Comparative Studies of Height and Weight as a
Blood Volume Reference Standard in Normal
Children and Children with Sickle
Cell Anemia
SAMUEL GROSS, M.D.,
Department
AND JOHN C. GODEL,
M.D.
of Pediatrics at Case Western Reserve University School of Medicine and
University Hospitals, Cleveland, Ohio 44106
ABSTRACT
Gross, Samuel, and Godel, John C.: Comparative studies of height and weight
as a blood volume reference standard in normal children and children with
sickle cell anemia. Amer. J. Clin. Path. 55: 662-670, 1971. Blood volume
studies with the use of IHSA 131I were done on 25 normal children and 25
children with sickle cell anemia. Values which appeared to be significantly
different when related to weight were no longer different when related to
height. The best correlation was obtained when log blood volume was related
to log height. Study of this relationship indicated that there was no significant volume difference between the anemic and normal children. Since
volume relates best to lean body mass or to body water, the use of body weight
alone as the basis for its determination will be inaccurate in individuals
whose weights deviate from normal, if this deviation is clue essentially to fat.
Thus, previous studies of high volume values in anemic children were probably related to the use of weight as the reference parameter. The followingformula is recommended to calculate blood volume based on height: log B.V.
= 0.247 + 2.14 l o g H t .
MOST reports of blood volume data in children customarily use a body weight reference parameter.2-10> 15>10-18' 19>21 There is
serious doubt, however, as to the validity
of correlating blood volume with weight
in children. Most of the correlation studies
have been carried out on adults and agree,
in principle, that weight deviations due
either to obesity or to thinness can lead to
error when calculations are based solely on
weight. 1 ' 11 - 13 ' 23 Opinion also differs relative to blood volume data in certain anemic
Received May 14, 1970; received revised manuscript July 26, 1970; accepted tor publication July
30, 1970.
Supported by the Greater Cleveland Health Fund
and the Wellington, Ohio, United Appeal.
states, as shown by the studies of Jenkins
and associates,8 who noted a total blood
volume increase, and Erlandson and coworkers,4 who described a plasma volume
increase in sickle cell disease. In both studies volumes were related to body weight,
and no data were offered to indicate degrees of obesity.
In an attempt to answer the questions
relative to the physical standard which
correlates best with blood volume, the feasibility of volume predictions, and the determination of possible differences between
normal children and those with sickle cell
anemia, the following study was carried
out.
662
June 1971
663
H E I G H T BASED BLOOD VOLUME
Table 1. Comparisons of Ages, Hematocrits, and Height-to-\Veight Ratios in
Normal Children and Children with Sickle Cell Anemia*
Normal
Mean
Age (yr.)
Hct. (%)
Height (m.)
Weight (kg.)
Ht./vvt. ratio
u.o
37.0
1.44
40.1
0.401
Sickle Cell Disease
Range
Mean
Range
3.5-17.3
35.0-44.0
1.0-1.8
12.3-80.5
0.209-0.712
9.3
23.0
1.29
25.0
0.538
3.4-14.0
15.5-32.0
1.0-1.6
13.3-40.0
0.397-0.797
Includes two patients with sickle thalassemia.
Materials and Methods
Subjects
Twenty-five healthy children, with an age
range from 3.5 to 17.3 years, were selected
from the faculty population. Included in
this group were 10 girls (mean age 12.7
years) and 15 boys (mean age 10.0 years).
In addition to the normal controls, 25 children with sickle cell disease (age range 3.4
to 14.6 years) were also studied. The distribution consisted of 10 girls (mean age
8.0 years) and 15 boys (mean age 10.2 years).
None of the group with sickle cell disease
had impressive splenomegaly, nor was there
evidence of either hyperhemolytic or aplastic crises with increased tactoid formation
that might have influenced volume changes
resulting from capillary thromboses.
Studies
Volume measurements were made with
radioiodinated human serum albumin
(IHSA 131I) in a dosage of 0.2 ^c. per kg.
to a maximum of 5 /j.c. No additional carrier protein was used. Informed consent
was obtained in each case. All subjects received a solution of supersaturated potassium iodide daily for 3 days to block thyroid uptake of circulating 131 I. Samples of
venous blood, taken 10 and 25 min. after
injection, were read directly as liters of
total volume on the Picker Hemolitre. 20
The samples were read in duplicate and
varied by no more than 3%, with a mean
of 1%. Duplicate hematocrit determina-
tions were performed with micropipettes
and read on a circular reader after a 5-min.
spin in the International Model MB microcapillary centrifuge. In order to eliminate
the potential error of stasis, tourniquets
were applied only as a means of locating
the veins. The values of blood volumes
(BVp) are based on analyses of venous
blood samples. Based on the whole body
hematocrit (Hb) to venous hematocrit (Hv)
ratio of 0.91,3 the following formula was
used to calculate true blood volume (BVt)2"':
BV t = BVP X
1 - Hv
1 - (0.91 X Hv)
Heights and weights of the subjects were
compared with those of normal children.
The normal values were obtained from
graphs developed by the Iowa Child Welfare Station and published by the University of Iowa.
Statistical
Analysis
The IBM 360/model 67 computer of the
University of Alberta was used for data
analysis. Regression equations were obtained by the use of a computer program
based on the method of least squares. The
method of Steele and Torrie 2 0 was used to
analyze the variance of the regression equations. The logarithmic computations were
logc.
Results
Table 1 is a compilation for the two
groups of the mean ages, hematocrits,
664
GROSS AND GODEL
heights, weights, and height:weight ratios.
No attempt was made to correlate values
according' to sex and race in view of well
established data indicating a lack of significant blood volume distinctions relative to
sex or race in the pediatric age range. 2 ' 17
However, there was a striking difference
between the height to weight ratios in the
two age-matched groups, the significance of
which is described below.
Relationship of Blood Volume to
Body Weight
The mean blood volume of the normal
controls was 71.3 ml. per kg., compared
with 96.3 ml. per kg. in the patients with
sickle cell anemia, significant difference
(£<0.01).
Regression equations relating blood volume in liters to weight in kilograms were
then calculated for the two groups.
Normal controls:
B.V. = 0.737 + 0.050 Wt. (R2 = 0.8760)
Sickle cell anemia:
B.V. = 0.046 + 0.094 VVt. (R2 = 0.8269)
Lines representing the regression equations
are plotted in Figure 1 and clearly indicate
the distinct difference between weight
based blood volumes in the normal and
sickle cell anemia groups.
A.J.C.P.— Vol. 55
Relationship
of Blood, Volume to Height
Regression equations resulting from the
analysis of the blood volume-height relationship are:
Normal controls:
B.V. = - 3 . 2 7 + 4.20 Ht. (R2 = 0.8383)
Sickle cell anemia:
B.V. = - 2 . 8 8 + 4.12 Ht. (R2 = 0.8660)
There is no significant difference between children with sickle cell anemia and
normal controls when this relationship is
used (p>0.\).
Observation of the data
plotted in Figure 2A indicates that the
relationship between blood volume and
height is not linear and that an exponential relationship might be more appropriate. Several of these relationships were explored in an effort to find a better correlation with the data which are represented
in Figures 2B through 2D.
Previous studies on adults indicated a
good correlation between blood volume and
the cube of the height. 1 ' 1S The following
regression equations were obtained from an
analysis of this relationship.
Normal controls:
B.V. = 0.601 + 0.694 Ht.' (R2 = 0.8408)
Sickle cell anemia:
B.V. = 0.495 + 0.848 Ht.' (R2 = 0.9133)
5.0r
to
rr
t 4.0
_i
I
UJ
§
3.0
_J
O
>
o
o
o
2.0
m
1.0
• NORMAL CONTROLS
71.3 m l / k g ]
MEAN B.V.
o SICKLE CELL ANEMIA—96.3 ml/kg )
10
20
40
50
30
WEIGHT-KILOGRAMS
60
_l_
70
80
FIG. 1. Blood volumes
plotted with respect to
weight. T h e lines represent plots of regression
equations for each group.
Blood volumes of patients with sickle cell anemia and normal control
subjects are significantly
different when their regression
equations
are
compared (p < 0.001).
June 1971
665
H E I G H T BASK!) BLOOD VOLUME
NORMAL CONTROL - SICKLE CELL ANEMIA
5.0
4.0
UJ
t
A
3.0
2.0
1.0
03
i
LU
HEIGHT-METERS
HEIGHT-METERS
O
Ul
5.0
Q
O
O
_J
CO
UJ
4.0 "5 U
LIT
>
//
13
_J
Ss//
3.0 . O
>
OOD
20
/ •
_i
v*v
^jSs
co
1.0- o
o
0
HEIGHT-METERS3
'.
0.4
i
I
1
0.8
1.2
1.6
LOG HEIGHT-METERS
i_
2.0
HEIGHT-METERS
EIG. 2. Blood volumes calculated from formulae which represent various mathematical relationships of blood volume and height. A, Blood volume related to height, li, Blood volume
related to height cubed. C, Log blood volume related to height. D, Log blood volume related
to log height. This relationship best fits the data (R.2 = 0.9376), and there is no significant difference between the regression lines of the various groups (p > 0.5).
Figure 25 is a plot of the curves obtained
when the above formulae are used. Overall
correlation is slightly better than that
found when the linear relationship of
blood volume to height is used to characterize the data.
A second relationship was that of log
blood volume to height (Fig. 2C). T h e regression equations obtained are given below
and are comparable in significance to those
derived from the blood volume to height
relationships.
Normal controls:
log B.V. = -1.43 + 1.66 Ht. (R2 = 0.8741)
Sickle cell anemia:
log B.V. = -1.39 + 1.72 Ht. (R2 = 0.8917)
A better relationship was obtained by relating log blood volume to log height (Fig.
2D) with the following regression equations.
Normal controls:
log B.V. = 0.162 + 2.27 log Ht. (R2 = 0.8730)
Sickle cell anemia:
log B.V. = 0.311 + 2.13 log Ht. (R2 = 0.8676)
The lack of significance is indicated by the
value of p > 0.5.
The effects of differences in obese body
weight on blood volume, expressed in ml.
per kg., are shown in Table 2. Both groups
of children had essentially similar heights
and blood volumes. Their weights, however, differed markedly and are reflected in
the different values of weight based blood
volumes. In order to determine if the differences were due to variations in fat
weight, assessments of height-to-weight ratios were made. These ratios tend to be
high in thin individuals and low in obese
individuals. Figure 3 shows the height-to-
666
A.J.C.P.—Vol. 55
GROSS AND GODEL
Table 2. Differences in Weight Reflected in
Blood Volume (ml./kg.)
Height (cm.)
Weight (kg.)
Subject A
Subject B
154.0
56.5
156.5
36.3
Blood volume
Total (1.)
ml./cm.
ml./kg.
3.62
23.5
64.1
3.74
23.8
103.0
weight ratios of the normal controls and
of the patients with sickle cell anemia,
plotted with respect to age and compared
with an "average." This "average" was obtained from the 50th percentile for height
and weight from data compiled by the
Iowa Child Welfare Research Station and
published in graphic form by the State
University of Iowa. Twenty-one of the 25
subjects with sickle cell anemia had heightto-weight ratios above "average." The mean
deviation from this "average" was +17%.
On the other hand, only seven of the
25 control subjects had above "average"
height-to-weight ratios. The majority were
below the "average," with a mean deviation
of - 4 % .
12.0
Since there is no significant dillcrence
between the groups when blood volume is
related to height, a single formula derived
from all of the data may be used to predict
blood volume in children. The following
formula relating log blood volume to logheight gave the best correlation with the
data:
log B.V. = 0.247 + 2.14 log Ht. (R2 = 0.9376)
Figure 4 is a plot on a log-log scale of a
line (A) representing the equation with
data from this study. Data regarding blood
volumes in premature newborns from a
paper by Usher and Unci 2 1 have also been
plotted. A second line (A') plotted to conform to both sets of data has a good fit
and does not significantly alter the log B.V.
formula, which may thus be used to calculate blood volumes in small infants as well
as in older children. Figure 5 shows the
relationship of calculated to actual blood
volume using the above formula.
Several formulae which included both
height and weight were evaluated, and the
following gave the best overall correlation
with the data (R2 = 0.09470):
log B.V. = -0.525 + 1.50 log Ht. -f 0.282 log Wt.
"AVERAGE"
• NORMAL CONTROLS
o SICKLE CELL ANEMIA
10.0
2
Fie. 3. Plot o£ the
height-to-weight ratios
of the individuals in
the study with respect
to age. "Average" is
calculated from the
50th p e r c e n t i l e for
height and weight of
normal children of varous ages.
8.0
<
or
>- 6.0
x
o
4.0
i
o
w 2.0
8
10
AGE- YEARS
12
14
16
18
June 1911
667
H E I G H T RASED 1H.OOD VOLUME
5.0
4.0
* NORMAL PREMATURES
• NORMAL CONTROLS
° SICKLE CELL ANEMIA
A* A
{USHER)/.
Fie. 4. Values o£ blood
volume with respect to
height o£ individuals in
the study are plotted on
a log-log scale. Line A is
a plot of the following regression equation: Log
li.V. = 0.247 + 2.14 log
lit. T h e cluster of values
at the lower end of the
regression line are values
of blood volumes, related
to length, in premature
newborn infants. 4 Line A'
results from the inclusion
of the premature infants.
0.3
The relationship using this formula is
plotted in Figure 6. Instead of resulting in
calculated values of blood volume which
are closer to the actual values than before,
the introduction of weight resulted in a
further separation of the two groups. The
values for children with sickle cell anemia
became lower and those of normal controls
became higher than those which occurred
when height alone was used as a basis for
blood volume calculations. This again reflects the changes seen when weight alone
is used and is further evidence against the
use of body weight in the calculation of
total blood volume, if the variation in
weight is due to body fat.
0.506 0.8 1.0
HEIGHT-METERS
1.5 2.0
Discussion
The injection of either chromate-labelled
erythrocytes or 1HSA 131I plasma provides
an accurate index of blood volume values
in most infants and children. With the use
of automated direct readout equipment,
the technic is quick and without loss in
accuracy. However, when labelled plasma
is used, the formula for calculating true
blood volume must be employed to correct
for the inconstancy in the venous plasmatocrit to body plasmatocrit ratio. 9 An additional point of interest, as it applies to this
study, is related to the data of Fudenberg
and associates,5 who noted that the accepted
body hematocrit to venous hematocrit ratio
668
CO
CL
UJ
A.J.CP.—Vol.
GROSS AND GODEL
55
5.0
•V
t-
4.0 ~
°.y*
i
UJ
o/.o.
3.0
FIG. 5. Plot o£ the actual values of blood volume against blood volumes calculated from the
following formula: Log
B.V. = 0.247 + 2.14 log
Ht.
o
>
Q
O 2.0
O
_J
CD
i.°.
_l
< 1.0
o
<
• NORMAL CONTROLS
O SICKLE CELL ANEMIA
—i
0
1
1
i
i
1.0
2.0
3.0
4.0
5.0
6.0
CALCULATED BLOOD V O L U M E - L I T E R S
(Hb/Hv) no longer applied in patients
with moderate to severe splenomegaly. In
their study, H b / H v ratios ranged from
0.986 (moderate splenomegaly) to 1.156
(massive splenomegaly). In splenectomized
individuals the ratio was 0.88. Other studies have shown that minimal splenomegaly
does not alter the H b / H v ratio. 3 In the
present investigation, none of the children
with sickle cell disease had even moderately
enlarged spleens, and the ratio of 0.91 was
used for all the children.
Previous studies by Gibson and co-workers ° and Gregerson and Rawson 7 indicated
blood volume reductions in certain chronic
anemias. In this regard, Whyte 24 described
a blood volume decline of 4% for each 10%
deficiency of hemoglobin, on the assumption that the body attempts to maintain a
normal hemoglobin by reducing plasma
volume to correspond to the decrease in
cell volume. However, their volumes were
derived from weight based studies of adults,
most of whom had chronic blood losses or
nutritional iron deficiency. Also noteworthy
is the probability that weight fluctuations
in adults are not comparable to the variations which occur in infants and children,
thereby rendering comparisons between
adults and children inappropriate.
The difference between weight based
blood volumes in children with sickle cell
anemia and normal children may be related primarily to the lean or fat free body
mass. The plasma component of the blood
volume is directly related to the aqueous
phase of body composition 11 and is also
independent of fatty tissue. Hence, if blood
volume relates best to lean body mass or to
body water, the use of weight as the sole
basis for its estimation may be inaccurate
in an individual whose weight deviates
from normal, if this deviation is due to fat.
An example of how a difference in body
weight due to obesity can influence the
blood volume, expressed in ml. per kg., is
shown in Table 2. That this difference is
paradoxical is shown by the inverse relationship, i.e., as weight increases, blood
volume in ml. per kg. decreases. The children with sickle cell anemia were thinner
and, therefore, had greater height-to-weight
June
1971
669
HEIGHT BASED BLOOD VOLUME
5.0 ui
J -
3 4.0
FIG. D. Plot of the actual values o£ blood volume against blood volumes calculated from both
height and weight using
the following formula:
Log H.V. = -0.525 + 1.50
log Ht. + 0.282 log Wt.
Note the divergence at
higher values of blood
volume of patients with
sickle cell anemia from
normal controls.
o /
/
/
'
ui
3 3.0
o
J*/
>
O 2.0
O
CO
_l
<
1.0 -
• NORMAL CONTROLS
O SICKLE CELL ANEMIA
H
o
<
'/
0
1.0
2.0
3.0
4.0
5.0
6.0
CALCULATED BLOOD VOLUME - LITERS
ratios than the n o r m a l controls, thereby
accounting for the observed differences of
weight related blood volumes. A more accurate estimation of blood volume might
be achieved by using a formula which includes a dimension which considers the
fact that all individuals of the same height
do not have the same build. If the weight
variation is due to a variation in lean body
mass, a formula for calculating blood volume which includes both height and weight
should yield calculated values which are
closer to the actual values t h a n those obtained when height alone is used. Otherwise, blood volumes calculated from height
a n d weight of thin individuals will be low,
whereas those of fat individuals will be
high. Retzlaff and colleagues 1 4 showed that
a formula using both height and weight
gave a good correlation with actual blood
volume in adults. T h e results in children,
however, led to the conclusion that if
weight introduces a spurious variable, its
inclusion in the calculation of blood volu m e is not justifiable. A l t h o u g h its effect
in combination with height is less, it still
results in significant skewing. T h e practical
difficulties of using skin-fold thickness in
addition to a height a n d weight formula do
not make the additional measurements
worthwhile.
I t is also noteworthy that the use of
height alone as a predictive standard would
not suffice in disorders involving fluid escape to the extravascular space or in certain structural conditions such as kyphoscoliosis. A l t h o u g h the typical habitus of
the child with sickle cell disease varies
from the normal, it is not structurally abn o r m a l . I n situations of sickle cell disease
with moderate to excessive splenomegaly,
the use of previously described correction
factors 5 may be applied to the formula.
I t is not within the scope of this study to
compare the I H S A 131 I blood volume height
based d a t a to previous volume weight
based information obtained in children
with 5 1 Cr labelled erythrocytes. 2 1 G e r m a n e
only to this study is the knowledge that in
children height as a basis for predicting
blood volume in most situations is a more
reliable p a r a m e t e r than weight. Accord-
670
GROSS AND GODEL
ingly, the following formulae are suggested,
in order of preference:
log B.V. = 0.247 + 2.14 log Ht.
log B.V. = -0.525 + 1.5 log ht. + 0.282 log VVt.
References
1. Allen T H , Peng MX, Chen KP, et al.: Prediction of blood volume and adiposity in man
from body weight and cube of height. Metabolism 5:328-345, 1956
2. Brines JK, Gibson JG II, Kunkel P.: T h e blood
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3. Chaplin H, Mollison PL, Vclter H: T h e body/
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a wide hematocrit range. J Clin Invest 32:
1309-1316, 1953
4. Erlandson ME, Schulman I, Smith CH: Congenital hemolytic syndromes. III. Rate of destruction and production of erythrocytes in
sickle cell anemia. Pediatrics 25:629-644, 1960
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8. Jenkins ME, Scott RB, Ferguson AD: Studies
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A.J.C.I'.—Vol. 55
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19. Ibid 56:43-47, 1960
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Book Company, 1960, pp 161-183, 319-320
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al.: Red cell mass determinations in infancy
and childhood with the use of radioactive
chromium. J Pediat 59:903-908, 1961
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54:419-431, 1965
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Red cell, plasma and blood volume in healthy
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height and weight combined. J Clin Invest
38:1065-1077, 1959
24. Whyte HM: Plasma and blood volume in anemia and the effects of transfusion. Aust Ann
Med 5:192-202, 1956
25. William JA: Blood volume: Comments on
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26. William JA, Fine J: Measurement of blood
volume with new apparatus. New Eng J Med
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