George R. DeMuth, M.D., William F. Howaft, M.D., and Bruce M. Hill, Ph.D.
Departments of Pediatrics and Mathematics, University of Michigan, Ann Arbor
I. LUNG
VOLUMES
T
HE GROWTH of the lung and its functionhave been studied by a variety of tests
in 147 normal children. In 101 children the
tests were repeated in about 16 months to
obtain longitudinal data. For some of these
tests no datum from normal children was
available. More importantly, data from
lon-gitudinal studies were not available for any
of the tests. Repeated studies on the same
individual permitted us to look at the
in-dividual’s growth and to compare it to that
of the group by the use of covariance
analy-sis. The performance of a spectrum of tests
of different lung functions on each child
allowed us to compare the growths of these
different functions. From these
compari-sons we have obtained patterns of growth.
Lastly by the use of this particular group
of subjects we have examined the
relation-ship of lung function to intelligence,
scho-lastic achievement, and physical strength.
The following tests were carried out:
(a) lung volumes (vital capacity, expiratory
reserve volume, and functional residual
ca-pacity); (b) forced flow rates (peak
inspira-tory and peak expiratory flow rates and the
flow rates at the points where 50% and 75%
of the vital capacity have been expired);
(c) intrapulmonary gas distribution (the
nitrogen clearance during oxygen
breath-ing, the oxygen equilibration index, and the
single-breath oxygen test); and (d) lung
diffusing capacity (carbon monoxide
breathing method). For comparison of the
results to body size and growth, the age
and various anthropomorphic
measure-ments were obtained. The results of
stand-ardized tests of intelligence, academic
achievement, and muscle strength were
available on the majority of these students.
In this, the first paper, we will
character-ize the population of children, discuss the
methods of analysis, and present the (lata
on lung volumes.
SUBJECTS
The 147 subjects for the study were
stu-dents at University School (Ann Arbor,
Michigan). They were in grades from the
junior kindergarten through the 12th and
ranged in age from 4 to 18 years. From
each class above kindergarten 10 subjects
were randomly selected for testing. This
was not possible in the kindergarten and
below where the subjects were chosen by
the teacher for their expected ability to
co-operate. In all about one-third of the
students in the school participated. The
medical history as recorded by the school
physician was examined for each child. The
available information included his and the
school nurses’ observations as well as
his-tory forms filled out by the parents. Those
children with chronic or recurrent lung
dis-ease were excluded. The children were
Caucasian, except for one Negro child.
Intelligence tests (Stanford-Binet,
Wechs-ler Intelligence Scale for Children,
\Vechs-ler Adult Intelligence Scale) and the
Cali-fornia Reading Achievement Tests are
rou-tinely given in this school. Grip Age was
obtained on children in the third grade and
higher. For this study we used the results
of those tests that were obtained at the
time of our second series of tests, if
avail-able, or the nearest preceding one.
At the time of pulmonary testing the
fol-lowing measurements of physical size were
made: (1) height (without shoes) in
centi-meters; (2) weight (without shoes, but
schoolroom clothing) in kilograms; (3)
sit-ting height in centimeters; (4) biacromial
width in centimeters (by calipers); (5) chest
This study was supported by Grant A-3575 from the National Institute of Arthritis and Metabolic
Diseases.
SUPPLEMENT 163
dimensions in centimeters (by calipers) at
the end-tidal or resting position: (a) A-P
diameter at xyphi-sternal junction, (b) A-P
diameter at angle of Louis, (c)
transthor-acic diameter at level of xyphi-sternal
junc-tion, (d) sternal length-suprasternal notch
to xyphoid. The surface area was
calcu-lated by use of a nomogram based on the
formula of Dubois and Dubois.1 The age
was rounded off to the nearest month and
expressed as a decimal fraction.
All tests of each series were carried out
on a majority of the subjects during a
single examination in which the tests were
performed in a systematic order. In a few
of the smaller children the testing was split
into two parts and done separately, usually
on succeeding days. The first series of tests
on the 147 subjects was spread over a
20-month period (July, 1959, to April, 1961).
During this time ten subjects had repeated
studies done 2-4 weeks after the initial
study. Beginning in February, 1962, all of
the 147 subjects who were available were
asked to participate in another series of
tests. One hundred three were still in the
school; two declined to participate. The
time between examinations varied from 10
to 18.5 months, the median being 15.3
months. Ninety-five per cent were at least a
year apart.
METHOD AND EQUIPMENT
Vital Capacity and Expiratory
Reserve Volume
A stainless steel Krogh spirometer was
constructed with a curved end. Knife edges
were used at the axis of rotation. The
mov-able top portion was counter-balanced by
adjustable weights. The rotation of the top
was measured by the use of a Microsyn No.
1C-020B variable inductance angular
trans-ducer, the output of which was rectified to
give a direct current potential proportional
to the position. For the vital capacity and
expiratory reserve the output was recorded
on a Mosley X-Y recorder using a time base.
The spirometer was calibrated through the
range of use with a 50 ml syringe. It was
virtually linear. The characteristics of this
spirometer are given in the fifth paper in
this series.2
During the examination the subject was
allowed to breath normally for a few
breaths and then perform the vital capacity
maneuver. The spirometer was then rinsed
with fresh air, and a second trial was done.
The time between tests was less than 5
minutes. The higher of the two values was
selected and then corrected to BTPS.3 The
expiratory reserve volume was obtained
from the same tracing and similarly
cor-rected.
Functional Residual Capacity
A measurement of the functional residual
capacity (FRC) was obtained in the test of
diffusing capacity.4 The subject rebreathed
into a bag in a “box” during forced
hyper-ventilation. The dead space of the system
was known. The volume of the bag and its
changes during equilibration were obtained
from the spirometer to which the “box” was
connected. The helium concentration was
measured after the bag and dead space had
been allowed to equilibrate and
continu-ously during the rebreathing process by
circulating the gas through the Cambridge
Helium Katharometer. In this test
rebreath-ing at a high ventilatory rate was continued
for about 50 seconds. The calculation was
as follows:
VFRC = (V50 X He0) - (V., X He,) He,
Vs = volume of bag and dead space
He = helium concentration
Subscript 0 = at start of test; subscript
= final value. No correction was made
for helium absorbed. This test was carried
out in duplicate, and the mean values
reported.
The lung space occupied by the helium
after 45 seconds of hyperventilation should
be very close to the functional residual
capacity in normal children. Equilibration
is probably nearly complete by 15 seconds
carbon monoxide concentration against
time. This technique, however, is an
ab-breviation of the usual helium rebreathing
method and may not be applicable to
dis-eased subjects. Its validity for studying
growth in normal subjects is apart from its
ability to measure accurately the FRC. An
estimate of its ability for the latter
pur-poses can be obtained by comparing its
results with those obtained by other
methods.
METHODS OF ANALYSIS
In studying the relationship of the results
of the lung function tests to independent
variables, two methods of statistical
analy-sis were customarily used. The first was the
calculation of simple or multiple ordinary
regressions; the second was an analysis of
covariance.5 The calculations of ordinary
regression were made to compare the data
of one series with those of the other, to
examine general relations among the
vari-ables, and to compare our data with those
of others who have used this form of
analysis.
The covariance analysis is a refinement
of ordinary regression in which one looks
at the individuals’ growth lines rather than
at the group growth line. In this analysis,
as in ordinary regression analysis, one
as-sumes that the dependent variable is a
linear function of the independent variable.
For example, one assumes that the log vital
capacity is a linear function of the log
height, characterized by a slope () and
intercept (a). In covariance analysis one
assumes that different individuals have the
same slope or , which slope measures an
intrinsic property of the relationship
be-tween the variables. The individuals may
have different intercepts or a’s. The a
meas-ures a characteristic of the individual and
may be interpreted as a measure of his
height-adjusted vital capacity. In the ideal
circumstance the slopes would all be
paral-lel, and the spread of values at any point
would be due to the a’s. Each person would
maintain his own position within the group.
A further assumption is that the
loga-rithm of an individual’s measured lung
volume fluctuates randomly about the value
of his “true” line and that all such
fluctiia-tions are independent with mean zero. On
each occasion two readings of the
func-tional residual capacity were taken, which
allowed us to obtain a relatively
uncon-taminated measure of the basic variability
of the observation (of a given person at a
given time). The measure that we used was
a sample variance from the deviations of
such observations about the mean of the
pair and is called the estimate Sd2 of the
duplicability variance ,j2. In addition, the
variability of the means of such pairs from
the lines fitted by covariance analysis yields
another sample variance called the
esti-mated residual variance S,.2 which estimates
the residual variance o2. If the assumptions
underlying the analysis of covariance held
exactly, we would have O2 = % d2 since
rr2 is based upon the average of two
obser-vations, each with variance Cd. However,
these assumptions only hold in an
approxi-mate sense, and Sr2 will tend to be inflated
due to non-linearity and variability of
from person to person.#{176}
When the increments in the independent
variable (e.g., log height) are small, the
estimated regression coefficient or slope
()
from covariance analysis is sensitive to
even small systematic changes in the
de-pendent variable (e.g., log VC). As an
ex-ample, in this study the systematic change
between the vital capacity tests in the two
series for boys, as estimated by the
differ-ence in intercepts between the two series
using a common slope, was approximately
0.004. This difference did not appear sig..
nfficant; but when the second series was
adjusted down 0.004 log units to agree in
intercept with the first series, the covariance
slope based on this adjusted data was
de-creased by about 0.1 units in the log system
oThe ratio Sr’ to 52 is sometimes used to test
the underlying assumptions. The values here are
high. We are aware that these assumptions do not
hold exactly, but nevertheless feel that they hold
sufficiently well to yield an appropriate analysis
BOYS
90%
MEAN
10 S 90%
MEAN
90190
ISO, 80
70 70
160 160
50 ISO
140 40
30 130
20 20
110 110
tOO 00
90 90
Fic. 1. The heights of the subjects in relation to their ages. Points connected by a solid line represent
two measurements on the same individual. The dotted lines connect points representing the 10th, 50th,
and 90th percentiles from a growth table.
4 5 6 7 8 9 0 II 12 3 14 IS 16 17 8 ‘9
AGE IN YEARS
890112I3 I I 7 ‘en
AGE IN YEARS
SUPPLEMENT 165
HEIGHT IN CM HEIGHT IN CM
200 200
G/RLS
and then agreed roughly with the pooled
slope 2.81. Thus a systematic difference
even as low as 0.004 can materially affect
the covariance slope. It is unknown
whether the 0.004 difference is an artifact
or whether it represents a small but real
increase in the level of VC at any given
height. We suggest in this case that it is
an artifact (perhaps due to calibration) but
have no definite evidence.
It is always possible to estimate the
sys-tematic difference (whatever its source)
be-tween the two series by the foregoing
method. Generally such differences have
very little effect on the estimated slope or
residual variance from ordinary regression,
and so we have neglected this adjustment
in our discussion of ordinary regression. As
noted, the adjustment may be crucial in
determining the slope from covariance
analysis. When the adjustments are made,
the covariance slope becomes very nearly
equal to the pooled slope while the residual
variance from the covariance analysis barely
changes; thus generally it is sufficient to
obtain the pooled slope and treat it as the
adjusted covariance slope, using the
resid-ual variance from the unadjusted
covari-ance analysis. Since the latter is typically
much smaller than the residual variance
about the ordinary regression, we have
substantially increased our ability to
pre-dict lung volume as a function of height.
RESULTS
The “Normality” of the Subjects
Figures 1 and 2 show the heights and
weights of these subjects against age for
each sex. The heavy lines connect points
representing the mean, 10th and 90th
per-centiles from the tables of Meredith,
pub-lished in a standard text.6 Light lines
con-nect values on the same individual. It will
be noted that in 5 subjects the second value
was less than the first. These drops, though
small, must represent measurement errors.
The children appear to be normal in these
BOYS
WEIGHT IN KG.
GIRLS
/
41/2 6 3 14 7 eVa 41/2 6 7
AGE IN YEARS AGE IN YEARS
Fic. 2. The weights of the subjects in relation to their ages. Points connected by a solid line represent
two measurements on the same individual. The dotted lines connect points representing the 10th, 50th,
and 90th percentiles from a growth table.
IS 112 166
heavy for their heights and ages. The
in-telligence of the children was above the
general population level. The mean I.Q.
was 129, with a range from 97 to 197.
Lung Volumes
The vital capacity (VC) and functional
residual capacity (FRC) data from the two
series of tests were first examined by
com-paring the results of regression analyses of
the volumes on height (separately for boys
and girls). For either lung volume and
either sex the slopes and intercepts for the
two series were not significantly different.
The data from the two series were added
together for some of the remaining analyses.
Thus, on such combined data more than
one observation on most individuals were
included.
The results of the analyses of vital
capac-ity against various body measurements are
given in Table I (separately for each sex).#{176}
* ‘Flie estimated standard deviation about a regres-sion line is taketi as the square root of the estimated
WEIGHT IN KG
In Figures 3 and 4 the distribution of the
vital capacity against height for each sex
are shown with a log-log plot. The light
lines connect observations on the same
child and illustrate his growth in
compari-son to the group’s growth. Isolated dots
represent children who were not retested.
The heavy lines represent the calculated
regression line and parallel lines 2.0
stand-residual variance. The standard deviation of the original variable can be expressed as a fraction of the predicted value (median) by the equation
SD(V)
----‘---
ln,10S.I). Pred. (1)when the standard deviation was obtained after taking logarithms to the base 0. Using 0.00077 as the residual variance from the covariance analysis of log \‘C on log height (boys) we obtain SDc .306 /0.00077
TABLE I
ANALYSES OF VITAL CAPACITY AND PHYSICAL MEASUREMENTS
Indep. Variable Number Correlation Coefficient Reridual Variance Regression Coefficient (Stand. Error) Coefficient Intercept Boys (2) Boys (3) Boys (4) Boys (5) Girls (2) Girls (3) Girls (4) Girls (5) Boys (5) Girls (5) Boys (1) Boys (5) Girls (I) Girls (5) Boys (4) Boys (5) Boys (1) Boys (3) Girls (3) Boys (2) Boys (5) Girls (2) Girls (5) Boys (5) Girls (5) Boys (5) Girls (5) Boys (5) Girls (5) 121 72 49 121 139 88 51 139 121 139 72 121 88 139 49 121 72 72 88 121 121 139 139 121 139 121 139 121 139 Height Height Height Height Height Height Height height Age Weight Biaeroniial Sitting height Surface area JHeight & age Jlleight & age ,1Height & weight fHeight & veight Jlleight & biacrom itil fhleight & ibiacromial height & age & weight Height & age & weight Height & age & biacromial Height & age & biacromial Height & age & weight & biacromial Height & age & weight & biacromial .944 962 .930 .950 925 .937 923 .933 .918 892 .930 .933 .898 .914 .905 .906 .783 .865 .905 .948 .947 .918 928 952 .936 .953 .940 952 .933 .956 942 .953 .936 .956 .943 148497 .00294 .00457 .00355 101806 .00407 .00329 .00377 .00572 .00599 197136 .00467 147763 .00481 .00614 .00648 570386 .00979 .00608 139587 .00376 109678 .00408 .00342 .00364 .00335 .00344 .00346 .00379 .00321 .00333 .00336 .00367 .00321 .00334 51.35 2.817 2.807 2.810 42.21 2.892 2.664 2.818 1.160 0.895 62.56 0.980 53.20 0.938 2.593 2.557 71.22 2.450 2.631 3016. 1.466 2529. 1 .450 2.265 0.247 2.283 0.192 2.027 0.290 1 .914 0.328 2.379 0.441 2.776 0.039 1 .422 0.260 0.301 1.444 0.178 0.318 1 .939 0.224 0.385 2.290 0.193 -0.008 1.313 0.245 0.271 0.227 1 .503 0.187 0.334 0.116 1 .64 .096 .162 .085 1.49 .116 .159 .093 .046 .039 2.970 0.035 2.818 .036 .178 .109 6.87 .170 .134 93. .046 93. .050 .252 .107 .241 .080 .293 .104 .257 .087 232 .221 .180 .139 .375 .104 102 .324 .077 .086 .311 .107 .220 .271 .081 .138 .390 .105 .106 .223 .331 .078 .088 .135 -4726 -2 .67714 -2.66172 -2.66612 -3728 -2.88793 -2.40082 -2 .73104 2.22379 2.42455 176. 1.84902 209. 1.85953 -0.45036 -0.38363 -2677. -1 .20837 -1.59516 -1150. 3.26117 -829 3. 21310 -1.7398 -1.79525 -1.43371 -1.30088 -2.38921 -2.69718 -0.41069 -0 .45516 -1.58495 - 1.77905 -0.44944 -0 .44559
Boys (5) 121
Girls (5) 139
Boys (5) 121
Girls (5) 139
Boys (5) 121
Girls (5) 139
6000
5000
4000
3000
2000
100 110 120 I0 i4o I0 I0 I. 80 90
HEIGHT IN CM
Fic. 3. The vital capacity In relation to height (boys) on logarithmic scales. Points connected by a solid
line are on the same subject. The dashed lines indicate the calculated regression line and two
stand-arc! deviations on either side.
LUNG VOLUMES
ard deviations on either side (from the
ordinary regression).
The results of ordinary regression
analy-ses of the functional residual capacity data
are given for each sex in Table II. The
FRC values plotted against height are
shown on logarithmic scales in Figures 5
and 6 in a manner similar to that for the
vital capacity. The systematic difference
between the two series is 0.018. This is not
significant but is greater than that for the
vital capacity. The variance obtained from
the study of the duplicability was 0.01146
L2. The standard deviation of duplicates is
0.107 L which is 6.55% of the mean value.
As noted in the presentation of the
meth-ods of analysis the regression coefficients
obtained from covariance analysis are very
sensitive to small systematic differences
when the change in the independent
vari-ables is small. For this reason the
coeffi-cients are not given. The residual variances
VITAL CAPACITY
IN ML.
obtained from these analyses are valid and
important. The residual variances from the
covariance analyses for the log vital
capac-ity on log height are 0.00077 for boys and
0.00117 for girls. The corresponding figures
from the ordinary regression are 0.00345
and 0.00377. Thus the covariance analyses
reduce the residual variances about 78%
(boys) and 69% (girls) below those obtained
from ordinary regression analyses. For the
log FRC on log height the residual
vari-ances from covariance analyses were
0.00441 (boys) and 0.00335 (girls) which
are about half those obtained from ordinary
regression analyses.
The calculation of regression lines after
logarithmic transformation shows a
rela-tionship such as the following for vital
ca-pacity and height:
Log VC = b X log height + a (Equation 1)
The antilog of the foregoing gives
GIRLS
6’
V/,-110 20 130
SUPPLEMENT 169
VITAL CAPACITY IN ML
5000
4000
3000
2000
1000
750
100 140 150 160 ITO 180
HEIGHT IN CM
Fic. 4. The vital capacity in relation to height (girls) on logarithmic scales. Points connected by a solid
line are from the same subject. The dashed lines indicate the calculated regression line and two standard deviations on either side.
In the relation of vital capacity to height,
the sizes of the “b’s” or exponents in the
ordinary regression equations are similar
to some previously published.7-9 We did
find the a factor (intercept in Equation 1,
constant multiplier in Equation 2) was
dif-ferent for the two sexes (t = 3.0, p < .001).
This indicates that for the same height girls
have statistically significant lower vital
capacities than boys. This finding was
sus-pected by Engstrom et al.7 but could not be
demonstrated statistically from their
find-ings.
In order to make an easy comparison of
our data with some other reports of studies
of normal children7’1 Table III has been
prepared using our formulas from the
or-dinary regression analyses of the log lung
volume on log height and their suggested
formulas, some of which used age and
weight as well as height. This gives
pre-dicted values for the VC and FRC for
8-and 14-year-old boys and girls of normal
heights and weights. The predicted values
from tile other studies fall within our mean
± 1 SD, except for tile small FRC
pre-dicted by Bernstein’s formula for 8-year-old
boys and except for the large FRC’s
ob-tained from Helliesen’s and Cook’s formulas
for the 14-year-old girls. Helliesen noted
that his functional residual capacities
seemed large, and these data are included
in Cook’s report. Aside from these
discrep-ancies the predicted values are similar,
al-though there were differences in technique.
The values predicted from Cherniack’s
paper are calculated from his regression
equations. Much higher values were
ob-tained from his nomograms.
Correlation Variable . Coefficient Residual . arianee Regression . Coefficient St. ( Error . intercept oefficient Boys Height Sitting height Surface area Age Vital capacity Height Age Height Weight Height Biacromial .881 .836 .866 .850 .881 .883 .881 .889 .00940 .01262 .01052 .01163 .00986 .00932 .00949 .00892 2.928 2.576 1.481 1.163 .992 2.329 .263 ‘3.0429 - .0414 1 .875 1 .061 160 .172 .087 .073 .054 .465 191 585 203 .450 .425 -3.13596 -1.65581 3.04548 2.00328 -0.189190 -2. 10856 -3.31805 -2.43371 Girls height Sitting height Surface area Age Vital capacity height Age Height Weight .874 .870 .842 .862 .846 .884 .874 .00645 .00661 .00791 .00701 .00744 .00600 .00647 2.538 2.350 1.261 0.837 0.795 1 .551 0.355 2.828 -0.104 134 .126 .076 .047 .047 348 377 .126 -2. 32046 -1. 26188 3.1)3540 2.29031 0.49115
- 0. 55753
-2.77990
170
physical size measurements are related after
logarithmic transformation, the exponent
(b) becomes of interest, for it indicates the
dimensional relationship between the
vari-ables. Volume and, indirectly, weight are
three dimensional quantities; surface area
is two dimensional; and height and
biacro-mial width are one dimensional
measure-ments. Age has one dimension only (time).
When the lung volume is related to any one
of these variables, the value of the
ex-ponent, as in Equation 2, does approach
the ratio of the dimensional natures of the
variables. For example, in tile regressions
of the lung volumes on height, biacromial
diameter, sitting height, or age, tile
ex-ponents are approximately 3/1, or 3. For
the lung volumes on surface area the
ex-ponent is approximately 3/2, or 1.5. For
lung volumes, weight, or another lung
vol-ume the exponents are about 3/3, or 1. If
the exponents are adjusted for their
dimen-sional qualities by dividing the slope of the
volume on linear measurements by 3, that
TABLE II
SUPPLEMENT 171
TABLE III
COMPAHISON OF PREDICTED VAit:s
.4gc Present
Sex Weight height Data Engstrom Bernstein Ildiiesen Cook Cherniaek
(!/r.)
_____
_____
_____ ____I?ital (‘opacity
Boy S 27.3K 130 cm. I ,880 ml. 1867 ml 1922 ml 1902 ml 1932 ml 2025 ml
(1 ,639-2, 156)*
Boy 14 48.8K 163cm. 3,549 3480 3307 3641 3831 3671
(‘3,094-4,071)’
Girl 8 26.4K 128cm. 1,611 1790 1764 1820 1726 1738
(1,401-1,848)’
(;irl 14 49.2K 160cm. 3,021 3305 3061 3452 3312 3176
(2,623-3,480)’
Functional Residual Capacity
Boy 8 27.3K 130cm. 1,132 1023 878 1247 1175
(905-1,415)’
Boy 14 48.8K 163 cm. 2,195 1953 1943 2410 2478
(1,745-2,743)’
Girl 8 26.4K 128cm. 1,066 978 900 1193 1161
(880-1292)’
Girl 14 49.2K 160cm. 1,878 1851 1755 2283 2346
(1,550-2,275)’
* \lea,i ± I standard deviation.
on areal measurements by 3/2, and that on ratio does not greatly reduce the limits of
volume measurements by 1, then the values normality. The standard deviations of the
can be compared (see Table IV). It is in- groups are 0.076 and 0.079 and those about
teresting that when tile regression for lung
volume is calculated simultaneously against TABLE IV
two or more independent variables, tile RATIOS OF l)IIENsIoNALIY ADJUSTED ExIONENTS
sum of the adjusted exponents is also equal
Functional
to about one. The significance of these Vital
Residual
values in respect to growth will he dis- Capacity
apaci1y cussed later.
The expiratory reserve volume was ex- Boys Girls Boys Girls
amined as a fraction of tile vital capacity.
For boys the means was 0.3213; the stand- Height .94 .94 .98 .85
ard deviation, 0.0762; the standard error of Sitting height .82 .88 .86 .78
Surface area .98 .97 .99 .84
the mean, 0.0069. For girls the comparable Age 1.16 .90 1.16 .84
values were 0.3269, 0.0788, and 0.0067. Tile Vital capacity .99 .80
difference between the mean values was Biacromial .85
not significant (t* = 0.578; 0.5 < p <0.6). Weight .98 .94
height & age I (10 .95 1.04 .87
The correlations of this ratio with body Height & weight .97 .97 .97 .84
height, surface area, age, and vital capacity Height & biacroinial .94 .94 .98
are significant, but not striking (Table V). hleight, age, weight 1.04 .98
Tile highest correlations are found with hleight, age,
hiacromial I (10 .95
age. However, the use of age to predict the hleighit, age, weight,
FRC(ML)
5000
4500 BOYS
4000
3500
3000
2500
1500
#{149}1
I00 130 40
HEIGHT IN CM.
Fic. 5. The functional residual capacity in relation to height (boys) on logarithmic scales. Points
con-nected by a solid line are from the same subject. The dashed lines indicate the calculated regression line and two standard deviations on either side.
160 ITO
172
the lines are 0.072 and 0.076 for boys and
girls, respectively.
COMMENT
Studies of the growth of the external
thoracic dimensions from birth to
adult-hood in relation to the body growthl2
sug-gest that after birth the lung volume does
not increase as a linear function of body
size (as indicated by physical
measure-ments) even after logarithmic
transforma-tion. Above about 100 cm of height or age
4 years the relationships can be simplified
by logarithmic transformation. A third
de-gree polynomial function of a physical
size measurement (e.g., height) also yields
a good approximation to the lung volume
data. However, the use of the logarithmic
relationship appears better for several
rea-sons. It is simpler than the general third
degree polynomial, involving fewer
param-eters. Secondly, the residual variances by
the two methods are not much different.
Thirdly, the population of lung volumes at
a given size is positively skewed; hence, the
log transformation acts to normalize the
data. Finally, the “true” regression is very
likely convex in the range studied. The
log-arithmic transformation then tends to
lin-earize what is otherwise a quite complex
relationship.
The single variable which gave the best
correlations with lung volumes was height.
Almost as high correlations are found with
surface area. No advantage to the use of
in-TABLE V
REoltsssIoN ANALYSES OF THE EXPIRATORY RESERVE VOLUME
VITAI CAPACITY
Independent .
Variable Sex Number
Correlation .
Coefficient
Standard . .
Demation
t Value of
. Regression
Age Boys
Girls
121
139
.351
.283
.072*
.076t
4.09
3.46
Height Boys
Girls
121
139
.318
.208
.073
.077
3.66
Q.49
Surface area Boys Girls
121
139
.311
.166
.078
.078
8.56
1.97
Vital capacity Boys
Girls
121
139
.341
.215
.072
.077
3.95
%.57
SUPPLEMENT 173
* SD of group= 0.0762. t SD of group=0.0788.
volves an additional calculation.#{176} A second
reason for the preference of height is that
weight due to fat (especially in the
abnor-mal with obesity) is thought to have an
ad-verse effect on the lung function. Thirdly,
with chronic lung disease growth is often
disturbed, and it is probable that the
growth of the lung will more nearly follow
the height than the weight.
The estimates of residual variance
ob-tained from the ordinary regressions reflect
tile variations of the data around the fitted
lines. The estimated residual variances from
tile covariance analysis are smaller because
allowances are made for a quality in the
subject, viz., his inherent deviation from
the mean of a group of his size. The more
nearly the individuals’ growths are parallel
to the common growth line, the smaller
will be the residual variance obtained from
covariance analysis. The more nearly
par-allel their growths, the more the
individ-uals maintain their own respective positions
within the group. Thus, the reduction in
residual variance by use of covariance
anal-ysis indicates how well an individual should
As expected, the multiple correlation
coeffi-cient was a little higher for vital capacity with
height and weight, if the relationship of height
and weight was not constrained to Dubois and
Dubols’ formula.
maintain his relative position. This is
appli-cable only to the serial examination of
pa-tients. The variation on successive tests to
be expected from the calculated growth
in-crement is the standard deviation obtained
from the covariance analysis and not that
from the ordinary regression analysis. As
an example, if a subject’s vital capacity
is 10% below that predicted from his height
on one occasion, on the next occasion the
subject’s vital capacity would be expected
to be 10% below that predicted from his
new height, with some variation which can
be estimated by the SD from covariance
analysis (6.4% for boys). This is more
pre-cise than would be obtained from ordinary
regression and so enhances the perception
of significant deviation from normal growth.
By comparison of the residual variances
from the ordinary regressions and from
co-variance analysis one can see that about
three-fourths of the variance obtained from
the ordinary regression is removed by
al-lowing for a quality inherent in the
mdi-vidual. This remarkable reduction occurred
despite the relatively narrow limits of
nor-mality for this test (compared to some of
the other tests). For the FRC the
reduc-tion, about 50%, though not as striking as
that with the vital capacity, is still helpful
GIRLS FRC (ML)
4000
3500.
3000
2500
2000
1500
‘-.., ,
‘-,
.
1000
5O0
100
I I I I
110 120 130 140
HEIGHT IN CM. 174
I I
150 160 170 180 190
FIG. 6. The functional residual capacity in relation to height (girls) on logarithmic scales. Points con-nected by a solid line are from the same subject. The dashed lines indicate the calculated regression
line and two standard deviations on either side.
The dimensionally adjusted exponents
from the various regression equations
(Table IV) are informative about the
growth of the lungs. These values show
that in this age period the lungs grow as
the body does and that the independent
variables (age, height, sitting height,
weight, surface area, and biacromial width)
appear to each reflect the same body growth.
This point is confirmed by the relatively
small decreases in residual variance
re-sulting from the use of more than one of
these independent variables (Tables I and
II) to predict the lung volumes. Age,
though one dimensional in nature, does
not conform as well as the other factors.
This is not surprising since the body
growth is not a simple function of age.
The dimensionally adjusted ratios of lung
volume to age are also different for boys
and girls. This reflects tile different body
growth of the two sexes.
From further examination of Table IV
three additional facts become evident. First,
the size of the adjusted exponents for the
relationship of FRC to height in girls is
ap-preciably lower than for FRC to height in
boys and VC to height in boys and girls.
This does not mean that the values of FRC
are lower in girls than boys of the same
size (which they are) but that the
incre-ment of log FRC per increment of log body
size is less than for the other groups. The
reason for this is not clear. Secondly, for
all groups the values of the adjusted sitting
height exponents are lower than those of
the other physical measurements. This
oc-curs because the sitting height to total
height ratio changes with increasing age.
mdi-SUPPLEMENT 175
cate functional growth than does sitting
height. Thirdly, there is a difference
be-tween the sexes in the adjusted exponents
for age. This results from the smaller body
growth rate for girls than boys, and the
lung volumes reflect the body size.
The expiratory reserve volume can be
predicted from the predicted vital capacity.
In the entire age range it was about 32%
of the vital capacity, with some change in
this ratio as height increases. We feel that
a few “normal” breaths preceding the vital
capacity maneuver gave only a rough
indi-cation of end-tidal resting point and
intro-duced error in the expiratory reserve
vol-ume measurement. For this reason more
elaborate analysis was not done. It is
in-teresting that despite much variability,
in-crease in the ratio of expiratory reserve to
vital capacity with increasing age, though
not large is statistically significant.
Formulas for predicting the vital
capac-ity and functional residual capacity using
different single independent variables or
combinations of independent variables can
be obtained from the tables. From the
pre-ceding discussion it is evident that we feel
height alone is a suitable choice for routine
use. The formulas for using this
independ-ent variable after transformations of the
data in Tables I and II are as follows
(vol-umes in milliliters, height in centimeters):
VC (boys) = 2.157 X 10 X ht28’
VC (girls) = 1.858 X 10 X ht282
FRC (boys) = 7.312 X 10 X ht293
FRC (girls) = 4.781 X 10 X hr254
SUMMARY
A three-year longitudinal study of a
va-riety of lung function tests in 147 normal
children has been carried out to permit
better separation of growth effects (by
co-variance analysis) from individual
varia-tion, to supply information not previously
available, and to permit study of the
inter-relationships of the tests in normal subjects.
In this, the first of a series of papers, we
have presented the results of the study of
lung volumes. Height is the best single
in-dicator of physical size for predicting
nor-mality. Comparison of residual variances
indicates that the use of multiple
independ-ent variables offers little advantage.
Although there is reason to believe that
the lung volumes do not increase in a
sim-ple exponential relationship to height after
birth, after 5 years of age the lung volumes
do increase as approximately the cube of
height. When the values of the exponents
obtained from regression analyses of the
lung volumes on different independent
vari-ables are adjusted by the dimensional
re-lationships of the variables, several points
become evident. Among them are: (1) the
various independent variables (except
sit-ting height) are all reflecting the same
gen-eral body growth; (2) the exponents for the
FRC in girls are less than those for vital
capacity in boys or girls and less than the
FRC in boys; (3) there is a difference
be-tween boys and girls in the exponent for
age. The latter only reflects the relatively
smaller body growth of girls for each age
increment.
Analyses of covariance made possible by
the longitudinal studies indicate that about
three-fourths of the residual variance
ob-tained from the ordinary regression of log
vital capacity on log height (and one-half
of that of log FRC on log height) is due to
a quality inherent in the individual.
Knowl-edge of this factor permits future estimates
of a person’s lung volume with greater
pre-cision.
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