Metabolic modeling using statistical and spreadsheet software: Application to the glucose minimal model

Kinetic non-linear metabolic models are used extensively in medical research and increasingly for clinical diagnostic purposes. An example of such a model is the Glucose Minimal Model by Bergman and colleagues [1]. This model is similar to pharmacokinetic/pharmacodynamic models in that like pharmacokinetic/pharmacodynamic models, it is based on a small number of fairly simple ordinary differential equations and it aims to determine how the changing concentration of one blood constituent influences the concentration of another constituent. Although such models may appear prima facie, to be relatively simple, they have gained a reputation of being difficult to fit to data, especially in a consistent and repeatable fashion. Consequently, researchers and clinicians have generally relied on dedicated software packages to do this type of modeling. This article describes the use of statistical and spreadsheet software for fitting the Glucose Minimal Model to data from an insulin modified intravenous glucose tolerance test (IM-IVGTT). A novel aspect of the modeling is that the differential equations that are normally used to describe insulin action and the disposition of plasma glucose are first solved and expressed in their explicit forms so as to facilitate the estimation of Glucose Minimal Model parameters using the nonlinear (nl) optimization procedure within statistical and spreadsheet software. The most important clinical parameter obtained from the Glucose Minimal Model is insulin sensitivity (S_I). Using IM-IVGTT data from 42 horses in one experiment and 48 horses in a second experiment, we demonstrate that estimates of S_I derived from the Glucose Minimal Model fitted to data using STATA and Excel, are highly concordant with S_I estimates obtained using the industry standard software, MinMod Millennium. This work demonstrates that there is potential for statistical and spreadsheet software to be applied to a wide range of kinetic non-linear modeling problems.