Biomathematics modelling and simulationPDF电子书下载

1 Detecting Mosaic Structures in DNA Sequence Alignments&Dirk Husmeier 1

1 Introduction 1

2 A Brief Introduction to Phylogenetics 2

2.1 Topology and parameters of a phylogenetic tree 2

2.2 DNA sequences and sequence alignments 4

2.3 A mathematical model of nucleotide substitution 5

2.4 Likelihood of a phylogenetic tree 9

3 Recombination 13

4 A One-Minute Introduction to Hidden Markov Models 16

5 Detecting Recombination with Hidden Markov Models 19

5.1 The model 19

5.2 Naive parameter estimation 20

5.3 Maximum likelihood 21

5.3.1 E-step 24

5.3.2 M-step：Optimization of the recombination parameter 25

5.3.3 M-step：Optimization of the branch lengths 25

5.3.4 Reason for not optimizing the prior probabilities 25

5.3.5 Algorithm 26

6 Test Data 27

6.1 Synthetic data 27

6.2 Gene conversion in maize 27

6.3 Recombination in Neisseria 28

7 Simulation 29

7.1 Synthetic DNA sequence alignment 31

7.2 Gene conversion in maize 32

7.3 Recombination in Neisseria 32

8 Discussion 32

References 34

2 Application of Statistical Methodology and Model Design to Socio-Behaviour of HIV Transmission&Jacob Oluwoye 37

1 Introduction 37

2 Deductive and Inductive Approach 39

3 Statistical Methodology and Model Design 40

3.1 Five steps in model building 42

3.2 Model building approach 43

4 Adaptation of“Seldom Do”Models to Human Behaviour 44

5 The Discrete Choice Modelling 47

6 Application of the Use of Logit Specification to Socio-Behaviour of HIV Transmission 52

6.1 Binary choice models 52

6.2 The linear probability model 53

6.3 The logit model 54

7 Conclusion 56

8 General Comments 56

Acknowledgements 57

References 57

Bibliography 58

3 A Stochastic Model Incorporating HIV Treatments for a Heterosexual Population：Impact on Threshold Conditions&Robert J.Gallop，Charles J.Mode and Candace K.Sleeman 59

1 Introduction 59

2 Parameters for a Heterosexual Population 61

3 Latent Risks for Transitions in Population 64

4 Stochastic Evolutionary Equations 70

5 Form of the Embedded ODE for Given Parameters 72

6 Determination of the Spread of the Disease 74

7 Results of Monte Carlo Simulation Experiments 75

8 Discussion and Summary 80

References 82

4 Modeling and Identification of the Dynamics of the MF-Influenced Free-Radical Transformations in Lipid-Modeling Substances and Lipids&J.Bentsman，I.V.Dardynskaia，O.Shadyro，G.Pellegrinetti，R.Blauwkamp and G.Gloushonok 85

0 Introduction 85

1 Objectives and Motivation 89

2 Framework for Fitting Mathematical Models to the Experimental Data 90

3 Modeling and Identification of the MF-Influenced Oxidation of Hexane 92

3.1 Experimental part 92

3.2 Reaction scheme and differential equations，describing the process of photo-induced oxidation of hexane 95

3.3 Localization of the influence of magnetic field in the system description 99

3.4 Development of the model with dependence on magnetic field 102

3.5 Procedures for identification of the reaction dynamics under MF infLuence using the flow-through experimental data 104

3.6 Identification results 113

3.7 Validation of the nonlinear mathematical model and the region of model validity 113

4 Modeling and Identification of the MF-Influenced Oxidation of Linolenic Acid 114

4.1 Experimental part 114

4.2 Reaction scheme and differential equations，describing the process of photo-induced oxidation of linolenic acid 115

4.3 Identification of the reaction dynamics under MF influence using the flow-through experimental data 122

4.4 Sensitivity of the concentration growth rates to magnetic field strength in the batch and flow-through experiments 128

4.5 Development of nonlinear equation constants and dependence on magnetic field 132

5 Problems 133

Acknowledgement 133

References 133

5 Computer Simulation of Self Reorganization in Biological Cells&Donald Greenspan 137

1 Biological，Physical and Computational Preliminaries 137

1.1 Introduction 137

1.2 Classical molecular mechanics 137

1.3 The computer algorithm 138

2 Supercomputer Examples 139

2.1 A morphogenesis simulation 139

2.2 Other examples 145

References 147

6 Modelling Biological Gel Contraction by Cells：Consequences of Cell Traction Forces Distribution and Initial Stress&S.Ramtani 149

1 Introduction 149

2 The Mechanocellular Model 151

3 Model Predictions and Discussion 155

3.1 Uniaxial cell traction force effect 155

3.2 Initial stress effect 160

References 164

7 Peristaltic Transport of Physiological Fluids&J.C.Misra and S.K.Pandey 167

1 Phenomena Associated with Peristalsis 168

2 Physiological Systems Associated with Peristalsis 169

2.1 Digestive system 169

2.2 Oesophagus 169

2.3 Stomach 170

2.4 Small intestine 171

2.5 Ureter 173

2.6 Vas deferens 174

2.7 Experimental investigations on peristalsis 174

3 Theoretical Studies on Peristaltic Transport 177

3.1 Newtonian flows 177

3.2 Non-Newtonian flows 180

3.3 Non-stationary initial flows 182

3.4 Two-phase flows 183

3.5 Two-layer flows 186

4 Flows through Tubes of Non-Uniform Cross-Section 188

5 Numerical Investigations 189

References 190

8.Mathematical Modelling of DNA Knots and Links&J.C.Misra and S.Mukherjee 195

1 Introduction 195

2 Mathematical Background 199

2.1 Topological tools for DNA analysis 199

2.2 Definitions 201

2.3 2-string tangles 202

2.4 Rational tangle 203

2.5 4-plats 205

2.6 Classification of 4-plats 206

3 Biological Statement and Assumptions 208

4 Tangle Model Assumptions 209

4.1 Other substrates 211

5 Site-Specific Recombination 211

6 Processive Recombination 214

7 Useful Facts and Theorems About Tangles 215

8 Model for the Tn3 Resolvase 218

9 Model for the Xer Recombinase and Topoisomerases Ⅲ and Ⅳ 219

9.1 Biological model for recombinases and topoisomerases 220

9.2 Biological model（unknotted substrates） 220

9.3 Biological model（catenated substrates） 220

9.4 Tangle equations for unknotted substrates 220

9.5 Tangle equations for catenated substrates 221

9.6 Problems 221

9.7 Results 221

10 Modelling Conclusions 222

Acknowledgement 223

References 224

9 Using Monodomain Computer Models for the Simulation of Electric Fields During Excitation Spread in Cardiac Tissue&G.Plank 225

1 Introduction 225

2 Physiological Background 228

2.1 Properties of cardiac cells 228

2.2 The action potential 231

3 Modelling the Membrane Kinetics 233

4 Modelling of Action Potential Propagation in Cardiac Tissue 237

4.1 Core conductor model 237

4.1.1 Electrical parameters of a cylindrical fiber 237

4.1.2 Electrical model of a single fiber 238

4.1.3 Cable equations 240

4.1.4 Linear subthreshold conditions 242

4.1.5 The propagating action potential 244

4.1.6 Finite length cables 247

4.2 Monodomain models 250

4.2.1 One-dimensional fiber 250

4.2.2 Multi-dimensional tissue 251

4.2.3 Discontinuous monodomain models 253

4.3 Numerical solution of monodomain equations 253

4.3.1 Spatial discretization of equations 255

4.3.2 Monodomain integration methods 258

4.3.3 Advanced techniques 260

5 Recovery of Extracellular Potentials and Fields 262

5.1 Source-field concept 263

5.2 Volume conductor fields of cylindrical fibers 264

6 Volume Conductor Potentials and Fields during Depolarization 267

6.1 Two-dimensional tissue model 267

6.2 Spatial source distribution at the central fiber 268

6.3 Time course of intra- and extracellular signals 269

6.4 The electric field evoked by an elliptic wavefront 270

Acknowledgments 271

References 271

10 Flow in Tubes with Complicated Geometries with Special Application to Blood Flow in Large Arteries&Girija Jayaraman 279

0 Introduction 279

0.1 Wall shear stress and atherosclerosis 281

0.2 Arterial stenosis 281

0.3 Entry flows 282

0.4 Influence of curvature 282

0.5 Artefacts of catheters 285

1 Mathematical Formulation 287

1.1 Flow geometry 287

1.2 Co-ordinate system 287

1.3 Governing equations of motion 288

1.4 Boundary conditions 289

2 Methods of Solution 290

2.1 Perturbation analysis 290

2.2 Numerical approach 291

3 Discussions 293

3.1 Pressure drop and impedance 294

3.2 Wall shear stress 299

3.3 Flow behavior 300

4 Concluding Remarks 301

References 302

11 Mathematical Modeling in Reproductive Biomedicine&Shivani Sharma and Sujoy K.Guha 305

1 Introduction 305

2 Mechanics of Ovulation 306

3 Transport of Gametes 307

3.1 Ovum transport 307

3.2 Transport of spermatozoa 308

4 Mechanics of Sperm-Egg Interaction 309

5 Fetal Head Molding 310

6 Fertility Index of Spermatozoa 312

7 Conclusion 313

References 314

12 Image Theory and Applications in Bioelectromagnetics&P.D.Einziger，L.M.Livshitz and J.Mizrahi 315

1 Introduction 316

1.1 Bioelectromagnetic interaction between electric field and biological tissue：computational aspects 316

1.2 Harmonic school 316

1.3 Image school 317

1.4 Brief summary 319

2 Rigorous Image Series Expansion of Green’s Function for Plane-Stratified Media 321

2.1 Finite image integral expansion 321

2.1.1 Integral representation 322

2.1.2 Image integral expansions 325

2.1.3 Unbounded medium，n＝0 326

2.1.4 Semi-infinite medium，n＝1 326

2.1.5 Single slab configuration，n＝2 326

2.1.6 Double slab configuration，n＝3 327

2.1.7 Generalized image integral expansion（n≥1） 330

2.2 Image series expansion 332

2.2.1 Properties of R（ξ） 333

2.2.2 Quasistatic point-charge potential 335

2.3 Infinite image series expansions 336

2.3.1 Unbounded medium，n＝0 336

2.3.2 Semi-infinite medium，n＝1 336

2.3.3 Single slab configuration，n＝2 337

2.3.4 Double slab configuration，n＝3 338

2.3.5 n ＋ 1 layered media 339

2.4 Convergence and truncation-error estimation：the collective image approach 340

2.4.1 Single slab configuration，n＝2 340

2.4.2 Double slab configuration，n＝3 341

2.4.3 n＋1 layered media 342

3 Electrode Array in Layered Media 344

3.1 Integral equation formulation 344

3.2 Electrode array 346

3.3 Moment method 347

3.4 Electrode array excitation of layered biological tissue：numerical simulations 349

3.4.1 Potential map 349

3.4.2 Two-electrode configuration 351

4 Conclusion 352

Acknowledgments 354

References 354

13 Dynamics of Humanoid Robots：Geometrical and Topological Duality&Vladimir G.Ivancevic 359

1 Introduction 359

2 Topological Preliminaries 360

3 HD-Configuration Manifold and Its Reduction 362

3.1 Configuration manifold 362

3.2 Reduction of the configuration manifold 364

4 Geometrical Duality in Humanoid Dynamics 365

4.1 Lie-functorial proof 365

4.2 Geometrical proof 367

5 Topological Duality in Humanoid Dynamics 371

5.1 Cohomological proof 371

5.2 Homological proof 373

6 Global Structure of Humanoid Dynamics 374

References 375

14 The Effects of Body Composition on Energy Expenditure and Weight Dynamics During Hypophagia：A Setpoint Analysis&Frank P.Kozusko 379

1 Introduction 379

2 Modeling Human Daily Energy Expenditure 381

2.1 Equilibrium models 382

2.2 Setpoint analysis and modeling nonequilibrium energy needs 382

2.3 Comparing models 385

3 Energy from Fat/Nonfat Body Mass 386

3.1 The personnel fat ratio 386

3.2 The ratio of nonfat loss to total weight loss 387

3.3 The energy density and the energy density ratio 388

4 The Setpoint/Body Composition Adjusted Energy Rate Equation 388

5 Analysis 389

5.1 The Minnesota experiment 389

5.2 The characteristic time and rate of weight loss 390

5.3 Comparing the models in dynamics 392

5.4 Comparing the models in equilibrium 394

6 Discussion and Conclusions 396

References 397

15 Mathematical Models in Population Dynamics and Ecology&Rui Dilao 399

1 Introduction 399

2 Biotic Interactions 402

2.1 One species interaction with the environment 402

2.2 Two interacting species 406

3 Discrete Models for Single Populations.Age-Structured Models 416

4 A Case Study with a Simple Linear Discrete Model 419

5 Discrete Time Models with Population Dependent Parameters 424

6 Resource Dependent Discrete Models 427

7 Spatial Effects 432

8 Age-Structured Density Dependent Models 437

9 Growth by Mitosis 443

10 Conclusions 444

Acknowledgements 447

References 447

16 Modelling in Bone Biomechanics&J.C.Misra and S.Samanta 451

1 Introduction 451

2 Bone Biomechanics and Its Mathematical Analogues 452

3 Material Response of Structural Solids to External Excitations 454

4 Deformable Solids 458

4.1 Basic concepts 458

4.2 Equilibrium equation 459

4.3 Linear viscoelastic constitutive relations：non-piezoelectric materials 459

5 The Human Skeletal System 462

6 Long Bones 462

7 Intervertebral Discs 464

8 Composition of Bone 465

9 Microscopic Anatomy of Bone Tissue 465

10 Physical Properties of Bones 466

11 Bone Anisotropy 467

12 Viscoelastic Properties of Osseous Tissues 469

13 Piezoelectric Effects in Bone 471

14 Bone Inhomogeneity 474

15 Bone Remodelling 474

16 Current State-of-the-Art 478

References 484

Index 493