History of Modern Stereology

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1 History of Modern Stereology Saturday, December , 12:35 PM History of Modern Stereology Citation: Mouton, Peter R. (2005) History of Modern Stereology, IBRO History of Neuroscience [ Accessed: (date) Peter R. Mouton* The Feldberg Meeting Stereology literally translates from the Greek as 'the study of objects in 3-D'. The 3-D analysis of objects dates to ancient Egypt and the development of Euclidean geometry. Stereology, however, officially began as a scientific discipline until less than half a century ago, at a meeting of diverse researchers from fields of biology, geology, engineering, and materials sciences in A biologist, Professor Hans Elias, had the idea of organizing this meeting at a resort called the Feldberg in the Black Forest of Germany for the benefit of scientists in several disciplines who had one thing in common: They were struggling with the quantitative analysis of 3-D images based on their appearance on 2- D sections. At this meeting, Prof. Elias suggested stereology as a useful term to describe their discussions. Shortly after the first stereology meeting at the Feldberg, Prof. Elias sent a small announcement on the proceedings to the journal Science. Soon thereafter, he received a large response from researchers in academia, government agencies, and private industry at institutions around the world. They contacted Prof. Elias for information about the next stereology meeting. What Elias suspected had been right: Scientists across a broad spectrum of disciplines needed new approaches for the analyses of 3-D objects based on their appearance on 2-D sections. The International Society for Stereology The following year, in 1962, the International Society for Stereology (ISS) was established with the 1st Congress of the International society for Stereology in Vienna, Austria. At this congress, Prof. Hans Elias was elected the founding president (Table 1). Table 1. Origins of Stereology (Hans Elias, 1961) Geology Biology Materials Science Engineering First Congress of the International Society for Stereology (1SS), Vienna, Austria, /17

2 The First Decade of Stereology ( ) As a result of recent technological innovations in microscopy, biologists in the 1960s could view tissues, cells, blood vessels and other objects in tissue with greater clarity and specificity than ever before. These developments included the availability of affordable, high- resolution optics for light microscopy; refinements in electron- microscopy instruments and methods for preparation of specimens, and immune- based visualization of specific proteins in biological tissue (immunocytochemistry). With the ability to see more objects in greater detail than ever before, they began to ask the obvious question: How much is there? To answer this question, biologists focused on a simple goal: To obtain reliable 3- D information about biological objects based on their 2- D appearance. For ideas on how to proceed, they turned toward the objective mathematic- based methods emerging from the field of stereology. At ISS congresses held every other year, stereologists from many disciplines began to present research and discuss their theories on how best to solve their common problems. Biologists attending these meetings discovered that their stereology colleagues in different fields had developed practical approaches that would be of immediate use in their research, including the following: In 1637, Bonaventura Cavalieri, a student of Galileo Galilei in Florence during the height of the Italian Renaissance, showed that the mean volume of a population of non- classically shaped objects could be estimated accurately from the sum of areas on the cut surfaces of the objects (right). The Cavalieri Principle provides the basis for the volume estimation of biological structures from their areas on tissue sections (Figure 1). Fig 1. Sectioning for volume estimation by Cavalieri principle In 1777, Count George Leclerc Buffon presented the Needle Problem to the Royal Academy of Sciences in Paris, France. The Needle Problem supplies the probability theory for current approaches to estimate the surface area and length of biological objects in an unbiased (accurate) manner (Figure 2). 2/17

3 Fig 2. Buffon's Needle problem In 1847, the French mining engineer and geologist, Auguste Delesse, demonstrated that the expected value for the volume of an object varies in direct proportion to the observed area on a random section cut through the object. The Delesse Principle provides the basis for accurate and efficient estimation of object and regions volumes by point counting (Figure 3) (Table 2). Fig 3. Methods for estimation of profile area on random sections Table 2. First Decade of Stereology ( ) Biology discovers methods used in materials science Improvements in tissue processing and microscopy methods Bi- annual, multidisciplinary ISS congresses The Second Decade of Modern Stereology ( ) In the 1970s biologists began to favor the newer stereology approaches over more rough assessments by so- called 'experts', and subjective (biased) sampling methods. Two peer- review journals were established that focused primarily on stereology: the Journal of Microscopy and Acta Stereologica (now Image Analysis & Stereology). Stochastic Geometry and Probability Theory An important breakthrough occurred in the 1970s when mathematicians joined the ISS and began to apply their unique expertise and perspective to problems in the field. Mathematicians, also known as theoretical stereologists, recognized the fault in the traditional approaches to quantitative biology based on modeling biological structures as classical shapes (spheres, cubes, straight lines, etc.), for the purpose of applying Euclidean geometry formulas, e.g. area = πr2. These formulas, they argued, only apply to objects that fit the classical models, which biological objects did not. They also rejected so- called 'correction factors' intended to force biological 3/17

4 objects into Euclidean models based on false and non- verifiable assumptions. Instead, they proposed that stochastic geometry and probability theory provided the correct foundation for quantification of arbitrary, non- classically shaped biological objects. Furthermore, they developed efficient, unbiased sampling strategies for analysis of biological tissue at different magnifications (Figure 4, Table 3). Fig 4 Systematic- random sampling Table 3. Unbiased Sampling Strategies Developed for Analysis of Anatomically Defined Reference Spaces in Biological Tissue. Matheron (1972) Random Set Theory and Applications to Stereology J. Microscopy 95: Miles (1976) Precise and General Conditions for the Validity of a Comprehensive Set of Stereology Formulae J. Microscopy 107: Cruz- Orive (1976) Sampling Designs for Stereology J. Microscopy 122: The combination of these unbiased sampling and unbiased geometry probes were then used to quantify the first- order stereological parameters (number, length, area, and volume) to anatomically well- defined regions of tissue. These studies showed for the first time that it might be possible to use assumption- and model- free approaches of the new stereology to quantify firstorder stereological parameters (number, length, surface area, volume), without further information about the size, shape, or orientation of the underlying objects (Table 4). Table 4. Second Decade of Stereology ( ) Seek mathematical justification for methodology Solidify on grounds of stochastic geometry and probability theory The Third Decade of Modern Stereology ( ) By the 1980s, biologists had identified the most severe sources of methodological bias that introduced systematic error into the quantitative analysis of biological tissue. Yet before the field could gain greater acceptance by the wider research community, stereologists would have to resolve one of the oldest, well- known, and most perplexing problems: How to make reliable counts of 3- D objects from their appearance on 2- D tissue sections? 4/17

5 The Corpuscle Problem The work of S. D. Wicksell in the early 20th century (Wicksell, 1925) demonstrated the Corpuscle Problem - the number of profiles per unit area in 2-D observed on histological sections does not equal the number of objects per unit volume in 3-D; i.e. NA NV. The Corpuscle Problem arises from the fact that not all arbitrary- shaped 3- D objects have the same probability of being sampled by a 2- D sampling probe (knife blade). Larger objects, objects with more complex shapes, and objects with their long axis perpendicular to the plane of sectioning have a higher probability of being sampled (hit) by the knife blade, mounted onto a glass slide, stained and counted (Figure 5). Fig 5. The Corpuscle problem Correction Factors A close examination of classical geometry reveals a number of attractive formulas that, if they could be applied to biological objects, would provide highly efficient but assumption- and modelbased approaches for estimation of biological parameters of tissue sections. Since the work of S. D. Wicksell in the 1920s, many workers have proposed a variety of correction factors in an effort to 'fit' biological objects into classical Euclidean formulas. This approach using correction formulas requires assumptions and models that are rarely, if ever, true for biological objects. These formulas simply add further systematic error (bias) to the results. For example, imagine that we decide that a group of cells has, on average, shapes that are about '35% non-spherical'. Unless these assumptions fit all cells, then correcting raw data using formulas based on this assumption would lead to biased results (e.g. Hedreen, 1998). The problems arise immediately when one inspects the underlying models and assumptions required for correction factors. How does one quantify the nonsphericity of a cell? How does one account for the variability in nonsphericity of a population of cells? Or in the case of a study with two or more groups, should not different effects on cells 5/17

6 require different factor to correct for relative differences in nonsphericity between groups? To verify these assumptions is so difficult, impossible, or time- and labor- intensive that it prohibits their use in routine biological research studies. The bottom line is that correction factors fail because the magnitude and direction of the bias cannot be known; if it could, there would be no need for the correction factor in the first place! Note, however, that if the assumptions of a correction factor were correct, the correction factor would work. Despite numerous attempts using so- called 'correction factors', this approach failed to overcome the Corpuscle Problem. By the early 1980s, the Corpuscle Problem remained a significant test for the credibility of the newly emerging field of unbiased stereology. The Disector Principle The solution to the Corpuscle Problem came in a Journal of Microscopy report in 1984 by D. C. Sterio, the one- time pseudonym of a well- known Danish stereologist. The solution, known as the Disector principle** (Figure 6), became the first unbiased method for the estimation of the number of objects in a given volume of tissue (Nv), without further assumptions, models or correction factors. A disector is a 3-D probe that consists of two serial sections a known distance apart (disector height), with a disector frame of known area superimposed on one section. In 1986 Gundersen expanded the Disector principle from two sections a known distance apart (physical disector) to optical planes separated by a known distance through a thick section (optical disector). The number of objects in which the 'tops' fall within the disector volume provides an unbiased estimate of the number per unit volume of tissue. The disector makes use of Gundersen's unbiased counting rules (Gundersen, 1977), which avoids biases (i.e. double counts) arising from objects at the edge of the counting frame (edge effects). Fig 6. The Disector principle The fractionator method, a further refinement for counting total object number, eliminated the potential effects of tissue shrinkage in the estimation of total object number in an anatomically defined volume of tissue (Gundersen, 1986; West et al., 1991). The disector and fractionator methods provide reliable estimates of objects in a known volume by repeatedly applying the disector counting method at systematic- random locations through an anatomically defined volume of reference space (Figure 7). 6/17

7 Fig 7. Fractionator principle The combination of disector- based counting with highly efficient, systematic- random sampling allowed optimal counting efficiency by counting only about 200 cells per individual. Other techniques introduced in the 1980s included methods for unbiased estimation of object sizes, including the nucleator, rotator, and point- sampled intercepts (Gundersen et al., 1988 a, b) (Figure 8). Fig 8. Size estimators By this point it became clear that making an unbiased estimate of any stereological parameter required choosing the correct probe, the one that does not 'miss' any objects of interest. By ensuring that the dimensions (dim) in the parameter of interest with a probe containing sufficient dimensions so that the total dimensions in the parameter and probe equal at least 3 (parameterdim + probedim > 3) (Table 5). Table 5. Dimensions (dim) of Objects and Probes in 3D 7/17

8 Parameter (dim) Probe (dim) Total dim (parameter + probe) Volume (3) Point grid (0) 3 Area (2) Line (1) 3 Length (1) Plane (2) 3 Number (0) Disector (3) 3 All Variation Considered Biologists realized that by avoiding all source of error (variation) arising from assumptions and models, the total observed variation in their results, as measured by the (coefficient of variation (CV = std dev/mean), could be accurately partitioned into its two independent sources: biological variation (inter- individual) and sampling error (intra- individual). Inter- individual differences arising from biological sources (evolution, genotype, environmental factors, etc.) typically constitute the largest source of variation in any morphological analysis of biological tissue. By sampling more individuals from the population, this source of variation will diminish and thereby reduce the total observed variation in the data. However, the cost of analyzing more individuals is high in terms of time, effort, and resources. For this reason it can be important to examine first the second contributor to the total observed variation, sampling error, which is variation arising from the intensity of sampling within each individual. Sampling error is expressed in terms of coefficient, CE. In general terms, reducing sampling error, i.e. by sampling more sections and/or more regions within each section, costs less in terms of time and resources than sampling more individuals. Thus, by partitioning the observed variation in stereological results into variation arising from biological sources and sampling error, bio- stereologists learned to design sampling schemes that were optimized for maximal efficiency. Do More, Less Well Prior to the modern era of stereological approaches, the amount of work exerted to make an estimate provided the best means of assessing the value of that estimate. In the 1960s, for example, a worker in one influential publication spent two years counting 242,681 cells in a particular area on one side of the brain! Through the multidisciplinary efforts of biologists, mathematicians, and statisticians in the ISS, stereologists learned that an optimal level of sampling within each individual could be defined, regardless of the organism or structure of interest: Question: What is the optimal number of animals and sections to analyze to make a reliable estimate of a stereological parameter (number, length, surface area, volume)? Answer: The sampling intensity that most efficiently reduces the total observed variation per unit of time spent analyzing tissue. In practice, the starting point is to sample the reference space, i.e. the volume of tissue containing the objects of interest, into about 10 systematic- random sections, quantify the parameter of interest, and then repeat this on about 2-3 individuals for each group. From these results the fraction of the total observed variation contributed by biological and sampling error can be estimated. When the sampling error (CE) achieves a point of diminishing returns, i.e. when further sampling of sections and regions within individuals causes only minor reductions in the observed variation, then time and effort are best shifted toward analyzing more individuals from the population of interest. Once a representative number of individuals have been analyzed, usually n = 5 to 10 per group, the results should provide accurate, precise, and efficient data for statistical testing of the hypothesis of biological interest, such as: Is there a statistically significant difference in cell number between the two groups? The esteemed Swiss stereologist, Prof. Ewald Weibel, named this approach 'Do More, Less Well' 8/17

9 The esteemed Swiss stereologist, Prof. Ewald Weibel, named this approach 'Do More, Less Well' (Table 6). Table 6. Third Decade of Stereology ( ) Accurate, precise, and efficient estimates of all stereological parameters in biological tissue. Do More Less Well The Fourth Decade of Modern Stereology ( ) Modern stereology introduced an entirely new set of rules for quantification of biological objects in tissue sections. Many biologists acquired stereology training from comprehensive 3-4 day workshops held in conjunction with national and international meetings, including the Society For Neurosciences (USA), International Brain Research Organization, and the ISS. As a result, stereology publications in the peer- review literature continued to grow in an exponential manner from the early 1960s through the 1990s, as shown in Figure 9. Fig 9. Stereology citations in pubmed database ( ) Objections to New Stereology Not surprisingly, resistance arose from old- guard biologists who objected to the 'new stereology' on several grounds, which contributed to the slow acceptance of these approaches during the last four decades. First, as usual in the case of progress, there was the inertia of tradition - highly regarded papers used older, assumption- and model- based approaches to the morphometric

10 analysis of biological tissue. Many authors of these works simply did not wish to change. To use the analogy from baseball - you don't change the line-up when you get to the World Series. A second reason for the slow conversion to new stereology was that, without consideration for the demonstrated accuracy of the new approaches over older methods, many biologists considered new stereology as too radical. The group of modern stereologists led by Profs Hans Gundersen of Denmark, Luis Cruz- Orive of Spain, and Adrian Baddeley of Australia argued that the older methods biased sampling approaches and Euclidean- based assumptions and models (e.g. 'Assume a cell is a sphere...') should be rejected entirely. Their critics felt that this approach failed to follow the time-honored tradition of step-by-step progress built on the existing body of knowledge. In response, the stereologists contended that Euclidean- based methods simply did not apply to populations of arbitrary- shaped biological objects. A third reason some biologists were slow to adopt the new stereology arose from confusion over the term bias, which has several different connotations. In the colloquial usage, bias refers to prejudice or predisposition. To stereologists, however, biased refers to the presence of systematic error in a method. When a method avoids bias in the form of faulty and non- verifiable assumptions and models, increased sampling of the reference space will cause mean estimates of the parameter to converge on the true mean value for the population. In order to avoid the controversy involving 'biased vs. unbiased' data, many bio- stereologists now prefer the term design- based stereology to refer to the assumption- and model- free methods of modern stereology. Stereological Bias and Precision Bias refers to the deviation of a result from the expected or true value as a result of systematic error (Figure 10). Stereological bias arises from faulty assumptions, erroneous models, and incorrect 'correction' factors that cause morphometric measurements such as the number, surface area of volume of cells to diverge from the true value by an unknown and un-measurable amount. With care to ensure that no known sources of bias enter the data, the results from unbiased methods should cluster around the true or expected value, as shown in the two upper targets in the figure. Fig 10. Predicted accuracy and precision for biased and unbiased methods Unbiased methods provide the first step toward accurate data in morphometric analysis of 10/17

11 Unbiased methods provide the first step toward accurate data in morphometric analysis of biological tissue, but equally important is the idea of 'accuracy before precision'. That is, even with biased, inaccurate, and assumption- and model- based, methods, the data cluster around a value other than the true value, Increased sampling will reduce variability (increase precision), regardless of whether the methods are biased or not, as shown by the two lower targets in the figure. The issue is that with biased methods, the effort to increase precision is misguided if the investigator lacks confidence in the accuracy of the results. In contrast, a characteristic of unbiased methods is that additional sampling (more probes, sections, and animals) will reduce the variation around the central tendency, causing the sample estimate to converge on the true mean value of the parameter. One important caveat: As shown by Figure 11, at the start of a study investigators are unaware of the target values; otherwise, there would be little point in doing the study. Therefore, to ensure that the collection of data focused the results on the true value, morphometric studies should start with unbiased methods. Fig 11. Lack of target values at start of study Non-Stereological Bias Not all sources of systematic error (bias) in morphometric data arise from faulty models, assumptions, and correction factors. The processes in preparing tissue for stereological analysis can contribute systematic error to data in the form of non- stereological bias. For example, artifacts of tissue processing, e.g. shrinkage, needed to view microscopic objects can cause sample estimates to differ from true values. Other examples of non- stereological sources of error range from ascertainment bias, which occurs when estimates based on samples from one population are extrapolated to another population, and failure of stains to penetrate through tissue and fully reveal objects of biological interest bias, leading to recognition bias. Whereas stereological bias cannot be quantified, non- stereological bias can be identified, minimized, and eliminated; hence non- stereological bias can be referred to as uncertainty. Instead of relying on unbiased sampling and geometric probes to guarantee unbiased results, those involved in all aspects of stereology studies must use their skills and experience to avoid procedures that introduce stereological and non-stereological bias. 11/17

12 Studies in the 1990s using new stereology clarified an important issue concerning the degree of brain cell (neuron) loss during normal aging. The accepted dogma at the time held that marked neuron loss begins around age 50 and continues through old age. This explanation appeared to provide a logically compelling explanation for the clear age- related reduction in motor skills and some cognitive abilities. Since these studies were based on incomplete sampling and density estimators (number cells per unit volume or area, i.e. NV or NA), which can be affected by changes in neurons and/or changes in the reference space, several studies approached this question using design- based stereological methods. These studies found no evidence of agerelated neuron loss in the same regions reported by studies using density estimators to undergo neuron loss during normal aging. The findings by Prof. Herbert Haug of Germany showed that an inverse relationship exists between age and tissue shrinkage. Since older tissue undergoes less shrinks than younger tissue, then the changes reported as neuronal loss by density estimators were actually changes in the reference space, i.e. the denominators in NV and NA. By the year 2000, many journal editors and reviewers, regulatory agencies, and funding organizations began to state preferences for new stereology approaches, which they regarded as the state- of- the- art methodology for the morphological quantification of biological tissue. This acceptance, backed by the implied consequences for publications, approval, and funding, sent a strong message to research scientists in the biomedical research community (Table 7). Table 7. Fourth Decade of Modern Stereology ( ) Journal editors publish editorials that modern stereology as 'state-of-the-art'. Grant agencies prefer hypothesis- driven studies using new stereology. The Fifth Decade of Modern Stereology (2001-present) Several major developments underway around the turn of the 21st century inaugurated modern stereology into its fifth decade (Figure 12). Thus far, these achievements have been the commercial availability of affordable computerized systems that combine high- resolution microscopy, hardware (motorized stages, computers, video cards) with user- friendly software for unbiased sampling and probes. These modern systems generate 1, 2, and 3- D probes (left, virtual spheres for length; right, virtual cycloids for surface area) for sections cut in any convenient orientation (Figure 13, (Figure 14). 12/17

13 Fig 12. Computerized stereology system (The Stereologer) Fig 13. Length estimation using virtual sphere probe 13/17

14 Fig 14. Surface area estimation using virtual cycloids These computerized hardware- software systems made cutting- edge stereology affordable for all interested biologists, in support of accurate, precise, and efficient approaches for testing a wide variety of biological hypotheses. Conclusion Since Prof. Hans Elias convened the historic first meeting at the Feldberg, the field of modern stereology has developed state- of- the- art approaches for morphometric analysis of biological tissue. These achievements are the result of sustained efforts from stereology 'disciples' in the fields of statistics, biology, microscopy materials science, and computer sciences during the past four decades. Peter Mouton, Ph.D. Director Stereology Resource Center ( 104 Ringneck Court Chester MD USA E- mail: peter@disector.com *Author of Principles and Practices of Modern Stereology: An Introduction For Bioscientists, The Johns Hopkins University Press, Baltimore, May **Alert readers will recognize that 'Disector' and 'D. C.Sterio' are anagrams, e.g. 'Flit on cheering angels' = 'Florence Nightingale'. References 14/17

15 Buffon G.L. Compte de (1977) Essai d'arithmétique morale. Supplemental Histoire Naturelle, Vol. 4. Imprimarie Royale, Paris. Calhoun M.E. & Mouton P.R. (2001) New developments in neurostereology: length measurement and 3d imagery. J. Chem. Neuroanat. 21: Cavalieri, B (1635) Geometria Indivisilibus Continuorum. Typis Clementis Bonoiae. Reprinted 1966 as Geometris degli Indivisibili. Union Tipografico- Editrice, Torinese, Torino. Cruz- Orive (1976) Sampling designs for stereology. J. Microsc 122: Dam, AM. (1979) Brain shrinkage during histological procedures. J. Hirnforschung 20, Delesse, M.A. (1847) Procédé mécanique pour déterminer la composition des roches. Compte- Rendus d' Académie des Sciences, Paris, 25, Dorph- Petersen, K.A., Nyengaard, J.R., & Gundersen, H.J. (2001) Tissue shrinkage and unbiased stereological estimation of particle number and size. J. Microsc. 204: Gokhale, A.M., Evans, R.A., Mackes, J.L., & Mouton, P.R. (2004) Design- based estimation of surface area in thick tissue sections of arbitrary orientation using virtual cycloids. J. Microsc. 216: Gundersen, H.J.G. (1977) Notes on the estimation of the numerical density o arbitrary profiles: the edge effect. J. Microsc. 111: Gundersen, H.J.G. (1979) Estimation of tubule or cylinder LV, SV, and VV on thick sections. J. Microsc. 117, Gundersen, H.J.G., Osterby, R. (1981) Optimizing sampling efficiency of stereological studies in biology: Or 'Do more less well!' J. Microsc. 121: Gundersen, H.J.G. (1986) Stereology of arbitrary particles. A review of number and size estimators and the presentation of some new ones, in memory of William R. Thompson. J. Microsc. 143:3-45. Gundersen H.J.G. & Jensen E.B. (1987) The efficiency of systematic sampling in stereology and its prediction. J. Microsc. 147: Gundersen H.J.G. & Jensen E.B. (1987) The efficiency of systematic sampling in stereology and its prediction. J. Microsc. 147: Haug, H., Kuhl, S., Mecke, E., Sass, N., & Wasner, K. (1984) The significance of morphometric procedures in the investigation of age changes in cytoarchitectonic structure of human brain. J. fur Hirnforschung 25: Hedreen, J.C. (1998) What was wrong with the Abercrombie and empirical cell counting methods? A review. Anatomical Record, 250, Hedreen, J.C. (1988) Lost caps in histological counting methods. Anatomical Record 250, Hilliard, J.E. (1967) Determination of structural anisotropy. Proceedings of the Second International Congress for Stereology (ed. H. Elias). Springer, Berlin. Jensen Vedel, E.B & Gundersen, H.J.G. (1993) The Rotator. J. Microsc. 170: Larsen, J.O., Gundersen, H.J. & Nielsen, J. (1998) Global spatial sampling with isotropic virtual 15/17

16 planes: estimators of length density and total length in thick, arbitrarily orientated sections. J. Microsc. 191: Long, J.M., Mouton, P.R., Jucker, M, & Ingram, D.K. (1999) What counts in brain aging? Designbased stereological analysis of cell number. J. Gerontology 54A: B407- B417. Matheron (1972) Random set theory and applications to stereology. J. Microsc. 95: Mandelbrot, B.B. (1977). Form, Chance, and Dimension. W.H. Freeman & Co., New York. Mattfeldt, T. & Mall, G. (1984) Estimation of surface and length of anisotropic capillaries. J. Microsc. 153, Miles, R.E. (1976) Precise and general conditions for the validity of a comprehensive set of stereology formulae. J. Microsc. 107: Mouton, P.R., Pakkenberg, B., Gundersen, H.J.G., & Price, D.L. (1994) Absolute number and size of pigmented locus coeruleus neurons in the brains of young and aged individuals. J. Chem. Neuroanat. 7: Mouton, P.R., Martin, L.J., Calhoun, M.E., Dal Forno, G., & Price, D.L. (1998) Cognitive decline strongly correlates with cortical atrophy in Alzheimer's dementia. Neurobiol. Aging 19, Mouton, P.R. (2002) Principles and Practices of Unbiased Stereology: An Introduction for Bioscientists. The Johns Hopkins University Press, Baltimore. Mouton, P.R., Long, J.M., Lei D-L, Howard, V., Jucker, M., Calhoun, M.E. & Ingram, D.K. (2002) Age and gender effects on microglia and astrocyte number in brains of mice. Brain Research 956, Mouton, P.R., Gokhale, A.M., Ward, N.L. & West, M.J. (2002b) Stereological length estimation using spherical probes. J. Microsc. 206, Pakkenberg, B., & Gundersen, H.J.G. (1997) Neocortical neuron number in humans: effects of sex and age. J. Comp. Neurol. 384, Paumgartner, D., Losa, G. & Weibel, E.R. (1981). Resolution effect on the stereological estimation of surface and volume and its interception in terms of fractal dimension. J. Microsc. 121, Saper, C.B. (1996) Any way you cut it: A new journal policy for the use of unbiased counting methods. J. Comp. Neurol. 354:5. Smith, C.S. & Guttman, L. (1953) Measurement of internal boundaries in three- dimensional structures by random sectioning. Trans. AIME 197, Sterio, D.C. (1984) The unbiased estimation of number and sizes of arbitrary particles using the disector. J. Microsc. 134: Weibel, E.R. (1979) Stereological Methods, Vol. 1. Practical Methods for Biological Morphometry. Academic Press, London. Weibel, E.R. (1980) Stereological Methods, Vol. 2. Theoretical Foundations. Academic Press. London. Wicksell, S.D. (1925) The corpuscle problem. A mathematical study of a biometric problem. Biometrika 17:

17 West, M.J., Slomianka, L., & Gundersen, H.J.G. (1991) Unbiased stereological estimation of the total number of neurons in the subdivisions of the rat hippocampus using the optical fractionator. Anatomical Record 231, West, M.J. (1999) Stereological methods for estimating the total number of neurons and synapses: issues of precision and bias. TINS 22: Appendix Twenty Central Concepts of Modern Stereology ( ) 1. Developed by materials scientist, mathematicians, and biologists since the early 1960s. 2. Estimates volume, surface area, length, number and their variability. 3. Based on stochastic geometry and probability theory. 4. Advanced mathematical background not required for users. 5. Applicable to all biological structures, regardless o size, shape or orientation. 6. Appropriate for defined reference space, rather than arbitrary 'regions of interest'. 7. Uses highly efficient systematic- random sampling. 8. Focuses on unambiguously defined objects. 9. Unbiased for absolute parameters, not ratios, e.g. density. 10. Tissue processing requirements different from older methods. 11. Avoids tissue- processing artifacts, i.e., tissue shrinkage/expansion, lost caps, etc. 12. Avoids models and assumptions, e.g. 'Assume a cells is a sphere...' 13. Does not use inappropriate correction formulas. 14. Sampling optimized for maximum efficiency ('Do More, Less Well'). 15. Efficient sampling based on true biological variability. 16. Does not require computerized hardware- software systems. 17. Computerized stereology systems are highly efficient. 18. Statistical power cumulative for multiple studies on same populations. 19. Preferred by journal editors and grant reviewers since early 1990s. 20. Potential for dissemination of results through Web- accessible database. 17/17