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Development and validation of simplified renal clearance
methods has required a research data base of multiple blood samples drawn over a substantialtime interval, which is difficultto obtainfor children.Whilethe medicalrisksentailed in drawing multiple samples may be negligible, the problems of parental and institutional consent make such studies more
difficultin the pediatric population. Scaling for patient size
permits combining data from patients of different age and
limits the number of studies required. A scaling technique is presented and evaluated here. With scaling, adult data can
be used successfully to predict pediatric responses and to
develop pediatric methods based on adult data alone. Inclu sion of pediatric data improves the fit and permits develop ment of generic methods that work with both adults and
children.
J NuclMed 1991;32:1821—
implified renal clearancemethodsrequiring only one
or two plasmasampleshave proven useful for measuring
renal function in adults, but have been less well studied in
children. Each of these methods has been derived from a
research database of blood clearance curves: multiple
blood samples obtained over a substantial time interval, 3
hr or more in the caseof glomerular filtration rate (GFR)
agents. Such data are difficult to obtain for children be
cause of the practical problems related to informed con
sent.
Ifthe data are scaled for patient size, then measurements
from patients of different size can be combined so that
fewer data are required. A method of scaling is presented
here. To validate it, scaled methods for orthoiodohippurate
(OIH) clearance were first developed using plasma clear
ance curves from adults and then cross-tested against
pediatric data from the literature. After thus validating the scaling procedure, adult and pediatric data were combined to create general methods valid for all patients in the study
population (which included both adults and children).
Received Jan. 8, 1991 ; revision accepted Mar. 27, 1991. For reprints contact: Charles 0. Russell, MD, Division of Nuclear Medicine, Universityof Alabama Hospital, 619-19th St. South, Birmingham,AL 35233.
Iodine- 13 l-OIH plasma clearance curves were measured in 68 adults and in 30 children of 38 lb or more. The children ranged in age from 4 to 18 yr and in weight from 38 to 227 lb (median 73 Ib). Data were pooled from four prior publications, where the technical procedures were described in detail (1—4).We have analyzed the adult data elsewhere (5). One previously reported adult patient was eliminated from the present study because the weight ofthe patient was not recorded. Sampling ranged from six samples over 10—60mm to nine samples over 10—90mm.
A two-exponentialcurvewasfittedto eachdatasetandthe
fitted curves were used for subsequent analysis. OIH clearance was calculated from the fitted curves by the conventional Sapir stein method (6) except for four anephric adult patients, where the clearance was set to the true value of zero despite a small positive clearance by the Sapirstein calculation. Clearance was calculated by two methods: (1) an empirical single-sample formula and (2) a two-sample method based on a two-compartment model. These are described in detail in the appendix. The empirical scaled formula was derived by fitting the dimensionless quantity Ft/yE (where F represents clearance, t sample time, and VE extracellular fluid volume) with a poly nomial in the dimensionless quantity VI/VE (where V@is the apparent volume of distribution at time of sampling). Since volumes are scaled by weight, weight can be substituted for volume by incorporating the constant of proportionality into the coefficients of the polynomial. One term of this polynomial corresponded to a one-compartment model. If the other terms are regarded as a correction, then this can be called a corrected one-compartment model, with the correction accounting for the effects of additional compartments. To describe the two-compartment model, we shall follow the notation ofTauxe (7), with injection into compartment 1 having volume V,, which exchanges tracer with compartment 2 at flow rate F2. This model is defined by four parameters, which can be chosen in various ways that are mathematically equivalent. We @ have chosen as parameters the volume of compartment 1, the flow F3 from compartment I to the outside (i.e., to the bladder), and the two quantities k1 = F12/V1and k2 = F12/V2.(V2, the volume of the second compartment, is not independent and can be calculated from V1, k1, and k2.) Conventional physiologic scaling for size and species entails scaling volumes (such as extracellular fluid) by weight and scaling fluxes [such as GFR or effective renal plasma flow (ERPF) by surface area. It follows from dimensional analysis (8) that the sampling time should also be scaled. Ifvolume is measured in ml and flux in ml/min, then time, which is proportional to volume/
Simplified Renal Clearance in Children a Russell et al 1821
Simplified Methods for Renal Clearance in
Children: Scaling for Patient Size
Charles D. Russell, Eva V. Dubovsky, and Johnny W. Scott
Division ofNuclear Medicine, University ofAlabama Hospital, and Nuclear Medicine Service, Veterans Administration Medical Center—Birmingham, Birmingham, Alabama
METHODS OF PROCEDURE
flux,shouldbe scaledas weight/area.Scaledtimes willthus vary
approximately as the cube root of the body weight, so that 60
mm for a 70-kgadult correspondsto 28 mm for a 7-kgchild.
To clarifythe need for scalingthe sampletimes, considerthe
measurementofGFR, which hasunits volume/time. SinceGFR
is a flux, it is proportionalto surfacearea.Sincevolumeis
proportional to weight, then for consistency, time must be pro portional to weight/area. This makes the scale factors cancel so
that the physical relationship is independent of the units of
measurement. The result is easily verified in the case of a one compartment model, since the mean transit time for that case is known to be the volume divided by the flux and is hence proportional to weight/area.
The two-samplemethod employeda differentapproach.Solv
ing the four-parameter model when only two plasma measure ments are given requires two additional data. For theseadditional data, we used scaled population “averages―ofk3 and k2—notthe arithmetic mean of individual measurements, but parameters giving the best least-squares fit of calculated to observed ERPF
for the patient population as a whole. Since these quantities
represent a flux divided by a volume, they were scaled by body
surfaceareadividedby bodysurfacearea dividedby bodyweight.
RESULTS
The scaled models were tested as follows. First, they
were fit to the adult data by least squares. These scaled
adult models were then examined to see how well they fit
the pediatric data. The results, displayed in Figures 1 and
2, showthatthepediatricdatacouldbefit reasonablywell
using models created from adult data alone. The observed errors were within acceptable limits for clinical use: the
residual standard deviation was 67 ml/min for the one
sample method and 36 mi/mm for the two-sample method, measured from the line ofidentity. Scatter around
the regression line was even less, with correlation coeffi
dents of 0.966 and 0.987, respectively.
Both pediatric and adult data were then combined and
the parameters of the model were recalculated for best fit.
FIGURE1. OIHclearance(mI/mm-i.73 m@)inchildren,each
calculatedfrom a singlesample,versus that calculatedfrom the
complete clearance curve. The single-samplemethod was de
nved solely from OIHclearance data in 68 adufts. The line of
identityis ShOWn.
500 1000 MuItIs•m@ERPF (mI/ni-1.73 m')*
FIGURE2. OIHclearance(mI/mm-i.73 m@)inchildren,each
calculated from two samples, versus that calculated from the completeclearancecurve. The two-samplemethod was derived solely from OlH clearance data in 68 adults using the two
compartmentmodel(see Appendix).Scaled sample times of 10
and 60 mmwere used. The line of identity is shown.
Even better fit was obtained by combining the data in this
way than by cross-testing pediatric data against the fitted
adult model (Figs. 3 and 4).
The calculation was repeated for different sample times,
with results summarized in Table 1. Best results for the
single-sample method were found when the sample was drawn at a scaled time of 60 mm, although timing was not critical and good results were also obtained at 45 or 75
mm. These scaled times refer to the standard 70 kg, 1.
m2, adult; the actual times of measurement were shorter
in children, in proportion to weight/area. For the two sample method, best results were obtained at scaled times of 10 and 90 mm.
With the two-compartment model, the optimum values
of k10 and k20 were both found to be 0.042 min' for a patient with 1.73 m2 surface area. (Tauxe (7) obtained
values of 0.041 and 0.061 respectively for mean values of
FIGURE3. OlHclearance(mI/mm-i.73m@)in30 childrenand
68 adults, each calculated from a single sample, versus that calculatedfrom the completeclearancecurve.The single-sample methodwas chosenfor best fit to all 98 data. The lineof identity is shown.
J@soo
0 500 1000 MuItI..mpIs ERPF (mI/inln-1.73m')
500 1000 Multlsampl• (mI/mEr-1.73 ERPF m')
1822 The Journal of Nuclear Medicine •Vol.32 •No. 9 •September
One-Sample Empirical Method
Calculation of ERPF by a single-injection single-sample
plasma clearance method using an empirical formula is made as follows:
- Calculate f from Equation Al and obtain plasma sample at @@ time t (mm) in the interval 45f t 75f. The early end of this range is better for patients with good renal function, the later end for patients with poor function.
2. Calculateparametersa andb usingtheformulas:
a = 13.7740 —0.234133 (t/f)+ 0.00129778 (t/t) b = —2.2l400e—2+ 5.04666e—4(t/f) —3.33333e— 6 (t/f)
- Calculate the scaled ERPF using the formula
SCALED ERPF = a(70/wp) + b(70/wp)2 ml/min-l.73m2,
where p is plasma activity (fraction of administrated dose per liter plasma), h is height (cm), and w is weight (kg).
Sample Calculation
Given an adult patient of height, h, = 183 cm and weight, w, = 82 kg, from Equation Al we have f = 0.99, so that the plasmasampleshould be drawn between(45) (0.99) = 44.5 mm
and(75)(0.99)= 74.2mm. (Thiscalculationwillgivesignificantly
shorter times for small children). A blood sample was drawn at 59 mm and the count rate for 1 ml ofplasma was found to be 4781 cpm. A duplicate ofthe dose was diluted in two steps to the equivalent of 10 liters, and a l-ml aliquot counted as standard. The count rate for the standard was 53,621 cpm. The plasma activity per liter, p, as a fraction of administered dose, was thus:
(478lXl000) = 8.92 x iO-@. (53621X1000X10)
Using the values t = 59 and f = 0.99 in the above equations for a and b,
a = 4.43 and b = —3.90x l0@.
Then substituting a, b, p. and w into the formula for scaled ERPF, one obtains:
SCALED ERPF
Tauxe's k,2 and k21, respectively, where in the Tauxe notation the first number designates the volume of origin and the second the destination. (In Sapirstein's notation (6),
theseare respectivelyalpha/V1and alpha/V2.)The valueof
these parametersfor a standard 70-kg 1.73-rn2adult willbe
designated kl0 and k20. Best fit for the combined pediatric and adult populations was found when klO = 0.042 min and k20 = 0.042 min@. Given these scaled values, to calculate ERPF, first calculate unscaled values ofkl and k appropriate for the height and weight of the given patient by using the scale factor t scale: = (ws/70)/(area/l .73); sothat
k3: = klO/tscale; k2: = k20/tscale;
The following subprogram, GETCL, based on equations from Tauxe (7), calculates as output the parameters cl,c2,ll ,12 of the general two-exponential clearance curve
(concentrationc versustime t):
c = cl x exp(—llx t) + c2 x exp(—l2x t) Eq. A
given as input the ERPF(here designated 13)and the param eters kl, k2, and vl ofthe two-compartment model. Procedure GETCL (kl ,k2,vl,f3,cl ,c2,l1,l2); begin
k3: = f3/vl; dum: = sqrt (sqr(kl+k3—k2) + 4*klsk2); 12: = (kl+k2+k3—dum)/2; 11: = (kl+k2+k3+dum)/2; cl:= (k2—ll)/(l2—ll)/vl; c2: = (12—k2)/(12--ll)/vl; end lof procedure getcl@;
Using GETCL and Equation A2, the plasma concentrations at the two sampletimes can be calculatedfrom trial values of vl and £3.Newton's method (15) can then be used to solve the inverse problem, that of finding those values of vl and £3that correspond to the two measured concentrations. The value of 13 computed by Newton's method is the required ERPF.
ACKNOWLEDGMENTS
This work was supported by the Veterans Administration MediCal Research Service Developmental Funds of the Division of Nuclear Medicine. We are indebted to Dr. James Mountz for criticism and comments and to Ms. Dorothea Ballard and Mrs. Judith Russell for assistance with the manuscript.
REFERENCES
I. Tauxe WN, Hagge W, Stickler GB. Estimation of effective renal plasma flow in children by use of a single plasma sample after injection of orthoiodohippurate. In: Dynamic studies with radioisotopes in medicine, Volume1. Vienna:IAEA;1974:265—275.
- Tauxe WN, Dubovsky EV, Kidd T, Diaz F, Smith LR. New formulae for the calculationofeffectiverenal plasma flow.Eur J NuciMed 1982,7:51—
- RussellCD, DubovskyEV. Uncontrolledvariablesin the measurementof renal function. JNuclMed l986;27: 1644.
- RussellCD, Thorstad B, Yester MV, Stutzman M, Baker 1, Dubovsky EV.ComparisonofTc-99m-MAG3with1-l31-hippuranbya simultaneous dual-channel technique. J NuciMed l988;29: 1189—1193.
- Russell CD, Dubovsky EV, Scott JW. Estimation of ERPF in adults from plasma clearance ofl-l 3 1-hippuran using a single injection and one or two bloodsamples.NuclMedBiol 1989;l6:38l—383.
= 4.43 x (70/(82 x 8.92 x 10@)) — 3.90 x l0@ x (82 x 8.92 x lO_3) = 4.43 x 95.7 — 3.90 x l0@ x (957) = 388 ml/min — 1 .73 m
Two-Sample Two-Compartment Method Calculation of ERPF by a single-injection two-sample plasma clearance method using a two-compartment computer model can bemade asfollows:
- Calculate ffrom Equation Al. Obtain two plasma samples, one at l0f—l5fminand one at 60f—90fmin(preferably near lOfand 90t). 2. Calculatethe ERPF by the followingalgorithm,whichwill be presented in Pascal-like pseudocode. Notation and theory follow Tauxe (7). Briefly, v1 represents the volume of com partment 1 ofa two-compartment model, the compartment into which tracer is directly injected. k3and k2are fractional intercompartmental rate constants corresponding to
1824 The Journal of Nuclear Medicine •Vol. 32 •No. 9 •September 1991
- SapirsteinLA,VidtGD, MandelMi, HanusekG. Volumesof distribution and clearancesofintravenouslyinjectedcreatininein the dog.AmJPhysiol 1955;181:330—336.
- Tauxe WN, Maher FT, Taylor WF. Effective renal plasma flow: estimation from theoretical volumes of distribution of intravenously injected 1-131- orthoiodohippurate. Mayo Clin Proc 197l;46:524—31.
- BridgmanPW. Dimensionalanalysis, second edition. New Haven: Yale University Press; 1935.
- Alestig K, Hood B, Vikgren P. Berakning av glomerulusfiltrationen med engangsinjektion av inulin (I). Lakartidningen 1966;63:l554—l559.
- RussellCD, DubovskyEV. Measurementof renalfunctionwith radio nuclides.J NuclMed l989;30:2053—2057.
- Tauxe WN, BagchiA, Tepe PG, Krishnaiah PR. Single-samplemethod for the estimation of glomerular filtration rate in children. J Nucl Med
1987;28:366—371.
- Russell CD, Bischoff PG, Kontzen F, et al. Measurement of glomerular filtration rate by the single injection plasma clearance method without urine collection: a comparison of single-sample, double-sample, and mul tiple-sample methods using Tc-99m-DTPA and Yb.169-DTPA. J NucI Med 1985;26:l243—1247.
- Russell CD, Taylor A, Eshima D. Estimation of Tc-99m-MAG3 plasma clearance in adults from one or two blood samples. J Nucl Med l989;30:1955—1959.
- Haycock GB, Schwartz GJ, Wisotsky DH. Geometric method for meas uring body surface area: a height-weight formula validated in infants, children, and adults. J Pediat 1978;93:62—66.
- PressWH, FlanneryBP,TeukolskySA,VetterlingWT. Numericalrecipes. Cambridge:UniversityPress;1986:269—272.
Simplified Renal Clearance in Children •Russell et al^1825
