BME210Notebook

BME210Notebook - Biomedical Computer Simulation Methods...

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Biomedical Computer Simulation Methods Student Notebook for BME 210 Spring Semester 2010 by David Z. D’Argenio, Ph.D. Professor of Biomedical Engineering Department of Biomedical Engineering University of Southern California
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BME 210 Table of Contents i Table of Contents Measuring Cardiac Output I Introduction II. Cardiovascular System A. Function B. Structures C. Distribution of Cardiac Output D. Regulation III. Technique of Dye Dilution IV. Formula for Cardiac Output V. Correction for Recirculation VI. Injection and Sample Sites VII. Numerical Integration A. The Problem B. Rectangular Approximation C. Trapezoidal Approximation D. Simpson’s Rule E. MATLAB: trap and quad VIII. Approximation by Spline Functions A. Background B. Cubic Spline Approximation C. Example D. MATLAB Function and Example IX. Thermal Dilution and Swan-Ganz Catheter Study Problems and Solutions
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BME 210 Table of Contents ii Receptor Kinetics I Introduction II. Receptor Ligand Kinetics E. Chemical Rate Laws F. One Binding Site – One Conformational State C. One Binding Site – Two Conformational States D. Enzyme Kinetics III. Numerical Solution of a Single Differential Equation – The Problem IV. Euler’s Method X. Runge-Kutta Method of Order 2 XI. Fourth-Order Runge-Kutta Forumula (RK4) XII. Implicit Euler’s Method XIII. Examples with Matlab Implementation XIV. More Than One Differential Equation A. The Problem B. Converting One nth Order ODE to n 1 st Order ODEs C. Euler's Method for n Differential Equations D. Example of Euler’s Method for 2 ODEs E. RK2 for n Differential Equations X. Matlab’s ODE Solvers A. Overview of ODE45 B. Example – Frictionless Pendulum C. Example – Hepatitis C Viral Dynamics XI. Analysis of Errors A. Local Error B. Error Tolerance Study Problems and Solutions
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BME 210 Table of Contents iii Medical Imaging: Computerized Tomography I Introduction II. X-Ray Computed Tomography A. Introduction B. Data Collection for CT C. CT Numbers III. Solution of Linear Algebraic Equations by LU Decomposition A. LU Decomposition B. Crout’s Algorithm C. Example D. Forward/Backward Substitution E. Example Continued IV. MATLAB Solution A. Left Division B. Plotting – Image Function V. Other imaging modalities Study Problems and Solutions
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BME 210 Table of Contents iv Therapeutic Drug Development I Introduction II. Compartment Models A. Examples of Compartment Transfer B. General Compartment Models C. Examples of Compartment Models III. Compartment Matrices IV. Least Squares Estimation – An Example V. Root of an Equation – One Unknown A. Newton’s Methods B. Secant Methods C. Application to Least Squares VI. MATLAB Implementation A. Newton’s Method B. Secant Methods VII. Least Squares Estimation – General Formulation VIII Solution to General Least Squares via Direct Function Minimization Study Problem Solutions
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BME 210 Table of Contents v Modeling Spread of Disease I Introduction to the Spread of Disease II Some Basic Probability III. Computer Simulation of Chance Events IV. One Population Spread of Disease Problem Defined V. Simulating the One Population Spread of Disease Problem
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This note was uploaded on 03/30/2010 for the course BME 210 taught by Professor D'argenio during the Spring '07 term at USC.

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BME210Notebook - Biomedical Computer Simulation Methods...

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