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Home > Stereology Educational Program > The History Of Modern Stereology
 
The History Of Modern Stereology


The History Of Modern Stereology

Peter R. Mouton, Ph.D.
Professor of Stereology
Department of Pathology & Cell Biology
University of South Florida School of Medicine
Tampa, Florida

Accuracy and Precession



The Feldberg meeting


Stereology literally translates from the Greek to, the study of objects in 3-D. Human interest in this subject dates to ancient Egypt and the development of Euclidean geometry in Greece. As a scientific discipline, however, stereology started in the early 1960s at a multidisciplinary meeting of biologists, geologists, engineers, and materials scientists. This gathering at a resort called the Feldberg in the Black Forest of Germany. was organized by a biology professor named Hans Elias. The idea for this meeting came about in response to Elias' perception that scientists in different disciplines shared a problem common: the need to quantify 3-D images from the appearance of the objects on 2-D sections. During the course of this meeting, Prof. Elias and others agreed that the term "stereology" provided a workable description for the purpose of their meeting. 

After the first stereology meeting, Prof. Elias published a short announcement about the event in the journal Science. Soon thereafter, Elias received a flood of inquiries from researchers interested in more details about the meeting on the Feldberg, as well as plans for future stereology conferences. Elias realized that he could be on to something. 


The International Society For Stereology

The following year, 1962, the International Society For Stereology (ISS) came into existence at a congress in Vienna, Austria, with Prof. Hans Elias elected founding president. From that time to the present, stereologists from a wide variety of disciplines and nations have gathered at bi-annual conferences to exchange ideas and research findings viz-a-viz the analysis of 3-D objects based on their appearance on 2-D sections.  


The First Decade Of Stereology (1961-1971)

Following a number of technological innovations, biologists in the 1960s began to visualize microstructures such as cells, blood vessels, and fibers with remarkably improved clarity and specificity. Examples include the mass production of affordable, high-magnification objectives for light microscopes, refinements in electron microscopy instruments and methods for preparation of specimens, and immune-based visualization of specific proteins in tissue sections (immunocytochemistry). These developments encouraged bioscientists to find more reliable methods to quantify microstructures in health, disease, and following experimental manipulations. They needed to answer a simple question -- How much is there?

This demand lead to the rejection of subjective, expert-based assessments in favor of relatively objective, mathematically justifiable methods emerging from the field of stereology. From the previous work of materials scientists and geologists, biologists became aware of several existing approaches:

  • In 1637, Bonaventura Cavalieri, a student of Galileo Galilei in Florence duringCavalieri principle for arbitrary object the high Italian Renaissance, developed the Theory of Indivisibles. This concept laid the theoretical basis for the Cavalieri Principle, the approach used today for the unbiased estimation of the Volume of non-classically shaped biological objects from their areas on tissue sections. The Theory of Indivisibles also provided the foundation for the integration piece of the calculus in the 18th century.  



  • In the 18th century, George Leclerc "Count" Buffon presented the Needle Problem to the BuffonRoyal Academy of Sciences in Paris, France. Random intersections between a probe of known dimensions with unknown structure exemplifies the role of probability theory in modern stereology. The Needle Problem supplies the conceptual basis for current approaches to estimate the Surface Area and Length of non-classically shaped biological objects in an unbiased (accurate) manner. 




  • In 1847, the French mining engineer and geologist, Achille Ernest Delesse, demonstrated that the expected value of the volume fraction for an object varies in direct proportion to the observed area fraction of the object's profile, i.e., volume fraction is proportional to area fraction. Later investigators confirmed that the length fraction and the point fraction hold the same relationship to volume fraction. Today, the Delesse principle provides the basis for accurate and efficient estimates for object and regions volumes of non-classically shaped biological objects.









The Second Decade Of Modern Stereology (1971-1981)

In time, mathematicians joined the ISS and began to apply their unique expertise and perspective to problems in the field. Two peer-review journals, Journal of Microscopy and Acta Stereologica (now Image Analysis & Stereology), assumed critical roles for the cutting-edge work of modern stereology.  
Systematic Sampling
During this time stereologists recognized the fault in the traditional approaches to quantitative biology based on modeling biological structures as classical shapes (spheres, cubes, straight lines). Rather than rely on assumption- and model-based correction factors, which in effect try to force biological objects in the Euclidean models through non-verifiable assumptions and faulty models, they turned to stochastic geometry and probability theory. 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. This paradigm shift, combined with systematic-random sampling (Table 1), formed a new foundation for quantification of arbitrary non-classically shaped biological objects.


Table 1. 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 95:15-23.

  • Miles (1976) Precise and General Conditions for the Validity of a Comprehensive Set of Stereology Formulae J. Microscopy 107:211-220.

  • Cruz-Orive (1976) Sampling Designs for Stereology J. Microscopy 122:235-237.


Increasing numbers of bioscientists began to use assumption- and model-free stereology approaches to quantify biological objects in anatomically well-defined reference spaces. These studies showed promise to quantify first-order stereological parameters (number, length, surface area, volume), without further assumptions related to the size, shape, or orientation of the objects of interest.



The Third Decade of Modern Stereology (1981-1991)


By the 1980s, the more severe sources of methodological bias were identified, though not necessarily eliminated. One of the oldest, well-known and most perplexing problems was the following: How to make accurate estimates of the number of 3-D objects based on their appearance in 2-D tissue sections?


The Corpuscle Problem


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.



Correction Factors

A close examination of classical geometry reveals a number of attractive formulas that would provide accurate and efficient methods to quantify biological parameters of tissue sections, if those methods could be applied to biological objects. After the work of S.D. Wicksell in the 1920s, many workers attempted to make accurate estimates of the number of biological objects on tissue sections, i.e., overcome the Corpuscle Problem, using a variety of assumption- and model-based correction factors, in effect, attempts to force biological objects into classical Euclidean formulas. The problem is that these so-called "correction" formulas require assumptions and models that are rarely, if ever, met by populations of biological objects. Rather than correcting bias introduced by the Corpuscle problem, these formulas simply add further systematic error (bias) to the data. By 1984 the intense efforts of stereologists to avoid the introduction of this bias finally led to a solution that would work for biological objects.



The Disector Principle

A practical solution to the Corpuscle Problem came in a Journal of Microscopy paper published in 1984 by D.C. Sterio, the pseudonym of a well-known stereologist [2]. 
Disector pairsKnown as the Disector principle, the approach became the first unbiased method to make accurate estimates of the number of objects in a given volume of tissue (Nv), without further assumptions, models, or correction factors. A disector is a virtual 3-D probe consisting of two sections a known distance apart (disector height), with a grid (disector frame) of known area superimposed on one section. The disector makes use of Gundersens unbiased counting rules (Gundersen 1977), which avoids biases arising from objects at the edge of the counting frame (edge effects).  

Optical Fractionator
The number of objects tops that fall within the disector volume (the product of disector height and disector frame area), counted at about 100 locations in the x-y axis, provides an unbiased estimate of the number per unit volume of tissue in the reference space.  In 1986 Gundersen expanded the Disector principle from two physical sections to optical planes separated by a known distance through a thick section (optical disector). 




The fractionator method, a sampling scheme to estimate total parameter (e.g., Total N, Total L), eliminated the potential effects of tissue shrinkage (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 reference space.

The combination of disector-based counting with highly efficient, systematic-random sampling allowed optimal efficiency by counting between 100 and 200 probe-object intersections per reference space. Other techniques introduced in the 1980s included methods for unbiased estimation of object sizes, including the nucleator, rotator, and point-sampled intercepts (for review, see Gundersen et al., 1988 a, b; Mouton 2002).

PSI NucleatorBy 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).







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 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 relatively high in terms of time, effort, and resources.  The second contributor to the total observed variation, sampling error is variation arising from the intensity of sampling within each individual. Error variance from all levels of within-individual sampling is expressed in terms of coefficient, CE. Typically, reducing sampling error by sampling more sections and/or more regions within each section costs less in terms of time and resources than sampling more individuals. By partitioning the observed variation in stereological results into variation arising from biological sources and sampling error, biostereologists learned to design sampling schemes that were optimized for maximal efficiency. The Swiss stereologist, Prof. Ewald Weibel, termed this approach, Do More, Less Well.



Do More, Less Well

Prior to the modern era of stereological approaches, the amount of work required to quantify tissue sections provided an acceptable basis for assessing the value of results. In the 1960s, for example, one paper in influential peer-reviewed publication described a study that reported a count of 242,681 cells in an anatomically defined region on one side of the brain, a study that required two years to complete. Using modern stereology approaches with assistance from a computerized stereology system, once an optimal level of sampling within each individual is determined, reliable results from this particular study can be obtained in a single hour today.

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 leads to 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 will provide accurate, precise, and efficient data for statistical testing of the hypothesis of biological interest.



Objections to Modern Stereology Approaches

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 analysis of biological tissue. Many authors of these works simply did not wish to change their approaches.

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. 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.

Third, some biologists chose not to adopt the methods of modern stereology due to confusion over the term bias, which like the word "theory" has different connotations in scientific and lay usages. In the colloquial usage, bias refers to prejudice or predisposition; to mathematicians, bias refers to the presence of systematic error that prevents results from converging on the true value as sampling increases. Accordingly, the term "unbiased" refers to a method that avoids all known forms of systematic error such as increased sampling of the reference space cause mean estimates of the parameter to converge on the true mean value for the group. In order to avoid the controversy involving the terms biased vs. unbiased, many biostereologists prefer the term design-based stereology to refer to the assumption- and model-free methods of modern stereology.



Stereological Bias And Precision

Unbiased methods provide the first step toward generating accurate data for morphometric analysis of biological tissue. Bias refers to inaccuracy, i.e., the deviation of a result from the expected or true value as a result of 
Accuracy vs precision
systematic error (upper and lower right targets in figure). Biased stereological methods cause morphometric data to cluster around an incorrect value. This bias arises from faulty assumptions, erroneous models, and incorrect correction factors that force morphometric determinations of parameters such as the number, surface area, or volume to diverge from the true value by an unknown and unknowable amount. By eliminating all known sources of bias, results from unbiased methods tend to cluster around the true or expected value, as shown in the two left targets in the figure.

Equally important is the idea that "accuracy comes before precision. Increased sampling will reduce variability, i.e., increase precision, regardless of whether the methods is biased or not, as shown by the two lower targets in the figure above. With biased methods, however, the effort to increase precision is misguided if the method lacks accuracy. A characteristic of unbiased methods is that additional sampling (more probes, sections, and animals) increases precision around the central tendency, causing the sample estimate to converge on the true mean value of the parameter.



Non-Stereological Bias

Not all sources of systematic error (bias) in morphometric data arise from faulty models, assumptions, and correction factors. The processing required to prepare tissue for stereological analysis has the potential to introduce systematic error in the form of non-stereological bias. For example, artifacts such as tissue shrinkage may cause sample estimates to differ from true values. Other examples of non-stereological sources of error include ascertainment bias that arises when estimates from one population are extrapolated to another population. Also, failure of stains to penetrate through tissue and fully reveal objects of biological interest bias can lead to recognition bias.

Whereas stereological bias cannot be quantified, non-stereological bias (uncertainty) can be identified, minimized, and eliminated. 


The Fourth Decade of Modern Stereology (1991-2001)


Modern stereology introduced an new set of rules for quantification of biological objects in tissue sections. To gain proficiency in these approaches, many biologists acquired stereology training from comprehensive 3-4 day workshops held in conjunction with national and international meetings, including the Society For Neurosciences, European Neuroscience Society, and ISS meetings. As a result, stereology publications in the peer-review literature grew in an exponential manner from the early 1960s through the 1990s.

Studies in the 1990s using modern stereology clarified an important issue concerning the degree of brain cell (neuron) loss during normal aging. The accepted dogma at that time held that significant neuron loss starts around age fifty and continues to decline 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 age-related 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 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 modern stereology approaches. This acceptance, backed by the implied consequences for publications, approval, and funding, continues to send powerful pro-stereology messages to biomedical scientists.

 

The Fifth Decade of Modern Stereology (2001- present) 


Several technological developments around the turn of the 21st century accompaniedmodern stereology into its fifth decade. High performance computerized stereology systems combine high-resolution microscopy, hardware (motorized stages, computers, digital imaging) with user-friendly software for unbiased sampling and probes (The Stereologer system, SRC, Chester, MD). These computerized stereology systems make affordable, high-through stereology approaches available to all bioscientists.




Space balls



spaceBalls.2virtual Cycloids



Conclusion

In 1961, Prof, Hans Elias convened a historic stereology meeting at the Feldberg in the Black Forest of Germany. Over the past five decades the international, multidisciplinary community of stereologists have led to the progressive development in the field, leading to cost-effective, computer-assisted, state-of-the-art systems such as the Stereologer for morphometric analysis of biological tissue. 


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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.
[1] Director of the Stereology Resource Center (www.disector.com) and
author of Principles and Practices of Modern Stereology: An Introduction For Bioscientists, The Johns Hopkins University Press, Baltimore, May 2002.
[2] Alert readers will recognize that Disector and D.C. Sterio are anagrams, e.g., Flit on cheering angels = Florence Nightingale.