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Areal growth in the human fetal parietal bone.

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Areal Growth in the Human Fetal Parietal Bone
Department of Health and Physical Education, Tokyo University of
Agriculture and Technology, Harumicho, Fuchushi, Tokyo 183, JAPAN
Fetus, Cranial bone, Allometric analysis, Marginal growth, Surface
The areal growth of the human fetal parietal bone is described
using 51 dissected right parietal bones of Japanese fetuses ranging from the
fifth month to term. Their shadows were taken on printing paper and analyzed
by a sonic digitizer.
The absolute growth of the projected area of the fetal parietal bones progresses at a fairly constant rate during the latter half of the fetal period, despite
some deceleration in the 9-10th month. By allometric analysis, the allometric
coefficients against crown-rump length are 2.201 for males, 2.202 for females,
and 2.204 for both sexes, respectively. The allometry is essentially monophasic,
showing no inflection point, indicating a change in the slope of the regression
line; that is, the growth of the human fetal parietal bone is continuous with a
constant specific growth
rate. These results are discussed in connection with
growth in thickness of the bone.
Quantitative changes in some cranial bones
in the human fetal period have been described
in detail (Scammon and Calkins, '29; Inman,
'34; Inman and Saunders, '37; Noback, '43;
Moss, '55, '64; Moss et al., '56; Nishida, '59;
Misaki, '59a,b; Koura and Yokota, '60; Ohtsuki, '77; and others). These studies are generally concerned with developmental changes
of one or more cranial bones separately. The
morphology of the head is, however, the result
not only of bone growth, but of the integral
growth of all its components. Isolated cranial
growth d a t a may be correlated with t h e
growth of other structure (Moss et al., '56;
Moss and Young, '61) and the growth data for
each cranial bone would be more meaningful
if growth of its three-dimensions were to be
The present study presents information on
the areal growth of the parietal bone, and a
discussion of the relationship between marginal growth (two-dimensional growth from
the ossification center toward the peripheral
border) and surface growth (one-dimensional
growth in thickness) reported previously
(Ohtsuki, '77 ).
The materials used for this study were 51
dissected right parietal bones of Japanese fetuses, 22 males and 29 females, ranging from
0092-948318015301-0005$01.40", 1980 ALAN It. LISS, INC.
t h e 5 t h month t o t e r m (Table 1). T h e i r
shadows were printed on printing paper and
analyzed by a sonic digitizer-the contours of
bones traced by a stylus that emitted sounds
a t a given interval. These sounds were picked
up by condenser microphones set on both x
and y-axes. The lapse of time after the emission of the sounds until they were recorded by
the microphones was converted t o distance
from that location to each axis. Thus, the coordinates could be read and the total area of
each parietal bone calculated.
The absolute and relative growth of the
area of the parietal bone were investigated
(Huxley, '32). The allometric equation is represented as y = bx- and is usually transformed into logarithms, log y = a log x + log
b; any values in this formula plotted on a double logarithmic grid fall along straight lines.
In the equation, a is the allometric coefficient
and log b is the initial growth coefficient
(Huxley and Teissier, '36). The value of a
gives the ratio between the specific growth
rate of the dimensions y and x. When a is
1.00, the slope of the line is 45" and specific
growth rates of x (the abscissa1 value) and of y
(the ordinate value) are equal, that is, isometric. When the value of a is greater than 1.00
A part of this paper was read before t h e 83rd Annual Meeting of
the Japanese Association of Anatomists in Ube-shi In April 1978.
Received May 21, 1979, accepted September 13,1979.
TABLE I . Growth of projected area of human fetal
parietal bones
Fetal age
in months
Projected area i n mm2
3,464.9 1
N, number of fetuses.
SD, standard deviation.
Materials utilized for this study a r e derived from th e same
source a s those o f t h e previous report (Ohtsuki, '711, which were
obtained in a fresh condition from various hospitals and
preserved in 10% formalin solution. As shown i n Table 2, 22 a r e
males and 29 females.
and ratio favors the ordinate value (y), there
is positive allometry. When the value of a is
less than 1.00 and the ratio favors the abscissa] values (x),there is negative allometry.
In the present study, the projected area for
each fetal parietal bone is taken as the ordinate (y) and is plotted on double logarithmic
paper taking crown-rump length as the abscissa (x), and the regression line was obtained by the method of least squares, using
log y and log x as the dependent and independent variables. Detailed statistical procedures of the allometric analysis are given by
Sholl ('48, '50) and Sagami ('69).
Marginal growth
Table 1 presents the mean and standard deviation of the projected area of the parietal
bone by fetal age in months; plots are shown
i n Figure 1. Taking t h e value of t h e 5th
month as 1for comparison, the area is approximately twofold in the 6th month, threefold in
the 7th month, fourfold in the 8th month, and
fivefold in the 9-10th month. Therefore, plots
of the mean value by month are on a straight
line, but the value of the 9-10th month is less
than might be projected from the estimated
straight line (Fig. 1).This may partly be due
to the method employed. Even though the parietal bone is comparatively flat, t h e projected area is smaller than the actual area
and this difference may be more conspicuous
in the circumnatal period. It is reasonable to
assume that the absolute growth in the projected area of the fetal parietal bones is progressive a t a fairly constant rate during the
latter half of the fetal period.
The allometric method is shown to provide
a good model. In Table 2, the allometric coefficients ( a ) and the initial growth coefficients
Fig. 1. Plots of the projected area'for the human fetal
parietal bane in mmz against the age in months.
TABLE 2 . Allometric coefficients of the projected area of
human fetal parietal bones against C-R length
log b
M + F
2,201 t 0.341
2.202 t 0.291
2.204 ? 0.214
M. males
All a values a r e significantly greater than 1.00 a t the
probability level of0.01 by F-test, which means these ar e
positive allometry
(log b) are shown. Alpha is the slope of the
regression line and log b is the y intercept.
The allometric coefficient against crownrump length is 2.201 for males, 2.202 for
females, and 2.204 for both sexes combined.
No statistically significant difference was
found between the sexes, and no critical point
t h a t makes any change of t h e linear slope
could be found, that is, the allometry is essentially monophasic during this fetal period.
The straight line was drawn on the plots in
Figure 2.
The a value of the projected area for the parietal bone i s shown in Figure 3 with t h e
other variables of the same bone, namely, the
thickness a t the ossification center (OC) and
the vertical and transverse arc lengths. Numerals indicated in the first row of the figure
show a scale of allometric coefficients.
In Figure 3, the points of vertical and trans-
nial bone of human fetuses, 14 mm to 175 mm
crown-rump length, a stage of development
just earlier than that of the present series,
and found no difference from that of postcranial bones. A change of linear slope or interphase favoring the x-axis was generally
noted a t 80-89 mm crown-rump length for
each osseous dimension, when each dimen5000
sion was plotted against the log of crownrump length or against the log of time. Excep4000
tional growth characteristics were exhibited,
however, in width of the cartilaginous portion
of the occipital squama, which showed either
a n interphase favoring the y-axis or no interphase at the same crown-rump length as in
the others. A correlation was suggested be2000
tween this cartilaginous growth and growth
of brain, that is, the growth in width of the
cerebellar hemispheres. This brain dimension
does not begin its growth until the end of the
third fetal month (Noback and Moss, '56).
The growth of the brain is accompanied by
enlargement of the neurocranial capsule. In
the cambial layer of capsular tissues, the cra800
nial bone appears as a primary ossification
center and then bony trabeculae expand radi600
ally outward as if to cover and protect the underlying
brain. By the gradual expansion of
the cerebral contents, the cranial bone moves
outward passively within the capsular con400
nective tissue; however, the present results
for the fetal parietal bone show that the cranial bone is ossifying a t its own relatively
constant rate as described by Moss et al. ('56).
200 250 300350
Although the osteogenesis a t the sutural area
C-R L E N G T H m m
occurs as compensation for the cerebral expansion and tends t o keep the sutural area inFig. 2. Logarithmic plots of areal dimension for the parietal bone against crown-rump length. Regression line is tact (Moss and Young, '61), this does not mean
simply that acceleration in growth at the sudrawn on them.
t u r a l a r e a is taking place. The marginal
verse arc lengths located near the vertical growth of each cranial bone itself has in one
line approximating to 1 and that of the pro- sense nothing t o do with the relocation in
jected area deviates far from the line approx- space during this period of development.
imating t o 2. It has been generally suggested
Marginal versus surface growth
that a value approximating t o 1 is for oneThe thickness of cranial bones was investidimensional growth, 2 for two-dimensional or
areal growth, and 3 for three-dimensional or gated by Roche ('53) in a subadult sample
(3-21 years) and by Hack1 ('66) in adult cravolumetric growth.
The fact that growth of human fetal parie- nia (under 50 years). The quantitative data in
tal bones is essentially continuous with a con- this dimension for the fetal period, however,
stant specific growth rate is of importance. seem t o be scarce a s far a s t h e author is
Not only t h e vertical and transverse arc aware. The absolute values of parietal bone
lengths, but the projected area of the fetal pa- thickness at the ossification center in human
rietal bone are found t o be monophasic (Fig. fetuses were found by Ohtsuki ('77) to be 95.0
2); that is, the slope is linear on the log-log p in the 4-5th fetal month, 216.9 p in the 6th
month, 417.0 p in the 7th month, 496.0 p in
Moss ( ' 5 5 ) analyzed the growth of the cra- t h e 8th month and 543.0 p in the 9-10th
G r a p h i c R e p r e s e n t a t i o n of .-value
f o r the Dimensions
of t h e P a r i e t a l Bone
0 imens i on s
2 5
Thickness IOCI
Vertical Arc length
Transverse Arc Length
Projected Area
OC. O s s i f i c a t i o n C e n t e r
Positive Allometry
Fig. 3. Graphic representation of allometric coefficients against crown-rump length. Numerals indicated in
the first row show a scale of allometric coefficients. The data of thickness (OC), vertical arc length, and
transverse arc length are derived from Ohtsuki ('771. Note that DI value approximates to 1for one-dimensional
growth except thickness (OC1 and, 2 for two-dimensional or areal growth. The peculiarlty of the value in
thickness (OCi was discussed (Ohtsuki, '771
month. Plots of these values against fetal age
in months, therefore, a r e on a curved line
showing some deceleration a s t e r m is
By allometric analysis taking crown-rump
length as an abscissa (x),the allometric coefficient ( a )is 2.38 and the initial growth coefficient (log b), 0.39 (Fig. 3). Accordingly, t h e
slope of t h e regression line drawn on double
logarithmic paper is extremely steep. No critical point that changes the slope of the line
could be found by the test of linearity; t h a t is,
the parietal bone thickness a t the ossification
c e n t e r i s e s s e n t i a l l y progressive, w i t h a
higher specific growth rate during the latter
half of t h e fetal period. Some discussion regarding t h e exceptionally high a value with
one-dimensional variables h a s been
published (Ohtsuki, '77).
Hoyte ('661, in his review of neurocranial
growth, did not agree with the distinction between marginal and surface growth. He
ascribed this to the lack of histological control
or t o the utilization of animals t h a t were too
Although t h e present study is not histological, t h e quantitative relationship between
marginal and surface growth of the parietal
bone can be inferred from our data. The absolute value of the parietal bone thickness is
very small, as previously described; however,
a n exceptionally high specific growth rate is
observed i n t h i s d i m e n s i o n . T h e s u r f a c e
growth of t h e parietal bone must occur simultaneously with marginal growth.
This may be confirmed by the previous findings of Ohtsuki ('77), t h a t the allometric coef-
ficients of occipital bone thickness at the ossification c e n t e r a n d m i d d l e point a g a i n s t
crown-rump length a r e 2.49 and 2.03, respectively. The middle point is located in the middle of t h e ossification center to t h e highest
point of squamo-occipital along the midsaggital line. This point moves relatively away
from the ossification center toward the bone
margin a t t h e earlier developmental stage
with advancing of fetal age. However, the specific growth rate of the thickness at this point
is a s high a s t h a t of t h e ossification center,
which indicates t h a t surface growth occurs all
over the bone and even in the marginal area.
As suggested by Hoyte ('66), i t is presumably
a misconception to consider t h a t t h e marginal
growth of t h e cranial bones occurs first, followed by surface growth.
The marginal growth of t h e human fetal
parietal bone is essentially continuous with a
fairly constant specific growth r a t e during
the latter half of the fetal period. Irrespective
of the absolute value, the surface growth of
the parietal bone occurs simultaneously with
t h e marginal growth.
The a u t h o r i s deeply indebted to Drs. S.
Morita and K. Itoh for their cordial direction
throughout t h e study. Also, thanks a r e due to
Dr. A. F. Roche for his reading of the manuscript and offering many suggestions to t h e
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