TY - JOUR
T1 - Periodic pattern formation in reaction-diffusion systems
T2 - An introduction for numerical simulation
AU - Miura, Takashi
AU - Maini, Philip K.
N1 - Funding Information:
The authors thank Professor Stuart Newman (New York Medical College) and Dr Chad Perlin (Department of Human Anatomy and Genetics, University of Oxford) for their critical reading of the manuscript. This work was supported by the Japan Society for the Promotion of Science.
PY - 2004/9
Y1 - 2004/9
N2 - The aim of the present review is to provide a comprehensive explanation of Turing reaction-diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The reaction-diffusion model is widely studied in the field of mathematical biology, serves as a powerful paradigm model for self-organization and is beginning to be applied to actual experimental systems in developmental biology. Despite the increase in current interest, the model is not well understood among experimental biologists, partly because appropriate introductory texts are lacking. In the present review, we provide a detailed description of the definition of the Turing reaction-diffusion model that is comprehensible without a special mathematical background, then illustrate a method for reproducing numerical calculations with Microsoft Excel. We then show some examples of the patterns generated by the model. Finally, we discuss future prospects for the interdisciplinary field of research involving mathematical approaches in developmental biology.
AB - The aim of the present review is to provide a comprehensive explanation of Turing reaction-diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The reaction-diffusion model is widely studied in the field of mathematical biology, serves as a powerful paradigm model for self-organization and is beginning to be applied to actual experimental systems in developmental biology. Despite the increase in current interest, the model is not well understood among experimental biologists, partly because appropriate introductory texts are lacking. In the present review, we provide a detailed description of the definition of the Turing reaction-diffusion model that is comprehensible without a special mathematical background, then illustrate a method for reproducing numerical calculations with Microsoft Excel. We then show some examples of the patterns generated by the model. Finally, we discuss future prospects for the interdisciplinary field of research involving mathematical approaches in developmental biology.
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U2 - 10.1111/j.1447-073x.2004.00079.x
DO - 10.1111/j.1447-073x.2004.00079.x
M3 - Review article
C2 - 15453612
AN - SCOPUS:4544388824
SN - 1447-6959
VL - 79
SP - 112
EP - 123
JO - Anatomical Science International
JF - Anatomical Science International
IS - 3
ER -