Contents:

Part I Theoretical Background of Computational Methods 1 Notation – Matrices and Tensors 1.1 Matrix representation of mathematical objects 1.2 Basic relations in matrix algebra 1.3 Definition of tensors and some basic tensorial relations 1.4 Vector and tensor differential operations and integral theorems 1.5 Examples 2 Fundamentals of Continuum Mechanics 2.1 Definitions of stress and strain 2.2 Linear elastic and viscoelastic constitutive relations 2.3 Principle of virtual work 2.4 Nonlinear continuum mechanics 3 Heat Transfer, Diffusion, Fluid Mechanics, and Fluid Flow through Porous Deformable Media 3.1 Heat conduction 3.2 Diffusion 3.3 Fluid flow of incompressible viscous fluid with heat and mass transfer 3.4 Fluid flow through porous deformable media Part II Fundamentals of Computational Methods 4 Isoparametric Formulation of Finite Elements 4.1 Introduction to the finite element method 4.2 Formulation of 1D finite elements and equilibrium equations 4.3 Three-dimensional (3D) isoparametric finite element 4.4 Two-dimensional (2D) isoparametric finite elements 4.5 Isoparametric shell finite element for general 3D analysis 5 Dynamic Finite Element Analysis 5.1 Introduction to dynamics of structures 5.2 Differential equations of motion 5.3 Integration of differential equations of motion 5.4 System frequencies and modal shapes 5.5 Examples 6 Introduction to Nonlinear Finite Element Analysis 6.1 Introduction 6.2 Principle of virtual work and equilibrium equations in nonlinear incremental analysis 6.3 Examples 7 Finite Element Modeling of Field Problems 7.1 Introduction 7.2 Heat conduction 7.3 Diffusion 7.4 Fluid flow with heat and mass transfer 7.5 FE equations for modeling large change of fluid domain – arbitrary Lagrangian–Eulerian (ALE) formulation 7.6 Solid–fluid interaction 7.7 Fluid flow through porous deformable media 8 Discrete Particle Methods for Modeling of Solids and Fluids 8.1 Molecular dynamics 8.2 Dissipative particle dynamics (DPD) method 8.3 Multiscale modeling, coupling DPD-FE for fluid flow 8.4 Smoothed particle hydrodynamics (SPH) 8.5 Element-free Galerkin (EFG) method Part III Computational Methods in Bioengineering 9 Introduction to Bioengineering 9.1 The subject and scope of bioengineering 9.2 The role of computer modeling in bioengineering 10 Bone Modeling 10.1 The structure and forms of bones 10.2 The mechanical properties of bone and FE modeling 10.3 Bone fracture – medical treatment and computer modeling 10.4 Internal fixation of hip fracture – two solutions and computer models 11 Biological Soft Tissue 11.1 Introduction to mechanics of biological tissue 11.2 Modeling methods for isotropic tissue 11.3 Examples 12 Skeletal Muscles 12.1 Introduction 12.2 Muscle modeling 12.3 Examples 13 Blood Flow and Blood Vessels 13.1 Introduction to the cardiovascular system 13.2 Methods of modeling blood flow and blood vessels 13.3 Human aorta 13.4 Abdominal aortic aneurysm (AAA) 13.5 Blood flow through the carotid artery bifurcation 13.6 Femoral artery with stent 13.7 Blood flow in venous system 13.8 Heart model 14 Modeling Mass Transport and Thrombosis in Arteries 14.1 Introduction 14.2 Modeling thrombosis by continuum-based methods 14.3 Modeling of thrombosis by DPD 15 Cartilage Mechanics 15.1 Introduction 15.2 Differential equations of balance in cartilage mechanics 15.3 Finite element modeling of cartilage deformation 15.4 Examples 16 Cell Mechanics 16.1 Introduction to mechanics of cells 16.2 Cell mechanical models 16.3 Examples: modeling of cell in various mechanical conditions 17 Extracellular Mechanotransduction: Modeling Ligand Concentration Dynamics in the Lateral Intercellular Space of Compressed Airway Epithelial Cells 17.1 Autocrine signaling in airway epithelial cells 17.1.1 Introduction 17.2 The dynamic diffusion model 17.3 The dynamic diffusion and convection model 18 Spider Silk: Modeling Solvent Removal during Synthetic and Nephila clavipes Fiber Spinning 18.1 Determination of the solvent diffusion coefficient in a concentrated polymer solution 18.2 Modeling solvent removal during synthetic fiber spinning 18.3 Modeling solvent removal during Nephila clavipes fiber spinning 19 Modeling in Cancer Nanotechnology 19.1 Introduction 19.2 The transport of particulates in capillaries 19.3 The mathematical model 19.4 The concentration profile 19.5 Comments and discussions of the analytical models and solutions 19.6 Numerical modeling of particle motion within capillary Index

Summary:

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 Modelling in Bioengineering offers a comprehensive reference for a large number of bioengineering topics, presenting important computer modelling 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 modelling methods, and each application is structured to explain the physiological background, phenomena that are to be modelled, 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 modelled problem; these features promote easier learning and will help lecturers with presentations. Computer Modelling 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.

Author

Milos Kojic, Senior Research Scientist, Harvard School of Public Health, Harvard University, Boston, MA 02215 Milos Kojic is professor of mechanical engineering, University of Kragujevac, Serbia; and Senior Research Scientist, Harvard School of Public Health, Harvard University, Boston. He is one of the leading scientists in computational mechanics. He has published, as the author or mainly the first author, around 60 journal papers, among which are papers in leading international journals, as Int. J. Num. Meth. Engng, Comp. Meth. Appl. Mech. Engng., Comp. Mech., Int. J. Vehicle Design, Appl. Mech., Computers and Struct, Biophysical J., Phys. Rev., etc. His research spans from the finite element method in general, methods of inelastic analysis of solids and structures, field and coupled problems, to biomechanics, and recently molecular dynamics and discrete particle methods. Nenad Filipovic, Faculty of Mechanical Engineering, S. Janjic 6, 34000 Kragujevac, Serbia and Montenegro Nenad Filipovic is associate professor of mechanical engineering, University of Kragujevac, Serbia; and research associate at Harvard School of Public Health, Harvard University, Boston. He is young scientist and author and co-author of a number of papers in international journals Boban Stojanovic, University of Kragujevac, J. Cvijica bb, 34000 Kragujevac, Serbia and MontenegroBoban Stojanovic is a Ph.D. candidate in Bioengineering at Multidisciplinary Graduate Studies of University of Kragujevac. He received his B.S. at Faculty of Mechanical Engineering of University of Kragujevac, as first in his generation and most talented students. During his studies he participated significantly in development of the finite element program PAK. Akira Tsuda, 665 Huntington Ave., Building 1, Room 1311, Boston, MA 02115 Akira Tsuda is Principal Research Scientist, in the Physiology Program, Harvard School of Public Health. He is an expert in biofluid mechanics, specifically in the field of respiratory flow and aerosol physiology. He has published extensively in this field and in the related field. He has been the principal investigator of several research projects, including international bioengineering projects Nikola Kojic, 71 Fulkerson St. # 207, Cambridge, MA 02141, USA Nikola Kojic is a Ph.D. candidate in the Harvard-MIT Division of Health Sciences and Technology. He received his M.S. in Mechanical Engineering in 2003 from MIT, working on synthetic and natural spider silk. Specifically, his focus was on the application of computational models to synthetic and natural spider silk fiber spinning.