Faculty version with model answers

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1 Faculty version with model answers Bruce M. Koeppen, M.D., Ph.D. University of Connecticut Health Center 1. Inulin is used in an experiment to measure the glomerular filtration rate (GFR). Inulin is continuously infused to achieve a steady-state concentration in the plasma of 1.0 mg/dl. Urine is collected over a 10 hour period. The total volume of urine is 1.5 L, and the urinary concentration of inulin is 440 mg/l. What is the GFR, as determined from the inulin clearance? Inulin = GFR = 110 ml/min Calculations: Urine flow rate = 1,500 ml/600 min = 2.5 ml/min Urine [inulin] = 440 mg/l = 0.44 mg/ml Plasma [inulin] = 1.0 mg/dl = 0.01 mg/ml Inulin clearance = GFR = (2.5 ml/min x 0.44 mg/ml)/0.01 mg/ml = 110 ml/min 2. In clinical situations the GFR of a patient is usually determined by measuring the clearance of creatinine. Like inulin, creatinine is freely filtered at the glomerulus. However, in contrast to inulin, a small amount is also secreted (approximately 10% of all creatinine excreted in the urine reflects this secretory component). Therefore creatinine is not an ideal marker for GFR. Despite this error, creatinine is used to measure GFR because it is produced endogenously by skeletal muscle, and does not require an infusion. Therefore it is easy to do a creatinine clearance, because the patient can do it at home by simply collecting their urine (usually over a 24 hr period), and having a single blood sample obtained to measure the plasma [creatinine]. What would be the estimated GFR of a patient with the following values for plasma and urine [creatinine] and urine volume. Calculation: Plasma [creatinine] = 1.5 mg/dl Urine volume = 1.5 L/24 hours Urine [creatinine] = 1.44 gm/l Creatinine?~ GFR = 100 ml/min Urine flow rate = 1,500 ml/1440 min = 1.04 ml/min Urine [creatinine] = 1.44 gm/l = 1.44 mg/ml Plasma [creatinine] = 1.5 mg/dl = mg/ml Creatinine GFR = (1.04 ml/min x 1.44 mg/ml) / mg/ml = 100 ml/min 3. One important consequence of renal disease is loss of nephrons. As nephrons are lost the GFR will decrease (remember that GFR is the sum of the filtration rates of all the nephrons in the kidneys). Therefore, as renal disease progresses the GFR declines, and the plasma [creatinine] increases. The relationship between GFR and plasma [creatinine] is illustrated below. Bruce M. Koeppen, M.D., Ph.D., University of Connecticut Health Center -1-

2 10 8 Plasma [ creat inine] (mg/ dl) GFR (ml/ min) How do you explain the shape of this relationship, and what limitations does this present when trying to estimate GFR from a single plasma creatinine value? This curve reflects the fact that to maintain steady-state balance, excretion of creatinine by the kidneys must equal its production by skeletal muscle, and remain constant (this assumes production rate is constant). Because the excretion rate of creatinine essentially equals the creatinine filtered load (ignoring the secretory components of creatinine excretion), the following relationship applies: U cr x V = GFR x P cr Since U cr x V is constant (ie., steady-state balance), the plasma concentration of creatinine (P cr ) must increase as GFR declines. Note that when GFR first begins to decline with renal disease, the change in plasma [creatinine] is quite small. In fact an individual can lose 1/3 to 1/2 of renal function and still have a plasma [creatinine] that is only slightly elevated above the normal reference value. Similarly, large changes in plasma [creatinine] occur with advanced renal disease even when only a small fraction of additional nephrons are lost. Thus predicting a precise GFR value from a single plasma [creatinine] determination is relatively inaccurate. However, monitoring the change in plasma [creatinine] over time is a useful way to monitor progression (or resolution) of renal disease. 4. A 25 year old man weighing 60 kg has a plasma [creatinine] of 1.4 mg/dl (nl = mg/dl). A 24 hour urine collection is done to determine his creatinine clearance, and thereby estimate his GFR. The following data are obtained: Urine [creatinine] = 833 mg/l Urine volume = 1,080 ml/24 hour What is his creatinine clearance? Calculation: Creatinine clearance = 44.6 ml/min Urine flow rate = 1,080 ml/1440 min = 0.75 ml/min Urine [creatinine] = 833 mg/l = mg/ml Plasma [creatinine] = 1.4 mg/dl = mg/ml Bruce M. Koeppen, M.D., Ph.D., University of Connecticut Health Center -2-

3 Creatinine ~ GFR = (0.75 ml/min x mg/ml) / mg/ml = 44.6 ml/min If the normal range of GFR for adult males is ml/min, what would you conclude about the renal function of this man? The value of 44.6 ml/min for a creatinine clearance would seem to indicate a significant reduction in renal function (perhaps 50%). While his plasma [creatinine] is within the normal range (upper limit of normal), it is difficult to interpret because there is no baseline value. For example, it may have been 0.8 mg/dl previous to this current determination. This emphasizes the point that early on in renal disease small increases in plasma [creatinine] can occur with large initial declines in renal function. What error could lead to the calculation of a creatinine clearance that does not reflect the actual GFR? How could you determine if such an error occurred in this man, without having to repeat the 24 hour urine collection? (Hint: Muscle creatinine production is relatively constant and proportional to muscle mass. In adult males, the creatinine production rate is mg/kg body weight/day, and in adult females it is mg/kg body weight/day). A falsely low creatinine clearance will be calculated if the urine collection was incomplete (ie., collected for less than a 24 hr period). Because creatinine production is relatively constant and proportional to muscle mass a simple calculation of the total amount of creatinine excreted in the urine will allow you to determine if the collection was complete. For example, this man weighs 60 kg, and his creatinine production should be in the range of 1,200-1,500 mg/24 hr. This should equal his creatinine excretion rate. However, his excretion rate is only about 900 mg/24 hr (1,080 ml x mg/ml). Therefore, it appears that the low value for creatinine clearance may not a reflection of decreased renal function, but the result of an incomplete urine collection. Note: there is some reason to believe that perhaps this man does have some degree of decreased renal function. By taking the expected creatinine excretion rate of 1,200-1,500 mg/24 hr, a predicted creatinine clearance of ml/min can be calculated. Unfortunately, because it is not know exactly how much urine was not collected, an accurate measure can only be obtained after the man does an appropriate 24 hour urine collection. 5. The renal handling of Na + and K + and urea are examined in two individuals. Both individuals eat the same diet, and are in steady-state balance. However, they have different glomerular filtration rates. Subject A has a GFR of 170 L/day, while the GFR of subject B is 50 L/day. The following data are obtained. Na + Intake K + Intake Urea Production GFR Urine Flow Subject meq/day meq/day gm/day L/day L/day A B Serum [Na + ] Serum [K + ] Serum BUN* GFR Subject meq/l meq/l mg/dl L/day A Bruce M. Koeppen, M.D., Ph.D., University of Connecticut Health Center -3-

4 B *BUN = blood urea nitrogen Assume that the kidneys represent the only excretion route for Na +, K + and urea. Calculate the following: Subject A Subject B Na + (L/day) K + (L/day) Urea (L/day) Filtered Load Na + (meq/day) 24,650 7,250 K + (meq/day) Urea (mg/day) 17,000 17,000 Fractional Excretion Na + (%) K + (%) Urea (%) Tubular Reabsorption Na + (meq/day) 24,550 7,150 K + (meq/day) Urea (mg/day) 8,500 8,500 The following formulae are used: = excretion rate / plasma concentration Filtered Load = GFR x serum concentration Fractional Excretion = excretion rate / filtered load x 100 Tubular reabsorption = filtered load - excretion rate Calculations subject A: 100 meq/d / 145 meq/l = 0.69 L/day 50 meq/d / 3.5 meq/l = 14.3 L/day Bruce M. Koeppen, M.D., Ph.D., University of Connecticut Health Center -4-

5 Urea: Filtered Load Urea: 8,500 mg/d / 100 mg/l = 85 L/day 170 L/d x 145 meq/l = 24,650 meq/day 170 L/d x 3.5 meq/l = 595 meq/day 170 L/d x 100 mg/l = 17,000 mg/day Fractional Excretion 100 meq/d / 24,650 meq/d x 100 = 0.4% 50 meq/d / 595 meq/d x 100 = 8.4% Urea: 8,500 mg/d / 17,000 mg/day x 100 = 50% Tubular Reabsorption 24,650 meq/d meq/d = 24,550 meq/day K+: 595 meq/d - 50 meq/d = 545 meq/day Urea: 17,000 mg/d - 8,500 mg/d = 8,500 mg/day Calculations subject B: Urea: Filtered Load Urea: 100 meq/d / 145 meq/l = 0.69 L/day 50 meq/d / 3.5 meq/l = 14.3 L/day 8,500 mg/d / 340 mg/l = 25 L/day 50 L/d x 145 meq/l = 7,250 meq/day 50 L/d x 3.5 meq/l = 175 meq/day 500 L/d x 340 mg/l = 17,000 mg/day Fractional Excretion 100 meq/d / 7,250 meq/d x 100 = 1.4% 50 meq/d / 175 meq/d x 100 = 28.6% Urea: 8,500 mg/d / 17,000 mg/day x 100 = 50% Tubular Reabsorption 7,250 meq/d meq/d = 7,150 meq/day 175 meq/d - 50 meq/d = 125 meq/day Urea: 17,000 mg/d - 8,500 mg/d = 8,500 mg/day Based on the above data, explain each of the following: Note: questions A-D are all related, the point of each is to understand how Na +, K + and urea are handled by the kidney, and how this can be discerned from the above calculations. There are several key concepts to emphasize: 1. The concept of steady-state and that intake (production) must equal excretion. Therefore the excretion rate for each solute is equal to the intake (production) rate. 2. All three solutes are freely filtered. 3. All three solutes are reabsorbed (K + is both reabsorbed by the nephron, but overall net reabsorption occurs in these two subjects). However, the tubular transport of Na + and K + is Bruce M. Koeppen, M.D., Ph.D., University of Connecticut Health Center -5-

6 regulated, but the transport of urea is not (the majority of the filtered load of urea is reabsorbed by solvent drag in the proximal tubule). A. Why are the clearances of Na + and K + the same in subjects A and B, but the clearance of urea is different? The excretion of both Na + and K + is regulated by the kidneys to maintain steady-state balance. Therefore the excretion rates are the same in both subjects, as are their plasma concentrations (the homeostatic mechanisms involved in Na + and K + balance serve to maintain the ECF concentrations for these ions within a narrow range). Since clearance is the volume of plasma that must be cleared to account for the amount of the solute excreted, this value will not change. In contrast, the excretion of urea is not regulated to maintain a constant serum concentration of urea, but occurs as a consequence of glomerular filtration and proximal tubule reabsorption (reflect back on question 3 and point out the similarities and differences between the renal handling of urea and creatinine). Therefore, excretion rate can only be matched to production by an increase in the serum concentration (increases filtered load). With the higher serum concentration of urea, and the same excretion rate, the clearance of urea decreases. Said another way, the volume of plasma that must be cleared of urea to account for the observed excretion rate is less in the condition of an elevated serum urea concentration. B. Why do the filtered loads of Na + and K + differ in subjects A and B, but the filtered load of urea is the same? Filtered load is calculated from the product of the GFR and the serum/plasma concentration of the solute. As noted in part A, the serum concentrations of Na + and K + are regulated and maintained constant. However, the GFR of the subjects is different. Therefore, the filtered load of Na + and K + will decrease because of the decrease in GFR. In contrast, urea excretion is dependent on glomerular filtration, and its reabsorption by the nephron is not regulated. Therefore as GFR decreases the serum concentration of urea increases. The reasoning is identical to that discussed in question #3. The filtered load is unchanged, which allows the excretion rate to be matched to the production rate (in the simplified situation outlined here the reabsorption of urea by the proximal tubule is a fixed percentage of the filtered load). C. Why are the serum concentrations for Na + and K + the same in subject A and subject B, but the serum BUN concentration is greater in subject B than in subject A? See the answer to parts A and B. This is just another way to try and understand the differences between the renal handling of Na +, K +, and urea. D. How do you explain the differences in fractional excretion and tubular transport of Na +, K + and urea? Without going into detail, the transport of Na + and K + is regulated to maintain their concentrations in the ECF within a very narrow range. To accomplish this they must maintain excretion rate equal to intake. In the setting of a reduced GFR, this requires an increase in the fractional excretion. Again, the transport of urea is not regulated to maintain a constant ECF concentration (see above). Bruce M. Koeppen, M.D., Ph.D., University of Connecticut Health Center -6-