Brain Research, 6fi9 (1993) 2 6 2 - 2 ~ '~:' 1993 Elsevier Science Publishers B.V. All rights reserved 0006-8993/93/$06.0fl
Total numbers of various cell types in rat cerebellar cortex estimated using an unbiased stereological method Lise Korbo, Birgitte Bo Andersen,
and Arne Moiler
Neurological Research Laboratory, Bartholin Instituttet, Kommunehospitalet Copenhagen, StereologicalResearch Laboratory, Aarhus University, Aarhus (Denmark) and Institute of Toxicology National Food Agency, Scborg (Denmark) (Accepted 17 November 1992)
Key words: Cerebellum; Cell number; Disector; Neurostereology; Rat; Stereology; Toluene; Vertical section
A new and efficient stereological method for estimating the total number of the different cell types in rat cerebellar cortex is presented. The cells have been subdivided into the following categories: Purkinje cells, granule cells, Golgi cells, glial cells in the granular layer, Bergmann glial cells and neurons and glial cells in the molecular layer. The method has been used to estimate the total number of some of the cell types in rats exposed to orally administered toluene at doses of 200, 400 and 800 m g / k g / d a y for 12 weeks compared with a control group. No statistically significant differences were found between the exposed and non-exposed animals. The described method can be used in a number of both biological and experimental studies. With the use of new stereological methods it is possible to get precise estimates of total cell numbers in a much shorter time than earlier required. This makes it possible to improve the reliability of the final result by increasing the number of cases processed.
INTRODUCTION Previous studies have estimated the total number of Purkinje cells in rat cerebellar cortex or, as is more often the case, estimated density (cells per unit volume) of different cell types in the rat cerebellar cortex 4,18,2°. All previous methods are rather time consuming and based on assumptions, which are influenced by histological procedures, tissue processing, etc. The described stereological method, which employs the disector principle 23, has been applied to several brain regions in both humans and animals 16'21. The method relies on the fact that one can without any assumptions regarding size, shape or orientation, count a cell the first time it is present in one focal plane and not in the previous one of adjacent planes. A subset of uniformly selected disectors, taken with a known, fixed but arbitrary probability is sufficient for the estimation of the total number of particles. In the disector cells are counted in three dimensions instead of two, producing unbiased results. An efficient modification of the physical disector, the optical disector 1°, has been
applied to human neocortex 7'2z and hippocampus in man 25 and to rats 26. In the present study the optical disector is used to estimate the total number of seven cell types in rat cerebellar cortex. Much is known about the structural organisation of the cerebellar cortex. In addition it is relevant to know the total number of the various cell types in cerebellar cortex and especially the ratio of cells to Purkinje cells. Besides the method can be used, as in this study, in screening for neurotoxicity resulting in cell degeneration in cerebellum. MATERIALS AND METHODS Brain preparation Twenty-five cerebelli from 7-month-old male Wistar rats were divided into three groups of differentially exposed animals and a control group (n = 9). The treated groups were exposed to toluene given oral doses of 200 (n = 6), 400 (n = 6) and 800 (n = 4) m g / k g / day, respectively, for 12 weeks, followed by a 4-week period without exposure prior to sacrifice. The brains were perfusion-fixed with formalin, removed from the cranium and fixed in phosphate-buffered formalin (pH 7.4) for 3 months. The cerebellum was dissected from the brain stem, weighed and divided into two hemispheres, cutting through the vermis at the
Correspondence: L. Korbo, Neurological Research Laboratory, Bartholin Institunet, Kommunehospitalet, DK-1399 Copenhagen K, Denmark. Fax: (45) (33) 938566.
263 midline. Each hemisphere was placed with the medial cut surface facing down. T h e left hemisphere was randomly rotated, see Fig. 1, and the right hemisphere was rotated clockwise 90 ° relative to the left one. The hemispheres were embedded in 7% agar and cut into 1-mm thick slabs to produce 8 - 1 0 slabs. T h e two hemispheres were placed side by side so parts of the two hemispheres were present in most of the slabs. By cutting in this m a n n e r the slabs were by definition vertical sections 2. All the slabs containing tissue were used to estimate the volume of the cerebellum, according to the principle of Cavalieri lI. Accordingly, each slab was viewed at 20 × in a stereomicroscope (Olympus XT_A0) with a test system with points spaced 1.5 × 1.5 m m 2 on transparent plastic placed randomly on each slab. All points on the grid hitting the tissue were counted. It should be mentioned that there was some overprojection in the estimate which was partly corrected using a correction formula 1° (see also Discussion). Each slab was then dehydrated in increasing concentrations of alcohol (70%, 2h; 96%, 2 h; 99%, 1 h) and e m b e d d e d in glycolmethacrylate (Historesin®). A section of 25 /~m thickness was cut from the anterior side of each e m b e d d e d slab and stained with a modified Weil's stain 24. Although several Nissl stains were tried in a pilot study, it was concluded that Weil's stain, even though it is a myelin stain, was best for distinguishing cytoplasm-surrounded neurons (with the exception of the granule cells) from nuclei of the glial cells, see Fig. 2.
Volume The resulting 8-10 sections from each cerebellum were used for estimation of the volume of the molecular layer and the granule layer using t h e Cavalieri principle. Because the Purkinje cell layer is so relatively thin at low magnification, it was not possible to estimate the volume of this layer separately, and it was included in the granule layer. The total volume of the cerebellum was also estimated to determine whether any shrinkage or swelling of the tissue had occurred
Fig. 1. Two cerebellar hemispheres seen from above are placed with the medial cut surface down. The left half is rotated randomly using a random n u m b e r between 1 and 12. The right half is rotated 90 ° clockwise to the left one. Orientated like this the two hemispheres are e m b e d d e d in agar and cut into 1-mm-slabs in the 10-4 direction. The random orientation of the hemispheres makes estimation of the surface area of cerebellum unbiased.
during embedding. Volume estimations were done by pointcounting at a magnification of 18 x using a projection microscope. The counting grid had a point density of 0.62 mm 2, corrected for magnification. The volumes (V) of the different layers were estimated using the Cavalieri-formula: V = ~a(p)XP
where ~ is the average thickness of the slabs of the cerebellum, that is, the average distance between sections (1 mm), a(p) is the area associated with each point of the grid, corrected for the magnification of the projected image, EP is the total number of points that hits the layer.
Surface An unbiased estimate of the surface of the cerebellum was obtained by counting all intersections between the cerebellar surface on all sections and the arcs of a projected cycloid test system at a final magnification of 18 × , see Fig. 3. The total surface area (S) was estimated using the following equation: 2
Xl --V l(p) X P
where 2~I is the number of intersections between the cycloids and the cerebellar surface, XP is the number of points hitting cerebellar tissue, and l(p) is the testline length per point. A vertical section is a plane section perpendicular to a given 'horizontal" plane. The meaning of a horizontal plane is only a plane of reference, which defines the orientation of the section. Four requirements must be fulfilled for the use of vertical sections. (1) Either the tissue must possess an identifiable (vertical) direction axis or it must be generated. (2) All the vertical sections must be parallel to the vertical, i.e., normal to the horizontal, and the vertical direction must be identified in each section. (3) Relative to the common horizontal plane, the vertical sections must have random positions and random rotations. (4) On the vertical section, a test line is given a weight proportional to the sine of the angle between the test line and the vertical direction. There are many ways to create correct test lines (see Baddeley et al.Z), but for the practical purpose of surface estimation on vertical sections, cycloids are the most .suitable. Surface area estimated on vertical sections, according to the principles outlined here, is free of any assumptions about shape. For further information on surface estimation on vertical sections, see Baddeley et al. z and Gundersen et al. lz.
264 F r o m the a r e a of surface a n d the v o l u m e of the m o l e c u l a r layer it was possible to e s t i m a t e the a v e r a g e thickness (7) of the m o l e c u l a r layer ?(mol) = V(mol)/S(pia)
Cell counts T h e u n b i a s e d e s t i m a t i o n of t h e total n u m b e r of cells was o b t a i n e d using the optical d i s e c t o r (Fig. 4), a m o d i f i c a t i o n o f the physical d i s e c t o r principle. T h e optical d i s e c t o r is a t h r e e - d i m e n s i o n a l p r o b e g e n e r a t e d with aid of a m i c r o s c o p e with a high n u m e r i c a l a p e r ture ( N A = 1.40) oil i m m e r s i o n objective, in which it is possible to o b s e r v e thin focal p l a n e s within a thick section. T h e m i c r o s c o p e is c o n n e c t e d via a v i d e o came r a to a v i d e o c o l o u r m o n i t o r . A m i c r o c a t o r , used to m e a s u r e d i s t a n c e s in t h e z axis, is m o u n t e d on the m i c r o s c o p e . A given v o l u m e within a thick section can
be d e f i n e d by the a r e a being o b s e r v e d a n d the dist a n c e s b e t w e e n the focal planes. T h e cells c o u n t e d in this v o l u m e constitute o n e e s t i m a t e of the n u m e r i c a l density. F o r f u r t h e r d e s c r i p t i o n , see G u n d e r s e n et al. 1°'~~. T h e m i c r o s c o p e stage is c o n n e c t e d to a set of motors, which are used to move the section in steps of a known length in the x - a n d y - d i r e c t i o n . C o m p u t e r g e n e r a t e d c o u n t i n g f r a m e s a r e s u p e r i m p o s e d on the v i d e o i m a g e of the section t h r o u g h a video G e n l o c k - c a r d using the G r i d software p a c k a g e , Bico A / S , G l o s t r u p , D e n m a r k . F o r f u r t h e r details, see K r e k u l e and G u n d e r s e n 17.
Counting procedure Every s e c o n d of the sections u s e d for v o l u m e a n d surface e s t i m a t i o n was u s e d for cell counting. Starting in o n e c o r n e r o f the section the m i c r o s c o p e stage was m o v e d step-wise in a m e a n d e r p a t t e r n over the e n t i r e
Fig. 2. The different cell types were best distinguished by using a modified Weil's stain. The following cell types are shown on the picture: * Purkinje cells, I~ neuron in molecular layer, t> glial cell in molecular layer, OBergmann glial cell, ~granule cell. The frame is placed on Purkinje cells seen at focus inside a thick section. All Purkinje cell nucleoli inside the frame and touching the dotted line are included in the counts, while all nucleoli touching the full drawn line are excluded from the counts. The marked Purkinje cells in focus are counted.
the section. A cell was defined to be in focus, w h e n its widest and most sharply defined nuclear profile was seen. T h e following cell types were c o u n t e d in five cerebelli: Purkinje cells, granule ceils, Golgi cells, B e r g m a n n glial cells, glial cells in the granular layer and n e u r o n s and glial cells in the molecular layer. In the 20 remaining cerebelli only Purkinje cells, granule cells and neurons and glial cells in the molecular layer were counted.
Fig. 3. Estimation of the cerebellar surface area was done by placing a cycloid test system on the projected image of each vertical section. All the intersections between the cerebellar pial surface and the arcs of the cycloid test system were counted. The vertical axis is perpendicular to the medial horizontally cut surface.
T h e Purkinje cells were c o u n t e d using the granular layer as the reference volume. A counting frame was applied with an area, a (frame), of 215 × 302 m m 2, a magnification of 2,350 x using a 60 x oil objective with N A = 1.40. O n average 80 disector samples were made per cerebellum. T h e cell was c o u n t e d if the nucleolus was in focus inside the counting frame. In a pilot study 300 Purkinje cells in all regions of the cerebellar cortex were examined in 40 ~ m thick sections, and only about 1% were found to have m o r e than one nucleolus.
Granule cells section. In a pilot study the step-length was adjusted to provide a sufficient n u m b e r of counting fields for every cell type (see below). F o r every counting frame it was n o t e d w h e t h e r the u p p e r right corner of the frame was inside the reference space (the layer) that contained a particular cell type. Using an unbiased counting frame 9 all the cells that c a m e into focus inside the frame were c o u n t e d as the focal plane was m o v e d 1 0 / z m t h r o u g h
These neurons were c o u n t e d using a counting frame of area, a (frame) = 20.5 x 50 m m 2, at a magnification of 3,900 x using a 100 × oil, N A = 1.40 objective. Approximately 50 disectors were sampled m a d e per cerebellum.
Golgi cells and glial cells in the granular layer T h e Golgi cells are large pale n e u r o n s in the granular layer. They are divided into large and small Golgi cells and are most n u m e r o u s just below the Purkinje cells and just above the white matter 2°. T h e L u g a r o cell 2° was included in this group. Only cells with identifiable cytoplasm were c o u n t e d as Golgi cells. Glial cells in the granular layer include both astrocytes, oligodendrocytes and a few microglial cells. All the cells were c o u n t e d using a frame with an area a (frame) of 215 x 302 m m 2 at a magnification of 2,350 x using a 60 x oil N A = 1.40 objective. O n average 60 disectors were used per cerebellum.
Bergman glial cells Fig. 4. The optical disector is used for counting the cells inside a given volume in a thick section. The optical disector consists of a microscope with a high NA oil immersion objective, a configuration which makes it possible to observe a thin focal plane inside a thick section. The microscope is connected via a video camera to a video monitor and a digital length gauge (microcator) measuring movements in the z-axis. The microscope is furthermore connected to a pair of motors, which make steps of a known length in the x- and y-axis. The computer-generated counting frames are superimposed on the video image of the section through a software package (see text).
B e r g m a n glial cells are large pale astrocytes lying just above the Purkinje cells TM, also referred to as Golgi epithelial cells 2°. These cells are larger and paler than the rest of the glial cells in the cerebellum and can easily be identified. T h e y were c o u n t e d using a frame with an area a (frame) of 1 5 0 x 1 0 3 m m 2, and a magnification of 2,350 x (60 x oil objective). O n average 80 disectors per cerebellum were sampled. T h e granular layer was used as reference volume.
266 "FABLE I Mean values of the parameters for the different groups Coefficient of variation (CV = SD/mean) shown in brackets. No statistically significant differences for any of the parameters were found between the exposed groups and the control group.
Control (9 animals) 200mg/kg/day (6 animals) 400mg/kg/day (6 animals) 800mg/kg/day (4 animals)
V fresh (mm 3)
V embedded (ram3)
Surface area (mm 2)
V mol layer (mm 3)
V gr layer (mm 3)
V white matter (mm 3)
t mol. layer (mm)
357 (0.067) 329 (0.080) 343 (0.019) 349 (0.068)
277 (0.091) 261 (0.090) 287 (0.037) 270 (0.031)
231 (0.134) 211 (0.099) 247 (0.126) 218 (0.150)
373 (0.178) 330 (0.194) 360 (0.127) 327 (0.149)
90 (0.141) 82 (0.215) 91 (0.245) 71 (0.249)
71 (0.133) 63 (0.169) 75 (0.125) 67 (0.178)
70 (0.206) 67 (0.159) 81 (0.178) 80 (0.171)
0.24 (0.110) 0.25 (0.068) 0.25 (0.204) 0.22 (0.233)
N e u r o n s a n d glial cells in the m o l e c u l a r layer Stellate cells, basket cells a n d glial cells of the
Total n u m b e r o f neurons T h e total n u m b e r ( N ) of the different cells in rat
molecular layer were c o u n t e d using a frame with a n area a (frame) of 74 x 102 m m 2 at a m a g n i f i c a t i o n of
c e r e b e l l a r cortex was d e t e r m i n e d from:
2,350 × (60 x oil objective). O n average 100 disectors
s a m p l e d per
cerebellum. Only cytoplasm-sur-
~Q- v Ev (dis)
r o u n d e d nuclei with a n u c l e o l u s were d e f i n e d as n e u rons.
Statistical m e t h o d T h e u n p a i r e d S t u d e n t ' s t-test was used t h r o u g h o u t .
N u m e r i c a l density T h e n u m e r i c a l density N v, the ratio of the total n u m b e r of nerve cells to the total v o l u m e of the
g r a n u l a r or m o l e c u l a r layer, is
Weights, surface areas a n d v o l u m e s of the cerebelli in the four groups of rats are shown in T a b l e I. T h e total n u m b e r s of the different cell types are listed in
where E Q - is the total n u m b e r of a p a r t i c u l a r cell type c o u n t e d in a total disector v o l u m e E V (dis), V (dis) = h • a (frame), h the height of the disector (10 ~ m ) a n d a (frame) is p r e s e n t e d above for the different
T a b l e II. No statistically significant differences bet w e e n the t r e a t e d groups a n d the control g r o u p were f o u n d for any of the p a r a m e t e r s . T h e ratio of Golgi cells a n d P u r k i n j e cells was f o u n d to be essentially 1 : 1 (CV = S D / m e a n = 0.23), a n d for every P u r k i n j e cell
9.65 n e u r o n s in the m o l e c u l a r layer were f o u n d (CV =
TABLE II Total number of cells (10 6) The mean values of the total cell numbers for the different groups. The estimates of Golgi cells, Bergmann glial cells and glial in the granular layer have only been done on five control animals. Coefficient of variation (CV = SD/mean) shown in brackets.
Number of animals Purkinje Granule Neurons in Mol.layer Glial in Mol.layer
Control 9 0.61 (0.214) 265 (0.246) 6.90 (0.217) 8.54 (0.356)
Number of animals Golgi cells Bergmann Glial in gr.layer
Control 5 0.64 (0.160) 4.90 (0.255) 2.18 (0.327)
200 mg/kg/days 6 0.73 (0.204) 273 (0.133) 5.39 (0.358) 9.86 (0.168)
400 mg/kg/day 6 0.71 (0.227) 300 (0.111) 6.39 (0.350) 8.77 (0.292)
800 mg/kg/day 4 0.71 (0.221) 289 (0.144) 6.32 (0.490) 6.82 (0.149)
267 0.40). For the granule cells a ratio of 419 granule cells for every Purkinje cell was found (CV = 0.22). The density of granule cells ( N v) was 4.0.106 cells per mm 3 (CV = 0.40). DISCUSSION This study presents the first unbiased estimation of the total number of all major cell types in rat cerebellar cortex. Although some difficulties were encountered when attempting to identify all the glial cells in the granular layer due to the presence of the densely packed granule cells, this had no consequences for the estimate of the granule cells, since the glial cells only constitute about 1% of the granule cells. It is possible that a slightly higher number of glial cells would have been found if a specific glial cell staining were used. The differentiation of Golgi and glial cells in the granular layer was also problematic. However, only cells with a clearly identifiable cytoplasm and a nucleolus were counted as Golgi cells. Estimation of total cerebellar volume was done twice: at the level of a macroscopic volume with a slice thickness of 1 mm, and after histological processing with a section thickness of 25/xm. The volume shrinkage, estimated as the difference between the two estimates, was 15-20%. The first measurement was biased, since the total area estimated at 20 x , on slabs with a thickness of only 1 / 5 to 1 / 1 0 of the diameter of the organ creates overprojection. This was partly compensated for by the use of a correction formula for convex objects. The second volume measurement after processing might be influenced by tissue shrinkage during the histological processing. The two volume estimates did not deviate more than 20%, and the shrinkage was approximately the same in all the four groups. However, the total volume of the unprocessed cerebellum is only used to estimate shrinkage, and therefore does not influence the total number of the different cell types. The method is rather efficient. The total number of, e.g., granule cells in the cerebellar cortex can be estimated with a coefficient of error of about 12% in less than 1 hour. The estimation of the total number of all the seven cell types takes about 8 h per cerebellum. The total number of Purkinje cells has previously been estimated to range from 200,000 to 500,00015,19. In a study 8 approximately 200,000 Purkinje cells in 30to 60-days-old rats was found using an approximation of the fractionator principle described by Gundersen 1°. No data are available on the total number of the remaining cell types. The ratio of granule cells to Purkinje cells have been estimated to range from 335
to 8973'18'19 . In this study the ratio is found to be 419 granule cells per Purkinje cell. Compared to results for the human cerebellum 1, the number of Purkinje cells is 45 x higher in the human cerebellum compared to the rat, but the density is 0.81 • 103 Purkinje cells per mm 3 compared to 10.1 • 103 Purkinje cells per mm 3 for the rat. The density of granule cells in the human cerebellum is found to be 2.7.106 ceils per mm 3, which is 1.5 times less than the density of granule cells in rat cerebellar cortex. For the ratio of cells a higher number of cells per Purkinje cell were found in the human cerebellum, for example 3,300 granule cells for one Purkinje cell has been found 1'5 compared to 419 for the rat. For Golgi cells, a ratio of 2.7 related to Purkinje cells in human cerebellum was found, compared to a ratio of 1 in the rat. Finally, for neurons in the molecular layer a ratio of 54.5 was found in the human cerebellum, compared to a ratio of 9.65 neurons in the molecular layer per Purkinje cell in the rat. These findings confirm what previously has been reported 18-2°, that in the human cerebellum a much higher number of neurons per Purkinje cell is found compared to cerebellum in other mammals. Optimizing the estimation of total cell number in rat cerebellar cortex An average of 50 disectors per cerebellum was used for estimation of the total number of granule cells. This sample size provides a coefficient of error (CE) of 0.12, which is quite acceptable, since the contribution to the total variance between animals is only 1/4: C E 2 / C V 2 = 0.122/0.242= 0.25. For the Purkinje cells on average 80 disectors were used per cerebellum, but because of the inhomogeneous distribution of the Purkinje cells in the granular layer, CE was still as large as 0.17. A number of disectors of 100-150 will only cause a little extra work and will provide an estimate with a better precision. The rest of the cell estimates have CE's between 0.11 and 0.18. A good way of improving the precision of the densities would be to use all sections for counting cells and adjust the distances between disectors accordingly. Acknowledgements. The authors wish to thank Hans J0rgen G. Gundersen for his excellent advice with design and statistics and Hans J0rgen Jensen, Lykke Steffensen, Susanne Primdahl and Lone Nielsen for their skilful technical assistance. We also wish to thank for the support given by Sygekassernes Helsefond, The Lundbeck Foundation, The Boel Foundation and Erik H0rslev og hustru Birgit H0rslevs fond. REFERENCES 1 Andersen, B.B., Korbo, L. and Pakkenberg, B., Quantitative stereology in the human cerebellum, J. Comp. Neurol., in press.
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