|
|
|
是近代生物數學方面的名著。第三版，在原來版本的基礎上做了全面修訂。近年來這個科目的茁壯成長和新知識點的不斷涌現，新的版本將原來的一卷集分成上下兩卷，擴大了知識容量，第二卷絕大多數是新增知識點。書中對生物學中的反應擴散方程和形態發生學的數學理論及最新研究成果作了全面介紹，是學習與研究生物數學的一部不可多得的參考書。
CONTENTS,VOLUME H
Preface to the Third Edition
Preface to the First Edition
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-ω Reaction 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 Diffusion 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 Patterns in 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.coil 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 Potential
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 Cell Movement 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.Growth and 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 Invasion in 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 Firing with a Simple Activation-Inhibition Model
12.2 A Mechanism 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 of the Black Death 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 U: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.Woff Territoriality,Woff-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
