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Preface | |

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Fundamentals | |

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Modeling Biosystems | |

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Biomedical Engineering | |

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Fundamental Aspects of Biomedical Engineering | |

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Constructing Engineering Models | |

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A framework for problem solving | |

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Formulating the mathematical expression of conservation | |

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Using balance equations | |

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How conservation laws lead to the Nernst equation | |

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Examples of Solving Biomedical Engineering Models by Computer | |

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Modeling rtPCR efficiency | |

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Modeling transcranial magnetic stimulation | |

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Modeling cardiac electrophysiology | |

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Using numerical methods to model the response of the cardiovascular system to gravity | |

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Overview of the Text | |

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Part I: Fundamentals | |

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Part II: Steady-state behavior (algebraic models) | |

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Part III: Dynamic biosystems (differential equations) | |

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Part IV: Modeling tools and applications | |

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Lessons Learned in this Chapter | |

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Problems | |

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References | |

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Introduction to Computing | |

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Introduction | |

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The Role of Computers in Biomedical Engineering | |

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Programming Language Tools and Techniques | |

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Sequences of statements | |

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Programs that are sequences of statements | |

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Conditional execution | |

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Simple control flow using if...then...else | |

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Use of the switch statement | |

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Iteration | |

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The use of while loops | |

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Using for...end loops | |

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Encapsulation | |

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Using scripts and functions | |

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Fundamentals of Data Structures for MATLAB | |

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Number representation | |

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Number representation in MATLAB | |

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Complex numbers | |

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Arrays | |

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Indexing arrays in MATLAB | |

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Characters and strings | |

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Character strings as arrays | |

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Logical or Boolean data types | |

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Logical indexing in MATLAB | |

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Cells and cell arrays | |

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Cell arrays and mixed data types | |

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Structure arrays and mixed data types | |

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Data structures not explicitly found in MATLAB | |

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Data structures in MATLAB: implementing a stack | |

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Data type conversion | |

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Data type conversion | |

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An Introduction to Object-Oriented Systems | |

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Simple object-oriented programs that are sequences of statements | |

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Analyzing Algorithms and Programs | |

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Polynomial complexity | |

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Operation counting | |

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Measuring execution time as a function of the amount of data | |

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Lessons Learned in this Chapter | |

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Problems | |

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Concepts of Numerical Analysis | |

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Scientific Computing | |

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Numerical Algorithms and Errors | |

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Taylor Series | |

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How truncation errors and roundoff errors arise | |

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Keeping Errors Small | |

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An ill-posed problem | |

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Floating-Point Representation in MATLAB | |

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The IEEE 754 standard for floating-point representation | |

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IEEE 754 floating-point representation | |

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Floating-point arithmetic, truncation, and rounding | |

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Propagation of floating-point errors | |

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Machine precision in MATLAB | |

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Roundoff error accumulation and cancellation error | |

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Avoiding overflow | |

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Avoiding cancellation errors | |

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Using Taylor series expansions to avoid cancellation errors | |

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Lessons Learned in this Chapter | |

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Problems | |

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References | |

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Steady-State Behavior | |

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Linear Models of Biological Systems | |

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Introduction | |

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Examples of Linear Biological Systems | |

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Force balance in biomechanics | |

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Biomedical imaging and image processing | |

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Metabolic engineering and cellular biotechnology | |

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Simultaneous Linear Algebraic Equations | |

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Illustration of simple Gauss elimination for a 3 x 3 matrix | |

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Matrix notation of Gaussian elimination | |

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Application of the Gauss elimination method | |

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The Gauss-Jordan Reduction Method | |

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Application of the Gauss-Jordan reduction method | |

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Iterative Approach for Solution of Linear Systems | |

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The Jacobi method | |

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Application of the iterative Jacobi method | |

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The Gauss-Seidel method | |

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Application of the iterative Gauss-Seidel method | |

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Lessons Learned in this Chapter | |

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Problems | |

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References | |

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Nonlinear Equations in Biomedical Engineering | |

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Introduction | |

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General Form of Nonlinear Equations | |

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Examples of Nonlinear Equations in Biomedical Engineering | |

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Molecular bioengineering | |

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Cellular and tissue engineering | |

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Bioheat transport: photothermal therapy | |

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Biomedical flow transport dynamics | |

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The Method of Successive Substitution | |

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The Method of False Position (Linear Interpolation) | |

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The Newton-Raphson Method | |

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Cardiovascular physiology | |

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Solution of the Colebrook equation using Newton-Raphson | |

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Successive substitution method for solution of nonlinear equation | |

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Solution of the Colebrook equation using linear interpolation | |

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Solution of a Michaelis-Menten kinetics equation using the Newton-Raphson method | |

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Newton's Method for Simultaneous Nonlinear Equations | |

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Determination of receptor occupancy during receptorligand dynamics | |

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Lessons Learned in this Chapter | |

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Problems | |

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References | |

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Dynamic Behavior | |

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Finite Difference Methods, Interpolation and Integration | |

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Introduction | |

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Symbolic Operators | |

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Backward Finite Differences | |

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Express the first-order derivative in terms of backward finite differences with error of order h | |

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Express the first-order derivative in terms of backward finite differences with error of order h[superscript 2] | |

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Forward Finite Differences | |

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Express the first-order derivative in terms of forward finite differences with error of order h | |

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Express the second-order derivative in terms of forward finite differences with error of order h | |

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Central Finite Differences | |

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Express the first-order derivative in terms of central finite differences with error of order h[superscript 2] | |

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Express the second-order derivative in terms of central finite differences with error of order h[superscript 2] | |

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Interpolating Polynomials | |

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Interpolation of Equally Spaced Points | |

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Gregory-Newton interpolation | |

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Gregory-Newton method for interpolation of equally spaced data | |

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Interpolation of Unequally Spaced Points | |

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Lagrange polynomials | |

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Spline interpolation | |

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Integration Formulas | |

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The Newton-Cotes Formulas of Integration | |

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The trapezoidal rule | |

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Simpson's 1/3 rule | |

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Simpson's 3/8 rule | |

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Summary of Newton-Cotes integration | |

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Integration formulas-Trapezoidal and Simpson's 1/3 rules | |

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Lessons Learned in this Chapter | |

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Problems | |

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References | |

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Dynamic Systems: Ordinary Differential Equations | |

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Introduction | |

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Pharmacokinetics: the dynamics of drug absorption | |

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Tissue engineering: cell differentiation, cell adhesion and migration dynamics | |

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Metabolic Engineering: Glycolysis pathways of living cells | |

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Transport of molecules across biological membranes | |

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Classification of Ordinary Differential Equations | |

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Transformation to Canonical Form | |

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Transformation of ordinary differential equations into their canonical form | |

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Nonlinear Ordinary Differential Equations | |

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The Euler and modified Euler methods | |

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The Runge-Kutta methods | |

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Simultaneous differential equations | |

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MATLAB functions for nonlinear equations | |

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Solution of enzyme catalysis reactions | |

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Linear Ordinary Differential Equations | |

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Method using eigenvalues and eigenvectors | |

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MATLAB functions for linear equations | |

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The dynamics of drug absorption | |

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Steady-State Solutions and Stability Analysis | |

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Numerical Stability and Error Propagation | |

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Advanced Examples | |

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Metabolic engineering: Modeling the glycolysis pathways of living cells | |

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The dynamics of membrane and nerve cell potentials | |

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The dynamics of stem cell differentiation | |

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Tissue engineering: models of epidermal cell migration | |

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Lessons Learned in this Chapter | |

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Problems | |

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References | |

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Dynamic Systems: Partial Differential Equations | |

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Introduction | |

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Examples of PDEs in Biomedical Engineering | |

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Diffusion across biological membranes | |

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Diffusion of macromolecules and controlled release of drugs | |

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Cell migration on vascular prosthetic materials | |

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Fluid flow in physiological and extracorporeal vessels | |

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Classification of Partial Differential Equations | |

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Initial and Boundary Conditions | |

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Solution of Partial Differential Equations | |

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Elliptic partial differential equations | |

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Solution of the Laplace and Poisson equations | |

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Parabolic partial differential equations | |

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Migration of human leukocytes on prosthetic materials | |

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Hyperbolic partial differential equations | |

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Polar Coordinate Systems | |

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Stability Analysis | |

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PDE Toolbox in MATLAB | |

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Solution of Fick's second law of diffusion using the PDE toolbox | |

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Lessons Learned in this Chapter | |

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Problems | |

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References | |

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Modeling Tools and Applications | |

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Measurements, Models and Statistics | |

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The Role of Numerical Methods | |

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Measurements, Errors and Uncertainty | |

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Descriptive Statistics | |

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Computing statistics of MRI and CT image intensities | |

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Inferential Statistics | |

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Estimating the mean value of a population from a sample | |

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Hypothesis testing in DNA microarray analysis | |

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Least Squares Modeling | |

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Least square fit of a first-order polynomial (straight line) | |

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Least squares fit of a cubic polynomial | |

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Least squares fit of a nonlinear model | |

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Least squares fit of a multivariate model | |

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Curve Fitting | |

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Lagrange interpolating polynomials | |

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Newton divided difference interpolating polynomials | |

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Splines | |

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Resampling and baseline correction of MALDI-TOF mass spectra data | |

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Fourier Transforms | |

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Separating EEG frequency components | |

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Lessons Learned in the Chapter | |

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Problems | |

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References | |

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Modeling Biosystems: Applications | |

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Numerical Modeling of Bioengineering Systems | |

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PhysioNet, PhysioBank, and PhysioToolkit | |

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ECG simulation | |

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Using the MATLAB script ECGwaveGen to synthesize ECG data | |

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Reading PhysioBank data | |

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Read and visualize PhysioBank signals and annotations | |

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Signal Processing: EEG Data | |

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Differential brain activity in the left and right hemispheres | |

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Diabetes and Insulin Regulation | |

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Simulink model of glucose regulation | |

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Renal Clearance | |

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Renal clearance | |

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Correspondence Problems and Motion Estimation | |

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Estimating motion from features on a rigid body | |

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Physbe Simulations | |

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Normal PHYSBE operation | |

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Coarctation of the aorta | |

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Simulink model of coarctation of the aorta | |

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Aortic stenosis | |

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Simulink model of aortic valve stenosis | |

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Ventricular septal defect | |

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Ventricular septal defect | |

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Left ventricular hypertrophy | |

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Left ventricular hypertrophy | |

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Pressure-volume loops | |

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References | |

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Appendices | |

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Introduction to MATLAB | |

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Introduction to Simulink | |

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Review of Linear Algebra and Related MATLAB Commands | |

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Analytical Solutions of Differential Equations | |

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Numerical Stability and Other Topics | |

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Index | |