Cell Tiss. Res. 170, 341-351 (1976)
Cell and Tissue Research ~i by Springer-Verlag 1976
Ovarian Follicles of Normal NMRI Mice and Homozygous "Nude" Mice 1. Quantitative Methodological Study in the Pubescent "Node" Mouse* ** P. S p r u m o n t * * * Department of Anatomy, University of Fribourg, Switzerland (Head: Prof. A. Faller)
Summary. It is possible to determine statistically the repartitions of shapes or sizes in a population of particles from the recurrence of shapes or sizes of their outlines in microscopical sections. This method was applied to a population of 1326 follicular profiles randomly sampled from 30 ovaries of pubescent homozygous "Nude" mice. Under experimental conditions, the follicles were not spherical but could be assimilated to prolate ellipsoids with a mean eccentricity of 0.81. The average radius of the follicles taken as a whole was 20.2 • 0.7 (S.E.) gm. From these, the average radius of only the non-primary follicles was 58.1 _+ 1.3 (S.E.) gm. The volumetric repartition of the ovarian follicles indicated that 62~o of the total follicular mass was made of follicles with a radius greater than 115 gm, although these represent only 2~o of the total number of follicles. Key words: "Nude" mice - Ovarian follicles - Morphometry Introduction Ovaries contain numerous corpuscles of various sizes according to age and physiological state. These corpuscles, the follicles, are readily observed, counted and measured with the light microscope. They have previously been investigated quantitatively especially in rodents such as the hamster (Greenwald, 1961, 1974; Moore and Greenwald, 1974), rat (Mandl and Zuckerman, 1952; Mariana, 1972; de Reviers and Maul6on, 1973; Goldenberg et al., 1973; Land et al., 1974), mouse Send offprint requests to: P. Sprumont, Institut d'Anatomie de l'Universit6, 1, rue Albert Gockel, CH-1700 Fribourg, Switzerland * Dedicated to Professor Dr. Drs. h.c.W. Bargmann on the occasion of his 70th birthday ** The present work was partly performed at the Department of Histology, University of Louvain (Belgium) under tenure of a Personal Career Grant from the Swiss National Science Foundation *** I wish to thank Prof. P. Baudhuin (Louvain) and Dr. A. Achour (Fribourg) who made their computing facilities available. The technical skills of Mrs. H. Toffel are gratefully acknowledged. My thanks as well to Miss M. Aebischer for typing the manuscript and help with the computer data.
342
P. Sprumont
(Peters, 1969; Pedersen, 1969, 1970; Ryle, 1969, 1972) and vole (Peters and Clarke, 1974). Fundamentally, the ovarian finite volume includes a variable number of follicles with various shapes and sizes. These tridimensional corpuscles can only be appreciated from bidimensional microscopical sections. In order to ascertain their spatial dimensions, most authors (Mandl and Zuckermann, 1952; Ryle, 1969; Mariana, 1972; de Reviers and Maul6on, 1973; Greenwald, 1974; Moore and Greenwald, 1974) have identified and measured "the equatorial section" from each follicle, taking as a standard the presence of the oocyte nucleolus in the section. They thus postulated that follicles possess a spherical shape, the center of which was located inside the oocyte nucleus. Greenwald (1961) and Pedersen (1969) considered as "equatorial" the follicular profile with the largest area. An extensively used classification was proposed by Pedersen and Peters (1968) who took as standards the oocyte diameter and the localization and number of granulosa cells. However, the exact identification of "the equatorial section" of a follicle is increasingly more difficult to ascertain as the size of the follicle increases and as its shape differs from that of a sphere. Therefore, to gain objectivity, a more precise morphometric method should not have to take into consideration such a section. Wicksell (1925, 1926) developed a method allowing statistical determination of the frequency distribution either of shapes or of sizes of spherical, spheroidal and ellipsoidal corpuscles from randomized sections, provided that no more than one section is measured per corpuscle. This method was more recently applied by Baudhuin and Berthet (1967) and Weibel et al. (1969) and extensively investigated by Baudhuin (1968) for a quantitative study of liver mitochondria in electron microscopical sections. The present work uses the same method to determine the size and shape frequency distributions of the ovarian follicles in "Nude" mice at the age of 28 days, the onset of puberty occurring from the 30th day on in this species.
Material and Methods Animals Twelve female and four male mice heterozygous for the "Nude" gene were obtained through the courtesy of Dr. Cordier (Histology Department, University of Louvain). They were the first progeny from matings of homozygous Nu/Nu sires with conventional NMRI dams. A small colony was developed from these 16 original animals in a conventional environment without special lighting but with temperature maintained at 23~ + 1~C. In this colony, no female homozygous Nu/Nu mice were ever fertile. The present investigation was undertaken on animals bom from heterozygous Nu/NMRI females mated with homozygous Nu/Nu males. Fifteen female "Nude" mice from different litters were isolated and kept together from the age of 21 days.
Histological Techniques The mice were killed by cervical dislocation at 28 days of age. Ovaries were dissected out under a stereoscopical microscope, immediately weighed and fixed by immersion in Bouin-Hollande's fluid (Nezelof et al., 1972) for 72 h. After embedding in Paraplast | they were serially sectioned at 5 ~tm.
Ovarian Follicles in Pubescent " N u d e " Mice
343
Section thickness was checked several times during the procedure by perpendicular re-embedding of section samples. The actual thickness was found to be within a range of 4.8 to 5.3 ~tm. All sections were numbered and stained with PAS followed by Mayer's or Ehrlich's haematoxylin.
Measuremen ts One section per ovary was analyzed. To avoid mistakes due to possible inhomogeneity in the repartition of the follicles within the ovary, the sections were selected by n u m b e r from a table of r a n d o m numbers. A total of 30 microscopical sections were measured. Measuring was performed on the screen of a Reichert Visopan microscope at a calibrated magnification of 515. All follicular profiles in each section were measured by means of a graduated cross which could be moved on the screen, without taking account of presence of an oocyte profile. Only obvious atretic follicles showing more than 20~o of pycnotic figures a m o n g the granulosa cells were discarded from the measurements. A final number of 1326 follicular profiles were consistently analyzed. Each follicular profile was considered to be limited by the PAS-positive basement m e m b r a n e surrounding the granulosa. The longest diameter was measured first and the longest axis perpendicular to that diameter was then evaluated. Both lengths from one follicle were noted as a pair in m m (Fig. 1).
Determination of Eccentricities From measurements of longer (a) and shorter (b) diameters, the eccentricity (e) of each profile could be computed as e =
~/ ~ ,
hence e = 0 in circular profiles and reaches 1 in infinitely elongated
profiles. Eccentricities were ordered into ten classes of width 0.1. They were normally considered as taken from prolate ellipsoids. Nevertheless, calculations were also performed assuming that the profiles e came from oblate ellipsoids with an eccentricity e" = ~ and corrected according to Wicksell (1926). The procedure of Wicksell (1926) for prolate ellipsoids was applied to the frequency distribution of measured eccentricities, after having divided each frequency from the distribution by 1/1 - e 2, e taken at the center of the class and being thus 0.05 for the first and 0.95 for the tenth class. The resulting series of reduced frequencies was multiplied by e. (1 - e2) 1/3 from the assumption that e varied independently of the follicular volumes (Wicksell, 1926). This hypothesis was later statistically confirmed. From the final results, the corrected mean eccentricity and its variance as well as the relative frequency distribution of the corrected eccentricities could be easily computed. Wicksell's correction (1926) for prolate eccentricities was applied twice, the first time to all observed profiles, the second time only to those with an eccentricity equal to or greater than 0.1. The second computation was designed to suppress completely a measurement artifact: in smaller profiles, the observer could not distinguish an axial length difference and tended thus to overestimate the number of circular profiles. The final result from this second correction gave an overestimation of the mean: some of the discarded profiles were actually circular.
Determination of Radii The method of spherical reduction was applied according to Wicksell (1925). The radius of each follicle was assumed to be equal to the geometrical mean 1/a • b/2 of the halves of its measured axes, a and b having been divided by the magnification. The first step of the calculation was to find the largest radius and to determine mean and variance of the observed follicular radii. These radii were ordered in frequency distribution by a class width of 2 ~tm and submitted to the procedure of Wicksell (1925). The corrected numerical parameters of the population having been expressed, the final histograms were computed by grouping together the frequencies of five or ten "small" classes. The same procedure was applied twice to each of the classifications, the first time to the whole of the follicular profiles and
344
P. Sprumont
Fig. 1. Part of a section of an ovary from a 28 day-old "Nude" mouse. In this micrograph, considered as a measuring screen, three follicles (numbered 1, 2 and 3) can be measured. Their axes (a and b) are marked by a black line. Mean radius and eccentricity are, for profile of follicle 1:137.9 tam and 0.82, for profile of follicle 2:32.0 tam and 0.49, for profile of follicle 3:17.9 tam and 0. The presence of the oocyte within the follicular profiles is not a prerequisite. The thick bar measures 100 tam
Ovarian Follicles in Pubescent " N u d e " Mice
345
the second time only to those follicular profiles, the observed radius of which was found to be greater than 20 Bm, in order to exclude from the data all profiles arising from primary follicles.
Indirect Volumetry The mean percentage of ovary follicular volume occupied by the follicles of each size was computed from the corrected size frequency distribution (Wicksell, 1925). The cube of the middle of each class was multiplied by 4/3~ and by the corrected frequency of the class. The results were expressed in percent of the assumed total volume.
Computing Procedures The above-described calculations were performed by a F O R T R A N IV program and using as a subroutine a sequence derived from that of Baudhuin (1968). The program also traced the histograms of all frequency distributions, Its size was approximately 22,000 bytes.
Results and Discussion
Follicular Shape The observed eccentricities were distributed as shown in the histogram of Fig. 2A. Wicksell's corrections resulted in a displacement of the histogram peak towards the right (Figs. 2B and C). These histograms represent the real distribution of eccentricities in the follicular population. Statistical parameters are given in Table 1. There was no discrepancy of the results expressed in terms of prolate and oblate ellipsoids. It was thus assumed that the follicles could be assimilated to prolate ellipsoids since the oblate shape, being more or less flattened, is most unprobable in the case of ovarian follicles. One question remains unsolved, whether the follicles are non-spherical in the living ovary or whether their elongated shape is clue to a processing artifact. A compression of the tissue due to sectioning did indeed occur Table 1. Eccentricity of ovarian follicles in 28 day-old " N u d e " mice (Figures in brackets correspond to oblate eccentricities) Observed data
Results after Wicksetl's Correction on all profiles (n = 1326)
on profiles with observed eccentricity > 0.1 (n = 1295)
Mean prolate eccentricity
0.64 (0.98)
0.81 (1.18)
0.81
Standard deviation
0.18 (0.50)
0.17 (0.54)
0.15
Standard error
0.03 (0.01)
0.02 (0.06)
0.02
1.30
! .69
1.72
Corresponding axes ratio a/b
346
P. Sprumont
and the reduction in width of the sections was evaluated at about 8~o. This compression certainly accounts for most of the eccentricity of the profiles. The ellipsoidal shape of ovarian follicles in microscopical sections raises some doubt about the concept of equatorial sections centered on the oocyte nucleolus or even the nucleus (Mandl and Zuckermann, 1952; Ryle, 1969; Mariana, 1972;
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Fig. 2 A - C . Histograms from normalized frequencies of follicular eccentricity. One star equals one percent. The values have been rounded to the next integer and the middle of each class is inscribed in the abscissa. A Repartition of observed eccentricities. B Corrected eccentricities from all profiles. C Corrected eccentricities from profiles with an eccentricity greater than 0.1. The repartition is more or less gaussian
Ovarian Folliclesin Pubescent"Nude" Mice
347
de Reviers and Maul~on, 1973; Greenwald, 1974; Moore and Greenwald, 1974). If this concept is accepted in the case of smaller follicles, it must be rejected when the follicle includes a developed antrum with a polar disposition of the oocyte. This is the case in most maturing and mature follicles. Measurement of radii from such "equatorial sections" are always underestimations of reality, with an average error of 3.5~o, the error being greater the larger the follicle. Such mistakes induce underestimations of more than 10~o of the mean volume. The concept of equatorial sections corresponding to the largest follicular profiles (Greenwald, 1961; Pedersen, 1969) is geometrically more accurate.
Follicular Size
In 28 day-old " N u d e " mice, the largest observed follicular radius was 178.3 gm. The statistical parameters of the sizes population are given in Table 2. There was no correlation between follicular size and shape (r = 0.08). The eccentricity varying independently of the radius, it was consequently valid to use Wicksell's procedure for determining the real size distribution of the follicular population (Wicksell, 1926). Moreover, the application of spherical reduction was also valid: for the mean corrected shape values of the follicular population, the approximation due to spherical reduction may be compared to the sampling errors in a frequency curve determined by the method of moments from 1000 observations (Wicksell, 1926). The corrected distribution of follicular sizes is documented in the histograms of Fig. 3. They all present more than one mode and correspond thus to a nonnormal population. If all observed follicles are considered (Fig. 3 B), the first peak is located in the class of follicles with a radius of up to 10 gm, which evidently are "primary" follicles. The second mode includes the follicles with a mean radius ranging from 40 to 60 gin. These are growing follicles in which the oocyte nearly reaches dimensions equivalent to those of the mature stage (type 5 A of Pedersen and Peters, 1968). If only those follicles are considered, having a profile radius longer than 20 jam, their number being 722, the corrected histogram allows a better analysis of the repartition of maturing and mature follicles (Fig. 3 C). Apart from the highest
Table 2. Radius of ovarian folliclesin 28 day-old "Nude" mice Observed data
Results after Wicksell's correction on all profiles (n = 1326)
on profileswith radius > 20 gm (n = 722)
Mean radius (gm)
39.5
20.2
58.1
Median Standard deviation Standard error of the mean
25.7 38.3 1.1
9.8 26.0 0.7
48.1 35.8 1.3
0
5.00 15.00 25.00 35.00 45.00 55.00 65.00 75.00 85.00 95.00 105.00 I15.00 125.00 135.00 145.00 155.00 165.00 175.00 185.00
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Fig. 3 A - C . Histograms from normalized frequencies of ~llicular radius. The values in the abscissa are in micrometers. Same scale as in Figure 2. A Repartition of observed radii by a class width of 10 pm. B Corrected frequency distribution from all profiles ~ r a class width of 10 pm. C Corrected frequency distribution from profiles with a radius greater than 20 ~m. The class width is 20 ~m
Ovarian Folliclesin Pubescent "Nude" Mice
349
peak between 20 and 60 jam, another peak appears at 130 ~tm, which extends towards the right. This peak corresponds to the maturing and mature follicles, where the antrum is conspicuous. As far as the radii are concerned, it appears that in pubescent " N u d e " mice, higher frequencies of non-primary follicles with two differents sizes are present. Such a distribution was not found by Pedersen (1969) in normal pubescent mice of the Bagg strain. However, his classification according to Pedersen and Peters (1968) did not directly account for size variations but for type variations of follicles. It is possible that follicles of identical type include corpuscles of various sizes. De Reviers and Maul6on (1973) have found that a size distribution similar to that described here does indeed exist in the pubescent rat. In this animal, there are two peaks of size frequencies: the first one for follicles with a radius of 55 jam and the second one for those with a radius of 120 jam, with another, less conspicuous, peak at 200 jam. These measurements were performed by measuring the area of "equatorial" sections centered on the oocyte nucleolus and are, therefore, somewhat under-estimated. The average radii were computed from the mean section areas published by these authors. Determinations of follicular radius according to Wicksell (1925) are liable to two types of errors, which were extensively discussed by Baudhuin (1968). Because of the corrected eccentricity of the follicles, the error value for the mean radii amounts to less than 8 ~ (Wicksell, 1926). It must, however, be pointed out that these eccentricities measured from paraffin sections are grossly overestimated because of the compression of the block. In order to assess the real significance of the section thickness variations, a simulation was performed in which the observed values were computed with an assumed section thickness of 6 jam instead of 5 jam. Even with such a crude overestimation, the variation of the computed mean radius was 1.7~o and the histograms were not altered. Keiding et al. (1972) have introduced a correction of Wicksell's procedure which provides a better analysis of the smaller profiles that eventually escape observation when their angle of intersection with the microtome is less than some fixed angle. This correction was not applied here since the diameter of the smallest follicles represents at least twice the section thickness. It can thus be considered that, in this particular case, the limiting angle of intersection with the microtome was extremely small and that Wicksell's procedure can be used as such.
Follicular Indirect Volumetry The proportion of follicular total volume occupied by follicles of given radius is illustrated in the histograms of Fig. 4. On the one hand, primary follicles with a radius smaller than 20 jam represent a negligible percentage of the follicular tissue (Fig. 4A), although their number is very high (Fig. 3 B). On the other hand, more than half the follicular volume is composed of follicles with a radius greater than 120 jam, although their number is small. When the radii of profiles smaller than 20 jam are omitted from the computation, there is but a slight difference in the volume distribution curve (Fig. 4B).
350
P. Sprumont 0
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3 0 . 0 0 $$ 50.00 70.00 90.00 110.00 130.00 ****************************** ************************* lq0,00 Fig. 4A and B. Histograms of corrected repartition of follicular volume. The follicles are ordered by radius with a class width of 20 ~tm. The ordinates give the percentage of total follicular volume occupied by the follicles of a given size. A Histogram from all observed profiles. B Histogram from profiles with a radius greater than 20 ~tm
According to de Reviers and Maul6on (1973) who measured the follicular size distribution variations in hypophysectomized rats injected with gonadotrophins, growth hormone and prolactin, those follicles with an "equatorial" section area of more than 50000 ixm2 (radius larger than 126 I~m) correspond to antral follicles secreting under the influence of FSH only. These authors found a positive correlation of the ovarian weight with the number of these large follicles. This correlation is confirmed by the present finding that follicles with a radius larger than 120 ~tm occupy 6 3 ~ of the follicular volume (Fig. 4A) in the pubescent "Nude" mouse. It is thus obvious that small variations in their number (since they account for less than 3 ~ of the total number of follicles, Fig. 3 B) will induce large variations of follicular volumetric repartition and so presumably also of ovarian weight.
References Baudhuin, P.: L'analyse morphologique quantitative de fractions subceUulaires. Th6se Louvain 1968 Baudhuin, P., Berthet, J.: Electron microscopic examination of subcellular fractions. II. Quantitative analysis of the mitochondrial population isolated from rat liver. J. Cell Biol. 35, 631-648 (1967)
Ovarian Follicles in Pubescent "Nude" Mice
351
Goldenberg, R.L., Reiter, E.O., Ross, G.T.: Follicle response to exogenous gonadotropins: an estrogen mediated phenomenon. Fertil. and Steril. 24, 121-125 (1973)
Greenwald, G.S.: Quantitative study of follicular development in the ovary of the intact or unilaterally 0varieetomized hamster. J. Repr0d. Fertil. 2, 351-361 (1961) Greenwald, G.S.: Quantitative aspects of follicular development in the untreated and PMS treated cyclic hamster. Anat. Rec. 178, 139 143 (1974) Keiding, N., Jensen, S.T., Ranek, L.: Maximum likelihood of the size distribution of liver cell nuclei from the observed distribution in a plane section. Biometrics 28, 813-829 (1972) Land, R.B., Reviers, M.-M. de, Thompson, R., Maul6on, P.: Quantitative physiological studies of genetic variation in the ovarian activity of the rat. J. Reprod. Fertil. 38, 29-39 (1974) Mandl, A.M., Zuckerman, S.: Cyclic changes in the number of medium and large follicles in the adult rat ovary. J. Endocr. 8, 341 346 (1952) Mariana, J.C.: Classification des follicules ovariens: principes et m6thodes d'6tude. Ann. Biol. anim. Biochim. Biophys. 12, 377-382 (1972) Moore, P.J., Greenwald, G.S.: Effect of hypophysectomy and gonadotropin treatment on follicular development and ovulation in the hamster. Amer. J. Anat. 139, 37-48 (1974) Nezelof, C., Galle, P., Hinglais, N.: Techniques microscopiques. 1st 6dition. Paris, Flammarion 1972 Pedersen, T.: Follicle growth in the immature mouse ovary. Acta endocr. (Kbh.) 62, 117-132 (1969) Pedersen, T.: Determination of follicle growth rate in the ovary of the immature mouse. J. Reprod. Fertil. 21, 81-93 (1970) Pedersen, T., Peters, H.: Proposal for a classification of oocytes and follicles in the mouse ovary. J. Reprod. Fertil. 17, 555 557 (1968) Peters, H.: The development of the mouse ovary from birth to maturity. Acta endocr. (Kbh.) 62, 98-116 (1969) Peters, H., Clarke, J.R.: The development of the ovary from birth to maturity in the Bank Vole (Clethrionomys glareolus) and the Vole (Microtus agrestis). Anat. Rec. 179, 241 251 (1974) Reviers, M.M. de, Maul6on, P.: Effect des hormones gonadotropes sur l'ovaire de ratte immature. Ann. Biol. anim. Biochim. Biophys. 13 hors-s6rie, 177-193 (1973) Ryle, M.: Morphological responses to pituitary gonadotrophins by mouse ovaries in vitro. J. Reprod. Fertil. 20, 307-312 (1969) Ryle, M.: The growth in vitro of mouse ovarian follicles of different sizes in response to purified gonadotrophins. J. Reprod. Fertil. 30, 395-405 (1972) Weibel, E.R., St~ubli, W., Gnagi, H.R., Hess, F.A.: Correlated morphometric and biochemical studies on the liver cell. I. Morphometric model, stereologic methods, and normal morphometric data for rat liver. J. Cell Biol. 42, 68-91 (1969) Wicksell, S.D.: The corpuscle problem. A mathematical study of a biometric problem. Biometrika 17, 84-99 (1925) Wicksell, S.D.: The corpuscle problem. Second memoir. Case of ellipsoidal corpuscles. Biometrika 18, 151 172 (1926)
Received February 22, 1976 / in final form March 26, 1976
Cell and Tissue Research ~i by Springer-Verlag 1976
Ovarian Follicles of Normal NMRI Mice and Homozygous "Nude" Mice 1. Quantitative Methodological Study in the Pubescent "Node" Mouse* ** P. S p r u m o n t * * * Department of Anatomy, University of Fribourg, Switzerland (Head: Prof. A. Faller)
Summary. It is possible to determine statistically the repartitions of shapes or sizes in a population of particles from the recurrence of shapes or sizes of their outlines in microscopical sections. This method was applied to a population of 1326 follicular profiles randomly sampled from 30 ovaries of pubescent homozygous "Nude" mice. Under experimental conditions, the follicles were not spherical but could be assimilated to prolate ellipsoids with a mean eccentricity of 0.81. The average radius of the follicles taken as a whole was 20.2 • 0.7 (S.E.) gm. From these, the average radius of only the non-primary follicles was 58.1 _+ 1.3 (S.E.) gm. The volumetric repartition of the ovarian follicles indicated that 62~o of the total follicular mass was made of follicles with a radius greater than 115 gm, although these represent only 2~o of the total number of follicles. Key words: "Nude" mice - Ovarian follicles - Morphometry Introduction Ovaries contain numerous corpuscles of various sizes according to age and physiological state. These corpuscles, the follicles, are readily observed, counted and measured with the light microscope. They have previously been investigated quantitatively especially in rodents such as the hamster (Greenwald, 1961, 1974; Moore and Greenwald, 1974), rat (Mandl and Zuckerman, 1952; Mariana, 1972; de Reviers and Maul6on, 1973; Goldenberg et al., 1973; Land et al., 1974), mouse Send offprint requests to: P. Sprumont, Institut d'Anatomie de l'Universit6, 1, rue Albert Gockel, CH-1700 Fribourg, Switzerland * Dedicated to Professor Dr. Drs. h.c.W. Bargmann on the occasion of his 70th birthday ** The present work was partly performed at the Department of Histology, University of Louvain (Belgium) under tenure of a Personal Career Grant from the Swiss National Science Foundation *** I wish to thank Prof. P. Baudhuin (Louvain) and Dr. A. Achour (Fribourg) who made their computing facilities available. The technical skills of Mrs. H. Toffel are gratefully acknowledged. My thanks as well to Miss M. Aebischer for typing the manuscript and help with the computer data.
342
P. Sprumont
(Peters, 1969; Pedersen, 1969, 1970; Ryle, 1969, 1972) and vole (Peters and Clarke, 1974). Fundamentally, the ovarian finite volume includes a variable number of follicles with various shapes and sizes. These tridimensional corpuscles can only be appreciated from bidimensional microscopical sections. In order to ascertain their spatial dimensions, most authors (Mandl and Zuckermann, 1952; Ryle, 1969; Mariana, 1972; de Reviers and Maul6on, 1973; Greenwald, 1974; Moore and Greenwald, 1974) have identified and measured "the equatorial section" from each follicle, taking as a standard the presence of the oocyte nucleolus in the section. They thus postulated that follicles possess a spherical shape, the center of which was located inside the oocyte nucleus. Greenwald (1961) and Pedersen (1969) considered as "equatorial" the follicular profile with the largest area. An extensively used classification was proposed by Pedersen and Peters (1968) who took as standards the oocyte diameter and the localization and number of granulosa cells. However, the exact identification of "the equatorial section" of a follicle is increasingly more difficult to ascertain as the size of the follicle increases and as its shape differs from that of a sphere. Therefore, to gain objectivity, a more precise morphometric method should not have to take into consideration such a section. Wicksell (1925, 1926) developed a method allowing statistical determination of the frequency distribution either of shapes or of sizes of spherical, spheroidal and ellipsoidal corpuscles from randomized sections, provided that no more than one section is measured per corpuscle. This method was more recently applied by Baudhuin and Berthet (1967) and Weibel et al. (1969) and extensively investigated by Baudhuin (1968) for a quantitative study of liver mitochondria in electron microscopical sections. The present work uses the same method to determine the size and shape frequency distributions of the ovarian follicles in "Nude" mice at the age of 28 days, the onset of puberty occurring from the 30th day on in this species.
Material and Methods Animals Twelve female and four male mice heterozygous for the "Nude" gene were obtained through the courtesy of Dr. Cordier (Histology Department, University of Louvain). They were the first progeny from matings of homozygous Nu/Nu sires with conventional NMRI dams. A small colony was developed from these 16 original animals in a conventional environment without special lighting but with temperature maintained at 23~ + 1~C. In this colony, no female homozygous Nu/Nu mice were ever fertile. The present investigation was undertaken on animals bom from heterozygous Nu/NMRI females mated with homozygous Nu/Nu males. Fifteen female "Nude" mice from different litters were isolated and kept together from the age of 21 days.
Histological Techniques The mice were killed by cervical dislocation at 28 days of age. Ovaries were dissected out under a stereoscopical microscope, immediately weighed and fixed by immersion in Bouin-Hollande's fluid (Nezelof et al., 1972) for 72 h. After embedding in Paraplast | they were serially sectioned at 5 ~tm.
Ovarian Follicles in Pubescent " N u d e " Mice
343
Section thickness was checked several times during the procedure by perpendicular re-embedding of section samples. The actual thickness was found to be within a range of 4.8 to 5.3 ~tm. All sections were numbered and stained with PAS followed by Mayer's or Ehrlich's haematoxylin.
Measuremen ts One section per ovary was analyzed. To avoid mistakes due to possible inhomogeneity in the repartition of the follicles within the ovary, the sections were selected by n u m b e r from a table of r a n d o m numbers. A total of 30 microscopical sections were measured. Measuring was performed on the screen of a Reichert Visopan microscope at a calibrated magnification of 515. All follicular profiles in each section were measured by means of a graduated cross which could be moved on the screen, without taking account of presence of an oocyte profile. Only obvious atretic follicles showing more than 20~o of pycnotic figures a m o n g the granulosa cells were discarded from the measurements. A final number of 1326 follicular profiles were consistently analyzed. Each follicular profile was considered to be limited by the PAS-positive basement m e m b r a n e surrounding the granulosa. The longest diameter was measured first and the longest axis perpendicular to that diameter was then evaluated. Both lengths from one follicle were noted as a pair in m m (Fig. 1).
Determination of Eccentricities From measurements of longer (a) and shorter (b) diameters, the eccentricity (e) of each profile could be computed as e =
~/ ~ ,
hence e = 0 in circular profiles and reaches 1 in infinitely elongated
profiles. Eccentricities were ordered into ten classes of width 0.1. They were normally considered as taken from prolate ellipsoids. Nevertheless, calculations were also performed assuming that the profiles e came from oblate ellipsoids with an eccentricity e" = ~ and corrected according to Wicksell (1926). The procedure of Wicksell (1926) for prolate ellipsoids was applied to the frequency distribution of measured eccentricities, after having divided each frequency from the distribution by 1/1 - e 2, e taken at the center of the class and being thus 0.05 for the first and 0.95 for the tenth class. The resulting series of reduced frequencies was multiplied by e. (1 - e2) 1/3 from the assumption that e varied independently of the follicular volumes (Wicksell, 1926). This hypothesis was later statistically confirmed. From the final results, the corrected mean eccentricity and its variance as well as the relative frequency distribution of the corrected eccentricities could be easily computed. Wicksell's correction (1926) for prolate eccentricities was applied twice, the first time to all observed profiles, the second time only to those with an eccentricity equal to or greater than 0.1. The second computation was designed to suppress completely a measurement artifact: in smaller profiles, the observer could not distinguish an axial length difference and tended thus to overestimate the number of circular profiles. The final result from this second correction gave an overestimation of the mean: some of the discarded profiles were actually circular.
Determination of Radii The method of spherical reduction was applied according to Wicksell (1925). The radius of each follicle was assumed to be equal to the geometrical mean 1/a • b/2 of the halves of its measured axes, a and b having been divided by the magnification. The first step of the calculation was to find the largest radius and to determine mean and variance of the observed follicular radii. These radii were ordered in frequency distribution by a class width of 2 ~tm and submitted to the procedure of Wicksell (1925). The corrected numerical parameters of the population having been expressed, the final histograms were computed by grouping together the frequencies of five or ten "small" classes. The same procedure was applied twice to each of the classifications, the first time to the whole of the follicular profiles and
344
P. Sprumont
Fig. 1. Part of a section of an ovary from a 28 day-old "Nude" mouse. In this micrograph, considered as a measuring screen, three follicles (numbered 1, 2 and 3) can be measured. Their axes (a and b) are marked by a black line. Mean radius and eccentricity are, for profile of follicle 1:137.9 tam and 0.82, for profile of follicle 2:32.0 tam and 0.49, for profile of follicle 3:17.9 tam and 0. The presence of the oocyte within the follicular profiles is not a prerequisite. The thick bar measures 100 tam
Ovarian Follicles in Pubescent " N u d e " Mice
345
the second time only to those follicular profiles, the observed radius of which was found to be greater than 20 Bm, in order to exclude from the data all profiles arising from primary follicles.
Indirect Volumetry The mean percentage of ovary follicular volume occupied by the follicles of each size was computed from the corrected size frequency distribution (Wicksell, 1925). The cube of the middle of each class was multiplied by 4/3~ and by the corrected frequency of the class. The results were expressed in percent of the assumed total volume.
Computing Procedures The above-described calculations were performed by a F O R T R A N IV program and using as a subroutine a sequence derived from that of Baudhuin (1968). The program also traced the histograms of all frequency distributions, Its size was approximately 22,000 bytes.
Results and Discussion
Follicular Shape The observed eccentricities were distributed as shown in the histogram of Fig. 2A. Wicksell's corrections resulted in a displacement of the histogram peak towards the right (Figs. 2B and C). These histograms represent the real distribution of eccentricities in the follicular population. Statistical parameters are given in Table 1. There was no discrepancy of the results expressed in terms of prolate and oblate ellipsoids. It was thus assumed that the follicles could be assimilated to prolate ellipsoids since the oblate shape, being more or less flattened, is most unprobable in the case of ovarian follicles. One question remains unsolved, whether the follicles are non-spherical in the living ovary or whether their elongated shape is clue to a processing artifact. A compression of the tissue due to sectioning did indeed occur Table 1. Eccentricity of ovarian follicles in 28 day-old " N u d e " mice (Figures in brackets correspond to oblate eccentricities) Observed data
Results after Wicksetl's Correction on all profiles (n = 1326)
on profiles with observed eccentricity > 0.1 (n = 1295)
Mean prolate eccentricity
0.64 (0.98)
0.81 (1.18)
0.81
Standard deviation
0.18 (0.50)
0.17 (0.54)
0.15
Standard error
0.03 (0.01)
0.02 (0.06)
0.02
1.30
! .69
1.72
Corresponding axes ratio a/b
346
P. Sprumont
and the reduction in width of the sections was evaluated at about 8~o. This compression certainly accounts for most of the eccentricity of the profiles. The ellipsoidal shape of ovarian follicles in microscopical sections raises some doubt about the concept of equatorial sections centered on the oocyte nucleolus or even the nucleus (Mandl and Zuckermann, 1952; Ryle, 1969; Mariana, 1972;
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Ovarian Folliclesin Pubescent"Nude" Mice
347
de Reviers and Maul~on, 1973; Greenwald, 1974; Moore and Greenwald, 1974). If this concept is accepted in the case of smaller follicles, it must be rejected when the follicle includes a developed antrum with a polar disposition of the oocyte. This is the case in most maturing and mature follicles. Measurement of radii from such "equatorial sections" are always underestimations of reality, with an average error of 3.5~o, the error being greater the larger the follicle. Such mistakes induce underestimations of more than 10~o of the mean volume. The concept of equatorial sections corresponding to the largest follicular profiles (Greenwald, 1961; Pedersen, 1969) is geometrically more accurate.
Follicular Size
In 28 day-old " N u d e " mice, the largest observed follicular radius was 178.3 gm. The statistical parameters of the sizes population are given in Table 2. There was no correlation between follicular size and shape (r = 0.08). The eccentricity varying independently of the radius, it was consequently valid to use Wicksell's procedure for determining the real size distribution of the follicular population (Wicksell, 1926). Moreover, the application of spherical reduction was also valid: for the mean corrected shape values of the follicular population, the approximation due to spherical reduction may be compared to the sampling errors in a frequency curve determined by the method of moments from 1000 observations (Wicksell, 1926). The corrected distribution of follicular sizes is documented in the histograms of Fig. 3. They all present more than one mode and correspond thus to a nonnormal population. If all observed follicles are considered (Fig. 3 B), the first peak is located in the class of follicles with a radius of up to 10 gm, which evidently are "primary" follicles. The second mode includes the follicles with a mean radius ranging from 40 to 60 gin. These are growing follicles in which the oocyte nearly reaches dimensions equivalent to those of the mature stage (type 5 A of Pedersen and Peters, 1968). If only those follicles are considered, having a profile radius longer than 20 jam, their number being 722, the corrected histogram allows a better analysis of the repartition of maturing and mature follicles (Fig. 3 C). Apart from the highest
Table 2. Radius of ovarian folliclesin 28 day-old "Nude" mice Observed data
Results after Wicksell's correction on all profiles (n = 1326)
on profileswith radius > 20 gm (n = 722)
Mean radius (gm)
39.5
20.2
58.1
Median Standard deviation Standard error of the mean
25.7 38.3 1.1
9.8 26.0 0.7
48.1 35.8 1.3
0
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Fig. 3 A - C . Histograms from normalized frequencies of ~llicular radius. The values in the abscissa are in micrometers. Same scale as in Figure 2. A Repartition of observed radii by a class width of 10 pm. B Corrected frequency distribution from all profiles ~ r a class width of 10 pm. C Corrected frequency distribution from profiles with a radius greater than 20 ~m. The class width is 20 ~m
Ovarian Folliclesin Pubescent "Nude" Mice
349
peak between 20 and 60 jam, another peak appears at 130 ~tm, which extends towards the right. This peak corresponds to the maturing and mature follicles, where the antrum is conspicuous. As far as the radii are concerned, it appears that in pubescent " N u d e " mice, higher frequencies of non-primary follicles with two differents sizes are present. Such a distribution was not found by Pedersen (1969) in normal pubescent mice of the Bagg strain. However, his classification according to Pedersen and Peters (1968) did not directly account for size variations but for type variations of follicles. It is possible that follicles of identical type include corpuscles of various sizes. De Reviers and Maul6on (1973) have found that a size distribution similar to that described here does indeed exist in the pubescent rat. In this animal, there are two peaks of size frequencies: the first one for follicles with a radius of 55 jam and the second one for those with a radius of 120 jam, with another, less conspicuous, peak at 200 jam. These measurements were performed by measuring the area of "equatorial" sections centered on the oocyte nucleolus and are, therefore, somewhat under-estimated. The average radii were computed from the mean section areas published by these authors. Determinations of follicular radius according to Wicksell (1925) are liable to two types of errors, which were extensively discussed by Baudhuin (1968). Because of the corrected eccentricity of the follicles, the error value for the mean radii amounts to less than 8 ~ (Wicksell, 1926). It must, however, be pointed out that these eccentricities measured from paraffin sections are grossly overestimated because of the compression of the block. In order to assess the real significance of the section thickness variations, a simulation was performed in which the observed values were computed with an assumed section thickness of 6 jam instead of 5 jam. Even with such a crude overestimation, the variation of the computed mean radius was 1.7~o and the histograms were not altered. Keiding et al. (1972) have introduced a correction of Wicksell's procedure which provides a better analysis of the smaller profiles that eventually escape observation when their angle of intersection with the microtome is less than some fixed angle. This correction was not applied here since the diameter of the smallest follicles represents at least twice the section thickness. It can thus be considered that, in this particular case, the limiting angle of intersection with the microtome was extremely small and that Wicksell's procedure can be used as such.
Follicular Indirect Volumetry The proportion of follicular total volume occupied by follicles of given radius is illustrated in the histograms of Fig. 4. On the one hand, primary follicles with a radius smaller than 20 jam represent a negligible percentage of the follicular tissue (Fig. 4A), although their number is very high (Fig. 3 B). On the other hand, more than half the follicular volume is composed of follicles with a radius greater than 120 jam, although their number is small. When the radii of profiles smaller than 20 jam are omitted from the computation, there is but a slight difference in the volume distribution curve (Fig. 4B).
350
P. Sprumont 0
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3 0 . 0 0 $$ 50.00 70.00 90.00 110.00 130.00 ****************************** ************************* lq0,00 Fig. 4A and B. Histograms of corrected repartition of follicular volume. The follicles are ordered by radius with a class width of 20 ~tm. The ordinates give the percentage of total follicular volume occupied by the follicles of a given size. A Histogram from all observed profiles. B Histogram from profiles with a radius greater than 20 ~tm
According to de Reviers and Maul6on (1973) who measured the follicular size distribution variations in hypophysectomized rats injected with gonadotrophins, growth hormone and prolactin, those follicles with an "equatorial" section area of more than 50000 ixm2 (radius larger than 126 I~m) correspond to antral follicles secreting under the influence of FSH only. These authors found a positive correlation of the ovarian weight with the number of these large follicles. This correlation is confirmed by the present finding that follicles with a radius larger than 120 ~tm occupy 6 3 ~ of the follicular volume (Fig. 4A) in the pubescent "Nude" mouse. It is thus obvious that small variations in their number (since they account for less than 3 ~ of the total number of follicles, Fig. 3 B) will induce large variations of follicular volumetric repartition and so presumably also of ovarian weight.
References Baudhuin, P.: L'analyse morphologique quantitative de fractions subceUulaires. Th6se Louvain 1968 Baudhuin, P., Berthet, J.: Electron microscopic examination of subcellular fractions. II. Quantitative analysis of the mitochondrial population isolated from rat liver. J. Cell Biol. 35, 631-648 (1967)
Ovarian Follicles in Pubescent "Nude" Mice
351
Goldenberg, R.L., Reiter, E.O., Ross, G.T.: Follicle response to exogenous gonadotropins: an estrogen mediated phenomenon. Fertil. and Steril. 24, 121-125 (1973)
Greenwald, G.S.: Quantitative study of follicular development in the ovary of the intact or unilaterally 0varieetomized hamster. J. Repr0d. Fertil. 2, 351-361 (1961) Greenwald, G.S.: Quantitative aspects of follicular development in the untreated and PMS treated cyclic hamster. Anat. Rec. 178, 139 143 (1974) Keiding, N., Jensen, S.T., Ranek, L.: Maximum likelihood of the size distribution of liver cell nuclei from the observed distribution in a plane section. Biometrics 28, 813-829 (1972) Land, R.B., Reviers, M.-M. de, Thompson, R., Maul6on, P.: Quantitative physiological studies of genetic variation in the ovarian activity of the rat. J. Reprod. Fertil. 38, 29-39 (1974) Mandl, A.M., Zuckerman, S.: Cyclic changes in the number of medium and large follicles in the adult rat ovary. J. Endocr. 8, 341 346 (1952) Mariana, J.C.: Classification des follicules ovariens: principes et m6thodes d'6tude. Ann. Biol. anim. Biochim. Biophys. 12, 377-382 (1972) Moore, P.J., Greenwald, G.S.: Effect of hypophysectomy and gonadotropin treatment on follicular development and ovulation in the hamster. Amer. J. Anat. 139, 37-48 (1974) Nezelof, C., Galle, P., Hinglais, N.: Techniques microscopiques. 1st 6dition. Paris, Flammarion 1972 Pedersen, T.: Follicle growth in the immature mouse ovary. Acta endocr. (Kbh.) 62, 117-132 (1969) Pedersen, T.: Determination of follicle growth rate in the ovary of the immature mouse. J. Reprod. Fertil. 21, 81-93 (1970) Pedersen, T., Peters, H.: Proposal for a classification of oocytes and follicles in the mouse ovary. J. Reprod. Fertil. 17, 555 557 (1968) Peters, H.: The development of the mouse ovary from birth to maturity. Acta endocr. (Kbh.) 62, 98-116 (1969) Peters, H., Clarke, J.R.: The development of the ovary from birth to maturity in the Bank Vole (Clethrionomys glareolus) and the Vole (Microtus agrestis). Anat. Rec. 179, 241 251 (1974) Reviers, M.M. de, Maul6on, P.: Effect des hormones gonadotropes sur l'ovaire de ratte immature. Ann. Biol. anim. Biochim. Biophys. 13 hors-s6rie, 177-193 (1973) Ryle, M.: Morphological responses to pituitary gonadotrophins by mouse ovaries in vitro. J. Reprod. Fertil. 20, 307-312 (1969) Ryle, M.: The growth in vitro of mouse ovarian follicles of different sizes in response to purified gonadotrophins. J. Reprod. Fertil. 30, 395-405 (1972) Weibel, E.R., St~ubli, W., Gnagi, H.R., Hess, F.A.: Correlated morphometric and biochemical studies on the liver cell. I. Morphometric model, stereologic methods, and normal morphometric data for rat liver. J. Cell Biol. 42, 68-91 (1969) Wicksell, S.D.: The corpuscle problem. A mathematical study of a biometric problem. Biometrika 17, 84-99 (1925) Wicksell, S.D.: The corpuscle problem. Second memoir. Case of ellipsoidal corpuscles. Biometrika 18, 151 172 (1926)
Received February 22, 1976 / in final form March 26, 1976
