EDUCATIONAL REVIEW

Measuring and estimating glomerular filtration rate in children

Hans Pottel1

Received: 28 January 2016 /Revised: 8 March 2016 /Accepted: 8 March 2016# IPNA 2016

Abstract Glomerular filtration rate (GFR) is the best indexfor kidney function in health and disease. Knowledge of theGFR is essential for the detection (diagnosis) and monitoringof renal function during disease progression and for ensuringcorrect medication doses. Inulin clearance (plasma or urine) iscurrently considered to be the gold standard for measuringGFR, but in clinical practice the measurement of other exog-enous filtration markers from the plasma often replaces that ofinulin clearance. Different protocols can be used to determinethe area under the plasma disappearance curve, and an under-standing of these methods is important. GFR can also be esti-mated by GFR equations (eGFR), which are most often usedin clinical practice because they only require a knowledge ofthe serum creatinine or cystatin C level and demographic in-formation. eGFR equations are easy to use but they do havetheir limitations, and it is important to know how these equa-tions were derived and in which circumstances they can beused most accurately. The aim of this review is to explain howGFR can be measured using the renal clearance and the plas-ma clearance method and which eGFR equations can be ap-plied to children, as well as how and when these equations canbe used in clinical practice.

Keywords Glomerular filtration rate . Children .

Adolescents . Direct measurement . Estimating equations

Introduction

Glomerular filtration rate (GFR) describes the flow rateof filtered fluid through the kidney [1]. It is the volumeof plasma cleared from a specific substance per timeunit and is typically expressed in milliliters per minute.In most cases, this value is indexed for the body surfacearea (BSA) and thus expressed in milliliters per minuteper 1.73 m2. To obtain the GFR in these units, the GFRis expressed in milliliters per minute and then multipliedby 1.73/BSA. At the beginning of the 20th century thevalue of 1.73 m2 was considered to be the BSA of theaverage 25-year-old American [2]. A value of 1.95 m2

would probably be more appropriate for the averageBSA of today’s 25-year-old adult, but switching from1.73 m2 to 1.95 m2 has severe repercussions for thecurrent classification system for chronic kidney disease[3] which is based on fixed limits that are expressed inmilliliters per minute per 1.73 m2. The Du Bois and DuBois BSA equation, which dates from 1916, calculatesBSA from weight in kilograms (Wt) and height in cen-timeters (Ht) (BSA=0.007184 × Wt0.425 × Ht0.725) andis still widely used to normalize physiological parame-ters [4]. However, it has been shown that for childrenweighing <10 kg, the Du Bois formula does not givethe best results [5]. For the specific pediatric group, theformulas of Haycock et al. [6] (BSA = 0.02465 ×Wt0.5378 × Ht0.3964) or Mosteller [7] (BSA = (Wt0.5 ×Ht0.5)/60) are preferred.

It is important to note that a number of researchershave questioned the indexation of BSA to GFR, propos-ing alternative indexations, such as height, squaredheight, total body water or extracellular fluid volume(ECV). Indexing for BSA is particularly problematic inobese or anorectic children. ECV may be a more

* Hans PottelHans.Pottel@kuleuven-kortrijk.be

1 Department of Public Health and Primary Care, Campus KulakKortrijk, KU Leuven, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium

Pediatr NephrolDOI 10.1007/s00467-016-3373-x

appropriate choice than BSA, even in cases of extremebody shape and volume [2]. It may also be advisable toexpress GFR in milliliter per minute or to de-index es-timated GFR (eGFR) predictions for the follow-up ofthese particular cases with extreme body weight. Thefocus of this review article is the measurement and es-timation of GFR. All current eGFR equations have beendesigned for GFR indexed with BSA, and this contro-versial topic is beyond the scope of this article. Formore information on this topic, the interested reader isreferred to the article of Hoste and Pottel [2] and refer-ences therein.

Measuring GFR

Filtration markers

The ideal assessment of renal function or GFR shouldbe accurate, simple, safe and cost-effective. However,direct measurement of GFR is impossible because thefiltration process simultaneously takes place in millionsof glomeruli. Instead, methods that record the clearanceof an ideal filtration marker or exogenous substance areused.

Inulin, a 5200-Da inert, uncharged polymer of fruc-tose is the only known ideal filtration marker. Classicinulin clearance during the continuous infusion of care-fully timed collections of plasma and urine samples isconsidered to be the gold standard method for measur-ing GFR. Because inulin is the first reference method tohave been used, its role in GFR measurement has onlybeen asserted on the basis of (numerous) physiologicalstudies. Nevertheless, there are limitations to its use indaily clinical practice as the molecule is difficult tohandle, and the procedure described by Homer Smith[8] is invasive. This procedure includes fasting condi-tions in the morning, a continuous intravenous infusion,multiple clearance periods requiring repetitive blood andurine collections over 3 h, oral water loading to stimu-late diuresis, bladder catheterization to ensure completeurine collection and careful timing of blood sampling atthe midpoint of the urine collection. Moreover, inulinclearance is not practical for routine clinical purposesbecause of expense, limited commercial sources, restrict-ed availability of automated laboratory methods for in-ulin determination in plasma and urine samples and theneed for constant supervision during the procedure.Therefore, in clinical practice and research, other(exogenous) clearance markers and methods are beingused [9, 10].

The ideal filtration marker must have strict physiologicalcharacteristics: 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 renaltubules, inert and not toxic, exclusively excreted by the kid-neys, easily measured in both plasma and urine, preferablyinexpensive and easily available on the market. The markerscommonly employed for GFR measurement include radio-pharmaceuticals, such as chromium 51-labeled ethylenedi-aminetetraacetic acid (51Cr-EDTA), technetium 99-labeleddiethylenetriaminepentaacetic acid (99mTc-DTPA), iodine125-labeled iothalamate (125I-iothalamate), and radiographiccontrast agents, such as iohexol and non-radiolabelediothalamate. Strengths and limitations of the most commonlyused exogenous markers are presented in Table 1 [9, 11].Supportive scientific evidence for the sufficient accuracy ofdirect measurements of GFR in comparison with the goldstandard (continuous infusion of inulin) is presented in Table2 [12]. The most common method used to measure GFRin clinical practice is the measurement of endogenouscreatinine clearance, but this measurement may be diffi-cult to obtain or fraught with error. There is strongscientific evidence that endogenous creatinine clearanceas a direct GFR measurement has insufficient accuracy[12]. In actual fact, the ideal marker in the body(endogenous) does not exist: creatinine is secreted bythe renal tubules and urea is absorbed by the renal tu-bules. Essentially, there are two approaches for directGFR assessment: renal clearance and plasma clearancemethods, which can be used for most exogenous filtra-tion markers. The advantages and disadvantages of bothprocedures are listed in Table 3.

Renal clearance procedure

Renal clearance is the most direct method for measuringthe GFR. Clearance is computed as the urine concentra-tion ([U] in mg/mL) of the exogenous filtration marker,multiplied by the volume of the timed urine sample (Vin mL/min) and divided by the average plasma concen-tration ([P] in mg/mL) during the same time period[13]:

GFR ¼ U½ � � V

P½ �

expressed in milliliters per minute. Multiple (2–4) 20- to30-min urine collections are obtained after administra-tion of the marker. Blood samples are drawn in betweenurine collections, and both urine and blood samples areanalyzed in the laboratory to determine the concentra-tion of the filtration marker. The main advantage of thisprocedure is its relatively short duration. The main dis-advantage is the need for urine collections, which may

Pediatr Nephrol

be difficult in populations with impaired urinary incon-tinence or retention, such as the elderly or children andwhich increases risk for error caused by incompleteurine collections. The marker is administered by intra-venous bolus or bolus subcutaneous inject ion.Subcutaneous injection allows for a slower release ofthe marker into the circulation and more constant plas-ma levels [11]. Alternatively, the filtration marker maybe administered using continuous intravenous or subcu-taneous infusion.

Plasma clearance procedure

To avoid inconvenience and errors from timed urinecollections and because of the increasing importance ofmeasuring GFR in the aging population, interest in mea-suring GFR using plasma clearance is steadily increas-ing. GFR is calculated from plasma clearance after abolus intravenous injection of an exogenous filtrationmarker or tracer. Let us suppose that M(t) is the massof the tracer cleared from the plasma at time t,expressed in milligrams per minute, then ΔM/Δt isthe elimination rate (in mg/min) of that substance, andin the limit for Δt→ 0, this elimination rate can bewritten as the differential dM/dt. If we further suppose

that c(t) is the concentration of the substance, expressedin milligrams per milliliter, in the plasma at time t, then

Table 1 Strengths and limitations of exogenous markers for direct measurement of glomerular filtration ratea

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 125I 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 doses51Cr 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 material99mTc DTPA 393 Widely available in USA Storage and disposal of radioactive material

Accurate measurement Must be measured in the nuclear medicine department

Low radiation dose No standardization

Cheap and easily available Dissociation and protein binding

MW, Molecular weight; 51 Cr EDTA, chromium 51-labeled ethylenediaminetetraacetic acid; 99m Tc DTPA, technetium 99-labeleddiethylenetriaminepentaacetic acidaMeasurements complied from Delanaye 2012 [9] and Stevens and Levey 2009 [11]

Table 2 Accuracy of direct glomerular filtration rate measurementsa

Marker Sufficient accuracy Scientific evidenceb

Inulin

Renal clearance Yes ++++

Plasma clearance Yes ++

Iothalamate

Renal clearance Yes ++++

Plasma clearance – +51Cr-EDTA

Renal clearance Yes +++

Plasma clearance Yes +++99mTc-DTPA

Renal clearance Yes ++

Plasma clearance No ++

Iohexol

Renal clearance Yes ++

Plasma clearance Yes +++

a Reproduced from Soveri et al. 2014 [12], used with permission)b ++++ strong evidence, +++moderately strong evidence, ++ limited evi-dence, + insufficient evidence

Pediatr Nephrol

the GFR can be defined as the ratio between the elim-ination rate and the concentration at time t:

GFR ¼ dM=dt

c tð Þ

By integrating the above equation, we have

GFR ¼ limt→∞

M tð ÞZ ∞

0c tð Þdt

¼ injectedDose

AreaUnder theCurve

After an infinite time, the tracer has completely dis-appeared from the body, and M(t) will be equal to theinjected dose and the integral in the formula above willbe equal to the area under the concentration–time curve(AUC). The decline in serum levels is secondary to theimmediate disappearance of the marker from the plasmainto its volume of distribution (fast component) and torenal excretion (slow component).

Two-compartment model

This decline in serum levels is best estimated using atwo-compartment model [14] that requires blood sam-pling early (usually 3 time-points up to 60 min afteradministration) and late (3–4 four time-points from120 min forward). Most filtration markers need about1–2 h to complete the mixing process with the extracel-lular fluid. This combination of mixing and clearance

process results in a double exponential decay, wherethe fast component is a combination of mixing andclearance and the slow component is clearance only.We thus describe c(t) by a double exponential decay:

c tð Þ ¼ Aexp −αtð Þ þ Bexp −βtð Þ

From the curve-fitting procedure, the parameters A, α, Band β are obtained. The area under this curve is A/α+B/β.The GFR is thus defined as

GFR ¼ Dose= A=αþ B=β½ �

The concentration at time t= 0 is c(0) =A+B, andthis is also equal to Dose/V, with V being the distribu-tion volume. Consequently, from the parameters A, Band the injected dose, the distr ibution volumeV=Dose/(A+B) can be calculated.

This procedure can be illustrated with the followingexample. After an intravenous bolus injection of iohexol(dose = 4444 mg), nine blood samples were drawn andthe iohexol concentration was determined (Table 4). Theconcentration of iohexol is plotted against time andfitted using a double-exponential decay in Fig. 1. Thefitting is based on a non-linear least squares procedureand appropriate software should be used (e.g. GraphPadPrism; GraphPad Software, Inc., La Jolla, CA).

For this example, the parameters obtained from theleast-squares fitting procedure were: A = 0.2183,B= 0.1294, α= 0.01577 and β= 0.004155. The area un-der the c(t)-curve is therefore AUC=A/α+B/β= 0.2183/0.01577 + 0.1294/0.004155 = 44.98 mg/mL×min.

The value c(0) = A + B = 0.3477 = Dose/V. WithDose =4444 mg, the distribution volume equals V=Dose/c(0)=4444/0.3477=12781 mL=12.78 L. The GFR can beobtained from GFR = Injected Dose/AUC = 4444 mg /44.98 mg/ml ×min= 98.8 ml/min. This value can then becorrected for BSA. For a person of height = 180 cm and

Table 3 Advantages and disadvantages of various renal and plasmaclearance procedures

Advantages Disadvantages

Renal clearance

Gold standard method(inulin)

Invasive→ bladder catheter may berequired

Spontaneous bladderemptying

Possibility of incomplete bladderemptying

Patient comfort Difficult to apply in children

Less invasive

Plasma clearance

No urine collection needed No standardized protocol

Potential for higherprecision

Variable number of plasma samples

Variable time-points

Different correction protocols for slowGFR

Inaccuracy with one-sample technique

Longer duration required for low GFR

GFR, glomerular filtration rate

Table 4 Iohexolconcentration obtainedfrom timed collectedblood samples followingthe administration of anintravenous injection ofan absolute dose of4444 mg iohexola

Time (min) Iohexol (mg/mL)

30 0.25083

60 0.18256

90 0.14703

120 0.10866

180 0.07319

240 0.05393

360 0.02947

540 0.01303

600 0.01142

a This is an example. See text in sectionTwo-compartment model

Pediatr Nephrol

weight=90 kg, the Dubois formula gives BSA=2.099 m2.The GFR then equals 81.4 mL/min/1.73 m2.

Another interesting property is the mean transit time T,which is defined as

T ¼

Z ∞

0tc tð Þdt

Z ∞

0c tð Þdt

From this definition and for a double exponential decay thevalue of T can be calculated from

T ¼ A=a2 þ B=β2

A=aþ B=β

For our example, the mean transit time T=186 min. Theinverse 1/T (min−1) is a rate constant expressing how fast thetracer disappears from the body.

One-compartment model

A very frequently used renal clearance protocol is areduced protocol which requires the taking of samplesonly for the slow component. In other words, only time-points beyond 2 h are used, and the number of samplesis limited to two, three or four. In this case, it is notpossible to fit the data with a double-exponential decaycurve and, therefore, the decay curve of the concentra-tion is described by a single exponent:

c tð Þ ¼ Aexp −αtð Þwhere A= c(0) the starting concentration in milligramsper milliliter, and A=D / V, with D bing the dose in

milligrams and V the distribution volume (in mL). TheAUC=A/α.The GFR is thus defined as

GFR ¼ Dose=AUC ¼ D= A=αð Þ ¼ V� α

where GFR is expressed in milliliters per minute, i.e. the units ofa flow.

The one-compartment model c(t) =A exp(−αt) can befitted in two different ways. The first is to use non-linearleast squares fitting. The second is to logarithmicallytransform the c(t) equation to ln[c(t)] = ln(A) − αt, whichis the equation of a straight line which can easily be fittedin spreadsheet software, such as MS Excel. As a straightline is completely defined by a slope and an intercept, thismethod is often referred to as the ‘slope–intercept’ meth-od. It is important to note that the same results for A andα will not be obtained when both mathematical methodsare used to fit the data because there is different weightingof the data points during the fit in each method.

Using both the data from Table 4 for times of≥120 minand the slope–intercept method, A=0.1737 and α=0.0047,resulting in AUC=A/ α=36.96 mg/mL× minutes. Fromth i s va lue , t h e s l ow GFR = Dose /AUC = 4444 /36.96 =120.2 mL/min. This latter value is much larger thanthe 98.8 mL/min obtained from the two-compartment mod-el due to the underestimation of the AUC using a one-compartment model, as illustrated in Fig. 1. Therefore, anadditional step in the one-compartment protocol is the cor-rection for this underestimation of the AUC (and thus theoverestimation of the GFR).

To correct for the overestimation of the GFR whenthe one-compartment method (which determines theslow GFR) is used, Bröchner–Mortensen [15] plotted

Fig. 1 Iohexol concentrationversus time. Solid circles Bloodsample data from Table 4, solid-line curve best non-linear leastsquares fit for the two-compartment model, dotted-linecurve shows the best fit for theone-compartment model (onlyusing the data for time >120 min)

Pediatr Nephrol

(and fitted) the true GFR, measured with 51Cr-EDTA,against the slow GFR, resulting in a simple quadraticrelationship:

GFR ¼ 0:99078SlowGFR−0:001218� SlowGFRð Þ2

Schwartz et al. [16, 17] optimized the iohexol plasma dis-appearance curve method and presented the following correc-tion formula for iohexol:

GFR ¼ 1:0019� SlowGFR−0:001258� SlowGFRð Þ2

Other correction formulas have been proposed of the form:

GFR ¼ Slow GFR= 1þ γSlowGFR½ �where γ=0.0012 (iohexol; Ng et al. [18]) or γ=0.0017 (51Cr-EDTA; Fleming [19]) or γ=0.0032 × BSA−1.3 (51Cr-EDTA;Jödal [20]).

All correction formulas behavemore or less the same in therange 0–170 mL/min for the slow GFR, which is also theoriginal range for which the Bröchner–Mortensen formulahas been developed (Fig. 2). Outside the 0–170 ml/min range,the correction of Fleming [19] or Ng [18] is to be recommend-ed over the Bröchner–Mortensen correction [21].

One-sample method

A further simplification is to determine GFR from the concen-tration of a tracer in only one blood sample taken at a specifictime-point after injection. Multiple empirical formulas havebeen proposed that describe the relationship between the vol-ume of distribution at time t and the actual GFR by calculatingthe distribution volume from the injected dose and the con-centration of the tracer, derived from one blood sample, drawnat time t. One-sample methods for Cr51-EDTA mostly make

use of the Christensen and Groth formula [22], while foriohexol the Jacobsson formula [23] is preferred.

The one-sample method is based on the relationship be-tween the concentration at time t and the volume of distribu-tion at that time:

c tð Þ ¼ Dose=V tð Þ

The distribution volume at time t=2 h (120 min) is:

V120 ¼ Dose=c120

For children, Ham and Piepsz [24] demonstrated that therelationship between V120 and GFR can be given as

GFR ¼ 2:602V120�0:273

This method was used for the 623 children in the studies ofPiepsz et al. [25, 26] for whom the GFR50 results are presentedin Table 5.

Normal GFR for children

Because direct measurements are complex and invasive, veryfew GFR studies involving direct measurement have beenconducted in healthy children. GFR, expressed in millimetersper minute, evolves with age [27] in a more or less linearmanner for children between 2 and 14 years of age. To be ableto compare the kidney function (or GFR measurements)among children it is necessary to scale for a standard refer-ence. Scaling GFR for BSA shows that infants reach ‘adult’GFR values by about 2 years of age [13, 27]. There is somecontroversy about these ‘adult’ normal GFR values. Definingnormality is a difficult task in nephrology as it requires thatGFR is measured with high precision and accuracy.

Fig. 2 Different correctioncurves for calculating the trueglomerular filtration rate (GFR)from the slow GFR (one-compartment model). Solid-linecurveBröchner–Mortensencorrection (originally designed forthe 0–170 mL/min range, i.e.interpolation region), dashed-linecurveFleming correction, dotted-line curveNg correction

Pediatr Nephrol

Schwartz and Work [13] presented two tables with normalGFR values for children, one with inulin as the referencemethod, but dating from 1982 [28] and 1989 [29], and onewith the results of Piepsz et al. [25], dating from 2006. It is

important to draw attention to the difference between theseage-periods, as both tables in the Schwartz article reference‘normal’ values for GFR for children aged >2 years. In thefirst table mean normal GFR is about 120 mL/min/1.73 m2 as

Table 5 Meta-analysis dataa

Age (years) L50(cm) W50

(kg)Scr50(mg/dL)

GFR50

(mL/min)BSA(m2)

Indexed GFR50

(mL/min/1.73 m2)Integer k

Infants

0.15 57.4 5.0 0.24 6.3 0.2683 40.6 0.170

0.25 60.3 5.8 0.24 10.1 0.2962 59.0 0.235

0.35 62.6 6.5 0.24 12.5 0.3194 67.7 0.260

0.45 65.0 7.0 0.24 14.4 0.3388 73.5 0.272

0.55 67.0 7.5 0.25 15.9 0.3566 77.1 0.288

0.7 71.0 8.5 0.26 17.2 0.3922 75.9 0.278

0.9 74.0 9.4 0.27 20.4 0.4218 83.7 0.305

1.1 77.0 9.8 0.28 22.7 0.4419 88.9 0.323

1.3 79.0 10.4 0.28 24.8 0.4617 92.9 0.329

1.5 82.0 11.0 0.29 26.7 0.4858 95.1 0.336

1.7 84.5 11.6 0.29 28.3 0.5078 96.4 0.331

1.9 87.5 12.2 0.29 29.6 0.5321 96.2 0.319

Children

2.5 91.0 13.5 0.30 32.0 0.5716 96.9 0.319

3.5 99.5 15.5 0.32 38.7 0.6467 103.5 0.333

4.5 106.5 17.5 0.36 43.4 0.7153 105.0 0.355

5.5 113.0 20.0 0.38 50.2 0.7903 109.9 0.370

6.5 120.0 22.5 0.42 56.6 0.8679 112.8 0.395

7.5 126.5 24.5 0.44 58.3 0.9349 107.9 0.375

8.5 132.0 27.5 0.47 61.1 1.0127 104.4 0.372

9.5 137.0 31.5 0.49 66.7 1.1022 104.7 0.374

11 146.2 37.0 0.53 79.4 1.2372 111.0 0.402

13 158.8 46.6 0.59 91.0 1.4486 108.7 0.404

Female adolescents

15 164.7 54.9 0.64 96.6 1.5945 104.8 0.407

16 165.8 57.2 0.67 1.6310

17 166.2 58.5 0.69 1.6495

18 166.3 59.2 0.69 1.6586

19 166.4 59.6 0.70 1.6641

20 166.5 59.9 0.70 1.6684

Male adolescents

15 171.9 58.5 0.72 96.6 1.6904 98.9 0.414

16 175.8 62.8 0.78 1.7701

17 178.1 65.9 0.82 1.8244

18 179.4 68.0 0.85 1.8587

19 180.2 69.6 0.88 1.8832

20 180.8 70.7 0.90 1.9004

L50Median height,W50median weight, Scr50 median serum creatinine, GFR50 median glomerular filtration rate, where subscript 50 indicates themedianvalue. BSA Body surface areaaMeta-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:cGFR50 = k × L50/Scr50

Pediatr Nephrol

published in the 1980s and measured with the inulin clearancemethod, compared to the mean normal GFR value in the sec-ond table of about 105 mL/min/1.73 m2, obtained in 2006 andmeasured by 51Cr-EDTA. This difference may be partiallyexplained by the underestimation of the inulin GFR measure-ment by the 51Cr-EDTA GFR measurement [30], or, and thisis more probable, by the change in BSA in more recent years,as compared to 30 years ago. Delanaye et al. [31] reviewedliterature values for measured GFR (mGFR) normal referenceintervals for adults. These authors found that more recentstudies presented lower mGFR values as normal values, i.e.mean values of 100–110mL/min/1.73m2, compared to earlierstudies published some decades ago. These lower valuescould be explained by the BSA adjustment, as BSA has in-creased significantly during the last three decades and theBSA-unadjusted GFR did not show such a decrease [32].Therefore, we consider the results of Piepsz et al. [25] as thereference work for normal GFR values in children. Theseauthors measured GFR by plasma disappearance of 51Cr-EDTA in 623 children evaluated for potential mild urogenitalabnormalities, including only patients with no significant kid-ney defects. They showed that GFR rises progressively fromneonatal age to about 2 years of age, stabilizing at a value ofabout 107 mL/min/1.73m2, as calculated from the data report-ed by Pottel et al. [27]. Piepsz et al. had only partially pub-lished these results for GFR in milliliters per minute per1.73 m2 [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 calculateBSA from the median height and weight and expressed nor-mal GFR values in milliliters per minute per 1.73m2. The dataof Piepsz et al. expressed in the latter units were then fitted bya simple model [27]: GFR=107.3 × [1 – exp(−Age/0.5)] inwhich the term in brackets describes the rise in GFR between0 and 2 years old, stabilizing at 107.3 mL/min/1.73 m2 asexp(−Age/0.5) ≈ 0 for Age > 2 years. In that same articlePottel et al. also presented median serum creatinine (Scr)values for children of the same age groups. These Scr valueswere obtained from enzymatically measured isotope dilutionmass spectrometry-equivalent Scr concentrations [34]. Theresults of Piepsz et al. [26] and Pottel et al. [27] are summa-rized in Table 5.

The meta-analysis data in Table 5 can be considered asreference data for the average healthy (Belgian) child agedbetween 1 month and 15 years. As Belgium is centrally locat-ed in continental Europe, these data may be considered to berepresentative for the average healthy European child.However, there are a number of concerns regarding these data,as summarized by Schwartz [35]. The reference clearancevalues relied on the single-plasma method, described byHam and Piepsz [24]. The uncertainty of a single-point meth-od 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], whereasthe British Nuclear Medicine Society recommends the use ofthe Bröchner–Mortensen correction [37]. Also, the clearanceswere 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 ofhealthy Belgian children and represent average kidney func-tion values (GFR and Scr) and demographic information(height and weight) according to age.

Estimating GFR

Equations for estimating the GFR, based on serum concentra-tions of creatinine (Scr) or cystatin C (CysC), are popular inboth the clinical setting and in research studies. Continuousefforts 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 thecurrently available eGFR equations, and there is no real accu-rate and precise substitute for the direct measurement.Moreover, GFR estimating equations are based on the resultsof direct measurements and are constructed to match themGFR, which serves as the independent variable during thestatistical modeling. It is therefore important to realize thateGFR equations are heavily dependent on the data used duringthe development of the equation. Equations based on data fromhealthy children will therefore differ from equations based ondata from children with a diseased kidney.

Scr-based eGFR equations

Table 5 has been used to calculate the average GFR of107.3 mL/min/1.73 m2 for healthy children between 2 and15 years of age and to develop the FlandersMetadata equation[27]:

eGFR ¼ 0:0414� ln ageð Þ þ 0:3018ð Þ � L=Scr

This equation is of the form eGFR= k×L/Scr and differs onlyfrom the well-known bedside (and updated) Schwartz equa-tion [38]:

eGFR ¼ 0:413� L=Scr

by considering an age-dependent value for k. In Table 5, wecalculated the values of k at the corresponding ages, based oncGFR50× Scr50/L50, where this age-dependency is clearlydemonstrated. It should also be noted that Schwartz et al.published an older version of his famous bedside equation[39] (va l id for so-cal led 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

Pediatr Nephrol

(k=0.45) [40], children up to 14 years old (k=0.55) and maleadolescents (k=0.70) [41], where k=0.55 could still be usedfor female adolescents. This clearly suggests an age-dependency for the factor k, which was not modeled bySchwartz in his updated version. The Flanders Metadata equa-tion can thus be considered as an attempt to define an age-dependent k value for the updated bedside Schwartz equation.The k value in the Flanders Metadata equation [k -=0.0414× ln(age)+0.3018]varies from 0.3018 (at the age of1 year) to about 0.413 at the age of 15 years, meaning that thek = 0.413 in the Schwartz equation is too high for most(healthy) children. It should be noted that the updated bedsideSchwartz equation has been derived in 349 children aged be-tween 1 and 16 years, with established kidney disease (themedian iohexol-GFR was only 41.3 mL/min/1.73 m2). Thisis a completely different dataset than the data presented inTable 5, which describe the renal parameters and demo-graphics of healthy children. The 349 children in the cohortused by Schwartz to derive his bedside formula showed nota-ble growth retardation. The nature of the data and the limitedsample size of the Schwartz cohort, given the knowledge thatScr evolves with age (and height), were probably not sufficientto derive age-dependent k values. De Souza also questionedthe adequacy of one k value for all children [42] and arrived atfollowing simple adjustment to the Schwartz equation:

eGFR ¼ 0:368L=Scr ingirls all agesð Þandboys < 13yearseGFR ¼ 0:413L=Scr in boys ≥ 13 years

(0.368=32.5/88.4; 0.413=36.5/88.4, with 88.4 the conversionfactor for Scr expressed in μmol/L to mg/dL).

De Souza et al. re-estimated the k value and found that thevalue of 0.413 was too high for her population (360 Frenchchildren with 965 inulin measurements and 109 Swedish sub-jects), with the exception of male subjects aged≥13 years.From the above discussion, it is clear that to achieve the bestGFR estimation accuracy for formulas of the formeGFR = k × L/Scr, a ‘locally derived’ constant or age-dependent k value may be calculated. As the k value may alsodepend on the reference standard GFR method, it might be agood suggestion—when this simple form of an eGFR equa-tion is used within a specific center—to regress the mGFRagainst height/Scr and derive center-specific k values (for dif-ferent ages) [42–45].

A different approach to developing eGFR equations hasbeen proposed by Pottel et al. [46]. Table 5 can also be usedto demonstrate this alternative way of developing an eGFRequation. The underlying notion is that the average GFR valueof 107.3 mL/min/1.73 m2 for healthy children, which is inde-pendent of age, corresponds to the average Scr value. As theaverage Scr value depends on age, Pottel et al. proposed tonormalize Scr. To this end, for an individual subject, the Scrvalue was normalized with the median Scr value at the

corresponding age (Scr50 in Table 5). Assuming an inverserelationship between GFR and this normalized Scr (de-noted by Scr/Q), Pottel proposed and validated the fol-lowing simple relationship:

eGFR ¼ 107:3= Scr=Q½ �where Q is the value of Scr50 presented in Table 5.When Scr50 in Table 5 for children between 2.5 and13 years old is plotted against height (L50), with ther equ i r emen t t ha t t h e i n t e r c ep t i s z e ro , t h enQ=0.0035 ×L (R2 = 0.959) is obtained. Entering this re-lationship 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, withk = 0.375, close to the k value of 0.368 of theSchwartz–Lyon equation for children between 2 and13 years of age. The simple Pottel equation for eGFR[eGFR=107.3/(Scr/Q)] has some interesting properties:

1) The coefficient of 107.3 can be interpreted as the GFR forthe average healthy child corresponding to the mean ormedian normalized Scr/Q=1. Deviation of Scr/Q from‘1’ means that the Scr value of the child deviates fromthe ideal median Scr value for his/her specific age (orheight), and this results in a deviation from the ideal me-dian GFR value.

2) Pottel also showed that the distribution of Scr/Q isGaussian (bell-shaped) with a mean or median equal to‘1’ andwith lower 2.5th and upper 97.5th percentiles (Pct)of 0.67 and 1.33, respectively. From this, a lower 2.5th Pctfor eGFR=107.3/1.33=80.67mL/min/1.73m2 can easilybe derived. Taking the 99.5th Pct for Scr/Q=1.43, Pottelconcluded that eGFR=107.3/1.43=75 mL/min/1.73 m2

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 thechild, but also to his/her height, resulting in two differentversions for this simple equation—one that is age-dependent and one that is height-dependent.

Hoste et al. [48] extended the simple equation to adoles-cents and young adults and presented the age-dependent andheight-dependent forms of the equation. She found that foradolescents, height is a better predictor than age and, there-fore, that linking Q to height gives better predictions thanwhen Q is linked to age, although, for children up to 14 yearsof age both forms of the equation perform equivalently. Theadvantage of the height-independent Pottel equation is thatautomatic reporting of eGFR together with the Scr value canbe achieved, as height is usually not available in the clinicallaboratory database.

Pediatr Nephrol

If height is available for adolescents or young adults, thenthe height-dependent form of the equation is to be preferredbecause height serves as a good surrogate for muscle mass [35].

Pottel et al. [49] recently extended this equation to middle-aged and older adults, introducing an age-dependent decline fac-tor from 40 years onwards, resulting in an eGFR equation whichis valid for the full age spectrum (FAS), the FAS-equation:

eGFR ¼ 107:3 = Scr=Qð Þ for 2≤age≤40yearseGFR ¼ 107:3= Scr=Qð Þ � 0:988 Age−40ð Þ f or age > 40 years

Q-values are presented in Table 5; for adults and olderadults, Q=0.70 mg/dL for females and Q=0.90 mg/dL formales should be used.

More complex Scr-based formulas for children havebeen developed in which Scr is combined with only ageand gender, such as the BCCH2 (British ColumbiaChildren’s Hospital) equation [50], or with height, ageand gender, such as the BCCH1 equation [50] and theequation proposed by Gao et al. [51] and the Lund–Malmö equation [52].

BCCH 1 : ln eGFRð Þ ¼ 1:18þ 0:0016�Wtþ 0:01� Htþ 149:5= Scr � 88:4ð Þ–2141= Scr � 88:4ð Þ2BCCH 2 : eGFR ¼ �61:56þ 5886= Scr � 88:4ð Þ þ 4:83� Ageþ 10:02 if maleð ÞGao : eGFR ¼ 0:68� Ht=Scr�0:0008� Ht=Scrð Þ2 þ 0:48� Age� 21:53=25:68 if male=femaleð ÞLund−MalmP : eGFR ¼ exp 4:62�0:0112� Scr � 88:4�0:0124� Ageþ 0:339� ln Ageð Þ½ �

with weight (Wt) in kilograms, height (Ht) in centimeters, Scrin milligrams per deciliter and age in years.

For heal thy chi ldren— that is , for the data inTable 5—Pottel et al. [27] showed that the Lund–Malmöequation closely follows the median data of Table 5—overthe complete age range. The BCCH1 equation closely followsthe data for children aged <2 years but largely overestimatesthese data for children aged >2 years. The BCCH2 equationwas derived using only easily available demographic informa-tion, and this equation was not intended to be used outside thelocal laboratory unless locally derived constants for the for-mula were used [50]. Gao’s equation matches the equation ofPottel for children between 2 and 14 years of age or between85 and 165 cm, but it deviates for adolescents. For childrenwith normal or supra-normal GFR, the equations of Gao,Lund–Malmö and Pottel perform quite equally and are prob-ably the preferred choice. It should be noted, however, thatGao’s formula has been designed for the compensated Jaffeassay for Scr, while the other equations were designed for theenzymatic Scr assay, which is known to be IDMS-equivalent.For children with CKD and growth retardation, the Schwartzbedside formula is probably the preferred choice. Adult equa-tions are not applicable to children or adolescents [53, 54];however, the other way around is likely, with pediatric equa-tions being applicable to young adults up to the age of40 years, as shown by Pottel [49], Selistre [53] and Hoste[48]. A major drawback of all Scr-based equations is that theyclearly overestimate renal function in the case of children withreduced muscle mass (and thus with very low Scr) [55].

Most Scr-based eGFR equations are not applicable to chil-dren younger than 2 years of age, although there are formulas(e.g. Flanders Metadata [27] and the Pottel formula with ex-ponential term [46]), that can be applied for ages of>1 month.However, these applications lack validation for children aged

between 1month and 2 years and may show large bias [56]; assuch, they should be used with caution. At birth, children havean Scr level which reflects the maternal Scr concentration(0.70 mg/dL), and in the first postnatal month Scr decreasesrapidly from about 0.70 to 0.25 mg/dL, and then graduallyincreases when the child is gaining muscle mass [27]. Thisexplains why Scr-based eGFR equations are not applicable inthe first month of life.

CysC-based eGFR-equations

Cystatin C-based eGFR equations overcome the limita-tions of Scr-based eGFR equations. CysC is a smallprotein that is freely filtered at the glomerulus and notsignificantly affected by age, gender and muscle mass[45, 57], but it may be affected by the use of medica-tion (steroids) in renal transplant patients and patientswith inflammatory and thyroid disorders [45]. SeveralCysC formulas have been derived, and these formulashave proven to be interesting eGFR equations, but theydo not seem to be superior to Scr-based equations [44].However, they can be useful to replace Scr-based equa-tions in case of specific situations of reduced musclemass. They might also be more accurate than Scr-based equations for children aged <2 years [56]. Anon-exhaustive list of univariate CysC-based eGFRequations is as follows :

Hoek [58]: eGFR=−4.32+80.35×CysC− 1

Bricon et al. [59]: eGFR=78×CysC− 1 +4Larsson et al. [60]: eGFR=77.24×CysC− 1.2623

Rule et al. [61]: eGFR=76.6×CysC− 1.16

Filler and Lepage [62]: eGFR=91.62×CysC− 1.123

Zappitelli et al. [63]: eGFR = 75.94 × CysC− 1.17

Pediatr Nephrol

It should be noted that all of these equations have more orless the same mathematical form (univariate inverse powerrelations between GFR and CysC) and, in fact, these equationsare not really different in predicting GFR from the CysC con-centration. Reference values for CysC vary between approxi-mately 0.50 and 1.50 mg/L (for adolescents aged between 12and 17 years, the 1st and 99th Pcts of 0.57 and 1.21mg/L havebeen presented [64]). Table 6 lists the predicted eGFR valuesfor the various CysC-based eGFR equations for normal CysCconcentrations.

When the predicted eGFR values for the different formulasin Table 6 are plotted and fitted with a power function, asshown in Fig. 3, then the relationship eGFR = 79.7CysC−1.12 explains 96 % of the variation in the predictionsof all eGFR equations listed in Table 6. It is important to notethat all CysC-based equations in Table 6 were obtained be-tween 2000 and 2006, that is, 10–15 years ago when there wasno certified reference material available. All assays measureCysC, but there were considerable differences between assaysand, therefore, in measured CysC concentrations, explainingthe variety in coefficients for the CysC power functions. Thedifferences between equations are most pronounced in the lowCysC range (CysC<0.80 mg/L). This shows that it is notreally necessary to derive new (univariate) eGFR–CysC equa-tions, but multivariate models adding independent demo-graphic variables such as age, sex, height, weight and bloodmarker variables (like Scr) may still improve the GFR–CysCrelationship. An example of a CysC-based equation, addingdemographic information to the equation, is

eGFR= 86.49 ×CystC− 1.680 × 1.384(if age < 14 years)Grubb et al. [65]

but more external validation of this equation is necessary toevaluate the validity of the predictions.

One of the challenges with eGFR equations is to define whichequation to use in which circumstances. CysC-based equationsare definitely preferable over Scr-based equations in patients withsevere muscle mass reduction (Duchenne muscular dystrophypatients, anorexia patients, oncology patients, wheelchair pa-tients, among others) because Scr-based equations will severelyoverestimate the real GFR. It is not clear yet if CysC-basedequations have an improved or added value over Scr-basedeGFR equations for children in other situations, and given thatthe cost for CysC measurements is approximately eight- to nine-fold the cost of Scr measurements, CysC measurements are notroutinely recommended. The major reason for the diversity ofCysC-based eGFR equations is the previous lack of an interna-tional CysC calibrator and the non-equivalence of results fromdifferent CysC assays. Turbidimetric and nephelometric CysCassays lead to substantially different results, with the latter lead-ing tomore accurateGFR estimation.Now that there is a certifiedreference material (ERM-DA471/IFCC) [66], it should becomepossible to derive a simple CysC-based eGFR equation for chil-dren. The most recent simple, assay-independent CysC-basedequation is the CAPA equation (CAPA=Caucasian, Asian,Paediatric, Adult) which should also be valid for children :

CAPA [67]: eGFR=130×CysC− 1.069 × age− 0.117−7

The CAPA equation has been evaluated in a mixed cohortof Dutch and Swedish children (n=246). Underestimation ofthe GFR in children was noted, and the overall accuracy (P30)was around 75–80 %, suggesting that there is still work to do,specifically for children, in terms of deriving a more accurate

Table 6 Estimated glomerularfiltration rate predictions fordifferent univariate CystatinC-based equationsa

Cystatin C (mg/L) Estimated glomerular filtration rate (mL/min/1.73 m2)b

Hoek/2003[58]

Le Briconet al./2000[59]

Larssonet al./2004[60]

Rule et al./2006 [61]

Filler andLepage/2003 [62]

Zappitelliet al./2006[63]

0.50 156 160 185 171 200 171

0.60 130 134 147 139 163 138

0.70 110 115 121 116 137 115

0.80 96 102 102 99 118 99

0.90 85 91 88 87 103 86

1.00 76 82 77 77 92 76

1.10 69 75 68 69 82 68

1.20 63 69 61 62 75 61

1.30 57 64 55 57 68 56

1.40 53 60 51 52 63 51

1.50 49 56 46 48 58 47

a The first certified reference material was published in 2010 [66]b Values are presented according to the first author/year of the publication

Pediatr Nephrol

CysC-based eGFR equation using the international certifiedreference material.

Scr/CysC-based eGFR equations

Equations for eGFR that combine Scr and Cystatin C, withdemographic variables (height, weight, age, sex) and/or clin-ical conditions (renal transplant, among others) have also beenderived. Combining CysC and creatinine assays improvesGFR estimations and may reduce imprecision. However, theequations become complex; for example:

Zappitelli et al. [63]:

eGFR ¼ 43:82� exp 0:003� Htð Þð Þ= CysC0:635 � Scr0:547� �

�1:165 if renal transplant�1:57Scr0:925if spinabifida

Chehade et al. [68]:

eGFR ¼ 0:42� Ht=Scrð Þ–0:04� Ht=Scrð Þ2−14:5� CysCþ 0:69�Ageþ 18:25 if female; or 21:88 if maleð Þ

, with Scr in mg/dL, height in cm, Cystatin C inmg/L, agein years.Bouvet et al. [69]:

eGFR ¼ 63:2� Scr=96ð Þ−0:35 � CysC=1:2ð Þ−0:56

� Wt=45ð Þ0:30 � Age=14ð Þ0:40

Chronic Kidney Disease in Children (CKiD) Study [70]:

eGFR ¼ 39:8� Ht=Scrð Þ0:456 1:8=CysCð Þ0:418 30=BUNð Þ0:079

1:076male Ht=1:4ð Þ0:179

with Scr in micromoles per liter, height in meters, weightin kilograms, age in years, CysC in milligrams per literand blood urea nitrogen in milligrams per liter.

The CKiD equation (or the combined Schwartz equation)shows high accuracy and precision and minimal bias in theCKiD population. Confirmation of the utility of this equationis desirable in other populations of children (healthy and dis-eased). The Chehade formula could replace the combinedSchwartz formula for children with moderate chronic kidneydisease [68].

From a practical point of view, it is mostly important forclinicians to differentiate children with normal (GFR >75 mL/min/1.73m2) from those with abnormal GFR. The simple Scr-based 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 simpleScr-based formulas in these cases. When high accuracy isdesired, combining Scr and Cystatin C will certainly improvethe estimation, but these combined equations suffer from thesame drawbacks as the Scr-based equations. When there isgreat uncertainty, then the direct measurement of GFR is stillrecommended [71].

eGFR equations using other biomarkers

Ongoing research to improve the estimation of kidney func-tion 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 concludedthat BTP was superior to Scr and was an alternative for CysCto detect mildly reduced GFR in children, but he admitted thatit was not better than the Schwartz equation. However, todaythere are still no real accurate alternatives to the Scr-basedeGFR equations, with the exception of mixed Scr/CysCeGFR equations. Witzel et al. [73] has developed a sex-specific formula based on BTP, Scr and height, but externalvalidation is still required to estimate the validity and applica-bility of this new formula. A requirement for a new formula is

Fig. 3 Estimated glomerularfiltration rate (eGFR)-Cystatin C(CysC) relationship

Pediatr Nephrol

also the availability, cost and robustness of assays to deter-mine the concentration of biomarkers in routine practice.

Key summary points

1. Direct GFR measurements are performed using exoge-nous filtration markers: inulin (gold standard), iohexol,51Cr-EDTA, 99mTc-DTPA, Iothalamate.

2. Direct GFR measurements can be performed using twodifferent procedures: the renal clearance procedure, in-volving blood and urine samples and the plasma clearanceprocedure, involving only blood samples.

3. The plasma clearance protocol may be done using a two-compartment model (using early and late blood samples)or a one-compartment model (using late blood samplesonly). The one-compartment model requires a correctionmethod for the overestimation of the GFR.

4. Estimating GFR is mostly done using Scr-based eGFRequations. CysC-based eGFR equations are valid alterna-tives and the mixed Scr/CysC eGFR equations havehigher accuracy and precision.

Multiple choice questions (answers are providedfollowing the reference list)

1. Normal GFR for children is abovea. 60 mL/min/1.73 m2

b. 75 mL/min/1.73 m2

c. 90 mL/min/1.73 m2

d. 120 mL/min/1.73 m2

2. The gold standard for direct GFR measurement isa. Renal clearance of inulinb. Plasma clearance of iohexolc. Renal clearance of iothalamated. Plasma clearance of inulin

3. When the reduced plasma clearance protocol with onlylate blood samples is used, thena. The AUC is overestimated and can be corrected with

the Bröchner-Mortensen formulab. The AUC is underestimated and can be corrected with

the Bröchner-Mortensen formulac. The GFR is overestimated and can be corrected with

the Bröchner-Mortensen formulad. The GFR is underestimated and can be corrected with

the Bröchner-Mortensen formula

4. The updated bedside Schwartz equation isa. eGFR=0.368 L/Scr

b. eGFR=0.413 L/Scrc. eGFR=107.3/[Scr/Q]d. eGFR=0.413 L/CysC

5. Scr-based equations should be avoideda. For adolescentsb. For healthy childrenc. For children with CKDd. For children with reduced muscle mass

Compliance with ethical standards

Conflict of interest statement The author declares that he has no con-flict of interest.

References

1. Gaspari F, Perico N, Remuzzi G (1997)Measurement of glomerularfiltration rate. Kidney Int Suppl 63:S151–S154

2. Hoste L, Pottel H (2012) Is body surface area the appropriate indexfor glomerular filtration rate? In: Sahay M (ed) Basic Nephrologyand acute kidney injury. Rijeka, Intech, pp 1–20. Available at:http://cdn.intechopen.com/pdfs/29473.pdf

3. Kidney Disease: Improving Global Outcomes (KDIGO) CKDWork Group (2013) KDIGO 2012 Clinical practice guideline forthe evaluation and management of chronic kidney disease. KidneyInt Suppl 3:1–150

4. Du Bois D, Du Bois EF (1916) Clinical calorimetry: tenth paper aformula to estimate the approximate surface area if height andweight be known. Arch Intern Med 17:863–871

5. van der Sijs H, Guchelaar HJ (2002) Formulas for calculating bodysurface area. Ann Pharmacother 36:345–346

6. Haycock GB, Schwartz GJ, Wisotsky DH (1978) Geometric meth-od for measuring body surface area: a height–weight formula vali-dated in infants, children, and adults. J Pediatr 93:62–66

7. Mosteller R (1987) Simplified calculation of body surface area.New Engl J Med 317:1098

8. Smith HW (1951) The kidney: structure and function in health anddisease. Oxford University Press, New York

9. Delanaye P (2012) How measuring glomerular filtration rate?Comparison of reference methods. In: Sahay M (ed) BasicNephrology and acute kidney injury. Rijeka, Intech, pp 21–60.Available at: http://cdn.intechopen.com/pdfs/29474.pdf

10. Frennby B, Sterner G (2002) Contrast media as markers of GFR.Eur Radiol 12:475–484

11. Stevens LA, Levey AS (2009) Measured GFR as a confirmatorytest for estimated GFR. J Am Soc Nephrol 20:2305–2313

12. Soveri I, Berg UB, Björk J, Elinder CG, Grubb A, Mejare I, SternerG, Bäck SE, on behalf of the SBU GFR Review Group (2014)Measuring GFR: a systematic review. Am J Kidney Dis 64:411–424

13. Schwartz GJ, Work DF (2009) Measurement and estimation ofGFR in children and adolescents. Clin J Am Soc Nephrol 4:1832–1843

14. Sterner G, Frennby B, Mansson S, Nyman U, Van Westen D,Almén T (2008) Determining Btrue^ glomerular filtration rate inhealthy adults using infusion of inulin and comparing it with valuesobtained using other clearance techniques or prediction equations.Scand J Urol Nephrol 42:278–285

Pediatr Nephrol

15. Bröchner-Mortensen J (1972) A simple method for the determina-tion of glomerular filtration rate. Scand J Clin Lab Invest 30:271–274

16. Schwartz GJ, Furth S, Cole SR, Warady B, Muñoz A (2006)Glomerular filtration rate via plasma iohexol disappearance: pilotstudy for chronic kidney disease in children. Kidney Int 69:2070–2077

17. Schwartz GJ, Abraham AG, Furth SL, Warady BA, Muñoz A(2010) Optimizing iohexol plasma disappearance curves to mea-sure the glomerular filtration rate in children with chronic kidneydisease. Kidney Int 77:65–71

18. Ng DK, Schwartz GJ, Jacobson LP, Palella FJ, Margolick JB,Warady BA, Furth SL, Muñoz A (2011) Universal GFR determi-nation based on two time points during plasma iohexol disappear-ance. Kidney Int 80:423–430

19. Fleming JS (2007) An improved equation for correcting slope-intercept measurements of glomerular filtration rate for the singleexponential approximation. Nucl Med Commun 28:315–320

20. Bröchner-Mortensen J, Jødal (2009) Reassessment of a classicalsingle injection 51Cr-EDTA clearance method for determinationof renal function in children and adults. Part II: empirically deter-mined relationships between total and one-pool clearance. Scand JClin Lab Invest 69:314–322

21. Pottel H, Gheysens O (2015) Response to the letter concerningmeasuring glomerular filtration rate using chromium-51 EDTA:body surface area normalization before or after Bröchner-Mortensen correction? Nucl Med Commun 36:297–300

22. Christensen AB, Groth S (1986) Determination of 99m Tc-DTPAclearance by a single plasma method. Clin Physiol 6:579–588

23. Jacobsson L (1981) A method for the calculation of renal determi-nation by one plasma sample. Clin Physiol 3:297–305

24. Ham HR, Piepsz A (1991) Estimation of glomerular filtration ratein infants and in children using a single-plasma sample method. JNucl Med 32:1294–1297

25. Piepsz A, Tondeur M, Ham HR (2006) Revisiting normal (51)Cr-ethylenediaminetetraacetic acid clearance values in children. Eur JNucl Med Mol Imaging 33:1477–1482

26. Piepsz A, Tondeur M, Ham H (2008) Escaping the correction forbody surface area when calculating glomerular filtration rate inchildren. Eur J Nucl Med Mol Imaging 35:1669–1672

27. Pottel H, Mottaghy FM, Zaman Z, Martens F (2010) On the rela-tionship between glomerular filtration rate and serum creatinine inchildren. Pediatr Nephrol 25:927–934

28. Brodehl J, Gellissen K, Weber H (1982) Postnatal development oftubular phosphate reabsorption. Clin Nephrol 17:163–171

29. Gibb DM, Dalton NR, Barratt MT (1989) Measurement of glomer-ular filtration rate in children with insulin-dependent diabetesmellitus. Clin Chim Acta 182:131–139

30. Bröchner-Mortensen J (1973) The glomerular filtration rate duringmoderate hyperglycemia in normal man. Acta Med Scand 1–2:31–37

31. Delanaye P, Schaeffner E, Ebert N, Cavalier E, Mariat C,Krzesinski J-M, Moranne O (2012) Normal reference values forglomerular filtration rate: what do we really know? Nephrol DialTransplant 27:2664–2672

32. Poggio ED, Rule AD, Tanchanco R, Arrigain S, Butler RS, SrinivasT, Stephany BR, Meyer KH, Nurko S, Fatica RA, Shoskes DA,Krishnamurthi V, Goldfarb DA, Gill I, Schreiber MJ (2009)Demographic and clinical characteristics associated with glomeru-lar filtration rates in living kidney donors. Kidney Int 75:1079–1087

33. Roelants M, Hauspie R, Hoppenbrouwers K (2009) References forgrowth and pubertal development from birth to 21 years inFlanders, Belgium. Ann Hum Biol 36:680–694

34. Pottel H, Vrydags N, Mahieu B, Vandewynckele E, Croes K,Martens F (2008) Establishing age/sex related serum creatinine

reference intervals from hospital laboratory data based on differentstatistical methods. Clin Chim Acta 396:49–55

35. Schwartz GJ (2014) In Focus Height : the missing link in estimatingglomerular fi ltration rate in children and adolescents. Nephrol DialTransplant 29:944–947

36. Chantler C, Barratt TM (1972) Estimation of glomerular filtrationrate from plasma clearance of 51-chromium edetic acid. Arch DisChild 47:613–617

37. Fleming JS, Zivanovic M, Blake GM, Burniston M, Cosgriff PS(2004) Guidelines for the measurement of glomerular filtration rateusing plasma sampling. Nucl Med Commun 25:759–769

38. Schwartz GJ, Muñoz A, Schneider MF,Mak RH, Kaskel F,WaradyBAFS (2009) New equations to estimate GFR in children withCKD. J Am Soc Nephrol 20:629–637

39. Schwartz GJ, Haycock GB, Edelmann CM, Spitzer M (1976) Asimple estimate of glomerular filtration rate in children derivedfrom body length and plasma creatinine. Pediatrics 58:259–263

40. Schwartz GJ, Feld LG (1984) A simple estimate of glomerularfiltration rate in full-term infants during the first year of life. JPediatr 104:849–854

41. Schwartz GJ (1985) A simple estimate of glomerular filtration ratein adolescent boys. J Pediatr 106:522–526

42. de Souza VC, Rabilloud M, Cochat P, Selistre L, Hadj-Aissa A,Kassai B, Ranchin B, Berg U, Herthelius M, Dubourg L (2012)Schwartz formula: is one k-coefficient adequate for all children?PLoS One 7:1–7

43. Zappitelli M, Zhang X, Foster BJ (2010) Estimating glomerularfiltration rate in children at serial follow-up when height is un-known. Clin J Am Soc Nephrol 5:1763–1769

44. Bacchetta J, Cochat P, Rognant N, Ranchin B, Hadj-Aissa A,Dubourg L (2011) Which creatinine and cystatin C equations canbe reliably used in children? Clin J Am Soc Nephrol 6:552–560

45. Andersen TB, Eskild-Jensen A, Frøkiaer J, Brøchner-Mortensen J(2009) Measuring glomerular filtration rate in children; can cystatinC replace establishedmethods?A review. Pediatr Nephrol 24:929–941

46. Pottel H, Hoste L, Martens F (2012) A simple height-independentequation for estimating glomerular filtration rate in children. PediatrNephrol 27:973–979

47. Pottel H, Hoste L, Delanaye P (2015) Abnormal glomerular filtra-tion rate in children, adolescents and young adults starts below 75mL/min/1.73 m2. Pediatr Nephrol 30:821–828

48. Hoste L, Dubourg L, Selistre L, De Souza VC, Ranchin B, Hadj-Aïssa A, Cochat P, Martens F, Pottel H (2013) A new equation toestimate the glomerular filtration rate in children, adolescents andyoung adults. Nephrol Dial Transplant 29:944–947

49. Pottel H, Hoste L, Dubourg L, Ebert N, Schaeffner E, Eriksen BO,Melsom T, Lamb EJ, Rule AD, Turner ST, Glassock RJ, De SouzaV, Selistre L, Mariat C, Martens F, Delanaye P (2016) An estimatedglomerular filtration rate equation for the full age spectrum.Nephrol Dial Transplant. doi:10.1093/ndt/gfv454

50. Mattman A, Eintracht S,Mock T, Schick G, Seccombe DW, HurleyRM, White CT (2006) Estimating pediatric glomerular filtrationrates in the era of chronic kidney disease staging. J Am SocNephrol 17:487–496

51. Gao A, Cachat F, Faouzi M, Bardy D, Mosig D, Meyrat BJ,Girardin E, Chehade H (2013) Comparison of the glomerular fil-tration rate in children by the new revised Schwartz formula and anew generalized formula. Kidney Int 83:524–530

52. NymanU, Björk J, LindströmV, Grubb A (2008) The Lund-Malmöcreatinine-based glomerular filtration rate prediction equation foradults also performs well in children. Scand J Clin Lab Invest 68:568–576

53. Selistre L, De Souza V, Cochat P, Ferreira Antonello IC, Hadj-AissaA, Ranchin B, Dolomanova O, Varennes A, Beyerle F, Bacchetta J,Dubourg L (2012) GFR estimation in adolescents and young adults.J Am Soc Nephrol 23:989–996

Pediatr Nephrol

54. Astor BC (2012) Chronic kidney disease: estimating GFR-the rightequation for the right population. Nat Rev Nephrol 8:379–380

55. Braat E, Hoste L, De Waele L, Gheysens O, Vermeersch P, GoffinK, Pottel H, Goemans N, Levtchenko E (2015) Renal function inchildren and adolescents with Duchenne muscular dystrophy.Neuromuscul Disord 25:381–387

56. Abitbol CL, Seeherunvong W, Galarza MG, Katsoufis C,Francoeur D, Defreitas M, Edwards-Richards A, Sankar Raj VM,Chandar J, Duara S, Yasin S, Zilleruelo G (2014) Neonatal kidneysize and function in preterm infants: what is a true estimate ofglomerular filtration rate? J Pediatr 164:1026–1031

57. Filler G, BökenkampA, HofmannW, LeBricon T,Martínez-Brú C,Grubb A (2005) Cystatin C as a marker of GFR - history, indica-tions, and future research. Clin Biochem 38:1–8

58. Hoek FJ (2003) A comparison between cystatin C, plasma creati-nine and the Cockcroft and Gault formula for the estimation ofglomerular filtration rate. Nephrol Dial Transplant 18:2024–2031

59. Bricon TL, Thervet E, Froissart M, Benlakehal M, Legendre C,Erlich D (2000) Plasma cystatin C is superior to 24-h creatinineclearance and plasma creatinine for estimation of glomerular filtra-tion rate 3 months after kidney transplantation. Clin Chem 46:1206–1207

60. Larsson A, Malm J, Grubb A, Hansson LO (2004) Calculation ofglomerular filtration rate expressed in mL/min from plasma cystatinC values in mg/L. Scand J Clin Lab Invest 64:25–30

61. Rule AD, Bergstralh EJ, Slezak JM, Bergert J, Larson TS (2006)Glomerular filtration rate estimated by cystatin C among differentclinical presentations. Kidney Int 69:399–405

62. Filler G, Lepage N (2003) Should the Schwartz formula for estima-tion of GFR be replaced by cystatin C formula? Pediatr Nephrol 18:981–985

63. Zappitelli M, Parvex P, Joseph L, Paradis G, Grey V, Lau S, Bell L(2006) Derivation and validation of cystatin C-based predictionequations for GFR in children. Am J Kidney Dis 48:221–230

64. Fadrowski JJ, Neu AM, Schwartz GJ, Furth SL (2011) PediatricGFR estimating equations applied to adolescents in the generalpopulation. Clin J Am Soc Nephrol 6:1427–1435

65. Grubb A, Nyman U, Björk J (2012) Improved estimation of glo-merular filtration rate (GFR) by comparison of eGFRcystatin C andeGFRcreatinine. Scand J Clin Lab Invest 72:73–77

66. Grubb A, Blirup-Jensen S, Lindström V, Schmidt C, Althaus H,Zegers I (2010) First certified reference material for cystatin C inhuman serum ERM-DA471/IFCC. Clin Chem Lab Med 48:1619–1621

67. Grubb A, Horio M, Hansson L-O, Bjork J, Nyman U, Flodin M,Larsson A, Bökenkamp A, Yasuda Y, Blufpand H, Lindström V,Zegers I, Althaus H, Blirup-Jensen S, Itoh Y, Sjöström P, Nordin G,Christensson A, Klima H, Sunde K, Hjort-Christensen P,Armbruster D, Ferrero C (2014) Generation of a new cystatin c-based estimating equation for glomerular filtration rate by use of 7assays standardized to the international calibrator. Clin Chem 60:974–986

68. Chehade H, Cachat F, Jannot AS, Meyrat BJ, Mosig D, Bardy D,Parvex P, Girardin E (2014) New combined serum creatinine andcystatin C quadratic formula for GFR assessment in children. Clin JAm Soc Nephrol 9:54–63

69. Bouvet Y, Bouissou F, Coulais Y, Séronie-Vivien S, Tafani M,Decramer S, Chatelut E (2006) GFR is better estimated by consid-ering both serum cystatin C and creatinine levels. Pediatr Nephrol21:1299–1306

70. Schwartz GJ, Schneider MF, Maier PS, Moxey-Mims M,Dharnidharka VR, Warady BA, Furth SL, Muñoz A (2012)Improved equations estimating GFR in children with chronic kid-ney disease using an immunonephelometric determination ofcystatin C. Kidney Int 82:445–453

71. Benisty K, Zappitelli M (2015) Measures of GFR in health anddisease. Curr Pediatr Rep 3:101–110

72. Filler G, Priem F, Lepage N, Sinha P, Vollmer I, Clark H, Keely E,Matzinger M, Akbari A, Althaus H, Jung K (2002) b-trace protein,cystatin C, b2-microglobulin, and creatinine compared for detectingimpaired glomerular filtration rates in children. Clin Chem 48:729–736

73. Witzel SH, Huang SHS, Braam B, Filler G (2015) Estimation ofGFR using b-trace protein in children. Clin J Am Soc Nephrol 10:401–409

Solutions to multiple choice questions

1. b2. a3. c4. b5. d

Pediatr Nephrol