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2017 | Buch

Introduction to Modelling in Bioengineering Kapitel lesen Erstes Kapitel lesen

Modelling Organs, Tissues, Cells and Devices

Using MATLAB and COMSOL Multiphysics

verfasst von: Socrates Dokos

Verlag: Springer Berlin Heidelberg

Buchreihe : Lecture Notes in Bioengineering

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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SUCHEN

Über dieses Buch

This book presents a theoretical and practical overview of computational modeling in bioengineering, focusing on a range of applications including electrical stimulation of neural and cardiac tissue, implantable drug delivery, cancer therapy, biomechanics, cardiovascular dynamics, as well as fluid-structure interaction for modelling of organs, tissues, cells and devices. It covers the basic principles of modeling and simulation with ordinary and partial differential equations using MATLAB and COMSOL Multiphysics numerical software. The target audience primarily comprises postgraduate students and researchers, but the book may also be beneficial for practitioners in the medical device industry.

Inhaltsverzeichnis

Frontmatter

Bioengineering Modelling Principles, Methods and Theory

Frontmatter
Chapter 1. Introduction to Modelling in Bioengineering
Abstract
This chapter outlines the basic principles of computational modelling with particular application to physiology and medicine. An overview of the modelling process is provided, along with a description of basic model types, including linear versus non-linear, dynamic versus static, deterministic versus stochastic, continuous versus discrete, and rule-based. Finally, an overview of dimensional analysis and model scaling is also provided. Full Matlab code listings are provided for several example models, including stochastic ion channel kinetics, non-linear passive muscle mechanics, neuronal dendritic branching, and glucose-insulin kinetics. The chapter ends with ten problems covering the fundamentals of modelling, with particular relevance to physiological systems, biology and medicine, with solutions provided at the end of the text.
Socrates Dokos
Chapter 2. Lumped Parameter Modelling with Ordinary Differential Equations
Abstract
This chapter presents an overview of ordinary differential equations and their use in lumped parameter modelling of physical systems and physiological processes. Methods are described on how to solve some ODEs analytically, followed by a brief overview of numerical solution approaches using Matlab. Detailed examples are presented from models in cardiovascular dynamics and neural activation, followed by sample problems with fully-worked solutions given at the end of the text.
Socrates Dokos
Chapter 3. Numerical Integration of Ordinary Differential Equations
Abstract
This chapter presents an overview of numerical integration techniques for solving ODE systems, as implemented in Matlab and COMSOL. These techniques are broadly classified into one-step and multistep methods. One-step methods include forward and backward Euler, Runge–Kutta as well as generalized-\(\alpha \) methods, whilst multistep algorithms include the predictor-corrector schemes as well as the backward differentiation and numerical differentiation formula (BDF/NDF) methods. The chapter ends with problems with fully-worked answers in the Solutions section of the text.
Socrates Dokos
Chapter 4. Distributed Systems Modelling with Partial Differential Equations
Abstract
This chapter presents an overview of partial differential equations (PDEs) for modelling distributed systems. Differential operators such as the gradient, divergence, curl and Laplacian are introduced, as well as the divergence theorem for modelling conserved physical quantities. An overview of basic analytical and numerical solution techniques for PDEs is then provided, including separation of variables, the finite difference method and the method of lines. Examples of PDEs solved analytically are 1D diffusion as well as the electrical potential distribution around a disc electrode in a 3D semi-infinite volume conductor. Explicit and implicit finite difference methods are used to solve for 1D diffusion and the method of lines is used for solving neural propagation along an axonal fibre. All numerical examples provide complete Matlab code listings. The chapter ends with ten problems with fully-worked solutions provided in the solutions section of the text.
Socrates Dokos
Chapter 5. The Finite Element Method
Abstract
This chapter provides an overview of the finite element method (FEM) for the numerical solution of PDEs. It begins with FEM implementation for 1D systems, deriving the weak-form equivalent form of a time-dependent diffusion-type PDE example, then outlines the Galerkin method for its solution. System matrices are derived for 1D linear basis functions, comparing these with those obtained by the COMSOL FEM solver. The chapter then proceeds to describe higher-order 1D Lagrangian basis functions as well as cubic Hermite elements. Following these 1D methods, FEM is then described for 2D/3D PDEs, including higher-dimensional elements, as well as isoparametric elements for representing curved boundaries. The chapter concludes with FEM numerical implementation issues, as well as set of problems with fully-worked answers provided in the solution section.
Socrates Dokos

Bioengineering Applications

Frontmatter
Chapter 6. Modelling Electrical Stimulation of Tissue
Abstract
This chapter describes the theory and techniques for modelling the electrical activity of excitable cells and tissues, along with their electrical simulation, using COMSOL. It begins with a summary of Maxwell’s equations, before moving on to electrostatics and volume conductor theory. Examples in COMSOL are presented for designing an optimal electric field stimulator for cell cultures in a Petri dish, as well as determining the current density and access resistance of an isopotential disc electrode in an infinite medium. The chapter then proceeds to cover continuum models of excitable tissues such as nerve and muscle and their electrical stimulation, expressed as classical bidomain and monodomain formulations. Examples in COMSOL are presented for modelling reentrant spiral waves in a slab of cardiac tissue and a propagating action potential in a nerve axon embedded in a nerve bundle stimulated by extracellular cuff electrodes.
Socrates Dokos
Chapter 7. Models of Diffusion and Heat Transfer
Abstract
This chapter describes the theory and techniques for modelling the transport processes of diffusion and heat in COMSOL. It begins with a summary of Fick’s Laws of diffusion and the physics of convective transport, before moving on to heat transfer and the bioheat equation, including Joule and dielectric heating by applied electric fields as well as the Arrhenius measure of tissue damage. Detailed examples in COMSOL are presented for uptake and diffusion in a spherical cell, drug delivery in a coronary stent, as well as RF atrial ablation. The chapter concludes with a set of problems and simulation exercises, with fully-worked answers provided in the solution section of the text.
Socrates Dokos
Chapter 8. Solid Mechanics
Abstract
This chapter provides an overview of solid mechanics with applications in biomechanics. It begins wih a coverage of tensors, including the tensor transformation law and tensor invariants, before proceeding to the basic mechanical concepts of stress and strain. Stress and strain are then related via material constitutive laws, the most basic being that of linear elasticity. The concepts of hydrostatic stresses and strains are also introduced, along with the notion of von Mises stress as a representative scalar stress indicator. Other material laws relevant to biological tissues are presented, including linear viscoelasticity and hyperelasticity, as well as anisotropic hyperelastic material laws. Detailed examples of models solved in COMSOL include a strap tension testing device for a respirator mask, as well simulations of simple shear experiments in myocardial tissue. The chapter ends with a set of theoretical and computational COMSOL problems, with fully-worked answers provided in the solution section of the text.
Socrates Dokos
Chapter 9. Fluid Mechanics
Abstract
This chapter provides an overview of fluid mechanics, emphasizing applications in models of blood flow. It begins with the physics of fluid motion, including the concepts of viscosity and idealized Newtonian fluids, before proceeding to the Navier Stokes equations for incompressible fluids. The concepts of laminar and non-laminar flow are also introduced, including Reynolds number and turbulent flow. Finally, the chapter describes techniques for modelling blood flow, including the use of Windkessel models (hydraulic circuit equivalents) that can be incorporated as boundary conditions in finite element models of blood flow, as well as non-Newtonian aspects of blood flow, which may be of relevance at low blood shear rates or small vessel diameters. Detailed examples of models solved in COMSOL include laminar flow in a circular tube, a multiphysics model of drug delivery in a coronary stent, aortic blood flow, as well as model of axial streaming of a blood cell using COMSOL’s moving mesh interface. The chapter ends with a small set of theoretical and computational COMSOL problems, with fully-worked answers provided in the solution section of the text.
Socrates Dokos
Backmatter
Metadaten
Titel
Modelling Organs, Tissues, Cells and Devices
verfasst von
Socrates Dokos
Copyright-Jahr
2017
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-54801-7
Print ISBN
978-3-642-54800-0
DOI
https://doi.org/10.1007/978-3-642-54801-7

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