Glucose homeostasis is one of the most typical feedback control system. Therefore, the understanding of the individual homeostasis is very important to diagnose its glucose tolerance. This study was designed to investigate the universal and quantitative relationship between glucose tolerance and the dynamic property of insulin secretion.
0.3 g per Kg body weight of glucose as a 40 per cent solution in distilled water were administered intravenously in three minutes into 99 normal subjects, 56 borderline cases and 82 diabetics classified according to 50 g oral glucose tolerance test results. The relationship between blood glucose and insulin concentrations were analyzed with the aid of control theory.
The following results were obtained;
1) It has been accepted that when blood glucose or glucose excess values were plotted semilogarithmically against time on a linear axis, a straight line relationship was obtained during IVGTT. This meant that the glucose disposal rate (k) had been considered to be constant regardless of time. But in 111 cases, when blood glucose excess values were plotted on the same manner as mentioned before, the slope of lines got steeper in course of time and in each time intervals k values were high enough. This means that the glucose disposal rate (k) in normal glucose tolerance is not a constant regardless of time, but gets larger and larger with time.
In 126 cases whose glucose tolerance revealed to be abnormal, the change in glucose disposal rate with time was very small.
From these results the glucose disposal rate should be regarded as a function of time and following equation should be used to diagnose glucose tolerance;
where X (t), X (0) is the blood glucose concentration at time t, pre-stimulated, respectively.
2) The dynamic property of glucose-induced insulin secretion was expressed as the transfer function of a proportional and derivative action to blood glucose concentration, and weighting function was calculated from the blood glucose concentration as an input and plasma insulin concentration as an output by the deconvolution method. This weighting function reflects the insulin secretion amount per unit of changing rate of glucose concentration in blood. It was clearly shown that the gain in the weighting function was small and the response was slow even in the individual whose glucose tolerance was slightly abnormal.
Furthermore, the time course of weighting function revealed that the larger the weightng function, the larger the change in glucose disposal rate with time, showing that glucose tolerance was controlled by the insulin secreted based on the change in glucose concentration in blood.
This method which permits quantitation of insulin response against unit of changing rate in blood glucose level is considered to be effective for the diagnosis of early stage and even before manifestation of diabetes mellitus, and also useful method for the follow-up study of diabetics.