On Four-Dimensional Linear and Non-Linear Mathematical Models of the Glucose-Insulin Regulatory System.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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The set of linear differential equations formulated by Bolie to describe the mechanism of homeostatic control of blood glucose are written as a vector equation of the form dXdt AX Ft, where the elements of the A matrix represent combinations of the ten independent parameters of the Bolie model. Parameter values are determined by minimizing the system cost function, which is defined as the integrated square of the difference between the model solution and the actual data. The Fletcher-Reeves function minimization technique is used with the linear model to find the minimum of the cost function and therefore establish the most likely values of the linear system parameters. This model is then extended to include all possible second-order nonlinear terms. Analytical expressions are derived for both models for the cost function and gradient of the cost function in the direction of some general perturbation matrix. The analysis of the results indicate that seven of the ten model parameters are invariant for all patients and for all test dosages. The remaining three parameters are recommended for incorporation into the nonlinear model. The Bolie model is shown to be relatively good for small test dosages, and several areas for further study are recommended. Author
- Medicine and Medical Research
- Numerical Mathematics