J. Physiol. (1946) I05, I2*463*2

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1 223 J. Physiol. (1946) I05, I2*463*2 UREA EXCRETION BY RABBITS By E. M. VAUGHAN WILLIAMS From the Department of Pharmacology, Oxford (Received 13 February 1946) After some preliminary observations by Austin, Stillman & van Slyke (1921) on the excretion of urea by dogs and men, the 'urea clearance' was introduced as a clinical test of kidney function by Moller, Mackintosh & van Slyke in The latter found that, when U is the concentration of urea in the urine in mg./100 c.c., when B is the concentration of urea in the blood (which is assumed to remain constant during the observations) in mg./100 c.c., and when V is the volume of urine formed in c.c./min., their results could be expressed by the equation UV/B=K (=75), when V was greater than 2-0 c.c./min. (=the 'augmentation limit') and by the equation (U4V)/B=K (=54) when V was less than 2-0 c.c./ min. These equations, however, do not apply to rabbits. Although rabbits have often been used in experimental studies of kidney function, no equations for urea excretion in rabbits could be found in the literature. In the rabbit Richards & Plant (1915, 1922) demonstrated a relation between the rate of urine formation and blood pressure, MacKay & Cockrill (19) showed that the rate of excretion of urea was related to its plasma concentration, and Kaplan & Smith (1935) found that urea 'clearances' (U V/B) were diminished when the volume of urine was small. But, from the point of view of using the rate of urea excretion as a test of kidney function, there were insufficient data to enable physiological variations to be distinguished from changes which might be pathological, e.g. after poisoning by a toxic drug. The difficulty is best expressed by an example. hn a rabbit (M) weighing 2 kg. six observations were made of U and V, and two of B. In this example, which is purposely chosen as extreme, U varied from 4160 mg./100 c.c. to 317 mg./100 c.c., and V from 0 74 to c.c./min. Since these were consecutive observations, an equation which truly expressed the functional capacity of the kidneys should give the same answer in all of them. The following are the 'clearances' employing the equation UV/B =clearance: 1* *

2 224 B. M. VAUGHAN WILLIAMS The 'clearances' do not even approximate to a constant, the biggest being 2-8 times the smallest. Nor is the situation improved if the equation (UVV)/B =clearance is adopted. The results then become: *46 5l10 4*34 4*37 where, again, the largest is 2*57 times the smallest. Therefore it was clear that until some equation was found to express the physiological relationship between U, V and B, the rate of urea excretion could not be used as a kidney function test. METHODS Observations of U, B and V were made on eleven male rabbits of average weight 1 9 kg. They were given greens and water ad lib. for several days before the observations were made in order to avoid the dehydration common in laboratory animals. The rabbit selected for experiment was deprived of food, but not of water, for 24 hr. beforehand. On the morning of the experiment it was given 40 c.c. warm tap water/kg. by stomach tube and placed in a metabolism cage designed to collect urine free from faeces. Ninety minutes later it was given a further 40 c.c. water /kg., and, after another min., the first blood sample was taken from an ear vein. The bladder was then emptied, a careful note being made of the time, and the urine discarded. At intervals of about min. thereafter the bladder was emptied, time and volume being noted, and the urine kept for estimation of urea. When four or five urine samples had been obtained, a second blood sample was taken; this bleeding was purposely done at the beginning and end of the urine collection instead of in the middle, as manipulations during bleeding were inclined to inhibit the diuresis. The appropriate values of B were then obtained by interpolation on a graph. For the observations recorded in this paper the bladder was emptied by catheterization (no. 1 gum elastic, kept in hot water, and dipped in liquid paraffin) and by supra-pubic pressure. It is, perhaps, worth mentioning here that a better method, unhappily not hit upon until this series of observations was finished, is as follows. A no. 2 or 3 rubber catheter is passed, while an assistant holds the rabbit supine on the bench, and the free end of the catheter is then attached, via a collecting flask and a water-trap, to a suction pump. By manceuvring the catheter round and back and forth it is possible to ensure that the last drops of urine are sucked out. Urea in blood and in urine was estimated by the Conway (1942) and van Slyke methods. For the latter some specially designed deep aeration tubes, with ground-glass stoppers, were employed. RESULTS Urea excretion in rabbits. Altogether ninety-eight observations of U, B and V were obtained, and have been recorded in Fig. 1. It was noted that the values of V fell from 1.0 down to c.c./min. This range has been split up into a series of steps of 0 05 c.c./min. and at each step the mean of all the values of the ratio U/B which lie within 0*05 c.c./min. on either side of it have been plotted as circles. Thus each circle in the graph represents the mean of all those values of U/B which were observed within 0*05 c.c./min. of the value of V at which the circle is plotted. The course on which the circles lie suggests a regression line of the form log V+c log U/B =log K. The crosses in Fig. 1 represent the same points as the circles, but have been plotted as logarithms. They lie reasonably close to a straight line, which has

3 UREA EXCRETION BY RABBITS 225 been drawn by eye and represents the equation log V + 1F4 log U/B = 8-4. The continuous curve drawn in Fig. 1 passes through values of U/B calculated for each value of V from the equation (U/B)1'4 x V = This equation represents the series as a whole, but it is, of course, possible to work out the constants 1U/B 8 Q 78 c and K for each rabbit individually. 18 A Unfortunately, very little control can be 17 exercised over the rate of urine formation :50- F+ in a rabbit and the constant c cannot be -15./ determined with any accuracy, unless the -1-4 observations cover a fairly wide range 4a 13 of V. In Table 1 are shown some repre- 1 sentative series, starting with the observa- I tions on rabbit M, which have already 41.0 been mentioned as an example of the / l inapplicability of the equations U V/B = K. and (UJV)/B =K. The first column gives 0P/ observations of U, and the second the 07 interpolated values of B; instead of values of V, the actual volumes and times in l05 minutes between urine collections have been recorded in the next two columns. The constant c has been calculated for JO 09 a (>5 04 (3 b each rabbit, and the appropriate value. of K for set ofoservationisgivenfig. 1. Rabbits. Ordinates: Values of the of K for each set of observations is given ratio U/B. Abscissae: Rate of urine formain the final column. From these results tion in c.c./min. (V). The range of values it appears that in rabbits a urea excretion of V has been divided into 'steps' of constant' can be found which is equiva c.c./min. Each circle represents the consttoan estimation t of he'clearanequiva- mean of the observations of U/B which lent to an estimation of the 'clearance' in lie within 0.05 c.c./min. on each side of the man. When the appropriate value of value of V at which the circle is plotted. c has been determined, the equation The crosses represent exactly the same (UIB)II x V=K can be expected to give figures as the circles, but are plotted as results (esu/b) atvlecant least more be expecstedtto g logarithms. The continuous curve is drawn consistent than from the equation (U/B)' 4 x V = 6*92. the clearance equations UV/B =K and (UVV)/B =K, which are, in fact, special examples of the same basic equation, in which the values of c happen to be 1-0 and 2-0 respectively. Urea excretion in man. These results from rabbits led naturally to the conjecture that some similar equation might apply to urea excretion in man. There were, however, good reasons for diffidence in approaching the subject. In their 1928 paper, M6ller, Mackintosh & van Slyke are unequivocal. They say: 'The results of our experiments... confirm the conclusions of Austin, Stillman & van Slyke. There is a distinct augmentation limit. Below it, clearance increases

4 226 E. M. VAUGHAN WILLIAMS TABLE 1. Observations on individual rabbits Actual volumes of urine U B (c.c.) Rabbit M, 2 kg., c= * *4 18*5 Rabbit K5, 2-1 kg., c= * Rabbit G, 1-8 kg., c= Rabbit F, 1 9 kg., c=2-1 Rabbit H, 2-0 kg., c = *1 3* Tim( in mix betwe4 urine collecti K 5' Mean =6-57 a=13-4% ions Mean = 6-49 ac=13-9% X Mean = a =24% ' Mean = 0 a=15.2% Mean = 5*6 a=13-6%

5 UREA EXCRETION BY RABBITS 227 with increasing urine volume, while above it the clearance is independent of urine volume.' And, referring to their expressions (UVV)/B and UV/B they add: 'No other line or curve could follow the experimental points more closely.' Moreover, in their discussion of the literature they include a list, reminiscent of skeletons beside a desert track, of the attempts of previous workers to find a 'Urea excretion constant'. It was, therefore, in a spirit of curiosity rather than of confidence or criticism, that the results given in the 1928 paper were re-examined. The dotted lines given in Fig. 2 are drawn to the equations (UJV)/B=54 and UV/B=75. These lines intersect when U/B=38.88 and V=1-96c.c./min. Together they constitute a composite curve with a definite kink in it, representing the 'augmentation limit', above which the first, and below which the second, equation applies. From the lists of values of U, B and V given in Tables 3 and 4 of their paper, the ratios U/B have been calculated, and more than 100 of them have been plotted against the corresponding values of V in Fig. 2. The dotted lines do not lie very close to a pathway through the centre of these observations, the 'spread' of which is so great that the complex curve given by the dotted lines, with a kink at the 'augmentation limit', seems unnecessary, as has already been shown by Dominguez (1935), who himself suggested an equation, which was modified in a later paper (Dominguez & Pomerene, 1943) to UV/B=A (1- e-kv) + bv. However, it was thought that it might be possible to find an equation which was simpler than this and which was of the same form as that already described for rabbits. The equation (U/B)l.103 x V= 81-3 has been drawn as a continuous line in Fig. 2. It is not claimed that this is the only, or even the best, possible equation, but it has several features to recommend it. It is a single simple equation, applicable to all values of V, and it disposes of the 'augmentation limit' and of the necessity for two methods of calculation. Its course does pass approximately through the middle of the observed points. At the 'standard' rate of urine flow, namely 1 0 c.c./min., it gives the same value to the ratio U/B as does the old equation (UJV)/B=54, namely, 54. Finally, it does represent the observations more closely than either the equation UV/B = 75 or (UVV)/B = 54. Each observation of U/B above the critical value 38*88 (the augmentation limit) was used to calculate V from the equation (U4V)/B = 54; this calculated value of V was then compared with the observed value of V, in order to obtain a figure (D) representing the difference between observation and calculation; e.g. when U/B = 95-9, according to the equation (UVV)/B = 54, the value for V should be It was, in fact, 0-48; thus the value of D was Similarly, for all observations of U/B below 38-88, V was calculated from the equation U V/B = 75, and a figure D obtained in each instance by comparison with the observed value of V. Finally, V was calculated for all values of U/B from the equation

6 228 E. M. VAUGHAN WILLIAMS (U/B)103x V = 813, and once more figures for D obtained. Every single set of observations given in the 1928 paper was calculated in this way. The results are given in the table on p Thus it is clear that the equation U/B 90 ~~~~~~~~~~~~~~ , _ D40 it Z 11 1O V c.c. /min. Fig. 2. Man. Ordinates: Values of the ratio U/B. Abscissae: Rate of urine formation in c.c./min. (V). The upper dotted line is drawn from the equation (UVV)IB =54. The lower dotted line is drawn from the equation UVIB =75. The points are plotted from tables 3 and 4 of the paper quoted in the text. The continuous curve is drawn from the equation (U/B)l.1O3 x V = 81-3.frmteeuto UBIL0x (U/B)l.108 x V = 81-3 represents the observed relationship of U, B and V more closely than the two previous equations, to the extent of 24% when U/B is greater than 38-88, and of 15% when it is less.

7 UREA EXCRETION BY RABBITS Mean values of D. Usingtheequation(UVV)/B =54 Using the equation (U/B)1103 x V =81-3 When U/B is between The mean value of D is The mean value of D is and 100 Using the equation U V/B = 75 Using the equation (U/B)1103 x V = 81-3 When U/B is between The mean value of D is The mean value of D is and CONCLUSIONS 229 It appears that in man, as in the rabbit, the relationship between U, B and V can be expressed by an equation of the form V(U/B)C-= K. It is not suggested that the equation (U/B)1403 x V = 81*3 is the only possible equation for man, but it does correspond to the observations of U, V and B given by Moller, Mackintosh & van Slyke more closely than the equations (UUVV)!B = 54 and U V/B = 75. If it does represent the behaviour of the kidneys in excreting urea, it is apparent that the-increase in the concentration U is a function of the reabsorption of water over the whole range of values of V. From clearances of inulin and other substances believed to be filtered by the glomeruli, but not reabsorbed, the rate of glomerular filtration is known to be about 1 c.c./min. Thus, if no water were reabsorbed at all, V would become 1 c.c./min. Substituting this value in the equation (U/B)l103 x 1 = 81-3, then U = B. Assuming that such a large extrapolation is justifiable, then more than a quarter of the urea filtered at the glomeruli is removed from the tubular fluid even in conditions in which no water is reabsorbed, i.e. in which the concentration of urea in the tubules does not become greater than that in the blood. SUMMARY 1. The equations used to express urea clearance in man cannot be applied to the rabbit. 2. Experimental details are described of the methods by which a series of observations of U, B and V was made on rabbits. 3. It is shown that, in the means of observations on eleven rabbits, the relationship between U, B and V can be expressed by the equation (U/B)1'4x V=6-92. Representative lists of observations on individual rabbits are also recorded. 4. Observations of U, B and V in man made by Moller, Mackintosh & van Slyke (1928) are discussed, and shown to correspond more closely to the equation (U/B)1-'03 x V = 81-3 than to the equations (UVV)/B = 54 and UV/B=75. If this equation be assumed to hold over all possible values of V, it implies that more than a quarter of the urea filtered by the glomeruli is removed from the tubular fluid even in the absence of reabsorption of water. This work was done while the author was in receipt of a grant from the Wellcome Foundation, for which he desires to express his thanks. PH. CV. 16

8 2 E. M. VAUGHAN WILLIAMS REFERENCES Austin, J. H., Stillman, E. & van Slyke, D. D. (1921). J. biol. Chem. 46, 91. Conway, E. J. (1942). Biochem. J. 36, 655. Dominguez, R. (1935). Amer. J. Phy8iol. 112, 529. Dominguez, R. & Pomerene, E. (1943). J. clin. Invest. 22, 1. Kaplan, B. I. & Smith, H. W. (1935). Amer. J. Physiol. 113, 354. MacKay, E. M. & Cockrill, J. R. (19). Amer. J. Physiol. 94, 2. Moller, E., Mackintosh, J. F. & van Slyke, D. D. (1928). J. clin. Invest. 6, 427. Richards, A. N. & Plant, 0. H. (1915). J. Pharmacol. 7, 485. Richards, A. N. & Plant, 0. H. (1922). Amer. J. Physiol. 59, 144.