A Simple Method of Determining Pre-Diabetes

Abstract

A simple formula for determining pre-diabetes (the very early stage of diabetes mellitus) was derived from the model of Ackerman et al. (Bull Math Biophys 1965; 27: s21-37) for very smoothly varying time course patterns of blood glucose level. The natural period of blood glucose level in a healthy subject calculated using the formula was in good agreement with the value obtained by computer work. Diabetes mellitus (DM) is a disease associated with dis- ordered metabolism of carbohydrates, and pre-diabetes mel- litus (PD) is a very early stage of mild DM caused by disor- dered secretion of insulin, glucagons and epinephrine. The study of PD is of great importance in opening a way to the early discovery of mild DM. Although quite many ap- proaches to DM and PD on mathematical basis have been reported thus far (1-6), most of them require advanced mathematical and computer work ability. The purpose of this report was to provide a simple method of determining PD in order to help general practitioners with limited mathematical and computer ability. This study was based on a simple model presented by Ackerman et al. (1, 7), which was based on the simple assumption that the blood glucose level tends to be regulatory and is influenced and controlled by a wide variety of hormones and other metabolites. In this model all these hormones are combined into a net hormonal concentration and the cumulative effect of them is taken into account. And thus the model centers attention on the concentration of glucose in the blood, labelled G and that of the net hormonal complex, labelled H. The hormones such as insulin which decrease G are considered to increase H. On the other hand, the materials such as glucagons, epinephrine and cortisol which increase G are considered to decrease H. Coupled linear differential equations for G and H can be established and these two first order equations can be com- bined into two separate forms of second order linear equa- tion. The solution for G, with t = 0 at the time the glucose loading has been completed, is generally given in three damped oscillation patterns. Among them, in analogy with mechanical vibration systems, the underdamped case seems to be more appropriate for PD, by assuming that there is no serious deficiency in the controlling system. Thus we have