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A Finite Element Model Based on Discontinuous Galerkin Methods on Moving Grids for Vertebrate Limb Pattern Formation

J. Zhu, Y.-T. Zhang, S. A. Newman, M. S. Alber (2009)

Mathematical Modelling of Natural Phenomena

Skeletal patterning in the vertebrate limb, i.e., the spatiotemporal regulation of cartilage differentiation (chondrogenesis) during embryogenesis and regeneration, is one of the best studied examples of a multicellular developmental process. Recently [Alber et al., The morphostatic limit for a model of skeletal pattern formation in the vertebrate limb, Bulletin of Mathematical Biology, 2008, v70, pp. 460-483], a simplified two-equation reaction-diffusion system was developed to describe the interaction...

A mechanochemical model of angiogenesis and vasculogenesis

Daphne Manoussaki (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Vasculogenesis and angiogenesis are two different mechanisms for blood vessel formation. Angiogenesis occurs when new vessels sprout from pre-existing vasculature in response to external chemical stimuli. Vasculogenesis occurs via the reorganization of randomly distributed cells into a blood vessel network. Experimental models of vasculogenesis have suggested that the cells exert traction forces onto the extracellular matrix and that these forces may play an important role in the network forming...

A mechanochemical model of angiogenesis and vasculogenesis

Daphne Manoussaki (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Vasculogenesis and angiogenesis are two different mechanisms for blood vessel formation. Angiogenesis occurs when new vessels sprout from pre-existing vasculature in response to external chemical stimuli. Vasculogenesis occurs via the reorganization of randomly distributed cells into a blood vessel network. Experimental models of vasculogenesis have suggested that the cells exert traction forces onto the extracellular matrix and that these forces may play an important role in the network forming...

A Minimal Model of Pursuit-Evasion in a Predator-Prey System

Y. Tyutyunov, L. Titova, R. Arditi (2010)

Mathematical Modelling of Natural Phenomena

A conceptual minimal model demonstrating spatially heterogeneous wave regimes interpreted as pursuit-evasion in predator-prey system is constructed and investigated. The model is based on the earlier proposed hypothesis that taxis accelerations of prey and predators are proportional to the density gradient of another population playing a role of taxis stimulus. Considering acceleration rather than immediate velocity allows obtaining realistic solutions even while ignoring variations of total...

An Age and Spatially Structured Population Model for Proteus Mirabilis Swarm-Colony Development

Ph. Laurençot, Ch. Walker (2008)

Mathematical Modelling of Natural Phenomena

Proteus mirabilis are bacteria that make strikingly regular spatial-temporal patterns on agar surfaces. In this paper we investigate a mathematical model that has been shown to display these structures when solved numerically. The model consists of an ordinary differential equation coupled with a partial differential equation involving a first-order hyperbolic aging term together with nonlinear degenerate diffusion. The system is shown to admit global weak solutions.

Analysis of a Mathematical Model for the Molecular Mechanism of Fate Decision in Mammary Stem Cells

O. U. Kirnasovsky, Y. Kogan, Z. Agur (2008)

Mathematical Modelling of Natural Phenomena

Recently, adult stem cells have become a focus of intensive biomedical research, but the complex regulation that allows a small population of stem cells to replenish depleted tissues is still unknown. It has been suggested that specific tissue structures delimit the spaces where stem cells undergo unlimited proliferation (stem cell niche). In contrast, mathematical analysis suggests that a feedback control of stem cells on their own proliferation and differentiation (denoted Quorum Sensing) suffices...

Analysis of pattern formation using numerical continuation

Vladimír Janovský (2022)

Applications of Mathematics

The paper deals with the issue of self-organization in applied sciences. It is particularly related to the emergence of Turing patterns. The goal is to analyze the domain size driven instability: We introduce the parameter L , which scales the size of the domain. We investigate a particular reaction-diffusion model in 1-D for two species. We consider and analyze the steady-state solution. We want to compute the solution branches by numerical continuation. The model in question has certain symmetries....

Analysis of Space-Temporal Symmetry in the Early Embryogenesis of Calla palustris L., Araceae

I.V. Rudskiy, G.E. Titova, T.B. Batygina (2010)

Mathematical Modelling of Natural Phenomena

Plants and animals have highly ordered structure both in time and in space, and one of the main questions of modern developmental biology is the transformation of genetic information into the regular structure of organism. Any multicellular plant begins its development from the universal unicellular state and acquire own species-specific structure in the course of cell divisions, cell growth and death, according to own developmental program. However the cellular mechanisms of plant development are...

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