葡萄糖靜脈内投與による血糖變化の數學的分析 (第2報)

抄録

In the preliminary paper it has been reported that the change of blood sugar certain period following the intravenous administration of glucose could be expressed as follows:
y=c₁e^-λ₁t+c₂e^-λ₂t
y: Concentration of blood sugar.
t: Time after the administration.
e: Basis of natural logarithm.
C₁, C₂, λ₁, λ₂: Constant based on the experiment.
Since c₁e^-λt decreases very rapidly within few minutes following the administration, the formula could be simplified as
y=ce^-λt
C and e^-λ may be easily obtained by plotting the blood sugar values on semi-logarithmic graph. e^-λ especially indicates the ability of glucose assimilation in an individual, namely, the higher the value the lower the assimilating function and the lower the value the higher the function.
This was also proved to be valid in single intravenous tolerance test performed in 20 human subjects, 9 normal and 11 rabbits with electrolytic lesion of hypothalamus.
Fairly marked rebound hypoglycemia following the hyperglycemic response produced intravenous glucose injection was observed in several cases.
The values of e^-λ following triple intravenous glucose tolerance test in 58 healthy subjects and cases with various diseases, 15 normal and 12 rabbits with electrolytic lesion of hypothalamus indicated the ability of glucose assimilation was accelerated by the initial injection in most of the healthy human and all of the rabbits.
In diabetic cases, however, there were two types, i. e., the one which showed progressive increase in glucose assimilation ability and the other progressive decrease in glucose assimilation ability following the repeated glucose injection.