Measuring and estimating glomerular filtration rate in children

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1 DOI /s x EDUCATIONAL REVIEW Measuring and estimating glomerular filtration rate in children Hans Pottel 1 Received: 28 January 2016 /Revised: 8 March 2016 /Accepted: 8 March 2016 # IPNA 2016 Abstract Glomerular filtration rate (GFR) is the best index for kidney function in health and disease. Knowledge of the GFR is essential for the detection (diagnosis) and monitoring of renal function during disease progression and for ensuring correct medication doses. Inulin clearance (plasma or urine) is currently considered to be the gold standard for measuring GFR, but in clinical practice the measurement of other exogenous filtration markers from the plasma often replaces that of inulin clearance. Different protocols can be used to determine the area under the plasma disappearance curve, and an understanding of these methods is important. GFR can also be estimated by GFR equations (egfr), which are most often used in clinical practice because they only require a knowledge of the serum creatinine or cystatin C level and demographic information. egfr equations are easy to use but they do have their limitations, and it is important to know how these equations were derived and in which circumstances they can be used most accurately. The aim of this review is to explain how GFR can be measured using the renal clearance and the plasma clearance method and which egfr equations can be applied to children, as well as how and when these equations can be used in clinical practice. Keywords Glomerular filtration rate. Children. Adolescents. Direct measurement. Estimating equations * Hans Pottel Hans.Pottel@kuleuven-kortrijk.be 1 Department of Public Health and Primary Care, Campus Kulak Kortrijk, KU Leuven, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium Introduction Glomerular filtration rate (GFR) describes the flow rate of filtered fluid through the kidney [1]. It is the volume of plasma cleared from a specific substance per time unit and is typically expressed in milliliters per minute. In most cases, this value is indexed for the body surface area (BSA) and thus expressed in milliliters per minute per 1.73 m 2. To obtain the GFR in these units, the GFR is expressed in milliliters per minute and then multiplied by 1.73/BSA. At the beginning of the 20th century the value of 1.73 m 2 was considered to be the BSA of the average 25-year-old American [2]. A value of 1.95 m 2 would probably be more appropriate for the average BSA of today s 25-year-old adult, but switching from 1.73 m 2 to 1.95 m 2 has severe repercussions for the current classification system for chronic kidney disease [3] which is based on fixed limits that are expressed in milliliters per minute per 1.73 m 2.TheDuBoisandDu Bois BSA equation, which dates from 1916, calculates BSA from weight in kilograms (Wt) and height in centimeters (Ht) (BSA = Wt Ht )and is still widely used to normalize physiological parameters [4]. However, it has been shown that for children weighing <10 kg, the Du Bois formula does not give the best results [5]. For the specific pediatric group, the formulas of Haycock et al. [6] (BSA = Wt Ht ) or Mosteller [7] (BSA=(Wt 0.5 Ht 0.5 )/60) are preferred. It is important to note that a number of researchers have questioned the indexation of BSA to GFR, proposing alternative indexations, such as height, squared height, total body water or extracellular fluid volume (ECV). Indexing for BSA is particularly problematic in obese or anorectic children. ECV may be a more

2 appropriate choice than BSA, even in cases of extreme body shape and volume [2]. It may also be advisable to express GFR in milliliter per minute or to de-index estimated GFR (egfr) predictions for the follow-up of these particular cases with extreme body weight. The focus of this review article is the measurement and estimation of GFR. All current egfr equations have been designed for GFR indexed with BSA, and this controversial topic is beyond the scope of this article. For more information on this topic, the interested reader is referred to the article of Hoste and Pottel [2] andreferences therein. Measuring GFR Filtration markers The ideal assessment of renal function or GFR should be accurate, simple, safe and cost-effective. However, direct measurement of GFR is impossible because the filtration process simultaneously takes place in millions of glomeruli. Instead, methods that record the clearance of an ideal filtration marker or exogenous substance are used. Inulin, a 5200-Da inert, uncharged polymer of fructose is the only known ideal filtration marker. Classic inulin clearance during the continuous infusion of carefully timed collections of plasma and urine samples is considered to be the gold standard method for measuring GFR. Because inulin is the first reference method to have been used, its role in GFR measurement has only been asserted on the basis of (numerous) physiological studies. Nevertheless, there are limitations to its use in daily clinical practice as the molecule is difficult to handle, and the procedure described by Homer Smith [8] is invasive. This procedure includes fasting conditions in the morning, a continuous intravenous infusion, multiple clearance periods requiring repetitive blood and urine collections over 3 h, oral water loading to stimulate diuresis, bladder catheterization to ensure complete urine collection and careful timing of blood sampling at the midpoint of the urine collection. Moreover, inulin clearance is not practical for routine clinical purposes because of expense, limited commercial sources, restricted availability of automated laboratory methods for inulin determination in plasma and urine samples and the need for constant supervision during the procedure. Therefore, in clinical practice and research, other (exogenous) clearance markers and methods are being used [9, 10]. The ideal filtration marker must have strict physiological characteristics: it must be freely and fully filtered through the glomerulus, neither secreted nor absorbed by the renal tubules, not bound to plasma protein, not metabolized by the renal tubules, inert and not toxic, exclusively excreted by the kidneys, easily measured in both plasma and urine, preferably inexpensive and easily available on the market. The markers commonly employed for GFR measurement include radiopharmaceuticals, such as chromium 51-labeled ethylenediaminetetraacetic acid ( 51 Cr-EDTA), technetium 99-labeled diethylenetriaminepentaacetic acid ( 99m Tc-DTPA), iodine 125-labeled iothalamate ( 125 I-iothalamate), and radiographic contrast agents, such as iohexol and non-radiolabeled iothalamate. Strengths and limitations of the most commonly used exogenous markers are presented in Table 1 [9, 11]. Supportive scientific evidence for the sufficient accuracy of direct measurements of GFR in comparison with the gold standard (continuous infusion of inulin) is presented in Table 2 [12]. The most common method used to measure GFR in clinical practice is the measurement of endogenous creatinine clearance, but this measurement may be difficult to obtain or fraught with error. There is strong scientific evidence that endogenous creatinine clearance as a direct GFR measurement has insufficient accuracy [12]. In actual fact, the ideal marker in the body (endogenous) does not exist: creatinine is secreted by the renal tubules and urea is absorbed by the renal tubules. Essentially, there are two approaches for direct GFR assessment: renal clearance and plasma clearance methods, which can be used for most exogenous filtration markers. The advantages and disadvantages of both procedures are listed in Table 3. Renal clearance procedure Renal clearance is the most direct method for measuring the GFR. Clearance is computed as the urine concentration ([U] in mg/ml) of the exogenous filtration marker, multiplied by the volume of the timed urine sample (V in ml/min) and divided by the average plasma concentration ([P] in mg/ml) during the same time period [13]: GFR ¼ ½U V ½P expressed in milliliters per minute. Multiple (2 4) 20- to 30-min urine collections are obtained after administration of the marker. Blood samples are drawn in between urine collections, and both urine and blood samples are analyzed in the laboratory to determine the concentration of the filtration marker. The main advantage of this procedure is its relatively short duration. The main disadvantage is the need for urine collections, which may

3 Table 1 Strengths and limitations of exogenous markers for direct measurement of glomerular filtration rate a Marker Molecular weight (Da) Strengths Limitations Inulin 5200 Gold standard Expensive and not easily available on the market No side effects Difficult to dissolve and maintain into solution No standardized method to measure inulin in plasma and urine Iothalamate 637 Inexpensive Probable tubular secretion Long half-life Storage of radioactive substances when 125 I used as tracer Use of non-radioactive iothalamate requires expensive assay No use in patients with iodine allergy Iohexol 821 Not radioactive Possible tubular reabsorption or protein binding Inexpensive Low dose requires expensive assay Low dose possible No use in patients with iodine allergy Standardized Risk for allergic reactions at high doses 51 Cr EDTA 292 Inexpensive Probable tubular reabsorption Accurate measurement Must be measured in the nuclear medicine department Easy available in Europe Not approved by Federal Drug Administration (only available in Europe) Long half-life/low dose Storage of radioactive material 99m Tc DTPA 393 Widely available in USA Storage and disposal of radioactive material Accurate measurement Low radiation dose Cheap and easily available Must be measured in the nuclear medicine department No standardization Dissociation and protein binding MW, Molecular weight; 51 Cr EDTA, chromium 51-labeled ethylenediaminetetraacetic acid; 99m Tc DTPA, technetium 99-labeled diethylenetriaminepentaacetic acid a Measurements complied from Delanaye 2012 [9] and Stevens and Levey 2009 [11] be difficult in populations with impaired urinary incontinence or retention, such as the elderly or children and which increases risk for error caused by incomplete urine collections. The marker is administered by intravenous bolus or bolus subcutaneous injection. Subcutaneous injection allows for a slower release of the marker into the circulation and more constant plasma levels [11]. Alternatively, the filtration marker may be administered using continuous intravenous or subcutaneous infusion. Plasma clearance procedure To avoid inconvenience and errors from timed urine collections and because of the increasing importance of measuring GFR in the aging population, interest in measuring GFR using plasma clearance is steadily increasing. GFR is calculated from plasma clearance after a bolus intravenous injection of an exogenous filtration marker or tracer. Let us suppose that M(t) is the mass of the tracer cleared from the plasma at time t, expressed in milligrams per minute, then ΔM/Δt is the elimination rate (in mg/min) of that substance, and in the limit for Δt 0, this elimination rate can be written as the differential dm/dt. If we further suppose that c(t) is the concentration of the substance, expressed in milligrams per milliliter, in the plasma at time t, then Table 2 Accuracy of direct glomerular filtration rate measurements a Marker Sufficient accuracy Scientific evidence b Inulin Renal clearance Yes ++++ Plasma clearance Yes ++ Iothalamate Renal clearance Yes ++++ Plasma clearance + 51 Cr-EDTA Renal clearance Yes +++ Plasma clearance Yes m Tc-DTPA Renal clearance Yes ++ Plasma clearance No ++ Iohexol Renal clearance Yes ++ Plasma clearance Yes +++ a Reproduced from Soveri et al [12], used with permission) b++++ strong evidence, +++ moderately strong evidence, ++ limited evidence, + insufficient evidence

4 the GFR can be defined as the ratio between the elimination rate and the concentration at time t: GFR ¼ dm=dt ct ðþ By integrating the above equation, we have GFR ¼ lim Z t 0 Mt ðþ ct ðþdt ¼ injected Dose Area Under the Curve After an infinite time, the tracer has completely disappeared from the body, and M(t) will be equal to the injected dose and the integral in the formula above will be equal to the area under the concentration time curve (AUC). The decline in serum levels is secondary to the immediate disappearance of the marker from the plasma into its volume of distribution (fast component) and to renal excretion (slow component). Two-compartment model This decline in serum levels is best estimated using a two-compartment model [14] that requires blood sampling early (usually 3 time-points up to 60 min after administration) and late (3 4 four time-points from 120 min forward). Most filtration markers need about 1 2 h to complete the mixing process with the extracellular fluid. This combination of mixing and clearance Table 3 Advantages and disadvantages of various renal and plasma clearance procedures Advantages Renal clearance Gold standard method (inulin) Spontaneous bladder emptying Patient comfort Less invasive Plasma clearance No urine collection needed Potential for higher precision GFR, glomerular filtration rate Disadvantages Invasive bladder catheter may be required Possibility of incomplete bladder emptying Difficult to apply in children No standardized protocol Variable number of plasma samples Variable time-points Different correction protocols for slow GFR Inaccuracy with one-sample technique Longer duration required for low GFR process results in a double exponential decay, where the fast component is a combination of mixing and clearance and the slow component is clearance only. We thus describe c(t) by a double exponential decay: ct ðþ¼aexpð αtþþbexpð βtþ From the curve-fitting procedure, the parameters A, α, B and β are obtained. The area under this curve is A/α +B/β. The GFR is thus defined as GFR ¼ Dose= ½A=α þ B=β The concentration at time t =0 is c(0)=a+b, and this is also equal to Dose/V, with V being the distribution volume. Consequently, from the parameters A, B and the injected dose, the distribution volume V = Dose/(A + B) can be calculated. This procedure can be illustrated with the following example. After an intravenous bolus injection of iohexol (dose = 4444 mg), nine blood samples were drawn and the iohexol concentration was determined (Table 4). The concentration of iohexol is plotted against time and fitted using a double-exponential decay in Fig. 1. The fitting is based on a non-linear least squares procedure and appropriate software should be used (e.g. GraphPad Prism; GraphPad Software, Inc., La Jolla, CA). For this example, the parameters obtained from the least-squares fitting procedure were: A = , B = , α = and β = The area under the c(t)-curve is therefore AUC = A/α +B/β = / / = mg/ml min. The value c(0) = A + B = = Dose/V. With Dose = 4444 mg, the distribution volume equals V = Dose/ c(0) = 4444/ = ml = L. The GFR can be obtained from GFR = Injected Dose/AUC = 4444 mg / mg/ml min = 98.8 ml/min. This value can then be corrected for BSA. For a person of height = 180 cm and Table 4 Iohexol concentration obtained from timed collected blood samples following the administration of an intravenous injection of an absolute dose of 4444 mg iohexol a Time (min) Iohexol (mg/ml) a This is an example. See text in section Two-compartment model

5 Fig. 1 Iohexol concentration versus time. Solid circles Blood sample data from Table 4, solidline curve best non-linear least squares fit for the twocompartment model, dotted-line curve shows the best fit for the one-compartment model (only using the data for time >120 min) weight = 90 kg, the Dubois formula gives BSA = m 2. The GFR then equals 81.4 ml/min/1.73 m 2. Another interesting property is the mean transit time T, which is defined as T ¼ Z Z 0 0 tcðþdt t ct ðþdt From this definition and for a double exponential decay the valueoftcanbecalculatedfrom T ¼ A=a2 þ B=β 2 A=a þ B=β For our example, the mean transit time T = 186 min. The inverse 1/T (min 1 ) is a rate constant expressing how fast the tracer disappears from the body. One-compartment model A very frequently used renal clearance protocol is a reduced protocol which requires the taking of samples only for the slow component. In other words, only timepoints beyond 2 h are used, and the number of samples is limited to two, three or four. In this case, it is not possible to fit the data with a double-exponential decay curve and, therefore, the decay curve of the concentration is described by a single exponent: ct ðþ¼aexpð αtþ where A = c(0) the starting concentration in milligrams per milliliter, and A = D / V, with D bing the dose in milligrams and V the distribution volume (in ml). The AUC = A/α.The GFR is thus defined as GFR ¼ Dose=AUC ¼ D= ða=αþ ¼ V α where GFR is expressed in milliliters per minute, i.e. the units of aflow. The one-compartment model c(t) = A exp( αt) canbe fitted in two different ways. The first is to use non-linear least squares fitting. The second is to logarithmically transform the c(t) equationtoln[c(t)] = ln(a) αt, which is the equation of a straight line which can easily be fitted in spreadsheet software, such as MS Excel. As a straight line is completely defined by a slope and an intercept, this methodisoftenreferredtoasthe slope intercept method. It is important to note that the same results for A and α will not be obtained when both mathematical methods are used to fit the data because there is different weighting of the data points during the fit in each method. Using both the data from Table 4 for times of 120 min and the slope intercept method, A = and α = , resulting in AUC = A/ α = mg/ml minutes. From this value, the slow GFR = Dose/AUC = 4444/ = ml/min. This latter value is much larger than the 98.8 ml/min obtained from the two-compartment model due to the underestimation of the AUC using a onecompartment model, as illustrated in Fig. 1. Therefore, an additional step in the one-compartment protocol is the correction for this underestimation of the AUC (and thus the overestimation of the GFR). To correct for the overestimation of the GFR when the one-compartment method (which determines the slow GFR) is used, Bröchner Mortensen [15] plotted

6 (and fitted) the true GFR, measured with 51 Cr-EDTA, against the slow GFR, resulting in a simple quadratic relationship: GFR ¼ 0:99078SlowGFR 0: ðslowgfrþ 2 Schwartz et al. [16, 17] optimized the iohexol plasma disappearance curve method and presented the following correction formula for iohexol: GFR ¼ 1:0019 SlowGFR 0: ðslow GFRÞ 2 Other correction formulas have been proposed of the form: GFR ¼ Slow GFR= ½1 þ γslowgfr where γ = (iohexol; Ng et al. [18]) or γ =0.0017( 51 Cr- EDTA; Fleming [19]) or γ = BSA 1.3 ( 51 Cr-EDTA; Jödal [20]). All correction formulas behave more or less the same in the range ml/min for the slow GFR, which is also the original range for which the Bröchner Mortensen formula has been developed (Fig. 2). Outside the ml/min range, the correction of Fleming [19]or Ng[18]is to be recommended over the Bröchner Mortensen correction [21]. One-sample method A further simplification is to determine GFR from the concentration of a tracer in only one blood sample taken at a specific time-point after injection. Multiple empirical formulas have been proposed that describe the relationship between the volume of distribution at time t and the actual GFR by calculating the distribution volume from the injected dose and the concentration of the tracer, derived from one blood sample, drawn at time t. One-sample methods for Cr 51 -EDTA mostly make use of the Christensen and Groth formula [22], while for iohexol the Jacobsson formula [23] is preferred. The one-sample method is based on the relationship between the concentration at time t and the volume of distribution at that time: ct ðþ¼dose=vðþ t The distribution volume at time t =2h(120min)is: V 120 ¼ Dose=c 120 For children, Ham and Piepsz [24] demonstrated that the relationship between V 120 and GFR can be given as GFR ¼ 2:602V 120 0:273 This method was used for the 623 children in the studies of Piepsz et al. [25, 26] for whom the GFR 50 results are presented in Table 5. Normal GFR for children Because direct measurements are complex and invasive, very few GFR studies involving direct measurement have been conducted in healthy children. GFR, expressed in millimeters per minute, evolves with age [27] in a more or less linear manner for children between 2 and 14 years of age. To be able to compare the kidney function (or GFR measurements) among children it is necessary to scale for a standard reference. Scaling GFR for BSA shows that infants reach adult GFR values by about 2 years of age [13, 27]. There is some controversy about these adult normal GFR values. Defining normality is a difficult task in nephrology as it requires that GFR is measured with high precision and accuracy. Fig. 2 Different correction curves for calculating the true glomerular filtration rate (GFR) from the slow GFR (onecompartment model). Solid-line curve Bröchner Mortensen correction (originally designed for the ml/min range, i.e. interpolation region), dashed-line curve Fleming correction, dottedline curve Ng correction

7 Table 5 Meta-analysis data a Age (years) L 50 (cm) W 50 (kg) Scr 50 (mg/dl) GFR 50 (ml/min) BSA (m 2 ) Indexed GFR 50 (ml/min/1.73 m 2 ) Integer k Infants Children Female adolescents Male adolescents L 50 Median height, W 50 median weight, Scr 50 median serum creatinine, GFR 50 median glomerular filtration rate, where subscript 50 indicates the median value. BSA Body surface area a Meta-analysis data are obtained from Pottel et al. [27] and Piepsz et al. [26]. The value of the integer k is calculated from the inverse Schwartz equation: cgfr 50 = k L 50 /Scr 50 Schwartz and Work [13] presented two tables with normal GFR values for children, one with inulin as the reference method, but dating from 1982 [28] and 1989 [29], and one with the results of Piepsz et al. [25], dating from It is important to draw attention to the difference between these age-periods, as both tables in the Schwartz article reference normal values for GFR for children aged >2 years. In the first table mean normal GFR is about 120 ml/min/1.73 m 2 as

8 published in the 1980s and measured with the inulin clearance method, compared to the mean normal GFR value in the second table of about 105 ml/min/1.73 m 2,obtainedin2006and measured by 51 Cr-EDTA. This difference may be partially explained by the underestimation of the inulin GFR measurement by the 51 Cr-EDTA GFR measurement [30], or, and this is more probable, by the change in BSA in more recent years, as compared to 30 years ago. Delanaye et al. [31] reviewed literature values for measured GFR (mgfr) normal reference intervals for adults. These authors found that more recent studies presented lower mgfr values as normal values, i.e. mean values of ml/min/1.73 m 2,comparedtoearlier studies published some decades ago. These lower values could be explained by the BSA adjustment, as BSA has increased significantly during the last three decades and the BSA-unadjusted GFR did not show such a decrease [32]. Therefore, we consider the results of Piepsz et al. [25] as the reference work for normal GFR values in children. These authors measured GFR by plasma disappearance of 51 Cr- EDTA in 623 children evaluated for potential mild urogenital abnormalities, including only patients with no significant kidney defects. They showed that GFR rises progressively from neonatal age to about 2 years of age, stabilizing at a value of about 107 ml/min/1.73 m 2, as calculated from the data reported by Pottel et al. [27]. Piepsz et al. had only partially published these results for GFR in milliliters per minute per 1.73 m 2 [25], with most expressed in milliliters per minute [26]. To convert the GFR expressed in milliliters per minute, Pottel et al. [27] used Belgian Growth Curves [33] to calculate BSA from the median height and weight and expressed normal GFR values in milliliters per minute per 1.73 m 2. The data of Piepsz et al. expressed in the latter units were then fitted by asimplemodel[27]: GFR = [1 exp( Age/0.5)] in which the term in brackets describes the rise in GFR between 0 and 2 years old, stabilizing at ml/min/1.73 m 2 as exp( Age/0.5) 0forAge>2years.Inthatsamearticle Pottel et al. also presented median serum creatinine (Scr) values for children of the same age groups. These Scr values were obtained from enzymatically measured isotope dilution mass spectrometry-equivalent Scr concentrations [34]. The results of Piepsz et al. [26] and Pottel et al. [27] are summarized in Table 5. The meta-analysis data in Table 5 can be considered as reference data for the average healthy (Belgian) child aged between 1 month and 15 years. As Belgium is centrally located in continental Europe, these data may be considered to be representative for the average healthy European child. However, there are a number of concerns regarding these data, as summarized by Schwartz [35]. The reference clearance values relied on the single-plasma method, described by Ham and Piepsz [24]. The uncertainty of a single-point method could increase the variability in the GFR determination. Piepsz et al. [26] also did not use the Bröchner Mortensen correction, but the Chantler linear correction [36], whereas the British Nuclear Medicine Society recommends the use of the Bröchner Mortensen correction [37]. Also, the clearances were not performed on those whose Scr values are presented. The same can be said about the height and weight information, obtained from the National Belgian Growth Curves. In fact, the data in Table 5 are collected from the same population of healthy Belgian children and represent average kidney function values (GFR and Scr) and demographic information (height and weight) according to age. Estimating GFR Equations for estimating the GFR, based on serum concentrations of creatinine (Scr) or cystatin C (CysC), are popular in both the clinical setting and in research studies. Continuous efforts are ongoing to improve or develop new (and better) GFR estimating equations for children (and adolescents). However, at this time, imprecision is the main flaw of the currently available egfr equations, and there is no real accurate and precise substitute for the direct measurement. Moreover, GFR estimating equations are based on the results of direct measurements and are constructed to match the mgfr, which serves as the independent variable during the statistical modeling. It is therefore important to realize that egfr equations are heavily dependent on the data used during the development of the equation. Equations based on data from healthy children will therefore differ from equations based on data from children with a diseased kidney. Scr-based egfr equations Table 5 hasbeenusedtocalculatetheaveragegfrof ml/min/1.73 m 2 for healthy children between 2 and 15 years of age and to develop the Flanders Metadata equation [27]: egfr ¼ ð0:0414 lnðageþþ0:3018þ L=Scr This equation is of the form egfr = k L/Scr and differs only from the well-known bedside (and updated) Schwartz equation [38]: egfr ¼ 0:413 L=Scr by considering an age-dependent value for k. In Table 5, we calculated the values of k at the corresponding ages, based on cgfr 50 Scr 50 /L 50, where this age-dependency is clearly demonstrated. It should also be noted that Schwartz et al. published an older version of his famous bedside equation [39] (valid for so-called Jaffe-type Scr assays; egfr = 0.55 L/Scr) in which he, in following publications, differentiated between full-term infants up to 1 year old

9 (k =0.45)[40], children up to 14 years old (k = 0.55) and male adolescents (k =0.70) [41], where k = 0.55 could still be used for female adolescents. This clearly suggests an agedependency for the factor k, which was not modeled by Schwartz in his updated version. The Flanders Metadata equation can thus be considered as an attempt to define an agedependent k value for the updated bedside Schwartz equation. The k value in the Flanders Metadata equation [k - = ln(age) ]varies from (at the age of 1 year) to about at the age of 15 years, meaning that the k = in the Schwartz equation is too high for most (healthy) children. It should be noted that the updated bedside Schwartz equation has been derived in 349 children aged between 1 and 16 years, with established kidney disease (the median iohexol-gfr was only 41.3 ml/min/1.73 m 2 ). This is a completely different dataset than the data presented in Table 5, which describe the renal parameters and demographics of healthy children. The 349 children in the cohort used by Schwartz to derive his bedside formula showed notable growth retardation. The nature of the data and the limited sample size of the Schwartz cohort, given the knowledge that Scr evolves with age (and height), were probably not sufficient to derive age-dependent k values. De Souza also questioned the adequacy of one k value for all children [42] and arrived at following simple adjustment to the Schwartz equation: egfr ¼ 0:368 L=Scr ingirlsðallagesþandboys < 13years egfr ¼ 0:413 L=Scr in boys 13 years (0.368 = 32.5/88.4; = 36.5/88.4, with 88.4 the conversion factor for Scr expressed in μmol/l to mg/dl). De Souza et al. re-estimated the k value and found that the value of was too high for her population (360 French children with 965 inulin measurements and 109 Swedish subjects), with the exception of male subjects aged 13 years. From the above discussion, it is clear that to achieve the best GFR estimation accuracy for formulas of the form egfr = k L/Scr, a locally derived constant or agedependent k value may be calculated. As the k value may also depend on the reference standard GFR method, it might be a good suggestion when this simple form of an egfr equation is used within a specific center to regress the mgfr against height/scr and derive center-specific k values (for different ages) [42 45]. A different approach to developing egfr equations has been proposed by Pottel et al. [46]. Table 5 can also be used to demonstrate this alternative way of developing an egfr equation. The underlying notion is that the average GFR value of ml/min/1.73 m 2 for healthy children, which is independent of age, corresponds to the average Scr value. As the average Scr value depends on age, Pottel et al. proposed to normalize Scr. To this end, for an individual subject, the Scr value was normalized with the median Scr value at the corresponding age (Scr 50 in Table 5). Assuming an inverse relationship between GFR and this normalized Scr (denoted by Scr/Q), Pottel proposed and validated the following simple relationship: egfr ¼ 107:3= ½Scr=Q where Q is the value of Scr 50 presented in Table 5. When Scr 50 in Table 5 for children between 2.5 and 13 years old is plotted against height (L 50 ), with the requirement that the intercept is zero, then Q = L (R 2 = 0.959) is obtained. Entering this relationship in the equation above results in egfr ¼ 107:3 0:0035 L=Scr ¼ 0:375 L=Scr which is again of the form egfr = k L/Scr, with k = 0.375, close to the k value of of the Schwartz Lyon equation for children between 2 and 13 years of age. The simple Pottel equation for egfr [egfr = 107.3/(Scr/Q)] has some interesting properties: 1) The coefficient of can be interpreted as the GFR for the average healthy child corresponding to the mean or median normalized Scr/Q = 1. Deviation of Scr/Q from 1 means that the Scr value of the child deviates from the ideal median Scr value for his/her specific age (or height), and this results in a deviation from the ideal median GFR value. 2) Pottel also showed that the distribution of Scr/Q is Gaussian (bell-shaped) with a mean or median equal to 1 and with lower 2.5th and upper 97.5th percentiles (Pct) of 0.67 and 1.33, respectively. From this, a lower 2.5th Pct for egfr = 107.3/1.33= ml/min/1.73 m 2 can easily be derived. Taking the 99.5th Pct for Scr/Q = 1.43, Pottel concluded that egfr = 107.3/1.43= 75 ml/min/1.73 m 2 was the lower limit for normal GFR values in children, adolescents and young adults [47]. 3) From Table 5, Q values can be linked to the age of the child, but also to his/her height, resulting in two different versions for this simple equation one that is agedependent and one that is height-dependent. Hoste et al. [48] extended the simple equation to adolescents and young adults and presented the age-dependent and height-dependent forms of the equation. She found that for adolescents, height is a better predictor than age and, therefore, that linking Q to height gives better predictions than when Q is linked to age, although, for children up to 14 years of age both forms of the equation perform equivalently. The advantage of the height-independent Pottel equation is that automatic reporting of egfr together with the Scr value can be achieved, as height is usually not available in the clinical laboratory database.

10 If height is available for adolescents or young adults, then the height-dependent form of the equation is to be preferred because height serves as a good surrogate for muscle mass [35]. Pottel et al. [49] recently extended this equation to middleaged and older adults, introducing an age-dependent decline factor from 40 years onwards, resulting in an egfr equation which is valid for the full age spectrum (FAS), the FAS-equation: egfr ¼ 107:3 = ðscr=qþ for2 age 40 years egfr ¼ 107:3= ðscr=qþ 0:988 ðage 40Þ forage > 40 years Q-values are presented in Table 5; for adults and older adults, Q = 0.70 mg/dl for females and Q = 0.90 mg/dl for males should be used. More complex Scr-based formulas for children have been developed in which Scr is combined with only age and gender, such as the BCCH2 (British Columbia Children s Hospital) equation [50], or with height, age and gender, such as the BCCH1 equation [50] andthe equation proposed by Gao et al. [51] and the Lund Malmöequation[52]. BCCH 1 : lnðegfrþ ¼ 1:18 þ 0:0016 Wt þ 0:01 Ht þ 149:5= ðscr 88:4Þ 2141= ðscr 88:4Þ BCCH 2 : egfr ¼ 61:56 þ 5886= ðscr 88:4Þþ4:83 Age þ ð10:02 if maleþ Gao : egfr ¼ 0:68 Ht=Scr 0:0008 ðht=scrþ 2 þ 0:48 Age ð21:53=25:68 if male=femaleþ Lund MalmP : egfr ¼ exp½4:62 0:0112 Scr 88:4 0:0124 Age þ 0:339 lnðageþ with weight (Wt) in kilograms, height (Ht) in centimeters, Scr in milligrams per deciliter and age in years. For healthy children that is, for the data in Table 5 Pottel et al. [27] showed that the Lund Malmö equation closely follows the median data of Table 5 over the complete age range. The BCCH1 equation closely follows the data for children aged <2 years but largely overestimates these data for children aged >2 years. The BCCH2 equation was derived using only easily available demographic information, and this equation was not intended to be used outside the local laboratory unless locally derived constants for the formula were used [50]. Gao s equation matches the equation of Pottel for children between 2 and 14 years of age or between 85 and 165 cm, but it deviates for adolescents. For children with normal or supra-normal GFR, the equations of Gao, Lund Malmö and Pottel perform quite equally and are probably the preferred choice. It should be noted, however, that Gao s formula has been designed for the compensated Jaffe assay for Scr, while the other equations were designed for the enzymatic Scr assay, which is known to be IDMS-equivalent. For children with CKD and growth retardation, the Schwartz bedside formula is probably the preferred choice. Adult equations are not applicable to children or adolescents [53, 54]; however, the other way around is likely, with pediatric equations being applicable to young adults up to the age of 40 years, as shown by Pottel [49], Selistre [53] and Hoste [48]. A major drawback of all Scr-based equations is that they clearly overestimate renal function in the case of children with reduced muscle mass (and thus with very low Scr) [55]. Most Scr-based egfr equations are not applicable to children younger than 2 years of age, although there are formulas (e.g. Flanders Metadata [27] and the Pottel formula with exponential term [46]), that can be applied for ages of >1 month. However, these applications lack validation for children aged between 1 month and 2 years and may show large bias [56]; as such,theyshouldbeusedwithcaution.atbirth,childrenhave an Scr level which reflects the maternal Scr concentration (0.70 mg/dl), and in the first postnatal month Scr decreases rapidly from about 0.70 to 0.25 mg/dl, and then gradually increases when the child is gaining muscle mass [27]. This explains why Scr-based egfr equations are not applicable in the first month of life. CysC-based egfr-equations Cystatin C-based egfr equations overcome the limitations of Scr-based egfr equations. CysC is a small protein that is freely filtered at the glomerulus and not significantly affected by age, gender and muscle mass [45, 57], but it may be affected by the use of medication (steroids) in renal transplant patients and patients with inflammatory and thyroid disorders [45]. Several CysC formulas have been derived, and these formulas have proven to be interesting egfr equations, but they do not seem to be superior to Scr-based equations [44]. However, they can be useful to replace Scr-based equations in case of specific situations of reduced muscle mass. They might also be more accurate than Scrbased equations for children aged <2 years [56]. A non-exhaustive list of univariate CysC-based egfr equations is as follows : Hoek [58]: egfr = CysC 1 Bricon et al. [59]: egfr = 78 CysC 1 +4 Larsson et al. [60]: egfr = CysC Rule et al. [61]: egfr = 76.6 CysC 1.16 Filler and Lepage [62]: egfr = CysC Zappitelli et al. [63]: egfr = CysC 1.17

11 It should be noted that all of these equations have more or less the same mathematical form (univariate inverse power relations between GFR and CysC) and, in fact, these equations are not really different in predicting GFR from the CysC concentration. Reference values for CysC vary between approximately 0.50 and 1.50 mg/l (for adolescents aged between 12 and 17 years, the 1st and 99th Pcts of 0.57 and 1.21 mg/l have been presented [64]). Table 6 lists the predicted egfr values for the various CysC-based egfr equations for normal CysC concentrations. When the predicted egfr values for the different formulas in Table 6 are plotted and fitted with a power function, as shown in Fig. 3, then the relationship egfr = 79.7 CysC 1.12 explains 96 % of the variation in the predictions of all egfr equations listed in Table 6. It is important to note that all CysC-based equations in Table 6 were obtained between 2000 and 2006, that is, years ago when there was no certified reference material available. All assays measure CysC, but there were considerable differences between assays and, therefore, in measured CysC concentrations, explaining the variety in coefficients for the CysC power functions. The differences between equations are most pronounced in the low CysC range (CysC <0.80 mg/l). This shows that it is not really necessary to derive new (univariate) egfr CysC equations, but multivariate models adding independent demographic variables such as age, sex, height, weight and blood marker variables (like Scr) may still improve the GFR CysC relationship. An example of a CysC-based equation, adding demographic information to the equation, is egfr = CystC (if age < 14 years) Grubb et al. [65] but more external validation of this equation is necessary to evaluate the validity of the predictions. One of the challenges with egfr equations is to define which equation to use in which circumstances. CysC-based equations are definitely preferable over Scr-based equations in patients with severe muscle mass reduction (Duchenne muscular dystrophy patients, anorexia patients, oncology patients, wheelchair patients, among others) because Scr-based equations will severely overestimate the real GFR. It is not clear yet if CysC-based equations have an improved or added value over Scr-based egfr equations for children in other situations, and given that the cost for CysC measurements is approximately eight- to ninefold the cost of Scr measurements, CysC measurements are not routinely recommended. The major reason for the diversity of CysC-based egfr equations is the previous lack of an international CysC calibrator and the non-equivalence of results from different CysC assays. Turbidimetric and nephelometric CysC assays lead to substantially different results, with the latter leading to more accurate GFR estimation. Now that there is a certified reference material (ERM-DA471/IFCC) [66], it should become possible to derive a simple CysC-based egfr equation for children. The most recent simple, assay-independent CysC-based equation is the CAPA equation (CAPA = Caucasian, Asian, Paediatric, Adult) which should also be valid for children : CAPA [67]: egfr = 130 CysC age The CAPA equation has been evaluated in a mixed cohort of Dutch and Swedish children (n = 246). Underestimation of the GFR in children was noted, and the overall accuracy (P30) was around %, suggesting that there is still work to do, specifically for children, in terms of deriving a more accurate Table 6 Estimated glomerular filtration rate predictions for different univariate Cystatin C-based equations a Cystatin C (mg/l) Estimated glomerular filtration rate (ml/min/1.73 m 2 ) b Hoek/2003 [58] Le Bricon et al./2000 [59] Larsson et al./2004 [60] Rule et al./ 2006 [61] Filler and Lepage/ 2003 [62] Zappitelli et al./2006 [63] a The first certified reference material was published in 2010 [66] b Values are presented according to the first author/year of the publication

12 Fig. 3 Estimated glomerular filtration rate (egfr)-cystatin C (CysC) relationship CysC-based egfr equation using the international certified reference material. Scr/CysC-based egfr equations Equations for egfr that combine Scr and Cystatin C, with demographic variables (height, weight, age, sex) and/or clinical conditions (renal transplant, among others) have also been derived. Combining CysC and creatinine assays improves GFR estimations and may reduce imprecision. However, the equations become complex; for example: Zappitelli et al. [63]: egfr ¼ ð43:82 expð0:003 HtÞÞ= CysC 0:635 Scr 0:547 1:165 if renaltransplant 1:57Scr 0:925 if spinabifida Chehade et al. [68]: egfr ¼ 0:42 ðht=scrþ 0:04 ðht=scrþ 2 14:5 CysC þ 0:69 Age þ ð18:25 if female; or 21:88 if maleþ, with Scr in mg/dl, height in cm, Cystatin C in mg/l, age in years. Bouvet et al. [69]: egfr ¼ 63:2 ðscr=96þ 0:35 ðcysc=1:2þ 0:56 ðwt=45þ 0:30 ðage=14þ 0:40 Chronic Kidney Disease in Children (CKiD) Study [70]: egfr ¼ 39:8 ðht=scr Þ 0:456 ð1:8=cyscþ 0:418 ð30=bunþ 0:079 1:076 male ðht=1:4þ 0:179 with Scr in micromoles per liter, height in meters, weight in kilograms, age in years, CysC in milligrams per liter and blood urea nitrogen in milligrams per liter. The CKiD equation (or the combined Schwartz equation) shows high accuracy and precision and minimal bias in the CKiD population. Confirmation of the utility of this equation is desirable in other populations of children (healthy and diseased). The Chehade formula could replace the combined Schwartz formula for children with moderate chronic kidney disease [68]. From a practical point of view, it is mostly important for clinicians to differentiate children with normal (GFR >75 ml/ min/1.73 m 2 ) from those with abnormal GFR. The simple Scrbased formulas are perfectly suitable to do this, unless Scr is (extremely) low because of specific patient conditions. Cystatin C-based univariate formulas may replace the simple Scr-based formulas in these cases. When high accuracy is desired, combining Scr and Cystatin C will certainly improve the estimation, but these combined equations suffer from the same drawbacks as the Scr-based equations. When there is great uncertainty, then the direct measurement of GFR is still recommended [71]. egfr equations using other biomarkers Ongoing research to improve the estimation of kidney function may lead to the development of new egfr equations, using biomarkers like β-2 microglobulin or β-trace protein (BTP). As early as in 2002, Filler et al. [72] had concluded that BTP was superior to Scr and was an alternative for CysC to detect mildly reduced GFR in children, but he admitted that it was not better than the Schwartz equation. However, today there are still no real accurate alternatives to the Scr-based egfr equations, with the exception of mixed Scr/CysC egfr equations. Witzel et al. [73] has developed a sexspecific formula based on BTP, Scr and height, but external validation is still required to estimate the validity and applicability of this new formula. A requirement for a new formula is

13 also the availability, cost and robustness of assays to determine the concentration of biomarkers in routine practice. Key summary points 1. Direct GFR measurements are performed using exogenous filtration markers: inulin (gold standard), iohexol, 51 Cr-EDTA, 99m Tc-DTPA, Iothalamate. 2. Direct GFR measurements can be performed using two different procedures: the renal clearance procedure, involving blood and urine samples and the plasma clearance procedure, involving only blood samples. 3. The plasma clearance protocol may be done using a twocompartment model (using early and late blood samples) or a one-compartment model (using late blood samples only). The one-compartment model requires a correction method for the overestimation of the GFR. 4. Estimating GFR is mostly done using Scr-based egfr equations. CysC-based egfr equations are valid alternatives and the mixed Scr/CysC egfr equations have higher accuracy and precision. Multiple choice questions (answers are provided following the reference list) 1. Normal GFR for children is above a. 60 ml/min/1.73 m 2 b. 75 ml/min/1.73 m 2 c. 90 ml/min/1.73 m 2 d. 120 ml/min/1.73 m 2 2. The gold standard for direct GFR measurement is a. Renal clearance of inulin b. Plasma clearance of iohexol c. Renal clearance of iothalamate d. Plasma clearance of inulin 3. When the reduced plasma clearance protocol with only late blood samples is used, then a. The AUC is overestimated and can be corrected with the Bröchner-Mortensen formula b. The AUC is underestimated and can be corrected with the Bröchner-Mortensen formula c. The GFR is overestimated and can be corrected with the Bröchner-Mortensen formula d. The GFR is underestimated and can be corrected with the Bröchner-Mortensen formula 4. The updated bedside Schwartz equation is a. egfr = L/Scr b. egfr = L/Scr c. egfr = 107.3/[Scr/Q] d. egfr = L/CysC 5. Scr-based equations should be avoided a. For adolescents b. For healthy children c. For children with CKD d. For children with reduced muscle mass Compliance with ethical standards The author declares that he has no con- Conflict of interest statement flict of interest. References 1. Gaspari F, Perico N, Remuzzi G (1997) Measurement of glomerular filtration rate. Kidney Int Suppl 63:S151 S Hoste L, Pottel H (2012) Is body surface area the appropriate index for glomerular filtration rate? In: Sahay M (ed) Basic Nephrology and acute kidney injury. Rijeka, Intech, pp Available at: 3. Kidney Disease: Improving Global Outcomes (KDIGO) CKD Work Group (2013) KDIGO 2012 Clinical practice guideline for the evaluation and management of chronic kidney disease. Kidney Int Suppl 3: Du Bois D, Du Bois EF (1916) Clinical calorimetry: tenth paper a formula to estimate the approximate surface area if height and weight be known. Arch Intern Med 17: van der Sijs H, Guchelaar HJ (2002) Formulas for calculating body surface area. Ann Pharmacother 36: Haycock GB, Schwartz GJ, Wisotsky DH (1978) Geometric method for measuring body surface area: a height weight formula validated in infants, children, and adults. J Pediatr 93: Mosteller R (1987) Simplified calculation of body surface area. New Engl J Med 317: Smith HW (1951) The kidney: structure and function in health and disease. Oxford University Press, New York 9. Delanaye P (2012) How measuring glomerular filtration rate? Comparison of reference methods. In: Sahay M (ed) Basic Nephrology and acute kidney injury. Rijeka, Intech, pp Available at: Frennby B, Sterner G (2002) Contrast media as markers of GFR. Eur Radiol 12: Stevens LA, Levey AS (2009) Measured GFR as a confirmatory test for estimated GFR. J Am Soc Nephrol 20: Soveri I, Berg UB, Björk J, Elinder CG, Grubb A, Mejare I, Sterner G, Bäck SE, on behalf of the SBU GFR Review Group (2014) Measuring GFR: a systematic review. Am J Kidney Dis 64: Schwartz GJ, Work DF (2009) Measurement and estimation of GFR in children and adolescents. Clin J Am Soc Nephrol 4: Sterner G, Frennby B, Mansson S, Nyman U, Van Westen D, Almén T (2008) Determining Btrue^ glomerular filtration rate in healthy adults using infusion of inulin and comparing it with values obtained using other clearance techniques or prediction equations. Scand J Urol Nephrol 42:

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