CHAPTER 2
Protocol How to Use the Optical Fractionator:
an Example Based on the Estimation of Neurons in the Hippocampal CA1 and CA3 Regions of Tree Shrews
J.I.H. Keuker
1, G.K. Vollmann-Honsdorf
1, E. Fuchs Brain Research Protocols 7(3): 211-221, 2001
1 J.I.H. K. and G.K. V.-H. should be considered cofirst authors by virtue of their contributions to this work.
Abstract
Until recently, exposure of the hippocampus to prolonged elevated glucocorticoid levels was thought to result in damage and loss of pyramidal neurons. Most of the earlier studies were based on measures of neuronal density and used assumptions- based counting methods. Using a stereological technique, the optical fractionator, which eliminates potential biases inherent in the assumption-based techniques, we were able to demonstrate that chronic psychosocial stress in tree shrews has no effect on neuronal number in the hippocampal CA1 and CA3 regions. The present report will focus on the practical aspects of the optical fractionator, by describing in detail how to estimate the total number of neurons in the hippocampal CA1 and CA3 regions of tree shrews. In this example the group sizes have been increased over those used in the earlier study. The present study supports our previous conclusion that stress does not affect the number of hippocampal neurons in the CA1 and CA3 areas as suggested by other authors. The results obtained with the optical fractionator can be used to estimate the precision of the data.
Theme:
Other systems of the CNS Topic:
Comparative neuroanatomy Keywords:
Quantification Stereology Optical fractionator Cell loss Neuronal loss Degeneration
2.1. Type of research
The protocol can be used for the quantification of the number of cellular and sub-cellular structures and is applicable for all parts of the nervous system.
§ Estimating the total number of objects, e.g. neurons or glia, in a fast, simple, efficient, and unbiased manner.
§ Compatibility of the data with procedures for making estimates of the precision of the study.
§ Optimizing the amount of work required for a study with a desired level of precision.
This includes reducing the number of animals in a study to a minimum by providing a strategy for calculating the number of animals needed in an experiment.
2.2. Time required
§ Perfusion: half a day.
§ Embedding in glycolmethacrylate: 2 days.
§ Sectioning and staining depending on the amount of sections: 3-4 h per block.
§ Counting plus calculation of the total number of particles: 3-4 h per structure.
2.3. Materials
The experiment was conducted with adult male tree shrews (Tupaia belangeri; bodyweight ± 200 g) from the breeding colony at the German Primate Center (Göttingen, Germany; for details about housing see Fuchs (1999)).
Adult male tree shrews display an intense territoriality that can be used to establish a naturally occurring stressful situation under experimental control in the laboratory (Fuchs et al., 1996). The experimental design for this paradigm of psychosocial conflict has previously been described in detail (Fuchs et al., 1996). After a 7-day pre-stress period, psychosocial stress was induced by introducing a naive animal into the cage of a dominant animal. The animals readily engaged in a competition for the territory, and after establishment of a clear dominant/
subordinate relationship, the two males were separated by a transparent wire mesh barrier.
During the following 28-day period meant to induce psychosocial conflict, the wire mesh was removed every day for approximately one hour. Under these conditions the subordinate animals (n=7) displayed characteristic subordination behavior. Eight control animals lived in separate quarters elsewhere in the animal facility. At the end of the experiment, the animals were transcardially perfused (see 2.4.1) and the brains investigated. All animal experimentation was conducted in accordance with the European Communities Council Directive of November 24th, 1986 (86/EEC) and was approved by the Government of Lower Saxony, Germany.
2.3.1. Special equipment
§ Microscope (e.g. Zeiss III RS, Carl Zeiss, Oberkochen, Germany), 2.5´ or 6.3´ objective lens (Zeiss Plan, numerical aperture (N.A.) 0.08 or 0.16 resp.), 40´ objective lens (e.g. Zeiss Neofluar, N.A. 0.75) and 100´ oil objective lens (Zeiss Neofluar, N.A. 1.3).
§ Videocamera (e.g. CF 15/2, KAPPA opto-electronics GmbH, Gleichen, Germany), video monitor (e.g. Sony Triniton KX-14CP1), defined stepping motor in x,y axes (LUDL Electronic Products, Hawthorne, NY, USA), electronic microcator (Heidenhahn MT 12, Dr. Joh.
Heidenhahn GmbH, Traunreut, Germany) attached to the z axis of the microscope, controller
(MAC 2000 Communicator Interface, LUDL Electronic Products), computer with a monitor (e.g.
Sony CPD-200GS 16” viewing image) and stereology software program (e.g.
STEREOINVESTIGATOR3.16, MicroBrightField, Colchester, VT, USA).
2.3.2. Chemicals and reagents
§ 4% paraformaldehyde (Merck, Darmstadt, Germany) in 0.1 M phosphate buffer (PB; pH 7.2).
§ 96% ethanol.
§ Glycolmethacrylate plastic resin Technovit 7100 consisting of three components (Kulzer, Weinheim, Germany), fast-curing methylmethacrylate-based resin Technovit 3040 consisting of two components (Kulzer).
§ Cresyl violet (Aldrich, Milwaukee, WI, USA), methylene blue and azur II (115943 and 109211, Merck), Eukitt mounting medium (O. Kindler GmbH & Co., Freiburg, Germany).
2.4. Detailed procedure 2.4.1. Tissue processing
Animals were anaesthetized with 1 ml of a mixture of 50 mg ketamin (Ketavet®, Pharmacia &
Upjohn, Erlangen, Germany), 10 mg xylazin (Rompun®, Bayer, Leverkusen, Germany) and 0.1 mg atropin (WDT, Hannover, Germany) dissolved in 1 ml double distilled water. The animals were transcardially perfused with 100 ml of a 0.9% NaCl solution, followed by 200 ml 4% paraformal- dehyde in 0.1 M PB, pH 7.2. For more information about how to prepare the paraformaldehyde solution, see Fujioka (1993). To avoid post-perfusion artefacts (Cammermeyer, 1978), the entire head of each animal was post-fixed in fresh fixative at 4°C overnight, after which the brains were gently removed from the skulls. The hippocampal formation was then dissected from each of the brains. To preserve the characteristic three-dimensional structure of the tissue, the hippocampi were embedded in glycolmethacrylate resin (Technovit 7100). The surface of such plastic sections have been shown to be very regular when compared to paraffin sections (Helander, 1983).
2.4.1.1. Embedding in glycolmethacrylate
The hippocampi were placed separately in standard paraffin embedding cassettes and the fixative was removed from the tissue blocks by washing in double distilled water for 16 h. The tissue was dehydrated for 8 h in 70% ethanol and, subsequently, 16 h in 96% ethanol. The tissue blocks were then pre-infiltrated with 96% ethanol and base liquid Technovit 7100, mixed in equal volume parts, for approximately 8 h. Infiltration with the stock solution (1 g hardener I dissolved in 100 ml base liquid of Technovit 7100) took place for 16 h. All washing and infiltration steps took place in a beaker placed on a stirring magnet at room temperature. For polymerization, hardener II was mixed with the stock solution according to the user instructions. Before this polymerization solution was prepared, small pieces of filter paper were placed on the bottoms of the plastic molding tray cavities. The polymerization fluid was then poured into the cavities, and within 5 minutes, the hippocampi were positioned in the filled cavities. Each cavity with a specimen was filled with polymerization fluid to the upper edge of the molding tray. The plastic was cured at room temperature. After approximately 2 h, the plastic blocks were ready for further processing.
The non-polymerized supernatant was removed with tissue paper. To fasten the glycol- methacrylate blocks in the microtome, specimen adapters were mounted on top of the resin blocks by fixing the adapters with the fast-curing Technovit 3040, as described in the user instructions.
This was done while the polymerized blocks were still in the molding tray. After approximately one hour, the mounted plastic blocks were removed from the molding tray cavities and the sectioning was started.
2.4.1.2. Sectioning
Each complete plastic block was serially sectioned at a thickness of 30 µm with a rotating microtome (Leica RM 2065) using a histoknife with D-grinding on a 5° cutting angle. To avoid fractures in the sections, the plastic block was slightly moistened with distilled water for approximately 15–30 seconds before a section was cut. The speed of sectioning was relatively low, approximately 2 mm/sec for the microtome specimen holder. On the Leica RM 2065 microtome with the electronic control panel, this speed corresponded to 20% of the maximum cutting speed.
The sections were collected with a brush and/or tweezers, floated on a bath filled with distilled water at room temperature, and picked up from underneath with a glass microscope slide. The sections were immediately dried on a 60°C heating plate and stored overnight in an oven at the same temperature.
2.4.1.3. Staining
Not every section was evaluated with the optical fractionator technique. Consequently, only the sections to be used were stained (for details about the selection of sections, see paragraph 2.4.2).
However, the remaining sections may be stored until completion of the study, because it may be desirable to change the sampling scheme (see 2.4.2), and e.g. to include extra sections in the study.
In our experiment, we used the following staining solution: 80 ml of standard cresyl violet solution were mixed with 20 ml methylene blue solution and 20 ml azur II solution and heated to 60°C (for exact protocols see Romeis (1989)). The sections were stained for 2 min in the staining solution at 60°C and then rinsed in double distilled water at room temperature. If necessary, the sections could be differentiated in 1% acetic acid for a few seconds and washed in double distilled water again. The sections were dried on a heating plate of 60°C, mounted with Eukitt and coverslipped.
2.4.2. Stereology
In this paragraph, the properties and application of the optical fractionator will be explained. The optical fractionator is a combination of the optical disector, a 3- dimensional probe used for counting, and fractionator sampling, a scheme involving the probing of a known fraction of the tissue (West et al., 1991). Three sampling fractions are used with the optical fractionator method. First, the section sampling fraction (ssf) represents the proportion of microscopical sections of the entire, serially sectioned brain structure that is sampled for evaluation. The area sampling fraction (asf) corresponds to the proportion of the sectional area that is investigated within the sampled sections. And finally, the thickness sampling fraction (tsf) captures the part of the investigated cross-sectional area of the sampled sections. The estimated total number of particles (N) of a brain structure in an animal is obtained by multiplying the reciprocals of the fractions with the total particle count (SQ-) per brain structure, obtained with the optical disectors (West et al., 1991):
The size of the region of interest (ROI) is implicitly determined from the combination of these fractions. This means that, with the optical fractionator technique, no information of the size of the ROI or the magnification of the microscope is needed.
This also implies that this counting technique is independent of e.g. swelling and/or shrinking of the tissue during processing (West, 1993a; Howard and Reed, 1998).
A pilot study is helpful to design an efficient sampling scheme for the determination of the ssf, asf, and tsf. As shown by Gundersen et al. (1987), sampling of 100-200 particles, counted on 10–20 evenly distributed sections, is sufficient for almost all studies. As a thumb rule, 100–200 disectors are used on the set of sampled sections to count 100-200 particles, i.e. on average 1–2 particles should be counted per optical disector. With this empirical approach, we determined all dimensions of the sampling fractions and optical disectors in a pilot study. If the variation between the animals is not known, it is recommended that the pilot study is performed with five animals per group, because if the number of particles is found to be e.g. decreased in all five individuals of one experimental group, the probability of this event happening by chance is less than 5% (P = (½)5» 0.03), and the experiment could be conclusive (Cruz-Orive and Weibel, 1990; West, 1994). Thus, after this pilot study it can be decided whether additional animals should be included or additional sampling is necessary to achieve the goal of the study (see also 2.4.2.1) (West, 1999).
As an example, our experiment on pyramidal neurons in the CA3 region of the tree shrew hippocampal formation will be outlined in the forthcoming descriptions of optical disector counting with fractionator sampling. To yield unbiased estimates of the total number of neurons in a brain region, all sampling should be done systematically and randomly, which means a random choice (of e.g. a section) within the first interval and sampling (of e.g. further sections) at predetermined intervals thereafter throughout the entire region. The ssf was chosen as follows: 15–20 sections at equally spaced intervals along the entire extent of the hippocampal formation were selected. One tree shrew hippocampus was on average represented on 115 sections. Dividing 115 by 20 gives 5.75, so every 6thsection of the hippocampal formation was selected to include approximately 20 sections in the ssf. Starting with the 4thsection, which was randomly selected with a random number table, section numbers 4, 10, 16, etc., were analyzed. The ssf was consequently1/6. If the intra- and inter-individual variabilities of the tissue under investigation have not yet been established, it is advisable to keep all sections of the entire brain structure until the pilot study is completed, so that the section sampling fraction can be adjusted, e.g. when the statistically relevant sampling error has to be reduced. The description of estimating the precision of the study is presented under 2.4.2.1.
Subsequently, the dimensions the optical disector were determined. The optical disector is an imaginary cube that is placed into the section (Fig. 2.1). The optical disector has three exclusion sides, which can be defined as the front, the top, and the left side of the cube (Fig. 2.2). The function of the exclusion sides is to equally divide the space around the optical disector to assure that all objects, regardless of different size and
orientation, have an equal probability of being counted. The square or rectangle in the x,y plane, i.e. parallel to the sectional plane, is called the counting frame of the optical disector (Fig. 2.2). From the top view, the exclusion sides appear as the left and bottom lines of the optical disector counting frame (Fig. 2.2). These exclusion lines are extended into infinity to take into account that not all biological objects are round. The computer system produces a 2-dimensional image of the optical disector, representing the counting frame, on the monitor. With help of the microcator, an electronic device that measures the vertical displacement of the microscope stage, and with the x,y stepping motor attached to the microscope stage, the virtual position of the counting frame is moved within the z direction and x,y plane of the section, respectively. A video image of the actual microscopic field of the real section, which is moved in x, y, and z directions, is additionally displayed on the computer screen. Counting neurons with the optical disector means that, as one moves the focal plane downwards over a specified depth through a single thick sections, one counts the particles with the superimposed counting frame and unbiased counting rules, explained in the following.
Figure 2.1
Schematic representation of a section with optical disector counting locations. The x,y-plane is the sectional plane; the z-direction depicts the cross-sectional plane. Shown are the area sampling fraction (asf) and the thickness sampling fraction (tsf). The imaginary optical disector is placed in the section, and is moved from one lower left corner of the imaginary mesh grid to the next. The rough-cut surface represents one quadrant of the imaginary mesh grid. The product of the distances in x- and y-directions in the mesh grid form the area of the x,y step, A(x,y step).
The area sampling fraction is thus the quotient of the area of the optical disector counting frame, a(frame), and the A(x,y step). The thickness sampling fraction is determined by the ratio of the height of the disector counting frame (h) and the measured section thickness (t). Because of section surface irregularities, the distance between the section surface and the optical disector should be 4 µm on both sides (guard zones).
Abbreviations: x and y = x,y distances in the mesh grid that define the disector positions, A(x,y step) = area associated with each x,y step of the stepping motor, h = height of the optical disector, t = section thickness, a(frame) = area of the optical disector counting frame, thick black lines = exclusion lines, dark gray frame of optical disector = top exclusion side
The optical disector counting rules ensure that all objects regardless of their size, shape, or orientation have an equal probability of being sampled. The principle of the unbiased counting rules of the optical disector is as follows: all particles which are partly or fully located within the optical disector are counted – provided that they do not in any way touch the (extended) exclusion sides (marked with thick, black lines in Figs.
2.1 and 2.2) or the top plane of the optical disector (dark gray in Figs. 2.1 and 2.2). A particle that lies in a counting location should not be counted more than once. Therefore, a specific attribute of the particle of interest should be chosen as a counting criterion, that is possessed by every such particle to be counted, yet this attribute has to be unique (Sterio, 1984; Gundersen et al., 1988; Howard and Reed, 1998). A cell nucleus may be used to apply the counting rules on (for some series of photographs, see West et al. (1991) and West (1994)). In such studies, a neuron is counted, when (i) the top of the nucleus first comes into focus, (ii) this nuclear top is situated within the depth of the optical disector, and (iii) the edge of the nucleus at this focal depth does not touch an exclusion line of the counting frame (Gundersen et al., 1988; Pakkenberg and Gundersen, 1988; West and Gundersen, 1990; West, 1990; West et al., 1991; Sousa et al., 1998a). One may also choose the clearest visible center of the nucleus as a counting criterion, as long as the counting criterion during an experiment is always the same. Two investigators may detect a “top of the nucleus” or “center of the nucleus” in different focal planes, and may therefore include or exclude the same object differently into the counts. This so-called “early” or
“late” recognition will probably not influence the estimate of the neuron number (West et al., 1991). However, for better reproducibility a more objective counting criterion may be chosen. In the present study, we applied the counting rules for optical disector counting of neurons as follows (Vollmann-Honsdorf et al., 1997). With the optical disector counting frame a neuron was counted, when its nucleolus first came into focus and, at this focal plane in the optical disector, the nucleus was within the 2-dimensional counting frame, not touching any exclusion line or its extensions. In addition, the focal plane in which the nucleolus first came into focus may not have been in the top plane of the optical disector. However, the nucleolus may have been outside the 2-dimensional frame of the optical disector, because the nucleolus only defined the focal plane in the z-axis of the optical disector probe. When a nucleus with more than one nucleoli was encountered, we always took into account the first nucleolus of a complete nucleus that came into focus.
To assess the fraction of the section thickness (tsf), the average thickness of the sections was measured during the counting procedure with the microcator in at least 5 of the selected sections at various random places. The optical components of the microscope should yield highest resolution and precision possible (see also 2.6.2.3). The height of the optical disector should be approximately 8 µm less than the section thickness, so that it can be placed at least 4 µm from the top and bottom of any surface irregularity. The tsf is the height of the optical disector divided by the section thickness.
After processing of 30 µm glycolmethacrylate sections, the measured section thickness in
our experiment was between 21 and 27 µm; we used an optical disector height of 15 µm, and an upper guard zone of 4 µm. It should be mentioned that “early” or “late”
recognition of the top and bottom planes of a section during measuring the section thickness may cause biases in an estimate of neuron number (West et al., 1991).
Therefore, sections thinner than 20 µm should be avoided, and glycolmethacrylate sections are to be preferred over paraffin and cryostat sections.
The area sampling fraction (asf) is defined by the ratio of the counting frame area and the product of the distances between the optical disector positions in the x and y directions within the sectional plane of each section: a(frame)/A(x,y step) (see also Fig.
2.1). Therefore, both a(frame) and A(x,y step) were figured out by trying and changing the dimensions in the stereology software while counting in a representative section. In a heterogeneous region like the Cornu Amonis (CA) of the hippocampal formation, a
Figure 2.2
Detailed view of the optical disector. Exclusion sides of the optical disector are defined as the top, the front and the left side of the cube. From the top view of the section, the 3-dimensional optical disector appears as a 2-dimensional frame in the x,y plane (dark gray), of which the left and the bottom line plus the extensions (marked with the thick, black lines) are “forbidden”. In addition, the first focal plane of the disector (dark gray) is an exclusion side.
In the basic counting rule depicted in this figure, only tops of particles are counted, i.e. particles are counted when they first come into focus, provided the visible small intersected top plane of the particle does not touch an exclusion line or side in this focal plane. Therefore, a particle with its top in the uppermost optical plane of the optical disector is also excluded from being counted.
These basic counting rules can be slightly modified (see paragraph 4.2).
All three particles shown in the figure are partly or fully located in the optical disector. The tops of the particles do not touch the upper plane of the optical disector. However, particle number 1 is not counted, because it touches the left exclusion side, exactly where the top of the particle is in focus. Particle 2 lies completely within the optical disector and does not touch any line and is thus counted. Particle 3 is partly inside the optical disector, and its top exactly cuts a non-forbidden side, and is counted as well.
Thick black lines = exclusion lines, dark gray frame of optical disector = top exclusion side
representative number of pyramidal neurons can be found on sections from a middle position of the septotemporal axis of the hippocampus (Table 2.1). The dimensions of the a(frame) were tested first. Using a lower magnification, the area of interest, e.g. the hippocampal CA3 region, was delineated. The appropriate dimensions of the asf were tested in the delineated area only, with the highest possible objective lens to identify the counting criteria on the computer screen. The x and y dimensions of the optical disector counting frame were defined such that the average number of particles counted per optical disector (with a height of 15 µm) was about 1–2 (see Table 2.1). For the purpose of first establishing proper dimensions of a(frame), the x and y measures of the imaginary mesh grid (see below) were provisionally set at e.g. 200 ´ 200 µm. In our experiment, the area of the counting frame was slightly bigger than the neurons themselves. When dispersely distributed or larger particles are counted, the frame area needs to be larger to count approximately 1–2 particles per disector on average. In our pilot experiment, the a(frame) in hippocampal CA3 area was chosen 520 µm2. The counting frame should be a square or close to a square.
When the approximate dimensions of the counting frame had been determined, and 1-2 neurons were counted per optical disector with the counting rules explained above and in Figure 2.2, the x and y measures of the A(x,y step) were worked out in the representative section. An imaginary mesh grid with changeable x and y distances was created by the computer system and randomly superimposed onto the section, and optical disectors were placed in e.g. each lower left corner of the mesh grid (see Fig. 2.1). Notice that, like sampling of the sections to be investigated, systematic random sampling is applied on the level within sections as well. Neurons were counted in all optical disector locations that were superimposed over the delineated area, according to the counting rules explained above. When a computer-based analysis is used, the stepping motor connected with the x and y axes of the microscope stage is moving the section step by step according to the defined x and y distances to all optical disector locations. However, if no computerized system is available a lattice with coordinates can be used (West et al., 1991; West, 1994). In our experiment, we started with provisional x and y step sizes of 200 ´ 200 µm. If less than 10 neurons were counted in the delineated area of the representative section with the defined optical disector (see above), the x and y steps were reduced to increase the number of counting locations; if more than 20 counts were made in the section, the x and y steps were increased to yield less counting locations. In our previous experiment, we set the x and y step sizes in the CA3 area of the tree shrew hippocampus at 230 ´ 230 µm (Vollmann-Honsdorf et al., 1997).
The approximate x and y step sizes and optical disector dimensions, assessed in the representative section, were then used with the section sampling scheme (1/6) to determine the total number of CA3 neurons in one animal. The sum of the actually counted neurons in one animal should be between 100 and 200 (Gundersen and Jensen, 1987), and the coefficient of error (CE) (see 4.2.1) should be under 0.10 (for calculation of
the CE, see Table 2.1). If this is not the case, the sampling scheme could be adjusted, where preferentially the x and y steps or the amount of sections could be varied. When the approximate average of 1–2 neurons per optical disector is either not reached or exceeded, the counting frame area should be increased or decreased, respectively.
Section
no. Q- Counts per
disector (Q-)2 Q-´Q-next section Q-´Q-section after next
4 0 0 0 0 0
10 3 1, 2 9 39 30
16 13 2, 1, 1, 1, 2, 3, 2, 1 169 130 247
22 10 1, 1, 1, 2, 1, 2, 1, 1 100 190 450
28 19 1, 1, 3, 1, 0, 1, etc. 361 855 741
34 45 2025 1755 1395
40 39 1521 1209 1638
46 31 961 1302 775
52 42 1764 1050 756
58 25 625 450 475
64 18 324 342 234
70 19 361 247 228
76 13 169 156 156
82 12 144 144 48
88 12 144 48 72
94 4 16 24 8
100 6 36 12 -
106 6 4 - -
S 313 8733 7953 7253
The CE is calculated according to the formula:
For this example the resulting CE is:
Table 2.1
Calculation of the sum of neuronal counts (SQ-), the total estimated neuron number and the intra-individual CE in the CA3 region for a control animal. Q-´ Q-next section for section 10 is calculated with the total counts in section 10 (Q-= 3), and with the total counts in section 16 (Q-next section= 13). h: 15 µm, x and y steps: 230 ´ 230 µm, a(frame): 520 µm2, mean section thickness (for this animal; not rounded off): 25.1475 µm, every 6thsection was evaluated
When all sampling fractions were satisfactorily assessed in one animal to meet the guidelines, the pilot study with 5 animals per group was performed. The sampled sections for each animal were coded and the quantification was carried out
“blind”. After completing the pilot study, the estimates of the total neuron numbers, the intra-individual CEs, the mean group CE, and the group coefficient of variation (CV=SD/mean) were calculated. These results were then used to determine whether it was necessary to increase the sampling to achieve the goals of the study (see 2.4.2.1).
In our first study, we counted between 199 to 394 CA3 neurons (Vollmann- Honsdorf et al., 1997). We optimized the sampling scheme, and decreased in the CA3 evaluation the optical disector frame from 520 to 506 µm2, and changed the ssf to1/5. Additionally, we found the optimal x and y step sizes to be 300 ´ 300 µm. After optimizing the sampling scheme, the amount of counted neurons in the CA3 region of the additional individuals varied between 148 and 286. Strictly, these amounts better approach, but still exceed the recommendation of counting 100–200 neurons. However, in our experiment, counting more neurons yielded more precision, which could be desirable when a negative result is expected. Moreover, if the inter-individual variation is expected to be greater than in our experiment, it may be advantageous to increase the number of counted neurons per individual.
2.4.2.1. Precision of the study
The precision of an individual estimate (of e.g. neuron number) is expressed by the coefficient of error, CE. This value expresses the intra-individual variation due to stereological estimating procedure, i.e. sampling of sections and counting locations. As a thumb rule, the individual CE should be under 0.10. However, it depends also on the type of study; the role of the CE in relation to the CV is explained in the following.
Recently, the formula to calculate the individual CE was slightly modified (Gundersen et al., 1999). This formula is now thought to be more appropriate when estimating the intra-individual variation of a region along an axis, e.g. a series of histological sections.
We modified this formula (see Table 2.1) to fit neuron counting.
To design an optimal, efficient sampling scheme, it is necessary to ensure that the coefficient of variance of the estimates (e.g. of the neuron number), expressed by the mean CE2(see Table 2.2), makes the minor contribution to the observed group coefficient of variance, CV2. Regarding the equation CV2= BCV2+ CE2, the squared mean CE needs therefore to be less than the true biological coefficient of variance (BCV2) and thus be less than 50% of the CV2(Gundersen, 1986; West and Gundersen, 1990; Holm and West, 1994;
Howard and Reed, 1998). For example, in our study the CV2of the counts in the CA3 region of control animals is 0.03734 and the mean CE2is 0.00504 (Table 2.2). Hence, the CE2 is 13.5% of the CV2, and the BCV2 contributes therefore with 86.5% to the CV2. Therefore, we can be almost absolutely certain that the observed group variance is the result of biological, and not methodology-related variance. In studying biological material, the variance of the estimate (from the stereological method) should always be substantially lower than the biological variance.
After completion of the pilot study, it may be desired that the CV has to be reduced. It is therefore helpful to analyze the contributions from the BCV2and CE2to the CV2. When the BCV2is more than half of the CV2, it is more efficient to investigate additional experimental animals (West, 1999). A rule for stereological studies, especially for investigating treatment effects, is “do more less well” (Gundersen and Østerby, 1981), which means that the accuracy for the optical fractionator method is increased more efficiently by examining more animals, rather than by sampling more sections or counting locations per subject. On the other hand, the number of animals in experiments should be kept to a minimum. If it is desirable to reduce the CE2in order to decrease the CV, the CEs of the subjects could be reduced by counting more sections (<ssf), or by reducing the x and y steps or increasing the area of the counting frame (<asf; see 2.4.2) (West, 1999). The reason for this is that the variance of an individual estimate is inversely proportional to the sampled volume fraction (West, 1994; Harding et al., 1994).
Control N
CA1 CE Stress N
CA1 CE Control N
CA3 CE Stress N
CA3 CE
1 313221 0.063 1 242602 0.073 1 202974 0.081 1 211649 0.082
2 296999 0.068 2 330136 0.064 2 242265 0.078 2 193064 0.084
3 329268 0.071 3 344070 0.061 3 192201 0.082 3 228802 0.061
4 262622 0.061 4 390937a 0.063 4 223396 0.066 4 245807a 0.067 5 412470a 0.061 5 402570a 0.052 5 223156a 0.067 5 274764a 0.052 6 324973a 0.069 6 423360a 0.061 6 320296a 0.058 6 232950a 0.067 7 488943a 0.061 7 461806a 0.058 7 310022a 0.064 7 274342a 0.063
8 334455a 0.056 8 234063a 0.072
Mean 345369 0.064b 370783 0.062b 243547 0.071b 237340 0.069b
SD 71844 72183 47064 30425
CV(=SD/mean) 0.20802 0.19468 0.19324 0.12819
CV2=0.208022 0.04327 0.03790 0.03734 0.01643
CE2=0.0642= 0.00410 0.00384 0.00504 0.00476
BCV2=0.04327–
0.00410= 0.03917 0.03406 0.03230 0.01167
BCV2(in% of CV2)» 90.5% 89.8% 86.5% 71.0%
CE2(in% of CV2)» 9.5% 10.1% 13.5% 29.0%
aIndividual estimates published by Vollmann-Honsdorf et al. (1997); CA1: P=0.507, CA3: P=0.373 (two-tailed Student’s t-test, a=0.05).
bMean CE is calculated by . Table 2.2
Pyramidal neurons in unilateral hippocampal CA1 and CA3 regions of unstressed control and psychosocially stressed tree shrews: individual neuronal numbers (N), mean group numbers, standard deviation (SD), and individual and mean CE. The BCV2is calculated from the CE2and CV2 (CE = coefficient of error; CV = coefficient of variation; BCV = biological coefficient of variation)
2.4.2.2. Reporting stereological results
In a publication, the following experimental parameters should be reported: section thickness, t; height of the optical disector, h; thickness sampling fraction, tsf; area of the counting frame, a(frame); x and y step sizes, A(x,y step); area sampling fraction, asf;
section sampling fraction, ssf; amount of counted neurons per individual, SQ-; estimated neuronal number, N; mean N, SD, and coefficient of variation (CV=SD/mean N);
individual coefficient of error, CE, and mean CE (see Table 2.2); group size, n.
2.5. Results
Using the glycolmethacrylate embedding procedure, the three-dimensional structure of the sections is maintained and the variation in section thickness is low (mean ± SD: 23.7 ± 2.0 µm) (Helander, 1983). With slightly varying section thickness and a standard optical disector height (15 µm) the tsf varied between 0.561–0.719. In a previous study in tree shrews (Vollmann-Honsdorf et al., 1997), the a(frame) for the hippocampal CA1 and CA3 subfields were 414 µm2and 520 µm2, respectively. The x and y steps were set at 250 ´ 250 µm in CA1 and at 230 ´ 230 µm in CA3. After optimizing the sampling scheme, the a(frame) was 361 µm2in the CA1, and 506 µm2in the CA3 area. The x and y steps for CA3 were optimized to 300 ´ 300 µm. The optimized asf was therefore 0.0058 in CA1 and 0.0056 in CA3. The ssf was1/5, yielding 11–23 section to evaluate per animal. With the previous sampling schemes, we counted between 214 and 389 neurons (SQ-) in CA1, and between 199 and 394 in CA3, respectively. Using the optimized sampling schemes, the number of counted CA1 neurons varied between 197 and 271, and in the CA3 region between 148 and 286 neurons were counted per individual.
The calculation of the neuronal number and the individual CE for the CA3 region of one tree shrew is exemplified in Table 2.1. The mean number of unilateral CA1 pyramidal neurons in control animals (n=8) was 345369, in stressed tree shrews (n=7) 370783 (Table 2.2). The corresponding mean CEs were 0.064 and 0.062, respectively. On average, the control group contained 243547 CA3 pyramidal neurons unilaterally (mean CE: 0.071), the stressed group 237340 CA3 neurons (mean CE: 0.068) (Table 2.2).
All stereological evaluations were performed “blind”, and the sections were only decoded after completion. For statistical evaluation, group differences of neuronal number in CA1 and CA3 areas were assessed by the two-tailed unpaired Student’s t-test, using a probability level of a=0.05. We obtained a P value=0.507 for CA1, and a P value=0.373 for CA3. Therefore, we found no statistical differences in CA1 and CA3 neuronal numbers between the psychosocially stressed tree shrews and control animals.
2.6. Discussion
The focus of this report is to describe the practical procedure to employ the optical fractionator, exemplified by counting CA1 and CA3 pyramidal neurons in the hippocampus of tree shrews. We explained how the features of the optical disector and the fractionator sampling scheme are used, adjusted and optimized to efficiently obtain an estimate of the total neuron number. In addition, we demonstrated how the optical fractionator counting technique enables calculating the precision of the counting method.
It was a breakthrough in the quantification of numbers in three-dimensional structures when the disector principle was first described in 1984 (Sterio, 1984). Since then it became common to use stereological tools in neurobiological research. This new approach was used to assess the total numbers of e.g. pyramidal neurons in the hippocampus of rats (West et al., 1991) and humans (West and Gundersen, 1990) in an unbiased way. Currently, unbiased stereological tools are increasingly used to study e.g.
hippocampal pyramidal neuron numbers during aging (West, 1993b, 1994; Rapp and Gallagher, 1996; Rasmussen et al., 1996), or to investigate whether the number of pyramidal neurons is affected by stress or corticosterone/cortisol treatment. According to the glucocorticoid cascade hypothesis, prolonged activation of the HPA-axis could produce neuron loss in the hippocampus of rats and primates (Sapolsky et al., 1986).
Using unbiased stereology, it has become clear that stress or administration of corticosterone/cortisol does not influence the number of pyramidal neurons in the hippocampal formation of rats (Sousa et al., 1998a, 1998b), tree shrews (Vollmann- Honsdorf et al., 1997), and nonhuman primates (Leverenz et al., 1999). Importantly, these stereological studies, although performed in different laboratories, show a larger consistency when compared to studies with biased counting techniques.
2.6.1. Trouble shooting
2.6.1.1. Embedding in glycolmethacrylate
Unsuccessful polymerization of the specimen bottom is recognized by the appearance of white spots on the bottom surface of the specimen. For proper polymerization it is important to ensure a film of polymerization solution between the bottom of the molding tray cavity and the tissue specimen. It is recommended to place pieces of filter paper on the bottom of the molding tray cavities, before the polymerization solution is poured into the cavities and the tissue specimens are positioned.
Sometimes, white spots may appear in the middle of the polymerized tissue block. This may be indicative for an ineffective polymerization due to inappropriate infiltration with the stock solution (Technovit 7100 + hardener I) before polymerizing.
This can be avoided by elongating the infiltration time in the stock solution, e.g. from 16 h to 24 h. A second reason for the appearance of white spots may be that the glycolmethacrylate polymerized before the polymerization solution (Technovit 7100 + hardener I + hardener II) could penetrate towards the middle of the tissue block. In this
case, the polymerization process has to be slowed down by changing the curing temperature to 4°C. Because the polymerization fluid cures relatively fast, the hardener II should be added to the stock solution at room temperature, but this polymerization solution should be transferred to 4°C immediately after mixing.
2.6.1.2. Sectioning and staining
Splintering of the sections during cutting can be avoided by moistening the plastic block with a stroke of a brush or a wet fingertip. Air bubbles between the section and the glass slide should be removed before the section is dried.
Sections should be stained properly throughout the entire extent. To prevent over-staining, sections could be differentiated in 1% acetic acid for a few seconds and washed in double distilled water again. For differentiation, the use of ethanol should be avoided, because alcoholic solutions soften the glycolmethacrylate plastic.
Sections may sometimes loosen from the microscope slides during staining.
This can be avoided by coating the glass slides with 0.1% gelatin before usage, or by using SuperFrost microscope slides (Menzel-Gläser, Braunschweig, Germany).
After coverslipping it may occur that it is impossible to focus through the entire section. In this case, the sections are mounted with too much mounting medium. A flat weight of about 30–60 g placed on the coverslips prevents thick mounting.
2.6.2. Alternative protocols 2.6.2.1. Tissue processing
If the region of interest is too big for embedding in glycolmethacrylate in toto, the brain tissue may be cut in perpendicular slabs (e.g. 2–3 mm thickness), e.g. with a tissue slicer (Gundersen et al., 1988; Perl et al., 2000). This macroscopical cutting provides a possibility for sampling slabs in a multi-stage fractionator design (West, 1993a; Howard and Reed, 1998). Slabs are then separately embedded in glycolmethacrylate and sectioned. Depending on the specimen thickness, the infiltration time can be shortened or elongated (see 2.6.1.1). When slabs of 2–3 mm are processed, is it recommended that infiltration (Technovit 7100 + hardener I) lasts at least 16 h, preferentially 24 h. After this infiltration step, it may even be advisable to place the specimens in fresh infiltration solution for another 16–24 h. Polymerization (Technovit 7100 + hardener I + hardener II) should be slowed down by changing the curing temperature to 4°C (see 2.6.1.1). While sectioning the slabs, it may happen that the region of interest only partly appears in a section, because the sectioning direction probably will not be perfectly parallel to the surface of a tissue slab. Nevertheless, such a section with a non-complete region could be selected for quantification with a random sampling scheme, and should be included in the study anyway. However, counting particles in non-complete regions does not affect the unbiasedness of the counting procedure, it merely increases the variance (Pakkenberg and Gundersen, 1988).
A brain region, such as the human hippocampus, may have such dimensions, that 10–15 slabs of 2–3 mm are separately embedded in glycolmethacrylate (West and Gundersen, 1990; West, 1993b). Because serial sections of those slabs will be too time-consuming, one section is made from the face of each slab (West and Gundersen, 1990). Neurons are then counted in these 10–15 sections with the optical disector, and the estimate of the total neuronal number is obtained with the NV´ Vrefmethod (see 2.6.2.4) (West and Gundersen, 1990; West, 1993b, 1994).
2.6.2.2. Immunocytochemistry
The described technique with optical disector counting and fractionator sampling can be used for immunocytochemically stained particles as well. For the optical fractionator, rather thick (³ 20 µm nominal thickness) sections should be used. Cryostat or vibratome sections are commonly used for free-floating immunocytochemical incubations, and allow sectioning of usually 70 µm and 200 µm (nominal thickness), respectively.
However, in regard to vibratome sections, the distances from the top and bottom surfaces of the section to the optical disector should be more than 4 µm, because of the shattered section surface.
Unbiased analysis of immunocytochemically stained particle numbers in paraffin sections is also possible (Calhoun et al., 1996). However, paraffin sections are usually thinner (5–10 µm) than e.g. cryostat or vibratome sections, and therefore the stereological tool the physical disector should be used (Sterio, 1984; Gundersen, 1986;
Gundersen et al., 1988; Pakkenberg and Gundersen, 1988; Cruz-Orive and Weibel, 1990).
The fractionator sampling scheme, as described in this study, is then used to obtain pairs of adjacent thin sections (physical disector), instead of single thicker sections (optical disector). For the physical disector it is essential that each section is at least a fourth or a third smaller than the particle to be counted (Gundersen et al., 1988; Pakkenberg and Gundersen, 1988), because a particle has to have a chance of appearing in the physical disector, i.e. in both sections.
Antibody penetration is a crucial issue for optical disector counting when using rather thick sections. It should be checked carefully that the antibody has penetrated into the tissue over a sufficiently large distance. The stained part of the section should unquestionably be deeper than the guard zone plus the optical disector height to accommodate optical disectors (West, 1993a).
2.6.2.3. Light microscopy
The optical disector technique described in this protocol is conducted with conventional transmission light microscopy. Because the material of interest is optically sectioned, it is important that the optical sections are as thin as possible (Gundersen et al., 1988; Howard and Reed, 1998). The smallest possible depth is achieved by using lenses with highest numerical apertures, i.e. oil lenses. Also the numerical apertures of the condensor should match the lens that is used (Gundersen et al., 1988; Howard and Reed, 1998). A large focal
depth may increase the variance of the estimate of the total neuronal number, but it does not influence the unbiasedness of the estimate. Concerning the unbiasedness, the more important point is that an investigator consistently uses the exact same criteria (e.g. top of neuron or nucleus, or center of nucleus) for counting with the optical disector. Moreover, the optical components of the microscope should be of such quality that the counting criteria of each object of interest can be clearly identified on the computer screen, also by different investigators.
The refraction index (RI) of the lens, immersion oil, and the coverslip should be matched as closely as possible, so that the movement of the microscope stage, which the microcator measures, is equal to the movement of the plane of focus (Gundersen et al., 1988; Howard and Reed, 1998). Also the use of glycolmethacrylate embedded sections, as opposed to paraffin or cryostat sections, contributes to a higher precision. To increase the resolution of the image, an oil immersion condensor may be used to match the RI of the space between the high N.A. condensor and the bottom plane of the microscope glass slide to the RI of glass.
High N.A. water lenses may be convenient for certain protocols and may be used for optical disector counting. The mounting medium for the specimen should then have a RI equal to water. It should be noticed that a small loss in the precision of the study may occur when the section thickness of glycolmethacrylate sections, embedded with Eukitt, is measured with an air lens (e.g. 40´). However, when neurons are too large or disperse to be counted with a 100´ oil lens, it is important to use the same lens for counting neurons as for measuring the section thickness.
2.6.2.4. Electron microscopy
Stereological tools can be applied for estimating the total number of particles on the electron microscopical (EM) level, too (Gundersen et al., 1988; Geinisman et al., 1996).
Because one cannot focus through the depth of ultrathin sections, the physical disector, i.e. pairs of neighboring sections, is used. The fractionator sampling scheme may be used to select pairs of sections from the region of interest, and the number of particles, e.g.
synapses, is estimated by multiplying the total particle counts with the reciprocal fractions (Geinisman et al., 1996). However, because the fractionator technique is difficult and time-consuming for EM sections, the two-stage analysis is preferred. First, the reference volume (Vref) is estimated according to Cavalieri on light microscopical sections (Geinisman et al., 1996; Howard and Reed, 1998), taken from the faces of 10–15 slabs. The area of the region is determined in these sections by point counting, and multiplied by the thickness of the epoxy resin embedded slabs (usually 150–200 µm), which is measured in a light microscope. Secondly, the numerical density (NV) is estimated by the mean number of particles per physical disector divided by the disector volume, which is calculated from the frame area of the disector and the thickness of one (i.e. the reference) ultrathin section. This is mostly done according to Small’s method of minimal folds (Geinisman et al., 1996). The total number of particles is then calculated by multiplying the NVwith the Vref(Geinisman et al., 1996).
2.7. Essential literature references
References (Gundersen, 1986; Gundersen et al., 1988; West and Gundersen, 1990;
Cruz-Orive and Weibel, 1990; West et al., 1991; Harding et al., 1994)
2.8. Quick procedure
1. Perfusion, embedding in glycolmethacrylate, sectioning, staining.
2. Find optimal proportions of fractions (tsf, asf) in one representative section:
count approximately 1–2 neurons per disector, per section 10–20 neurons.
When necessary, adjust fraction proportions of tsf and asf.
3. Calculate optimal ssf and determine neuron number in one subject, using appropriate tsf and asf. Take 10–20 sections per subject to count 100–200 neurons. The CE should be lower than 0.10. When necessary, adjust ssf.
4. Perform pilot study with 5 subjects per group, calculate all individual CEs, the group mean CEs and group CVs, and determine whether the predicted precision of the estimates is sufficient.
5. In case of an acceptable CV in the pilot experiment, the pilot experiment may be adequate to have reached the goals of the study. However, in case of a high CV, either the BCV2or the CE2should be reduced by including additional individuals or by additional sampling within the individuals already included, respectively.