Miguel Ángel Moreles
A DE-Constrained optimization problem for fitting OGTT data
In the Oral Glucose Tolerance Test (OGTT), a patient, after an overnight fast ingests a load of glucose. Then measurements of glucose concentration are taken every 30 minutes during two hours. The test is used to aid diagnosis of diabetes, namely, type 2 diabetes mellitus and glucose intolerance. Several mathematical models have been introduced to describe the glucose/insulin system during an OGTT. Models consist on systems of differential equations where most parameters are unknown. Estimation of these parameters is the aim of this talk. We present a minimal model and pose the problem of parameter estimation as an optimization problem constrained by the system of differential equations. We contend that two of such parameters can be used as a tool for diagnostic, as illustrated by a SVM classification technique.
Dr. Miguel Ángel Moreles obtained his Mathematics Degree from the Guanajuato University, and his Master’s thesis and his PhD (in 1995) from the University of Minnesota, USA. He has been a CIMAT researcher since 1996 and is a Member of the National System of Investigators within the Area of Physics, Mathematics and Earth Sciences (SNI Level II).
Dr. Moreles has published several research articles in Differential Equations, Functional Analysis, Numerical Methods, and Fractional Mechanics. He has organized workshops and national and international conferences in Differential Equations and Numerical Methods. As teaching experience, he has taught undergraduate and graduate courses. Regularly, he teaches courses on Differential Equations, Mathematical Analysis and Numerical Methods. He has directed several Bachelor’s and postgraduate theses.