The units of renal clearance are often confusing to the first-time reader, so let us be sure of the meaning. First, the units are volume per time (not amount of a substance per time). The volume is the volume of plasma that supplies the amount excreted in a given time. For example, suppose each liter of plasma contains 10 mg of a substance X, and 1 mg of substance X is excreted in 1 hour. Then 0.1 L of plasma supplies the 1 mg that is excreted, that is, the renal clearance is 0.1 L/h. The reader should appreciate that removing all of a substance from a small volume of plasma is equivalent to removing only some of it from a larger volume, which is actually the way the kidneys do it. If all of substance X is removed from 0.1 L in 1 hour, this is equivalent to removing half of it from 0.2 L, or one quarter of it from 0.4 L, and so on. The clearance is 0.1 L/h in all these cases.
These concepts are illustrated in Figure 3–1. As the kidneys clear a substance, plasma leaving the kidney in the renal vein has a lower concentration of the substance than does plasma entering the kidney in the renal artery. This is equivalent to dividing the plasma into sequential segments in which all of the substance is removed from some segments and none from others.
Renal clearance. When plasma is cleared of a solute, the solute concentration in venous plasma leaving the kidney is lower than in arterial plasma entering the kidney, as shown in the upper part of the figure. This is equivalent to dividing the plasma into segments in which all the solute is removed from some segments and none from others, as shown in the bottom of the figure. The volume of plasma from which all the solute has been removed, when expressed on a time basis, is the clearance of the solute in units of volume per time.
The general meaning and specific renal meaning of clearance are illustrated by comparing how the body handles 2 substances with similar-sounding names but very different properties: inulin and insulin. Insulin is the familiar pancreatic hormone involved in regulating blood glucose. It is a protein with a molecular weight of 5.8 kD and is small enough to be freely filtered by the glomerulus. Once in Bowman's space, it moves along with every other filtered substance into the proximal convoluted tubule, where it is largely taken up by endocytosis and degraded into its constituent amino acids. Very little insulin escapes this uptake, and very little of the filtered insulin makes it all the way to the urine. Thus, the kidney takes part in clearing insulin from the blood, but because so little appears in the urine, the specific renal clearance is very low (<1 mL/min). However, the body has additional mechanisms for clearing insulin, and its metabolic clearance rate is quite high (half-life less than 10 minutes). Let us contrast this with inulin. Inulin is a polysaccharide starch of about 5-kD molecular weight that is not usually found in the body. Like insulin, it is freely filtered by the glomerulus, but it is not reabsorbed or secreted by the nephron. All the inulin that is filtered flows through the nephron and appears in the urine. Thus, the renal clearance of inulin is relatively large. Inulin in the blood is not taken up by other tissues, and the kidneys are the only excretion route. As we will see, this makes inulin a very special substance for measuring GFR.
Clearance measures the volume of plasma from which all of the substance is removed and excreted in a given time.
Quantification of Clearance
Consider again a substance X that is excreted in the urine. How do we actually calculate its clearance in the proper units? The amount of X removed from plasma in a given time equals the amount excreted in the urine in that same time. The amount removed from the plasma in a given time is the product of the volume of plasma cleared per unit time (Cx) and the plasma concentration (Px) (Equation 3-1). That same amount now appearing in the urine during this time is the product of the urine flow rate (V) and the urine concentration of X (Ux) (Equation 3-2). We equate these quantities in Equation 3-3 and rearrange to solve for clearance in Equation 3-4 expressed in the proper units—volume per time.
While addressing the quantification of clearance, note that the product of urine flow rate and urine concentration of X (Equation 3-2) is the excretion rate. Therefore, we can also state that the clearance of substance X is the excretion rate divided by the plasma concentration.
Let us now examine the clearance of several substances important for the quantification of renal function, starting with inulin. Inulin, as described previously, is a polysaccharide that is freely filtered and neither reabsorbed nor secreted. Thus, once filtered, it must flow through the nephron into the urine (Figure 3–2). The volume of plasma cleared of inulin is the volume filtered. Therefore, inulin clearance equals the GFR. Inulin clearance is indeed the hallmark experimental method of measuring the GFR.
Renal handling of inulin. All filtered inulin is excreted. Since the volume of plasma cleared of inulin is the volume filtered, the inulin clearance equals the GFR.
Can something have a clearance greater than the GFR? Indeed, yes. One such substance is para-aminohippurate (PAH). This is a small (molecular weight of 194 D) water-soluble organic anion not normally found in the body, but that is used experimentally. It is freely filtered and also avidly secreted by the proximal tubule epithelium. Therefore, much more is removed than just that which is filtered. The secretion rate is saturable. (That is, there is a maximum rate of PAH secretion into the tubule. Such a tubular maximum, or Tm, is common in transport systems [see Chapter 4].) However, at low plasma concentrations, almost all of the PAH entering the kidney is removed from the plasma and excreted in the urine. Its clearance, therefore, is nearly as great as the renal plasma flow. In fact, the PAH clearance can be used experimentally as a measure of renal plasma flow, usually called the effective renal plasma flow to indicate that its value is slightly less than the true renal plasma flow.
What can the clearance of any freely filtered substance tell us? If we know the GFR (as assessed from inulin clearance) and the clearance of the substance, then any difference between its clearance and GFR represents net secretion or reabsorption (or, in a few rare cases, renal synthesis). If the clearance is greater than the GFR, there must have been net secretion, whereas a clearance less than the GFR indicates net reabsorption. If the clearance of a substance exactly equals the GFR, then there has been no net reabsorption or secretion. The word net in this description is important because, as we will see in later chapters, a number of substances are reabsorbed in certain regions of the nephron and secreted in other regions. The net result of these processes is the sum of everything that happens along the nephron. Of course, if a substance is not freely filtered, low clearance may simply indicate that little of the substance entered the tubule in the first place.
Creatinine clearance is the common method to measure GFR.
A Practical Method of Measuring GFR: Creatinine Clearance
The gold standard for measuring GFR is the inulin clearance, and this method is used in research studies. The method is cumbersome, however, because inulin must either be infused at a rate sufficient to keep its plasma concentration constant during the period of urine formation and collection, or there must be multiple samplings and a complex regression analysis. For routine assessment of GFR in patients, there is a much easier method: creatinine clearance. Creatinine is an end product of creatine metabolism and is exported into our blood continuously by skeletal muscle. The rate is proportional to skeletal muscle mass, and to the extent that muscle mass is constant in a given individual, the creatinine production is constant. Creatinine is freely filtered and not reabsorbed. A small amount, however, is secreted by the proximal tubule. Therefore, the creatinine appearing in the urine represents a filtered component (mostly) and a much smaller secreted component. Because of the secretion, creatinine clearance is slightly higher than the GFR, normally by about 10% to 20%. For routine assessment of GFR, this degree of error is acceptable. How does one measure creatinine clearance? Usually, a patient's urine is collected for 24 hours, and a blood sample is taken sometime during the collection period. Blood and urine are assayed for creatinine concentration, and we apply the clearance formula (Equation 3-4) to yield creatinine clearance.
Plasma creatinine concentration varies inversely with GFR and is a practical indicator of how well the kidneys are filtering.
For a patient with a very low GFR, the secreted component is a relatively larger fraction of the total amount excreted; therefore, the creatinine clearance more severely overestimates GFR in patients with a very low GFR than in those with higher GFR values. Nevertheless, because of low cost and convenience, creatinine clearance continues to be the most common method for routine assessment of patient GFR and the integrity of renal filtration.
Plasma Creatinine to Estimate GFR
Although creatinine clearance is a valuable clinical determinant of GFR, in routine practice, it is far more common to measure plasma creatinine alone and to use this as an indicator of GFR. If we ignore the small amount secreted, there should be an excellent inverse correlation between plasma creatinine concentration and GFR (Figure 3–3).
Steady-state relation between plasma creatinine and GFR for a person with a normal creatinine production. When GFR is low, plasma creatinine rises to high levels, making plasma creatinine a convenient indicator of GFR.
A healthy person's plasma creatinine concentration is about 1 mg/dL. It remains stable because the amount of creatinine excreted is equal to the amount of creatinine produced each day. Suppose one day, the GFR suddenly decreases by 50% because of an obstruction in the renal artery. On that day, the person filters only 50% as much creatinine as normal. Therefore, creatinine excretion is also reduced by 50%. (We are ignoring the small contribution of secreted creatinine.) Assuming no change in creatinine production, the person transiently goes into positive creatinine balance, and the plasma creatinine increases. However, despite the persistent 50% GFR reduction, the plasma creatinine does not continue to rise indefinitely; rather, it stabilizes at 2 mg/dL (ie, after it has doubled). At this point, the person once again is able to excrete creatinine at the rate it is produced and so goes back in balance with a stable plasma level. The 50% GFR reduction has been just offset by the doubling of plasma creatinine concentration, restoring the filtered load of creatinine to normal. To illustrate this point, assume an original daily filtration volume of 180 L (1800 dL).
In the new steady state, creatinine excretion is normal, even though the plasma concentration has doubled (the person is in balance). In other words, creatinine excretion is below normal only transiently until plasma creatinine has increased as much proportionally as the GFR has fallen.
What if the GFR then decreased to 300 dL/day? Again, creatinine retention would occur until a new steady state had been established (ie, until the person was again filtering 1800 mg/day). What would the new plasma creatinine be?
The increase in plasma creatinine results directly from the decrease in GFR. Therefore, plasma creatinine gives a reasonable indication of GFR. It is not completely accurate, however, for several reasons: (1) as before, some creatinine is secreted; (2) an original creatinine measurement when GFR was normal may not be available for comparison; (3) creatinine production may not remain completely unchanged. However, an increasing plasma creatinine is a red flag that there may be a renal problem.
A common method to quantify creatinine clearance based on plasma concentration uses a formula known as the Cockcroft-Gault formula (Equation 3-9). The formula includes plasma creatinine, age, body weight, and gender. For a 20-year-old 70-kg male with a plasma creatinine of 1.0 mg/mL, the formula predicts a creatinine clearance of 117 mL/min. The age factor in the Cockcroft-Gault formula shows the normal reduction in renal function as a person gets older. It predicts a decline in creatinine clearance of 33% as a person ages from 20 to 60 years old. The use of this formula, or any of several others that have been derived over the years, while subject to error, is still useful as a guide where a precise clearance value is not really needed.
Finally, because urea is also handled by filtration, the same type of analysis suggests that the measurement of plasma urea concentration could also serve as an indicator of GFR. However, it is a much less accurate indicator than plasma creatinine because the range of normal plasma urea concentration varies widely, depending on protein intake and changes in tissue catabolism, and because urea excretion is under partial hormonal regulation.