Biomathematics modelling and simulation【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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1 Detecting Mosaic Structures in DNA Sequence Alignments&Dirk Husmeier1

1 Introduction1

2 A Brief Introduction to Phylogenetics2

2.1 Topology and parameters of a phylogenetic tree2

2.2 DNA sequences and sequence alignments4

2.3 A mathematical model of nucleotide substitution5

2.4 Likelihood of a phylogenetic tree9

3 Recombination13

4 A One-Minute Introduction to Hidden Markov Models16

5 Detecting Recombination with Hidden Markov Models19

5.1 The model19

5.2 Naive parameter estimation20

5.3 Maximum likelihood21

5.3.1 E-step24

5.3.2 M-step：Optimization of the recombination parameter25

5.3.3 M-step：Optimization of the branch lengths25

5.3.4 Reason for not optimizing the prior probabilities25

5.3.5 Algorithm26

6 Test Data27

6.1 Synthetic data27

6.2 Gene conversion in maize27

6.3 Recombination in Neisseria28

7 Simulation29

7.1 Synthetic DNA sequence alignment31

7.2 Gene conversion in maize32

7.3 Recombination in Neisseria32

8 Discussion32

References34

2 Application of Statistical Methodology and Model Design to Socio-Behaviour of HIV Transmission&Jacob Oluwoye37

1 Introduction37

2 Deductive and Inductive Approach39

3 Statistical Methodology and Model Design40

3.1 Five steps in model building42

3.2 Model building approach43

4 Adaptation of“Seldom Do”Models to Human Behaviour44

5 The Discrete Choice Modelling47

6 Application of the Use of Logit Specification to Socio-Behaviour of HIV Transmission52

6.1 Binary choice models52

6.2 The linear probability model53

6.3 The logit model54

7 Conclusion56

8 General Comments56

Acknowledgements57

References57

Bibliography58

3 A Stochastic Model Incorporating HIV Treatments for a Heterosexual Population：Impact on Threshold Conditions&Robert J.Gallop，Charles J.Mode and Candace K.Sleeman59

1 Introduction59

2 Parameters for a Heterosexual Population61

3 Latent Risks for Transitions in Population64

4 Stochastic Evolutionary Equations70

5 Form of the Embedded ODE for Given Parameters72

6 Determination of the Spread of the Disease74

7 Results of Monte Carlo Simulation Experiments75

8 Discussion and Summary80

References82

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.Gloushonok85

0 Introduction85

1 Objectives and Motivation89

2 Framework for Fitting Mathematical Models to the Experimental Data90

3 Modeling and Identification of the MF-Influenced Oxidation of Hexane92

3.1 Experimental part92

3.2 Reaction scheme and differential equations，describing the process of photo-induced oxidation of hexane95

3.3 Localization of the influence of magnetic field in the system description99

3.4 Development of the model with dependence on magnetic field102

3.5 Procedures for identification of the reaction dynamics under MF infLuence using the flow-through experimental data104

3.6 Identification results113

3.7 Validation of the nonlinear mathematical model and the region of model validity113

4 Modeling and Identification of the MF-Influenced Oxidation of Linolenic Acid114

4.1 Experimental part114

4.2 Reaction scheme and differential equations，describing the process of photo-induced oxidation of linolenic acid115

4.3 Identification of the reaction dynamics under MF influence using the flow-through experimental data122

4.4 Sensitivity of the concentration growth rates to magnetic field strength in the batch and flow-through experiments128

4.5 Development of nonlinear equation constants and dependence on magnetic field132

5 Problems133

Acknowledgement133

References133

5 Computer Simulation of Self Reorganization in Biological Cells&Donald Greenspan137

1 Biological，Physical and Computational Preliminaries137

1.1 Introduction137

1.2 Classical molecular mechanics137

1.3 The computer algorithm138

2 Supercomputer Examples139

2.1 A morphogenesis simulation139

2.2 Other examples145

References147

6 Modelling Biological Gel Contraction by Cells：Consequences of Cell Traction Forces Distribution and Initial Stress&S.Ramtani149

1 Introduction149

2 The Mechanocellular Model151

3 Model Predictions and Discussion155

3.1 Uniaxial cell traction force effect155

3.2 Initial stress effect160

References164

7 Peristaltic Transport of Physiological Fluids&J.C.Misra and S.K.Pandey167

1 Phenomena Associated with Peristalsis168

2 Physiological Systems Associated with Peristalsis169

2.1 Digestive system169

2.2 Oesophagus169

2.3 Stomach170

2.4 Small intestine171

2.5 Ureter173

2.6 Vas deferens174

2.7 Experimental investigations on peristalsis174

3 Theoretical Studies on Peristaltic Transport177

3.1 Newtonian flows177

3.2 Non-Newtonian flows180

3.3 Non-stationary initial flows182

3.4 Two-phase flows183

3.5 Two-layer flows186

4 Flows through Tubes of Non-Uniform Cross-Section188

5 Numerical Investigations189

References190

8.Mathematical Modelling of DNA Knots and Links&J.C.Misra and S.Mukherjee195

1 Introduction195

2 Mathematical Background199

2.1 Topological tools for DNA analysis199

2.2 Definitions201

2.3 2-string tangles202

2.4 Rational tangle203

2.5 4-plats205

2.6 Classification of 4-plats206

3 Biological Statement and Assumptions208

4 Tangle Model Assumptions209

4.1 Other substrates211

5 Site-Specific Recombination211

6 Processive Recombination214

7 Useful Facts and Theorems About Tangles215

8 Model for the Tn3 Resolvase218

9 Model for the Xer Recombinase and Topoisomerases Ⅲ and Ⅳ219

9.1 Biological model for recombinases and topoisomerases220

9.2 Biological model（unknotted substrates）220

9.3 Biological model（catenated substrates）220

9.4 Tangle equations for unknotted substrates220

9.5 Tangle equations for catenated substrates221

9.6 Problems221

9.7 Results221

10 Modelling Conclusions222

Acknowledgement223

References224

9 Using Monodomain Computer Models for the Simulation of Electric Fields During Excitation Spread in Cardiac Tissue&G.Plank225

1 Introduction225

2 Physiological Background228

2.1 Properties of cardiac cells228

2.2 The action potential231

3 Modelling the Membrane Kinetics233

4 Modelling of Action Potential Propagation in Cardiac Tissue237

4.1 Core conductor model237

4.1.1 Electrical parameters of a cylindrical fiber237

4.1.2 Electrical model of a single fiber238

4.1.3 Cable equations240

4.1.4 Linear subthreshold conditions242

4.1.5 The propagating action potential244

4.1.6 Finite length cables247

4.2 Monodomain models250

4.2.1 One-dimensional fiber250

4.2.2 Multi-dimensional tissue251

4.2.3 Discontinuous monodomain models253

4.3 Numerical solution of monodomain equations253

4.3.1 Spatial discretization of equations255

4.3.2 Monodomain integration methods258

4.3.3 Advanced techniques260

5 Recovery of Extracellular Potentials and Fields262

5.1 Source-field concept263

5.2 Volume conductor fields of cylindrical fibers264

6 Volume Conductor Potentials and Fields during Depolarization267

6.1 Two-dimensional tissue model267

6.2 Spatial source distribution at the central fiber268

6.3 Time course of intra- and extracellular signals269

6.4 The electric field evoked by an elliptic wavefront270

Acknowledgments271

References271

10 Flow in Tubes with Complicated Geometries with Special Application to Blood Flow in Large Arteries&Girija Jayaraman279

0 Introduction279

0.1 Wall shear stress and atherosclerosis281

0.2 Arterial stenosis281

0.3 Entry flows282

0.4 Influence of curvature282

0.5 Artefacts of catheters285

1 Mathematical Formulation287

1.1 Flow geometry287

1.2 Co-ordinate system287

1.3 Governing equations of motion288

1.4 Boundary conditions289

2 Methods of Solution290

2.1 Perturbation analysis290

2.2 Numerical approach291

3 Discussions293

3.1 Pressure drop and impedance294

3.2 Wall shear stress299

3.3 Flow behavior300

4 Concluding Remarks301

References302

11 Mathematical Modeling in Reproductive Biomedicine&Shivani Sharma and Sujoy K.Guha305

1 Introduction305

2 Mechanics of Ovulation306

3 Transport of Gametes307

3.1 Ovum transport307

3.2 Transport of spermatozoa308

4 Mechanics of Sperm-Egg Interaction309

5 Fetal Head Molding310

6 Fertility Index of Spermatozoa312

7 Conclusion313

References314

12 Image Theory and Applications in Bioelectromagnetics&P.D.Einziger，L.M.Livshitz and J.Mizrahi315

1 Introduction316

1.1 Bioelectromagnetic interaction between electric field and biological tissue：computational aspects316

1.2 Harmonic school316

1.3 Image school317

1.4 Brief summary319

2 Rigorous Image Series Expansion of Green’s Function for Plane-Stratified Media321

2.1 Finite image integral expansion321

2.1.1 Integral representation322

2.1.2 Image integral expansions325

2.1.3 Unbounded medium，n＝0326

2.1.4 Semi-infinite medium，n＝1326

2.1.5 Single slab configuration，n＝2326

2.1.6 Double slab configuration，n＝3327

2.1.7 Generalized image integral expansion（n≥1）330

2.2 Image series expansion332

2.2.1 Properties of R（ξ）333

2.2.2 Quasistatic point-charge potential335

2.3 Infinite image series expansions336

2.3.1 Unbounded medium，n＝0336

2.3.2 Semi-infinite medium，n＝1336

2.3.3 Single slab configuration，n＝2337

2.3.4 Double slab configuration，n＝3338

2.3.5 n ＋ 1 layered media339

2.4 Convergence and truncation-error estimation：the collective image approach340

2.4.1 Single slab configuration，n＝2340

2.4.2 Double slab configuration，n＝3341

2.4.3 n＋1 layered media342

3 Electrode Array in Layered Media344

3.1 Integral equation formulation344

3.2 Electrode array346

3.3 Moment method347

3.4 Electrode array excitation of layered biological tissue：numerical simulations349

3.4.1 Potential map349

3.4.2 Two-electrode configuration351

4 Conclusion352

Acknowledgments354

References354

13 Dynamics of Humanoid Robots：Geometrical and Topological Duality&Vladimir G.Ivancevic359

1 Introduction359

2 Topological Preliminaries360

3 HD-Configuration Manifold and Its Reduction362

3.1 Configuration manifold362

3.2 Reduction of the configuration manifold364

4 Geometrical Duality in Humanoid Dynamics365

4.1 Lie-functorial proof365

4.2 Geometrical proof367

5 Topological Duality in Humanoid Dynamics371

5.1 Cohomological proof371

5.2 Homological proof373

6 Global Structure of Humanoid Dynamics374

References375

14 The Effects of Body Composition on Energy Expenditure and Weight Dynamics During Hypophagia：A Setpoint Analysis&Frank P.Kozusko379

1 Introduction379

2 Modeling Human Daily Energy Expenditure381

2.1 Equilibrium models382

2.2 Setpoint analysis and modeling nonequilibrium energy needs382

2.3 Comparing models385

3 Energy from Fat/Nonfat Body Mass386

3.1 The personnel fat ratio386

3.2 The ratio of nonfat loss to total weight loss387

3.3 The energy density and the energy density ratio388

4 The Setpoint/Body Composition Adjusted Energy Rate Equation388

5 Analysis389

5.1 The Minnesota experiment389

5.2 The characteristic time and rate of weight loss390

5.3 Comparing the models in dynamics392

5.4 Comparing the models in equilibrium394

6 Discussion and Conclusions396

References397

15 Mathematical Models in Population Dynamics and Ecology&Rui Dilao399

1 Introduction399

2 Biotic Interactions402

2.1 One species interaction with the environment402

2.2 Two interacting species406

3 Discrete Models for Single Populations.Age-Structured Models416

4 A Case Study with a Simple Linear Discrete Model419

5 Discrete Time Models with Population Dependent Parameters424

6 Resource Dependent Discrete Models427

7 Spatial Effects432

8 Age-Structured Density Dependent Models437

9 Growth by Mitosis443

10 Conclusions444

Acknowledgements447

References447

16 Modelling in Bone Biomechanics&J.C.Misra and S.Samanta451

1 Introduction451

2 Bone Biomechanics and Its Mathematical Analogues452

3 Material Response of Structural Solids to External Excitations454

4 Deformable Solids458

4.1 Basic concepts458

4.2 Equilibrium equation459

4.3 Linear viscoelastic constitutive relations：non-piezoelectric materials459

5 The Human Skeletal System462

6 Long Bones462

7 Intervertebral Discs464

8 Composition of Bone465

9 Microscopic Anatomy of Bone Tissue465

10 Physical Properties of Bones466

11 Bone Anisotropy467

12 Viscoelastic Properties of Osseous Tissues469

13 Piezoelectric Effects in Bone471

14 Bone Inhomogeneity474

15 Bone Remodelling474

16 Current State-of-the-Art478

References484

Index493