Modelling organs, tissues, cells and devices : using MATLAB and COMSOL multiphysics

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-s...

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Bibliographic Details
Main Author Dokos, Socrates (Author)
Format Electronic eBook
LanguageEnglish
Published Berlin, Germany : Springer, 2017.
SeriesLecture notes in bioengineering.
Subjects
Computational biology.
Bioinformatics.
elektronické knihy
electronic books
Online AccessFull text
ISBN9783642548017
9783642548000
Physical Description1 online resource (xiii, 502 pages) : illustrations

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Table of Contents:
  • Preface; Contents; Acronyms; Part I Bioengineering Modelling Principles, Methods and Theory; 1 Introduction to Modelling in Bioengineering; 1.1 Modelling and Simulation in Medicine and Biology; 1.2 The Modelling Process; 1.3 Mathematical Model Types; 1.3.1 Linear Versus Non-linear; 1.3.2 Dynamic Versus Static; 1.3.3 Deterministic Versus Stochastic; 1.3.4 Continuous Versus Discrete; 1.3.5 Rule-Based; 1.4 Dimensional Analysis; 1.4.1 Dimensions and Units; 1.4.2 Buckingham -Theorem; 1.5 Model Scaling; References; 2 Lumped Parameter Modelling with Ordinary Differential Equations.
  • 3.4 ODE Solver Implementations in Matlab and COMSOL3.5 Further Reading; References; 4 Distributed Systems Modelling with Partial Differential Equations; 4.1 Modelling with PDEs; 4.1.1 The Gradient; 4.1.2 The Divergence; 4.1.3 The Curl; 4.1.4 The Divergence Theorem; 4.1.5 Conservation Law Formulation; 4.1.6 The Laplacian; 4.1.7 PDE Boundary Conditions; 4.2 Basic Analytical and Numerical Solution Techniques; 4.2.1 Separation of Variables; 4.2.2 Finite Difference Method; 4.2.3 Method of Lines; 4.3 Further Reading; References; 5 The Finite Element Method; 5.1 Finite Elements for 1D Systems.
  • 5.1.1 Weak Form PDE Equivalent5.1.2 Basis Function Approximation; 5.1.3 Higher-Order Basis Functions; 5.2 Finite Elements for 2D/3D Systems; 5.2.1 Weak Form Description; 5.2.2 Basis Function Approximation; 5.3 FEM Numerical Implementation; 5.3.1 Assembly of System Matrices; 5.3.2 Gaussian Quadrature; 5.3.3 Non-Linear Systems; 5.4 Further Reading; References; Part II Bioengineering Applications; 6 Modelling Electrical Stimulation of Tissue; 6.1 Electrical Stimulation; 6.1.1 Maxwell's Equations; 6.1.2 Electrostatic Formulations; 6.1.3 Volume Conductor Theory.
  • 6.1.4 Example: Cell Culture Electric Field Stimulator6.1.5 Example: Access Resistance of Electrode Disc; 6.2 Modelling Electrical Activity of Tissues; 6.2.1 Continuum Models of Excitable Tissues; 6.2.2 Example: Modelling Spiral-Wave Reentry in Cardiac Tissue; 6.2.3 Modelling PDEs/ODEs on Boundaries, Edges and Points; 6.2.4 Example: Axonal Stimulation Using Nerve Cuff Electrodes; 6.3 Further Reading; References; 7 Models of Diffusion and Heat Transfer; 7.1 Diffusion; 7.1.1 Fick's Laws of Diffusion; 7.1.2 Example: Diffusion and Uptake into a Spherical Cell; 7.1.3 Convective Transport.

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