Journal of the Neurological Sciences, 1979,40:169-188 © Elsevier/North-HollandBiomedicalPress
169
HUMAN BRAIN GROWTH IN THE 19TH AND 20TH CENTURY
H.-J. KRETSCHMANN,A. SCHLEICHER,F. WINGERT,K. ZILLESand H.-J. LOBLICH Department of Neuroanatomy, Medical School of Hannover, Hannover ; Institute of Medical Information Science and Biomathematics, University of Miinster; Miinster; and Institute of Pathology, Krankenhaus Nordstadt of the Landeshauptstadt Hannover, Hannover (F.R.G.)
(Received27 July, 1978) (Accepted 29 September, 1978)
SUMMARY Data of 2399 brain weights and ages from populations before 1880, 1885 to 1900 and 1966 to 1976 were obtained from German anatomical and pathological institutes, analyzed with non-linear and multiple linear regression analyses and the results compared. The influence of the absolute age (sample period) on brain weights of adults (age of at least 10 years of ontogenesis) could not be verified. Different averages in the different samples seem to be stipulated by inhomogeneities of the age distributions. Sex differences were confirmed for the different periods. There is an accelerated degree of maturity of brain weights between the population sampled from 1966 to 1976 and the two older populations. The growth rate of the degree of maturity reveals the same fact, i.e., the growth rate is more rapid than 100 years ago. These differences may be explained by changed causes of death in the autopsy samples, but it is possible that they are at least partly caused by an acceleration of brain development in the early postnatal period. In all populations analyzed brain weights in females develop faster than in males. The development of the brain weight in 6 more samples is compared with the results for the Medical School Hannover sample.
INTRODUCTION The objective of this study is to reveal whether the growth of human brain weight has changed over long periods of time. The growth of the human brain weight is analyzed as a function of time by non-linear regression analysis. Brain weight data This work was supported by the Deutsche Forschungsgemeinschaft. Reprint requests to: Prof. Dr. H.-J. Kretschmann,Department of Neuroanatomy,Medical School of Hannover, Karl-Wiechert-Allee9, D 3000Hannover61, West-Germany.
170 have been sampled in anatomical and pathological institutes over time periods usually ranging from 5 to more than 10 years. These data, therefore, represent samples from populations which died in one of these time periods. The scatter diagrams of human postnatal brain weight versus age indicate a large dispersion and a non-linear dependence. Experimental studies show a similar dependence in homogeneous populations of mammals but with a comparatively smaller dispersion when compared with human postmortem data (Kretschmann and Wingert 1971; Kretschmann, Schleicher, Wingert and Zilles 1975; Kretschmann, Schleicher, Wingert and Zilles 1976). This may be caused by various endogenous and exogenous influences during pre- and postnatal development. The new statistical results are based on published original data. Previous authors mostly published only averages instead of original data (Vierordt 1906; Miihlmann 1927; Roessle and Roulet 1932; Spector 1956; Altman and Dittmer 1962) and frequently the criteria for the scaling of the age intervals were not well defined. Only von Bischoff (1880) and Marchand (1902) published original data with a precise age scale and are, therefore, compared with our data sampled within the German districts of Frankfurt/M, Darmstadt and Hannover from 1966 to 1976. Von Bischoff published a sample of 988 brain weight data from a Bavarian population gathered before 1880. Marchand published a sample of 1168 brain weight data from a Hessian population gathered between 1885 and 1900. Additionally, the data of Vierordt (1906), Miihlmann (1927), Roessle and Roulet (1932), White House Conference (1933), Spector (1956) and Altmann and Dittmer (1962) were analyzed - - with the above mentioned restrictions regarding the time scale-- and compared with the other samples. The main questions to be answered are concerned with differences dependent on sex, age and sample periods. It must be emphasized that it is impossible to define precisely the population from which a special sample may be regarded as a random sample. Consequently, statistical methods are only descriptive. Statistical tests may raise suppositions but are no proofs of the hypotheses. However, even though statistical analysis based on test theory could not be done in the classical sense, even descriptive methods are of considerable value. MATERIAL AND METHOD In order to compare the populations the same time scale had to be established for the data from different sources. The prenatal period had to be considered in all growth analyses, because living neonates of the 26th and 42nd week of gestation differ in age by more than 100 days. Neglecting this difference would have resulted in an error in the true age, which is especially serious in the age range of neonates. Therefore, all age data have been expressed as "years of ontogenesis" (Y = years after conception) or "days of ontogenesis" (D = Y-365 = days after conception). The most probable age for each sample element was determined according to the following available informations : [1] D = date 3-date 1--14 if date 3 and date 1 are known, else [2] D = date 3-date 2 + 268 if date 3 and date 2 are known, else
171 [3] D = d + 268 = w-7 q- 268 = m.30 q- 268 = y-365 q- 268 if the respective values are known and age < 4 years, else [4] D = (y q- 0.5).365 q- 268, where date 1 = first day of last menstruation of the mother; date 2 = birth date of patient; date 3 = date of death of patient; d, w, m, y = number of days, weeks, months, years, respectively, of postnatal age. Except for [1 ] a "normal" gestation of 268 days was assumed. Our sample (Medical School Hannover sample) consists of the age and weight of 129 male and 104 female brains, sampled between 1966 and 1976 in the regions of Frankfurt/Main, Darmstadt and Hannover. The weight of the fresh brain including meninges was determined immediately after post-mortem examination with precision scales. The precision of our age data is high (formula [1] or [2]) compared with previously published data. Brains with neuropathologic changes as revealed by autopsy and clinical reports, were excluded. The Marchand sample (1902) was the largest one analyzed for this paper and contains 716 male and 452 female brains. The weights of the fresh brains including meninges were determined between 1885 and 1900 in the Institute of Pathology in Marburg/Lahn with a precision of 5 g. The ages were calculated with either formula [3] or [4], because the precise date of birth and death was not published. Brains with a pathological weight were excluded. However, this procedure was not performed sufficiently strictly and thus low grade hydrocephalic brains were included. Since the cause of death was usually not given, the data could not be cleaned. The von Bischoff sample (1880) consists of 594 male and 404 female brains mostly from Bavaria and also contains some pathological brains. The weights were determined before 1880. These data are the oldest considered in this paper. The ages were also calculated with either formula [3] or [4]. Fresh brains including meninges were weighed with a precision of 1 g. Causes of death were published only for patients older than 17 years. The period before the 17th postnatal year was completed by yon Bischoff with data published by other authors (Sims 1835; Tiedemann 1837); these weights were calculated in Anglo-Saxon units; in some cases the origin of the data is unknown. The age range of some data was too small for a sufficient analysis of the growth process (Pfister 1903; Michaelis 1907; Scammon 1936; Woljpin 1902; Altmann and Dittmer 1962). Frequently, averages were published for certain age ranges (Vierordt 1906; Miihlmann 1927; Roessle and Roulet 1932; White House Conference 1933; Scammon 1936; Spector 1956; Altmann and Dittmer 1962) which further impeded a sufficient statistical analysis. Calculation of the age in years of ontogenesis was done using the published data in order to find the most probable value. Statistical analysis of the transformed data was done using the program LOGI (Wingert 1969) to calculate the parameters of the logistic growth function, the BMD-programs for nonlinear regression analysis and the SPSS-system for linear regression analysis. The graphs of the growth functions were drawn with a plotter (WANG 702) and a desk calculator (WANG 720C) controlled by self adapted programs.
172 The generalized (5-parametric) logistic growth function P1 y= 1 + e (1"2 + 1,a.t + 1,4.tg + rs.ta) was used as the model for the analysis of brain weight y as a function of ontogenetic age t (signed as (5) in figs. 1-3). Specializations of this model are: P4 = P5 = O (signed as (3) in Figs. 1-3), resp. P5 = O (signed as (4) in Figs. 1-3). This growth function has a relatively simple mathematical structure and can be easily interpreted. The position of the right asymptote is the "ideal value". The "half-life time" is the age when half the ideal value has been reached. The "growth factor" is an estimate by which the expected brain weight of the neonate must be multiplied in order to obtain the ideal value. This growth factor is calculated using the value of the growth function at "normal" age of birth (268 days of ontogenesis). The first derivative of the growth function is the "growth speed" and is often called "growth rate" (Fisher 1921). The "degree of maturity" is the standardized growth function (ideal value P1 -- 1). It can also be interpreted as a percentage of the ideal value as a function of age. The term "degree of maturity", as used here, is primarily a statistical expression. To detect the influence of absolute age, multiple linear regression analysis was done using specimens with an age of at least l0 years of ontogenesis. The regression function is: b w = a.D + b - T + c where bw = brain weight in g; D = age in days of ontogenesis; T = absolute age (number of days between date of birth and date 01/01/1780), a, b, c are coefficients. RESULTS From the data various hypotheses arise: Figs. 1-3: there is a decrease in brain weight with increasing age in adult brains. Table 2: there is an increase in brain weight from the older samples (before 1900) to the younger (1966-1976). Table 2: sex influences the brain weight. Since the data of von Bischoff and Marchand are incomplete, date of birth was estimated by subtracting the estimated ontogenetic age from January 1st of the publication year (estimated date of death). Another error arises from the fact that the von Bischoff sample contains data published by other authors. To gain an impression of the influence of the latter error, the multiple linear regression analysis was performed with and without the von Bischoff sample (Table 3). Due to the impreciseness of the data the results must be interpreted with caution. An influence of absolute age on the brain weight of adults could not be proved due to the problems connected with the older samples. In contrast, there is a distinct influence of ontogenetic age in that the weights of brains with an age of at least 10 years of ontogenesis decrease with ontogenetic age. The differences in the averages in Table 2 are probably dependent on an inhomogeneous age distribution and not on the "absolute age" (T) of the sample. Another way of attacking the problem of brain development is to fit the above mentioned logistic growth function to the data.
173 TABLE 1 P A R A M E T E R S (first line) A N D S T A N D A R D DEVIATIONS (second line) OF T H E LOGISTIC GROWTH FUNCTION FOR THE FRESH BRAIN WEIGHT Sample
PI
P~
P3
P4
P5
V
W
n
VonBischoff(1880) male
1369 5
1.16 0.13
--0.775 0.085
0.0178 0.0023
4--0.000108 0.000017
2.8 0.2
1.56 0.10
594
VonBischoff(1880) female
1223 6
1.29 0.14
---0.978 0.090
0.0234 0.0025
0.000147 0.000019
2.8 0.2
1.36 0.08
404
Marchand(1902) male
1386 5
1.84 0.09
--1.373 0.070
0.0324 0.0022
---0.000200 0.000021
3.3 0.1
1.39 0.03
716
Marchand(1902) female
1256 6
1.89 0.11
--1.531 0.095
0.0369 0.0026
4.000230 0.000020
3.2 0.I
1.27 0.03
452
MedicalSchoolHannover male
1389 16
2.10 0.20
--1.885 0.186
0.0419 0.0044
--0.000238 0.000027
3.1 0.2
1.15 0.03
129
Medical School H a n n o v e r female
1221 12
2.45 0.26
--2.335 0.264
0.0499 0.0061
~.000272 0.000038
3.0 0.2
1.06 0.03
104
P1-P5 = parameters of the logistic growth function; V = growth f a c t o r ; W = half-life time in years of ontogenesis; n = n u m b e r of data.
TABLE 2 AVERAGES A N D EMPIRICAL CORRELATION COEFFICIENTS OF BRAIN WEIGHT F R O M 10 TO 50 YEARS O F O N T O G E N E S I S Sample
Male n SE r P Female n SE r P
Von Bischoff (1880)
Marchand (1902)
Medical School Hannover
386 1370 6 ---0.04 0.21
318 1401 6 0.04 0.23
26 1439 28 --0.49 0.01
259 1235 6 0.05 0.23
190 1273 7 0.01 0.46
19 1246 20 --0.30 0.11
n = n u m b e r of b r a i n s ; $ = average in g; SE = standard deviation of the average in g; r : Pearson's correlation coefficient; P = significance level of r.
174 TABLE 3 RESULTS OF MULTIPLE LINEAR REGRESSION ANALYSIS: bw - a- D -k b • T ÷ c (bw = brain weight, D = ontogenetic age in days (D >_ 3650), T = absolute age in days (for explanation see text), a, b, c - regression coefficients). Male
Female
Regression
Regression
I
II
I
(n=1154)
(n=597)
(n = 727)
1I (n = 376)
a SE Fa
--0.00264 0.00063 17.6
~0.00369 0.00081 20.9
--43.00327 0.00061 28.5
---0.00495 0.00080 38.2
b SE Fb
0.00099 0.00042 5.4
~0.00008 0.00060 0.0
0.00087 0.00043 4.2
--0.00084 0.00058 2.1
c
1389
1446
1260
1356
r
0.195
0.214
0.252
0.310
Fr
22.8
14.3
24.6
19.8
r = multiple correlation coefficient; n = number of data; F~, Fb -- F-values for the respective coefficients (test of regression coefficient = 0); F r - - F-value for test of multiple correlation coefficient = 0; SE = standard deviation of the coefficient. I = regression analysis including the von Bischoff, Marchand and Medical School Hannover samples; I[ = regression analysis including the Marchand and Medical School Hannover samples.
Figures 1-3 are scatter d i a g r a m s o f b r a i n weight versus age in d a y s o f ontogenesi s a n d age in years o f ontogenesis. The male a n d female d a t a were calculated s e p a r a t e l y with the 3-, 4- a n d 5-parametric logistic g r o w t h function. The 5-parametric fit always resulted in a m a r k e d r e d u c t i o n o f the residual sum o f squares a n d was therefore used for the following interpretations. The dispersion o f the d a t a was especially r e m a r k a b l e for adults. The range o f a d u l t b r a i n weights was smaller for the M e d i c a l School H a n n o v e r sample t h a n for the von Bischoff a n d M a r c h a n d samples. The 5 - p a r a m e t r i c logistic g r o w t h function follows the decline o f the b r a i n weight in the senile age range. The following increase is stipulated by the small n u m b e r o f d a t a in the senile age range a n d b y the rigidity o f the function. This final increase is o f no biological interest. The ideal values again reveal t h a t the expected b r a i n weight in adults is i n d e p e n d e n t o f the age o f the sample. This analysis detected a definite influence o f sex on b r a i n weight, which was seen in all 3 samples. The ideal values for the male d a t a were higher by 146 g (von Bischoff), 130 g ( M a r c h a n d ) a n d 168 g ( M e d i c a l School H a n n o v e r ) t h a n the ideal values for the respective female d a t a (Table 1). Similar differences could be f o u n d in the averages for the age range f r o m the 10th to the 50th year o f ontogenesis (Table 2). The different g r o w t h p a t t e r n s o f male a n d female b r a i n weight was revealed by the degree o f m a t u r i t y (Figs. 4-6). The degree o f m a t u r i t y o f the female b r a i n is equal to or greater t h a n t h a t o f the male b r a i n for the total age range in all 3 samples. T h a t
175 2000"
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Fig. 1. a: logistic g r o w t h f u n c t i o n s fitted to 594 m a l e brain weights (data f r o m v o n Bischoff 1880); b: logistic g r o w t h f u n c t i o n s fitted to 404 female brain weights (data f r o m y o n Bischoff 1880).
176 i
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177 2000
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Fig. 3. a: logistic growth functions fitted to 129 male brain weights (data from Medical School H a n n o ver); b: logistic growth functions fitted to 104 female brain weights (data from Medical School H a n n o ver).
178 1.0 -
degreeof maturity of brain weight v. BI SCHOFF
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degreeof maturity of brain weight MARCHAND
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3
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years of ontogenesis
Fig. 5. Degree of maturity of male:and female brain weight (data from Marchand 1902).
179 1.0
degree of maturity of brain weight Medical School H a n n o v e r ~ ~ ' ~
0.8
0.6
0.4
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' 0 .... 0
i 250
i ~0
2 11 750
3 i I lO00
i 1250
4 II 1500
5 = I 1750
yeats of oatogenesis = ~000 days of ontogenesis
Fig. 6. Degree of maturityof male and femalebrain weight(data from MedicalSchool Hannover). means that the females reach their respective degree of maturity at a younger age than do males, and brain growth, consequently, is completed at a younger age than male brain growth. Figures 7-9 show the growth rate for the degree of maturity. The initially faster growth of the female brain, i.e. a greater proportional increase in weight per unit time, could be seen in all 3 samples. A phase of more rapid growth of the male brain starts where both graphs intersect. These sex differences in brain development necessitate a separate analysis for male and female brain growth if brain development is to be compared over different periods of time. The growth dynamics of the 3 populations show remarkable differences (Fig. 10, Table 1). The degree of maturity of the male brain reaches 0.95 (95 %) after 6.13, 3.82, and 2.85 years of ontogenesis, in the 3 samples, respectively. At an age of 2.4 years of ontogenesis, the degree of maturity of the brain growth in the Medical School Hannover sample is 25 % greater than in the sample from 90 years ago (yon Bischoff). The more rapid growth rate of the initial postnatal brain development of the Medical School Hannover sample can be seen in Fig. 10b. The growth rate of this sample also decreased faster than those of the von Bischoff and Marchand samples. The relations were analogous for the female samples (Fig. 11). The 95 %-values for the degree of maturity of the female brain weight was reached after 4.88, 3.44 and 2.44 years of ontogenesis in the 3 samples, respectively. The different growth dynamics of the 3 populations was also demonstrated by the age at which the growth rates of the male and female samples intersect (Figs. 7-9).
180 0. 0020 -
growth rate of the degree of maturity of brain weight v. BI SCHOFF
O.0016
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1 0
r
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II
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1250
years of ontogenesis
r t
1500
F
I
1750
2000 days of ontogenesis
Fig. 7. Growth rate of the degree of maturity of male and female brain weight (data from yon Bischoff 1880).
0.0020 -
growth rate of the degree of maturity of brain weight MARCHAND
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O.0012
0.0008-
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years of ontogenesis
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750
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Fig. 8. Growth rate of the degree of maturity of male and female brain weight (data from Marchand 1902).
181 0.0t~0 -
growth rate of the degreeof maturity of brain weight Medical School Hannover
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years of ontogenesis
2
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750
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Fig. 9. Growth rate of the degree of maturity of male and female brain weight (data from Medical School Hannover). This intersection is located at 2.93 (von Bischoff), 1.97 (Marchand) and 1.70 (Medical School Hannover) years of ontogenesis. The growth functions for the data of Vie rordt (1906), MiJhlmann (1927), Roessle and Roulet (1932), White House Conference (1933), Spector (1956) and Altmann and Dittmer (1962) can be compared with these results with the restrictions mentioned above. The similarity of the development of the degree of maturity can be seen in Fig. 12a. The Medical School Hannover sample is located above these growth functions. Figure 12b shows the initially higher and afterwards more rapidly decreasing growth rate of the Medical School Hannover sample. Similar figures can be demonstrated for the respective female samples (Fig. 13). The differing figures for the data of Vierordt (1906) are caused by the very low brain weights in the range between 3 and 5 years of ontogenesis. DISCUSSION
The application of conceptional age ("days of ontogenesis" or "years of ontogenesis" i.e., days or years after conception) is better than postnatal age. Postnatal years or days are imprecise, because immature stillborns and premature children are frequently found in the usual autopsy samples of neonates and of young children. Growth functions based on age data without knowledge of the prenatal age can lead to a bias, if individuals with an abnormal gestation are included. Age differences of 3
182 degree of maturity of brain weight c~
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Fig. 10. Dcgi~e o f maturity (a) and growth rate o f the degree of maturity (b) o f male brain weight (data from yon Bischoff 1880, M a r c h a n d 1902 and Medical School Hannover).
183 1.0- degree of maturity of brain weight 9
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days of ontogenesis
Fig. 11. Degree of maturity (a) and growth rate of the degree of maturity (b) of female brain weight (data from von Bischoff 1880, Marchand 1902 and Medical School Hannovcr).
184 1.0- degree of maturity of brain weight.,._./.,.(~........ i *. :. :. ~."
169
HUMAN BRAIN GROWTH IN THE 19TH AND 20TH CENTURY
H.-J. KRETSCHMANN,A. SCHLEICHER,F. WINGERT,K. ZILLESand H.-J. LOBLICH Department of Neuroanatomy, Medical School of Hannover, Hannover ; Institute of Medical Information Science and Biomathematics, University of Miinster; Miinster; and Institute of Pathology, Krankenhaus Nordstadt of the Landeshauptstadt Hannover, Hannover (F.R.G.)
(Received27 July, 1978) (Accepted 29 September, 1978)
SUMMARY Data of 2399 brain weights and ages from populations before 1880, 1885 to 1900 and 1966 to 1976 were obtained from German anatomical and pathological institutes, analyzed with non-linear and multiple linear regression analyses and the results compared. The influence of the absolute age (sample period) on brain weights of adults (age of at least 10 years of ontogenesis) could not be verified. Different averages in the different samples seem to be stipulated by inhomogeneities of the age distributions. Sex differences were confirmed for the different periods. There is an accelerated degree of maturity of brain weights between the population sampled from 1966 to 1976 and the two older populations. The growth rate of the degree of maturity reveals the same fact, i.e., the growth rate is more rapid than 100 years ago. These differences may be explained by changed causes of death in the autopsy samples, but it is possible that they are at least partly caused by an acceleration of brain development in the early postnatal period. In all populations analyzed brain weights in females develop faster than in males. The development of the brain weight in 6 more samples is compared with the results for the Medical School Hannover sample.
INTRODUCTION The objective of this study is to reveal whether the growth of human brain weight has changed over long periods of time. The growth of the human brain weight is analyzed as a function of time by non-linear regression analysis. Brain weight data This work was supported by the Deutsche Forschungsgemeinschaft. Reprint requests to: Prof. Dr. H.-J. Kretschmann,Department of Neuroanatomy,Medical School of Hannover, Karl-Wiechert-Allee9, D 3000Hannover61, West-Germany.
170 have been sampled in anatomical and pathological institutes over time periods usually ranging from 5 to more than 10 years. These data, therefore, represent samples from populations which died in one of these time periods. The scatter diagrams of human postnatal brain weight versus age indicate a large dispersion and a non-linear dependence. Experimental studies show a similar dependence in homogeneous populations of mammals but with a comparatively smaller dispersion when compared with human postmortem data (Kretschmann and Wingert 1971; Kretschmann, Schleicher, Wingert and Zilles 1975; Kretschmann, Schleicher, Wingert and Zilles 1976). This may be caused by various endogenous and exogenous influences during pre- and postnatal development. The new statistical results are based on published original data. Previous authors mostly published only averages instead of original data (Vierordt 1906; Miihlmann 1927; Roessle and Roulet 1932; Spector 1956; Altman and Dittmer 1962) and frequently the criteria for the scaling of the age intervals were not well defined. Only von Bischoff (1880) and Marchand (1902) published original data with a precise age scale and are, therefore, compared with our data sampled within the German districts of Frankfurt/M, Darmstadt and Hannover from 1966 to 1976. Von Bischoff published a sample of 988 brain weight data from a Bavarian population gathered before 1880. Marchand published a sample of 1168 brain weight data from a Hessian population gathered between 1885 and 1900. Additionally, the data of Vierordt (1906), Miihlmann (1927), Roessle and Roulet (1932), White House Conference (1933), Spector (1956) and Altmann and Dittmer (1962) were analyzed - - with the above mentioned restrictions regarding the time scale-- and compared with the other samples. The main questions to be answered are concerned with differences dependent on sex, age and sample periods. It must be emphasized that it is impossible to define precisely the population from which a special sample may be regarded as a random sample. Consequently, statistical methods are only descriptive. Statistical tests may raise suppositions but are no proofs of the hypotheses. However, even though statistical analysis based on test theory could not be done in the classical sense, even descriptive methods are of considerable value. MATERIAL AND METHOD In order to compare the populations the same time scale had to be established for the data from different sources. The prenatal period had to be considered in all growth analyses, because living neonates of the 26th and 42nd week of gestation differ in age by more than 100 days. Neglecting this difference would have resulted in an error in the true age, which is especially serious in the age range of neonates. Therefore, all age data have been expressed as "years of ontogenesis" (Y = years after conception) or "days of ontogenesis" (D = Y-365 = days after conception). The most probable age for each sample element was determined according to the following available informations : [1] D = date 3-date 1--14 if date 3 and date 1 are known, else [2] D = date 3-date 2 + 268 if date 3 and date 2 are known, else
171 [3] D = d + 268 = w-7 q- 268 = m.30 q- 268 = y-365 q- 268 if the respective values are known and age < 4 years, else [4] D = (y q- 0.5).365 q- 268, where date 1 = first day of last menstruation of the mother; date 2 = birth date of patient; date 3 = date of death of patient; d, w, m, y = number of days, weeks, months, years, respectively, of postnatal age. Except for [1 ] a "normal" gestation of 268 days was assumed. Our sample (Medical School Hannover sample) consists of the age and weight of 129 male and 104 female brains, sampled between 1966 and 1976 in the regions of Frankfurt/Main, Darmstadt and Hannover. The weight of the fresh brain including meninges was determined immediately after post-mortem examination with precision scales. The precision of our age data is high (formula [1] or [2]) compared with previously published data. Brains with neuropathologic changes as revealed by autopsy and clinical reports, were excluded. The Marchand sample (1902) was the largest one analyzed for this paper and contains 716 male and 452 female brains. The weights of the fresh brains including meninges were determined between 1885 and 1900 in the Institute of Pathology in Marburg/Lahn with a precision of 5 g. The ages were calculated with either formula [3] or [4], because the precise date of birth and death was not published. Brains with a pathological weight were excluded. However, this procedure was not performed sufficiently strictly and thus low grade hydrocephalic brains were included. Since the cause of death was usually not given, the data could not be cleaned. The von Bischoff sample (1880) consists of 594 male and 404 female brains mostly from Bavaria and also contains some pathological brains. The weights were determined before 1880. These data are the oldest considered in this paper. The ages were also calculated with either formula [3] or [4]. Fresh brains including meninges were weighed with a precision of 1 g. Causes of death were published only for patients older than 17 years. The period before the 17th postnatal year was completed by yon Bischoff with data published by other authors (Sims 1835; Tiedemann 1837); these weights were calculated in Anglo-Saxon units; in some cases the origin of the data is unknown. The age range of some data was too small for a sufficient analysis of the growth process (Pfister 1903; Michaelis 1907; Scammon 1936; Woljpin 1902; Altmann and Dittmer 1962). Frequently, averages were published for certain age ranges (Vierordt 1906; Miihlmann 1927; Roessle and Roulet 1932; White House Conference 1933; Scammon 1936; Spector 1956; Altmann and Dittmer 1962) which further impeded a sufficient statistical analysis. Calculation of the age in years of ontogenesis was done using the published data in order to find the most probable value. Statistical analysis of the transformed data was done using the program LOGI (Wingert 1969) to calculate the parameters of the logistic growth function, the BMD-programs for nonlinear regression analysis and the SPSS-system for linear regression analysis. The graphs of the growth functions were drawn with a plotter (WANG 702) and a desk calculator (WANG 720C) controlled by self adapted programs.
172 The generalized (5-parametric) logistic growth function P1 y= 1 + e (1"2 + 1,a.t + 1,4.tg + rs.ta) was used as the model for the analysis of brain weight y as a function of ontogenetic age t (signed as (5) in figs. 1-3). Specializations of this model are: P4 = P5 = O (signed as (3) in Figs. 1-3), resp. P5 = O (signed as (4) in Figs. 1-3). This growth function has a relatively simple mathematical structure and can be easily interpreted. The position of the right asymptote is the "ideal value". The "half-life time" is the age when half the ideal value has been reached. The "growth factor" is an estimate by which the expected brain weight of the neonate must be multiplied in order to obtain the ideal value. This growth factor is calculated using the value of the growth function at "normal" age of birth (268 days of ontogenesis). The first derivative of the growth function is the "growth speed" and is often called "growth rate" (Fisher 1921). The "degree of maturity" is the standardized growth function (ideal value P1 -- 1). It can also be interpreted as a percentage of the ideal value as a function of age. The term "degree of maturity", as used here, is primarily a statistical expression. To detect the influence of absolute age, multiple linear regression analysis was done using specimens with an age of at least l0 years of ontogenesis. The regression function is: b w = a.D + b - T + c where bw = brain weight in g; D = age in days of ontogenesis; T = absolute age (number of days between date of birth and date 01/01/1780), a, b, c are coefficients. RESULTS From the data various hypotheses arise: Figs. 1-3: there is a decrease in brain weight with increasing age in adult brains. Table 2: there is an increase in brain weight from the older samples (before 1900) to the younger (1966-1976). Table 2: sex influences the brain weight. Since the data of von Bischoff and Marchand are incomplete, date of birth was estimated by subtracting the estimated ontogenetic age from January 1st of the publication year (estimated date of death). Another error arises from the fact that the von Bischoff sample contains data published by other authors. To gain an impression of the influence of the latter error, the multiple linear regression analysis was performed with and without the von Bischoff sample (Table 3). Due to the impreciseness of the data the results must be interpreted with caution. An influence of absolute age on the brain weight of adults could not be proved due to the problems connected with the older samples. In contrast, there is a distinct influence of ontogenetic age in that the weights of brains with an age of at least 10 years of ontogenesis decrease with ontogenetic age. The differences in the averages in Table 2 are probably dependent on an inhomogeneous age distribution and not on the "absolute age" (T) of the sample. Another way of attacking the problem of brain development is to fit the above mentioned logistic growth function to the data.
173 TABLE 1 P A R A M E T E R S (first line) A N D S T A N D A R D DEVIATIONS (second line) OF T H E LOGISTIC GROWTH FUNCTION FOR THE FRESH BRAIN WEIGHT Sample
PI
P~
P3
P4
P5
V
W
n
VonBischoff(1880) male
1369 5
1.16 0.13
--0.775 0.085
0.0178 0.0023
4--0.000108 0.000017
2.8 0.2
1.56 0.10
594
VonBischoff(1880) female
1223 6
1.29 0.14
---0.978 0.090
0.0234 0.0025
0.000147 0.000019
2.8 0.2
1.36 0.08
404
Marchand(1902) male
1386 5
1.84 0.09
--1.373 0.070
0.0324 0.0022
---0.000200 0.000021
3.3 0.1
1.39 0.03
716
Marchand(1902) female
1256 6
1.89 0.11
--1.531 0.095
0.0369 0.0026
4.000230 0.000020
3.2 0.I
1.27 0.03
452
MedicalSchoolHannover male
1389 16
2.10 0.20
--1.885 0.186
0.0419 0.0044
--0.000238 0.000027
3.1 0.2
1.15 0.03
129
Medical School H a n n o v e r female
1221 12
2.45 0.26
--2.335 0.264
0.0499 0.0061
~.000272 0.000038
3.0 0.2
1.06 0.03
104
P1-P5 = parameters of the logistic growth function; V = growth f a c t o r ; W = half-life time in years of ontogenesis; n = n u m b e r of data.
TABLE 2 AVERAGES A N D EMPIRICAL CORRELATION COEFFICIENTS OF BRAIN WEIGHT F R O M 10 TO 50 YEARS O F O N T O G E N E S I S Sample
Male n SE r P Female n SE r P
Von Bischoff (1880)
Marchand (1902)
Medical School Hannover
386 1370 6 ---0.04 0.21
318 1401 6 0.04 0.23
26 1439 28 --0.49 0.01
259 1235 6 0.05 0.23
190 1273 7 0.01 0.46
19 1246 20 --0.30 0.11
n = n u m b e r of b r a i n s ; $ = average in g; SE = standard deviation of the average in g; r : Pearson's correlation coefficient; P = significance level of r.
174 TABLE 3 RESULTS OF MULTIPLE LINEAR REGRESSION ANALYSIS: bw - a- D -k b • T ÷ c (bw = brain weight, D = ontogenetic age in days (D >_ 3650), T = absolute age in days (for explanation see text), a, b, c - regression coefficients). Male
Female
Regression
Regression
I
II
I
(n=1154)
(n=597)
(n = 727)
1I (n = 376)
a SE Fa
--0.00264 0.00063 17.6
~0.00369 0.00081 20.9
--43.00327 0.00061 28.5
---0.00495 0.00080 38.2
b SE Fb
0.00099 0.00042 5.4
~0.00008 0.00060 0.0
0.00087 0.00043 4.2
--0.00084 0.00058 2.1
c
1389
1446
1260
1356
r
0.195
0.214
0.252
0.310
Fr
22.8
14.3
24.6
19.8
r = multiple correlation coefficient; n = number of data; F~, Fb -- F-values for the respective coefficients (test of regression coefficient = 0); F r - - F-value for test of multiple correlation coefficient = 0; SE = standard deviation of the coefficient. I = regression analysis including the von Bischoff, Marchand and Medical School Hannover samples; I[ = regression analysis including the Marchand and Medical School Hannover samples.
Figures 1-3 are scatter d i a g r a m s o f b r a i n weight versus age in d a y s o f ontogenesi s a n d age in years o f ontogenesis. The male a n d female d a t a were calculated s e p a r a t e l y with the 3-, 4- a n d 5-parametric logistic g r o w t h function. The 5-parametric fit always resulted in a m a r k e d r e d u c t i o n o f the residual sum o f squares a n d was therefore used for the following interpretations. The dispersion o f the d a t a was especially r e m a r k a b l e for adults. The range o f a d u l t b r a i n weights was smaller for the M e d i c a l School H a n n o v e r sample t h a n for the von Bischoff a n d M a r c h a n d samples. The 5 - p a r a m e t r i c logistic g r o w t h function follows the decline o f the b r a i n weight in the senile age range. The following increase is stipulated by the small n u m b e r o f d a t a in the senile age range a n d b y the rigidity o f the function. This final increase is o f no biological interest. The ideal values again reveal t h a t the expected b r a i n weight in adults is i n d e p e n d e n t o f the age o f the sample. This analysis detected a definite influence o f sex on b r a i n weight, which was seen in all 3 samples. The ideal values for the male d a t a were higher by 146 g (von Bischoff), 130 g ( M a r c h a n d ) a n d 168 g ( M e d i c a l School H a n n o v e r ) t h a n the ideal values for the respective female d a t a (Table 1). Similar differences could be f o u n d in the averages for the age range f r o m the 10th to the 50th year o f ontogenesis (Table 2). The different g r o w t h p a t t e r n s o f male a n d female b r a i n weight was revealed by the degree o f m a t u r i t y (Figs. 4-6). The degree o f m a t u r i t y o f the female b r a i n is equal to or greater t h a n t h a t o f the male b r a i n for the total age range in all 3 samples. T h a t
175 2000"
brain weight in g v. 81SCHOFF d
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brain weight in g v. 81SCHOFF~
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Fig. 1. a: logistic g r o w t h f u n c t i o n s fitted to 594 m a l e brain weights (data f r o m v o n Bischoff 1880); b: logistic g r o w t h f u n c t i o n s fitted to 404 female brain weights (data f r o m y o n Bischoff 1880).
176 i
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Fig. 2. a: logistic g r o w t h f u n c t i o n s fitted to 716 male brain weights (data f r o m M a r c h a n d 1902); b: logistic g r o w t h f u n c t i o n s fitted to 452 female brain weights (data f r o m M a r c h a n d 1902).
177 2000
brain weight in g Medical School Hannover d
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Fig. 3. a: logistic growth functions fitted to 129 male brain weights (data from Medical School H a n n o ver); b: logistic growth functions fitted to 104 female brain weights (data from Medical School H a n n o ver).
178 1.0 -
degreeof maturity of brain weight v. BI SCHOFF
0.8-
0.6-
o.,-
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i
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years of ontogenesis , L
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2000 daysof ontogenesis
Fig. 4. Degree of maturity of male and female brain weight (data from yon Bischoff 1880)
1.0
-
degreeof maturity of brain weight MARCHAND
0.8-
0.6
0.4
0.2-
1
2
3
4
5
I
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years of ontogenesis
Fig. 5. Degree of maturity of male:and female brain weight (data from Marchand 1902).
179 1.0
degree of maturity of brain weight Medical School H a n n o v e r ~ ~ ' ~
0.8
0.6
0.4
/
0.2-
' 0 .... 0
i 250
i ~0
2 11 750
3 i I lO00
i 1250
4 II 1500
5 = I 1750
yeats of oatogenesis = ~000 days of ontogenesis
Fig. 6. Degree of maturityof male and femalebrain weight(data from MedicalSchool Hannover). means that the females reach their respective degree of maturity at a younger age than do males, and brain growth, consequently, is completed at a younger age than male brain growth. Figures 7-9 show the growth rate for the degree of maturity. The initially faster growth of the female brain, i.e. a greater proportional increase in weight per unit time, could be seen in all 3 samples. A phase of more rapid growth of the male brain starts where both graphs intersect. These sex differences in brain development necessitate a separate analysis for male and female brain growth if brain development is to be compared over different periods of time. The growth dynamics of the 3 populations show remarkable differences (Fig. 10, Table 1). The degree of maturity of the male brain reaches 0.95 (95 %) after 6.13, 3.82, and 2.85 years of ontogenesis, in the 3 samples, respectively. At an age of 2.4 years of ontogenesis, the degree of maturity of the brain growth in the Medical School Hannover sample is 25 % greater than in the sample from 90 years ago (yon Bischoff). The more rapid growth rate of the initial postnatal brain development of the Medical School Hannover sample can be seen in Fig. 10b. The growth rate of this sample also decreased faster than those of the von Bischoff and Marchand samples. The relations were analogous for the female samples (Fig. 11). The 95 %-values for the degree of maturity of the female brain weight was reached after 4.88, 3.44 and 2.44 years of ontogenesis in the 3 samples, respectively. The different growth dynamics of the 3 populations was also demonstrated by the age at which the growth rates of the male and female samples intersect (Figs. 7-9).
180 0. 0020 -
growth rate of the degree of maturity of brain weight v. BI SCHOFF
O.0016
O.0012
0.0008-
dl O. 0004_
1 0
r
2
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250
I
500
3
II
750
J
i
1000
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1250
years of ontogenesis
r t
1500
F
I
1750
2000 days of ontogenesis
Fig. 7. Growth rate of the degree of maturity of male and female brain weight (data from yon Bischoff 1880).
0.0020 -
growth rate of the degree of maturity of brain weight MARCHAND
0. 0016
O.0012
0.0008-
0.00(0-
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years of ontogenesis
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750
1000
1250
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2000 days of ontocjenesis
Fig. 8. Growth rate of the degree of maturity of male and female brain weight (data from Marchand 1902).
181 0.0t~0 -
growth rate of the degreeof maturity of brain weight Medical School Hannover
0. 0016
O.0012 c~
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0.0004
1
years of ontogenesis
2
i
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250
500
750
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1250
1500
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2000 days of ontocjenesis
Fig. 9. Growth rate of the degree of maturity of male and female brain weight (data from Medical School Hannover). This intersection is located at 2.93 (von Bischoff), 1.97 (Marchand) and 1.70 (Medical School Hannover) years of ontogenesis. The growth functions for the data of Vie rordt (1906), MiJhlmann (1927), Roessle and Roulet (1932), White House Conference (1933), Spector (1956) and Altmann and Dittmer (1962) can be compared with these results with the restrictions mentioned above. The similarity of the development of the degree of maturity can be seen in Fig. 12a. The Medical School Hannover sample is located above these growth functions. Figure 12b shows the initially higher and afterwards more rapidly decreasing growth rate of the Medical School Hannover sample. Similar figures can be demonstrated for the respective female samples (Fig. 13). The differing figures for the data of Vierordt (1906) are caused by the very low brain weights in the range between 3 and 5 years of ontogenesis. DISCUSSION
The application of conceptional age ("days of ontogenesis" or "years of ontogenesis" i.e., days or years after conception) is better than postnatal age. Postnatal years or days are imprecise, because immature stillborns and premature children are frequently found in the usual autopsy samples of neonates and of young children. Growth functions based on age data without knowledge of the prenatal age can lead to a bias, if individuals with an abnormal gestation are included. Age differences of 3
182 degree of maturity of brain weight c~
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Fig. 10. Dcgi~e o f maturity (a) and growth rate o f the degree of maturity (b) o f male brain weight (data from yon Bischoff 1880, M a r c h a n d 1902 and Medical School Hannover).
183 1.0- degree of maturity of brain weight 9
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1(~0
"'"'-........
- _ ~ " " ~ .,.,,- . . . . . . . . . .
I
I
1250
1500
years of ontogenesis .
I
I
1750
2000
days of ontogenesis
Fig. 11. Degree of maturity (a) and growth rate of the degree of maturity (b) of female brain weight (data from von Bischoff 1880, Marchand 1902 and Medical School Hannovcr).
184 1.0- degree of maturity of brain weight.,._./.,.(~........ i *. :. :. ~."
