**2. Clearance concept and ideal marker for glomerular filtration rate**

The history of the renal physiology is deeply influenced by the book published by Homer W. Smith in 1951 (Figure 1) : « The kidney: structure and function in health and disease »(Smith, 1951b). In this best-seller of nephrology, Smith compiled all the physiological data (more than 2300 references) which have been published in the scientific literature until 1951. Smith, himself, has largely contributed to the physiological knowledge of the kidney. A large part of this book is dedicated to the GFR measurement. The concept of clearance is well explicated. Actually, the Danish physiologist, Poul Brandt Rheberg was the first to use and define the concept of clearance in 1926 even if this author did not use the word "clearance". Rheberg studied on himself the urea and creatinine clearances to prove that kidney has a filtrating and not only a secreting action (Rehberg, 1926b; Rehberg, 1926a). The term clearance was used for the first time by Möller in 1929 and was then concerning the urea clearance which was proposed as the first evaluation of renal function (Möller et al., 1929). Smith has largely contributed to make popular and classical this concept of clearance to assess GFR (Smith, 1951a). Renal clearance of a substance is defined as the volume of plasma cleared from this substance per time unit (mL/min). Clearance is thus a virtual volume but will permit to apprehend GFR and renal function. However, the concept of clearance is applicable to any internal or external substances. To be considered as a reference method, a marker must have strict physiological characteristics (Smith, 1951b):

<sup>1.</sup> Marker production and marker plasma concentration must be constant if GFR does not change

How Measuring Glomerular Filtration Rate? Comparison of Reference Methods 23

GFR=([U] x V) / [P] (where [U] = urinary concentration, [P] = plasma concentration, V = urinary volume) The calculated value will be then divided by the time interval where the urine collection has been made. *Sensu strict,* the plasma concentration must be sampled from arterial blood but errors induced by venous samples are very limited (Laake, 1954; Handelsman & Sass, 1956; Nosslin, 1965). In the same view, the transit time through the urinary system should also be taken into consideration but, once again, error linked to this transit time is negligible (Ladegaard-Pedersen, 1972; Nosslin, 1965). The method originally proposed by Smith for measuring GFR is not an easy task. Actually, the marker (inulin see below) must be intravenously injected and then perfused at a constant rate to reach stable plasma concentrations. Thereafter, urine collection must be realized, which is a potential source of errors. For this reason, Smith recommended urine collection on 10 and 15 minutes with the use of urinary catheter. Smith recommended three successive collections. The patient was hydrated to assume a sufficient urinary flow though these collections. The mean of the three collection was considered as the GFR measurement (Smith, 1951a). Nowadays, the urine collections are done without urinary catheter and on a longer period of time (60 minutes) to decrease the impact of

The renal clearance will be easily calculated with the following equation:

urine collection errors on the final result (Levey et al., 1991; Robson et al., 1949).

limitations both from an analytical and clinical point of view.

**3. Inulin** 

The ideal marker does not exist in the organism (or has still not been discovered if we want to be optimistic). Both urea and creatinine clearance have strong limitations, notably because creatinine is secreted and urea is absorbed by renal tubules (Dodge et al., 1967; Morgan et al., 1978). Therefore, exogenous markers are used to measure GFR. We will successively describe the markers which are still used in clinical practice in 2011: inulin, 51Cr-EDTA, 99Tc-DTPA, iothalamate and iohexol. For every marker, we will describe strengths and

Inulin is still considered nowadays as the gold standard to measure GFR. Smith has deeply studied this marker and makes it the most popular. Inulin is a polymer of fructose which is found in some plants which uses it as energy provider in place of amidon. Its molecular weight is 5200 Da (Gaspari et al., 1997). Some plants are especially rich in inulin: chicory, garlic, leek and Jerusalem artichoke. Humans are not able to metabolize inulin. Because inulin is the first reference method to have been used, its role in the GFR measurement has only be asserted on basis of physiological studies (because the first method is not comparable to any other !). Once again, we often refer to the studies published by Smith and Shannon (New York university)(Smith, 1951a; Smith, 1951c) and by another pioneer Richards (Philadelphia university)(Richards et al., 1934). Inulin was obviously considered as a safe product with any effect on GFR (Shannon, 1934). Inulin is freely filtrated through a semi-permeable membrane which is a strong argument for the absence of binding to protein. This has been shown by Shannon in 1934 (Shannon, 1934) and by Richards in 1937 (Hendrix et al., 1937). In the same publication, Richards proved that inulin was freely and fully filtrated through the glomerulus because he measured the same inulin concentration both in the plasma and the glomerulus of a frog and a salamander (Hendrix et al., 1937). The absence of both tubular absorption and secretion has been demonstrated by an important article published by Shannon in 1934 (Shannon, 1934). In this article, this author showed the


Table 1. Creatinine-based equations. SCr: Serum Creatinine, GFR: glomerular filtration rate, MDRD: Modified diet in renal disease, CKD-EPI: Chronic Kidney Disease-Epidemiology group.

Fig. 1. Homer W. Smith

The renal clearance will be easily calculated with the following equation:

#### GFR=([U] x V) / [P]

(where [U] = urinary concentration, [P] = plasma concentration, V = urinary volume)

The calculated value will be then divided by the time interval where the urine collection has been made. *Sensu strict,* the plasma concentration must be sampled from arterial blood but errors induced by venous samples are very limited (Laake, 1954; Handelsman & Sass, 1956; Nosslin, 1965). In the same view, the transit time through the urinary system should also be taken into consideration but, once again, error linked to this transit time is negligible (Ladegaard-Pedersen, 1972; Nosslin, 1965). The method originally proposed by Smith for measuring GFR is not an easy task. Actually, the marker (inulin see below) must be intravenously injected and then perfused at a constant rate to reach stable plasma concentrations. Thereafter, urine collection must be realized, which is a potential source of errors. For this reason, Smith recommended urine collection on 10 and 15 minutes with the use of urinary catheter. Smith recommended three successive collections. The patient was hydrated to assume a sufficient urinary flow though these collections. The mean of the three collection was considered as the GFR measurement (Smith, 1951a). Nowadays, the urine collections are done without urinary catheter and on a longer period of time (60 minutes) to decrease the impact of urine collection errors on the final result (Levey et al., 1991; Robson et al., 1949).

The ideal marker does not exist in the organism (or has still not been discovered if we want to be optimistic). Both urea and creatinine clearance have strong limitations, notably because creatinine is secreted and urea is absorbed by renal tubules (Dodge et al., 1967; Morgan et al., 1978). Therefore, exogenous markers are used to measure GFR. We will successively describe the markers which are still used in clinical practice in 2011: inulin, 51Cr-EDTA, 99Tc-DTPA, iothalamate and iohexol. For every marker, we will describe strengths and limitations both from an analytical and clinical point of view.

#### **3. Inulin**

22 Basic Nephrology and Acute Kidney Injury

2. Marker must be free in plasma (not binding to protein) and must be freely and fully

Table 1. Creatinine-based equations. SCr: Serum Creatinine, GFR: glomerular filtration rate, MDRD: Modified diet in renal disease, CKD-EPI: Chronic Kidney Disease-Epidemiology

filtrated through the glomerulus

group.

Fig. 1. Homer W. Smith

4. Marker must be inert and, of course, not toxic

3. Marker is neither secreted nor absorbed by renal tubules

5. Marker excretion must be exclusively excreted by kidneys 6. Marker must be easily measured in both plasma and urine

> Inulin is still considered nowadays as the gold standard to measure GFR. Smith has deeply studied this marker and makes it the most popular. Inulin is a polymer of fructose which is found in some plants which uses it as energy provider in place of amidon. Its molecular weight is 5200 Da (Gaspari et al., 1997). Some plants are especially rich in inulin: chicory, garlic, leek and Jerusalem artichoke. Humans are not able to metabolize inulin. Because inulin is the first reference method to have been used, its role in the GFR measurement has only be asserted on basis of physiological studies (because the first method is not comparable to any other !). Once again, we often refer to the studies published by Smith and Shannon (New York university)(Smith, 1951a; Smith, 1951c) and by another pioneer Richards (Philadelphia university)(Richards et al., 1934). Inulin was obviously considered as a safe product with any effect on GFR (Shannon, 1934). Inulin is freely filtrated through a semi-permeable membrane which is a strong argument for the absence of binding to protein. This has been shown by Shannon in 1934 (Shannon, 1934) and by Richards in 1937 (Hendrix et al., 1937). In the same publication, Richards proved that inulin was freely and fully filtrated through the glomerulus because he measured the same inulin concentration both in the plasma and the glomerulus of a frog and a salamander (Hendrix et al., 1937). The absence of both tubular absorption and secretion has been demonstrated by an important article published by Shannon in 1934 (Shannon, 1934). In this article, this author showed the

How Measuring Glomerular Filtration Rate? Comparison of Reference Methods 25

physiological studies exist for some markers) but by studies comparing these markers with inulin. Unhopefully, most of these studies comparing different GFR tests lack of strong statistical methodology. Actually, most of the authors have only shown a good correlation between the markers, which is expected but not sufficient. Ratio of new markers results on inulin results are also used (the result being considered as good if ratio is near to 1). The use of such ratio may be misleading (for example, if one method overestimates true GFR in low GFR levels but underestimates GFR in high levels, the ratio will be near to 1 although the method is actually not precise enough). To compare the performance of a new GFR measurement compared to inulin, we need to know the bias (mean difference between the two results) and the precision (standard deviation (SD) around the bias) of this new measurement. Bland and Altman analysis is thus required

Regarding the other GFR markers, we must also stress that GFR can be measured by plasma clearance and using a bolus injection (instead of constant infusion rate) which makes the GFR measurement much more simple. Method to measure GFR by plasma clearances can be very different (number of samples, timing of samples, mathematical model used). We must keep in mind that results of plasma and urinary clearances are not strictly comparable (plasma clearances overestimate urinary clearances even if the overestimation decreases if plasma samples are drawn after 24 hours) and this must be integrated when these GFR

51Cr-EDTA is an isotopic marker which has a low molecular weight (292 Da). Most of the authors consider that 51Cr-EDTA is not binding to proteins (<0,5% (Brochner-Mortensen, 1978; Bailey et al., 1970; Garnett et al., 1967; Stacy & Thorburn, 1966; Forland et al., 1966; Kempi & Persson, 1975; Forland et al., 1966)) even if Rehling described a binding to protein of 10% (Rehling et al., 1995; Rehling et al., 2001). Due to its low molecular weight, 51Cr-EDTA is freely filtrated through the glomerulus. Physiological studies about renal handling of 51Cr-EDTA are few but it seems that 51Cr-EDTA is neither secreted nor absorbed by renal tubules (Eide, 1970). This absence of secretion and absorption is also confirmed by Forland in dogs (Forland et al., 1966). Regarding the potential extra-renal excretion of 51Cr-EDTA, Garnett described a salivary and a fecal excretion under 1% in one anephric patient (Garnett et al., 1967). Brochner-Mortensen later confirmed the poor fecal excretion (less than 0.1% of the injected dose). Studying the renal excretion and the corporal global radioactivity of 8 healthy subjects after 72 hours, Brochner-Mortensen estimated that 4.5% of the 51Cr-EDTA will be retained in the body, especially in the liver and kidneys (Brochner-Mortensen et al., 1969). The difference between 51Cr-EDTA total clearance and 51Cr-EDTA urinary clearance corresponds to extra-renal clearance of the marker. With this methodology, the same authors estimated extra-renal clearance at 4 mL/min (and this extra-renal clearance remains stable for all GFR ranges)(Brochner-Mortensen & Rodbro, 1976). Jagenburg had also calculated an extra-renal clearance of 2 mL/min in two anuric dialysis patients (Jagenburg et al., 1978). Only, Rehling described a

Measurement of 51Cr-EDTA by nuclear count is very precise and easy because 51Cr-EDTA half time is long (27 days)(Chantler et al., 1969). The quantity of 51Cr-EDTA injected is

methods are compared (Agarwal et al., 2009; Stolz et al., 2010).

**5. 51Cr-EDTA (Ethylenediaminetetra-acetic acid)** 

higher extra-renal clearance at 8.4% (Rehling et al., 1995).

**5.1 Physiological and analytical data** 

(Bland & Altman, 1986).

absence of inulin excretion in two types of aglomerular fishes (goosefish, *Lophius piscatorius*  and toadfish *Osteichthyes - Lophiidae*). In the same article, Shannon measured GFR by inulin clearance in another type of fish with glomerulus, the dogfish (*Chondrichthyes* – *Squalidae*). These fishes were then treated with phlorizin which was sensed to block all tubular activity. Although the creatinine clearance in this fish was increased, the inulin clearance was not modified by this treatment (Shannon, 1934). In the same year of 1934, inulin clearance was also measured in aglomerular fish and in dogs by Richards (Richards et al., 1934). The experimentation (measuring GFR with and without phlorizin) was then repeated in man by Smith and Shannon. The results obtained in animals were confirmed in humans. Shannon was the first human who was perfused by inulin in 1935 (Shannon & Smith, 1935; Smith, 1951c). These authors had thus suggested that inulin was not secreted by renal tubules. This assertion will be thereafter confirmed by other authors with the same type of methodology (Shannon & Smith, 1935; Alving et al., 1939; Laake, 1954). Additional arguments were developed in the sixties by animal studies using micropontions in the tubules (Gutman et al., 1965). After intravenous injection, inulin is fully excreted by kidneys in urine (Shannon & Smith, 1935), even if very low concentrations of inulin are found in bile (Höber, 1930; Schanker & Hogben, 1961).

Inulin is doubtless the marker who has been the most investigated from a physiological point of view. In this view, it is logical that inulin is still considered as the gold standard for GFR measurement. Nevertheless, there are limitations to its use in daily practice. Because its relatively high molecular weight (5200 Da), the molecule is relatively viscous and don't quickly reach its volume of distribution. Therefore, only methods using urinary clearance with constant infusion rate seem accurate for this marker. Such methods are more cumbersome. Moreover, inulin is not easily available on the market and remains relatively costly. From our point of view, the most important limitation of inulin is the difficulty linked to its measurement in urine and plasma. Actually, several methods have been proposed and these methods are probably not interchangeable. There is no standardization in inulin measurement. We have shown that GFR results could vary from -10 to +10 mL/min in the same patient only because inulin was measured by a different method (unpublished data). Moreover, most of the methods (except the enzymatic ones) are prone to interferences with glucose measurement which is a limiting factor when measuring GFR in diabetic patients (Little, 1949). Regarding the methods for measuring inulin, we can cite the "acid" methods (Kuehnle et al., 1992; Shaffer & Somogoyi, 1933; Alving et al., 1939; Corcoran, 1952; Rolf et al., 1949; Roe, 1934; Steinitz, 1938; Hubbard & Loomis, 1942; Lentjes et al., 1994; Heyrovsky, 1956; Rolf et al., 1949), the enzymatic methods (Day & Workman, 1984; Delanghe et al., 1991; Jung et al., 1990; Summerfield et al., 1993; Dubourg et al., 2010) and the new methods by high performance liquid chromatography (HPLC) (Ruo et al., 1991; Baccard et al., 1999; Dall'Amico et al., 1995; Pastore et al., 2001). Describing these methods in detail are beyond the scope of this chapter and we propose the readers the following reference if they are interested in this topic (Delanaye et al., 2011b).
