## Numerical Examples

1. In the example shown in Fig. 9, we assume that the plasma is dilute at 270 mOsm/kg H2O. In these circumstances, vasopressin release would be completely suppressed and plasma levels would be undetectable. If plasma flow into the kidney via the renal artery is 690 mL/min, then the rate of solute entry into the kidney via the renal artery would be (0.69 L/min • 270 mOsm/kg H2O) = 186.3 mOsmol/min. (1 kg of water is equivalent to 1 L; however, the unit of kg H2O has usually been used for expressing osmolalities.) For this example, assume that the resulting urine flow in the absence of vasopressin is 12 mL/min with an osmolality of 50 mOsm/kg H2O. This would give a solute excretion rate of (0.012 L/min • 50 mOsm/kg H2O) = 0.6 mOsmol/min. Because this volume of fluid is lost from the plasma flowing through the kidney, the plasma flow out of the renal vein would be (690 — 12) = 678 mL/ min. The solute flow out of the renal vein would be the difference between the inflow via the renal artery and the loss in the urine; that is, (186.3 — 0.6) = 185.7 mOsm/min. If this solute flow rate is divided by the volume flow rate in the renal vein (185.7 mOsmol/min ^ 0.678 L/min), the resulting osmolality of the plasma flowing out of the renal vein would be 274 mOsm/kg H2O. In other words, by producing hypo-osmotic urine, the kidney returns a more concentrated plasma to the general circulation via the renal vein. If we calculate the free water clearance in this example, we obtain —9.78 mL/min. The plasma that flows through the kidney is being concentrated at a rate equivalent to that which would be produced if

9.78 mL/min of pure water were removed from the plasma each minute. The difference between this free water clearance and the urine volume flow rate is that fraction of the urine flow that can be regarded to be isosmotic to plasma. 2. An example for the case of urinary concentration is shown in Fig. 10. In this case, we assume that the plasma osmolality is 300 mOsm/kg H2O, which would cause plasma vasopressin to be elevated. The rate of solute entry into the kidney via the renal artery would be (0.69 L/min • 300 mOsm/kg H2O) = 207 mOsmol/min. Because of the high vasopressin levels, the urine flow rate is quite low at 0.5 mL/min, and the urine osmolality is maximal at 1200 mOsm/kg H2O. Thus, the rate of solute excretion is the same as in the previous example, or 0.6 mOsmol/min. Because only 0.5 mL/min of fluid has been lost from the plasma flow, the rate of plasma flow out of the renal vein is 689.5 mL/min. The solute flow out of the renal vein would be (207 — 0.6) = 206.4 mOsmol/min. If we divide this by the renal vein plasma flow (206.4 mOsmol/min ^ 0.6895 L/min), we obtain a renal vein plasma osmolality of 299.3 mOsm/kg H2O. In other words, the production of hyperosmotic urine has resulted in a dilution of the plasma flowing through the kidney by 0.7 mOsm/kg H2O. If we calculate the free water clearance from these data, we obtain a negative free water clearance of 1.5 mL/min. The kidney in this case is operating to dilute the plasma at a rate equivalent to the effect of adding 1.5 mL/min H2O to the renal plasma flow.

of Henle and is deposited in the medullary interstitium. In other words, salt delivery to the medulla by the loop exceeds the delivery of water.

Medullary hyperosmolality is also conserved because most of the water reabsorbed by the connecting tubule and collecting duct during antidiuresis is reabsorbed in the cortex. This appears to be counterintuitive because the osmolality of the urine rises to only 300 mOsm/kg H2O in the cortex, but to 1200 mOsm/kg H2O in the medulla. However, consider the amount of water reabsorbed to achieve these increases in osmolality. Assuming a flow of 12 mL/min into the distal convolution, for the osmolality to rise from 100 mOsm/kg H2O to 300 mOsm/kg H2O, the flow must be reduced by at least two-thirds to 4 mL/min, which flows on into the medullary collecting ducts. This flow into the medulla is actually even less because NaCl is constantly reabsorbed in the cortical collecting tubule and must be accompanied by water in antidiuresis. This would reduce the flow into the medulla by at least another 1 mL/min. If 3 mL/min flows into the medulla and the osmolality rises from 300 mOsm/kg H2O to 1200 mOsm/kg H2O at a final urine flow rate of 0.5 mL/min, then 2.5 mL/min of water must have been reabsorbed. This is about one-third of the 8 mL/min reabsorbed in the cortex to raise the urine osmolality to 300 mOsm/kg H2O. In other words, more water must be reabsorbed to raise the osmolality of a given volume of solution from

FIGURE 9 Example of positive free water clearance resulting in increased concentration of the plasma leaving the kidney. (See Numerical Example box for explanation.)

100 mOsm/kg H2O to 300 mOsm/kg H2O in the cortex than the additional water that must be reabsorbed in the medulla to further increase the osmolality to 1200 mOsm/kg H2O.

It may also seem to be paradoxical that more water may be reabsorbed in the medulla in water diuresis than in antidiuresis. Although the permeability of the medullary collecting duct is very low in the absence of vasopressin, there is a large osmotic gradient between the dilute tubular fluid and the more concentrated medullary interstitium. Because of the larger osmolality difference, despite its very low water permeability more water may be reabsorbed in the medullary collecting duct in water diuresis than in antidiuresis. Furthermore, there is an increase in medullary blood flow during diuresis, and both increased blood flow and increased water entry in diuresis serve to dilute the osmolality of the medullary interstitium during diuresis, as illustrated in Fig. 4 compared to Fig. 3.

### Medullary Blood Flow

Although the loop of Henle delivers more solute than water to the medullary interstitium as discussed earlier, it is still not readily apparent why the blood flow does not simply wash away solutes in the medulla and bring the osmolality back to isosmotic. One reason is that the blood flow is slow through the medulla. Only 5-10% of the renal plasma flow, or an average of about 50 mL/ min, flows into the medulla.

Despite the blood flow, one would still expect that if a capillary bed in the medulla were organized as in other tissues, the interstitium would be diluted. Consider the hypothetical capillary arrangement shown in Fig. 11. In this example, blood is flowing into a capillary bed at a rate of 50 mL/min and has an osmolality of 300 mOsm/ kg H2O. If the capillary bed lies in a tissue region with a hyperosmotic interstitial fluid, one would expect a rapid diffusion of solutes into the isosmotic capillary from the hyperosmotic interstitial fluid, because of the high permeability of the capillary bed. (Little water flow would occur because small solutes exert no osmotic force across the capillary endothelium.) Thus, blood would flow out of the region with an osmolality that would be the same as the hyperosmotic interstitial fluid.

The reason why the renal medulla escapes this type of washout of solute is because of the organization of each capillary into a long loop, called the vasa recta. The blood first flows down the long descending limb of the vasa recta and then returns in a countercurrent flow up the ascending vasa recta. The result of this counter-current flow is shown in Fig. 12. The total blood flow into the medulla is about 50 mL/min, and, for the sake of convenience, assume that the plasma osmolality is 300 mOsm/kg H2O. As this isosmotic fluid flows down the descending limb, it is exposed to the hypertonicity of the medulla. Just as in the capillary shown in Fig. 11, the plasma in the descending vasa recta is concentrated by the entry of NaCl and urea and to a much lesser extent

FIGURE 10 Example of negative free water clearance resulting in dilution of the plasma leaving the kidney. (See Numerical Example box for explanation.)

Capillary Plasma

300 mOsmol/kg H20

Hypothetical Hyperosmotic Interstitial Region

600 mOsmol/kg H20

300 mOsmol/kg H20

600 mOsmol/kg H20

FIGURE 11 Hypothetical equilibration of isosmotic capillary plasma with a hyperosmotic interstitial region. Plasma flowing through a capillary bed in a hyperosmotic region would rapidly gain solutes by diffusion so that, on exiting, it would have the same osmolality as the hyperosmotic region.

600 mOsmol/kg H20

FIGURE 11 Hypothetical equilibration of isosmotic capillary plasma with a hyperosmotic interstitial region. Plasma flowing through a capillary bed in a hyperosmotic region would rapidly gain solutes by diffusion so that, on exiting, it would have the same osmolality as the hyperosmotic region.

the descending limb of the loop of Henle and the medullary collecting duct, the medulla would continuously swell unless net fluid were removed by the blood flow. Consequently, the blood flow out of the medulla is 20-50% higher than the blood flow in, as shown in Fig. 12.

Countercurrent exchange explains how the medullary blood flow is organized so that it does not rapidly wash out the medullary hypertonicity. However, this still leaves the question of how this medullary hyperosmo-lality is generated in the first place. The high concentration of solutes in the medullary interstitium compared with the adjacent tissue of the cortex represents a nonequilibrium distribution of the solutes that requires energy to be maintained. The development and maintenance of the medullary hyperosmolality is a function of the unique permeability properties of the loop of Henle and the active NaCl reabsorptive process in the thick ascending limb of the loop of Henle.

### Countercurrent Multiplication System

Clues to the mechanism involved in medullary concentration came early in this century with the observation that the ability of different mammals to concentrate the urine was correlated with the length of the papilla and, thus, of the loop of Henle. For example, the Australian desert rat mentioned previously has an by the loss of water to the hyperosmotic medulla. Thus, at the tip of a vasa recta, which extends to the papillary tip, the osmolality would be 1200 mOsm/kg H2O and the plasma flow rate would be somewhat less than 50 mL/min.

The blood flow then reverses direction at the tip of the vasa recta and proceeds back up through the less concentrated regions of the medulla. As it flows upward through the medulla, NaCl and urea diffuse from the capillary into the interstitium and some water is regained from the less concentrated medullary intersti-tium. For this reason, solute recirculates in loops within the medullary interstitium, first entering the descending limb of the vasa recta and then exiting from the ascending limb as the blood flows back upward.

The process just described is referred to as a countercurrent exchange. However, it is not perfectly efficient. The osmolality of the blood flowing out of the ascending vasa recta into the cortex is still hyperosmotic to the normal plasma, but much less so than it was at the tip of the vasa recta. The rate of blood flow out of the ascending vasa recta is also more rapid than the flow in. This is a necessary consequence of mass balance. Because fluid is constantly being delivered to the medullary interstitium by water lost in

Capillary Plasma

50 ml/min

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