Paper - The growth of the central nervous system in the human fetus as expressed by graphic analysis and empirical formulae (1921)

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Dunn AL. The growth of the central nervous system in the human fetus as expressed by graphic analysis and empirical formulae. (1921) J Comp. Neurol. 32: 405-492.

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Mark Hill.jpg This historic 1921 paper by Dunn describes the growth of the central nervous system in the human fetus.



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The Growth of the Central Nervous System in the Human Fetus as expressed by Graphic Analysis and Empirical Formulae

Halbert L.Dunn

Departtnent of Anatomy, University of Minnesota

Thirty-Eight Figures


Introduction

The growth of the human central nervous system has long been a matter of interest and many studies on this subject have been published, some of the earher ones dating back almost a century. These investigations have given us a general knowledge of the growth of the brain as a whole from birth to maturity and have furnished us some information regarding the modifications in absolute and relative size of the various brain parts in early postnatal life.


Our knowledge of the growth of the central nervous system in the prenatal period is much less complete. While the numerous studies on the morphogenesis of the brain and spinal cord in the first trimester of fetal life enable us to draw some general conclusions concerning the early prenatal growth of these structures, there are practically no quantitative data available for this period. Data on the later prenatal growth of the brain are more extensive, and a survey of the literature gives about 500 published records of the weight of the brain between the third fetal month and birth. The more important of these collections are those of Rudinger (77), Brandt ('86), .^novljevic ('84), Michaelis ('06), Jackson ('09), and Valtorta ('09). A small amount of this material has been presented in graphic form by Zangemeister ('11). The only collection of records of the weights or volumes of the various parts of the brain in fetal life seems to be a short series of figures on the cerebrum, cerebellum, and brain stem published by Valtorta ('09).

The spinal cord has received far less attention than the brain, doubtless because of its smaller size and the technical difficulties of its removal. Our knowledge of the growth of the cord in postnatal fife is very incomplete, being limited to the data of Pfeister ( '03) and Danielbekoff ( '85) . Information regarding the changes in fetal life is apparently confined to a study by Giese ('98), pubhshed as a St. Petersburg dissertation, which is available only in abstract at the present time.

The following study was undertaken with the hope that a part of this large gap in our knowledge of human growth might be spanned by the systematic examination and measurement of the brain and spinal cord in a large series of human fetuses ranging from the second fetal month to birth, and by the treatment of these data by some of the more modern methods of statistical and graphic analysis. The work was done under the direction of Dr. R. E. Scammon, to whom the writer is very much indebted for constant advice and aid throughout the entire study.


Material and Methods Material

The material used in this study consisted of 150 human fetuses. Fifty-four of these specimens were males, fifty-six were females, and the sex of forty-six was unknown. The specimens ranged from 3.1 to 53.6 cm. in total or crown-heel length and were quite evenly distributed between these extremes. At least one specimen was available for each centimeter interval of crown-heel length and in many of the centimeter intervals below 30 cm. there were three, four, or five specimens. All of the material was selected from a much more extensive series of cases, with a view to securing specimens in which the brains were well preserved; however, a number of brains which were rather soft were used for certain measurements which were not affected by this condition.

The great majority of the specimens were fixed in 10 per cent formaUn to wliich 1 per cent chromic acid had been added in some instances, and all were afterwards preserved in 10 per cent formalin. Five specimens of the entire series were fixed m Zenker's or Miiller's fluid and were subsequently preserved in 70 per cent alcohol. All of the material had been in the preservation for six months or more.

The effect of formalin fixation upon the fetal brain must be kno\Mi in order to interpret the data correctly. It is imfortunate that no comparison has been made between fresh and preserved material. The fresh brain of the fetus is too friable for any delicate, quantitative measurements to be taken upon it. Consequently, fixation was prerequisite to the collection of the material for this study.

The only checks upon the relationship of fixed and unfixed material at our disposal consist of, 1) the determination of the effects of formahn upon the size of the fetal body and, 2) the relation of the curves of fresh brain weight to that of fixed brain volume.

Several investigators have determined the effects of formalin fixation on the fetus. Patten and Philpott ('21) record an average increase in the crown-rump length of 4.8 per cent in a series of twenty-two pig embryos which had been in 10 per cent formalin for six months. Schultze ('19) reports an average gain in crown-rump length of 2.3 per cent in a group of eighteen human fetuses which had been in 10 per cent formalin for nine months. The average gain in head length and head breadth of the same series was 1.1 per cent and 5.2 per cent, respectively. Calkins ('21) has found that the effect of fixation on the several diameters of the head is very small and that formalin injection causes the greatest part of this by a distention of the superficial tissues of the scalp. The fetal cranium increases, therefore, very little in size when it is fixed by formalin. The brain, on the other hand, is supposed to gain greatly in volume. King ('10) obtained a percentage gain in weight of from 30 to 50 when the brains of several white rats were subjected to formalin fixation. Such an increase in brain weight or volume could take place in the fetus only at the expense of the dural and subdural spaces, since the circumference and the diameters of the fetal head are but little affected. However, these spaces were found to be quite large in most of the preserved specimens in this series. The volume of the brain, therefore, could not have been increased to any great extent.

The relationship of the curve of fresh brain weight to that of fixed brain volume can be compared readily by tables 2 and 3. Table 2 shows the calculated volume of the central nervous system for each 5 cm. C H interval. Table 3 sets forth the empirically determined values for weights of fresh fetal brains collected from the literature. In each respective C H interval the weight is seen to be slightly greater than is the volume. This difference may be caused in part by the formalin fixation, but the greater part seems to be due to the fact that midsagittal sections of the brain were made before volumes were determined and that intraventricular fluid was lost by this procedure. On the whole, therefore, it is doubtful if there is any considerable change of the fetal bram volume upon formalin fixation.

Five cases of the series were subjected to Zenker- or Miilleralcohol fixation instead of formalin. The effects of various fixing fluids upon brain tissues have been determined by King ('10) and Hrdlicka ('06). The work of King was done upon the brain of tlie rat, and is analogous, in all probability, to the effects of the fixing fluids upon the fetal brain. Calculated from her findings, the absolute values of the five fetal brains subject to Zenker- or Miiller-alcohol fixation would be 10 to 40 per cent lower than the brains which were fixed by formalin. Three of the fetal brains in the present series which were fixed by the Zenkeror Miiller-alcohol method lie in the C H interval of o to 10 cm. and two are in the C H interval of 10 to 15 cm. A glance at figure 2 shows that these cases adhere closely to the central tendency. Hrdlicka subjected the brains of twenty-seven mammals and birds to 10 per cent formalin fixation. Ten sheep brains showed an average increase of 13 per cent after one month of fixation; seven brains of birds an average gain of 20 per cent and six brains of various manmials about 24 per cent. He left the brains in 10 per cent formalin for eighteen months, and then found that they had decreased in size to about 92 per cent of their original weight.

From the results of these investigators as well as the data of this series, it is obvious that 10 per cent formalin fixation has a comparatively slight effect upon the volumetric determination of the fetal brain.

Methods of collecting data

The magnitudes and proportions of the various parts of the central nervous system were determined by several different methods — by lineal measurements, by weighing and determining the volume of each part, by making tracings of median sagittal sections, and by photographing the lateral surfaces of the specimens. The details of these methods and the descriptions of the measurements taken will be considered separately.

Lineal measurements. All lineal measurements were made with a steel vernier caliper which could be read accurately to 1 mm. by the major and to 0.1 mm. by the minor scale. They were made with the brain and spinal cord in situ and always represented the shortest distance between two given points.


Weight. The ponderal determinations were made on a scale accurate to 0.01 gram. Before weighing in every instance the brain part was stripped of its meningeal coverings and was placed on a pad of dry gauze for 30 seconds to remove approximately the same amount of surplus fluid in each case. Weights were always taken upon preserved material.

Volumes. The volumetric determinations w^ere made with a special apparatus constructed according to a plan suggested by Prof. L. W. Jones, formerly of the Department of Chemistry of the University of Minnesota. A sketch of this device is shown in figure 1. It consists of an iron chemical stand (A) to which a clamp (B) is attached. This clamp holds a hard-rubber stopper (C), to which is attached a slender wire (D) about 15 cm. in length. A small disk of mica about 1 cm. in diameter slides freely on this wire. The wire is suspended in a jar or wide-mouthed bottle (F) which has a spigot at its base and which is partially filled with water. In using the apparatus the water in the bottle is drawn off until the mica disk which floats on its surface touches the hair line on the wire. The mass to be measured is then placed in the bottle and the level of the fluid rises, carrying the disk with it. The water is then drawn off into a beaker of known weight until the mica disk has sunk again to the level of the hair hue on the wire. The beaker with the contained water is then weighed and the known weight of the beaker is subtracted from the total, thus giving the weight of the water displaced by the brain part. After the proper temperature correction, this value can be converted into a measure of volume. With practice and proper precautions, it is possible to determine small volumes quite accurately with this apparatus. When working with small bodies, it is desirable to use a bottle with a capacity of not over 30 to 40 cc. A difference of approximately 0.1 cc. in volume can be determined without trouble if a small container is used.

The lineal, volumetric, and ponderal determinations made were as follows:

1. CH: Crown-heel length, or total body length; from the vertex to the tip of the heel.

2. CR: Crown-rump length, or the sitting height; from the vertex to the tip of the coccyx.

3. FO: Front o-occipital diameter; from the frontal pole to the occipital pole of the cerebral hemisphere. The frontal pole is defined as that point where the anterior, lateral, and inferior surfaces of the frontal lobes meet. In large brains, in situ, this



Fig. 1 A figure representing the volumetric apparatus used in the collection of data. A, iron standard; B, clamp; C, stopper; D, wire; E, movable isinglass disk; F, bottle with spigot. The arrow indicates a hair line upon the wire.


point is adjacent to the crista galh. The occipital pole is defined as that point where the posterior, lateral, and the interior surfaces of the occipital lobes meet.

4. TT: Temporal diameter; from the right temporal pole to the left temporal pole of the cerebral hemispheres. The temporal pole is defined as the most lateral point on the anterior projection of the temporal lobe. This point becomes less definite in large fetuses, but can still be recognized with sufficient accuracy.

5. FS: Frontospinal length; from the frontal pole of the cerebral hemisphere to the point of origin of the first cervical nerve. This measurement was taken to the middle of the body of the first cervical vertebra, for it was sometimes difficult to identify the first cervical nerve because of error in securing exact midsagittal sections of the brain and the spinal cord.

6. SC: Spinal cord length; from the point of origin of the first cervical nerve to the tip of the conus medullaris ; . the measurement was made with cord in situ.

7. BC: Brain and cord length; the sum of S C (6) and FS(5).

8. PL: Pons length; the greatest inferior length of the pons.

9. C L: Colliculi length; from the most anterior point of the superior colliculus to the most posterior point of the inferior coUiculus.

10. V L: Vermis length; the greatest length of the vermis cerebelh parallel with the axis of the pons and medulla.

11. VH: Vermis height; the greatest height of the vermis cerebelli perpendicular to the long axis of the pons and medulla.

12. VSC: Volume of the spinal cord; cord taken from the first cervical nerve to the tip of the conus medullaris and freed of meninges and nerve roots.

13. VPM: Volume of the pons and medulla; pons and medulla cut posteriorly at the first cervical nerve and anteriorly just in front of the pons, meninges removed.

14. VMB: Volume of the midbrain; the midbrain was cut just in front of the pons posteriorly and just in front of the superior colliculi and through the peduncuh cerebri behind the mammillary bodies anteriorly, meninges removed.

15. V C: Volume of the cerebellum; the velum medullaris was severed anteriorly and posteriorly to free the cerebellum from the pons and medulla, meninges removed.

16. V R H : Volume of the right hemisphere, meninges removed.

17. VLH: Volume of the left hemisphere, menmges removed.

18. V B H : ^^olume of both hemispheres : computed by adding VRH (16) and VLH (17).

19. V E B : Volume of the entire brain or encephalon computed by adding 13, 14, 15, 16, and 17. This method was found to be more accurate in deahng with the soft brains than to take the actual volumes of all the parts, because of the possible loss of brain tissue in handling.

20. VCNS: Volume of the central nervous sj^stem; found by adding the volume of the spinal cord (12) to the entire brain or encephalon volume (19).

The ponderal determinations corresponding to the volumetric measurements were taken and are included in table 41.

Methods of treating data

While the accuracy of data of the kind here presented depends upon the nature of measures employed and the care with which these measures are determined, their significance can only be ascertained by the use of a variety of methods of graphic and numerical analysis. A number of these methods have been used in the present study. They may be arranged in order of procedure in five main groups, namely: 1) Oonstraction of field graphs with points of central tendencj^ and establishment of preliminary curves by inspection. 2) Reduction of these preliminary ciu-ves, as established by inspection, to empirical fomulae based on total body length, and construction of primary data tables. 3) Calculation of values at 5-cm. intervals of body length, calculation of absolute and percentage increments for each 5-cm. interval of body length, calculation of newborn ratios for each 5-cm. interval of body length, and expression of these values in the graphic form. 4) Conversion of the various values as determined bj^ empirical formulae from functions of the body length to functions of the age in fetal months by interpolation on the basis of Mall's ('12) tables of crown-heel length in fetal life. Determination of the monthly percentage and absolute increment on the basis of these conversions; graphic expression of these values. 5) Determinations of the relative weights of the various parts of the central nervous system as compared to that of the encephalon. These several methods of analysis will now be considered in more detail.


1. Construction of field graphs and establishment of preliminary curves by inspection. The data secured for each measurement of the central nervous system were first plotted on a field graph in which the length of the body (C H) was used for the abscissa and the measurement in question for the ordinate. The material was then divided into classes on the basis of 5-cm. intervals of crownheel length and the arithmetic mean or average and the median were determined for each of these classes. These means were then indicated in the graphs bj'- special symbols, their exact position being determined by weighting for the distribution of the cases according to crown-heel length in the 5-cm. intervals. A prehminary curve was then drawai by inspection on the basis of the combined evidence furnished by the position of the arithmetic mean, the median, and the general distribution of the cases. This method has distinct advantages over the practice of establishing curves of inspection on the basis of the arithmetic mean alone, particularly in those instances where a curve is rising rapidly in a smgle interval or where the cases are not regularly distributed. The use of both the arithmetic mean and the median enables one to correct for chance deviations in the mean alone with considerable confidence, particularly when the cases are all spread before one on the field graph.

2. Reduction of preliminary curves of inspection to numerical expression by means of empirical formulae. The curve of each value as determined by inspection was reduced to numerical expression in the form of an empirical formula on the crown-heel or total length of the body expressed in cm. This procedure in no way increases the reliability of the curve as determined by inspection nor does it increase the accuracy of the points upon which it is based, but it has several important advantages, for it permits an accurate and abbreviated expression of the curve, facilitates exact inteipolation and the conversion of values into different scales and forms of expression, and, in some cases, aids in classifying the curves as to form.


The empirical formulae expressing the curves obtained from the material are of several t5T3es. As certain of the lineal dimensions of the brain are straight lines when plotted against cro\^^l-heel length, they may be expressed by the formula:

F = aX + 6 where Y is the value m question expressed in cm., X is the cro^nheel length in cm., and a and 5 are empirically determined constants.

The growth of other lineal dimensions of the central nervous system is not so simply related to the lineal growth of the body as a whole and the expression of this relation is more complex. But all may be represented by formulae having the general form:

Y = {aX)^±c

where Y is the value in question (in cm.), X is the cro^Ti-heel length of the body (in cm.), and a, b, and c are empirically determined constants, h being a fractional exponent. Curves corresponding to formulae of this type may also be expressed fairly satisfactorily in the logarithmic form:

Y = aX +&logX±c which will be recognized as the formula which Hatai employed with great success in the study of the growth of the various organs of the albino rat and which is regarded by him as of fundamental importance as exemplifying the appUcation of the law of JNIaupertuis to the process of growth. However, the exponential form has been found the more convenient for apphcation in the present work.

The formulae for the exiDression of the inspected cm'ves of volumes of the various parts of the central nervous system have as their simplest form:

Y = (aZ)^ which is modified in certain instances to:

Y = (aXy ± c and in others to:

Y = d[{aX)^ ±c] In these formulae Y is the value in question in cc, X is the crownheel length in cm., and a, h, c, and d are constants, b being always an exponent with a value greater than 1.


Having obtained calculated values for the different measurements under consideration, tables of each dimension were drawn up in some detail. These are tables 1, 3, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 36, 38 of the present publication. In each of these is given the crown-heel length in 5-cm. intervals, the average crown-heel length, the maximum, minimum, and arithmetic mean (average) of the considered measurement in the interval, the calculated mean for the same measurement, and the absolute difference between the calculated and the observed means. Both the calculated and observed means are recorded to the nearest millimeter for length and to the nearest 0.1 cc. for volumes in these tables.

3. Calculation of secondary tables. Secondary determinations made on the basis of the above calculations are included in tables 2, 4, 5, 6, 10, 12, 14, 16. These include the absolute value of each measurement, as determined by calculation with the empirical formula, for each 5 cm. of bod}^ length from 5 to 55 cm., and the percentage and the absolute increment of these values for each 5-cm. interval between these points.^ Included in these tables is also the ratio of the calculated value of the measurement at each 5 cm. of the total bodj^ length to the calculated value of the new-born. It was assumed that the value at 50 cm. of crownheel length represented the new-born and the calculated values for the 5-cm. points below 50 are expressed in per cents of this one. The reduction of values to this common scale is of great convenience, since it permits their direct comparison regardless of their absolute magnitudes.

4. Conversion of the various valves from functions of the crownheel length to functions of the age in fetal {lunar) months. This was done by calculating the values by means of the empirical formulae

1 The percentage increment was determined in the customary manner. The absolute value at the beginning of an interval is subtracted from the absolute value at the close of the same interval. The result is divided by the absolute value at the beginning of the interval and the quotient thus obtained is multiplied by 100 in order to reduce it to a percentage basis. The percentage increment is the only simple form of expression of relative growth now in use which is at all satisfactory. However, it gives only a rough approximation of the actual rate of growth in a given interval.


from jMall's tables of the relation of crown-heel length to age in prenatal life (Keibel and Mall, Human Embryology, vol. 1, p. 199). The results obtained by this procedure are not to be regarded as final, for the exact relation between body length and age in fetal life is still open to question. They are included, however, because they give, in a rough way at least, some concept of the relation of the growth of the central nervous system to time in the prenatal period and because they aid in the interpretation of its percentage increment. Since Mall's table stops at 270 days, it has been extended by graphic exterpolation to ten full lunar months (280 days) and the length at this age (51.5 cm.) was considered as the norm for the new-born in this type of calculation. The monthly percentage increments of the principal volumetric determinations were calculated secondarily from the values obtained in this manner. They are shown in table 42. 5. Determination of the relative weights of the various parts of the central nervous system in terms of per cents of the encephalon is an obvious procedure which needs no particular description. The results obtained are shown in table 40.

Summary of Observations

Growth of the central nervous system as a whole

The curve of the absolute volume of the central nervous system (fig. 2), when based upon crown-heel or total body length, is concave like all other curves of volume growth of the fetal organs. It may be expressed by the empirical formula: Central nervous system volume (cc.) = [0.114 (C H length cm.)]^-^ + 2.0

The absolute volume of the central nervous system is about 7 cc. at 10 to 15 cm. (C H). This increases steadily to 36 cc. at 25 cm. (C H), and is then deflected upward sharply to reach 337 cc. at 50 cm. (C H).

When calculated according to age in fetal months, the absolute volume of the central nervous system (fig. 34, curve I) is found to be 2 cc. at the beginning of the third month, rising to 36 cc. at the beginning of the sixth month, and to about 340 cc. at birth.



The rate of growth of the volume of the central nervous system as determined by the 5-cm. interval percentage increment (page 413), (fig. 26, curve I) is approximately 120 per cent for the lO-to-15-cm. interval and descends gradually to about 40 per cent for the 50-to-55-cm. interval.


TABLE 1

Volume of the central nervous system

Formula: Volume of the central nervous system (cc.) =

length cm.)]3-34 + 2.0

(146 cases)


[0.114 (crown-heel


CROWN-HEEL LENGTH


ORSERVED VOLUME OP CENTRAL NERVOD8 SYSTEM


CALCULATED VOLUME OF CENTRAL NERVOUS SYSTEM


DIFFERENCE

BETWEEN

OBSERVED AND

CALCULATED

MEANS


NUMBER


Range


Mean


Maximum


Minimum


Mean



cm.

to 5 5 to 10 10 to 15 15 to 20 20 to 25 25 to 30 30 to 35 35 to 40 40 to 45 45 to 50 50 to 55


cm.

3.9 7.2 12.2 16.8 22.6 27.1 32.8 37.2 42.2 48.0 52.2


cc.

0.7

2.4

8.6

22.5

49.5

65.4

144.2

222.8

256.9

412.5

414.3


0.1

0.6

2.1

3.0

17.4

24.7

45.8

102.2

145.3

207.0

332.3


0.3

1.3

5.4

12.5

31.1

46.9

81.8

141.4

197.7

306.0

367.5


CC.

5.0

10.8

25.6

45.3

83.9

126.7

187.6

294.0

388.5


CC.

-0.4

-1.7

-5.5

-1.6

+2.1

-14.7

-10.1

-12.0

+21.0


4

12 21 16 19 12 18 17 12 7 8


TABLE 2 Calculated volume of the central nervous system at 5-cm. intervals of crown-heel length


CROWN-HEEL LENGTH


VOLUME OF CENTRAL NERVOUS SYSTEM


INCREMENT IN EACH 5-CM. INTERVAL


RATIO TO NEW-BORN


cm.

5 10


CC


CC.


per cent


per cent


3.6




1.1


15


8.0


4^.4:


122.0


2.4


20


17.7


9.7


121.2


5.3


25


35.0


17.3


97.6


10.4


30


62.8


27.8


79.4


18.6


35


103.5


40.7


65.0


30.7


40


160.9


57.4


55.4


47.7


45


237.3


76.4


47.5


70.3


60


336.8


99.5


41.9


100.0


55


462.2


125.4


37.2


137.0


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 419


The percentage increment, when calculated for time, is about 600 in the fourth fetal month. This drops to 185 in the fifth month and to 22 per cent in the tenth month.



Fig. 2 Field graph and curve of the growth of the central nervous system in fetal life. Abscissa: total body length in cm. Ordinate: central nervous system weight and volume in grams (cc). Individual cases are indicated by solid dots (for weight) and by circles (for volume). Curve drawn to the formula: Y = (0.114Z)3-3-i _^ 2.0. (Data from tables 1 and 2.)

Growth of the encephalon

The curve of the absolute volume of the entire brain (fig. 3) when based on crown-heel length is a concave curve expressed by the empirical formula: Encephalon volume (cc.) = (0.125 (C H length cm.))^-!^ + 1.5


420


HALBERT L. DUNN


The absolute volume of the entire bram when based on crownheel length (fig. 3) is about 3.5 cc. at 10 cm. (C H). This increases to 38 cc. at 25 cm. (C H) and then more rapidly to 330 cc. at 50 cm. (C H).

TABLE 3 Encephalon volume Formula: Encephalon volume (cc.) = (0.125 crown-heel length cm.)3-i6 + 1.5 (144 cases)


CKOWN-HEEL LENGTH


OBSERVED VOLUME OP ENCEPH.^LON


CALCULATED VOLUME OP ENCEPHALON


DIFFERENCE

BETWEEN

OBSERVED AND

CALCULATED

MEANS


NUMBER


Range


Mean


Maximum


Minimum


Mean



cm.


cm.


cc.


cc


cc.


cc.


CC.



to 5


3.9


0.7


0.1


0.3




4 .


5 to 10


7.2


1.8


0.6


1.2


2.2


+1.0


11


10 to 15


12.3


9.5


2.0


5.4


5.4



21


15 to 20


16.9


22.4


2.8


11.9


12.1


+0.2


16


20 to 25


22.3


48.8


16.7


30.8


27.1


-3.7


19


25 to 30


27.1


64.7


27.3


45.8


48.7


+2.9


12


30 to 35


32.2


106.3


45.2


76.5


83.0


+6.5


17


35 to 40


37.2


221.8


101.2


132.1


130.1


-2.0


18


40 to 45


42.8


255.1


144.1


191.2


201.5


+10.3


10


45 to 50


48.0


409.4


226.7


299.1


289.0


-10.1


8


50 to 55


52.2


412.3


331.4


364.9


376.5


+11.6


8


TABLE 4 Calculated volume of encephalon at 5-cm. intervals of crown-heel length


CROWN-HEEL LENGTH


VOLUME OP THE ENCEPHALON


INCREMENT IN EACH 5-CM.

INTERVAL OP

CROWN-HEEL LENGTH


R.ATIO TO NEW-BORN


cm.

5 10


cc.


cm.


per cent


per cent


3.5




1.1


15


8.4


4.9


140.0


2.5


20


19.6


11.2


133.5


6.0


25


38.1


18.5


94.4


11.6


30


66.6


28.5


74.8


20.2


35


107.6


41.0


61.5


32.7


40


163.3


55.7


51.8


49.6


45


236.1


72.8


44.5


71.8


50


328.9


92.8


39.4


100.0


55


444.0


115.1


35.0


135.0


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 421

When calculated to age in fetal months (fig. 34, curve I), the volume of the entire brain is about 1 cc. at the beginning of the third month. It increases to 14 cc. by the first of the fifth month, and reaches the value of 330 cc. by birth.

The rate of growth of the encephalon when determined by 5-cm. percentage increment (fig. 26, curve II) is approximately


Calculated weight of the encephalon (based on collected data) at 5-cni. intervals of crown-heel length


CROWN-HEEL LENGTH


WEIGHT OF THE ENCEPHALON


INCREMENT IN EACH 5-CM. INTERVAL


R.4.TI0 TO NEW-BORN


cm.

5 10


grams


grams


per ce?it


per cent


3.3




0.8


15


9.4


6.1


185.0


2.4


20


22.1


12.7


135.0


5.6


25


44.0


21.9


97.5


11.2


30


77.8


33.8


76.8


19.8


35


126.6


48.8


62.7


32.2


40


193.3


66.7


52.7


49.1


45


281.0


87.7


45.4


71.4


50


392.9


111.9


42.4


100.0


55


532.1


139.2


35.4


135.5


VoUime of the encephalon {data of Jackson, '09) (31 cases)


CROWN-HEEL LENGTH


ENCEPHALON VOLUME


NUMBER


Range


Mean


Maximum


Minimum


Mean



cm.

to 5


C7n.

1.8


cc.

0.4


cc.

0.25


cc.

0.18


3


5 to 10


7.7


3.6


2.0


2.83


3


10 to 15


12.3


20.0


10.0


13.7


3


15 to 20


17.2


40.0


18.0


27.2


5


20 to 25


22.4


60.0


30.6


45.9


4


25 to 30


27.4


129.0


52.7


85.4


5


30 to 35


32.7


126.7


120.0


123.3


2


35 to 40


38.5


140.0


140.0


140.0


1


40 to 45


44.2


321.3


321.3


321.3


1


45 to 50


45.9


358.0


278.2


322.6


2


50 to 55


51.9


385.0


363.0


374.0


2


422


HALBERT L. DUNN


140 per cent for the lO-to-15-cm. interval. It descends rapidly to 75 per cent of the 25-to-30-cm. interval, and then more slowly to 40 per cent in the 50-to-55-cm. mterval.

The percentage increment of the entire brain volume when calculated against age in fetal months (fig. 28, curve VI) is about 580 per cent in the fourth month, descending to 22 per cent in the tenth month.



SEciti.


Fig. 3 Field graph and curve of the growth in weight and volume of the encephalon in fetal life (the curve of growth taken from brain weights reported in the literature). Abscissa: total body length in cm. Ordinate: entire brain weight and volume in grams (cc). Individual cases are indicated by solid dots (for weight). I, curve of eneephalon volume drawn to the formula:

Y = (0.125X)3-i6 + 1.5. (Data from tables 3 and 4.) II, curve of

eneephalon weight based upon data from the literature and drawn to the formula: F = (0.13X)-i9 + 1.0 (Data from tables 5 and 6.)


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 423

Growth of the cerebrum

The growth of the cerebral hemispheres is portrayed by figures 3 to 9, inclusive, and figures 37 and 38, and is shovm numerically in tables 3 to 16, inclusive. It may be expressed by the empirical formula : Volume of the cerebrum (cc.) = (0.12 (C H length cm.))^-!^

TABLE 7

Volume of the right hemisphere

Formula: Right hemisphere volume (cc.) = (0.1 crown-heel length (cm.))^-

(115 cases)


CROWN-HEEL LENGTH


RIGHT HEMISPHERE VOLUME


CALCULATED

RIGHT

HEMISPHERE

VOLUME


DIFFERENCE

BETWEEN

OBSERVED AND

CALCULATED

MEANS


NUMBER


Range


Mean


Maximum


Minimum


Mean


OF CASES


cm.


cm.


cc.


cc.


cc.


cc.


cc.



to 5









5 to 10









10 to 15


12.5


4.2


1.6


2.6


2.0


-0.6


12


15 to 20


16.9


10.6


2.1


6.0


5.2


-0.8


14


20 to 25


22.6


21.8


9.3


14.2


12.8


-0.4


19


25 to 30


27.1


32.7


12.4


21.8


22.7


+0.9


12


30 to 35


32.6


73.1


21.1


39.2


40.4


+1.2


17


35 to 40


37.2


109.3


48.7


65.8


61.1


-4.7


16


40 to 45


42.5


126.6


67.2


94.6


92.6


-2.0


10


45 to 50


48.0


191.5


102.9


139.0


135.6


-3.4


7


50 to 55


52.2


185.3


148.0


166.0


176.4


+10.4


8


TABLE 8 Calculated volume of the right cerebral hemisphere at 5-cm. intervals of crown-heel

length


CROWN-HEEL LENGTH


VOLUME OP BIGHT CEREBRAL HEMISPHERE


INCREMENT IN EACH 5-CM. INTERVAL


RATIO TO NEW-BORN


cm.


CC.


cm.


per cent


per cent


5 10


1.0




0.6


15


3.6


2.6


260.0


2.3


20


8.8


5.2


144.0


5.7


25


17.6


8.8


100.0


11.4


30


31.1


13.5


76.6


20.2


35


50.5


19.4


62.3


32.7


40


76.4


25.9


51.2


49.5


45


110.8


34.4


45.0


71.8


50


154.2


43.4


39.2


100.0


55


207.7


53.5


34.7


134.5


424


HALBERT L. DUNN


The absolute volume of the right and of the left hemispheres (figs. 4 and 5) shows no marked differences — the minor distinctions between the two falling within the margin of experimental error.



Fig. 4 Field graph and curve of the growth in weight and volume of the right cerebral hemisphei-e in fetal life. Abscissa: total body length in cm. Ordinate: right hemisphere weight and volume in grams (cc). Individual cases are indicated by solid dots (for weight) and by circles (for volume). Curve drawn to the formula: Y = (0.1Z)3-i=. (Data from tables 7 and 8.)


The absolute volume curve of the hemispheres shows the same concave form as the volume of the central nervous ststem (fig. 2) . At 15 cm. (C H) the hemispheres are 1.8 cc. in volume, while in


GEOWTH OF THE FETAL CENTRAL NERVOUS SYSTEM


425


fetuses of 25 to 30 cm. (C H) they have reached an average volume of about 32 cc. After this time the volume curve increases more rapidly, attaining the average of about 300 cc. at 50 cm. (C H). When examined in relation to age (fig. 34, curve II) the absolute volume of the right cerebral hemisphere is found to be 2 cc.


TABLE 9 Volume of the left cerebral hemisphere Formula: Volume of the left cerebral hemisphere (cc.) length (cm.))^-"*


(0.105 crown-heel


CRO'W>f-HEEL LENGTH


OBSERVED VOLUME OF THE LEFT HEMISPHERE


C.4.LCUL.\TED

VOLUME OP

THE LEFT

HEMISPHERE


DIFFERENCE

BETWEEN

OBSERVED .\ND

CALCULATED

MEANS


NUMBER


Range


Mean


Maximum


Minimum


Mean



cm.


cm.


cc.


cc.


cc.


cc.


CC.



to 5









5 to 10









10 to 15


12.5


4.4


1.3


2.6


2.3


-0.3


12


15 to 20


16.9


10.5


2.3


6.0


5.7


-0.3


14


20 to 25


22.4


20.0


10.2


14.8


13.5


-0.3


16


25 to 30


27.1


30.0


13.0


21.7


24.0


+2.3


13


30 to 35


32.8


50.0


21.0


38.2


42.9


+4.7


18


35 to 40


37.2


89.6


46.8


64.1


62.9


-1.2


16


40 to 45


42.5


110.7


67.0


92.2


94.4


+2.2


10


45 to 50


48.0


188.0


98.5


138.0


136.6


-1.4


7


50 to 55


52.2


192.0


142.0


170.0


176.2


+6.2


8


TABLE 10

Calculated volume of left cerebral hemisphere at 5-cm. intervals of crown-heel length


CROWN-HEEL LENGTH


VOLUME OF LEFT CEREBR.U:. HEMISPHERE


INCREMENT IN EACH

■5-CM. INTERV.AL

OF CROWN-HEEL LENGTH


RATIO TO NEW-BORN


5 10


CC.


CC.


per cent


per cent


1.2




0.8


15


4.0


2.8


233.0


2.6


20


9.6


5.6


140.0


6.2


25


18.8


9.2


96.0


12.1


30


32.8


14.0


74.5


21.2


35


52.5


19.7


60.0


33.9


40


78.3


25.8


49.1


50.6


45


111.2


32.9


42.0


71.9


50


154.9


43.7


39.2


100.0


55


200.3


45.4


29.3


129.2


426


HALBERT L. DUNN


at the beginning of the third month, and this rises at first slowly and then rapidly to about 150 cc. at birth.



Fig. 5 Field graph and curve of the growth in weiglit and volume of the left cerebral hemisphere in fetal life. Abscissa: total body length in cm. Ordinate: left hemisphere weight and volume in grams (cc). Individual cases indicated by solid dots (for weight) and by circles (for volume). Curve drawn to the formula : F = (O.lOoX)^-*. (Data from tables 9 and 10.)


The percentage increment of the hemispheres (fig, 26, curve VI) approximates that of the entire brain. It is about 265 per cent for the interval between 10 and 15 cm. (C H) length and steadily declines from this value until it reaches the level of 35 per cent for the 50-to-55-cm. (C H) interval (birth).


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 427

The percentage increment of the hemispheres, when calculated by fetal months (fig. 28, curve V), shows an approximate rate of growth of 600 per cent in the fourth fetal month. This rate descends rapidly at first, and then more slowly to about 22 per cent in the tenth fetal month.

TABLE 11

Volume of both cerebral hemispheres

Formula: Volume of both cerebral hemispheres (cc.) = (0.12 crown-heel length

(cm.))3-i9 (115 cases)


CROWN-HEEL LENGTH


OBSERVED VOLUME OF BOTH HEMISPHERES


CALCULATED

VOLUME OF

BOTH

HEMISPHERES


DIFFERENCE

BETWEEN

OBSERVED AND

CALCULATED

MEANS


NUMBER


Range


Mean


Maximum


Minimum


Mean



to 5 5 to 10 10 to 15 15 to 20 20 to 25 25 to 30 30 to 35 35 to 40 40 to 45 45 to 50 50 to 55


cm.

12.5 16.9 22.4 27.1 32.8 37.2 42.3 48.0 52.2


cc.

8.6

20.5

46.2

62.5

137.1

210.8

239.3

380.4

377.3


cc.

2.2

4.8

18.0

25.4

56.5

95.5

134.2

201.2

302.0


cc.

5.2

12.2

29.4

46.6

76.1

131.4

184.8

277.0

334.4


CC.

3.65

9.5

22.9

43.0

79.1

118.2

178.1

266.5

348.3


CC.

-1.55

-2.7

-6.5

-3.6

4-3.0

-13.2

-6.7

-10.5

-13.9


12 14 16 12 18 17 11 7 8


TABLE 12

Calculated volume of both cerebral hemispheres at 5-c.m. intervals of crown-heel length


CROWN-HEEL LENGTH


VOLUME OF BOTH

CEREBRAL

HEMISPHERES


INCREMENT IN EACH S-CM. INTERVAL


RATIO OF NEW-BORN


cm.

5 10


CC.


CC.


per cent


Ver cent


1.79




0.6


15


6.52


4.73


264.0


2.1


20


16.33


9.81


150.0


5.4


25


33.27


16.94


103.0


10.8


30


59.51


26.24


78.8


19.6


35


97.31


37.80


63.5


32.1


40


149.0


51.69


53.2


49.1


45


216.9


69.7


45.5


71.5


50


303.6


86.7


40.0


100.0


55


411.2


107.6


34.5


135.0


428


HALBERT L. DUNN


The per cent which the volume of both hemispheres forms of the entire brain volume (fig. 7) reflects the relative growth of the other brain parts. The cerebral hemispheres form only from



5 10 15 10 ' £5 30 j5 AO

Fig. 6 Field graph and curve of the growth in weight and volume of both cerebral hemispheres in fetal life. Abscissa: total body length in cm. Ordinate: hemispheres weight and volume in grams (cc). Individual cases indicated by solid dots (for weight) and by circles (for volume). Curve drawn to the formula: Y = {Q.l2Xy-^\ (Data from tables 11 and 12.)


88 to 90 per cent of the entire brain volume in the third fetal month. This proportion increases rapidly to between 94 and 95 per cent during the sixth fetal month, but after this time it descends to about 91.5 per cent at birth. This decline is due mainly to the tremendous relative growth of the cerebellum.


GKOWTH OF THE FETAL CENTKAL NERVOUS SYSTEM


429


The two linear measurements of the cerebral hemispheres (the fronto-occipital and the temporal diameters) also furnish some information concerning the growth of this part of the brain. The



Fig. 7 Field graph and curve (connecting each 5-cm. crown-heel interval) of the per cent which the volume of both cerebral hemispheres forms of the encephalon volume. Abscissa: total body length in cm. Ordinate: hemisphere volume in per cent of the encephalon volume. Individual cases indicated by solid dots. (Data from table 40.)


fronto-occipital diameter is a very constant measure, due perhaps to its close conformance to the skull and to the fact that it is not affected greatly by the torsion of the brain parts or of the brain axis during growth. Its reliability has justified its use to some extent as a basic measurement.


430


HALBERT L. DUNN


The absolute fronto-occipital diameter (fig. 8) when plotted to the crown-heel length is a straight line ascending from 2 cm. at 10 cm. (C H) to 9 cm. at 50 cm. (C H). Its empirical formula is:

Fronto-occipital diameter (cm.) = 0.175 CH body length (cm.)

+ 0.25

TABLE 13

Fronto-occipital diameter

Formula: Fronto-occipital diameter (cm.) = .175 crown-heel length (cm.) + .25

(151 cases)


CROWN-HEEL LENGTH


OBSERVED FRONTOOCCIPITAL DIAMETER


CALCULATED PRONTOOCCIPITAL DIAMETER


DIFFERENCE

BETWEEN

OBSERVED AND

CALCULATED

MEANS


NUMBER


Range


Mean


Maximum


Minimum


Mean



C7n.


cm.


cm.


cm.


cm.


cm.


cm.



to 5


4.0


1.1


0.7


0.9


0.9



3


5 to 10


7.1


2.0


1.2


1.6


1.5

-0.1


10


10 to 15


12.3


2.7


1.4


2.3


2.4


-FO.l


21


15 to 20


16.7


3.3


2.3


3.2


3.2



15


20 to 25


22.6


4.9


3.6


4.3


4.2


-0.1


21


25 to 30


27.0


6.5


4.4


5.1


5.0


-0.1


16


30 to 35


32.6


7.0


5.1


6.0


6.0



19


35 to 40


37.1


7.7


6.3


6.8


6.7


-0.1


19


40 to 45


42.3


8.4


7.2


7.8


7.6


-0.2


11


45 to 50


48.2


9.3


7.5


8.6


8.7


+0.1


8


50 to 55


52.2


10.0


8.0


9 2


9.4


+0.2


8


TABLE 14 Calculated fronto-occipital diameter at 5-cm. intervals of crown-heel length


CROWN-HEEL LENGTH


FRONTO-OCCIPITAL DIAMETER


INCREMENT IN EACH 5-CM. INTERVAL


RATIO TO NEW-BORN


cm.


cm.


cm.


■per cen.t


■per cent


5


1.125




12.5


10


2.000


0.875


78.0


22.2


15


2.875


0.875


43.7


31.9


20


3.750


0.875


30.3


41.6


25


4.625


0.875


23.3


51.4


30


5.500


0.875


18.9


61.1


35


6.375


0.875


15.9


70.8


40


7.250


0.875


13.6


80.5


45


8.125


0.875


12.1


90.3


50


9.000


0.875


10.8


100.0


55


9.875


0.875


9.7


109.8


GKOWTH OF THE FETAL CENTKAL NERVOUS SYSTEM


431


The absolute fronto-occipital diameter when considered in relation to age (fig. 32, curve I) is about 1.3 cm. in the middle of the third fetal month and increases at first rapidly and then more slowly to 9 cm. at birth.

The percentage increment of the fronto-occipital length for 5-cm. intervals of body length (fig. 25, curve I) gradually declines



Fig. 8 Field graph and curve of the growth of the cerebral hemispheres in fetal life as shown by the fronto-occipital diameter. Abscissa: total body length in cm. Ordinate: fronto-occipital diameter in cm. Individual cases indicated by solid dots. Curve drawn to the formula. Y = 0.175X + 0.25. (Data from tables 13 and 14.)

from about 80 per cent in the 5-to-lO-cm. interval to about 10 per cent in the 50-to-55-cm. interval.

The percentage increment of the fronto-occipital length, when calculated for fetal months (fig. 27, curve I), shows an approximate rate of growth of 150 per cent in the third fetal month. This descends rapidly to 31 per cent in the fifth month and gradually to 9.5 per cent in the last fetal month.


432


HALBERT L. DUNN


The linear measurement from the frontal to the occipital pole indicates therefore a steady absolute cerebral growth in the anteroposterior axis (when compared to crown-heel length) and a constant diminution of the rate of growth (when compared to time).

TABLE 15

Temporal diameter

Formula: Temporal diameter (cm.) = 0.138 crown-heel length (cm.) + 0.3 •

(141 cases)


CROWN-HEEL LENGTH


OBSERVED TEMPORAL DIAMETER


CALCULATED TEMPORAL DIAMETER


DIFFERENCE

BETWEEN

OBSERVED AND

CALCULATED MEANS


NUMBER


Range


Mean


Maximum


Minimum


Mean


OP CASES


cm.


cm.


c?«.


cm.


cm.


cm.


cm.



to 5


3.9


1.0


0.7


0.85


0.85



4


5 to 10


8.1


2.0


1.1


1.45


1.4


-0.03


7


10 to 15


12.4


3.5


1.5


2.1


2.0


-0.1


19


15 to 20


16.6


3.4


1.8


2.6


2.6



15


20 to 25


22.6


4.2


2.6


3.3


3.4


+0.1


21


25 to 30


27.0


4.6


3.2


4.1


4.0


-0.1


15


30 to 35


32.6


5.0


3.8


4.5


4.8


+0.3


16


35 to 40


37.1


6.8


4.6


5.5


5.4


-0.1


18


40 to 45


42.3


6.7


5.6


6.2


6.1


-0.1


11


45 to 50


48.2


7.2


6.6


6.7


6.95


+0.25


8


50 to 55


52.2


10.4


6.9


7.9


7.5


-0.4


7 ■


TABLE 16 Calculated temporal diameter at 5-cm. intervals of crown-heel length


CROWN-HEEL LENGTH


TEMPORAL DIAMETER


INCREMENT IN EACH 5-CM. INTERVAL


R.ITIO TO NEW-BORN


cm.


cm.


cm.


■per cent


-per cent


5


0.99




13.7


10


1.68


0.69


69.7


23.4


15


2.37


0.69


41.1


32.9


20


3.06


0.69


29.1


42.6


25


3.75


0.69


22.5


52.1


30


4.44


0.69


18.4


61.6


35


5.13


0.69


15.5


71.3


40


5.82


0.69


13.4


81.0


45


6.51


0.69


11.8


90.4


50


7.20


0.69


10.6


100.0


55


7.89


0.69


9.6


109.5


GKOWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 433


The curve of absolute temporal diameter (fig. 9) is also a straight line when based on crown-heel length. Starting at about 1 cm. at the 5 cm. (C H), it increases steadily to about 72 cm. at 50 cm. (C H). Its empirical formula is: Temporal diameter (cm.) = 0.138 C H body length (cm.)

+0.3

When studied in relation to time (fig. 32, curve II), this diameter is found to be 1 cm. at the beginning of the third fetal






10


15


no


Lb


30


05 40


45


50


Fig. 9 Field graph and curve of the growth of the cerebral hemispheres in fetal life as shown by the temporal diameter. Abscissa: total bodj- length in cm. Ordinate: temporal diameter in cm. Individual cases indicated by solid dots. Curve drawn to the formula: Y = 0.138X + 0.3. (Data from tables 15 and 16.)

month and to rise at first fairly rapidly and then more slowl}^ to 7.2 cm. at birth.

The rate of growth of the temporal diameter (fig. 25, curve II) decreases steadily from 70 per cent for the 5-to-lO-cm. interval to about 10 per cent for the 50-to-55-cm. interval.

The percentage increment of the temporal diameter, when calculated for fetal months (fig. 27, curve II), is approximately 70 per cent in the fourth fetal month and falls to about 35 per


434


H ALBERT L. DUNN


cent in the fifth month and to 9.2 per cent in the tenth month. Or, in other words, the transverse axis of the cerebral hemispheres shows a constant diminution in the rate of growth throughout the fetal period,

TABLE 17

Volume of the cerebellum

Formula: Volume of cerebellum (cc.) = .01 (.095 crown-heel length

(cm.))^-9 + 20.0

(114 cases)


CROWN-HEEL LENGTH


OBSERVED VOLUME OP CEREBELLUM


CALCULATED


DIFFERENCE BETWEEN








VOLUME OF CEREBELLUM


OBSERVED AND CALCULATED

MEANS



Range


Mean


Maximum


Minimum


Mean



cm.


cm.


cc.


cc.


cc.


cc.


CC.



to 5









5 to 10









10 to 15


12.8


0.5


0.1


0.3


0.5


+0.2


10


15 to 20


16.9


0.7


0.2


0.4


0.5


+0.1


14


20 to 25


22.6


2.0


0.5


0.9


0.6


-0.3


18


25 to 30


27.0


2.7


0.9


1.3


1.2


-0.1


13


30 to 35


32.7


4.0


1.0


2.4


2.8


+0.4


16


35 to 40


37.2


9.3


3.4


5.4


5.1


-0.3


17


40 to 45


42.3


11.5


5.7


8.9


9.3


+0.4


11


45 to 50


48.0


22.0


14.0


19.0


17.1


-2.0


7


50 to 55


52.2


26.0


18.0


21.3


25.7


+4.4


8


TABLE 18 Calculated cerebellum volume at 5-cm. intervals of crown-heel length


CROWN-HEEL LENGTH


CEREBELLUM VOLUME


INCREMENT IN EACH 5-CM. INTERVAL


RATIO TO NEW-BORN


cm.

5 10


CC.


CC.


per cent


per cent


0.20




1.0


15


0.28


0.08


40.0


1.3


20


0.43


0.15


53.6


2.1


25


0.89


0.46


107.0


4.3


30


1.89


1.00


112.0


9.1


35


3.80


1.91


100.1


18.2


40


7.13


3.33


87.8


34.1


45


12.60


5.47


76.8


60.3


50


20.90


8.30


65.8


100.0


55


33.40


12.50


59.8


160.0


GEOWTH OF THE FETAL CENTRAL NERVOUS SYSTEM


435


Growth of the cerehellwn

The growth of the cerebellum is portrayed by the graphs in figures 10 to 1.3, inclusive, and by the outline sketches in figure 38. The absolute volume of the cerebellum, when plotted against



50 55c


Fig. 10 Field graph and curve of the growth of the cerebellum in weight and volume in fetal life. Abscissa: total body length in cm. Ordinate: cerebellum weight and volume in grams (cc). Individual cases indicated by solid dots (for weight) and by circles (for volume). Curve drawn to the formula: Y = 0.01 f(0.095X)4-9 + 20.0]. (Data from tables 17 and IS.)

crown-heel body length (fig. 10), presents a concave volume curve

expressed by the empirical formula :

Volume of the cerebellum (cc.) = 0.01 (0.09.5 C H body length

(cm.))^-3+20.0


THE JOURNAL OF COMPARATIVE NEUROLOGY, VOL. ',


436


HALBERT L. DUNN


The cerebellum is not grossly visible before the fetus is about 10 cm. (C H) long. At 20 cm. (C H) its volume is about 0.4 cc, and this increases slowly to about 2 cc. at 30 cm. (C H). The



5 10 15 £0 £5 30 35 40 45

Fig. 11 Field graph and curve (connecting the average points of each 5-cm. crown-heel interval) of the per cent which the volume of the cerebellum forms of the encephalon volume. Abscissa: total body length in cm. Ordinate: cerebellum volume in per cent of entire brain volume. Individual cases indicated by solid dots. (Data from table 40.)


absolute volume curve then turns sharply upward and rises very rapidly to 21 cc. at 50 cm. (C H).

On the basis of time (figs. 34 and 35), the volume of the cerebellum is about 0.4 cc. at four fetal months and approximately


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 437

2.3 cc. at six fetal months. At this time it begins to enlarge rapidly, increasing almost ten-fold in the last four months of intra-uterine life and reaching a volume of 21 cc. at birth. This tremendous growth in volume in the last three or four months of fetal life, at a time when all other brain parts are growing far less rapidly, is a peculiar characteristic of the cerebellum.

The percentage increment of the cerebellum volume (fig. 26, curve VII) reflects the pecuharities of the curve of absolute volume. Starting at a comparatively low value, it rises to a peak of 112 per cent for the 25-to-30-cm. interval and descends to 60 per cent m the 50-to-55-cm. interval.

The percentage increment of the cerebellum volume, when calculated for time (fig. 28, curve IV), shows an approximate rate of growth of about 160 per cent in the fifth month, and then falls rapidly to 54 per cent for the tenth month.

The relative growth of the cerebellum is also illustrated by the per cent which it forms of the entire brain volume at various periods in fetal life (fig. 11). This value is, with slight variations, about 3 per cent until the middle of the sixth fetal month. At this time the tremendous growth of the cerebellum becomes an important factor in the total increase of the brain as a whole, and by birth it forms about 6 per cent of the entire brain volume.

The absolute length of the vermis cerebelli, when plotted to crown-heel body length (fig. 12), is expressed by the formula:

Vermis cerebelli length (cm.) = 0.01 [(C H length (cm.))i-i

+0.15]

It also portrays the great growth of this part of the brain in the last four fetal months. At 10 cm. (C H) the vermis cerebelH length is only about 0.4 cm. It ascends in a very shallow curve to 2.6 cm. at 50 cm. (C H).

The absolute length of the vermis cerebelU when calculated for fetal months (fig. 31, curve I) rises in practically a straight line from 0.4 cm. at the beginning of the fourth month to 2.64 cm. at birth.

The rate of growth of the vermis cerebelU length (fig. 25, curve III) shows a gradual decrease from 50 per cent in the lO-to-15-cm. interval to 13 per cent at the 50-to-55-cm. interval. The entire


438


H ALBERT L. DUNN


percentage increment curve, however, is much higher than any other percentage increment based upon a straight-hne measurement (with the single exception of the vermis cerebelH height, fig. 25, curve IV).

TABLE 19

Length of the vermis ccrebelli

Formula: Vermis cerebelli length (cm.) = .01 [(crown-heel length (cm.))'-" + 0.15]

(124 cases)


CROWN-HEEL LEXGTH


LENGTH OP VERMIS CEREBELLI


CALCULATED LENGTH OF

VERMIS CEREBELLI


DIFFERENCE

BETWEEN

OBSERVED AND

CALCILATED

MEANS


NUMBER


Range


Mean


Maxi

Minimum


Mean



C7n.


cm.


cm.


cm.


cm.


cm.


cm.



to 5









5 to 10









10 to 15


12.7


0.9


0.3


0.5


0.5


0.0


16


15 to 20


16.9


1.1


0.4


0.6


0.7


+0.1


14


20 to 25


22.5


1.2


O.G


0.9


1.0


+0.1


IS


25 to 30


27.0


1.8


0.9


1.15


1.2


+0.05


14


30 to 35


32.8


1.7


1.1


1.5


1.5



16


35 to 40


37.1


2.6


1.3


1.8


1.8



18


40 to 45


42.2


2.5


1.7


2.1


2.1



12


45 to 50


48.2


2.7


2.2


2.5


2.5



8


50 to 55


52.2


3.4


2.5


2.7


2.8


+0.1


8


TABLE 20

Calculated vermis cerebelli length at 5-cm. intervals of crown-heel length


CROWN-HEEL LENGTH


VERMIS CEREBELLI

LENGTH


INCREMENT IN EACH 5-CM. INTERVAL


CVl.


cm.


CW.


■per cent


5





10


0.41




15


0.61


0.20


49.0


20


0.83


0.22


36.1


25


1.08


0.25


30.2


30


1.36


0.28


25.9


35


1.65


0.29


21.3


40


1.96


0.31


18.8


45


2.29


0.33


16.8


50


2.64


0.35


15.3


55


2.99


0.35


13.3


RATIO TO NEW-BORN


15.5 23.1 31.5 40.9 51.6 62.6 74.3 86.8 100.0 113.2


GEOWTH OF THE FETAL CENTEAL NEEVOUS SYSTEM 439

The percentage increment of the vermis cerebelh length when calculated for fetal months (fig. 27, curve VIII) is approximately 85 per cent in the fifth month, descending at first swiftly and then more slowly to about 12.5 per cent in the tenth month.



Fig. 12 Field graph and curve of the growth of the cerebellum in fetal life as shown by the vermis cerebelli length. Abscissa: total body length in cm. Ordinate: vermis cerebelli length in cm. Individual cases indicated by solid dots. Curve drawn to the formula : }' = 0.01 (Xi-« + 0.15) . (Data from taldes 19 and 20.)


440


HALBERT L. DUNN


The absolute height of the vermis cerebelH when plotted against crowTi-heel body length (fig. 13) also forms a shallow curve, expressed empirically by the formula:

Vermis cerebeUi height (cm.) = 0.01 (C H body length (cm.))^-"

It is 0.23 cm. at 10 cm. (C H) and rises to about 2.1 cm. at 50 cm.

(CH).

TABLE 21

Height of the vermis cerebelli Formula: Vermis cerebelli height (cm.) = .01 (crown-heel length (cm.))i"'^ (122 cases)


CROWN-HEEL LENGTH


OBSERVED HEIGHT OP VERMIS CEREBELLI


CALCULATED HEIGHT OF

VERMIS CEREBELLI


DIFFERENCE

BETV\-EEN

OBSERVED AND

CALCULATED

MEANS


NUMBER


Range


Mean


Maximum


Minimum


Mean



cm.

to 5 5 to 10 10 to 15 15 to 20 20 to 25 25 to 30 30 to 35 35 to 40 40 to 45 45 to 50 50 to 55


12.7 16.9 22.6 27.0 32.8 37.1 42.2 48.2 52.2


cm.

0.6 0.7 0.9 1.0 1.4 1.9 2.0 2.5 2.8


0.3 0.2 0.5 0.6 0.8 1.0 1.1 1.6 1.6


cm.

0.4 0.5 0.7 0.8 1.1 1.4 1.6 2.0 2.2


c/re.

0.3 0.5 0.7 0.9 1.2 1.4 1.7 2.0 2.2


OOOOOOOOO p


14 14 18 14 16 18 12 8 8


TABLE 22 Calculated vermis cerebelli height at 5-cm. intervals of crown-heel length


CBOWN-HEEL LENGTH


VERMIS CEREBELLI HEIGHT


INCREMENT IN EACH 5-CM. INTERVAL


RATIO TO NEW-BORN


cm.

5 10


cm.


cm.


per cent


per cent


0.23




10.8


15


0.41


0.18


78.1


19.2


20


0.61


0.20


48.8


26.6


25


0.82


0.21


34.4


38.5


30


1.06


0.24


29.2


49.8


35


1.31


0.25


23.6


61.5


40


1.57


0.26


19.8


73.7


45


1.84


0.27


17.2


86.3


50


2.13


0.29


15.8


100.0


55


2.42


0.29


12.0


113.7


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM


441


The absolute height of the vermis cerebelU when calculated for age in fetal months (fig. 31, curve II) rises in practically a straight Une from 0.23 cm. at the beginning of the foiu-th month to 2.1 cm. at birth.



Fig. 13 Field graph and curve of the growth of the cerebellum in fetal life as shown by the vermis cerebelli height. Abscissa: total body length in cm. Ordinate: vermis cerebelli height in cm. Individual cases indicated by solid dots. Curve drawn to the formula: Y = 0.01 (Xi-"). (Data from tables 21 and 22.)


The percentage increment of the vermis cerebelli height when calculated for 5-cm. intervals of crown-heel length (fig. 25, curve IV) is similar to that of the vermis cerebelh length except that it is somewhat greater at first and falls more rapidly.

The percentage increment of the vermis cerebelli height, when calculated for fetal months (fig. 27, curve IX), shows a rate of


442 H ALBERT L. DUNN

growth of about 126 per cent for the fourth month, falls to 58 per cent for the fifth month, and then descends steadily to about 13 per cent for the tenth month.

The growth of the cerebellum during the latter part of fetal life is also strikingly illustrated bj^ the midsagittal sections shown in figures 37 and 38. In the third fetal month (figure 38, C) the cerebellum grows posteriorly and parallel to the pons and medulla; bj^ the middle of the sixth fetal month (fig. 38, D, E, F) it assumes its characteristic shape and position in relation to the cerebral hemispheres. From the middle of the sixth fetal month to birth (fig. 38, G to I, inclusive) each succeeding tracing indicates a greater relative size in this portion of the brain.

It will be noted in this connection that the graphs of absolute growth of the cerebellum in both of the linear dimensions resemble volume curves much more closely than does the graphic expression of am^ other lineal dimensions of the nervous system.

Grouih of the pons and medulla

The growth of the pons and medulla (fig. 14) presents a typical volume curve having the empirical formula :

Pons and medulla volume (cc.) = 0.01 [(0.2 C H body length (cm.))-" + 20.0]

At 10 cm. (C H) their volimie is about 0.3 cc, by 30 cm. (C H) it is 1.4 cc, and at birth (50 cm. C H) it is approximately 5 cc "\^Tien calculated for age in fetal months (fig. 35, curve II), their volume is 0.2 cc. at three months and 1.4 cc. at six months. From this time it rises steadily to about 5 cc at birth.

The percentage increment of the volume (fig. 26, curve ^"III) is approximately 50 per cent for the lO-to-15-cm. (C H) interval and rises to about 56 to 57 per cent for the interval between 15 to 20 cm. It then descends steadily to about 27 per cent from 50 to 55 cm. (C H).

The percentage increment of the pons and meduUa volume as calculated for fetal months (fig. 28, curve II) shows a rate of growth of about 96 per cent for the fourth month, and then descends steadily to about 27.5 per cent for the last month of prenatal life.


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM


443


One of the most interesting facts concerning the prenatal growth of the pons and medulla is the per cent of the entire brain volume which they form during fetal Hfe (fig. 15 and table 40). In the middle of the fourth fetal month the pons and medulla make up 5.5 per cent of the entire brain volume, at 5 months they

TABLE 23

Volume of the pons and medtdla Formula: Pons and medulla volume (cc.) = .01 [(.2 crown-heel length (cm.))--" + 20] (112 cases)


CROWN-HEEL LENGTH


OBSERVED PONS AND MEDULLA VOLUME


CALCULATED PONS AND MEDULLA VOLUME


DIFFERENCE

BETWEEN

OBSERVED AND

CALCULATED

MEANS


NUMBER


Range


Mean


Masi

Minimum


Mean



cm.

Oto 5 5 to 10 10 to 15 15 to 20 20 to 25 25 to 30 30 to 35 35 to 40 40 to 45 45 to 50 50 to 55


cm.

12.6 16.9 22.5 27.0 32.7 37.0 42.3 48.0 52.2


cc.

0.5 0.7 1.0 1.4 2.1 3.2 3.9 5.5 6.3


cc.

0.2

0.15

0.4

0.5

0.9

1.6

2.5

3.7

4.5


cc.

0.3 0.4 0.8 0.9 1.5 2.4 3.1 4.3 5.2


CC.

0.3 0.5 0.8 1.1 1.7 2.3 3.2 4.4 5.4


CC.


-fO.l


+0.2 +0.2 -0.1 +0.1 +0.1 +0.2


11

14 16 13 17 16 11 6 8


TABLE 24

Calculated pons and viedulla volume at 5-cm. intervals of crown-heel length


CROWN-HEEL LENGTH


PONS AND MEDULLA VOLUME


INCREMENT IN EACH 5-CM. INTERVAL


RATIO TO NEW-BORN


cm.


CC.


CC.


per cent


per cent


5






10


0.26




5.3


15


0.39


0.13


50.0


8.0


20


0.61


0.22


56.5


12.5


25


0.94


0.33


54.1


19.3


30


1.40


0.46


49.0


28.7


35


2.01


0.61


43.5


41.2


40


2.78


0.77


38.3


57.0


45


3.73


0.95


34.2


76.4


50


4.88


1.15


30.8


100.0


55


6.23


1.35


27.7


128.0


444:


HALBERT L. DUNN


form only about 2.7 per cent, and from that time on to birth they gradually decrease in relative volume, so that they form only 1.5 per cent of the entire brain volume in the new-born. This


TO 6.5 6.0 55 50 45 40


1 1 \ \ r



20 £5 30 35 40 45 50 55c„


Fig. 14 Field graph and curve of the growth of the pons and medulla in weight and volume in fetal life. Abscissa: total body length in cm. Ordinate: pons and medulla weight and volume in grams (cc). Individual cases indicated by solid dots (for weight) and by circles (for volume) . Curve drawn to the formula : Y = 0.01 [(0.2Z)2.6' _j_ 20.0]. (Data from tables 23 and 24.)


relative decline is clearly due to the great increase in the absolute volume of the cerebral hemispheres and of the cerebellum during the last half of fetal life.


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 445

The pons length also shows some interesting changes in the course of fetal life. The graph of absolute pons length plotted against total body length (fig. 16) is practically a straight line having the formula: Length of pons (cm.) = 0.0263 C H body length (cm.) + 0.16



55an.


Fig. 15 Field graph and curve (connecting the average points of each 5-cin. crown-heel interval) of the per cent which the volume of the pons and medulla forms of the encephalon volume. Abscissa: total body length in cm. Ordinate: pons and medulla volume in per cent of the entire brain volume. Individual cases indicated by solid dots. (Data from table 40.)


The length increases steadily from 0.42 cm. at 10 cm. (C H) to about 1.53 cm. at birth (50 cm. C H).

When plotted against time, the pons length increases rather rapidly from the third to the beginning of the sixth month, and then grows more slowly at a uniform rate until birth.


446


H ALBERT L. DUNN


The percentage increment of the pons length against intervals of growth in body length (fig. 25, curve V) starts at 30 per cent between 10 and 15 cm. (C H) and falls steadily but slowly to 9.8 per cent in the 50-to-55-cm. interval.

The percentage increment of the pons length as calculated for fetal months (fig. 27, curve III) shows a rate of growth of about

TABLE 25

Pons length Formula: Pons length (cm.) = 0.0263 crown-heel length (cm.) + 0.16 (124 cases)


CROWN-HEEL LENGTH


OBSERVED PONS LENGTH



DIFFERENCE






CALCULATED PONS LENGTH


OBSERVED AND

CALCULATED

MEANS



Range


Mean


Maximum


Minimum


Mean


OF CASES


cm.


cm.


cm.


cm.


ctn.


cm.


cm.



to 5









5 to 10









10 to 15


12.2


0.6


0.3


0.5


0.5



18


15 to 20


16.7


0.8


0.5


0.6


0.6



13


20 to 25


22.6


0.9


0.7


0.8


0.8



18


25 to 30


27.0


1.1


0.6


0.9


0.9



13


30 to 35


32.8


1.2


0.9


1.0


1.0



16


35 to 40


37.1


1.5


1.0


1.2


1.1


—0.1


18


40 to 45


42.2


1.4


1.0


1.3


1.3



12


45 to 50


48.2


1.6


1.2


1.35


1.4


-0.05


8


50 to 55


52.2


1.7


1.3


1.5


1.5



8


TABLE 26

Calculated pons length at 5-cm. intervals of crown-heel length


CROWN-HEEL LENGTH


PONS LENGTH


INCREMENT IN E.ACH 5-CM. INTERVAL


R.\TIO TO NEW-BORN


cm.


cm.


cm.


per cent


per cerd


5


0.29





10


0.42


0.13+


44.8


28.7


15


0.55


0.13-f

30.0


37.6


. 20


0.68


0.13+


24.8


46.5


25


0.81


0.13+


19.2


55.4


30


0.94


0.13+


16.1


64.3


35


1.08


0.13+


13.9


73.3


40


1.21


0.13+


12.2


82.3


45


1.34


0.13+


11.8


91.2


50


1.47


0.13+


9.8


100.0


55


1.60


0.13+


8.9


108. S


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM


u:


75 per cent in the third month and descends steadily to approximately 7 per cent in the tenth month.

There is no doubt that the pons and medulla form a large part of the brain in early fetal life. Figures 38, a, b, c, and d, substantiate the percentage curve (fig. 18). They show that the pons and medulla form a very large portion of the entire brain volume at this time. By the middle of the third fetal month (fig. 38, b) fully one-third of the brain, as it is seen in mid


Fig. 16 Field graph and curve of the growth of the pons and medulla in fetal life, as shown by the pons length. Abscissa: total body length in cm. Ordinate: pons length in cm. Individual cases indicated by solid dots. Curve drawn to the formula: }' = 0.0263A' + 0.16. (Data from tables 25 and 26.)

sagittal section, is formed by the pons and medulla. In the fourth and fifth months (figs. 38, b, c, d, and e) the pons and medulla become relatively smaller.

Growth of the midbrain

A consideration of the colliculi and the midbrain does not lead to quite such clean-cut results as does the study of the other brain parts. The midbrain, as it was prepared for the volume and weight determinations, included not only the coUiculi above the iter, but also a portion of the brain stem below it.


448


HALBERT L. DUNN


The absolute volume of the midbrain when plotted against body length (fig. 17) presents a shallow curve and has the empirical formula:

Volume of midbrain (cc.) = 0.01 [(0.168 C H length (cm.))2-5« + 12.0]

TABLE 27

Volume of the midbrain

Formula: Midbrain volume (cc.) = .01 [ (.168 crown-heel length (cm.))^-" + 12]

(109 cases)


CROWN-HEEL LENGTH


OBSERVED MIDBRAIN VOLUME


CALCULATED

VOLUME OF MIDBRAIN


DIFFERENCE

BETWEEN

OBSERVED AND

CALCULATED

MEANS


NUMBER


Range


Mean


Maximum


Minimum


Mean



cm.


cm.


cc.


cc.


cc.


cc.


CC.



to 5









5 to 10









10 to 15


12.9


0.3


0.1


0.2


0.2



9


15 to 20


16.9


0.4


0.2


0.3


0.3



14


20 to 25


22.5


0.8


0.3


0.5


0.4


-0.1


17


25 to 30


27.0


0.9


0.4


0.6


0.6



13


30 to 35


32.7


1.4


0.4


0.8


0.9


+0.1


16


35 to 40


37.3


1.7


0.8


1.4


1.2


-0.2


14


40 to 45


42.3


2.2


1.2


1.6


1.6



11


45 to 50


48.0


3.1


1.5


2.4


2.2


-0.2


7


50 to 55


52.2


3.0


1.8


2.4


2.7


+0.3


8


TABLE 28 Calculated midbrain volume at 5-cm. intervals of crown-heel length


CROWN-HEEL LENGTH


MIDBRAIN VOLU.ME


INCRE.MENT IN EACH 5-CM. INTERVAL


RATIO TO NEW-BORN


cm.


CC.


CC.


per cent


per cent


5






10


0.16




6.6


15


0.23


0.07


43.7


9.4


20


0.34


0.11


47.8


13.9


25


0.51


0.17


50.0


20.9


30


0.75


0.24


47.0


30.7


35


1.05


0.30


40.0


43.0


40


1.43


0.38


36.2


58.5


45


1.89


0.46


32.0


77.4


50


2.44


0.55


29.1


100.0


55


3.12


0.68


27.8


128.0


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM


449


At 13 cm. (C H) the absolute midbrain volume is about 0.2 cc, and this steadily rises to 0.75 cc. at 30 cm. (C H). From this point the absolute volume increases at a faster pace to about 2.5 cc. at 50 cm. (C H).



55cm.


Fig. 17 Field graph and curve of the growth of the midbrain in weight and volume in fetal life. Abscissa: total body length in cm. Ordinate: midbrain weight and volume in grams (cc). Individual cases indicated by solid dots (for weight) and by circles (for volume). Curve drawn to the formula: Y = 0.01 [(0.168Z)2.66 + 12.0]. (Data from tables 27 and 28.)


The volume of the midbrain, when calculated for age in fetal months (fig. 35, curve III), is about 0.15 cc. at the third month and increases to about 0.8 cc. at six months. Thereafter it grows slowly to about 2.5 cc. at birth.


450


HALBERT L. DUNN


The percentage increment of the midbrain volume, when calculated for 5-cm. intervals of crown-heel length (fig. 26, curve IX), is about 45 per cent for the lO-to-15-cm. interval. It rises slightly at the 20-to-25-cm. interval and descends to 30 per cent for the 50-to-55-cm. interval.

The percentage increment of the midbrain volume as calculated for fetal months (fig. 28, curve III) is approximatelj' 81 per cent



30 35 40 45 50 55 err, Fig. 18 Field graph and curve (connecting the average points of each 5-cm. crown-heel interval) of the per cent which the midbrain volume forms of the encephalon volume. Abscissa: total body length in cm. Ordinate: mid-brain volume in per cent of the encephalon volume. Individual cases indicated bysolid dots. (Data from table 40.)

in the fourth month and descends to about 25 per cent in the last fetal month.

The slow growth of the midbram is reflected in the per cent which this brain part forms of the entire brain volume (figure 18 and table 40). Beginning at 2.9 per cent at three months, it steadily decluies to but 0.7 per cent of the entire brain volume at birth.


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 451

The length of the colliculi is not a true index of the midbrain growth in early fetal hfe, and its significance as a measure of growth of that portion of the mesencephalon below the iter is particularly questionable. In some fetuses of three to four months a sharp line of demarcation between the superior colliculi and the thalamencephalon may be present, while in other specimens of the same age no line of separation can be distinguished.

This conclusion is supported by evidence shown in figures 36, a, b, c. Figures 36, a, and 36, b, of specimens prior to the third fetal month show no colliculi; figure 36, c, shows colliculi well marked off and relatively larger than in a new-born specimen.

The curve of the absolute length of the colliculi, when plotted against body length (fig. 19), is a straight line. It starts at 0.7 cm. at 15 cm. (C H) and rises to 1.22 cm. in length at 50 cm. (C H). It may be expressed by the empirical formula:

Length of colliculi (cm.) = 0.015 C H body length (cm.) +0.47

The growth of the colliculi in absolute length when plotted against time (fig. 33, curve VI) approaches a straight line, although the rate of growth is more rapid in the fourth and fifth months than in the last four fetal months.

Groicth of the spinal cord

The growth of the spinal cord resembles that of the brain and particularly that of the pons and medulla. The absolute volume of the spinal cord plotted against crown-heel length (fig. 21) is a very shallow but typical volume curve, which may be expressed by the empirical formula :

Volume of the spinal cord (cc.) = 0.01 [(0.17 C H length (cm.)) 2" +11.0] The absolute volume at 15 cm. (C H) is approximately 0.22 cc. The curve rises steadily until it reaches about 1 cc. at 35cm. (CH). From this point it proceeds upward at a sharper pitch, reaching about 2.5 cc. at 50 cm. (C H).

The growth in absolute volume against time (fig. 35, curve IV) corresponds almost exactly with that of the midbrain and shows


452


HALBERT L. DUNN


a fairly rapid rate of absolute growth from the third to the beginning of the fifth month and a slower and more regular growth thereafter.

The data of Jackson ( '09) (table 35) show a uniformly higher average for the absolute spinal cord volumes. His small fetuses

TABLE 29

Length of the collicvli

Formula: Colliculi length (cm.) = .015 crown-heel length (cm.) + .47.

(117 cases)


CROWN-HEEL LENGTH


OBSERVED LENGTH OP THE COLLICULI


CALCUL.ITED


DIFFERENCE BETWEEN







LENGTH OP THE COLLICULI


OBSERVED AND CALCULATED

MEANS



Range


Mean


Maximum


Minimum


Mean


OP CASES


cm.


cm.


cm.


cm.


cm.


cm.


cm.



Oto 5









5 to 10









10 to 15


13.0


0.9


0.5


0.66


0.66



11


15 to 20


16.9


0.9


0.5


0.74


0.73


-0.01


14


20 to 25


22.5


1.0


0.7


0.80


0.81


+0.01


18


25 to 30


26.9


1.0


0.7


0.90


0.87


-0.03


12


30 to 35


32.8


1.7


0.8


0.99


0.96


-0.03


16


35 to 40


37.1


1.1


0.9


0.98


1.03


+0.05


18


40 to 45


42.2


1.2


1.0


1.10


1.10



12


45 to 50


48.3


1.4


1.1


1.23


1.20


-0.03


8


50 to 55


52.2


1.3


1.1


1.20


1.25


+0.05


8


TABLE 30 Calculated length of the collicvli at 5-cm. intervals of crown-heel length


CROWN-HEEL LENGTH


LENGTH OF COLLICULI


INCREMENT IN EACH 5-CM. INTERVAL


RATIO TO NEW-BORN


cm.


cm.


cm.


per cent


per cent


5






10






15


0.695




57.0


20


0.775


0.75


10.8


63.1


25


0.845


0.75


9.8


69.3


30


0.920


. 0.75


8.9


75.4


35


0.995


0.75


8.2


81.5


40


1.070


0.75


7.6


87.8


45


1.145


0.75


7.0


93.9


50


1.220


0.75


6.6


100.0


55


1.295


0.75


6.2


106.2


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM


453


(obtained by sectioning) show an absolute volume of 0.034 cc. at approximately the close of the first month, while his two largest fetuses (new-born) have a cord volume of about 3 cc.

The percentage increment of the spinal cord volume when determined for 5-cm. intervals of crown-heel body length (fig. 26,



Fig. 19 Field graph and curve of the growth of the midbrain in fetal life as shown by the coUiculi length. Abscissa: total body length in cm. Ordinate: colliculi length in cm. Individual cases indicated by solid dots. Curve drawn to the formula: Y = 0.015X + 0.47. (Data from tables 29 and 30.)


curve X) is 47 per cent for the lO-to-15-cm. interval. It rises_to about 55 per cent for the 15-to-20-cm. interval, and then falls to about 25 per cent for the 50-to-55-cm. interval.

The percentage increment of the spinal cord volume when calculated for fetal months (fig. 28, curve I) shows a rate of growth of approximately 94 per cent in the fourth month and then descends steadily to 26 per cent in the last fetal month.


454


H ALBERT L. DUNN


The relation of the spinal cord volume to the volume of the entire brain is shown in figure 22 and in table 40. At the middle of the second month the cord volume is equal to 4.4 per cent of the total brain volume. It then drops rapidly at first and afterward more slowly to about 0.85 per cent of the total brain volume at birth.

TABLE 31

Frontospinal length

Formula: Frontospinal length (cm.) = (2 crown-heel length (cm.))^^ — 2.2

(145 cases)


CROWN-HEEL LENGTH


OBSER-VED FRONTOSPINAL LENGTH


CALCULATED

FRONTOSPINAL

LENGTH


DIFFERENCE

BETWEEN

OBSERVED AND

CALCULATED

MEANS


NUMBER


Range


Mean


Maximum


Minimum


Mean



cm.


cm.


cm.



cm.


cm.


cm.



to 5


4.0


1.0


0.7


0.9


0.5


-0.5


3


5 to 10


6.8


1.7


1.0


1.4


1.2


-0.2


9


10 to 15


12.1


2.9


1.9


2.1


2.3


+0.2


20


15 to 20


16.6


3.5


2.6


2.9


3.0


+0.1


14


20 to 25


22.6


4.5


3.0


3.8


3.8



20


25 to 30


27.0


4.6


3.4


4.1


4.3


+0.2


15


30 to 35


32.8


5.3


4.3


4.8


4.9


+0.1


17


35 to 40


37.1


6.5


4.0


5.3


5.4


+0.1


19


40 to 45


42.2


6.8


5.1


5.9


5.8


-0.1


12


45 to 50


48.2


6.9


5.9


6.3


6.4


+0.1


8


50 to 55


52.2


7.3


6.3


6.8


6.7


-0.1


8


TABLE 32

Calculated frontospinal length at 5-cm. intervals of crown-heel length


CROWN-HEEL LENGTH


CALCULATED FRONTOSPINAL LENGTH


INCREMENT IN EACH rx-M. :XTiai\AL


RATIO TO NEW-BORN


cm.


cm.


cm.


per cent


per cent


5


0.75




11.5


10


1.89


1.14


152.0


29.0


15


2.75


0.86


44.8


42.2


20


3.46


0.71


28.2


53.1


25


4.09


0.63


18.2


62.8


30


4.65


9.56


13.4


71.4


35


5.17


0.52


12.4


79.5


40


5.64


0.47


9.3


86.6


45


6.09


0.45


8.0


94.5


50


6.51


0.42


6.7


100.0


55


6.91


0.40


6.3


106.2


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 455


The absolute length of the spmal cord (fig. 23) ascends rather sharply from 2.2 cm. length at 5 cm. (C H) to 9.2 cm. at 25 cm. (C H). It then ascends more slowly to 14.2 cm. at birth (50 cm. C H). Its empmcal formula is:

Length of spinal cord (cm.) = (10.0 C H body

length (cm.))"" - 4.0

The curve of cord length, when plotted against time, is quite

similar to that plotted against body length, but the rise is a more

rapid one (fig. 32, curve IV).



55 40


Fig. 20 Field graph and curve of the growth of the brain stem in fetal life as shown by the fronto-spinal length. Abscissa: total body length in cm. Ordinate: fronto-spinal length in cm. Individual cases indicated by solid dots. Curve drawn to the formula : 7= (2.0X)-" - 2.2. (Datafrom tables 31 and 32.)

The percentage increment of the cord length as calculated for 5-cm. intervals of crown-heel length (fig. 25, curve VHI) is about 109 per cent for the 5-to-lO-cm. interval, falls rapidly to 23 per cent for the 15-to-20-cm. interval, and then gradually to 6 per cent for the 50-to-55-cm. interval.

The percentage increment of the spinal-cord length when calculated for fetal months (fig. 27, curve V) shows a rate of growth of approximately 400 per cent in the third month, descending rapidly to 26 per cent in the sixth month, and then gradually to nearly 6 per cent in the last month of the fetal period.


456


HALBERT L. DUNN


DISCUSSION

The discussion of the results of this work will be hmited to, 1) a comparison of the growth of the central nervous system as a whole with that of the various other viscera and parts of the body in the fetal period; 2) the analysis of the type of growth of the

TABLE 33

Volume of the spinal cord

Formula: Spinal cord volume (cc.) = .01 [(0.17 crown-heel length (cm.) )2" ^ n.]

(128 cases)


CROWN-HEEL LENGTH


OBSERVED VOLUME OF SPINAL CORD


CALCULATED VOLUME OP SPINAL CORD


DIFFERENCE

BETWEEN

OBSERVED AND

CALCULATED

MEANS


NUMBER


Range


Mean


Maximum


Minimum


Mean



cm.


cm.


cc.


cc.


cc.


cc.


cc.



to 5









5 to 10


7.2


0.05


0.05


0.05


0.13


0.08


3


10 to 15


12.5


0.3


0.1


0.2


0.2



IS


15 to 20


16.5


0.5


0.1


0.3


0.3



14


20 to 25


22.6


0.7


0.3


0.5


0.4


-0.1


19


25 to 30


26.9


1.1


0.3


0.65


0.6



14


30 to 35


32.6


1.4


0.5


0.9


0.9



17


35 to 40


37.0


2.1


0.7


1.1


1.1



17


40 to 45


41.9


2.3


1.2


1.7


1.7



11


45 to 50


48.0


3.1


1.4


2.4


2.3


-0.1


7


50 to 55


52.2


3.8


1.8


2.5


2.8


+0.3


8


TABLE 34

Calculated spinal cord volume at 5-cm. intervals of crown-heel length


CROWN-HEEL LENGTH


SPINAL CORD VOLUME


INCREMENT IN E.\CH 5-CM. INTERVAL


RATIO TO NEW-BORN


cm.


CC.


CC.


per cent


per cent


5






10


0.15




5.9


15


0.22


0.07


46.7


8.6


20


0.34


0.12


54.5


13.3


25


0.52


0.18


53.0


20.3


30


0.77


0.25


48.1


30.1


35


1.09


0.32


41.5


42.5


40


1.49


0.40


36.7


58.2


45


1.98


0.49


32.9


77.4


60


2.56


0.58


29.2


100.0


55


3.24


0.68


24.5


126.5


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 457

central nervous system into its component parts; 3) observations upon the relation of volumetric and lineal measurements of the nervous system, and, 4) a summary of the proportions which the



Fig. 21 Field graph and curve of the growth of the spinal cord in weight and volume during fetal life. Abscissa: total body length in cm. Ordinate: spinal cord weight and volume in grams (cc). Individual cases indicated by solid dots (for weights) and by circles (for volume). Curve drawn to the formula: Y = 0.01 [(0.17X)2." + 11.0]. (Data from tables 33, 34, 35.)


various bram parts form of the encephalon in prenatal life. The consideration of the growth of the fetal brain and the spinal cord in relation to the postnatal changes of these structures is reserved for a later publication. It is hoped also that it will be possible


458


H ALBERT L, DUNN


to present at a later time an outline of the prenatal growth of the various internal parts of the brain for which data are now being collected.

Groiiih of the central nervous system as a whole

The growth curve of the central nervous system (represented by the volume of the central nervous system, fig. 2) is analogous in both its character and its slope to the growth curves of nearly all the fetal viscera. - The abscissa of this curve is the crown


TABLE 35

Spinal cord volume and weight (data of Jackson, '09, and of Volpin, '02)



SPINAL-CORD VOLUME (jACKSON, '09)


SPINAL-CORD WEIGHT (v


3LPIN, '02)


RANGE OP








CHOWN-HEEL LENGTH


Average

crown-heel

length


Average cord volume


Number of cases


Average

crown-heel

length


Average cord weight


Number of cases


cm.


cm.


cc.



cm.


grams



Oto 5


1.77


0.02225


3





5 to 10


7.7


0.115


3





10 to 15


12.3


0.1671


3





15 to 20


17.1


0.3447


5


16.0


0.75


1


20 to 25


22.4


0.664


4


20.0


1.5


1


25 to 30


27.4


0.908


5


28.0


2.0


1


30 to 35


32.7


1.53


2


32.7


3.0


3


35 to 40


38.5


1.8


1


38.5


3.75


2


40 to 45


44.2


3.3


1


41.8


4.5


3


45 to 50





45.7


6.6


3


50 to 55


51.9


3.04


2


51.0


9.5


3


heel length and represents a simple lineal type of growth. The value of the central nervous system is therefore a function of the crown-heel length which has been raised to approximately the third powder. Obviously, this is a typical concave volumetric curve. It is similar in type to all of the visceral volumetric and ponderal curves of grow^th which have been worked out in this laboratory and of which a summary has been published elsewhere (Scammon, '21). It is also analogous to the curves of fetal body weight and of weights of body parts which have been expressed in functions of the crown-heel length of the fetus. In order to compare


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 459

the growth of the central nervous system to the growth of other parts of the body it has been considered as a unit. It is however a complex of four distinct subtypes of growth, all of which are dominated b}^ the growth of the bulky cerebral hemispheres.^



Fig. 22 Field graph and curve (connecting the average points of each 5-cm. crown-heel interval) of the per cent which the spinal cord volume forms of the encephalon volume. Abscissa: total body length in cm. Ordinate: spinal cord in per cent of the encephalon volume. Individual cases indicated by solid dots. (Data from table 40.)


- In order to compare these four types of growth, ten methods were used : 1) the various absolute length curves (fig. 29) were calculated against crown-heel body length (cm.) and reduced to a percentage basis; 2) the absolute volume curves likewise (fig. 30) were taken to crown-heel length and reduced to a per cent basis; 3) the absolute length curves (fig. 33) were calculated for age in fetal months and reduced to a common per cent; 4) the absolute volume curves also (fig. 36) were taken to age in fetal months and reduced to a percentage basis; 5) percentage increments of linear curves (fig. 25) were calculated for 5-cm. C H intervals;


460


HALBERT L. DUNN


TABLE 36

Length of the spinal cord Formula: Spinal cord length (cm.) = 10 crown-heel length (cm.)-«^ (144 cases)


CROWN-HEEL LENGTH


OBSERVED SPINAL CORD LENGTH


CALCULATED


DIFFERENCE BETWEEN








SPINAL CORD LENGTH


OBSERVED AND CALCULATED

MEANS



Range


Mean


Maximum


Minimum


Mean



cm.


cm.


cm.


cm.


cm.


cm.


cm.



Oto 5


3.9


2.5


1.4


1.9


1.4


-0.5


4


5 to 10


7.7


4.0


2.3


3.0


3.6


+0.6


9


10 to 15


12.1


6.2


4.0


4.7


5.4


+0.7


20


15 to 20


16.7


9.7


5.3


7.0


6.9


-0.1


14


20 to 25


22.7


10.7


7.0


8.7


8.6


-0.1


20


25 to 30


26.9


10.7


8.5


9.75


9.6


-0.1


14


30 to 35


32.6


13.3


9.0


10.6


10.9


+0.3


18


35 to 40


37.1


16.5


9.5


12.2


11.8


-0.4


17


40 to 45


42.2


14.0


11.0


12.4


12.8


+0.4


12


45 to 50


48.2


14.8


12.7


13.5


13.9


+0.4


8


50 to 55


52.2


15.8


13.2


14.5


14.6


+0.1


8


TABLE 37

Calculated spinal cord length at S-cm. intervals of crovm-heel length


CBOWN-HEEL LENGTH


SPINAL CORD LENGTH


INCREMENT IN EACH 5-CM. INTERVAL


RATIO TO NEW-BOKN


cm.


cm.


cm.


per cent


ppr rent


5


2.2




15.5


10


4.6


2.4


109.0


32.4


16


6.4


1.8


39.2


45.0


20


7.9


1.5


23.4


55.6


25


9.2


1.3


16.4


64.8


30


10.4


1.2


13.0


73.3


35


11.4


1.0


9.6


80.3


40


12.4


1.0


8.2


87.3


45


13.3


0.9


7.5


94.0


50


14.2


0.9


6.5


100.0


55


15.0


0.8


5.9


105.6


6) percentage increments of volume curves (fig. 26) were determined for 5-cm. intervals; 7) percentage increments of linear curves (fig. 27) were calculated for age in fetal months; 8) percentage increments of linear curves (fig. 28) were determined for age in fetal months; 9) the various linear formulae of the respective absolute curves (table 43), and, 10) the volumetric formulae of the absolute volume curves (table 43) were compared.


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 461

The j&rst type, cerebral growth, is characterized by a constant growth in Hnear measurements from the second fetal month until birth, and shows a steady and relatively slow increase in volume



Fig. 23 Field graph and curve of the growth of the spinal cord in fetal life as shown by the spinal cord length. Abscissa: total body length in cm. Ordinate: spinal cord length in cm. Individual cases indicated by solid dots. Curve drawn to the formula: Y = (lO.OX)."^ - 4.0. (Data from tables 36 and 37.)


before the sixth fetal month and a constant but more rapid increase from that time until bu'th. Brain stem and cord growth, on the other hand, advances much faster previous to the seventh fetal month than it does in the last four months of fetal life. Cerebellum growth, on the contrary, proceeds slowly imtil the


462


HALBERT L. DUNN


seventh fetal month and from that time until birth it exceeds all other growth activity in the central nervous system. The last type, compound growth, represents merely the combined effect of two or more of the above types predominated by the mass of the cerebral hemispheres. These varieties of growth will now be considered in more detail.

TABLE 38 Combined brain-cord length Formula: Brain-cord length (cm.) = (10 crown-heel length (cm.))-^'* —4 (137 cases)


CROWN-HEEL LENGTH


OBSERVED BU.UN-CORD LENGTH


CALCULATED BRAIN-CORD

LENGTH


DIFFERENCE

BETWEEN

OBSERVED AND

CALCULATED

MEANS


NU.MBER


Range


Mean


Maximum


Minimum


Mean



cm.


cm.


cm.


cm.


cm.


cm.


cm.



to 5


4.0


4.9


3.1


■ 3.0


2.7


-0.3


3


5 to 10


7.1


5.7


4.0


4.4


4.9


+0.5


7


10 to 15


12.1


8.5


5.0


6.9


7.8


+0.9


20


15 to 20


16.6


12.7


7.9


9.8


9.8



14


20 to 25


22.6


14.7


10.2


12.4


12.2


-0.2


19


25 to 30


26.9


15.1


12.1


13.8


13.8



13


30 to 35


32.8


18.4


14.1


15.4


15.6


-0.2


16


35 to 40


37.1


20.2


13.5


17.4


16.9


-0.5


17


40 to 45


42.2


19.7


16.1


18.1


18.4


-0.3


11


45 to 50


48.2


21.7


18.8


19.8


19.9


+0.1


9


50 to 55


52.2


23.1


20.4


21.3


20.9


-0.4


8


TABLE 39 Calculated combined brain-cord length at 5-cm. intervals oj crown-heel length


CROWN-HEEL LENGTH


BRAIN-CORD LENGTH


INCREMENT IN EACH 5-CM. INTERVAL


RATIO TO NEW-BORN


cm.


cm.


cm.


per cent


per cent


5


3.5




17.2


10


6.6


3.1


88.5


32.3


15


9.2


2.6


39.4 •


45.1


20


11.2


2.0


21.7


54.9


25


13.1


1.9


17.0


64.2


30


14.8


1.7


13.0


72.5


35


16.3


1.5


10.1


79.9


40


17.8


1.5


9.2


87.2


45


19.1


1.3


7.3


93.6


50


20.4


1.3


6.4


100.0


55


21.6


1.2


5.9


106.0


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 463

Cerebral growth. The growth of the cerebrum is characterized by a steady absolute increment in all of its hnear measurements from the second fetal month until birth. This can be observed by the inspection of the curves of the fronto-occipital length and the temporal diameter (fig. 29, curves I and II, respectively).



Fig. 24 Field graph and curve of the growth of the spinal cord and brain stem in fetal life as shown by the brain-cord length. Abscissa: total body length in cm. Ordinate: brain-cord length in cm. Individual cases indicated by solid dots. Curve drawn to the formula: Y = (10.0X)-=" -4.0. (Data from tables 38 and 39.)


These curves are both straight lines and he intermediate to the vermis cerebelh absolute curves below and to the curve of the spinal cord above. When calculated against time in fetal months (fig. 33, curves I and II), the fronto-occipital length and the

{Text continued on page 479)


464


HALBERT L. DUNN


TABLE 40

Ratios of the volumes of the various parts of the central nervous system to the entire brain volume





RATIO of:




CROWN-HEEL







LENGTH RANGE


Spinal cord


Pons and medulla


Midbrain


Cerebellum


Cerebral hemispheres


cm. 5 to 10


4.70






10 to 15


3.30


5.5


2.90


3.0


87.7


15 to 20


2.40


3.6


2.40


3.0


90.9


20 to 25


1.70


2.7


1.60


3.1


93.1


25 to 30


1.50


2.2


1.40


3.0


94.0


30 to 35


1.20


1.9


0.96


2.8


94.2


35 to 40


0.81


1.7


0.90


3.8


94.1


40 to 45


0.90


1.6


0.87


4.4


93.2


45 to 50


0.84


1.5


0.70


6.2


92.0


50 to 55


0.70


1.4


0.67


5.8


91.8


Table 41

Comparison or thcV/uohtj AnoVa-unca

or THE. 5piMALCoRD.Tnr; Dstirl Brain aho THt\^niou3 Parts or Tut Brain

IM THE FCTAL PcjUOD



Average. Vcioht(gm)amdVolumc(cc)in Cach 5cm. Interval (C.H.)



to 5


5 to 10


10


15


eo


E5 to

30


30 to

35


35 to

40


40


45


50 ^5


Spinal Cora lies cases)


Wl. Vol.


0015


0D5 CDs'


0.15 0.17


0Z9 "Offi


051 048


"o,65


092 088


1.23 1.14


16 L7


Lit 2,4


2.9

£5


Pons and Mdulla (109 cases)


Wl. Vd.'


z

-^

0.35 0.3^


047 044


Q6z:

077


092 Q92


17 'i5


26 24


3,2 31


-t


54

"^2


Midbrain (lOQcasGs)


Wl.



~


on ai9


0,32 0.30


050 'OAJ


0.64 "062


067

'oai


1.2

'14'


1.6 'T.6


lA


£6

"£"4


Cerebellum diseases)


Wl, Vol'


z

■£

0.25 026


0.43 "041


\.0l 0.9^5


139 134


2.50 '236


5.6 54


92 8.9"


189 " \Q3


21.9 "273


Ridil Cerebral Hemisphere diseases)


Wl "Vol"




lb


62 60"


15.1 "l4"6~


224 l\l


39.2 3a2


660 641


94.0 92 2


1420 1380


1740 1700


Leit Cerebral Hemisj^Gir (114 cases)


Wt


~


~


19


62

'(To"


146 14 2~


225 21.8


408 392"


666 658


975 94.6"


1452 139.0


171.8 1660


Lnlire Brain (meases)


Wl Vol


03 0.3 "


13


56

54


1^6 119


£99 308"


478 45,8


629 765


M36 152,0


196.2 191.2


3136 £99,1


3761 3649


Central Nervous System 046 coses)


Wt "Vof


033 03Z


1.4 13


55

54


129 1F5


324 31.1


465

46,9


a38_ 616


1448 141.8


1980 1977


3160 3060


3M 36r5


GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 465


Table; 41 Caitulatcd Absolute: and Plrccntage: Increimcnts or the Scvcral Papt^ or the Brain AMD or the: 5pinal Cord in [Iach Month or thc Ictal Peiriod


AGt

According

to Mall's Tabi r.,^

(FtTAL MOMTHS)


CCRCBRUM


CCRCBCLLUM


PoHS AMD Medulla


Midbrain


5pinalCord


Boih lemispher?: VduW


fronto occipilal Lei^Slh


Temporal RamGler


Cerebellum Vobmc


Vermis Cerebelli Length


Vermis Cerebelli neight


Fbnsand Medulla Volume


Pons Length


Midbrain Volume


Volume


Spinal Cord Length


c.c


%


cm.


%


cm.


%


C.C.


%


cm.


%


cm.


%


cc


%


cm.


%


cc


%


cc.


%


cm.


%


1



~






















2


'i.


~


0.77



0.71



0.20



0.22



0^5



0.20



024



0.12



0.04



Q9C



3


m


4^.


i.%


53.0


1.65


131


0.27


55.


0.40


81.6


0.2336a


0.26


3Q0 0.42


745


016


33.3


015


36.4


4.51*401.


4


11.67


5%.


lAO


m


£.7e


6a5


0.34


30.


074


85.0


0.52


126.


0.51


962


0.63


51.6


029


81.3


029


93.3


7.30 62.


5


33.n


185


A.bl


36.0


3.75


347


0.69


161.5


1.09


47.3


052


57.6


093


62.4 0.82


29.1


051 75.6


Q52


79.3


916! ,25.6


6


W3


109


5.76


ZAb


465


£3.9


2.25


153.0


1.45


33.0


1.13


376


1.56


676 099


20.9


0.83 62.8


0.861 654

1


10.68 16.3


7


IITX


68.5


6.74 17.0


^Al\ 16.7


4.99


121.9 1.76


226


1.41


247


2.31


m


1.14


14.9


1.20


44.6


1.25


45.4


1 1.54; 10.9


e


10Q6


542


7.69 M.d6.16 D.6


9.53


91.0 ] 2.13


19.7


1.70


206


^23


39.e


1.26


12.5


1.65


37.5


1.72:


376


12.86


6.8


9


mz j 3r.6


a.47


10.2 6.79


10.1


15.64


to.-3


2.43


14.1


1.95


I4J


.17


ffl.l


1.34


9.3


2.10


27.3


zzo


27.9


13.701 6.4


10


303.61 35.


9.00


95 1 7.eo

1


91


20.69' 541

1


264


\IA


2.13


13.2


4^


£7^


147


7.3


2.44


25.


2.56


26.


M.2


57


Table: 4J)

CmpiRICAL foRMULAE RcPRESENTlNO CupWEi or LjNEAR AND VoLUMCTFilC GrOWTH

or THE Central Nervous System in the Fetal Peiriod


MCAOJRCMENT

Ffonlo-occipilal LengJh Temporal -leropora) DiarocJer Pons Len^Jh CoUiculi Len^Jh Spinal Cord Length Brain Ccrd Len3fh fronfo -spinal Lengih

Vermis C«rebelii L?ngih \fenni5 CereboUi hfeight

Spinal Cord Volume

Fbns and Medulla Volume

Mid Brisin Volume

CzrebeJIum VslumG

Riaht HeiDLsphere \yumc Leit Hemisphere Volume Both Hemispheres Volume


5PECinC foRMULAE

(Cxponential)

Y=ai75X+a£5 Y=0136X+0.3 Y-Q0263X+QI6 Y= 0.01 5X+ 047

Y (100X)-'*^^-4.0 Y(10.0X)5"'-4.0

Y (Z.O-AY^^-ZZ Y001(X"+150) YO.OKX'^") Y00l[(QITX)"+||0l

Y 001 (Q2X)^ '■"^+2001

Y 00l[(O166X)"^+120!

Y- O01[(Q095X)^+2OO]

YCOIXP"

Y-(O105X)^°^

Y(QI2X)3"


Ihctphalcn Volume Cnc€phabn Waiaht Cenlral I^srvous System \fclume Y (0 1 14X)


Y(0125Xf"'+1.5 Y (0I3X)^


1.0 +20


Type or Iormula Y-aX+b

Y^faX^c Y=001CX^+b)

Y=Q0l[(aX)^+c]

Y(aX) Y=(aXJ^c


SpEcinc Formulae (Logarithmic)

Y0.175X+025 Y-0.138X+0.3 Y"01D263X+ai6 Y0.015X+0.47

Y=007X+10/o5'X-6.5 Y'ai7X + ll/4x-6.T Y=0.051X+4/^X-265

Y=Q01(0.073X+265;' Y-Q01(.07X+£45)'

Y- 1 .4(O02X+0.31)'-QOI3Xf Q I

Y-094(003X+0£P+OI

Y= 1. 5 (O.0iX+O.31J^-O027X+a3e

Y=Q0I(a025X+lO3)^

Y(QI085X-Q09)^ Y=(0.I06X-005)^


Type or foRMULA Y=aX+b

Y=aX+b/ojrX-c Y=O.OKaX+b)'

Y=aCbX+c)^±dX+e

Y=O.OI(aX+b)' Y=a(bX-cf


Y= 1. 1 (0. I37X- 07)'-0.4X+5.0 Y=l.l5(0.I4X+0C)'-X+ia0 Y-a(bX±c)'-dXi

Y'l.l7(0.137X-a03)'-l.I£X-hl60



Fig. 25 A series of curves illustrating the percentage increments of the various linear dimensions of the brain, brain parts, and spinal cord. Abscissa: total bodj- length in cm. Ordinates: percentage increments calculated from the formulae of the respective absolute curves. (Data from tables 14, 16, 20, 22, 26, 30, 32, 37, and 39.) I, percentage increment of fronto-occipital diameter. II, percentage increment of temporal diameter. Ill, percentage increment of vermis cerebelli length. IV, percentage increment of vermis cerebelli height. V, percentage increment of pons length. VI, percentage increment of colliculi length. VII, percentage increment of frontospinal length. VIII, percentage increment of spinal cord length. IX, percentage increment of brain-cord length.



Fig. 26 A series of curves illustrating the percentage increments of the various volumetric determinations of the brain, brain parts, and spinal cord. Abscissa: total body length in cm. Ordinates: percentage increments calculated from the formulae of the respective absolute growth curves. (Data from tables 2, 4, 5, 8, 10, 12, 18, 24, 28, and 34.) I, percentage increment of central nervous system volume. II, percentage increment of encephalon volume. Ill, percentage increment of entire brain weight by literature. IV, percentage increment of right hemisphere volume. V, percentage increment of left hemisphere volume. VI, percentage increment of both hemisphere volume. VII, percentage increment of cerebellum volume. VIII, percentage increment of pons and medulla volume. IX, percentage increment of midbrain volume. X, percentage increment of spinal cord volume.


Fig. 27 A series of curves illustrating the percentage increments of the vai'ious linear dimensions of the brain, brain parts, and spinal cord when interpreted in time in fetal months (as determined by Mall's convention). Abscissa: total time of fetal life in months. Ordinate: percentage increments calculated from the formulae cf corresponding absolute curves and transposed into time. (Data from table 41.) I, percentage increment of fronto-occipital diameter. II, percentage increment of temporal diameter. Ill, percentage increment of pons length. IV, peVcentage increment of colliculi length. V, percentage increment of spinal cord length. VI, percentage increment of brain-cord length. VII, percentage increment of frontospinal length. VIII, percentage increment of vermis cerebelli length. IX, percentage increment of vermis cerebelli height.



Fig. 28 A series of curves illustrating the percentage increment of the various volumetric determinations of the brain, brain parts, and spinal cord. Abscissa: total time in fetal months as determined by Mall's convention. Ordinates: percentage increments calculated from the formulae of respective absolute growth curves. (Data from tablets 2, 4, 5, 8, 10, 12, 18, 24, 28, and 34.) I, percentage increment of spinal cord volume. II, percentage increment of pons and medulla volume. Ill, percentage increment of midbrain volume. IV, percentage increment of cerebellum volume. V, percentage increment of both hemisphere volume. VI, percentage increment of the encephalon volume. VII, percentage increment of the volume of the central nervous sytem. VIII, percentage increment of the encephalon weight (cases collected from the literature).



Fig. 29 A series of curves illustrating the growth (in linear dimensions) of the brain, brain parts, and spinal cord in per cent of the respective new-born linear measurements. Abscissa: total body length in cm. Ordinates: linear dimensions calculated in per cents of the respective new-born measurements. Data from the formulae in table 43. I, frontal-occipital diameter. II, temporal diameter. Ill, vermis cerebelli length. IV, vermis cerebelli height. V, pons length. VI, coUiculi length. VII, frontospinal length. VIII, spinal cord length. IX, brain-cord length.



Fig. 30 A series of curves illustrating the growth in the volumes of the brain, brain parts, and spinal cord in per cent of the respective new-born volumetric determinations. Abscissa: total body length in cm. Ordinate: volumes calculated in per cents of the respective new-born volumetric determinations. (Data from the formulae in table 43.) I, volume of the central nervous system. II, encephalon volume. Ill, encephalon weight by cases from the literature. IV, right hemisphere volume. V, left hemisphere volume. VI, both hemisphere volumes. VII, cerebellum volume. VIII, pons and medulla volume. IX, midbrain volume. X, spinal-cord volume.



Fig. 31 A series of curves illustrating the growth of the pons, colliculi, and vermis cerebelli by linear measurements. Abscissa: fetal months (crown-heel reduced to time by Mall's convention). Ordinates: lengths of pons, colliculi, and vermis cerebelli in cm. (Data from formulae in table 43.) I, vermis cerebelli length. II, vermis cerebelli height. Ill, pons length. IV, colliculi length.



Fig. 32 A series of curves illustrating by linear measurements the growth of the cerebrum, brain stem, and spinal cord. Abscissa: fetal months (crownheel reduced to time by Mall's convention). Ordinates: lengths of the cerebrum, brain stem, and spinal cord in cm. (Data from formulae in table 43.) I, fronto-occipital diameter. II, temporal diameter. Ill, frontospinal length. IV, spinal cord length. V, brain-cord length.



Fig. 33 A series of curves illustrating the growth (in linear dimensions) of the brain, brain parts, and spinal cord calculated in per cents of the respective newborn linear measurements. Abscissa: fetal months (crown-heel length reduced to time by Mall's convention). Ordinates: linear dimensions calculated in per cents of the respective new-born measurements. (Data from the formulae in table 43.) I, fronto-occipital diameter. II, temporal diameter. Ill, vermis cerebelli length. IV, vermis cerebelli height. V, pon length. VI, coUiculi length. VII, frontospinal length. VIII, spinal-cord length. IX, braincord length.




Fig. 34 A series of curves illustrating the growth of the cerebrum and cerebellum as shown by volumetric determinations. Abscissa: fetal months fcrownheel length reduced to time by Mall'.s convention). Ordinates: volumes of the encephalon, right hemisphere, and cerebellum. (Data from formulae in table 43.) I, encephalon volume. II, right hemisphere volume. Ill, cerebellum volume. IV, central nervous sytem volume. V, encephalon weight (data collected from the literature). VI, both hemisphere volume.



Fig. 35 A series of curves illustrating the growth of the cerebellum, pons and medulla, midbrain, and spinal cord. Abscissa: fetal months (crown-heel reduced to time by Mall's convention). Ordinates: volumes of the cerebellum, pons and medulla, midbrain, and spinal cord. (Data from the formulae in table 43.) I, cerebellum volume. II, pons and medulla volume, III, midbrain volume. IV, spinal cord volume.



Fig. 36 A series of curves illustrating growth of the brain, brara parts, and spinal cord in per cent of the respective new-bom volumetric determinations. Abscissa: fetal months (crown-heel reduced to time by Mall's convention). Ordinates : per cents of volumes as compared with the respective new-born volumetric determinations. (Data from the formulae in table 43.) I, encephalon volume. II, cerebral hemispheres volume. Ill, cerebellum volume. IV, pons and medulla volume. V, midbrain volume. VI, spinal cord volume.



Fig. 37 A series of midsagittal tracings of the brain and brain stem. Each figure represents an average brain, in each 5-cm. crown-heel interval. A, ca. 4 cm. C H length. B, ca. 7.5 cm. CH length. C, ca. 2.5 cm. C H length. D, ca. 17.5 cm. C H length. E, ca. 22.5 cm. C H length. F, ca. 27.5 cm. C H length. G, ca. 32.5 cm. CH length. H, ca. 37.5 cm. CH length. I, ca. 42.5 cm. C H length. J, ca. 47.5 cm. C H length. K, ca. 52.5 cm. C H length.


temporal diameter are practically identical. They occupy the same characteristic intermediate position between the cerebellum and the brain stem and spinal cord absolute growth curves. The rate of growth of the fronto-occipital diameter, when calculated from 5-cm. C H intervals (fig. 25, curves I and II) and also when calculated for age in fetal months (fig. 27, curves I and II), portrays an intermediate percentage increment curve lying between the cerebellum above and the brain stem below. The formulae of the fronto-occipital length and the temporal diameter (table 43) likewise show a characteristic grouping of the hemispheres to the general formula: Y = aX + h, in which Y is the frontooccipital length or the temporal diameter in cm., X is the crownheel length in cm., and a and h are constants determined for the two formulae.

Cerebral growth in volume shows a steady and relatively slow increase before the sixth fetal month and then a constant but more rapid increase from that time until birth. This is indicated by the right hemisphere volume, left hemisphere volume, and both hemisphere volume (figs. 4, 5, and 6, respectively). When calculated against crown-heel length and reduced to percentage basis (fig. 30), the right hemisphere volume, left hemisphere volume, and the volume of both hemispheres (curves IV, V, and VI, respectiveljOj as well as the absolute curves of the central nervous system and the total brain volume (curves I and II, respectively), fall practically upon one another. The cerebellum volume curve lies below and the brain stem and spinal cord volume curve above the curves dominated by the factor of cerebral growth. Upon inspection of the curve of both hemisphere volume when calculated against time in fetal months and reduced to a percentage basis (fig. 36, curve II), a similar central grouping between the cerebellum volume, the brain stem volume, and spinal cord volume is observed. Turning to the figures upon the rate of growth of the cerebrum, which is determined for 5-cm. intervals (fig. 26, curves IV, V, and VI) and for age in fetal months (fig. 28, curve V), one observes the unswerving tendency of the cerebral growth to proceed faster before the sixth month and slower thereafter.



Fig. 38 A series of midsagittal tracings (of the specimens shown in figure 35) drawn to a standard fronto-occipital length. A, ca. 4 cm. C H length. B, ca. 7.5 cm. C H length. C, ca. 12.5 cm. C H length. D, ca. 17.5 cm. C H length.



E, ca. 22.5 cm. C H length. F, ca. 27.5 cm. C H length. G, ca. 32.5 cm. C H length. H, ca. 37.5 cm. C H length. I, ca. 42.5 cm. C H length. J, ca. 47.5 cm. C H length. K, ca. 52.5 cm. C H length.


The volumetric formulae of the right hemisphere volume, left hemisphere volume, and both hemisphere volume (table 43) are all expressed by the simple formula:

Y = {aX)b

in which Y is the value to be determined in cc. ; X, the crownheel length in cm., and a and h are constants for the respective volumes.

Brain stem and spinal cord growth. The growth of the brain stem and spinal cord, as shown by curves of absolute linear dimensions and absolute volumes, represents a second definite type of growth in the central nervous system. It is characterized by a relatively rapid absolute and relative increase previous to the sixth fetal month and a slow increase during the last four months of intra-uterine life.

The linear deterixiinations showing this type of growth are the frontospinal length, the spinal cord length, and the brain-cord length. When plotted against crown-heel length in centimeters and reduced to percentages of new-born values (fig. 29, curves

VII, VIIT, and IX) these three curves approximate one another and ascend more rapidly prior to the sixth fetal month than they do in the last four months. They are distinctly separated from the cerebral type of growth and, when calculated in fetal months and reduced to a per cent of the new-born (fig. 33, curves VII,

VIII, and IX, respectively), they show even more clearly the almost identical path which thej^ all follow. When calculated to time, they likewise show a rapid increase to the fifth fetal month and a comparatively slow one thereafter. The rates of growth of the brain stem and the spinal cord as shown by these three Unear determinations can be observed equally well when taken for 5 cm. intervals (fig. 25, curves VII, VIII, and IX, respectively), or when calculated for age in fetal months (fig. 27, curves VII, V, and VI, respectively). The brain stem and spinal cord grow at a slower rate both relatively and absolutely than do all other brain parts during the last four months of fetal life.

The classification indicated by comparison of the absolute linear curves is substantiated by a glance at their respective formulae (table 43). The growths of most of the group are expressed by the general empirical formula:

Y = {aXy - c

in which Y is the brain-part value in cm., X is crown-heel length in cm., and a, b, and c are constants determined separately in each case for the frontal spinal length, spinal cord length, and the brain-cord length.

Two other straight-line measurements, one of the colliculi length and the other of the pons length, do not follow the typical brain stem and spinal cord type of growth for some unknown reason. They are straight-line curves and evidently express the growth of some specific factor rather than the growth of the brain stem of which they are a part.

The brain stem and cord growth are portrayed also in the curves of the spinal cord volume, the pons and medulla volume, and the midbrain volume. When calculated against crown-heel length (fig. 30, curves X, VHI, and XI, respectively), these volume curves show a relatively rapid absolute growth previous to the sixth month and a slow growth in the last four months of fetal life. They also approximate each other and fall definitely above the cerebral type of growth curve. They are practically identical when calculated against fetal months and reduced to a per cent of the new-born value (fig. 36, curves VI, IV and V, respectively). When the percentage increments of the spinal cord volume, the pons and medulla volume, and the midbrain volume are compared (either when calculated for 5-cm. C H intervals (fig. 26, curves X, VIII, and IX, respectively) or for age in fetal months (fig. 28, curves I, II, and III, respectively)), the distinctive types of the brain stem and spinal cord growth are observed. They show a slow rate of relative growth in the third month, which increases three-fold in rapidity in the fourth month. From this time until birth the growth rate decreases in rapidity so that these portions show a less rapid relative increase in the last three fetal months than does any other brain part.

The classification is indicated also by volumetric formulae (table 43) which can be expressed by the general equation:

Y - 0.01 [{aXy+c]


in which Y is the value desired in cc, X is the crown-heel in cm., and a, h, and c, are constants determined for the spinal-cord volume, the pons and medulla volume, and the midbrain volume.

Cerebellum growth. Cerebellum growth, as shown by linear and volume absolute curves, proceeds slowly until the sixth fetal month, and from that time until birth outstrips all other growth activities in the central nervous system.

The lineal determinations expressing this type of growth are the vermis cerebelli length and the vermis cerebelli height (fig. 29, curves III and IV) . If plotted against crown-heel length and reduced to per cents of their new-born values, they lie close together and ascend slowly at first and then more rapidly to birth in very shallow concave curves. They are decidedly different from all other straight-line absolute curves of the nervous system, resembling volumetric curves rather than lineal progressions. They show a similar definite classification when calculated against fetal months (fig. 33, curves III and IV). The rate of growth of the cerebellum, as shown by the percentage increment curves of the vermis cerebelli length and the vermis cerebelli height either when calculated for 5-cm. C H intervals (fig. 25, curves III and IV) or for age in fetal months (fig. 27, curves VIII and IX), reflect the cerebellum tj^e of growth. During the last four fetal months the percentage increment of the vermis cerebelli length and the vermis cerebelli height is higher by 8 to 10 per cent than all other linear percentage increment curves of the central nervous system.

A consideration of the vermis cerebelli length and the vermis cerebelli height formulae (table 43) shows the volumetric tendency of these linear formulae. They can be expressed by the general empirical formula:

Y = 0.01 (Z" + h)

in which Y is the value desired in cm., X is crown-heel in cm., and a and h are constants determined for both the vermis cerebelli length and the vermis cerebelli height.

The curve of the volume of the cerebellum is striking in character and demonstrates the slow growth of the structure prior to the sixth fetal month and the tremendously rapid increment from that time until birth. When calculated against crown-heel length (fig. 30, curve VII), and also when calculated against time in fetal months (fig. 36, curve III), the distinct character of the cerebellum volume is apparent. The formula of the growth curve of the cerebellum (table 43) is also characteristic, although it falls with the same general formula as the brain stem and spinalcord volume, viz.:

Y = 0.01 [{aX)b + c]

However, it will be noticed that the b factor is 4.9 in the case of the cerebellum volume. This means that while the spinal cord volume, midbrain volume, and the pons and medulla volume are increasing practically as the cube and therefore Hke typical volume curves, the cerebellum volume is growing at a rate approaching the ninth power of the body length. The percentage mcrement of the cerebellum volume both when calculated for 5-cm. C H intervals (fig. 26, curve VII) or for age in fetal months (fig. 28, curve IV), also demonstrates a specific type of growth and shows the great increment of the part in the later fetal months as indicated by other measurements of cerebellum growth.

Compound growth. Compound growth indicates a summation of two or all types of growth in the central nervous system. It is typified by the volume and weight of the encephalon and the central nervous system volume. It is dominated by the growth of the cerebrum, since the cerebrum ranges between 85 and 95 per cent of the encephalon throughout fetal life. The rates of growth of the compound growth curves, as shown by percentage increments calculated for 5-cm. intervals (figs. 26, curves I, II, and III) and for fetal months (fig. 28, curves VI, VII and VIII), approximate the growth rate of the cerebrum. However, it will be noticed that in the early fetal months the rate of growth is not quite so high, due to the slow development of the other brain parts at this period.

The volumetric formulae (of the type here presented) of the central nervous system, the entire brain volume, and the encephalon weight require a third constant in their expression, while the volume of the cerebral hemispheres can be expressed mathematically with two constants. The general empirical formula of compound growth can be expressed:

Y = {oX)b + c

in which Y is the volume of the encephalon or entire central nervous system in cc, X is the crown-heel length in cm,, and a, b, and c are constants separately determined for the entire brain volume and the central nervous system volume.

The significance of the relation between lirieal and volumetric dimensions in the growth of the parts of the brain. The classification of the types of growth of the central nervous system is shown by both the volume and linear curves. For instance, both the volume curve of the cerebellum and the linear measurements of the vermis cerebelli length and the vermis cerebelU height indicate the characteristic cerebellum type of growth. It is logical that there should be a definite relation between the linear and the volume measurements of a brain part. It is also evident that the length of a brain part when it is cubed should form a curve identical in type and constant in relationship to the corresponding volume curve, provided that no additional factor, other than that which influences the growth in the linear dimensions, influences the growth in volume. Such a relationship actually exists between the formulae of the linear cerebellum curves and the formula of the cerebellum curve of volume. The formula for the cerebellum length when cubed is practically identical to the formula of the cerebellum volume. This relationship is seen somewhat better when those values are based on the cube of the body length as modified by three constants rather than by a formula based on the body length raised to a fractional exponent. The first formula is expressed below:

Cerebellum volume (cc.) = [0.01 (0.073 Vermis cerebelh length (cm.) +2.85)^]'^

Likewise, the formula of the cerebellum height when cubed and multipHed by the constant 2.13 is practically identical with the formula of the cerebellum volume:


Cerebellum volume (cc.) + [0.01 (0.07 Vermis cerebelli height (cm.) = 2.45)^]^

These indicate that the cerebellum volume is growing at relatively the same rate as are its vertical and horizontal diameters. The growth of the cerebellum must be controlled, therefore, by factors which act alike upon the entire cerebellum.

The formulae of the fronto-occipital length and the temporal diameter when cubed bear no relation to the cerebrum volume which may be expressed by a simple constant, and the same holds true of the spinal cord length when cubed. It is obvious, therefore, that in all other brain parts except the cerebellum there must be more than one factor influencing growth which act differently on the volumetric and linear growth.

The per cent of the brain parts and the spinal cord of the encephalon. The per cent which the various brain parts and the spinal cord form of the encephalon at each fetal month can be observed by a glance at table 40 and at figures 7, 11, 15, 18, 22, and 38. Table 40 tabulates the per cent which a respective volume of a brain part or of the spinal cord forms of the encephalon. Figures 7, 11, 15, 18, and 22 demonstrate graphically the per cent which the pons and medulla, midbrain, and the spinal cord, respectively, form of the encephalon volume. Figm^e 38 represents a series of composite midsagittal sections which are based upon average measurements and which represent therefore a typical fetal brain for the 5-cm. C. H. interval indicated. For purpose of comparison, a magnification of each individual figure was used. To obtain this magnification, the ratio of the respective frontooccipital diameters to the fronto-occipital diameter of the newborn was used. The detailed results of both figures and the table have been presented in the body of this paper. Taken in toto, the evidence shows conclusively : first, the high percentages which the pons and medulla, midbrain, and the spinal cord volumes form of the encephalon volume from the second to the fifth fetal month; second, the increased percentages w^hich the cerebellum volume forms of the encephalon volume in the last three fetal months, and, third, the predominating percentages which the volume of the cerebral hemispheres form of the encephalon volume at all times, rising to its maximum per cent (94.2 per cent) in the sixth fetal month.

Summary

I. The growth of the central nervous system in the fetal period is similar in general character to the growth of the other viscera and of the major parts of the body in this period.

II. An analysis of data on the volume and dimensions of the central nervous system in the fetal period shows four distinct subtypes or varieties of growth. These are:

1. The cerebral subtype, which is characterized by, a) a steady and relatively slow increase in volume from the second to the beginning of the sixth fetal month and a constant and more rapid increase from this time to birth, and, b) by a steady and constant growth in linear dimensions from the second fetal month to birth.

2. The brain stem and cord subtype, which shows a much more rapid growth from the second to the end of the fifth fetal month than it does in the last five months of fetal life.

3. The cerebellum subtype, which proceeds very slowly from the second to the end of the fifth fetal month and then increases tremendously from the sixth month to birth.

4. The compound subtype, which represents the combined effect of two or three or all of the above varieties, predominated by the cerebral subtype.

III. The factors which control the various subtypes of growth in the central nervous system may influence the volumetric and linear determinations of a respective brain part in two ways: 1) the factors may act differently upon the volumetric and linear values as they do in the case of the cerebral growth, brain stem, and cord growth, and in compound growth, or, ,2) they may act in the same manner as they do in the case of the cerebellum subtype of growth.

IV. An estimation of the percentages which the cerebrum, cerebellum, and the brain stem form of the encephalon at the various periods of fetal life offers a means of comparison of the relatiYe growth of these parts. The percentages which the brain stem and the spinal cord form of the encephalon are relatiYely high from the second to the fifth fetal month; the per cent which the cerebellum form of the encephalon is at its height in the last three fetal months, while the per cent wliich the hemispheres form of the encephalon reaches its maximum in the sixth fetal month. V. The four subtypes of growth of the central nervous sj^stem may be clearly expressed by a classification of the empirical formulae of the growth curves of the various parts as follows:

1. Cerebral growth:

a. General linear formula: Y = aX ± b.

b. Specific linear formulae:

a'. Front o-occipital diameter: Y = 0.175 X + 0.25. b'. Temporal diameter: Y = 0.138 X + 0.3.

c. General volumetric formula : Y = {aX)b.

d. Specific volumetric formulae:

a'. Right hemisphere volume: Y = (0.1 X)^i^ b'. Left hemisphere volume: Y = (0.105 X)-"^. c'. Both hemisphere volume : Y = (0.12 X)^-^^

2. Brain stem and cord growth:

a. General linear formula: Y = (aX)& — c. ■

b. Specific linear formulae:

a'. Fronto-spinal length: Y = (2.0 X)-^" - 2.2. b'. Spinal cord length: Y = (10.0 X)«' - 4.0. c'. Brain cord length: Y = (10.0 X)-^^ - 4.0.

c. General volumetric formula: Y = 0.01 [(aX)^ + c].

d. Specific volumetric formulae:

a'. Spinal cord volume: Y = 0.01 [(0.17 X)^"

+ 11.0]. b'. Pons and medulla volume: Y = 0.01 [(0.2 X)^"

+ 20.0]. c'. Midbrain volume :r = 0.01 [(0.168X)- ^« + 12.0].

3. Cerebellum growth:

a. General linear formula: Y = 0.01 [X" + b].

b. Specific linear formulae :

a'. Vermis cerebelh length: Y = 0.01 [X^^^ + 0.15]. y. Vermis cerebelh height: Y = 0.01 [X'-].

c. General volumetric formula: Y = 0.01 [{aXy + c]. rf. Specific volumetric formula:

a'. Cerebellum volume: Y = 0.01 [(0.095 Xy-^ + 20.0]. 4. Compound growth:

a. General volumetric formula: Y = {aXy + c. h. Specific volumetric formulae:

a'. Encephalon volume: Y = (0.125 X)»i« + 1.5. h'. Brain and spinal cord volume:

Y = (0.114 xy-^^ + 2.0.

c'. Encephalon weight by literature:

Y = (0.13 X)»-i9 + 1.0.

(In all of the above formulae, Y is the volume or length of the part under consideration (in cm. or cc), X is the crown-heel or total length of the body in cm., and a, b, and c are empirically determined constants.)


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Cite this page: Hill, M.A. (2021, January 20) Embryology Paper - The growth of the central nervous system in the human fetus as expressed by graphic analysis and empirical formulae (1921). Retrieved from https://embryology.med.unsw.edu.au/embryology/index.php/Paper_-_The_growth_of_the_central_nervous_system_in_the_human_fetus_as_expressed_by_graphic_analysis_and_empirical_formulae_(1921)

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