AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 53:5-9 (1980) Areal Growth in the Human Fetal Parietal Bone FUMIO OHTSUKI Department of Health and Physical Education, Tokyo University of Agriculture and Technology, Harumicho, Fuchushi, Tokyo 183, JAPAN KEY WORDS Fetus, Cranial bone, Allometric analysis, Marginal growth, Surface growth ABSTRACT 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 considered. 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 ). MATERIALS AND METHODS 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. 5 FUMIO OHTSUKI 6 TABLE I . Growth of projected area of human fetal parietal bones Fetal age in months 5 6 7 8 %lo N Projected area i n mm2 Mean SD 9 13 10 10 9 789.21 1,648.49 2,530.77 3,464.9 1 4,059.91 281.59 639.94 755.84 748.47 803.11 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). RESULTS AND DISCUSSION 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 0 5 7 6 Ag8 in 8 9-10 Month 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 Sex N (Y log b M F M + F 22 29 51 2,201 t 0.341 2.202 t 0.291 2.204 ? 0.214 -1.788 -1.760 -1.777 M. males i.:females. 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- AREAL GROWTH IN FETAL PARIETAL BONE mm' 7 nial bone of human fetuses, 14 mm to 175 mm crown-rump length, a stage of development P A R I E T A L BONE just earlier than that of the present series, (AREA) and found no difference from that of postcranial bones. A change of linear slope or interphase favoring the x-axis was generally 6000 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 3000 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 1500 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 1000 enlargement of the neurocranial capsule. In 900 the cambial layer of capsular tissues, the cra800 nial bone appears as a primary ossification 700 center and then bony trabeculae expand radi600 ally outward as if to cover and protect the underlying brain. By the gradual expansion of 500 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 I I I I l l constant rate as described by Moss et al. ('56). 100 150 200 250 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 scale. Moss ( ' 5 5 ) analyzed the growth of the cra- t h e 8th month and 543.0 p in the 9-10th 8 FUMIO OHTSUKI 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 15 1 2 5 2 0 Thickness IOCI Vertical Arc length 0 Transverse Arc Length o Projected Area 0 OC. O s s i f i c a t i o n C e n t e r 0 Positive Allometry B Isometry 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 approached. 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 old. 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. CONCLUSION 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. ACKNO WLEDGMENTS 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 author. AREAL GROWTH IN FETAL PARIETAL BONE 9 Moss, M.L., C.R. Noback, and G.G. Robertson (1956) Growth LITERATURE CITED of certain huma n fetal cranial bones. Am. J. Anat., Hackl, van H. (19661 Beobachtung uber Asymmetrien a n 48: 191-204. Leichenschadeln. Anat. Anz., 118:21%233. Moss, M.L., and R.W. Young (19611 A functional approach to Hoyte, D.A.N. (19661Experimental investigation of skull craniology Am. J. Phys. Anthropol., 18:281-292. morphology and growth. Int. Rev. Gen. Exp. Zool., 2:345Nishida, 0. (19591 Morphological study on the occipital bone 407. in Japanese fetuses. Tokyo Shikadai Kaibo Gyoseki., Huxley, J.S. (19321 Problem of Relative Growth. Methuen, 12:38%409. London. Noback, C.R. (1943)Some gross structural and quantitative Huxley, J.S., and G. Teissier (19361 Terminology of relative aspects of the developmental anatomy of the human emgrowth. Nature, 137:78@781. bryonic, fetal and circumnatal skeleton. Anat. Rec., 87 Inman, V.T. 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(1959bl Morphological study on the temporal bone Sagami, Y. (19691 The rate of growth of human mandible. in Japanese fetuses. Tokyo Shikadai Kaibo Gyoseki., Acta Anat. Nippon., 44:&22. 12:361-385. Moss, M.L. (19551Relative growth of the human fetal skele- Scammon, R.E., and L.A. Calkins (19291 The Development and Growth of the External Dimensions of the Human ton, cranial and postcranial. Ann. N.Y. Acad. Sci., 63: Body in the Fetal Period. University of Minnesota Press; 528-536. Minneapolis. Moss, M.L. (19641 Differential mineralization of growing human and r a t cranial bones. Am. J. Phys. Anthropol., Shall, D. (19481 The quantitative investigation of the vertebrate brain and the applicability of allometric formulae to 22:155-162. its study, Proc. Roy. Soc. London, B., 135:24%258. Shall, D. (19501 The theory of differential growth analysis. Proc. Roy. Soc. London, B., 137:47@474.

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