Is the impedance index (ht2/R) significant in predicting total body water?13

1. Is the impedance index (ht2/R) significant in
predicting total body water?13
Robert F Kushner, Dale A Schoeller, Carla R Fjeld, and Lynn Danford
ABSTRACT We investigated the general utility of bioelec- sex (4, 5). The selection of variables and their coefficients has
tncal impedance analysis (BIA) and the implications of BIA differed from one study to another because ofdissimilar subject
theory in populations ofvarious ages from infancy to adulthood populations ranging in age from infants to elderly adults. Fur-
by developing a single impedance equation. Four subject data#{149} thermore, some investigators have observed that these anthro-
sets representing 62 adults, 37 prepubertal children, 44 preschool pometnc variables can be even stronger predictors ofTBW than
children, and 32 premature low-birth-weight neonates were BIA. For example, Deurenberg et al (6) recently suggested that
combined. Subjects were randomly divided into a development the prediction of dFFM by the BIA method offered little or no
group (n = 1 16) and a cross-validation group (n = 59). The advantage over simpler anthropometric techniques that use
Downloaded from www.ajcn.org by on December 24, 2007
single best predictor of total body water (TBW) was height2,’ weight, height, sex, and age. Thus, it remains controversial
resistance (ht2lR), which explained 99% ofthe variation in TBW whether the high correlations reported for BIA prediction equa-
(SEE = 1 .67 kg). The addition of weight reduced the SEE to tions are primarily based on these additional independent subject
I .41 kg. A significant bias was only seen in the preschool children. characteristics or whether they are due to BIA (7).
These results were confirmed in the cross-validation group and Despite this controversy, we have noted a striking similarity
the best prediction formula was TBW = 0.59 ht2/R + 0.065 wt ofthe various regression equations relating impedance to TBW
+ 0.04. We conclude that the impedance index (ht2lR) is a sig- in a wide range of age groups studied by us and others (8- 1 1).
nificant predictor ofTBW and that there is some improvement This suggested to us that there may be a single relationship re-
in prediction ofTBW by inclusion ofa weight term. Am J lating impedance to TBW. Therefore, the aims of this study
C/in Nutr 1992:56:835-9. were to evaluate the underlying principle of BIA and develop a
single TBW-predictive equation, and to evaluate the importance
KEY WORDS Bioelectrical impedance analysis, body corn- ofthe impedance term (ht2lR) as a predictor ofTBW compared
position, anthropometry with other independent subject characteristics.
Introduction Subjects and methods
Four data sets from adults (group 1, n = 62), prepubertal
Bioelectrical impedance analysis (BIA) is based on the prim-
ciple that the impedance (Z) ofa cylindrical conductor is related children (group 2, n = 37), preschool children (group 3, n = 44),
to its length (L), cross-sectional area, and applied signal fre- and premature low-birth.weight neonates (group 4, n = 32) were
quency. On the basis of this relationship, it was proposed that used in this study. The subjects were previously enrolled in stud-
the volume of a conductor is proportional to L2/Z. More than ies on body-composition measurement andlor energy metabo-
30 y ago, Thomasset (1) and Hoffer et al (2) tested this hypothesis lism (8, 9, 12; L Danford, D Schoeller, R Kushner, unpublished
in a biological system and demonstrated that the volume of total observations for group 2, 1990). All participating adult subjects
body water (TBW) was indeed proportional to L2/Z. Thus, BIA or guardians for the children gave informed written consent for
the study, which was approved by the Institutional Review Board
could be used to estimate TBW by applying a predictive equation
based on the measured bioelectncal impedance of the subject. ofthe University ofChicago (groups 1 and 2) and ofthe Instituto
Using height as a measure of conductor length, Hoffer et al de Investigaci#{243}n Nutnci#{243}nal in Lima, Peru (group 3). Subjects
from group 4, taken from the study by Mayfield et al (12), were
showed that ht2lZ was a better predictor of 3H2O-denved TBW
than was the weight term alone in 20 normal volunteers (r = 0.92 studied during the first 24 h ofpostnatal life and at 4-7 d of age.
vs r = 0.74). Subsequent regression analyses by several investi- The protocol for group 4 was approved by the Institutional Re-
gators have also demonstrated that the impedance index (ht2l view Board of the University of Texas Southwestern Medical
R; where R is resistance) yielded larger correlation coefficients
than weight or height when used as predictors of TBW, densi-
I From the Clinical Nutrition Research Unit, University of Chicago,
tometrically determined fat-free mass (dFFM), or total body po-
and the Washington University School of Medicine, St Louis.
tassium (3, 4). 2 Supported by NIH grant DK 30031.
Although the impedance index has been shown to be a strong 3 Address reprint requests to RF Kushner, 584 1 South Maryland Av-
predictor of TBW, it has also been observed that the accuracy enue, MC4080, Chicago, IL 60637.
of predicting TBW or dFFM by BIA is significantly improved Received December 31, 1991.
by the inclusion ofadditional variables such as weight, age, and Accepted for publication May 7, 1992.
ImJC/in iVitr 1992:56:835-9. Printed in USA. © 1992 American Society forClinical Nutrition 835

2. 836 KUSHNER ET AL
Center. Physical characteristics and TBW measurements for all 125
175 subjects are shown in Table 1 . The combined data set was
rerandomized into a development group (n = 1 16) and a cross- 100
validation group (n - 59) by using a random number table.
Although each of these data sets has been previously reported, 75
the combination of the four data sets produced a unique pop-
ulation representing a broad range of ages (6 h-66 y), heights
50
(35.2- 183 cm), weights (0.82-200 kg), and TBW (0.68-74. 1 kg).
All subjects had height, weight, BIA, and TBW determined
25
on the same day. Prepubertal children and adults were asked to
fast from the previous evening. Height was measured without
shoes to the nearest 1.0 mm. Supine crown-heel length was used 0
instead of standing height in groups 3 and 4. Weight was mea- 0 10 20 30 40 50 60 70 80
sured to the nearest 0. 1 kg with a standard balance-beam scale
TBW, kg
in two groups and an electronic balance in the preschool children
and infants. BIA was performed with a body-composition an- FIG 1. Relationship between impedance index (ht2/R) and total body
alyzer (model BIA-lOl RJL Systems, Detroit) with a right-sided water (TBW) measured by stable-isotope dilution in the development
tetrapolar placement of electrodes as previously described (8). group (r = 0.996, SEE = 1.47 kg).
Whole-body R was recorded as the mean of three to five con-
secutive measurements made in immediate succession. The
mean CV for within-day repeated measurements was previously samples were collected for at least three postdose voids, the last
Downloaded from www.ajcn.org by on December 24, 2007
demonstrated to be 1.3% (8). 5 h postdose. Group 4 subjects were given 10% enriched H218O
TBW was obtained by deuterium dilution (D2O-TBW) in (0.6 mLlkg body wt) by gavage. After a 3-h equilibrium period,
groups 1 and 2 and by 80 dilution (‘8O-TBW) in groups 3 and 1 .5 mL venous blood was obtained for 180 dilution. D20-TBW
4 as previously described (8, 9). For the D2O-TBW technique, and “O-TBW were both analyzed by isotope-ratio mass spec-
baseline saliva samples were obtained followed by oral admin- trometry as previously described (8, 9). TBW was assumed to
istration of0.06 (group 1) and 0.08 g (group 2) D2O (99.8 atom be 96% ofD2O- and 99% ofH2t8O-dilution spaces, respectively.
% excess) per kg estimated TBW (TBW was assumed to ap- We previously demonstrated that these techniques for TBW do
proximate 60% of body weight). The D2O dilution space was not differ by > 1-2% (13).
measured by repeat saliva sampling at 3 h. The ‘8O-TBW in
group 3 was determined by obtaining a baseline morning urine Statistical analysis
sample followed by an oral dose of 0.08 g 180 (1 1.34 atom % Linear- and stepwise multiple-regression analyses were applied
excess) per kg body weight given as H218O by syringe. Urine to the data to determine the most significant variable or variables
TABLE I
Subject characteristics
Sex
Group Age (Male, Female) Height Weight TBW*
y cm kg kg
Equation development
Neonates
(n = 21) 0.02 NAt 41 (37-44) 1.6 (0.8-2.1) 1.3 (0.07-1.6)
Preschool children
(n = 29) 1.1 (0.3-2.5) 18, 1 1 71 (58-84) 7.6 (3.9-14.4) 4.9 (2.8-9.1)
Prepubertal children
(n = 24) 7.6 (4.8-9.8) 14, 10 129 (104-145) 31 (16-69) 16 (10-26)
Adults
(n = 42) 41 (23-66) 15, 27 170 (155-193) 85 (48-200) 38 (25-74)
Equation validation
Neonates
(n = 1 1) 0.02 (0.6-2.5) NAt 41 (35-46) 1.6 (0.8-2.2) 1.3 (0.7-1.8)
Preschool children
(n = 15) 1.3 (0.6-2.5) 12, 3 73 (60-86) 8.7 (5.2-1 1.6) 5.4 (4.1-7.4)
Prepubertal children
(n = 13) 7.9 (6.4-9.9) 9, 4 129 (108-143) 31 (17-57) 16 (10-23)
Adults
(n = 20) 39 (22-67) 1 1, 9 169 (150-180) 77 (58-144) 38 (27-5 1)
* Total body water.
t Not available.
1: 1 (range).

3. IMPEDANCE INDEX AND BODY WATER 837
5 and preschool-children groups. In this treatment impedance in-
4 dcx was identified as the most significant predictor and weight
3 as the only additional significant predictor. Again, residuals were
. 2 calculated for the cross-validation group. No significant bias was
I detected for the neonatal group (residual = 0.05 ± 0. 1 3 kg, NS),
e #{149} #{149} #{149}
. *
.
#{149}#{149}
#{149}.#{149} #{149}
.#{149} #{149}#{149}
but bias was detected for the preschool group (residual = -0.54
0 #{149}. . ± 0.34, P < 0.01), indicating that the preschool group was an
(0
0 outlier. The preschool group was deleted from all further regres-
-2
sion analysis of the development group.
-3
Entering predictor variables from the neonates, prepubertal
-4
children, and adults in the development group, stepwise regres-
-5
I 00 sion identified impedance index as the strongest predictor (r
10
= 0.995, SEE = 1 .67 kg) and weight as the only additional sig-
nificant predictor (r = 0.997, SEE = 1.41 kg). The developmental
TBW, kg
equations based on impedance index alone and impedance index
FIG 2. Residual plot for prediction of total body water (TBW) by and weight were tested in the cross-validation group (Table 2).
equation using impedance index (ht2/R) and weight. TBW is plotted on As expected, significant bias was detected in the preschool chil-
a semilog scale for visual purposes. dren. Among the other three groups bias was detected for equa-
tions based on impedance index alone and then only in the
neonates. The prediction equation based on impedance index
to predict TBW and to yield the lowest SEE. Statistical calcu- and weight had better precision than that based on impedance
Downloaded from www.ajcn.org by on December 24, 2007
lations were performed by using Minitab (Minitab Inc. State index alone; however, the improvement was only statistically
College, PA). The regression equations were then used to predict significant in the adult group. The recommended equation for
TBW in the cross-validation group. The bias, or mean residual predicting TBW (in kg) is 0.59 ht2/R + 0.065 wt + 0.04: however,
(TBW predicted - TBW measured), was tested for significance we are uncertain of its applicability among preschool children
by using a Student’s t test with P < 0.01 to adjust for five com- (ages 1-60 mo).
parisons. Precision, or SD ofthe residuals, ofthe various possible Importantly, the residuals calculated by using the equation
predictive equations was tested for significance relative to the based on impedance index and weight developed in the above
impedance index plus weight equation by using the F test. A P three groups were a relatively constant percentage of mean TBW
value < 0.0 1 was required for significance to adjust for five com- in each of the subject groups. The relative bias and CV for the
parisons. cross validation were neonates 0.8 ± 10.3%, prepubertal children
0.3 ± 3.2%, and adults -1.6 ± 4.5%.
To determine the relative importance ofthe impedance index
Results
in predicting TBW, single- and multiple-regression analyses were
Stepwise linear regression was performed by using height, performed for height, weight, height2, and llR among the de-
weight, age, ht2lR, height2, and llR for the 1 16 subjects in the velopment group and the results were compared with those ob-
development group. Impedance index (ht2lR) was the strongest tamed by using the impedance index (Table 3). Again, the pre-
predictor identified, explaining 99% of the variance in TBW (r school children were deleted from this comparison. Correlation
= 0.996, SEE - 1 .47 kg) (Fig 1). The only other predictor iden- coefficients for all other variables were smaller than those of
tified as significant was weight, which when combined with the impedance index plus weight. Similarly, SEEs were always larger
impedance index accounted for 99.5% ofthe variance (r = 0.997, than those for impedance index plus weight.
SEE= 1.24kg). To further investigate the predictive value of the impedance
Cross validation of the predictive equations based on imped- index relative to height2 and llR, we calculated the residuals
ance index plus weight (Fig 2), however, detected a significant among the cross-validation subjects (Fig 3A-D). Residuals for
bias among the neonates (residual = 0.24 ± 0. 1 3 kg, P < 0.00 1) the prediction ofTBW from either height2 or l,’R as single pre-
and preschool children (residual = -0.37 ± 0.34 kg, P < 0.01). dictors were quite large and not consistent across the range of
Because of the bias detected in cross validation, the stepwise subjects. Residuals using height2 and 1lR as independent van-
regression was repeated without both the low-birth-weight-infant ables resulted in relatively constant residuals across the range of
TABLE 2
Cross validation of predictive equations developed by using data from adults, children, and neonates*
Equation Adults Prepubertal children Preschool children Neonates
kg
TBW = 0.700 ht2/R - 0.32 -0.25 ± 2.53 0.21 ± 0.72 -0.74 ± 0.37t -0.25 ± 0.1St
TBW = 0.593 ht2/R + 0.O6Swt + 0.04 -0.61 ± l.71f 0.05 ± 0.51 -0.58 ± 0.34t 0.01 ± 0.13
* Residual . ± SD.
t Residual significantly different from 0, P < 0.01.
SD less than that predicted when only the impedance index was used, P < 0.05.

4. 838 KUSHNER ET AL
TABLE 3 to perform and it requires minimal operator training. Despite
Relative importance of the impedance index in predicting total body these potential benefits, tojustify the use ofBIA it must be shown
water in adults, children, and neonates
to significantly improve the accuracy and precision of predictive
Predictor r SEE equations compared with those based on anthropometric mea-
surements alone.
kg In a recent review of validation studies involving adults and
Height 0.897 7.59 children, which compared BIA with TBW or dFFM (14), the
Weight 0.959 4.87 impedance index was reported to be the best single predictor of
Height + weight 0.98 1 3.36 these compartments by multiple-regression analysis in 16 of 21
Height2 0.934 6.13 studies, accounting for 69% to 96% of the total predictive van-
Height2 + weight 0.986 2.84 ability (3- 10, 1 5-25). In five of the studies (7, 22-25), height
1/resistance 0.907 7.24 (or height2) and weight were more significant predictors than
Height2 + 1/resistance 0.982 3.25
were ht2/R or R alone.
Height2/resistance 0.995 1.67
Three of the latter studies incorporated a select group of sub-
Height2/resistance + weight 0.997 1.41
jects for their analysis and we postulated that this might reduce
the importance of ht2lR. For example, Diaz et al (7) studied a
small group of young adults consisting of postpartum women,
subjects, but were still relatively large. Only when the ht2-R ratio
farm laborers, and institute staffwhose body weights and heights
was used did the residuals become small enough (3-10%) for
were smaller than those in other validation studies involving
this technique to be practically useful within the neonatal and
prepubertal-children groups.
adults. Diaz et al found that after height and weight were entered
Downloaded from www.ajcn.org by on December 24, 2007
into the multivariate equation, ht2lR contributed 5% to the
prediction ofdFFM. In a study by Helenius et al (22) ofa group
Discussion
of overweight middle-aged men and women, it was observed
BIA has many advantages over other body-composition that ht2/R did not contribute to the estimation of densitometry-
methods in that it is safe, inexpensive, portable, rapid, and easy determined percent body fat when added to other selected an-
20 20
ht A hR B
.
-
10
.
.%
: -
-
10, ,v,
0 . . Cl) V TV y
#{149}#{149}.#{149}
#{149}#{149}
%. v
,,
y
< 0 < 0 V
#{149}#{149}. #{149}%#{149}S
#{149}
.
. :
.
V V V
(I) #{149} (1) V V
Lii . . w V
-10 #{149} -10 V
#{149} V
-20 -20
1 10 100 1 10
TBW, kg TBW, kg
20 20
ht2 & hR C ht2/R o
., 10 . 10
c/i’ #{163} #{163}
#{163}ah
#{163}* #{163} c#{244}’ #{149}
a a a #{149} #{149} #{149} #{149} #{149}
A AAA aaA < .#{149} #{149}
W.
0 #{232}A a t 1* U V #{149}y#{149}
#{149}
aia a a
0 ‘ I a Q ,
C,) a a)
w w
-10 -10
I
-20 -20
1 10 100 1 10 100
TBW, kg TBW, kg
FIG 3. Residual plots for total body water (TBW) predicted from various combinations of resistance (R) and height
indicate that the impedance index (ht2/R) is a better predictor than are other combinations of R and height in the
cross-validation group. A, TBW = -3.4 + 0.00140 ht2; B, TBW = -35.8 ± 37400/R; C, TBW = -23.7 + 19300/R
+ 0.000871 ht2; and D, TBW = -0.3 + 0.70 ht2/R. Regression coefficients and SEEs are given in Table 3. TBW is
plotted on a semilog scale for visual purposes.

5. IMPEDANCE INDEX AND BODY WATER 839
thropometric variables. Gray et al (23) found that weight and 3. Lukaski HC, Johnson PE, Bolonchuk WW, Lykken GI. Assessment
height2 were selected into a stepwise regression to explain a of fat-free mass using bioelectrical impedance measurements of the
greater portion ofthe variability by the statistical computer pro- human body. Am J Clin Nutr l985;41:8l0-7.
4. Segal KR, Gutin B, Presta E, Wang I, Van Itallie TB. Estimation
gram before ht2lR was used in a group of 87 adults, 75% of
of human body composition by electrical impedance methods: a
whom were obese. Only Jackson et al (24) and Van Loan and
comparative study. J AppI Physiol l985;58: 16-71.
Mayclin (25) observed that standard anthropometnc measure-
5. Lukaski HC, Bolonchuk WW, Hall CB, Siders WA. Validation of
ments were more powerful predictors of dFFM than was bio- tetrapolar bioelectrical impedance method to assess human body
electrical impedance in a broad sample of adult subjects. composition. J Appl Physiol l986;60: 1327-32.
The present study was therefore performed to determine 6. Deurenberg P, van der Kooy K, Leenen R, Weststrate JA, Seidell
whether a single BIA equation could be generated from a large, JC. Sex and age specific prediction formulas for estimating body
heterogenous population, and to reinvestigate the significance composition from bioelectrical impedance: a cross-validation study.
of the impedance term (ht2lR) as a predictor of TBW. The use IntiObes 199h;l5:l7-25.
of a large, heterogenous data set with a wide range of heights, 7. Diaz EO, Villar J, Immink M, Gonzales T. Bioimpedance or an-
weights, and TBWs gave us the opportunity to statistically assess thropometry? Eur J Gin Nutr l989;43: 129-37.
8. Kushner RF, Schoeller DA. Estimation oftotal body water by bio-
the relative importance of measuring whole-body R compared
electrical impedance analysis. Am J Chin Nutr 1986;44:4h7-24.
with simple anthropometric variables in a mixed population.
9. Fjeld CR, Freundt-Thurne J, Schoeller DA. Total body water mea-
Furthermore, using TBW as the reference method instead of sured by 80 dilution and bioelectrical impedance in well and mal-
dFFM, we eliminated the inherent errors in assuming a constant nourished children. Pediatr Res 1990;27:98-l02.
density and hydration factor for fat-free mass across age groups. 10. Davies PSW, Preece MA, Hicks Ci, Halhiday D. The prediction of
We also included a cross-validation group to assess the predictive total body water using bioelectncal impedance in children and ad-
value of the derived equations. olescents. Ann Hum Biol l988;l5:237-40.
Downloaded from www.ajcn.org by on December 24, 2007
First, our results show that ht2/R is the single best predictor 1 1. Lukaski HC, Bolonchuk WW. Estimation of body fluid volumes
of TBW (it results in the lowest SEE) and explains 99% of the using tetrapolar bioelectrical impedance measurements Aviat Space
variance in TBW. In comparison, the combination of the an- Environ Med 1988;59:l 163-9.
12. MayfIeld SR. Vauy R, Waidelich D. Body composition of low-birth-
thropometric variables weight and height alone yield an SEE
weight infants determined by using bioelectrical resistance and re-
that is twofold higher than ht2/R. The SEE is reduced slightly
actance. Am J Chin Nutr 199l;54:296-303.
by the substitution of height2 for height, as it is used in the
13. Schoeller DA, Kushner RF, Taylor P, Dietz WH, Bandini L. Mea-
impedance term. Second, the impedance index is a superior pre- surement oftotal body water isotope dilution techniques. In: Roche
dictor of TBW compared with either 1lR, height2, or both hR AF, ed. body composition assessments in youth and adults. Colum-
and height2, demonstrating the importance of the impedance bus, OH: Ross Laboratories, 1985:24-9.
term as suggested by the model originally described by Hoffer 14. Kushner RE. Bioelectrical impedance analysis: a review of principles
et al (2). and applications. J Am Coll Nutr 1992;l 1:199-209.
The finding that weight improves the precision ofthe equation, 15. Segal KR, Van Loan M, Fitzgerald P1, Hodgdon JA, Van Italic TB.
ie, reduces the SEE, most likely stems from the fact that the Lean body mass estimation by bioclectrical impedance analysis: a
four-site cross-validation study. Am J Gin Nutr 1988;47:7-l4.
human body does not behave as the ideal conductor proposed
16. Heitmann BL. Prediction ofbody water and fat in adult Danes from
during the development ofthe theory of BIA. BIA assumes that
measurement ofelectrical impedance. A validation study. Int J Obes
the body is a geometrical isotropic conductor with uniform length
l990;l4:789-802.
and cross-sectional area. However, the body more closely re-
17. Deurenberg P, van der Kooy K, Evers P, Hulshofl. Assessment of
sembles a series offive cylinders (two arms, two legs, and trunk), body composition by bioelectrical impedance in a population aged
each with a different geometry and resistivity. The addition of > 60 y. Am J Clin Nutr l990;5 1:3-6.
weight, sex, and age probably adjusts for differences between 18. Cordain L, Whicker RE, Johnson JE. Body composition determi-
individuals and the relative underrepresentation ofthe trunk by nation in children using bioelectiical impedance. Gmwth Dev Aging
whole-body impedance. 1988;52:37-40.
The -7% underestimate ofTBW by BIA in the Peruvian pre- 19. Deurenberg P, van der Kooy K, Paling A, Withagen P. Assessment
school children (group 3) cannot now be fully explained. How- of body composition in 8-I 1 year old children by bioelectrical
impedance. Eur J Gin Nutr l989;43:623-9.
ever, we do not believe that it results from the inclusion of mal-
20. Houtkooper LB, Lohman TO, Going SC, Hall MC. Validity of bio-
nourished subjects in this group because the bias was observed
electric impedance for body composition assessment in children. J
in both the well-nourished and malnourished subgroupings.
Appl Physiol l989;66:8h4-2l.
In summary, we conclude that the measurement of bioelec-
21. Deurenberg P, Kusters CSL, Smit HE. Assessment of body corn-
trical impedance significantly improves the prediction of TBW position by bioelectrical impedance in children and young adults is
as validated in a large heterogenous group ofadult and pediatric strongly age-dependent. Eur J Gin Nutr l990;44:26l-8.
subjects. The method should be useful in estimating the body 22. Helenius MYT, Albanes D, Micozzi MS, Taylor PR, Heinonen OP.
composition ofpopulation groups such as those in epidemiologic Studies ofbioelectnc resistance in overweight, middle-aged subjects.
studies. B Hum Biol l987;59:27l-9.
23. Gray DA, Bray GA, Gemayal N, Kaplan K. Effect of obesity on
bioelectrical impedance. Am J Gin Nutr 1989;50:255-60.
References
24. Jackson AS, Pollock ML, Graves JE, Mahar MT. Reliability and
1 . Thomasett A. Bio-electrical properties of tissue impedance mea- validity ofbioelectncal impedance in determining body composition.
surements. Lyon Med l962;207:l07-18. J Appl Physiol l988;64:529-34.
2. Hoffer ED, Meador CK, Simpson DC. Correlation of whole-body 25. Van Loan M, Mayclin P. Bioelectrical impedance analysis: is it a
impedance with total body water volume. I Appl Physiol 1969;27: reliable estimator of lean body mass and total body water? Hum
53 1-4. Biol l987;59:299-309.