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Biomedical Model Fitting and Error Analysis

This Teaching Resource introduces students to curve fitting and error analysis; it is the second of two lectures on developing mathematical models of biomedical systems. The first focused on identifying, extracting, and converting required constants—such as kinetic rate constants—from experimental literature. To understand how such constants are determined from experimental data, this lecture introduces the principles and practice of fitting a mathematical model to a series of measurements. We emphasize using nonlinear models for fitting nonlinear data, avoiding problems associated with linearization schemes that can distort and misrepresent the data. To help ensure proper interpretation of model parameters estimated by inverse modeling, we describe a rigorous six-step process: (i) selecting an appropriate mathematical model; (ii) defining a “figure-of-merit” function that quantifies the error between the model and data; (iii) adjusting model parameters to get a “best fit” to the data; (iv) examining the “goodness of fit” to the data; (v) determining whether a much better fit is possible; and (vi) evaluating the accuracy of the best-fit parameter values. Implementation of the computational methods is based on MATLAB, with example programs provided that can be modified for particular applications. The problem set allows students to use these programs to develop practical experience with the inverse-modeling process in the context of determining the rates of cell proliferation and death for B lymphocytes using data from BrdU-labeling experiments.

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Resource Type: Assessment- exam with answer key, Assignment/Activity (non-laboratory), Bibliography, Dataset, Diagram, Digital presentation (powerpoint), Illustration, Lecture/Lecture outline, Lesson plan, Teaching strategies & guidelines
Audience Level: Undergraduate upper division 15-16, Graduate, Professional (degree program)

Author and Copyright

Authors and Editors: Kevin D. Costa of Mount Sinai School of Medicine, New York, Steven H. Kleinstein of Department of Pathology, Yale School of Medicine, Uri Hershberg of Drexel University, Philadelphia
Publisher: American Association for the Advancement of Science
Format: application/vnd.ms-powerpoint, application/x-shockwave-flash, application/zip, text/html
Copyright and other restrictions: Yes
Cost: No


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