Computer Modeling in Bioengineering : Theoretical Background, Examples and Software

Bioengineering is a broad-based engineering discipline that applies engineering principles and design to challenges in human health and medicine, dealing with bio-molecular and molecular processes, product design, sustainability and analysis of biological systems. Applications that benefit from bioengineering include medical devices, diagnostic equipment and biocompatible materials, amongst others. Computer Modeling in Bioengineering offers a comprehensive reference for a large number of bioengineering topics, presenting important computer modeling problems and solutions for research and medical practice. Starting with basic theory and fundamentals, the book progresses to more advanced methods and applications, allowing the reader to become familiar with different topics to the desired extent. It includes unique and original topics alongside classical computational modeling methods, and each application is structured to explain the physiological background, phenomena that are to be modeled, the computational methods used in the model, and solutions of typical cases. The accompanying software contains over 80 examples, enabling the reader to study a topic using the theory and examples, then run the software to solve the same, or similar examples, varying the model parameters within a given range in order to investigate the problem at greater depth. Tutorials also guide the user in further exploring the modeled problem; these features promote easier learning and will help lecturers with presentations. Computer Modeling in Bioengineering includes computational methods for modelling bones, tissues, muscles, cardiovascular components, cartilage, cells and cancer nanotechnology as well as many other applications. It bridges the gap between engineering, biology and medicine, and will appeal not only to bioengineering students, lecturers and researchers, but also medical students and clinical researchers. Computer Modeling in Bioengineering......Page 4 Contents......Page 10 Contributors......Page 18 Preface......Page 20 Part I Theoretical Background of Computational Methods......Page 24 1.1 Matrix representation of mathematical objects......Page 26 1.2 Basic relations in matrix algebra......Page 27 1.3 Definition of tensors and some basic tensorial relations......Page 29 1.4 Vector and tensor differential operations and integral theorems......Page 31 1.5 Examples......Page 34 2.1.1 Stress......Page 38 2.1.2 Strain and strain rate......Page 42 2.1.3 Examples......Page 44 2.2.1 Linear elastic constitutive law......Page 49 2.2.2 Viscoelasticity......Page 52 2.2.4 Examples......Page 53 2.3.1 Formulation of the principle of virtual work......Page 60 2.3.2 Examples......Page 61 2.4 Nonlinear continuum mechanics......Page 63 2.4.1 Deformation gradient and the measures of strain and stress......Page 64 2.4.2 Nonlinear elastic constitutive relations......Page 68 2.4.3 Examples......Page 70 3.1 Heat conduction......Page 74 3.1.1 Governing relations......Page 75 3.1.2 Examples......Page 76 3.2.1 Differential equations of diffusion......Page 78 3.2.2 Examples......Page 80 3.3 Fluid flow of incompressible viscous fluid with heat and mass transfer......Page 81 3.3.1 Governing equations of fluid flow and of heat and mass transfer......Page 82 3.3.2 Examples......Page 83 3.4 Fluid flow through porous deformable media......Page 86 3.4.1 The governing equations......Page 87 3.4.2 Examples......Page 89 Part II Fundamentals of Computational Methods......Page 92 4.1 Introduction to the finite element method......Page 94 4.2.1 Truss finite element......Page 96 4.2.2 Equilibrium equations of the FE assemblage and boundary conditions......Page 101 4.2.3 Examples......Page 103 4.3.1 Element formulation......Page 104 4.3.2 Examples......Page 107 4.4 Two-dimensional (2D) isoparametric finite elements......Page 108 4.4.1 Formulation of the elements......Page 109 4.4.2 Examples......Page 112 4.5 Isoparametric shell finite element for general 3D analysis......Page 114 4.5.1 Basic assumptions about shell deformation......Page 115 4.5.2 Formulation of a four-node shell element......Page 117 4.5.3 Examples......Page 118 5.1 Introduction to dynamics of structures......Page 122 5.2 Differential equations of motion......Page 123 5.3 Integration of differential equations of motion......Page 124 5.4 System frequencies and modal shapes......Page 126 5.5 Examples......Page 127 6.1 Introduction......Page 132 6.2.1 Discrete system......Page 136 6.2.2 Principle of virtual work for a continuum......Page 137 6.2.3 Finite element model......Page 138 6.2.4 Finite element model with logarithmic strains......Page 140 6.3 Examples......Page 141 7.1 Introduction......Page 144 7.1.2 The Galerkin method......Page 145 7.2.1 The finite element equations......Page 147 7.2.2 Examples......Page 148 7.3.1 The finite element equations......Page 150 7.3.2 Examples......Page 151 7.4.1 The finite element equations......Page 152 7.4.2 Examples......Page 156 7.5.1 The ALE formulation......Page 158 7.5.2 Examples......Page 161 7.6 Solid–fluid interaction......Page 162 7.6.1 Loose coupling method......Page 163 7.6.2 Examples......Page 164 7.7.1 Finite element balance equations......Page 166 7.7.2 Examples......Page 168 8.1.1 Introduction......Page 170 8.1.2 Differential equations of motion and boundary conditions......Page 171 8.1.3 Examples......Page 173 8.2.1 Introduction to mesoscale DPD modeling......Page 174 8.2.2 Basic DPD equations......Page 175 8.2.3 Examples......Page 177 8.3.1 Introduction to multiscale modeling......Page 178 8.3.2 Basic equations and boundary conditions......Page 179 8.3.3 Examples......Page 183 8.4.2 The basic equations of the SPH method......Page 184 8.5.1 Introduction......Page 187 8.5.2 Formulation of the EFG method......Page 188 8.5.3 Examples......Page 191 Part III Computational Methods in Bioengineering......Page 194 9.1 The subject and scope of bioengineering......Page 196 9.2.1 Computational models......Page 198 9.2.2 Future advances in computer modeling......Page 200 10.1.1 The structure of bone tissue......Page 204 10.1.2 The form of bones......Page 206 10.1.3 Osteoporosis and bone density......Page 207 10.2 The mechanical properties of bone and FE modeling......Page 208 10.3.1 General considerations......Page 210 10.3.2 Fracture treatment......Page 211 10.3.3 FE modeling of femur comminuted fracture......Page 213 10.4.1 Solutions by parallel screws and by dynamic hip implant......Page 217 10.4.2 Finite element models of intracapsular fractures of the femoral neck......Page 218 11.1.1 Structure and function of biological tissue......Page 224 11.1.2 Basic experiments and mechanical models......Page 226 11.2.1 General concept of computational procedures......Page 230 11.2.2 Biaxial models of membranes, hardening and hysteretic behavior, action of surfactant......Page 232 11.2.3 Use of strain energy functions......Page 238 11.3 Examples......Page 240 12.1.1 Basic physiology of muscle mechanics......Page 250 12.1.2 Basics of muscle finite element modeling......Page 254 12.2.1 Hill’s phenomenological model......Page 257 12.2.2 Determination of stresses within muscle fiber......Page 258 12.2.3 Hill’s model which includes fatigue......Page 262 12.2.4 An extension of Hill’s model to include different fiber types......Page 265 12.3 Examples......Page 268 13.1.1 The circulatory system......Page 272 13.1.2 Blood......Page 274 13.1.3 Blood vessels......Page 278 13.2.1 Introduction......Page 279 13.2.2 Methods of blood flow modeling in large blood vessels......Page 280 13.2.3 Modeling the deformation of blood vessels......Page 283 13.2.4 Blood–blood vessel interaction......Page 284 13.3.1 Introduction......Page 285 13.3.2 Finite element model of the aorta......Page 286 13.3.3 Results and discussion......Page 287 13.4.1 Introduction......Page 288 13.4.2 Modeling of blood flow within the AAA......Page 290 13.4.3 Results......Page 291 13.5.1 Introduction......Page 293 13.5.2 Finite element model of the carotid artery bifurcation......Page 294 13.5.3 Example solutions......Page 296 13.6.1 Femoral artery anatomical and physiological considerations and endovascular solutions......Page 299 13.6.2 Analysis of the combined effects of the surrounding muscle tissue and inner blood pressure to the arterial wall with implanted stent......Page 301 13.7.1 Introduction......Page 305 13.7.2 Modeling blood flow through the veins......Page 306 13.8.1 Description of heart functioning......Page 309 13.8.2 Computational model......Page 312 14.1 Introduction......Page 318 14.2.1 The basic relations for mass transport in arteries......Page 320 14.2.2 Finite element modeling of diffusion–transport equations......Page 321 14.2.3 Examples......Page 322 14.3.1 Model description......Page 325 14.3.2 Examples......Page 327 14.4.1 General considerations......Page 329 14.4.2 Examples......Page 331 15.1 Introduction......Page 336 15.2.1 Basic physical quantities, swelling pressure and electrokinetic coupling......Page 339 15.2.2 Equations of balance......Page 341 15.3.1 Finite element balance equations......Page 343 15.4 Examples......Page 345 16.1 Introduction to mechanics of cells......Page 354 16.2.1 Stabilizing influence of CSK prestress – cellular tensegrity model......Page 357 16.2.2 Mathematical model of a six-strut tensegrity structure......Page 359 16.2.3 Biphasic models......Page 362 16.3 Examples: modeling of cell in various mechanical conditions......Page 363 17 Extracellular Mechanotransduction: Modeling Ligand Concentration Dynamics in the Lateral Intercellular Space of Compressed Airway Epithelial Cells......Page 372 17.1.1 Introduction......Page 373 17.1.2 The EGF–receptor autocrine loop in the LIS......Page 374 17.1.3 Modeling the effects of compressive stress on epithelial cells in vitro......Page 375 17.2.1 Introduction......Page 379 17.2.2 Finite element model of dynamic diffusion......Page 380 17.2.3 Exploring the parameter space of the diffusion equation......Page 382 17.3.1 Introduction......Page 385 17.3.2 Finite element model of coupled diffusion and convection......Page 386 17.3.3 Exploring the parameter space of the governing equations......Page 389 17.3.4 Rate sensitivity of extracellular mechanotransduction......Page 391 17.3.5 HB-EGF vs. TGF-alpha concentration dynamics......Page 395 17.3.6 Discussion......Page 398 18 Spider Silk: Modeling Solvent Removal during Synthetic and Nephila clavipes Fiber Spinning......Page 402 18.1.1 Introduction......Page 403 18.1.2 Numerical procedure......Page 404 18.1.3 Example......Page 409 18.2.1 Introduction......Page 411 18.2.2 Governing process during synthetic solvent removal......Page 413 18.2.3 Numerical modeling of synthetic internal solvent diffusion......Page 415 18.2.4 Example: Synthetic fiber spinning......Page 417 18.3.1 Introduction......Page 420 18.3.2 Nephila water diffusion coefficient......Page 421 18.3.3 Modeling of internal water diffusion......Page 423 18.3.4 Example: The Nephila spinning canal......Page 425 19.1 Introduction......Page 430 19.2 The transport of particulates in capillaries......Page 432 19.3 The mathematical model......Page 437 19.3.1 The governing equations......Page 438 19.3.2 The initial and boundary conditions......Page 439 19.3.3 Solution for K0 and f0......Page 440 19.3.4 Solution for K1 and f1......Page 441 19.3.5 Solution for K2......Page 442 19.3.6 The velocity distribution (effect of boundary depletion of the solvent)......Page 443 19.4 The concentration profile......Page 445 19.4.1 The mean dimensionless concentration m......Page 446 19.4.2 The local dimensionless concentration ......Page 447 19.5 Comments and discussions of the analytical models and solutions......Page 450 19.6.1 Computational procedure......Page 451 19.6.2 Example – trajectories of spherical and elliptical particles......Page 452 Index......Page 456 Plates......Page 470 This is a reference for a large number of bioengineering topics, presenting computer modeling problems important in research and medical practice. The book is divided into three parts - 'Theoretical Background', 'Fundamentals of Computational Methods' and 'Computer Modeling in Bioengineering'