The purpose of this study is to analyze the function of renal medulla applying a mathematical model of simple countercurrent system. The simple countercurrent system may be expressed as follows:
C=C
oexp (kx/au),
where C is the final osmolality in countercurrent system, C
o is the inital value of the osmolality, k is the rate constant of solute transport from ascending limb to descending limb, x is the length of the system, a is the crosssection of the tubule, and u is the velocity of fluid in the system.
Assuming that the urine osmolality and urine flow is proportional to the final osmolality in the countercurrent system (C) and to the fluid flow (au), rerpectively, the following relation may be expected :
U
osm=C
oexp(const/V)
where U
osm is the urine osmolality, V is the urine volume The following study was perfomed comparing the results obtained from clinical and animal experiments to the theoretical relation, and the following results were obtained.
(1) Experiments of the mongrel dogs, under water and osmolar (mannitol) diuresis, demonstrated that the relation of urine osmolality to the urine volume is identical to that expected from the theoretical equation. When hydrochlorothiazide is infused simultaneousaly, the change of the relation occurs in such a manner of increasing the initial osmolality of the urine (C
o). Therefore, this compound seemed to have its reaction site in the renal tubules other than Henle's loop.
(2) Fishberg's urine concentration and dilution test were performed in the patients with cirrhosis of the liver (6 cases), chronic glomerulonephritis (10 cases), chronic adrenal insufficiency (1 case), and in 5 healthy adults. As the osmolar load to the nephron can be considered to be constant in this experiment, the equation becomes :
U
osm=N/Vexp(const/V)
where N is the osmolar load. The reasonability of this equation was confirmed in each group of the patients.
In cirrhotic patients with marked asceites, as the urine volume did not increase significantly, the dilution of the urine did not occur substantially. In patients with moderate to svere renal damage, the relation of urine osmolality to urine volume was appearently different from those of normal and cirrhotics. In these cases, urine flow from each nephron may increase to an extent which can be calculated from the decrement of the glomerular filtration rate. When urine volume was corrected for decreased GFR as follows:
corrected V=V⋅GFR
normal/GFR
patientthe relation of urine osmolality to the corrected urine volume showed a fair agreement with those of the normal and cirrhotics. Therefore, the failure of urine concentration and dilution in the pationts with decreased renal function may be the result of increased urine flow in the countercurrent system.
In a patient with chronic adrenal insufficiency, the results of the experiment were similar to those of chronic glomerulonephritis. As the functioning nephron did not diminish in such a case, the same explana-tion could hardly be applied. In order to clarify this point, an experiment of acute constriction of renal artery was performed.
(3) To dogs with constricted right renal artery, a hypotonic solution (1.8% glucose, 1.2% mannitol and 0.05% saline) was infused. In most instances, the urine from the constricted kedney showed some-what lower osmolality than that of control. As the number of the functioning nephron did not decrease, the defect of urire concentration and dilution should be a consequence of decrement of osmolar load to each functioning nephron resulted from the GFR reduction. When the urinary osmolality was corrected for decreased GFR as follows :
corrected U
osm=U
osm⋅ GFR
normal/GFR
experimental
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