The morphostatic limit for a model of skeletal pattern formation in the vertebrate limb

DOI10.1007/s11538-007-9264-3zbMath1139.92003OpenAlexW2122749808WikidataQ51902214 ScholiaQ51902214MaRDI QIDQ932035

Tilmann Glimm, Yong-Tao Zhang, Stuart A. Newman, Mark S. Alber, Jian-Feng Zhu, H. George E. Hentschel, Bogdan Kaźmierczak

Publication date: 8 July 2008

Published in: Bulletin of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://cedar.wwu.edu/math_facpubs/56

zbMATH Keywords

reaction-diffusion modellimb developmentchondrogenesismesenchymal condensation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Developmental biology, pattern formation (92C15) Cell biology (92C37)

Related Items (8)

Modeling the morphodynamic galectin patterning network of the developing avian limb skeleton ⋮ The use of element free Galerkin method based on moving Kriging and radial point interpolation techniques for solving some types of Turing models ⋮ Aberrant behaviours of reaction diffusion self-organisation models on growing domains in the presence of gene expression time delays ⋮ Application of discontinuous Galerkin methods for reaction-diffusion systems in developmental biology ⋮ Reaction-diffusion systems and external morphogen gradients: the two-dimensional case, with an application to skeletal pattern formation ⋮ The influence of receptor-mediated interactions on reaction-diffusion mechanisms of cellular self-organisation ⋮ Mathematical modeling of vertebrate limb development ⋮ Mathematical modeling of chondrogenic pattern formation during limb development: recent advances in continuous models

Uses Software

• CompuCell3D

Cites Work

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• Pattern formation in reaction-diffusion models with nonuniform domain growth
• Speed of pattern appearance in reaction-diffusion models: implications in the pattern formation of limb bud mesenchyme cells
• Existence of solutions to a new model of biological pattern formation
• Feedback-mediated control of spiral waves
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• Three types of matrix stability
• Pattern formation in a generalized chemotactic model
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Some remarks on matrix stability with application to Turing instability
• On the spread of morphogens
• The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• The chemical basis of morphogenesis
• Stability ofn-dimensional patterns in a generalized Turing system: implications for biological pattern formation
• Turing instabilities in general systems

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