Mathematical Biology Spatial Models and Biomedical Applications

ISBN-10: 0387952284

ISBN-13: 9780387952284

Edition: 3rd 2003 (Revised)

Authors: James D. Murray
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Description: In the ten years since the first edition of this book appeared the field of mathematical biology has grown at an astonishing rate and has established itself as a distinct discipline. Mathematical modelling is now being applied in every major discipline in the biomedical sciences. Though the field has become increasingly large and specialized, this book remains important as a text that introduces some of the exciting problems that arise in biology and gives some indication of the wide spectrum of questions that modelling can address. Due to this tremendous development in recent years, for this new edition Murray is covering certain items in depth, giving new applications such as modelling marital interaction, growth of cancer tumours, temperature sex determination, wolf territoriality, wolf-deer survival etc. In other areas he discusses basic modelling concepts and provides further references as needed. He also provides even closer links between models and experimental data throughout the text. The book continues to present a broad view of the field of theoretical and mathematical biology and gives us an excellent background from which to begin geniune interdisciplinary research in the biomedical sciences.

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Book details

Edition: 3rd
Copyright year: 2003
Publisher: Springer
Publication date: 2/15/2011
Binding: Hardcover
Pages: 814
Size: 6.50" wide x 9.50" long x 1.75" tall
Weight: 2.882
Language: English

James D. Murray is Professor Emeritus of Applied Mathematics at the University of Washington.

Preface to the Third Edition
Preface to the First Edition
Multi-Species Waves and Practical Applications
Intuitive Expectations
Waves of Pursuit and Evasion in Predator-Prey Systems
Competition Model for the Spatial Spread of the Grey Squirrel in Britain
Spread of Genetically Engineered Organisms
Travelling Fronts in the Belousov-Zhabotinskii Reaction
Waves in Excitable Media
Travelling Wave Trains in Reaction Diffusion Systems with Oscillatory Kinetics
Spiral Waves
Spiral Wave Solutions of [lambda]-[omega] Reaction Diffusion Systems
Exercises
Spatial Pattern Formation with Reaction Diffusion Systems
Role of Pattern in Biology
Reaction Diffusion (Turing) Mechanisms
General Conditions for Diffusion-Driven Instability: Linear Stability Analysis and Evolution of Spatial Pattern
Detailed Analysis of Pattern Initiation in a Reaction Diffusion Mechanism
Dispersion Relation, Turing Space, Scale and Geometry Effects in Pattern Formation Models
Mode Selection and the Dispersion Relation
Pattern Generation with Single-Species Models: Spatial Heterogeneity with the Spruce Budworm Model
Spatial Patterns in Scalar Population Interaction Diffusion Equations with Convection: Ecological Control Strategies
Nonexistence of Spatial Patterns in Reaction Diffusion Systems: General and Particular Results
Exercises
Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms
Mammalian Coat Patterns--'How the Leopard Got Its Spots'
Teratologies: Examples of Animal Coat Pattern Abnormalities
A Pattern Formation Mechanism for Butterfly Wing Patterns
Modelling Hair Patterns in a Whorl in Acetabularia
Pattern Formation on Growing Domains: Alligators and Snakes
Stripe Pattern Formation in the Alligator: Experiments
Modelling Concepts: Determining the Time of Stripe Formation
Stripes and Shadow Stripes on the Alligator
Spatial Patterning of Teeth Primordia in the Alligator: Background and Relevance
Biology of Tooth Initiation
Modelling Tooth Primordium Initiation: Background
Model Mechanism for Alligator Teeth Patterning
Results and Comparison with Experimental Data
Prediction Experiments
Concluding Remarks on Alligator Tooth Spatial Patterning
Pigmentation Pattern Formation on Snakes
Cell-Chemotaxis Model Mechanism
Simple and Complex Snake Pattern Elements
Propagating Pattern Generation with the Cell-Chemotaxis System
Bacterial Patterns and Chemotaxis
Background and Experimental Results
Model Mechanism for E. coli in the Semi-Solid Experiments
Liquid Phase Model: Intuitive Analysis of Pattern Formation
Interpretation of the Analytical Results and Numerical Solutions
Semi-Solid Phase Model Mechanism for S. typhimurium
Linear Analysis of the Basic Semi-Solid Model
Brief Outline and Results of the Nonlinear Analysis
Simulation Results, Parameter Spaces and Basic Patterns
Numerical Results with Initial Conditions from the Experiments
Swarm Ring Patterns with the Semi-Solid Phase Model Mechanism
Branching Patterns in Bacillus subtilis
Mechanical Theory for Generating Pattern and Form in Development
Introduction, Motivation and Background Biology
Mechanical Model for Mesenchymal Morphogenesis
Linear Analysis, Dispersion Relation and Pattern Formation Potential
Simple Mechanical Models Which Generate Spatial Patterns with Complex Dispersion Relations
Periodic Patterns of Feather Germs
Cartilage Condensations in Limb Morphogenesis and Morphogenetic Rules
Embryonic Fingerprint Formation
Mechanochemical Model for the Epidermis
Formation of Microvilli
Complex Pattern Formation and Tissue Interaction Models
Exercises
Evolution, Morphogenetic Laws, Developmental Constraints and Teratologies
Evolution and Morphogenesis
Evolution and Morphogenetic Rules in Cartilage Formation in the Vertebrate Limb
Teratologies (Monsters)
Developmental Constraints, Morphogenetic Rules and the Consequences for Evolution
A Mechanical Theory of Vascular Network Formation
Biological Background and Motivation
Cell-Extracellular Matrix Interactions for Vasculogenesis
Parameter Values
Analysis of the Model Equations
Network Patterns: Numerical Simulations and Conclusions
Epidermal Wound Healing
Brief History of Wound Healing
Biological Background: Epidermal Wounds
Model for Epidermal Wound Healing
Nondimensional Form, Linear Stability and Parameter Values
Numerical Solution for the Epidermal Wound Repair Model
Travelling Wave Solutions for the Epidermal Model
Clinical Implications of the Epidermal Wound Model
Mechanisms of Epidermal Repair in Embryos
Actin Alignment in Embryonic Wounds: A Mechanical Model
Mechanical Model with Stress Alignment of the Actin Filaments in Two Dimensions
Dermal Wound Healing
Background and Motivation--General and Biological
Logic of Wound Healing and Initial Models
Brief Review of Subsequent Developments
Model for Fibroblast-Driven Wound Healing: Residual Strain and Tissue Remodelling
Solutions of the Model Equations and Comparison with Experiment
Wound Healing Model of Cook (1995)
Matrix Secretion and Degradation
Cell Movement in an Oriented Environment
Model System for Dermal Wound Healing with Tissue Structure
One-Dimensional Model for the Structure of Pathological Scars
Open Problems in Wound Healing
Concluding Remarks on Wound Healing
Growth and Control of Brain Tumours
Medical Background
Basic Mathematical Model of Glioma Growth and Invasion
Tumour Spread In Vitro: Parameter Estimation
Tumour Invasion in the Rat Brain
Tumour Invasion in the Human Brain
Modelling Treatment Scenarios: General Comments
Modelling Tumour Resection in Homogeneous Tissue
Analytical Solution for Tumour Recurrence After Resection
Modelling Surgical Resection with Brain Tissue Heterogeneity
Modelling the Effect of Chemotherapy on Tumour Growth
Modelling Tumour Polyclonality and Cell Mutation
Neural Models of Pattern Formation
Spatial Patterning in Neural Firing with a Simple Activation-Inhibition Model
A Mechanism for Stripe Formation in the Visual Cortex
A Model for the Brain Mechanism Underlying Visual Hallucination Patterns
Neural Activity Model for Shell Patterns
Shamanism and Rock Art
Exercises
Geographic Spread and Control of Epidemics
Simple Model for the Spatial Spread of an Epidemic
Spread of the Black Death in Europe 1347-1350
Brief History of Rabies: Facts and Myths
The Spatial Spread of Rabies Among Foxes I: Background and Simple Model
The Spatial Spread of Rabies Among Foxes II: Three-Species (SIR) Model
Control Strategy Based on Wave Propagation into a Nonepidemic Region: Estimate of Width of a Rabies Barrier
Analytic Approximation for the Width of the Rabies Control Break
Two-Dimensional Epizootic Fronts and Effects of Variable Fox Densities: Quantitative Predictions for a Rabies Outbreak in England
Effect of Fox Immunity on the Spatial Spread of Rabies
Exercises
Wolf Territoriality, Wolf-Deer Interaction and Survival
Introduction and Wolf Ecology
Models for Wolf Pack Territory Formation: Single Pack--Home Range Model
Multi-Wolf Pack Territorial Model
Wolf-Deer Predator-Prey Model
Concluding Remarks on Wolf Territoriality and Deer Survival
Coyote Home Range Patterns
Chippewa and Sioux Intertribal Conflict c1750-1850
Appendix
General Results for the Laplacian Operator in Bounded Domains
Bibliography
Index
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