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Neuronal loss and neuronal atrophy. Computer simulation in connection with Alzheimer's disease
Brain Research, 504 (1989) 94-100 Elsevier
94 BRES 15030
Neuronal loss and neuronal atrophy. Computer simulation in connection with Alzheimer's disease C. Duyckaerts,
E. Llamas*,
P. D e l a 6 r e ,
P. M i e l e a n d J . - J . H a u w
Laboratoire de Neuropathologie R. Escourolle, La Salpdtridre, Paris (France)
(Accepted 16 May 1989) Key words: Alzheimer's disease; Neuronal loss; Neuronal atrophy; Computer simulation
A decrease in the number of neuronal profiles in the isocortex of man may be observed on microscopic sections in aging and in degenerative diseases such as Alzheimer's disease. It can be the consequence of a loss of neurons per unit volume or of a reduction of the neuronal volume (i.e. pseudo-loss). This latter possibility has been tested by simulating neuronal atrophy, with sections of various thicknesses. An unfolding algorithm was used for the simulation. The data published in the current literature concerning Alzheimer's disease were treated with the unfolding algorithm. The neocortical pseudo-loss did not exceed a few percentage points, probably much less than the measurement error. New methods of cell counting have been recently proposed to discriminate real from pseudo-loss. They should be used when the risk of dealing with pseudo-loss is high. A chart to assess the percentage of pseudo-loss as a function of perikaryai atrophy is proposed: it relies on the evaluation of the size of the cell relative to the section thickness (relative caliper diameter). This chart may be used to correct ceil counts of homogeneous cell populations.
INTRODUCTION Neuronal loss causes a decrease in the density of neuronal profiles on tissue sections. On the other hand, it is well known that a decrease in the density of profiles is not necessarily due to neuronal loss: it can also be the cons¢quence of the atrophy of the neuronal perikaryon s. This is most evident for ultrathin sections whose thickness can be considered negligible when compared to that of the perikaryon: in such a situation, a drop of 50% of the neuronal density could be the consequence either of the loss of half the neurons per unit volume or of neuronal atrophy with a 50% reduction in cell size (actually caliper diameter; see further). In such a situation, the loss of neurons per unit area could be wrongly interpreted as a loss of neurons per unit volume. The evaluation of cell loss should be based on methods which allow the distinction between real loss and pseudo-loss due to perikaryal atrophy. The development of sets of size histograms based on measurement of the neuronal size on sections might provide a reasonable solution to this problem. Atrophy would then be defined as a situation causing the shift of a given neuron from one size class on the histogram to a
smaller one, while the total n u m b e r of neurons remained the same. This would be observed if the atrophy of particles could be observed in a given volume. However, on the tissue section, such size evaluations can at times be misleading because the probability of sectioning neurons is lower for small atrophic ones than for large normal ones. Pefikaryal atrophy leads thus to a reduction in the density of neuronal profiles since the gain in small profiles is less than the loss in the large ones. Therefore, pseudo-loss cannot be detected by size histograms without further calculations. Recent awareness of the importance of pseudo-loss has arisen in the field of the neurosciences 27. New techniques have been devised to evaluate exactly the density of cells per unit volume s, 9,12,22,27 Evaluation of neuronal density in the, aging human neocortex and in Alzheimer's disease has become a crucial issue. In the past few years, many investigators have come to recognize that the neuronal loss might be a better marker of the severity of the disease than the density of senile plaques and neurofibrillary tangles 16. The possibility of a pseudo-loss is raised when differences in neuronal densities between normal individuals and patients is measured on tissue sections 16,1s,24.
* Present address: Universidad Autonomia de San Luis Potosi, Escuela de Medicina, Departamento de Morfologia, San Luis Potosi, Mexico. Correspondence: C. Duyckaerts, Laboratoire de Neuropathologie R. Escourolle, H6pital de la Salp6tri6re, 47 BIvd de l'H6pital, 75651 Paris, Cedex 13, France. 0006-8993/89/$03.50 © 1989 Elsevier Science Publishers B.V. (Biomedical Division)
95 In o r d e r to s i m u l a t e p a t h o l o g i c a l situations, w e h a v e d e v e l o p e d a c o m p u t e r p r o g r a m using an a l g o r i t h m b a s e d on
a simple
m o d e l with
a few,
readily m o d i f i a b l e
variables. T h e e x p e r i m e n t a l data, a c q u i r e d f r o m t h e c e r e b r a l cortex o f a h u m a n case with n o n e u r o l o g i c a l illness, w e r e m o d i f i e d as i f n e u r o n a l loss or p e r i k a r y a l a t r o p h y h a d o c c u r r e d . Since t h e aim o f this s t u d y was to e v a l u a t e an o r d e r o f m a g n i t u d e r a t h e r t h a n an e x a c t ,,alue, w e p u r p o s e l y a c c e p t e d o v e r s i m p l i f y i n g a s s u m p tions: t h e p e r i k a r y o n was c o n s i d e r e d spherical; t h e t h i c k n e s s o f the section was t h o u g h t c o n s t a n t a n d its m e a s u r e , s u p p o s e d to be precise; the 'lost cap 's effect was n o t t a k e n into account. T h e m a g n i t u d e o f t h e p s e u d o - l o s s d e p e n d s o n t h e size o f t h e cell, c o m p a r e d to t h e section thickness: it will b e i d e n t i c a l for spherical cells o f 8 / ~ m in d i a m e t e r cut at a s e c t i o n thickness o f 1/~m a n d for spherical cells o f 16/zm cut at a section t h i c k n e s s o f 2 / ~ m . T h e ratio b e t w e e n s e c t i o n t h i c k n e s s a n d d i a m e t e r is t h e significant v a l u e ( h e r e 8 / ~ m / 1 / ~ m o r 1 6 / ~ m / 2 / ~ m ) , r a t h e r t h a n t h e actual d a t a . This ratio is n o t clearly d e m o n s t r a t e d in t h e classical A b e r c r o m b i e f o r m u l a ~. A different e x p r e s s i o n o f t h e f o r m u l a is s u g g e s t e d h e r e . It involves t h e relative
caliper diameter (Cr) o f t h e n e u r o n , i.e. caliper d i a m e t e r o f t h e n e u r o n d i v i d e d by t h e section thickness. T h e m a g n i t u d e o f t h e p s e u d o - l o s s is s h o w n to be c o n n e c t e d w i t h t h e C~ o f t h e n e u r o n in a n o n linear way. MATERIALS AND METHODS
Terminology We used the terminology proposed by Weibel2"~:the section of a particle (a neuron) gives rise to profiles examined on sections. The number of particles per unit volume is N v. The number of profiles per unit area is Na; t is the thickness of the section. The distance between 2 planes tangent to the particle and perpendicular to the plane of section is named tangent diameter or caliper diameter (C) of the particle "s. In this paper, the shape of the perikaryon is supposed to be spherical: caliper diameter is thus identical to diameter. 2-D means 2 dimensions on a section and 3-D, 3 dimensions in a volume: a 2-D histogram is a histogram of neuronal profiles and a 3-D histogram, that of neurons considered in a volume. Numerical simulation Normal histogram. The actual data, used as a basis for the simulation, came from samples collected from a 39 year-old woman, with no known neurologic or psychiatric illness, who died from cardiac insufficiency. A block from area 22 of Brodmann (area TB of vt a Economo) was embedded in paraffin and cut at a nominal thickness of 7.5/~m. Sections were stained with cresyl violet. Six hundred neuronal profiles were drawn on a digitizing tablet (Leitz ASM) at a magnification of 400x and t!'.eir surface was automatically measured. Large neurons were easily identified but there was a proportion of small neurons which were ; ard to distinguish from glia. We followed the rule of drawing oi:~y the cells with Nissl substance on the digitizing tablet. The cortical surface area scanned during counting was 2,000,900 lira'. Cells were taken into account even if the profiles were devoid of nuclei. Further computation involved diameters rather than surface area. Diameter was calculated as
Diameter = 2 x ~/surface area/:t the shape of the profiles being approximated by circles. A 2-D size histogram of these diameters was obtained, with a class interval of 1 ~um, from 0 to 24 F~m. The diameter characteristic for each class was half-way between the upper and the lower borders of the class (ref. 25, p. 192). Skipping from a histogram per unit volume to a histogram per unit area and ",'ice versa: unfolding procedure according to Cruz-OrivezS. Various algorithms have been proposed to find out numerical density of particles in 3-D using profile density obtained in 2-D, details of which can be found in Weibe125. All these algorithms are based on an'unfolding' procedure, first proposed by Wicksel126.This consists in subtracting from the various classes of the histogram per trait area the contribution due to the'recut' of the particles from the highest class and repeating the procedure. Once written in matrix calculus, these algorithms allow to skip easily from profiles per unit area to neurons per unit volume and vice versa, by inverting the transformatiot~ matrix. The transl'ormation matrix has been calculated for spheres by ~,arious authors 2°'26, and can take the thickness of the section into accou~lt5"1'~. The Cruz-Orive formula mentioned by Weibel2s was used in this study. The more recent algorithm by the same authora considers the loss of small profiles, either due to resolution threshold or to capping: we preferred to rely on the less elaborate form of the algorithm for the simulation. The histograms of profile size distributions in 2-D were thus deficient in the lower part of the plot becausesmall profiles fell out of the section, or were simply not recognized a.~ significant or were under the resolution threshold of the microsco~e25. Therefore, the transition from N a (profiles in 2-D) to N~ (neurons in 3-D) led to negative values of N~ for the small diameters. V¢~ corrected the actual histograms collected on sections for the lack of small profiles in such a way that no neuronal diameter in 3-D was less than 6~m and that N,, was always positive. An HP-85 microcomputer with an add-in ROM (Matrix ROM HP, 1980) was used for the calculations. The round-off error reached in the inversion of the transformation matrix was less than 1%. The computer program could be used to visualize the efl'ect of changing the section thickness: data collected per unit area were transformed into data per unit volume (2-D-~3-D) using the actual section thickness of the slide. The transformation was then reversed to go back to density per unit area (3-D--~2-D), using a different section thickness in the Cruz, Orive formula.
Evaluation of pseudo-loss as a fimction of perikaryal atrophy and of C r (relative caliper diameter) In Abercrombie's formula1'25: N, = N~(t + C)
(l)
Let a be a factor describing the atrophy of the neurons, from 0 (cell loss) to 1 (no atrophy). For example, a = 0.6 means that the diameter is 0.6 times the initial diameter, i.e. 40% (1-0.6) smaller after atrophy. When the density per unit volume and the thickness of the section are constant, the numerical density of the neuronal profiles per unit area after atrophy is:
N~'= Nv(t+aC) The quantity of lost profiles on section is thIns: N..-N,." = Nv(t+C)-N~ (t+aC) Expressing this as a percentage of loss with the initial density as referc.ce: (Na-N~')/N,. = (N,(t + C)-Nv(t+aC))/N~(t+C) Taking (N~-N.~')/Na as L~ (for loss per unit area): La = (Nv (t+C)-Nv (t+aC))/Nv(t+C) L~ = N,. (t+C-t-aC)/Nv(t+C)=(C-aC)/(t+C) or finally L~= (C-aC)/(t+C) (2) C, the c~diper diameter of the neuron, instead of being in #m, can be expressed as a relative caliper diameter (Cr):Cr = C/t i.¢. the
96 ratio of the caliper diameter to the section thickness: for example a red cell of caliper diameter 8 ~m cut at a section thickness of 4 l~m has a Cr of 2 (i.e. 8/~m/41tm) whereas the C, would be 4 (i.e. 81tm/2 /~m) if the section thickness was 2 t~m C,
=
Clt'. C
=
Crl
Replacing C by C~t in Eq.2,
L, = (C,t-aC,t)l(t+C,t); L. = (Cr-aCr)/(l +Cr) (3) In this last formula, the pseudo-loss appears to be directly dependent on the severity of the perikaryal atrophy (a) and on the size of the cell expressed in units relative to the section thickness.
simulated Iosss of 40% of the profiles with a diameter above 10.5 g r , . Such a simulation caused thus a decrease of 18% of the total number of profiles per unit area. The normal and the pathological 2-D histograms were then transformed into 3-D values by the unfolding procedure. The total number of neurons was 18,100/ram 3 in the 3-D
6,[ XlOOOIml~
RESULTS
Influence of the section thickness on the size histogram of perikaryal profiles The normal 3-D histogram (Fig. la) was transformed into 2-D histograms, using 3 different section thicknesses. With a 1/~m thick section, the relative number of small profiles, principally due to the recut of larger neurons, was greatly increased compared to 100/~m thick sections (Fig. lb). At the same time, irregularity of the 3-D histogram was smoothed. The absolute number of neurons observed per unit area increased linearily with the thickness of the section (Fig. lc).
o
~ I
6
11
16
Diameter (Urn) 161 i
Na Section Thickness
121 /
Illl
II
mm
20 wm
Wi
Simulated example of pseudo-loss An atrophy of 50% of the diameter of all the neurons above 10 Mm in diameter was simulated in 3D (Fig. 2a). It induced not only a translation of the mode of the 3-D histogram towards the small values but also a squeezing of the range of the diameters. The number of neurons before and after atrophy being the same, the areas covered by the black and the white columns of the histogram (Fig. 2a) were equal. The values of the 3-D histogram before and after atrophy (Fig. 2a) were transformed into 2-D values. The section was supposed to be 1 # m thick (Fig. 2b). The number of profiles was 407/ram 2 before atrophy and 327/mm 2 after it. An apparent loss of 80 neurons had occurred i.e. a pseudoloss of 19.6 %. In other words, although the number of neurons was the same, atrophy of only the largest ones mimicked a Cellular loss of 19.6 %.
Could the reported loss of neurons in Alzheimer's dementia be a pseudo-loss? Using the above-mentioned data, we tried to illustrate the reported loss of neurons in the cerebral cortex in the course of Alzheimer's disease. A maximal loss of 40% of neurons larger than 90/~m 2 (i.e. a diameter of 10.7 ~m) was reported in senile dementia of the Alzheimer's type, when using 20/~m thick sections ~8,24. In our simulation, the total number of profiles was 551/mm2 in the normal 2-D histogram when values were expressed with a section thickness of 20 /~m, and became 452/mm z after a
411
OS I
6
16 Diameter (lam)
II
Na
b
Section Thickness
I 400
I um 20 um I O0 ~m
200
0. . . . . . . . . . . . . . . . . . . . I
6
II
16
Diameter (um)
Fig. 1. Influence of the section thickness on the density of neuronal profiles per unit area. a: 3-D histogram of neuronal diameters, considered per unit volume, Nv, number of neurons per unit volume. Data were collected in a control case and unfolded following Cruz-Orive (Weibel, 1979). b: 2-D histogram of neuronal profiles, expressed as a percentage per unit area (%/mm2) with various section thicknesses (1/~m,20 ~m,100 #m). Na, number of neurons per unit area. The proportion of small profiles, due to the recut of large neurons, decreases when the section thickness increases, c: histogram of neuronal profiles, expressed as absolute values per unit area (n/mm2): the number of enumerated profiles increases linearly with the section thickness (1/~m, 20 ~m, 100 ~m). The number of small profiles, due to the recut of large neurons is the same with 3 section thicknesses (left side of the curve) but their proportion is much smaller for the large section thickness, as illustrated in c.
97 histogram after unfolding of the 2-D normal situation and 15,200/mm 3 after unfolding of the 2-D pathological situation, i.e. a total loss of 16% of the total number: the difference between the loss calculated on density per unit area and the one calculated per unit volume reached only 2%, which is below the presumable error of measurement of the current image analysers. The main difference between the histogram of diameters in 2-D (Fig. 3a) and that of diameters in 3-D (Fig.3b) was the increase in the number of neurons of the lower size classes observed in 3-D aft:Jr simulated loss. This increase in the density of the small neurons in the pathological case demonstrates the presence of some neuronal atrophy which is not visible on the 2-D histogram and is revealed by the unfolding procedure.
Numberof ~60 ~ u r ~ l profilesDer ram2
[~l i
Normal Pathological condition
140
(simulated)
,OO2o.6O O i20
0 ~rll'i['I $
I
17
13
9
Diameter in um
a
Numberoi 6
neuronsper ram3
5 4
Evaluation of the magnitude of the pseudo-loss A chart giving the percentage of the pseudo-loss as a function of neuronal atrophy was drawn (Fig. 4) with Eq.3 (Materials and Methods). It can be used to determine the order of magnitude of the pseudo-loss, as a function of the size of the particle and of the section
Before of
7, 6,
xlO00
r'i
_
II
L~
After atrophy of the perlkaryon
th#
:
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Fig. 3. a: a simulated loss of 40% of the neuronal profiles above 10 p m in diameter. Total number of neurones per unit area before atrophy: 551/mm 2, after atrophy: 452.2/mm 2 (18% loss), b: neuronal density per unit volume, corresponding to a, after unfolding. The total n u m b e r before atrophy was: 18,100/mm 3, after: 15, 200/mm 3 (16% loss). Note the increase in the proportion of small neurones, not visible in a.
atrophy
I
Nor neuror~/mm3
0.
perlkaryon
thickness. The slope of this curve is steeper with the increase of the relative caliper diameter, C r, but not in a proportional manner: e.g. for neurons of a 10 pm g~afive ..,'1 Caliper
Pseudo Loss%
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15
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Fig. 2. a: a simulated atrophy of the neurons above l0 pm in diameter, by 50% of their diameter, as considered in a volume. The total number of neurons is, by definition, identical before and after atrophy, b: corresponding histogram of neuronal profiles per unit area, using a section thickness of l p m : the total number before atrophy was: 407/mm 2, after it: 327/mm 2. Pseudo-loss = 80 neurons on a population of 407, i.e. a loss of 19.7 %.
I
25
50
75
gg.g
~eU~lr/ofbCakw Fig. 4. Chart giving the magnitude of the pseudo-loss (y axis) as a function of the atrophy of the caliper diamete~ (= diameter for spherical cells).
98 P1agnitude of the pseudo-loss
i,o o,a 0.6
/
0,4 0,2
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!
0
2
,
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4
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5 8 I0 Relative CaliperOiameter. Cr
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Fig. 5. Factor of pseudo-loss as a function of the relative caliper diameter (Cr). y-axis: slope of the curves of Fig. 4, i.e. the factor of proportionality between atrophy and pseudo-loss. The closest to 1 y lies, the highest the proportion of pseudo-loss. Note that the relationship is not linear and varies greatly for low values of Cr
diameter, the slope of the curve (Fig. 5) is 0.9 with a 1 pm thick section, 0.5 with a 10 pm section, and 0.09 with a 100 #m thick section. The various slopes of Fig. 5 can thus be used to evaluate the possible severity of the pseudo-loss: the closer to 1, the higher the pseudo-loss. The values of the slopes are linked to Cr in a non-linear way (Fig. 5) and are always smaller than 1 since the proportion of the psuedo-loss can obviously not exceed the propoi'tion of atrophy: e.g. an atrophy of 50% of the diameter cannot explain a loss of 5~% of the cellular profiles. Great variations in the severity of the pseudoloss were noted, especially for Cr levels below 2 (Fig. 5).
Evaluating the risk of pseudo-loss when counting m'urons The diameter equivalent circle of cortical neurons varies roughly from 6 (granule cells) to 60 pm (Betz cells): with a section thickness of 20 pro, the Cr varies from 0.3 to 3. The possible pseudo-loss for these Cr are not negligible: from 12.5% for the small neurons to more than 37% for the large ones, with an atrophy of 50% of the neuron diameter (see Fig. 5). Nucleoli have a diameter from 3.58 pm in normal cases to 2.84 #m in Aizheimer's dementia (values calculated from ref. 16). With the same section thickness of 20 pro, C. is 0.179 in normal cases and 0.142 during AIzheimer's disease. With the reported atrophy of 21% of their diameter, the pseudo-loss for nucleoli would then remain below 3.5% DISCUSSION
The consequences of neuronal atrophy are obviously numerous, the most conspicuous being the reduction of the synaptic area. In this paper, neuronal atrophy is dealt with only as a cause of pseudo-loss. Only those parts of the neuron which are usually enumerated when one tries to ascertain a neuronal loss were taken into account,
mainly the perikaryon and the nucleolus. Wrong conclusions may be drawn when the volume of these structures is reduced in relation with the pathological condition. Perikaryal atrophy has been known for a long time under various names: Nissl's chronic cell disease, shrinkage of nerve cells ~, cell sclerosis 21, simple atrophy ~'. Recent textbooks T M do not deal with this change although its very existence has now been ascertained by quantitative measurement 4"e3. Nucleolar atrophy has been demonstrated by Mann et a116'~7. Automatic counting of perikaryal profiles has been used ~8'e4 for the study of neuronal loss during senile dementia of the Alzheimer's type. With our normal data and the reported loss of perikaryal profiles, the pseudoloss would not exceed 2% (Fig. 3). However, these results have been obtained by assuming that the number of small profiles remained unchanged: this was not the case in the studies by Terry et al. 24 and by Mountjoy et al. ~s. In both, an increase in the number of small profiles which was found to be due to gila rather than to neurons was noted for some areas. With the unfolding procedure, the inference of a neuronal loss relies heavily upon the identification of these small profiles: had they been counted as neurons, the loss would have appeared much less significant. In these studies ~8'24, all the small profiles were considered glial. This systematic point of view could lead to an underevaluation of the density of small, atrophied neurons or of profiles due to the section of large neurons. We used Nissl substance to identify small neurons for the baseline data. This probably still underscored the density of small neurons. Immunocytochemistry could help to identify them: in the nucleus basalis of Meynert, neuron-specific enolase demonst, :ed that many of the small profiles which would not have been considered with Nissl stain were actually neuronal 4. Other authors relied upon the manual counting of profiles ~6a7 and took into account the number of nucleolated pyramidal cells within cortical layers Ill and V. As the Cr of nucleoli is particularly low (around 0.1), the amount of pseudo-loss, even at its worst, remains small (below 5%). Pseudo-loss is reduced when the ratio of particle caliper diameter to section thickness is small (low Cr). Increasing the section thickness is limited by practical considerations: the quality of the microscopic image is lower than with thin sections; focusing has to be changed in order to evaluate the entire field depth; and the number of neurons to be evaluated in the same area is much larger. Lowering the pseudo-loss can also be achieved by enumerating smaller particles such as nucleoli, as already mentioned. It will no be a surprise for most microscopists that the pseudo-loss with this old technique is small. Such a simple procedure of evaluating
99 neuronal density should be considered, possibly by looking at chart (Fig. 4), before implementing new, elaboi'ate or expensive morphometric methods. It may be added that the reduction in neuronal density in a small cortical sample, when considered alone, cannot give information on neuronal loss unless the total volume of the cerebral cortex and the shrinkage of the sample ~a are known. As both pieces of information are hard to collect with a sufficient precision, only the measure of the relative proportion of large and small _neurons is presently accurate and this underlines the significance of the repeated finding of a loss of large neurons 1s'24 or of large pyramidal cells 17. The link between the macroscopic measurement of cortical atrophy " u s , and the microscopic evaluation of cellular density ~'~a'24 is however still missing: the magnitude of the neuronal loss remains therefore unknown so far. Numerical unfolding is a useful and powerful instrument for simulation studies. On the other hand, the evaluation of the density per unit volume in reality can now be performed by more direct techniques than numerical computation: direct 3-dimensional counting 27 or using a dissector 22 or a selector 9. These techniques have to be implemented when the expected pseudo-loss is higher than the precision of the measurement. A n easy way to appreciate the risk of pseudo-loss and of its magnitude is suggested in this paper (chart of Fig. 4), REFERENCES 1 Abercrombie, M., Estimation of nuclear population from microtomic sections, Anat. Rec., 94 (1946) 239-247. 2 Adams, J.H., Corsellis, J.A.N. and Duchen, L.W., Greenfield's Neuropathology, 4th Edn., Edward Arnold, London, 1984. 3 Agduhr, E., A contribution to the technique of determining the number of nerve cells per volume unit of tissue, Anat. Rec., 80 (1941) 191-202. 4 Allen, S.J., Dawbarn, D. and Wilcock, G.K., Morphometric immunochemical analysis of neurons in the nucleus basalis of Meynert in AIzheimer's disease, Brain Research, 454 (1988) 275-281. 5 Bach, O. Kugelgr6ssenverteilung und Verteilung der Schnittkreise; ihre wechselseitigen Beziehungen und Verfahren zur Bestimmung der einen aus der andern, In E.R. Weibei and H. Elias (Eds.), Quantitative Methods in Morphology, Springer Verlag, Berlin, 1967, pp. 23-45. 6 Bielschowsky, M., Histopathology of nerve cells, In W. Penfield (Ed.), Cytology and Cellular Pathology of the Nervous System, P.B. Hoeber, New York, 1932, pp 147-188. 7 Blackwood, W., and Corsellis, J.A,N., Greenfield's Neuropathology, 3rd Edn., Edward Arnold, London, 1976, p. 16.. 8 Cruz-Orive, L.-M,, Distribution-free estimation of sphere size distribution from slabs showing overprojections and truncation, with a review of previous methods, J. Microsci., 131 (1983) 265-290. 9 Cruz-Orive, L.-M., Particle number can be estimated using a dissector of unknown thickness: the selector, J. Microsc., 145 (1986) 121-142. 10 Duyckaerts C., Hauw J-J, Piette E, Rainsard V., Poulain C., Berthaux E and Escourolle R., Cortical atrophy in senile dementia of the Alzheimer type is mainly due to a decrease in
The chart of Fig. 4 can also be used to find out the correction factor which has to be applied to a density of neuronal profiles when the atrophy of their diameter is known. The evaluation of neuronal density can be planned in the following way: a pilot study determines the mean diameter of the neurons in the samples of the normal situation. The C r is calculated by dividing the mean diameter by the section thickness. The size of the neuronal profiles is then controlled in the pathological cases and the degree of pseudo-loss is evaluated with the chart ~f Fig. 4. The study is performed without further corrections if the pseudo-loss is negligible. Otherwise, 3 methods can be applied: (1) a special way of counting the neurons u s i n g dissector, selector or direct 3-dimensional counting is used; these methods are probably the most accurate bur they are expensive in terms of working time or of equipment; (2) a computer is used to apply an unfolding algorithm; (3) if the neuronal population is homogeneous and the approximation of the neuronal shape by a sphere seems acceptable, the real loss is calculated (real 3-D loss = apparent 2-D loss-pseudo-loss) using the chart or Eq. 3 of Materials and Methods, or some other formulae, taking the lost cap into account ~i.
Acknowledgements. The critici'~msand help of Professor U. di Girolami and of Doctor P. Gaspar are greatly acknowledged. cortical length, Acta Neuropathol., 66 (1985) 72-74. 11 Floderus S., Untersuchungen fiber den Bau der menschlichen Hypophyse mit besonderer Berficksichtigung der quantitativen mikromorphologischen Verhfiltnisse, Acta Path. Microbiol. Scand., Suppl. 53 (1944) 1-276. 12 Gundersen, H.J.G., Stereology of arbitrary particles, a review of unbiased number and size estimators and the presentation of some new ones, J. Microsc., 147 (1986) 229-263. 13 Haug, H., Kfihl, S., Melke, E., Sass, N.-L. and Wasner, K., The significance of morphometric procedures in the investigation of age changes in cytoarchitectonic structures of human brain, J. Hirnforsch., 25 (1984) 333-374. 14 Hirano, A., Neurons, Astrocytes and Ependyma. In R.L. Davis and D.M. Robertson (Eds.), Textbook of Neuropathology., Williams & Wilkins, Baltimore, 1985, pp 1-92. 15 Hubbard, B.M. and Anderson, J.M., A quantitative study of cerebral atrophy in old age and senile dementia, J. Neurol. Sci., 50 (1981) 135-145. 16 Mann, D.M.A, Marcyniuk, B., Yates, P.O., Neary, D. and Snowden, J.S., The progression of the pathological c[:anges of AIzheimer's disease in frontal and temporal neocortex e~camined both at biopsy and at autopsy, Neuropath. Appl. Neurobiol., 14 0988) 177-195. 17 Mann, D.M.A, Yates, P.O. and Marcyniuk, B., Some morphometric observations on the cerebral cortex and hippocampus in presenile Alzheimer's disease, senile dementia of Al~.heimer type and Down's syndrome in middle age, J. Neurol., 69 (1985) 139-159. 18 Mountjoy, C.Q., Roth M, Evan N.J.R. and Evans, H.M., Cortical neuronal counts in normal elderly controls and demented patients, Neurobiol. Aging, 4 (1983) 1-11. 19 Rose, R.D. and Rohrlich, D., Counting sectionet~, cells via mathematical reconstruction, J. Comp. Neurol., 263 (1987)
100 365-386. 20 Saltykov, S.A., Stereometric metallography (1958) quoted by Weibel, 1979.. 21 Spielmeyer, W., Histopathologie des Nervensystems, Springer, Berlin, 1922, pp. 63-67. 22 Sterio, D.C., The unbiased estimation of number and sizes of arbitrary particles using the dissector, J. Microsc., 134 (1984) 127-136. 23 Terry, R.D., DeTeresa, R. and Hansen, L.A., Neocortical cell counts in normal human adult aging, Ann. Neurol., 21 (1987) 530-539. 24 Terry, R.D., Peck, A., DeTeresa, R., Schechter, R. and
Horoupian, D.S., Some morphometric aspects of the brain in senile dementia of the AIzheimer type. Ann. Neurol., 10 (1981) 184-192. 25 Weibei, E.R., Stereological methods. Vol 1. Practical Methods for Biological Morphometry, Academic Press, London, 1979 pp. 189-196.. 26 Wicksell, S.D., The corpuscle problem. A mathematical study of a biometric problem, Biometrika, 17 (1925) 84-99. 27 Williams R. and Rakic P., Three-dimensional counting, an accurate and direct method to estimate numbers of cells in sectioned material, J. Comp. Neurol., 278 (1988) 344-352.
94 BRES 15030
Neuronal loss and neuronal atrophy. Computer simulation in connection with Alzheimer's disease C. Duyckaerts,
E. Llamas*,
P. D e l a 6 r e ,
P. M i e l e a n d J . - J . H a u w
Laboratoire de Neuropathologie R. Escourolle, La Salpdtridre, Paris (France)
(Accepted 16 May 1989) Key words: Alzheimer's disease; Neuronal loss; Neuronal atrophy; Computer simulation
A decrease in the number of neuronal profiles in the isocortex of man may be observed on microscopic sections in aging and in degenerative diseases such as Alzheimer's disease. It can be the consequence of a loss of neurons per unit volume or of a reduction of the neuronal volume (i.e. pseudo-loss). This latter possibility has been tested by simulating neuronal atrophy, with sections of various thicknesses. An unfolding algorithm was used for the simulation. The data published in the current literature concerning Alzheimer's disease were treated with the unfolding algorithm. The neocortical pseudo-loss did not exceed a few percentage points, probably much less than the measurement error. New methods of cell counting have been recently proposed to discriminate real from pseudo-loss. They should be used when the risk of dealing with pseudo-loss is high. A chart to assess the percentage of pseudo-loss as a function of perikaryai atrophy is proposed: it relies on the evaluation of the size of the cell relative to the section thickness (relative caliper diameter). This chart may be used to correct ceil counts of homogeneous cell populations.
INTRODUCTION Neuronal loss causes a decrease in the density of neuronal profiles on tissue sections. On the other hand, it is well known that a decrease in the density of profiles is not necessarily due to neuronal loss: it can also be the cons¢quence of the atrophy of the neuronal perikaryon s. This is most evident for ultrathin sections whose thickness can be considered negligible when compared to that of the perikaryon: in such a situation, a drop of 50% of the neuronal density could be the consequence either of the loss of half the neurons per unit volume or of neuronal atrophy with a 50% reduction in cell size (actually caliper diameter; see further). In such a situation, the loss of neurons per unit area could be wrongly interpreted as a loss of neurons per unit volume. The evaluation of cell loss should be based on methods which allow the distinction between real loss and pseudo-loss due to perikaryal atrophy. The development of sets of size histograms based on measurement of the neuronal size on sections might provide a reasonable solution to this problem. Atrophy would then be defined as a situation causing the shift of a given neuron from one size class on the histogram to a
smaller one, while the total n u m b e r of neurons remained the same. This would be observed if the atrophy of particles could be observed in a given volume. However, on the tissue section, such size evaluations can at times be misleading because the probability of sectioning neurons is lower for small atrophic ones than for large normal ones. Pefikaryal atrophy leads thus to a reduction in the density of neuronal profiles since the gain in small profiles is less than the loss in the large ones. Therefore, pseudo-loss cannot be detected by size histograms without further calculations. Recent awareness of the importance of pseudo-loss has arisen in the field of the neurosciences 27. New techniques have been devised to evaluate exactly the density of cells per unit volume s, 9,12,22,27 Evaluation of neuronal density in the, aging human neocortex and in Alzheimer's disease has become a crucial issue. In the past few years, many investigators have come to recognize that the neuronal loss might be a better marker of the severity of the disease than the density of senile plaques and neurofibrillary tangles 16. The possibility of a pseudo-loss is raised when differences in neuronal densities between normal individuals and patients is measured on tissue sections 16,1s,24.
* Present address: Universidad Autonomia de San Luis Potosi, Escuela de Medicina, Departamento de Morfologia, San Luis Potosi, Mexico. Correspondence: C. Duyckaerts, Laboratoire de Neuropathologie R. Escourolle, H6pital de la Salp6tri6re, 47 BIvd de l'H6pital, 75651 Paris, Cedex 13, France. 0006-8993/89/$03.50 © 1989 Elsevier Science Publishers B.V. (Biomedical Division)
95 In o r d e r to s i m u l a t e p a t h o l o g i c a l situations, w e h a v e d e v e l o p e d a c o m p u t e r p r o g r a m using an a l g o r i t h m b a s e d on
a simple
m o d e l with
a few,
readily m o d i f i a b l e
variables. T h e e x p e r i m e n t a l data, a c q u i r e d f r o m t h e c e r e b r a l cortex o f a h u m a n case with n o n e u r o l o g i c a l illness, w e r e m o d i f i e d as i f n e u r o n a l loss or p e r i k a r y a l a t r o p h y h a d o c c u r r e d . Since t h e aim o f this s t u d y was to e v a l u a t e an o r d e r o f m a g n i t u d e r a t h e r t h a n an e x a c t ,,alue, w e p u r p o s e l y a c c e p t e d o v e r s i m p l i f y i n g a s s u m p tions: t h e p e r i k a r y o n was c o n s i d e r e d spherical; t h e t h i c k n e s s o f the section was t h o u g h t c o n s t a n t a n d its m e a s u r e , s u p p o s e d to be precise; the 'lost cap 's effect was n o t t a k e n into account. T h e m a g n i t u d e o f t h e p s e u d o - l o s s d e p e n d s o n t h e size o f t h e cell, c o m p a r e d to t h e section thickness: it will b e i d e n t i c a l for spherical cells o f 8 / ~ m in d i a m e t e r cut at a s e c t i o n thickness o f 1/~m a n d for spherical cells o f 16/zm cut at a section t h i c k n e s s o f 2 / ~ m . T h e ratio b e t w e e n s e c t i o n t h i c k n e s s a n d d i a m e t e r is t h e significant v a l u e ( h e r e 8 / ~ m / 1 / ~ m o r 1 6 / ~ m / 2 / ~ m ) , r a t h e r t h a n t h e actual d a t a . This ratio is n o t clearly d e m o n s t r a t e d in t h e classical A b e r c r o m b i e f o r m u l a ~. A different e x p r e s s i o n o f t h e f o r m u l a is s u g g e s t e d h e r e . It involves t h e relative
caliper diameter (Cr) o f t h e n e u r o n , i.e. caliper d i a m e t e r o f t h e n e u r o n d i v i d e d by t h e section thickness. T h e m a g n i t u d e o f t h e p s e u d o - l o s s is s h o w n to be c o n n e c t e d w i t h t h e C~ o f t h e n e u r o n in a n o n linear way. MATERIALS AND METHODS
Terminology We used the terminology proposed by Weibel2"~:the section of a particle (a neuron) gives rise to profiles examined on sections. The number of particles per unit volume is N v. The number of profiles per unit area is Na; t is the thickness of the section. The distance between 2 planes tangent to the particle and perpendicular to the plane of section is named tangent diameter or caliper diameter (C) of the particle "s. In this paper, the shape of the perikaryon is supposed to be spherical: caliper diameter is thus identical to diameter. 2-D means 2 dimensions on a section and 3-D, 3 dimensions in a volume: a 2-D histogram is a histogram of neuronal profiles and a 3-D histogram, that of neurons considered in a volume. Numerical simulation Normal histogram. The actual data, used as a basis for the simulation, came from samples collected from a 39 year-old woman, with no known neurologic or psychiatric illness, who died from cardiac insufficiency. A block from area 22 of Brodmann (area TB of vt a Economo) was embedded in paraffin and cut at a nominal thickness of 7.5/~m. Sections were stained with cresyl violet. Six hundred neuronal profiles were drawn on a digitizing tablet (Leitz ASM) at a magnification of 400x and t!'.eir surface was automatically measured. Large neurons were easily identified but there was a proportion of small neurons which were ; ard to distinguish from glia. We followed the rule of drawing oi:~y the cells with Nissl substance on the digitizing tablet. The cortical surface area scanned during counting was 2,000,900 lira'. Cells were taken into account even if the profiles were devoid of nuclei. Further computation involved diameters rather than surface area. Diameter was calculated as
Diameter = 2 x ~/surface area/:t the shape of the profiles being approximated by circles. A 2-D size histogram of these diameters was obtained, with a class interval of 1 ~um, from 0 to 24 F~m. The diameter characteristic for each class was half-way between the upper and the lower borders of the class (ref. 25, p. 192). Skipping from a histogram per unit volume to a histogram per unit area and ",'ice versa: unfolding procedure according to Cruz-OrivezS. Various algorithms have been proposed to find out numerical density of particles in 3-D using profile density obtained in 2-D, details of which can be found in Weibe125. All these algorithms are based on an'unfolding' procedure, first proposed by Wicksel126.This consists in subtracting from the various classes of the histogram per trait area the contribution due to the'recut' of the particles from the highest class and repeating the procedure. Once written in matrix calculus, these algorithms allow to skip easily from profiles per unit area to neurons per unit volume and vice versa, by inverting the transformatiot~ matrix. The transl'ormation matrix has been calculated for spheres by ~,arious authors 2°'26, and can take the thickness of the section into accou~lt5"1'~. The Cruz-Orive formula mentioned by Weibel2s was used in this study. The more recent algorithm by the same authora considers the loss of small profiles, either due to resolution threshold or to capping: we preferred to rely on the less elaborate form of the algorithm for the simulation. The histograms of profile size distributions in 2-D were thus deficient in the lower part of the plot becausesmall profiles fell out of the section, or were simply not recognized a.~ significant or were under the resolution threshold of the microsco~e25. Therefore, the transition from N a (profiles in 2-D) to N~ (neurons in 3-D) led to negative values of N~ for the small diameters. V¢~ corrected the actual histograms collected on sections for the lack of small profiles in such a way that no neuronal diameter in 3-D was less than 6~m and that N,, was always positive. An HP-85 microcomputer with an add-in ROM (Matrix ROM HP, 1980) was used for the calculations. The round-off error reached in the inversion of the transformation matrix was less than 1%. The computer program could be used to visualize the efl'ect of changing the section thickness: data collected per unit area were transformed into data per unit volume (2-D-~3-D) using the actual section thickness of the slide. The transformation was then reversed to go back to density per unit area (3-D--~2-D), using a different section thickness in the Cruz, Orive formula.
Evaluation of pseudo-loss as a fimction of perikaryal atrophy and of C r (relative caliper diameter) In Abercrombie's formula1'25: N, = N~(t + C)
(l)
Let a be a factor describing the atrophy of the neurons, from 0 (cell loss) to 1 (no atrophy). For example, a = 0.6 means that the diameter is 0.6 times the initial diameter, i.e. 40% (1-0.6) smaller after atrophy. When the density per unit volume and the thickness of the section are constant, the numerical density of the neuronal profiles per unit area after atrophy is:
N~'= Nv(t+aC) The quantity of lost profiles on section is thIns: N..-N,." = Nv(t+C)-N~ (t+aC) Expressing this as a percentage of loss with the initial density as referc.ce: (Na-N~')/N,. = (N,(t + C)-Nv(t+aC))/N~(t+C) Taking (N~-N.~')/Na as L~ (for loss per unit area): La = (Nv (t+C)-Nv (t+aC))/Nv(t+C) L~ = N,. (t+C-t-aC)/Nv(t+C)=(C-aC)/(t+C) or finally L~= (C-aC)/(t+C) (2) C, the c~diper diameter of the neuron, instead of being in #m, can be expressed as a relative caliper diameter (Cr):Cr = C/t i.¢. the
96 ratio of the caliper diameter to the section thickness: for example a red cell of caliper diameter 8 ~m cut at a section thickness of 4 l~m has a Cr of 2 (i.e. 8/~m/41tm) whereas the C, would be 4 (i.e. 81tm/2 /~m) if the section thickness was 2 t~m C,
=
Clt'. C
=
Crl
Replacing C by C~t in Eq.2,
L, = (C,t-aC,t)l(t+C,t); L. = (Cr-aCr)/(l +Cr) (3) In this last formula, the pseudo-loss appears to be directly dependent on the severity of the perikaryal atrophy (a) and on the size of the cell expressed in units relative to the section thickness.
simulated Iosss of 40% of the profiles with a diameter above 10.5 g r , . Such a simulation caused thus a decrease of 18% of the total number of profiles per unit area. The normal and the pathological 2-D histograms were then transformed into 3-D values by the unfolding procedure. The total number of neurons was 18,100/ram 3 in the 3-D
6,[ XlOOOIml~
RESULTS
Influence of the section thickness on the size histogram of perikaryal profiles The normal 3-D histogram (Fig. la) was transformed into 2-D histograms, using 3 different section thicknesses. With a 1/~m thick section, the relative number of small profiles, principally due to the recut of larger neurons, was greatly increased compared to 100/~m thick sections (Fig. lb). At the same time, irregularity of the 3-D histogram was smoothed. The absolute number of neurons observed per unit area increased linearily with the thickness of the section (Fig. lc).
o
~ I
6
11
16
Diameter (Urn) 161 i
Na Section Thickness
121 /
Illl
II
mm
20 wm
Wi
Simulated example of pseudo-loss An atrophy of 50% of the diameter of all the neurons above 10 Mm in diameter was simulated in 3D (Fig. 2a). It induced not only a translation of the mode of the 3-D histogram towards the small values but also a squeezing of the range of the diameters. The number of neurons before and after atrophy being the same, the areas covered by the black and the white columns of the histogram (Fig. 2a) were equal. The values of the 3-D histogram before and after atrophy (Fig. 2a) were transformed into 2-D values. The section was supposed to be 1 # m thick (Fig. 2b). The number of profiles was 407/ram 2 before atrophy and 327/mm 2 after it. An apparent loss of 80 neurons had occurred i.e. a pseudoloss of 19.6 %. In other words, although the number of neurons was the same, atrophy of only the largest ones mimicked a Cellular loss of 19.6 %.
Could the reported loss of neurons in Alzheimer's dementia be a pseudo-loss? Using the above-mentioned data, we tried to illustrate the reported loss of neurons in the cerebral cortex in the course of Alzheimer's disease. A maximal loss of 40% of neurons larger than 90/~m 2 (i.e. a diameter of 10.7 ~m) was reported in senile dementia of the Alzheimer's type, when using 20/~m thick sections ~8,24. In our simulation, the total number of profiles was 551/mm2 in the normal 2-D histogram when values were expressed with a section thickness of 20 /~m, and became 452/mm z after a
411
OS I
6
16 Diameter (lam)
II
Na
b
Section Thickness
I 400
I um 20 um I O0 ~m
200
0. . . . . . . . . . . . . . . . . . . . I
6
II
16
Diameter (um)
Fig. 1. Influence of the section thickness on the density of neuronal profiles per unit area. a: 3-D histogram of neuronal diameters, considered per unit volume, Nv, number of neurons per unit volume. Data were collected in a control case and unfolded following Cruz-Orive (Weibel, 1979). b: 2-D histogram of neuronal profiles, expressed as a percentage per unit area (%/mm2) with various section thicknesses (1/~m,20 ~m,100 #m). Na, number of neurons per unit area. The proportion of small profiles, due to the recut of large neurons, decreases when the section thickness increases, c: histogram of neuronal profiles, expressed as absolute values per unit area (n/mm2): the number of enumerated profiles increases linearly with the section thickness (1/~m, 20 ~m, 100 ~m). The number of small profiles, due to the recut of large neurons is the same with 3 section thicknesses (left side of the curve) but their proportion is much smaller for the large section thickness, as illustrated in c.
97 histogram after unfolding of the 2-D normal situation and 15,200/mm 3 after unfolding of the 2-D pathological situation, i.e. a total loss of 16% of the total number: the difference between the loss calculated on density per unit area and the one calculated per unit volume reached only 2%, which is below the presumable error of measurement of the current image analysers. The main difference between the histogram of diameters in 2-D (Fig. 3a) and that of diameters in 3-D (Fig.3b) was the increase in the number of neurons of the lower size classes observed in 3-D aft:Jr simulated loss. This increase in the density of the small neurons in the pathological case demonstrates the presence of some neuronal atrophy which is not visible on the 2-D histogram and is revealed by the unfolding procedure.
Numberof ~60 ~ u r ~ l profilesDer ram2
[~l i
Normal Pathological condition
140
(simulated)
,OO2o.6O O i20
0 ~rll'i['I $
I
17
13
9
Diameter in um
a
Numberoi 6
neuronsper ram3
5 4
Evaluation of the magnitude of the pseudo-loss A chart giving the percentage of the pseudo-loss as a function of neuronal atrophy was drawn (Fig. 4) with Eq.3 (Materials and Methods). It can be used to determine the order of magnitude of the pseudo-loss, as a function of the size of the particle and of the section
Before of
7, 6,
xlO00
r'i
_
II
L~
After atrophy of the perlkaryon
th#
:
--:
--;
~:
~ .
.
.
.
.
.
:
9
5
-
;
.
.
.
.
--
.
:
l
17
13
Diameter in am
b
Fig. 3. a: a simulated loss of 40% of the neuronal profiles above 10 p m in diameter. Total number of neurones per unit area before atrophy: 551/mm 2, after atrophy: 452.2/mm 2 (18% loss), b: neuronal density per unit volume, corresponding to a, after unfolding. The total n u m b e r before atrophy was: 18,100/mm 3, after: 15, 200/mm 3 (16% loss). Note the increase in the proportion of small neurones, not visible in a.
atrophy
I
Nor neuror~/mm3
0.
perlkaryon
thickness. The slope of this curve is steeper with the increase of the relative caliper diameter, C r, but not in a proportional manner: e.g. for neurons of a 10 pm g~afive ..,'1 Caliper
Pseudo Loss%
/
15
'~"'~'/~J 7
8~
/.,..~"
4333 3
1.667 !
0~ 6
~1
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~
b
~._-
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Fig. 2. a: a simulated atrophy of the neurons above l0 pm in diameter, by 50% of their diameter, as considered in a volume. The total number of neurons is, by definition, identical before and after atrophy, b: corresponding histogram of neuronal profiles per unit area, using a section thickness of l p m : the total number before atrophy was: 407/mm 2, after it: 327/mm 2. Pseudo-loss = 80 neurons on a population of 407, i.e. a loss of 19.7 %.
I
25
50
75
gg.g
~eU~lr/ofbCakw Fig. 4. Chart giving the magnitude of the pseudo-loss (y axis) as a function of the atrophy of the caliper diamete~ (= diameter for spherical cells).
98 P1agnitude of the pseudo-loss
i,o o,a 0.6
/
0,4 0,2
o.o
!
0
2
,
I
4
I
!
I
5 8 I0 Relative CaliperOiameter. Cr
I
12
I
14
I
15
Fig. 5. Factor of pseudo-loss as a function of the relative caliper diameter (Cr). y-axis: slope of the curves of Fig. 4, i.e. the factor of proportionality between atrophy and pseudo-loss. The closest to 1 y lies, the highest the proportion of pseudo-loss. Note that the relationship is not linear and varies greatly for low values of Cr
diameter, the slope of the curve (Fig. 5) is 0.9 with a 1 pm thick section, 0.5 with a 10 pm section, and 0.09 with a 100 #m thick section. The various slopes of Fig. 5 can thus be used to evaluate the possible severity of the pseudo-loss: the closer to 1, the higher the pseudo-loss. The values of the slopes are linked to Cr in a non-linear way (Fig. 5) and are always smaller than 1 since the proportion of the psuedo-loss can obviously not exceed the propoi'tion of atrophy: e.g. an atrophy of 50% of the diameter cannot explain a loss of 5~% of the cellular profiles. Great variations in the severity of the pseudoloss were noted, especially for Cr levels below 2 (Fig. 5).
Evaluating the risk of pseudo-loss when counting m'urons The diameter equivalent circle of cortical neurons varies roughly from 6 (granule cells) to 60 pm (Betz cells): with a section thickness of 20 pro, the Cr varies from 0.3 to 3. The possible pseudo-loss for these Cr are not negligible: from 12.5% for the small neurons to more than 37% for the large ones, with an atrophy of 50% of the neuron diameter (see Fig. 5). Nucleoli have a diameter from 3.58 pm in normal cases to 2.84 #m in Aizheimer's dementia (values calculated from ref. 16). With the same section thickness of 20 pro, C. is 0.179 in normal cases and 0.142 during AIzheimer's disease. With the reported atrophy of 21% of their diameter, the pseudo-loss for nucleoli would then remain below 3.5% DISCUSSION
The consequences of neuronal atrophy are obviously numerous, the most conspicuous being the reduction of the synaptic area. In this paper, neuronal atrophy is dealt with only as a cause of pseudo-loss. Only those parts of the neuron which are usually enumerated when one tries to ascertain a neuronal loss were taken into account,
mainly the perikaryon and the nucleolus. Wrong conclusions may be drawn when the volume of these structures is reduced in relation with the pathological condition. Perikaryal atrophy has been known for a long time under various names: Nissl's chronic cell disease, shrinkage of nerve cells ~, cell sclerosis 21, simple atrophy ~'. Recent textbooks T M do not deal with this change although its very existence has now been ascertained by quantitative measurement 4"e3. Nucleolar atrophy has been demonstrated by Mann et a116'~7. Automatic counting of perikaryal profiles has been used ~8'e4 for the study of neuronal loss during senile dementia of the Alzheimer's type. With our normal data and the reported loss of perikaryal profiles, the pseudoloss would not exceed 2% (Fig. 3). However, these results have been obtained by assuming that the number of small profiles remained unchanged: this was not the case in the studies by Terry et al. 24 and by Mountjoy et al. ~s. In both, an increase in the number of small profiles which was found to be due to gila rather than to neurons was noted for some areas. With the unfolding procedure, the inference of a neuronal loss relies heavily upon the identification of these small profiles: had they been counted as neurons, the loss would have appeared much less significant. In these studies ~8'24, all the small profiles were considered glial. This systematic point of view could lead to an underevaluation of the density of small, atrophied neurons or of profiles due to the section of large neurons. We used Nissl substance to identify small neurons for the baseline data. This probably still underscored the density of small neurons. Immunocytochemistry could help to identify them: in the nucleus basalis of Meynert, neuron-specific enolase demonst, :ed that many of the small profiles which would not have been considered with Nissl stain were actually neuronal 4. Other authors relied upon the manual counting of profiles ~6a7 and took into account the number of nucleolated pyramidal cells within cortical layers Ill and V. As the Cr of nucleoli is particularly low (around 0.1), the amount of pseudo-loss, even at its worst, remains small (below 5%). Pseudo-loss is reduced when the ratio of particle caliper diameter to section thickness is small (low Cr). Increasing the section thickness is limited by practical considerations: the quality of the microscopic image is lower than with thin sections; focusing has to be changed in order to evaluate the entire field depth; and the number of neurons to be evaluated in the same area is much larger. Lowering the pseudo-loss can also be achieved by enumerating smaller particles such as nucleoli, as already mentioned. It will no be a surprise for most microscopists that the pseudo-loss with this old technique is small. Such a simple procedure of evaluating
99 neuronal density should be considered, possibly by looking at chart (Fig. 4), before implementing new, elaboi'ate or expensive morphometric methods. It may be added that the reduction in neuronal density in a small cortical sample, when considered alone, cannot give information on neuronal loss unless the total volume of the cerebral cortex and the shrinkage of the sample ~a are known. As both pieces of information are hard to collect with a sufficient precision, only the measure of the relative proportion of large and small _neurons is presently accurate and this underlines the significance of the repeated finding of a loss of large neurons 1s'24 or of large pyramidal cells 17. The link between the macroscopic measurement of cortical atrophy " u s , and the microscopic evaluation of cellular density ~'~a'24 is however still missing: the magnitude of the neuronal loss remains therefore unknown so far. Numerical unfolding is a useful and powerful instrument for simulation studies. On the other hand, the evaluation of the density per unit volume in reality can now be performed by more direct techniques than numerical computation: direct 3-dimensional counting 27 or using a dissector 22 or a selector 9. These techniques have to be implemented when the expected pseudo-loss is higher than the precision of the measurement. A n easy way to appreciate the risk of pseudo-loss and of its magnitude is suggested in this paper (chart of Fig. 4), REFERENCES 1 Abercrombie, M., Estimation of nuclear population from microtomic sections, Anat. Rec., 94 (1946) 239-247. 2 Adams, J.H., Corsellis, J.A.N. and Duchen, L.W., Greenfield's Neuropathology, 4th Edn., Edward Arnold, London, 1984. 3 Agduhr, E., A contribution to the technique of determining the number of nerve cells per volume unit of tissue, Anat. Rec., 80 (1941) 191-202. 4 Allen, S.J., Dawbarn, D. and Wilcock, G.K., Morphometric immunochemical analysis of neurons in the nucleus basalis of Meynert in AIzheimer's disease, Brain Research, 454 (1988) 275-281. 5 Bach, O. Kugelgr6ssenverteilung und Verteilung der Schnittkreise; ihre wechselseitigen Beziehungen und Verfahren zur Bestimmung der einen aus der andern, In E.R. Weibei and H. Elias (Eds.), Quantitative Methods in Morphology, Springer Verlag, Berlin, 1967, pp. 23-45. 6 Bielschowsky, M., Histopathology of nerve cells, In W. Penfield (Ed.), Cytology and Cellular Pathology of the Nervous System, P.B. Hoeber, New York, 1932, pp 147-188. 7 Blackwood, W., and Corsellis, J.A,N., Greenfield's Neuropathology, 3rd Edn., Edward Arnold, London, 1976, p. 16.. 8 Cruz-Orive, L.-M,, Distribution-free estimation of sphere size distribution from slabs showing overprojections and truncation, with a review of previous methods, J. Microsci., 131 (1983) 265-290. 9 Cruz-Orive, L.-M., Particle number can be estimated using a dissector of unknown thickness: the selector, J. Microsc., 145 (1986) 121-142. 10 Duyckaerts C., Hauw J-J, Piette E, Rainsard V., Poulain C., Berthaux E and Escourolle R., Cortical atrophy in senile dementia of the Alzheimer type is mainly due to a decrease in
The chart of Fig. 4 can also be used to find out the correction factor which has to be applied to a density of neuronal profiles when the atrophy of their diameter is known. The evaluation of neuronal density can be planned in the following way: a pilot study determines the mean diameter of the neurons in the samples of the normal situation. The C r is calculated by dividing the mean diameter by the section thickness. The size of the neuronal profiles is then controlled in the pathological cases and the degree of pseudo-loss is evaluated with the chart ~f Fig. 4. The study is performed without further corrections if the pseudo-loss is negligible. Otherwise, 3 methods can be applied: (1) a special way of counting the neurons u s i n g dissector, selector or direct 3-dimensional counting is used; these methods are probably the most accurate bur they are expensive in terms of working time or of equipment; (2) a computer is used to apply an unfolding algorithm; (3) if the neuronal population is homogeneous and the approximation of the neuronal shape by a sphere seems acceptable, the real loss is calculated (real 3-D loss = apparent 2-D loss-pseudo-loss) using the chart or Eq. 3 of Materials and Methods, or some other formulae, taking the lost cap into account ~i.
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