Interprétation Physiologique Des Relations Mathématiques Existant Entre le Taux du Glucose Sanguin et le Débit Urinaire de Cette Substance

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Abstract
On a graph where the ordinales are « Excreted Glucose » and the abscissæ « Blood Glucose », the relation is first (below the minimal threshold) a straight line superposed to the abscissæ, then, (for moderate values of hyperglyæmia) a curve of exponential type, and finally (for high levels of blood sugar exceeding the maximum threshold) a straight line with the formula : Glucose excreted = (Blood glucose − Mean threshold) × Filtration. The meaning of the curvilinear portion has been rightly explained by H. Smith as being due to the unequal reabsorptive power of the individual nephrons. The author of the present paper underlines the reasons why three points of the relation « Excreted Glucose/Blood Glucose » deserve the name of threshold. a) The « Minimal threshold » is the lowest level of blood glucose at which sugar is found in the urine when the glycæmia is raising. This is the level ou blood sugar for which the reabsorptive power of the weakest, nephron is saturated. b) The « Maximal threshold » is the glycæmia at which tho reabsorptive power of the strongest nephron is saturated. c) The « Mean threshold » is the level of blood sugar at which the reabsorptive power of all the nephrons would be saturated if this power were equal to the statistical mean of the actual reabsorptive capacities of the individual nephrons. This « mean threshold » is the value which, in Shannon and Fisher’s formula, must be suhstracted from the blood sugar to calculate glucose excretion. A relation graphically similar tot that of « Excreted glucose/Blood glucose » would be found between the level of the water uphill and the water flow downhill, supposing that, in a water duct with a rectangular section, the flow of water were hindered by a transverse wall, sloping from side to side. The relation would be first a horizontal line superposed to the abscissæ, then an exponential curve, then a straight line with a definite slope.

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