Front cover -- Title page -- Copyright page -- Table of contents -- Preface -- Organization and Outline of the Book -- Part I: Fundamentals -- Chapter 1 Modeling Biosystems -- 1.1 Biomedical Engineering -- 1.2 Fundamental Aspects of Biomedical Engineering -- 1.3 Constructing Engineering Models -- 1.3.1 A framework for problem solving -- 1.3.2 Formulating the mathematical expression of conservation -- 1.3.3 Using balance equations -- 1.4 Examples of Solving Biomedical Engineering Models by Computer -- 1.4.1 Modeling rtPCR efficiency -- 1.4.2 Modeling transcranial magnetic stimulation -- 1.4.3 Modeling cardiac electrophysiology -- 1.4.4 Using numerical methods to model the response of the cardiovascular system to gravity -- 1.5 Overview of the Text -- 1.5.1 Part I: Fundamentals -- 1.5.2 Part II: Steady-state behavior (algebraic models) -- 1.5.3 Part III: Dynamic behavior (differential equations) -- 1.5.4 Part IV: Modeling tools and applications -- 1.6 Lessons Learned in this Chapter -- 1.7 Problems -- 1.8 References -- Chapter 2 Introduction to Computing -- 2.1 Introduction -- 2.2 The Role of Computers in Biomedical Engineering -- 2.3 Programming Language Tools and Techniques -- 2.3.1 Sequences of statements -- 2.3.2 Conditional execution -- 2.3.3 Iteration -- 2.3.4 Encapsulation -- 2.4 Fundamentals of Data Structures for MATLAB -- 2.4.1 Number representation -- 2.4.2 Arrays -- 2.4.3 Characters and strings -- 2.4.4 Logical or Boolean data types -- 2.4.5 Cells and cell arrays -- 2.4.6 Data structures not explicitly found in MATLAB -- 2.4.7 Data type conversion -- 2.5 An Introduction to Object-Oriented Systems -- 2.6 Analyzing Algorithms and Programs -- 2.6.1 Polynomial complexity -- 2.6.2 Operation counting -- 2.7 Lessons Learned in this Chapter -- 2.8 Problems -- Chapter 3 Concepts of Numerical Analysis -- 3.1 Scientific Computing.

3.2 Numerical Algorithms and Errors -- 3.3 Taylor Series -- 3.4 Keeping Errors Small -- 3.5 Floating-Point Representation in MATLAB -- 3.5.1 The IEEE 754 standard for floating-point representation -- 3.5.2 Floating-point arithmetic, truncation, and rounding -- 3.5.3 Roundoff error accumulation and cancellation error -- 3.6 Lessons Learned in this Chapter -- 3.7 Problems -- 3.8 References -- Part II: Steady-State Behavior -- Chapter 4 Linear Models of Biological Systems -- 4.1 Introduction -- 4.2 Examples of Linear Biological Systems -- 4.2.1 Force balance in biomechanics -- 4.2.2 Biomedical imaging and image processing -- 4.2.3 Metabolic engineering and cellular biotechnology -- 4.3 Simultaneous Linear Algebraic Equations -- 4.3.1 Illustration of simple Gauss elimination for a 3×3 matrix -- 4.3.2 Matrix notation of Gaussian elimination -- 4.4 The Gauss-Jordan Reduction Method -- 4.5 Iterative Approach for Solution of Linear Systems -- 4.5.1 The Jacobi method -- 4.5.2 The Gauss-Seidel method -- 4.6 Lessons Learned in this Chapter -- 4.7 Problems -- 4.8 References -- Chapter 5 Nonlinear Equations in Biomedical Engineering -- 5.1 Introduction -- 5.2 General Form of Nonlinear Equations -- 5.3 Examples of Nonlinear Equations in Biomedical Engineering -- 5.3.1 Molecular bioengineering -- 5.3.2 Cellular and tissue engineering -- 5.3.3 Bioheat transport: photothermal therapy -- 5.3.4 Biomedical flow transport dynamics -- 5.4 The Method of Successive Substitution -- 5.5 The Method of False Position (Linear Interpolation) -- 5.6 The Newton-Raphson Method -- 5.7 Newton's Method for Simultaneous Nonlinear Equations -- 5.8 Lessons Learned in this Chapter -- 5.9 Problems -- 5.10 References -- Part III: Dynamic Behavior -- Chapter 6 Finite Difference Methods, Interpolation and Integration -- 6.1 Introduction -- 6.2 Symbolic Operators.

6.3 Backward Finite Differences -- 6.4 Forward Finite Differences -- 6.5 Central Finite Differences -- 6.6 Interpolating Polynomials -- 6.7 Interpolation of Equally Spaced Points -- 6.7.1 Gregory-Newton interpolation -- 6.8 Interpolation of Unequally Spaced Points -- 6.8.1 Lagrange polynomials -- 6.8.2 Spline interpolation -- 6.9 Integration Formulas -- 6.10 The Newton-Cotes Formulas of Integration -- 6.10.1 The trapezoidal rule -- 6.10.2 Simpson's 1/3 rule -- 6.10.3 Simpson's 3/8 rule -- 6.10.4 Summary of Newton-Cotes integration -- 6.11 Lessons Learned in this Chapter -- 6.12 Problems -- 6.13 References -- Chapter 7 Dynamic Systems: Ordinary Differential Equations -- 7.1 Introduction -- 7.1.1 Pharmacokinetics: the dynamics of drug absorption -- 7.1.2 Tissue engineering: cell differentiation, cell adhesion and migration dynamics -- 7.1.3 Metabolic Engineering: Glycolysis pathways of living cells -- 7.1.4 Transport of molecules across biological membranes -- 7.2 Classification of Ordinary Differential Equations -- 7.3 Transformation to Canonical Form -- 7.4 Nonlinear Ordinary Differential Equations -- 7.4.1 The Euler and modified Euler methods -- 7.4.2 The Runge-Kutta methods -- 7.4.3 Simultaneous differential equations -- 7.4.4 MATLAB functions for nonlinear equations -- 7.5 Linear Ordinary Differential Equations -- 7.5.1 Method using eigenvalues and eigenvectors -- 7.5.2 MATLAB functions for linear equations -- 7.6 Steady-State Solutions and Stability Analysis -- 7.7 Numerical Stability and Error Propagation -- 7.8 Advanced Examples -- 7.9 Lessons Learned in this Chapter -- 7.10 Problems -- 7.11 References -- Chapter 8 Dynamic Systems: Partial Differential Equations -- 8.1 Introduction -- 8.2 Examples of PDEs in Biomedical Engineering -- 8.2.1 Diffusion across biological membranes -- 8.2.2 Diffusion of macromolecules and controlled release of drugs.

8.2.3 Cell migration on vascular prosthetic materials -- 8.2.4 Fluid flow in physiological and extracorporeal vessels -- 8.3 Classification of Partial Differential Equations -- 8.4 Initial and Boundary Conditions -- 8.5 Solution of Partial Differential Equations -- 8.5.1 Elliptic partial differential equations -- 8.5.2 Parabolic partial differential equations -- 8.5.3 Hyperbolic partial differential equations -- 8.6 Polar Coordinate Systems -- 8.7 Stability Analysis -- 8.8 PDE Toolbox in MATLAB -- 8.9 Lessons Learned in this Chapter -- 8.10 Problems -- 8.11 References -- Part IV: Modeling Tools and Applications -- Chapter 9 Measurements, Models and Statistics -- 9.1 The Role of Numerical Methods -- 9.2 Measurements, Errors and Uncertainty -- 9.3 Descriptive Statistics -- 9.4 Inferential Statistics -- 9.5 Least Squares Modeling -- 9.6 Curve Fitting -- 9.6.1 Lagrange interpolating polynomials -- 9.6.2 Newton divided difference interpolating polynomials -- 9.6.3 Splines -- 9.7 Fourier Transforms -- 9.8 Lessons Learned in the Chapter -- 9.9 Problems -- 9.10 References -- Chapter 10 Modeling Biosystems -- 10.1 Numerical Modeling of Bioengineering Systems -- 10.2 PhysioNet, PhysioBank, and PhysioToolkit -- 10.2.1 ECG simulation -- 10.2.2 Reading PhysioBank data -- 10.3 Signal Processing: EEG Data -- 10.4 Diabetes and Insulin Regulation -- 10.5 Renal Clearance -- 10.6 Correspondence Problems and Motion Estimation -- 10.7 PHYSBE Simulations -- 10.7.1 Coarctation of the aorta -- 10.7.2 Aortic stenosis -- 10.7.3 Ventricular septal defect -- 10.7.4 Left ventricular hypertrophy -- 10.8 References -- Appendices -- Appendix A: Introduction to MATLAB -- A.1 The MATLAB Environment -- A.1.1 Customizing the MATLAB environment -- A.1.2 The MATLAB path -- A.1.3 Where to find help for MATLAB -- A.2 Elementary Operations -- A.3 Vectors and Matrices.

A.3.1 MATLAB construction functions for special arrays -- A.3.2 Array arithmetic -- A.4 MATLAB Built-in Functions -- A.5 Graphics -- 2-D graphs -- 3-D graphs -- 2½-D Graphs -- Interactive Plot Creation -- A.6 Scripts and Functions -- A.7 Flow Control -- A.8 Display, Export, and Import of Data -- A.8.1 Displaying data and results -- A.8.2 Saving and loading data -- A.8.3 Generating data in a program and saving into a file -- A.9 Symbolic Computation -- A.9.1 Symbolic solution of algebraic equations -- A.9.2 Symbolic solution of differential equations -- A.9.3 Symbolic differentiation -- A.9.4 Symbolic integration -- A.10 MATLAB Toolboxes -- A.11 References -- Appendix B: Introduction to Simulink -- B.1 Dynamic System Simulation -- B.2 Getting Started -- B.2.1 A Simulink model of a sine wave generator -- B.2.2 Modifying Simulink models -- B.3 The Simulink Block Libraries -- B.4 Constructing Models -- B.4.1 Algebraic operations, signal routing and MATLAB variables -- B.4.2 Simultaneous differential equations -- B.4.3 PHYSBE and subsystems -- B.5 References -- Appendix C: Review of Linear Algebra and Related MATLAB Commands -- C.1 Matrix and Vector Operations -- C.2 Matrix Factorization -- Appendix D: Analytical Solutions of Differential Equations -- D.1 Ordinary Differential Equations of First Order -- D.1.1 Equations with separable variables -- D.1.2 Equations with homogeneous coefficients -- D.1.3 Exact equations -- D.1.4 Linear equations and the integrating factor -- D.1.5 Nonlinear equations and the integrating factor -- D.2 Ordinary Differential Equations of Higher Order -- D.2.1 Linear homogeneous equations with constant coefficients -- D.2.2 Linear nonhomogeneous equations (constant coefficients) -- D.3 Partial Differential Equations with Separable Variables -- D.3.1 The diffusion equation -- D.3.2 The potential equation.

D.3.3 Periodic functions and the Fourier series.