Related papers: Mathematical Modelings for Angiogenesis - A Cellul…
When modelling tissue-level cardiac electrophysiology, continuum approximations to the discrete cell-level equations are used to maintain computational tractability. One of the most commonly used models is represented by the bidomain…
Biological cells are built up from many different constituents of varying size and stiffness which all contribute to the cell's mechanical properties. Despite this heterogeneity, in the analysis of experimental measurements such as atomic…
Cell neighbor exchanges play a critical role in regulating tissue fluidity during epithelial morphogenesis and repair. In vivo, these neighbor exchanges are often hindered by the formation of transiently stable four-fold vertices, which can…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
We derive a mathematical model for the motion of several insulating rigid bodies through an electrically conducting fluid. Starting from a universal model describing this phenomenon in generality, we elaborate (simplifying) physical…
The 19-dimensional TP06 cardiac muscle cell model is reduced to a 17-dimensional version, which satisfies the required conditions for performing an analysis of its dynamics by means of bifurcation theory. The reformulated model is shown to…
Angiogenesis is the complex process by which new blood vessels develop from an existing vasculature in order to supply nutrients and/or metabolites to tissues, playing a fundamental role in many physiological and pathological conditions…
Arrhythmias are potentially fatal disruptions to the normal heart rhythm, but their underlying dynamics is still poorly understood. Theoretical modeling is an important tool to fill this gap. Typical studies often employ detailed…
Cerebral autoregulation plays a key physiological role by limiting blood flow changes in the face of pressure fluctuations. Although the involved cellular processes are mechanically driven, the quantification of haemodynamic forces in…
Angiogenesis is a multiscale process by which a primary blood vessel issues secondary vessel sprouts that reach regions lacking oxygen. Angiogenesis can be a natural process of organ growth and development or a pathological induced by a…
We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…
The simulation of morphogenetic problems requires the simultaneous and coupled simulation of signalling and tissue dynamics. A cellular resolution of the tissue domain is important to adequately describe the impact of cell-based events,…
The organization of cells within tissues plays a vital role in various biological processes, including development and morphogenesis. As a result, understanding how cells self-organize in tissues has been an active area of research. In our…
We study phase transitions in a long-range one-dimensional cellular automaton with two symmetric absorbing states. It includes and extends several other models, like the Ising and Domany-Kinzel ones. It is characterized by a competing…
Metabolic heterogeneity is widely recognised as the next challenge in our understanding of non-genetic variation. A growing body of evidence suggests that metabolic heterogeneity may result from the inherent stochasticity of intracellular…
In Part I of this article we have developed a novel mechanobiological model of a Tissue Engineering process that accounts for the mechanisms through which an isotropic or anisotropic adherence condition regulates the active functions of the…
The dynamics group of an asynchronous cellular automaton (ACA) relates properties of its long term dynamics to the structure of Coxeter groups. The key mathematical feature connecting these diverse fields is involutions. Group-theoretic…
A central challenge in modeling neurodegenerative diseases is connecting cellular-level mechanisms to tissue-level pathology, in particular to determine whether pathology is driven primarily by cell-autonomous triggers or by propagation…
A family of multi-value cellular automaton (CA) associated with traffic flow is presented in this paper. The family is obtained by extending the rule-184 CA, which is an ultradiscrete analogue to the Burgers equation. CA models in the…
A cellular automaton named Rule 184++C is proposed as a meta-model to investigate the flow of various complex particles. In this model, unlike the granular pipe flow and the traffic flow, not only the free-jam phase transition but also the…