Cellular Automaton Modeling of Biological Pattern Formation Characterization, Applications, and Analysis - Deutsch, Andreas; Dormann, Sabine; SpringerLink (Online service) (Boston, MA : Birkhäuser Boston, 2005)
This book focuses on a challenging application field of cellular automata: pattern formation in biological systems, such as the growth of microorganisms, dynamics of cellular tissue and tumors, and formation of pigment cell patterns. These phenomena, resulting from complex cellular interactions, cannot be deduced solely from experimental analysis, but can be more easily examined using mathematical models, in particular, cellular automaton models. While there are various books treating cellular automaton modeling, this interdisciplinary work is the first one covering biological applications. The book is divided into three parts: Part I deals with general principles, theories, and models of pattern formation; Part II examines cellular automaton modeling; and Part III explains various applications. The models and analytic techniques described may be extended to other exciting applications in biology, medicine, and immunology. Key topics and features: * Provides an introduction and historical account of the principles of biological pattern formation (morphogenesis) * Gives an overview of mathematical modeling approaches to morphogenesis, and an introduction to cellular automata and analytic techniques * A supplementary web-based Java applet---Cellular Automaton Simulator---enables interactive simulation of various cellular automaton applications described in the book; available on the internet at www.biomodeling.info * Self-contained presentation is accessible to a broad audience; only basic calculus and linear algebra are required * Careful balance of theory, models, and applications useful to both experimentalists and theoreticians * Includes suggestions for further research topics The book is aimed at researchers, practitioners, and students in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science interested in a cellular automaton approach to biological modeling. The book's accessible presentation and interdisciplinary approach make it suitable for graduate and advanced undergraduate courses and seminars in mathematical biology, biomodeling, and biocomputing.
General Principles, Theories, and Models of Pattern Formation -- and Outline -- On the Origin of Patterns -- Mathematical Modeling of Biological Pattern Formation -- Cellular Automaton Modeling -- Cellular Automata -- Applications -- Random Movement -- Growth Processes -- Adhesive Cell Interaction -- Alignment and Cellular Swarming -- Pigment Cell Pattern Formation -- Tissue and Tumor Development -- Turing Patterns and Excitable Media -- Discussion and Outlook.
Keywords: Life sciences; Computer simulation; Applied mathematics; Engineering mathematics; Mathematical models; Biomathematics; Life Sciences; Life Sciences, general; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Physiological, Cellular and Medical Topics; Applications of Mathematics; Simulation and Modeling; Electronic books