1．Multi-Species Waves and Practical Applications

1.1 Intuitive Expectations

1.2 Waves of Pursuit and Evasion in Predator-Prey Systems

1.3 Competition Model for the Spatial Spread of the Grey Squirrel in Britain

1.4 Spread of Genetically Engineered Organisms

1.5 Travelling Fronts in the Belousov-Zhabotinskii Reaction

1.6 Waves in Excitable Media

1.7 Travelling Wave Trains in Reaction Diffusion Systems with Oscillatory Kinetics

1.8 Spiral Waves

1.9 Spiral Wave Solutions of λ-ωReaction Diffusion Systems

Exercises

2．Spatial Pattern Formation with Reaction Diffusion Systems

2.1 Role of Pattern in Biology

2.2 Reaction Diffusion(Turing)Mechanisms

2.3 General Conditions for Diffusion-Driven Instability:Linear Stability Analysis and Evolution of Spatial Pattern

2.4 Detailed Analysis of Pattern Initiation in a Reaction Diffusion Mechanism

2.5 Dispersion Relation,Turing Space,Scale and Geometry Effects in Pattern Formation Models

2.6 Mode Selection and the Dispersion Relation

2.7 Pattern Generation with Single-Species Models:Spatial Heterogeneity with the Spruce Budworm Model

2.8 Spatial Patterns in Scalar Population Interaction Diffusion Equations with Convection:Ecological Control Strategies

2.9 Nonexistence of Spatial Patterns in Reaction Difrusion Systems:General and Particular Results

Exercises

3．Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms

3.1 Mammalian Coat Patterns—'How the Leopard Got Its Spots'

3.2 Teratologies:Examples of Animal Coat Pattern Abnormalities

3.3 A Pattern Formation Mechanism for Butterfly Wing Patterns

3.4 Modelling Hair Patternsin a Whorl in Acetabularia

4．Pattern Formation on Growing Domains:Alligators and Snakes

4.1 Stripe Pattern Formation in the Alligator:Experiments

4.2 Modelling Concepts:Determining the Time of Stripe Formation

4.3 Stripes and Shadow Stripes on the Alligator

4.4 Spatial Patterning of Teeth Primordia in the Alligator:Background and Relevance

4.5 Biology of Tooth Initiation

4.6 Modelling Tooth Primordium Initiation:Background

4.7 Model Mechanism for Alligator Teeth Patterning

4.8 Results and Comparison with Experimental Data

4.9 Prediction Experiments

4.10 Concluding Remarks on Alligator Tooth Spatial Patterning

4.11 Pigmentation Pattern Formation on Snakes

4.12 Cell-Chemotaxis Model Mechanism

4.13 Simple and Complex Snake Pattern Elements

4.14 Propagating Pattern Generation with the Cell-Chemotaxis System

5．Bacterial Patterns and Chemotaxis

5.1 Background and Experimental Results

5.2 Model Mechanism for E. coli in the Semi-Solid Experiments

5.3 Liquid Phase Model:Intuitive Analysis of Pattern Formation

5.4 Interpretation of the Analytical Results and Numerical Solutions

5.5 Semi-Solid Phase Model Mechanism for S. typhimurium

5.6 Linear Analysis of the Basic Semi-Solid Model

5.7 Brief Outline and Results of the Nonlinear Analysis

5.8 Simulation Results,Parameter Spaces and Basic Patterns

5.9 Numerical Results with Initial Conditions from the Experiments

5.10 Swarm Ring Patterns with the Semi-Solid Phase Model Mechanism

5.11 Branching Patterns in Bacillus subtilis

6．Mechanical Theory for Generating Pattern and Form in Development

6.1 Introduction,Motivation and Background Biology

6.2 Mechanical Model for Mesenchymal Morphogenesis

6.3 Linear Analysis,Dispersion Relation and Pattern Formation Potentiai

6.4 Simple Mechanical Models Which Generate Spatial Patterns with Complex Dispersion Relations

6.5 Periodic Patterns of Feather Germs

6.6 Cartilage Condensations in Limb Morphogenesis and Morphogenetic Rules

6.7 Embryonic Fingerprint Formation

6.8 Mechanochemical Model for the Epidermis

6.9 Formation of Microvilli

6.10 Complex Pattern Formation and Tissue Interaction Models

Exercises

7．Evolution,Morphogenetic Laws,Developmental Constraints and Teratologies

7.1 Evolution and Morphogenesis

7.2 Evolution and Morphogenetic Rules in Cartilage Formation in the Vertebrate Limb

7.3 Teratologies(Monsters)

7.4 Developmental Constraints,Morphogenetic Rules and the Consequences for Evolution

8．A Mechanical Theory of Vascular Network Formation

8.1 Biological Background and Motivation

8.2 Cell-Extracellular Matrix Interactions for Vasculogenesis

8.3 Parameter Values

8.4 Analysis of the Model Equations

8.5 Network Patterns:Numerical Simulations and Conclusions

9．Epidermal Wound Healing

9.1 Brief History of Wound Healing

9.2 Biological Background:Epidermal Wounds

9.3 Model for Epidermal Wound Healing

9.4 Nondimensional Form,Linear Stability and Parameter Values

9.5 Numerical Solution for the Epidermal Wound Repair Model

9.6 Travelling Wave Solutions for the Epidermal Model

9.7 Clinical Implications of the Epidermal Wound Model

9.8 Mechanisms of Epidermal Repair in Embryos

9.9 Actin Alignment in Embryonic Wounds:A Mechanical Model

9.10 Mechanical Model with Stress Alignment of the Actin Filaments in Two Dimensions

10．Dermal Wound Healing

10.1 Background and Motivation—General and Biological

10.2 Logic of Wound Healing and Initial Models

10.3 Brief Review of Subsequent Developments

10.4 Model for Fibroblast-Driven Wound Healing:Residual Strain and Tissue Remodelling

10.5 Solutions of the Model Equations and Comparison with Experiment

10.6 Wound Healing Model of Cook(1995)

10.7 Matrix Secretion and Degradation

10.8 CellMovement in an Oriented Environment

10.9 Model System for Dermal Wound Healing with Tissue Structure

10.10 One-Dimensional Model for the Structure of Pathological Scars

10.11 Open Problems in Wound Healing

10.12 Concluding Remarks on Wound Healing

11．Growthand Control of Brain Tumours

11.1 Medical Background

11.2 Basic Mathematical Model of Glioma Growth and Invasion

11.3 Tumour Spread In Vitro:Parameter Estimation

11.4 Tumour Invasionin the Rat Brain

11.5 Tumour Invasion in the Human Brain

11.6 Modelling Treatment Scenarios:General Comments

11.7 Modelling Tumour Resection in Homogeneous Tissue

11.8 Analytical Solution for Tumour Recurrence After Resection

11.9 Modelling Surgical Resection with Brain Tissue Heterogeneity

11.10 Modelling the Effect of Chemotherapy on Tumour Growth

11.11 Modelling Tumour Polyclonality and Cell Mutation

12．Neural Models of Pattern Formation

12.1 Spatial Patterning in Neural Firng with a Simple Activation-Inhibition Model

12.2 AMechanism for Stripe Formation in the Visual Cortex

12.3 A Model for the Brain Mechanism Underlying Visual Hallucination Patterns

12.4 Neural Activity Model for Shell Patterns

12.5 Shamanism and Rock Art

Exercises

13．Geographic Spread and Control of Epidemics

13.1 Simple Model for the Spatial Spread of an Epidemic

13.2 Spread ofthe BlackDeath in Europe 1347-1350

13.3 Brief History of Rabies:Facts and Myths

13.4 The Spatial Spread of Rabies Among Foxes Ⅰ:Background and Simple Model

13.5 The Spatial Spread of Rabies Among Foxes Ⅱ:Three-Species(SIR) Model

13.6 Control Strategy Based on Wave Propagation into a Nonepidemic Region:Estimate of Width of a Rabies Barrier

13.7 Analytic Approximation for the Width of the Rabies Control Break

13.8 Two-Dimensional Epizootic Fronts and Effects of Variable Fox Densities:Quantitative Predictions for a Rabies Outbreak in England

13.9 Effect of Fox Immunity on the Spatial Spread of Rabies

Exercises

14．Wolf Territoriality,Wolf-Deer Interaction and Survival

14.1 Introduction and Wolf Ecology

14.2 Models for Wolf Pack Territory Formation:Single Pack—Home Range Model

14.3 Multi-Wolf Pack Territorial Model

14.4 Wolf-Deer Predator-Prey Model

14.5 Concluding Remarks on Wolf Territoriality and Deer Survival

14.6 Coyote Home Range Patterns

14.7 Chippewa and Sioux Intertribal Conflict c1750-1850

Appendix

A．General Results for the Laplacian Operator in Bounded Domains

Bibliography

Index