It is now widely recognized that mechanical interactions between cells play a crucial role in epithelial morphogenesis, yet understanding the mechanisms through which stress and deformation affect cell behavior remains an open problem due…
Some mechanisms of cardiac arrhythmias can be presented as a composition of elementary acts of block and reflection on the contacts of homogeneous areas of the conducting tissue. For study this phenomena we use an axiomatic one-dimensional…
The circulatory system, comprising the heart and blood vessels, is vital for nutrient transport, waste removal, and homeostasis. Traditional computational models often treat cardiac electromechanics and blood flow dynamics separately,…
This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model…
We describe a hybrid agent-based model and simulation of urban morphogenesis. It consists of a cellular automata grid coupled to a dynamic network topology. The inherently heterogeneous properties of urban structure and function are taken…
In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and…
When modeling of tumor-driven angiogenesis, a major source of analytical and computational complexity is the strong coupling between the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network, and the…
Morphogenesis involves complex shape changes of biological tissues. Yet, tissue shape changes depend on tissue rheology, which in turn arises from the interplay of large numbers of cells. Here, we link cell- and tissue-scale mechanics by…
We investigate morphologies of proliferating cellular tissue using a newly developed numerical simulation model for mechanical cell division. The model reproduces structures of simple multi-cellular organisms via simple rules for selective…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
In this work we propose a car cellular automaton model that reproduces the experimental behavior of traffic flows in Bogot\'a. Our model includes three elements: hysteresis between the acceleration and brake gaps, a delay time in the…
The development of blood-handling medical devices, such as ventricular assist devices, requires the analysis of their biocompatibility. Among other aspects, this includes hemolysis, i.e., red blood cell damage. For this purpose,…
We describe a cellular-automaton based, two-dimensional (2D) lattice model which generates global oscillations in the EEG spectrum as well as time series of local field potentials resembling those observed during slow wave sleep. This is…
A new kind of cellular automaton (CA) for the study of the dynamics of urban systems is proposed. The state of a cell is not described using a finite set, but by means of continuum variables. A population sector is included, taking into…
In this paper we use the cellular automaton (CA) approach to model one-dimensional binary diffusion in solids. Employing a very simple state change rule we define an asynchronous CA model and take its continuum limit to obtain the governing…
Simple cellular automata models are able to reproduce the basic properties of highway traffic. The comparison with empirical data for microscopic quantities requires a more detailed description of the elementary dynamics. Based on existing…
The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as…
Coordinated motion of cell monolayers during epithelial wound healing and tissue morphogenesis involves mechanical stress generation. Here we propose a model for the dynamics of epithelial expansion that couples mechanical deformations in…
Synchronization of activity among myocytes constituting vital organs, e.g., the heart, is crucial for physiological functions. Self-organized coordination in such heterogeneous ensemble of excitable and oscillatory cells is therefore of…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…