BME 33400 / 3 Cr.
This course explores computational approaches to analyzing biological data and solving biological problems. Students will fit and interpret biological data, apply probabilistic and differential equation modeling techniques to biological processes, and assess numerical tools for biomedical applications. Special attention is given to the built-in analysis functions of MATLAB.
Available Online: No
Credit by Exam: No
Laptop required: No
P: MATH 26100, MATH 26600, and ENGR 29700.
Numerical Methods in Biomedical Engineering by Stanley M. Dunn, Alkis Conastantinides and Prabhas V. Moghe (2006), Academic Press
This course presents an engineering toolbox of computational approaches for solving common problems in biomedical engineering. It serves as an introduction not only to the methods themselves but to the strengths, drawbacks, and trade-offs of each, providing the student with the background needed not only to apply these computational tools but to recognize the conditions under which such tools are effective and appropriate. Furthermore, it introduces the students to such fundamental biomedical topics as ion channels and nerve cell potentials; cardiovascular dynamics; enzyme-substrate interaction; and DNA/protein sequence matching and classification.
Upon completion of this course, the student should be able to:
- Fit linear and nonlinear curves to data using least squares method.
- Interpolate data.
- Use MATLAB to solve a linear system of equations.
- Find the roots of an equation using the Newton-Raphson method.
- Use the Michaelis-Menten model to predict substrate concentrations in an enzyme reaction.
- Model a dynamic biological process using differential equations.
- Solve a system of differential equations using an appropriate numerical integrator.
- Predict nerve cell potentials.
- Use a Markov model to describe ion channel gating.
- Find database matches to DNA sequences.
BME33400 introduces several types of numerical tools, broadly classified into four categories:
- Fitting, analyzing and interpolating existing data with analytic functions.
- Using differential equations to describe biological processes, and selecting appropriate numerical tools to manipulate and solve those equations.
- Stochastic processes and probabilistic process modeling, including discussion of Markov and Monte Carlo simulations.
- Introduction to database search tools, text-string data processing, and other bioinformatics topics.
Topics and Associated Discussion/Homework Exercises Include:
- Data fitting. Linear, polynomial, and spline interpolation methods, least squares fits. Problems: Choosing an appropriate method for comparing and subtracting two membrane voltage records sampled at different rates. Fitting a curve to ion channel activation data.
- Matrix tools for solving linear systems of equations. Problems: Forces on a shoulder joint. Stoichiometric mass balance.
- Nonlinear equations in biomedical engineering. Finding the roots of an equation. Testing for convergence.Problems: Using the Michaelis-Menten model to predict substrate concentration. Predicting the opening time of the aortic valve.
- Finite difference methods. Numerical integration methods. Problem: Oxygen consumption during fermentation.
- Differential equation models. Setting up an appropriate model. Writing equations from a state diagram. Stability analysis. Stiff and nonstiff systems. Problems: Dynamics of drug absorption. Fick’s Law of Diffusion applied to cell membranes. Compartment models of metabolism. Continuous and discrete-time infectious disease models. Writing equations for a state model of ion channel dynamics. Michaelis-Menten equations for enzyme binding with similar and disparate rates. Hodgkin-Huxley squid axon model. Stem cell differentiation.
- Stochastic processes and probabilistic process modeling. Markov models and Monte Carlo simulations. Problems: Estimating the mean value of a population. Markov model of ion channel gating. Recognition and classification of DNA/protein sequences.
- Bioinformatics. Database search tools. Problems: Scoring goodness of fit for sequence matching. Using BLAST.