Numerical Methods in Biomedical Engineering

ISBN-10: 0121860310
ISBN-13: 9780121860318
Edition: 2005
List price: $124.00 Buy it from $26.55
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Description: "Numerical Modeling in Biomedical Engineering brings together the integrative set of computational problem solving tools important to biomedical engineers. Through the use of comprehensive homework exercises, relevant examples and extensive case  More...

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Book details

List price: $124.00
Copyright year: 2005
Publisher: Elsevier Science & Technology Books
Publication date: 11/8/2005
Binding: Hardcover
Pages: 632
Size: 7.50" wide x 9.25" long x 1.75" tall
Weight: 3.388
Language: English

"Numerical Modeling in Biomedical Engineering brings together the integrative set of computational problem solving tools important to biomedical engineers. Through the use of comprehensive homework exercises, relevant examples and extensive case studies, this book integrates principles and techniques of numerical analysis. Covering biomechanical phenomena and physiologic, cell and molecular systems, this is an essential tool for students and all those studying biomedical transport, biomedical thermodynamics & kinetics and biomechanics. 7 Supported by Whitaker Foundation Teaching Materials Program; ABET-oriented pedagogical layout 7 MATLAB problem sets and examples available electronically; UNIX, Windows, Mac OS compatible 7 Extensive hands-on homework exercises

Alkis Constantinides is a Professor of Chemical and Biochemical Engineering, with nearly forty years of academic and industrial experience. He is the author of the textbook Applied Numerical Methods with Personal Computers and the co-author of the textbook Numerical Methods for Chemical Engineers with MATLAB Applications. Dr. Constantinides has served as Chairman of the Department, Director of the Graduate Program, Director of the Undergraduate Program, and Director of Alumni Relations. He is the recipient of the prestigious Warren I. Susman Award for Excellence in Teaching (1991), and the recipient of the 1998, 1999, 2003, and 2005 Best Teacher of the Year Awards chosen by the Graduating Senior Class of the Department of Chemical and Biochemical Engineering

Preface
Fundamentals
Modeling Biosystems
Biomedical Engineering
Fundamental Aspects of Biomedical Engineering
Constructing Engineering Models
A framework for problem solving
Formulating the mathematical expression of conservation
Using balance equations
How conservation laws lead to the Nernst equation
Examples of Solving Biomedical Engineering Models by Computer
Modeling rtPCR efficiency
Modeling transcranial magnetic stimulation
Modeling cardiac electrophysiology
Using numerical methods to model the response of the cardiovascular system to gravity
Overview of the Text
Part I: Fundamentals
Part II: Steady-state behavior (algebraic models)
Part III: Dynamic biosystems (differential equations)
Part IV: Modeling tools and applications
Lessons Learned in this Chapter
Problems
References
Introduction to Computing
Introduction
The Role of Computers in Biomedical Engineering
Programming Language Tools and Techniques
Sequences of statements
Programs that are sequences of statements
Conditional execution
Simple control flow using if...then...else
Use of the switch statement
Iteration
The use of while loops
Using for...end loops
Encapsulation
Using scripts and functions
Fundamentals of Data Structures for MATLAB
Number representation
Number representation in MATLAB
Complex numbers
Arrays
Indexing arrays in MATLAB
Characters and strings
Character strings as arrays
Logical or Boolean data types
Logical indexing in MATLAB
Cells and cell arrays
Cell arrays and mixed data types
Structure arrays and mixed data types
Data structures not explicitly found in MATLAB
Data structures in MATLAB: implementing a stack
Data type conversion
Data type conversion
An Introduction to Object-Oriented Systems
Simple object-oriented programs that are sequences of statements
Analyzing Algorithms and Programs
Polynomial complexity
Operation counting
Measuring execution time as a function of the amount of data
Lessons Learned in this Chapter
Problems
Concepts of Numerical Analysis
Scientific Computing
Numerical Algorithms and Errors
Taylor Series
How truncation errors and roundoff errors arise
Keeping Errors Small
An ill-posed problem
Floating-Point Representation in MATLAB
The IEEE 754 standard for floating-point representation
IEEE 754 floating-point representation
Floating-point arithmetic, truncation, and rounding
Propagation of floating-point errors
Machine precision in MATLAB
Roundoff error accumulation and cancellation error
Avoiding overflow
Avoiding cancellation errors
Using Taylor series expansions to avoid cancellation errors
Lessons Learned in this Chapter
Problems
References
Steady-State Behavior
Linear Models of Biological Systems
Introduction
Examples of Linear Biological Systems
Force balance in biomechanics
Biomedical imaging and image processing
Metabolic engineering and cellular biotechnology
Simultaneous Linear Algebraic Equations
Illustration of simple Gauss elimination for a 3 x 3 matrix
Matrix notation of Gaussian elimination
Application of the Gauss elimination method
The Gauss-Jordan Reduction Method
Application of the Gauss-Jordan reduction method
Iterative Approach for Solution of Linear Systems
The Jacobi method
Application of the iterative Jacobi method
The Gauss-Seidel method
Application of the iterative Gauss-Seidel method
Lessons Learned in this Chapter
Problems
References
Nonlinear Equations in Biomedical Engineering
Introduction
General Form of Nonlinear Equations
Examples of Nonlinear Equations in Biomedical Engineering
Molecular bioengineering
Cellular and tissue engineering
Bioheat transport: photothermal therapy
Biomedical flow transport dynamics
The Method of Successive Substitution
The Method of False Position (Linear Interpolation)
The Newton-Raphson Method
Cardiovascular physiology
Solution of the Colebrook equation using Newton-Raphson
Successive substitution method for solution of nonlinear equation
Solution of the Colebrook equation using linear interpolation
Solution of a Michaelis-Menten kinetics equation using the Newton-Raphson method
Newton's Method for Simultaneous Nonlinear Equations
Determination of receptor occupancy during receptorligand dynamics
Lessons Learned in this Chapter
Problems
References
Dynamic Behavior
Finite Difference Methods, Interpolation and Integration
Introduction
Symbolic Operators
Backward Finite Differences
Express the first-order derivative in terms of backward finite differences with error of order h
Express the first-order derivative in terms of backward finite differences with error of order h[superscript 2]
Forward Finite Differences
Express the first-order derivative in terms of forward finite differences with error of order h
Express the second-order derivative in terms of forward finite differences with error of order h
Central Finite Differences
Express the first-order derivative in terms of central finite differences with error of order h[superscript 2]
Express the second-order derivative in terms of central finite differences with error of order h[superscript 2]
Interpolating Polynomials
Interpolation of Equally Spaced Points
Gregory-Newton interpolation
Gregory-Newton method for interpolation of equally spaced data
Interpolation of Unequally Spaced Points
Lagrange polynomials
Spline interpolation
Integration Formulas
The Newton-Cotes Formulas of Integration
The trapezoidal rule
Simpson's 1/3 rule
Simpson's 3/8 rule
Summary of Newton-Cotes integration
Integration formulas-Trapezoidal and Simpson's 1/3 rules
Lessons Learned in this Chapter
Problems
References
Dynamic Systems: Ordinary Differential Equations
Introduction
Pharmacokinetics: the dynamics of drug absorption
Tissue engineering: cell differentiation, cell adhesion and migration dynamics
Metabolic Engineering: Glycolysis pathways of living cells
Transport of molecules across biological membranes
Classification of Ordinary Differential Equations
Transformation to Canonical Form
Transformation of ordinary differential equations into their canonical form
Nonlinear Ordinary Differential Equations
The Euler and modified Euler methods
The Runge-Kutta methods
Simultaneous differential equations
MATLAB functions for nonlinear equations
Solution of enzyme catalysis reactions
Linear Ordinary Differential Equations
Method using eigenvalues and eigenvectors
MATLAB functions for linear equations
The dynamics of drug absorption
Steady-State Solutions and Stability Analysis
Numerical Stability and Error Propagation
Advanced Examples
Metabolic engineering: Modeling the glycolysis pathways of living cells
The dynamics of membrane and nerve cell potentials
The dynamics of stem cell differentiation
Tissue engineering: models of epidermal cell migration
Lessons Learned in this Chapter
Problems
References
Dynamic Systems: Partial Differential Equations
Introduction
Examples of PDEs in Biomedical Engineering
Diffusion across biological membranes
Diffusion of macromolecules and controlled release of drugs
Cell migration on vascular prosthetic materials
Fluid flow in physiological and extracorporeal vessels
Classification of Partial Differential Equations
Initial and Boundary Conditions
Solution of Partial Differential Equations
Elliptic partial differential equations
Solution of the Laplace and Poisson equations
Parabolic partial differential equations
Migration of human leukocytes on prosthetic materials
Hyperbolic partial differential equations
Polar Coordinate Systems
Stability Analysis
PDE Toolbox in MATLAB
Solution of Fick's second law of diffusion using the PDE toolbox
Lessons Learned in this Chapter
Problems
References
Modeling Tools and Applications
Measurements, Models and Statistics
The Role of Numerical Methods
Measurements, Errors and Uncertainty
Descriptive Statistics
Computing statistics of MRI and CT image intensities
Inferential Statistics
Estimating the mean value of a population from a sample
Hypothesis testing in DNA microarray analysis
Least Squares Modeling
Least square fit of a first-order polynomial (straight line)
Least squares fit of a cubic polynomial
Least squares fit of a nonlinear model
Least squares fit of a multivariate model
Curve Fitting
Lagrange interpolating polynomials
Newton divided difference interpolating polynomials
Splines
Resampling and baseline correction of MALDI-TOF mass spectra data
Fourier Transforms
Separating EEG frequency components
Lessons Learned in the Chapter
Problems
References
Modeling Biosystems: Applications
Numerical Modeling of Bioengineering Systems
PhysioNet, PhysioBank, and PhysioToolkit
ECG simulation
Using the MATLAB script ECGwaveGen to synthesize ECG data
Reading PhysioBank data
Read and visualize PhysioBank signals and annotations
Signal Processing: EEG Data
Differential brain activity in the left and right hemispheres
Diabetes and Insulin Regulation
Simulink model of glucose regulation
Renal Clearance
Renal clearance
Correspondence Problems and Motion Estimation
Estimating motion from features on a rigid body
Physbe Simulations
Normal PHYSBE operation
Coarctation of the aorta
Simulink model of coarctation of the aorta
Aortic stenosis
Simulink model of aortic valve stenosis
Ventricular septal defect
Ventricular septal defect
Left ventricular hypertrophy
Left ventricular hypertrophy
Pressure-volume loops
References
Appendices
Introduction to MATLAB
Introduction to Simulink
Review of Linear Algebra and Related MATLAB Commands
Analytical Solutions of Differential Equations
Numerical Stability and Other Topics
Index

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