ORIGINAL ARTICLE

Estimation of extracellular fluid volume in children

A. Michael Peters

Received: 19 November 2011 /Revised: 27 December 2011 /Accepted: 2 January 2012 /Published online: 16 March 2012# IPNA 2012

AbstractBackground Many equations have been developed to esti-mate various body fluid volumes from height and weight,but few have been developed for children. The aim of thisstudy was to compare four height/weight formulae for esti-mating extracellular fluid volume (eECV) in childrenagainst measured extracellular fluid volume (mECV).Methods The mECVwas obtained from plasma Cr-51-EDTAclearance data used for routine measurement of glomerularfiltration rate (GFR) in two groups of children (n0182 and 69,respectively). eECVobtained using the formulae of Abrahamet al. (Clin J Am Assoc Nephrol 6:741–747, 2011) andFriis-Hansen (Pediatrics 28:169–181, 1961) were comparedwith mECVin both patient groups. The formulae of Bird et al.(J Nucl Med 44:1037–1043, 2003) and of Peters (Nucl MedCommun 32:375–380, 2011) were originally based on groups1 and 2, respectively, so the eECV from them was comparedwith the mECV in groups 2 and 1, respectively.Results The eECV from the Friis-Hansen formula under-estimated the mECV in larger children. Biases (meandifferences between eECV and mECV) from the Bird(0.146 l) and Peters (0.029 l) formulae were not significantlydifferent from zero, but those from the Abraham formulawas higher than zero (0.694 and 0.588 l in groups 1 and 2;p<0.001). Precisions (standard deviations of the biases) of

these three formulae were similar, ranging from 0.731 l(Peters) to 0.878 l (Abraham, group 2; p>0.1).Conclusion The formulae of Bird, Peters and Abraham havesimilar precisions. The higher bias of the Abraham formulais probably due to the higher values of mECVon which theirformula was based. The Friis-Hansen formula no longer hasa place.

Keywords Glomerular filtration rate . Extracellular fluidvolume . Children . Cr-51-EDTA

Introduction

Many equations have been developed to estimate variousbody fluid volumes from height and weight, including totalbody water [1], blood volume [2] and extracellular fluidvolume (ECV) [3–7], but few have been developed forchildren.

ECV is an important volume and is the distributionvolume of indicators and tracers used to measure glo-merular filtration rate (GFR). This author is aware offour equations for estimating ECV that are applicable tochildren, two of which were developed specifically forchildren [4, 5] and two developed to encompass bothchildren and adults [6, 7].

The current study describes a simple method for mea-suring ECV from the same data from which GFR ismeasured using the slope–intercept technique (the clini-cal standard for measuring GFR in clinical practicethroughout the UK and Europe and also in many centresin North America). The study then goes on to make adirect comparison between the above-mentioned fourmethods of estimating ECV in children, using measuredECV (mECV) as the reference value.

A. M. Peters (*)Royal Sussex County Hospital,Audrey Emerton Building, Eastern Road,Brighton BN2 5BE, UKe-mail: a.m.peters@bsms.ac.uk

A. M. PetersDepartment of Nuclear Medicine, Harley St Clinic,London, UK

Pediatr Nephrol (2012) 27:1149–1155DOI 10.1007/s00467-012-2117-9

Methods

Participants

The participants, all children, were referred for routinemeasurement of GFR in a single institution. They weredivided into two groups.

The first group (n0182; Table 1) was studied between1999 and 2002 and formed part of the patient populationfrom which one of the ECV estimation formulae (Bird et al.[6]) was derived (see below). In this group, age ranged from0.9 to 15 years, body surface area (BSA) ranged from0.4 to 1.35 m2 (which, in the study of Bird et al. [6], wasset as the maximum) and GFR per unit ECV (GFR/ECV)ranged from 1.5 to 15.2 ml/min/l. The patients in thisgroup were referred for GFR measurement either formonitoring cancer chemotherapy (about two-thirds) orfor nephro-urological indications (about one-third).

The second group (n069) was studied after 2002 andformed part of the patient population from which anotherof the ECV estimation formulae (Peters [7]) was derived(see below). In this group, the age range was 0.5 to14 years, BSA ranged from 0.27 to 1.42 m2 and GFR/ECV

ranged from 4.5 to 10.4 ml/min/l. Because of the studyaims at the time, the patients in this group were restrictedto those referred for GFR measurement specifically fornephro-urological indications and to those with a GFR/ECVof >4.5 ml/min/l.

All data were analysed anonymously and retrospectivelyas a service improvement exercise, so ethical approval wasnot necessary.

Measurement of ECV

The ECV was measured (mECV) as the ratio of GFR toGFR/ECV, as previously described [8]. The GFR wasmeasured from three accurately timed blood samplestaken at about 120, 180 and 240 min after the injectionof Cr-51-EDTA using the slope–intercept method, scaledto a BSA of 1.73 m2 (GFR/BSA) using the equation ofHaycock et al. [9] to calculate the BSA from height andweight, and corrected for the assumption of a singlecompartment using the Brochner–Mortensen equationfor children [10]. Using BSA, the corrected GFR/BSAwas then ‘un-scaled’ to give absolute, single-compartmentcorrected GFR.

Table 1 Brief patient details compared between groups 1 and 2

Group Parameters Age(years)

Weight(kg)

BSA(m2)

BMI(kg/m2)

GFR/ECV(ml/min/l)

ECV/l(l/kg)

ECV/BSA(l/1.73 m2)

Group 1 Mean 6.42 22.3 0.831 16.1 7.89 0.223 9.84

Standard deviation 3.71 9.9 0.261 2.5 2.34 0.037 1.57

Group 2 Mean 5.95 21.5 0.806 16.5 7.60 0.222 9.69

Standard deviation 3.52 10.7 0.276 3.2 1.57 0.038 1.76

BSA, Body surface area; BMI, body mass index; GFR, glomerular filtration rate; ECV, extracellular fluid volume

1210864200

2

4

6

8

10

12

eECV (Peters) (l)

eEC

V (l

)

121086420

eECV (Bird) (l)

eECV (Abraham)eECV (Friis-Hansen)

1puorG1puorG

Fig. 1 Correlations betweenestimated extracellular volume(eECV) based on the Abraham(open circles) and Friis-Hansen(closed circles) (vertical axes)equations and eECV based onthe Peters equation in group 1(left panel) and Bird equationin group 2 (right panel)(horizontal axes). Lines areidentity

1150 Pediatr Nephrol (2012) 27:1149–1155

The GFR/ECV was expressed as the terminal rateconstant of the clearance curve (α2) with correction for theassumption of a single compartment using the followingequation described by Bird et al. [8]:

correctedGFR=ECV ¼ a2 þ a22 � 15:4

� �ml=min=ml ð1Þ

The ECV was then calculated as the ratio of un-scaledGFR and GFR/ECV, from which GFR cancels out. In arecent study, this method, using Cr-51-EDTA, gave an ECVin good agreement with ECV simultaneously measured frommulti-sample iohexol clearance [8].

Estimation of ECV (eECV) from weight (W; kg)and height (H; cm)

1. Peters (children and adults) [7]:

eECV ¼ 6:08� BSA1:34 ð2Þ

where [9]

BSA ¼ 0:0243�W0:538 � H0:396 ð3Þ

2. Bird et al. (children and adults) [6]:

eECV ¼ 0:0215�W0:647 � H0:724 ð4Þ

3. Abraham et al. (children) [5]:

eECV ¼ W0:5 � H ð5Þ

4. Friis-Hansen (children) [4]:

eECV ¼ 0:0682�W0:400 � H0:633 ð6Þ

The last three equations conform to the equationeECV 0 a⋅Wb⋅Hc, where a, b and c are constants. Note thatin Abraham’s equation, a00.01 (because H is expressed inm),b00.5 and c01.

Statistics

As the Bird and Peters equations were developed fromgroups 1 and 2, respectively, the Bird equation was testedonly in group 2 and the Peters equation tested only in group 1.Correlation between mECV and eECV was assessed usingPearson correlation analysis with correlation coefficient, r.The bias of eECV was measured as the mean differencebetween eECV and mECV, and precision was measuredas the standard deviation of the difference. Differencesbetween biases and zero were assessed using Student’s t test.Differences between precisions were assessed using the F test.Agreement between eECV and mECV was assessed usingthe Bland–Altman analysis, in which the difference betweenthe two variables being compared is regressed on theiraverage.

1210864201210864200

2

4

6

8

10

12

eEC

V (

l)121086420

mECV (l)

Abraham Peters Friis-Hansen

r = 0.936 r = 0.933 r = 0.940

Fig. 2 Correlations in group 1between measured extracellularvolume (mECV) and estimatedextracellular fluid volume(eECV) based on the Abraham(left panel), Peters (middle panel)and Friis-Hansen (right panel)equations, respectively.Lines are identity. The correlationcoefficient in the right panelis based on a second orderpolynomial fit

Table 2 Correlations between measured extracellular volume andestimated extracellular volume

Equations Intercept (l) Gradient r

Group 1 (n0182)

Friis-Hansen Polynomial Polynomial 0.940

Abraham 0.398 1.061 0.936

Peters 0.219 0.960 0.933

Group 2 (n069)

Fris-Hansen Polynomial Polynomial 0.937

Abraham 0.754 0.964 0.925

Bird 0.518 0.920 0.926

Pediatr Nephrol (2012) 27:1149–1155 1151

Results

Estimated ECV values respectively estimated by theAbraham and Peters equations in group 1 and the Abrahamand Bird equations in group 2 correlated very closely, withslightly higher values given by the Abraham formula (Fig. 1).In both groups, eECV from the Friis-Hansen equation, incontrast, showed a non-linear relation with eECV basedon the Peters and Bird equations (Fig. 1).

In group 1, all three estimates of eECV correlated closelywith mECV (Fig. 2; Table 2). For the Abraham and Petersestimates, the relations were linear, but for the Friis-Hansenequation, eECV increasingly underestimated mECV asmECV increased, and the regression was best fitted with asecond order polynomial. Similar correlations were seen ingroup 2 (Fig. 3; Table 2), in which the Peters equation wasreplaced by the Bird equation.

In group 1, the Bland-Altman analysis showed goodagreement between eECV estimated by the Abraham andPeters equations and mECV, with respective biases of 0.694(p<0.001 vs. 0) and 0.029 (p>0.05 vs. 0) l, respectively, andcorresponding precisions of 0.794 and 0.731 l (Fig. 4;

Table 3). Significant correlations were present betweenthe difference and average for the Abraham (r00.34; p<0.01)and Friis-Hansen (r0−0.69; p<0.001) formulae but notfor the Peters formula (r0−0.08). Similar results wererecorded in group 2 (Fig. 5; Table 3), except the onlyformula in which a significant correlation was recordedbetween the difference and average was the Friis-Hansenformula (r0−0.73; p<0.001). There were no significantdifferences in precision between all four equations ineither group.

The Peters formula (Eq. 2) was derived from the relationbetween ln BSA and ln ECV in children and adults.When this relation was applied to the children of groups1 and 2, eECV was 5.88 × BSA1.20 (r00.93) and 5.89 ×BSA1.24 (r00.94), respectively (Fig. 6), compared toeECV06.83 × BSA1.24 (r00.95) in the study of Abraham etal. [5]. These three equations give values of eECVat a BSA of1.73 m2 of 11.4, 11.6 and 13.5 l, respectively.

Abraham et al. [5] found that mECV/weight decreasedslightly with increasing age of the child, with median valuesof 0.26, 0.24 and 0.23 l/kg in age categories <5, 5–10 and10–15 years. Corresponding median values in the current

141210864200

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14Abraham

1412108642014121086420

mECV (l)eE

CV

(l)

nesnaH-siirFdriB

r = 0.925 r = 0.926 r = 0.937

Fig. 3 Correlations in group 1between measured extracellularfluid volume (mECV) andestimated extracellular fluidvolume (eECV) based on theAbraham (left panel), Bird(middle panel) and Friis-Hansen (right panel) equation,respectively. Lines are identity.The correlation coefficient inthe right panel is based on asecond order polynomial fit

121086420-4

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-2

-1

0

1

2

3

4

121086420 121086420

eEC

V -

mE

CV

(l)

(eECV + mECV)/2 (l)

Abraham Peters

Friis-Hansenr = 0.34 (p < 0.01) r = -0.08r = -0.69 (p < 0.001)

Fig. 4 Bland–Altman plots in group 1 showing agreement betweenmeasured extracellular fluid volume (mECV) and estimated extracellu-lar fluid volume (eECV) based on the Abraham (left panel), Peters(middle panel) and Friis-Hansen (right panel) equations, respectively.

Bold lines 0 0, fine lines 0 mean ± 2 standard deviations. Significantcorrelations are present between differences and averages for theAbraham and Friis-Hansen formulae but not for the Peters formula

1152 Pediatr Nephrol (2012) 27:1149–1155

study were 0.24, 0.21 and 0.21 l/kg in group 1, and 0.24,0.21 and 0.22 l/kg in group 2. For comparison with adults,recently published mean values of mECV/weight in largegroups of adult male (n0819) and female (n01,059)prospective renal transplant donors were both 0.18 l/kg[11].

Discussion

There are a limited number of clinical scenarios in which theestimation of ECV in children may be useful. The first is forscaling physiological variables, for example GFR, for bodysize. There has been much discussion recently about theshortcomings of BSA for physiological scaling, especiallyin children in whom the BSA is relatively large in relation tobody mass and gives a value of scaled GFR that is signifi-cantly lower in relation to the rate constant of the terminalexponential of the plasma clearance curve (α2) [6].Moreover, it is interesting to note that values of mECV inhealthy adult donors when scaled to BSA were 13.0 and12.0 l/1.73 m2 [11], respectively, which are much higher

than those in children (see Table 1) and the reverse of thedifference between adults and children seen with scaling toweight. The equation of Bird et al. (Eq. 4) was developedspecifically for the purpose of scaling GFR to eECV as analternative to BSA.

Another scenario for estimating ECV is for the esti-mation of lean body mass (LBM) in children. Equationsfor estimating LBM from height and weight are availablefor adults [12] but not children. Peters et al. recentlyreasoned that it is reasonable to assume that the relationbetween ECV and LBM is the same in children andadults [13]. They determined this relation in adults bymeasuring ECV using the same technique as that in thecurrent study and estimating LBM from the equationsdescribed by Boer [12], and then went on to find thatLBM (kg) is about 3.8 × ECV (l). Multiplication ofeECV determined using Eq. 4 by the factor 3.8 in childrentherefore gave an estimate of LBM [13].

The third scenario for estimating ECV is for epidemio-logical studies, especially in relation to childhood obesity inwhich LBM as a proportion of body weight is decreasedand probably a better measure of obesity than body massindex.

In the current study, it can be seen that the equation ofFriis-Hansen is only applicable to very small children andprogressively underestimates ECV in older children. It prob-ably therefore no longer has a place for estimating ECV. Theequations of Peters, Bird et al. and Abraham et al. all havesimilar precisions. This is remarkable for Abraham’s equa-tion given its disarming simplicity. Biases given by theequations of Peters and Bird et al., however, were close tozero, but bias given by the equation of Abraham et al. wassignificantly greater than zero. This difference is probablyexplained firstly by differences between the techniques formeasuring ECV and secondly by the patient populations.With respect to technique, Bird et al. [6] and Peters [7] used

Table 3 Precision and bias

Equations Bias (l) Precision (l) r

Group 1 (n0182)

Friis-Hansen −0.096 0.839 −0.69

Abraham 0.694* 0.794 0.34

Peters 0.029 0.731 −0.08

Group 2 (n069)

Fris-Hansen −0.104 1.039 −0.73

Abraham 0.588* 0.878 0.11

Bird 0.146 0.848 0.00

*p<0.001 vs. 0; no significant differences between precisions

eEC

V -

mE

CV

(l)

(eECV + mECV)/2 (l)

-6-5-4-3-2-101234

nesnaH-siirFdriBmaharbAr = 0.11 r = 0.00

r = -0.73 (p < 0.001)

121086420 121086420121086420

Fig. 5 Bland-Altman plots in group 2 showing agreement betweenmeasured extracellular fluid volume (mECV) and estimated extracellularfluid volume (eECV) based on the Abraham (left panel), Bird (middlepanel) and Friis-Hansen (right panel) equations. Bold lines 0 0, fine lines

0 mean ± 2 standard deviations. A significant correlation is presentbetween the difference and average for the Friis-Hansen formula butnot for the Abraham or Bird formulae

Pediatr Nephrol (2012) 27:1149–1155 1153

Cr-51-EDTA and three blood samples between 120 and240 min, while Abraham et al. [5] used iohexol and fourblood samples at 10, 30, 120 and 300 min; the latter authorsrecorded ECV/weight values of 0.23–0.26 l/kg with theirtechnique, slightly higher than those in the current groups of0.21–0.24 l/kg (see Results). Moreover, the relation betweenln BSA and ln mECV recorded by Abraham et al. giveshigher values of eECV at any value of BSA compared witheECV estimated from the relations between ln BSA and lnmECV determined in groups 1 and 2. These higher values ofmECV recorded by Abraham et al. in their study in whichthey developed their formula (Eq. 5) explains why eECVbased on Eq. 5 has a significant positive bias when com-pared with mECV measured using the current technique.With respect to the patient populations, the patients in thestudy of Abraham et al. all had renal impairment, a condi-tion in which ECV is may be modestly increased [14],which again would give a positive bias for Eq. 5 againstmECV measured in populations with predominantly normalfiltration function.

The clinical characteristics of the two patient groups inthe current study differed slightly as a result of patientselection for the specific aims of the original studies.Thus, in group 1, there were no exclusion criteria, soGFR, for example, showed a wider range of values as aresult of inclusion of patients with renal impairment andpatients with cancer who had hyperfiltration. In the secondgroup, however, patients in whom mECV may have beenabnormal were excluded, specifically those with cancer andthose with significant renal impairment. In spite of theseclinical differences, however, mECV and GFR were verysimilar between the two groups and the Bird and Petersequations gave very similar values of eECV.

In conclusion, the equations of Bird et al. [6], Peters [7],and Abraham et al. [5] have similar precisions. Bias,

however, is significantly greater with the Abraham equation,probably because of differences in technique for measuringECV and the characteristics of the patient population fromwhich the equation was derived. The Abraham equation isattractive on account of its simplicity. The Friis-Hansenformula no longer has a place.

References

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2. Nadler SB, Hidalgo JU, Bloch T (1962) Prediction of bloodvolume in normal human adults. Surgery 51:224–232

3. Silva AM, Wang J, Pierson RN, Wang ZM, Spivack J, Allison DB,Heymsfield SB, Sardinha LB, Heshka S (2007) Extracellular wateracross the adult lifespan: reference values for adults. Physiol Meas28:489–502

4. Friis-Hansen B (1961) Body water composition in children:changes during growth and related changes in body composition.Pediatrics 28:169–181

5. Abraham AG, Munoz A, Furth SL, Warady B, Schwarz GJ(2011) Extracellular volume and glomerular filtration rate inchildren with chronic kidney disease. Clin J Am Assoc Nephrol6:741–747

6. Bird NJ, Henderson BL, Lui D, Ballinger JR, Peters AM (2003)Indexing glomerular filtration rate to suit children. J Nucl Med44:1037–1043

7. Peters AM (2011) Re-evaluation of the new Jodal-Brochner-Mortensen equation for one-pool correction of slope-interceptmeasurement of glomerular filtration rate. Nucl Med Commun32:375–380

8. Bird NJ, Michell AR, Peters AM (2009) Accurate measurementof extracellular fluid volume from the slope/intercept techniqueafter bolus injection of a filtration marker. Physiol Meas30:1371–1379

9. Haycock GB, Schwarz GJ, Wisotsky DH (1978) Geometricmethod for measuring body surface area: a height-weight formulavalidated in infants, children and adults. J Pediatr 93:62–66

BSA (m2)E

CV

(l)

1

3

7

20

1.60.60.2 1.60.60.2

1

3

7

20ECV = 5.88 x BSA1.20

(r = 0.93)ECV = 5.89 x BSA1.24

(r = 0.94)

2puorg1puorg

Fig. 6 Correlations betweenbody surface area (BSA) andmeasured extracellular fluidvolume (mECV) in groups 1(left panel) and 2 (right panel).Lines are regression lines. Notelogarithmic co-ordinates

1154 Pediatr Nephrol (2012) 27:1149–1155

10. Brochner-Mortensen J, Haahr J, Christoffersen J (1974) A simplemethod for accurate assessment of the glomerular filtration rate inchildren. Scand J Clin Lab Invest 33:139–143

11. Peters AM, Perry L, Hooker CA, Howard B, Neilly MDJ, SeshadriN, Sobnack R, Irwin A, Snelling H, Gruning T, Patel NH, LawsonRS, Shabo G, Williams N, Dave S, Barnfield MC (2011) Extracel-lular fluid volume and glomerular filtration rate in 1,878 healthypotential renal transplant donors: effects of age, gender, obesityand scaling. Nephrol Dial Transplant. doi:10.1093/ndt/gfr479

12. Boer P (1984) Estimated lean body mass as an index fornormalization of body fluid volumes in man. Am J Physiol247:F632–F635

13. Peters AM, Snelling HLR, Glass DM, Bird NJ (2011) Estimationof lean body mass in children. Br J Anaesth 106:19–23

14. Peters AM, Glass DM, Bird NJ (2011) Extracellular fluid volumeand glomerular filtration rate: their relation and variabilities inpatients with renal disease and healthy subjects. Nucl Med Com-mun 32:649–653

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