MICROSCOPY RESEARCH AND TECHNIQUE 21:255-261 (1992)

Biological Stereology: History, Present State, Future Directions ROBERT P. BOLENDER Department of Biological Structure, University of Washington, School of Medicine, Seattle, Washington 981 95

KEY WORDS

Stereology, Morphometry, Quantitative morphology, Computers, Software, Tutorials, Simulations, Databases, Bio-Matrix Project

ABSTRACT The development of a quantitative structural platform for experimental biologyextending across a hierarchy of sizes ranging from molecules to organisms-has been punctuated by a series of major achievements over the last 30 years. Stereology, a form of quantitative morphology, has contributed handsomely to this success. A personal view is presented highlighting key events in the development of biological stereology. We also examine stereology with a view toward future developments in biology and speculate how stereology might contribute to the new biological infrastructure currently being built with computers. o 1992 Wiley-Liss, Inc. INTRODUCTION Stereology is a remarkable form of statistics. I t can recover 3-dimensional data from the 2-dimensional images of sections seen with light and electron microscopy. Modern stereological methods require only a small amount of raw data and in return can supply solid estimates for a wide range of structural parameters. The method is unique in experimental biology in that i t provides connected sets of information from structures ranging in size from molecules to organisms. These quantitative structural hierarchies offer a n ideal paradigm for organizing and interpreting information in biology. We will look briefly a t the stereology of the near past and then use this background to explain the driving forces behind recent advances. Exceptional events of the last few years have transformed stereology almost overnight into a powerful new platform for experimental biology. Using the view point of this platform, we will search for future directions. HISTORY The literature contains recent and excellent accounts of the history of stereology (Haug, 1987; Weibel, 1987; Cruz-Orive, 1987a). There are also several recent articles suggesting future directions for the discipline (Cruz-Orive, 198713; Davy, 1987; Cruz-Orive and Weibel, 1990). The historical review here will be short, examining only a few, but representative, key events that have played important roles in the development of biological stereology. Such a n approach provides a brief critique of the method and gives the reader unfamiliar with stereology some needed background. We begin by defining a key event as the introduction of a stereological method that created a new window of opportunity for experimental biology. The Densities Perhaps the first key event in the development of stereology was the discovery that the dimensional information lost as the result of sectioning could be

0 1992 WILEY-LISS, INC.

recovered statistically. Quantitative methods demonstrated-for the first time-just how difficult it was to evaluate structural changes by just looking at 2dimensional images of cells and tissues. Why is this so? Consider a set of objects contained within a 3-dimensional structure. We can readily describe the internal quantitative properties of the structure in terms of volumes, surface areas, lengths, and numbers of objects. Section this 3-dimensional structure and one dimension of the original information i t contains is lost; volumes become profile areas, surfaces lines, and lines points. Stereology rescues these areas, lengths, and points, which become trapped by sectioning into a “flatland,” and returns them to the real world of 3dimensional volumes, surfaces, and lengths! This remarkable feat is accomplished with simple algebraic equations. The textbooks of Underwood (1970), DeHoff and Rhines (1968), Weibel (1979, 1980), and Serra (1982) conveniently summarize the mathematical theory of stereology. Volume Densities. Collect a set of isotropic uniform random (IUR) sections from a n organ. Measure in the sections the area of all the profiles of a specific organ compartment (e.g., cells), as well as the area of the organ. Form a ratio of the cell profile areas to organ profile areas: A(cells)/A(organ). This ratio represents a n example of the raw data that can be measured in 2dimensional sections. A key event occurred when Delesse (1847) realized that such a ratio of the 2-dimensional areas was exactly equal to the ratio of the volumes in 3 dimensions. Continuing with our example, this is formally expressed as the volume density equation: V,(cells/organ) = A(cells,/A(organ,. A remarkable insight to be sure, but of limited practical value to

Received December 15, 1990; accepted in revised from January 14, 1991. Address reprint requests to Robert P. Bolender, Ph.D., Department of Biological Structure, SM-20, School of Medicine, University of Washington, Seattle, WA 98195.

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the biologist who usually had to measure the areas of profiles with highly irregular shapes. A much simpler method of collecting the raw data was needed. A pathologist working at the National Cancer Institute hit upon the ingenious idea of using a set of random points (Chalkley, 1943). He reasoned’correctly that the random points should fall into the various compartments in proportion to their relative areas. For biologists, this was a momentous event because it marked the beginning of what would later became known as “point counting stereology” (Weibel, 1979). Now a volume density could be estimated by simply counting points P falling into compartments and forming the ratio: VV(cell/oran) - P(cedP(organj.The new point counting method let the biologist estimate the relative volumes of organ and tissue compartments quickly and easily. Surfme Densities. If, for example, we add up the surface areas of all the mitochondrial membranes in a standard unit of organ volume, we get the surface density of the mitochondria. Since many biological mechanisms depend on the behavior of membranes, information about how their surface areas may be changing can be of considerable importance to experimental biologists. In transmission electron micrographs, membranes define the boundaries of most cell compartments and appear as dense black lines when cut perpendicular to their surface. Using the same sections of our volume density example, measure this time the boundary length B of the membrane traces for a particular compartment (e.g., mitochondria), as well as the area of the organ in which the lengths are measured. Form the ratio of the total boundary length of the mitochondrial profile boundary to the total organ area in which the boundaries were measured: Bmitochondria)/A~organ). Again, these are the raw data that can be measured in sections. Does this ratio of 2-dimensional data equal the 3-dimensional surface to volume ratio of the surface density, as it did for volume densities? No, this time it doesn’t work. The value of the 3-dimensional ratio is slightly larger than that of the 2-dimensional ratio. If we write the surface densitv eauations as “ * *B(mitochondrial profile boundary)/ SV(mitochondriaior an) A(oran profile, d e n a simulation with simple geometric moJe1s would allow us to discover empirically that k = 4/n. This time a constant is needed to move between 2and 3-dimensional space. Saltikov (1946) derived the surface density equation as Sv = (4/n)(B/A).This Key event was paralleled by a second that made the method practical for biologists. Tomkeieff (1945) introduced a simple point counting method that eliminated the need to measure the lengths of the boundaries: Sv = 2 * I/L, where I represents intersections and L the total length of the test line used to collect intersection counts. Take a set of needles and place them a t random into a structure containing objects, in our case mitochondria. The needles will pierce the objects in proportion to the amount of their surface area and the total length of the needles. When these “needles” are arranged as lines in a test grid and placed on a IUR section, the number of intersections between the lines and the boundaries can be quickly counted. The equation for our example would be Sv = 2 * I(mitochondria)/L~organ),

where the count of intersections with the profile boundary is divided by the total length L of the test lines that fell on the organ. Numerical Densities. Counting objects is the most difficult task in biological stereology and clearly one of the most important. Count the number of objects in a structure of known volume. To get a numerical density (Nv), calculate the ratio of number to volume (Nv = N/V). How do you get a numerical density starting with sections? When sectioned, the 3-dimensional objects appear as profiles. Now take IUR sections from the structure and count the number of profiles in a known area of a section to get the profile density (number of profiledarea of section). Does this ratio of the 2-dimensional profile counts equal the ratio of the 3-dimensional object counts (number of objects/volume)? Yes, but almost never; only when k = 1. If you know both counts of objects and profiles, then you can solve for the k in the equation NV(objects/structure) = * Nprofiles)/A~sections,. Thjs time the k turns out not to be a constant because it depends on the shapes and sizes of the objects being counted. The shapes and sizes of a population of objects can be summarized by a single term, the mean tangent diameter (I3 or HI. This numerical density expression was given by DeHoff and Rhines (1961) as N, = I3 * N/A. While the equation correctly defines the relationship between the 2-dimensional profiles and 3-dimensional objects, the task of estimating a mean tangent diameter for the irregular objects of biology is problematic. The inescapable result is an estimate for Nv with an unknown amount of bias. One can use, for example, an unfolding method for spheres (Wicksell, 1925) or slight ellipsoids (Wicksell, 19261,but such shapes are uncommon in sections of fixed and embedded cells and tissues. A working solution to the counting problem became the Weibel-Gomez equation (1962). This equation represented an important breakthrough because it provided a new way of estimating the sizes and distributions of objects from simple measurements of profiles in sections. The literature reveals that this equation helped biological stereology to flourish for more than two decades. Average Cells Stereological densities report the volumes, surfaces, lengths, and numbers of objects that are contained within a standard unit of volume. It is convenient to think of these density ratios as “morphologicalconcentrations.” For control or baseline studies, the densities provide an accurate quantitative summmary of structural parameters in cells, tissues, or organs. For experimental studies, however, this tidy view of densities disappears because the contents of both the numerator and denominator of the density ratio can change. When this occurs, comparing control and experimental densities can be analogous to comparing apples and oranges (Bolender, 1978). This critical problem of interpretation was noted by Loud in his landmark studies of the liver (1965, 1968). He clearly explained the limitation of stereological densities in an experimental setting and recommended instead the use of average cells. This was a key event

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because it warned biologists that stereology contained a potentially dangerous trap. To calculate average cell data, he suggested dividing a stereological density (of a cellular compartment) by the numerical density of cells. Although stereological methods supply an almost bewildering variety of different data types, only two are widely useful to biologists interested in looking for experimental changes in cells and organs. These include average cell and total organ (or tissue) data.

Total Organ Volume To detect changes in the structural composition of organs, stereological densities are multiplied by the volume of the total tissue or organ. The method was described by Weibel (1963) in his monograph on the human lung. This was a remarkable publication because it addressed and solved many of the key problems of early biological stereology. Weibel showed step-bystep how to quantify structural biology. Indeed, one can trace many of the primary roots of modern stereology to this watershed publication. Relating densities to a total organ volume was an ideal way of looking for global changes in organs, including such compartments as total gas exchange area of pulmonary alveoli or the total alveolar number of alveoli. However, total organ values may be misleading. When, for example, total organ compartments are calculated to study structural changes in cells, an apparent change in a total cell compartment of an organ can be the result of a change within the cell, a change in the number of cells, or some combination of both events. This means that the critical information for a biologist interested in studying changes in cells, tissues, and organs will always depend on reliable cell counts and average cell data (Bolender, 1992). Biological Hierarchies In biology, structures exhibit a broad size range extending from molecules to organs. Weibel (19791, for example, has systematically defined the concept of quantitative structural hierarchies in biology. In effect, he explained-with equations-how stereological data could be linked quantitatively from one level of magnification to the next, thereby establishing an unbroken chain of data extending from molecules to organs. He used this hierarchy to design the multiple stage sampling protocols that are today basic to the practice of biological stereology. PRESENT STATUS By the mid 1980s, the number of published papers using stereological methods exceeded 10,000. Stereology had become a major tool in experimental biology. The popularity of the method was further stimulated by the appearance of several excellent textbooks from Williams (1977), Weibel (1979, 1980), Aherne and Dunnhill (1982), and Elias and Hyde (1983). In spite of its obvious success, biological stereology was in trouble. There was no model-free method for counting objects in sections and there was no general method for sampling anisotropic structures such as brain, kidney, skin, vessels, gut, and skeletal muscle.

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In 1983, DeHoff published a key paper arguing that any unbiased counting method in stereology required a design-based approach, namely, one that did not use models based on assumptions about the shapes and sizes of the objects being counted. He also noted that unbiased counting would have to be done with serial sections. This represented a major departure from the long held view that stereology required IUR sections. Within a year of the DeHoff paper, a simplified serial sectioning method of counting appeared. It was called the disector (D.C. Sterio, 1984). (The spelling is not faulty; rearrange the letters in the author’s name and you get the anagram disector!) This key paper signalled a major breakthrough because it largely solved the long-standing counting problem for biologists. The disector’s importance became widely recognized and spawned a new generation of unbiased counting methods, including the selector (Cruz-Orive, 1987c), brick (Howard et al., 1985), fractionator (Gundersen, 1986; Pakkenberg and Gundersen, 1988; Ogbuihi and CruzOrive, 19901, and nucleator (Gundersen, 1988). It was such a good idea that it comes as no surprise that the major features of the disector were published 60 years ago by Thompson (19321, a pathologist working a t Yale! Thompson’s pioneering work had simply gotten “lost” in the literature and we had to wait more than 50 years for it to be independently rediscovered (Gundersen, 1986). This is a good example of how much we might have learned from the past-but didn’t. At about the same time as the publication of the new unbiased counting methods, there appeared a new category of random sectioning methods for estimating mean object volumes and numerical densities. They included the point-sampled intercept (Gundersen and Jensen, 1983), mean boundary (Gittes and Bolender, 19871, and boundary-sampled intercept (Gittes, 1990) methods. These new random sectioning methods are unbiased for shape, but still required assumptions about size. When used to count nuclei, for example, biases related to size appear largely unimportant for typical nuclei (Bertram and Bolender, 1990). The nucleator can give unbiased estimates for mean volumes without any shape or size assumptions (Gundersen, 1988). Another key event in biological stereology occurred in 1986. The elusive general sampling method for all biological structures was found (Baddeley et al., 1986). In this elegant paper, Baddeley and his colleagues described how structures can be sampled-without bias-using vertical sectioning. Here is how it works. The user chooses a vertical axis through a structure, slices the structure systematically along that axis, collects blocks and sections, and finally collects point counting data for stereological equations. (Note: A cycloid test grid is required to estimate surface densities.) At last, highly oriented structures, such as the brain, kidney, skin, vessels, and gut, could be sampled easily and without bias. However, there was one slight limitation. The vertical sectioning method could be used for estimating volume, surface, and numerical densities, but not length densities. Recall that a length density identifies the length of linear objects (e.g., vessels, dendrites, microtubules) in a unit of reference volume. Re-

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cently, this limitation has been removed by Gokhale (1990) who found a n ingenious way to estimate length densities from vertical sections-using projected images. Within the last few years, the principle of vertical sectioning has led to a cornucopia of new ideas and methods. For example, a modernized version of the Cavalieri principle can give highly efficient estimates for organ and tissue volumes-including subcompartments and such systematic sampling leads to far more efficient estimates (Gundersen and Jensen, 1987; CruzOrive and Mitchel, 1988).

building of such a n infrastructure? If we borrow from the blueprint of the Bio-Matrix, three directions seem promising in the near future: training (the ability to acquaint a new generation of users with quantitative morphology), technology transfer (the ability to distribute the latest methods to the user community), and organization of information (the ability to summarize and map structural patterns across biological hierarchies and taxa).

Training The major stumbling block to using stereology is stereology itself. It is a n intimidating method, one that is FUTURE DIRECTIONS difficult to learn, understand, and apply. It is also a At a recent meeting entitled “Macromolecules, powerful tool than can contribute a rock-solid foundaGenes, and Computers,” Walter Gilbert predicted that tion for structural biology. Since the hierarchical orgai t will take about ten years to sequence the human nization of the Bio-Matrix relies heavily on structural genome, but more than a hundred to figure out all the biology, training in this area assumes a new priority. Two challenging questions come to mind: How can gene functions. To meet this challenge he characterized the biology of the future as a science becoming largely we ease the burden of learning this difficult subject, computational. He anticipates a shift in emphasis from and how do we train the next generation of quantitadescriptive studies to studies of mechanisms and a shift tive biologists in the latest methods when there may be from wet labs to computers. If this turns out to be a n thousands of perspective students? Answers to such accurate vision of the future, then we can expect to see questions are fundamental not only to the future of the forging of bold new partnerships between biolo- stereology but to all the disciplines contributing to the development of the new biological infrastructure. One gists, computer scientists, and mathematicians. One trend seems to be well underway. The infra- point seems indisputable. Biologists are simply not structure of biology is being remodeled around comput- likely to use methods and data they don’t understanders. Most of us are already using computers for collect- even when they are conveniently stored and readily ing raw data, analyzing results, storing data, and accessible. Tutorials. Tutorials have consistently proven to be writing papers. Announcements of new software supporting our research have become commonplace, and the most intensive and powerful form of learning. Comwe are using more and more of these new tools in our puters can be used to create innovative and friendly laboratories. Soon we will be exchanging ideas and learning environments, especially through the use of data routinely over global networks and submitting interactive techniques and the new multimedia techour experimental results in electronic form for review, nologies. Using the current generation of software development packages, electronic tutorials can be written publication, and archiving. Can we imagine what the infrastructure of biology for biological stereology and distributed at low cost (Bomight be like in the year 2000? A promising approach lender, 1992). In the future, biologists can expect a n to divining the future is to decide what key events we electronic tutorial and calculation toolkit to accompany think are needed and then create the environment in the publication of most new stereological methods. Imagine a computer screen that lists several new which they are likely to occur. One of the best examples of this active approach to stereological methods. P u t the cursor on the item optithe future of biology comes from the Bio-Matrix Project cal disector. Press enter. A screen appears t h a t de(Morowitz and Smith, 1987). A broadly based coalition scribes the optical disector as a n unbiased counting of scientists have developed a blueprint for a new bio- method, followed by a brief critique. If the user wishes, logical infrastructure based on information technolo- “hot keys” can be pressed to look up the original refergies. The blueprint includes a n unlimited number of enceb) or to view lists of symbols, terms, or definitions. biological databases linked to information retrieval Press enter. The next screen reviews the principle of systems and knowledge bases and calls for sophisti- the method, and this is followed by a step-by-step excated user interfaces and new tools for integrating all planation of how to collect raw data from magnified types of biological data. The major promise of the Bio- images of tissue sections. The raw data are identified Matrix Project is to create a n entirely new platform for as the variables of stereological equations. The next discovery in the life sciences. The concept is remark- screen includes a table with open fields for entering the able in that i t views all of biology as a single, unified data and the user is given the option of using sample system of information, rather than a s a loose associa- data to try out the calculation. After the final value is tion of separate facts and ideas. The Bio-Matrix will entered, the program evaluates the equations and disinclude “The complete database of published biological plays the results-counts of objects expressed a s nuexperiments, structured by the laws, empirical gener- merical densities. Press the help key and the answers alizations, and physical foundations of biology and con- appear, along with a detailed explantion of the results. nected by all the interspecific transfers of information” A beginner completes this exercise in roughly 30 min(see Morowitz and Smith, 1987). utes and, after reading the original paper, is ready to How can biological stereology contribute to the use the method in the lab. The new method is no longer

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intimidating because the user understands the theory and knows how to apply it. Simulations. The data of biological stereology can be genuinely difficult to understand and interpret, especially when a biologist wishes to ask complex questions that may involve other types of data as well. A goal of the Bio-Matrix Project is to enhance our ability to deal with biological complexity-at and across all levels of biological research. Stereology can contribute substantially to this goal by providing real world examples of biological complexity, and, at the same time, supply some of the powerful new tools that will be needed to contend with complexity. One of most straightforward ways of developing a n understanding of a complex biological system is to use computer simulations. Running simulations can be a particularly satisfying experience because the user is in command of all the variables of a well-defined “biological” system, allowing a n exploration of the many interactions among organelles, cells, tissues, and organs. This ability to explore untethered by the usual limitations of a real world experiment is a powerful way to discover how to ask better questions. A smart way for a beginner or expert to design a stereological experiment is to spend a few hours running simulations. Often the reward of such a n exercise is a more realistic view of what to expect from the experimental data. Simulations can also help the user determine whether or not a n hypothesis can be properly tested with a particular experimental design. This interactive approach is exciting and fun because the student learns how to use stereology by a process of discovery. One of the first questions asked by a newcomer to stereology is what should be measured. A proper answer requires a careful statement of the biological question and a thorough understanding of the kinds of information that can be supplied by the methods. Once again, computer simulations can be very helpful. Consider the following scenario. A user is presented with a series of computer workscreens that include fields for data entry. The screens represent levels of a biological hierarchy ranging from molecules to organs. Stereological equations connect the data level by level into a fully integrated model. The user can change the data at any level and then look for the consequences across the entire model. With a little practice, the student will quickly identify the critical data needed to answer the experimental question. The lesson to be learned from such a n exercise is that one can encounter a surprisingly large number of pitfalls when designing and interpreting a n experiment. Computer simulations foster a much broader view of structural biology and of the experimental process. They hasten the process of understanding.

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sult in publications that are not easy to translate into routine laboratory protocols. This is especially true for a topic as complicated as stereology. Missing one or two subtle points about how to apply a method can have disastrous consequences. Clearly, new directions are needed that will result in a more efficient transfer of state-of-the-art technology from publications to laboratory benches. Suppose a n important new stereological method has just been accepted for publication. Typically, most biologists must wait six months to a year for the paper to appear in the library. By then, the author of the “new” method may have improved it or replaced it with a better one. Unquestionably, our current library model of transferring new technology from authors to users is sadly amiss. How can we solve these problems of technology transfer? A new model of technology transfer might be built around professional socieites, which can assume a new direction of leadership. Societies can play a more active role in supporting biologists by providing educational services in the form of regular courses, newsletters with descriptions of state-of-the-art methods, instructional software, literature databases, electronic bulletin boards, and telephone (or FAX) hotlines. Special interest groups (SIGs) can be organized a t national meetings and used as a forum for reviewing and discussing new stereological methods and their applications. It seems inevitable th a t biologists will increasingly tu rn to societies for assistance because competitive pressures and economic realities demand it.

Organization of Information The sheer volume and diversity of information in biological stereology signals the importance of setting new goals for data management. Biologists are creating a vast resource of stereological data, but this information is becoming more and more difficult to find, summarize, and interpret. While a n enormous effort has gone into the development of this resource, little is being done to make it more accessible and more useful to biologists. Databases. Relational databases are the primary building blocks of the Bio-Matrix Project (Morowitz and Smith, 1987). They offer many good solutions to the problems of accessing and using stereological data. The mere idea, however, of moving stereological data from the literature into computer databases is somewhat daunting. To take on such a project, one needs compelling reasons and assurances th a t it will be worth the effort. What new research opportunities would be created by storing stereological data in databases? If all the published data of biological stereology were stored in computer databases, then quantitative structural inTechnology Transfer formation-across all of biology-would be in standard It is fairly easy to build enthusiasm for a new ste- form and readily accessible. Data representing differreological method, but this enthusiasm can quickly ent organs, cells, species, exposures, ages, diseases, augive way to disillusionment when a potential user thors, methods, etc., could be browsed on lab PCs, looks up the reference and then tries unsuccessfully to quickly and easily. Access aside, the major difference between looking put the theory into practice. More often than not, the page limitations imposed by journals and reviewers re- up data in the library and calling up the same data

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from a database is what you can do next. At this point, well. Very soon, it will be just as important for a mothe database has a clear advantage over the traditional lecular biologist, biochemist, or computer scientist to library model in that it can be used as a tool for recon- have access to stereological data as it is today for the figuring published data into new representations th a t anatomist, physiologist, or pathologist. Now is the will help you find answers to your current research right time to look outward. Computer technologies are questions. For example, information about the surfaces creating a “super biology” that will embrace informaof organelles or numbers of cells in an organ of a spe- tion from all biological disciplines. We can expect that cific animal can be found by searching the original pub- in the future many of the new research tools will be lished data. If, however, you wanted to compare the built around databases, and disciplines with strong effects of a n exposure on these organelles or cells com- programs for developing databases can expect to enjoy ing from several different papers, then the original a strategic advantage in a n increasingly competitive data may not be well suited to this purpose. More often environment. than not, variations among animals and experimental REFERENCES procedures severely limit such paper-to-paper comparAherne, W.A., and Dunnhill, M.S. (1982) Morphometry. The Pitman isons. Press, Bath, U.K. The database tools can help to solve this problem of Baddeley, A.J., Gundersen, H.J.G., and Cruz-Orive, L.M. (1986) Escomparison by recalculating the experimental data of timation of surface area from vertical sections. J. Microsc., 142: the literature as a % change. This simple calculation 259-276. eliminates a major source of paper-to-paper variation Bertram, J.F., and Bolender, R.P. (1990) Counting cells with stereology: Random vs. serial sectioning. J. Electron. Microsc. Tech., 14: (i.e., differences among controls) and minimizes the ef32-38. fects of procedural differences and experimental biases Bolender, R.P. (1978) Correlation of morphometry and stereology with (Bolender and Bluhm, 1992). The result is a fresh view biochemical analysis of cell fractions. Int. Rev. Cytol., 55247-289. of the literature, one that is far more convenient for Bolender, R.P. (1992) Quantitative morphology for biologists and computer scientists: I. Computer-aided tutorial for biological stereolbrowsing and making comparisons. ogy (Version 1.0). Microsc. Res. Tech., 21:338-346. Can databases also make it easier to compare data Bolender, R.P., and Bluhm, J.M. (1992) Database literature review: A coming from different biological disciplines? Yes. Relanew tool for experimental biology. In: Advances in Mathematics in Computers and Medicine. Pergamon Press (in press). tional database models link databases, whereas uniH.W. (1943) Methods for quantitative morphological analversal data types are needed to link data. We define a Chalkley, ysis of tissue. J . Nat. Cancer Inst., 4:47-53. universal data type as a single representation that can Cruz-Orive, L.M. (1987a) Stereology: Historical notes and recent evbe calculated for all types of experimental data. The % olutions. Acta Stereol., 6/Sup 1 I1 43 56 change is a n example of such a data type. The ability to Cruz-Orive, L.M. (1987b) Stereoyogy::RLent solutions to old problems and a glimpse into the future. Acta Stereol., 6/Suppl. III:3-18. reformat different types of data into a single, universal Cruz-Orive, L.M. (1987~)Particle number can be estimated using a representation is a key attribute of databases. Since disector of unknown thickness: The selector. J . Microsc., 145:121most experimental data in biology have controls, % 142. change data offer a convenient way of comparing data Cruz-Orive, L.M., and Weibel, E.R. (1990) Recent stereological methods for cell biology: A brief survey. Am. J . Physiol. (Lung Cell. Mol. across all of biology. Physiol. 2), 258:L148-L156. In the future, databases are likely to become major Davy, P.J. (1987) Stereology: A view toward the future. Acta Stereol., research tools because they offer entirely new ways of 6/Su pl I1 81 86 asking and answering new questions in biology. Using DeHoff R:T. ‘(1983)’Quantitativeserial sectioning analysis: Preview. J . Microsc., 131:259-263. the % change data as a starting point, for example, the DeHoff, R.T., and Rhines, F.N. (1961) Determination of number of reliability of the different representations of stereologparticles per unit volume from measurements made on random ical data can be accessed, old data can be recycled into place sections: The general cylinder and the ellipsoid. Trans. Metall. SOC.AIME, 221:975-982. new, complex structural patterns can be searched for R.T., and Rhines, F.N. (1968) Quantitative Microscopy. Mcanalogies, and unique structural markers can be gen- DeHoff, Graw-Hill, New York. erated (Bolender and Bluhm, 1992). Delesse, M.A. (1847) Procede mechanique determiner la composition The Bio-Matrix. We need to address the most chaldes roches. C. R. Acad. Sci. (III), 25:544. lenging questions-ones that relate directly to contem- Elias, H., and Hyde, D. (1983) A guide to practical stereology. Karger, New York. porary biology. For example, how are structural pat- Gittes, F., and Bolender, R.P. (1987) Counting cell nuclei with random terns (detected with stereology) related to the genome? sections: The effect of shape and size. Micron Microsc. Acta, 18: This is exactly the type of question a biologist might 59-70. ask of the Bio-Matrix. Following the directions of the Gittes, F. (1990) Estimating mean particle volume and number from random sections by sampling profile boundaries. J. Microsc., 158: blueprint, we would link the stereology databases to 1-18. those of molecular biology, using as intermediate step- Gokhale, A.M. (1990) Unbiased estimation of curve length in 3D usping stones databases for the metabolic chart, proteins, ing vertical slices. J . Microsc., 159:133-141. RNA, and DNA (see Morowitz and Smith, 1987). A Gundersen, H.J.G. (1986) Stereology of arbitrary particles. A review of unbiased number and size estimators and the presentation of working model might include the creation of a series of some new ones, in memory of William R. Thompson. J. Microsc., structural and chemical phenotypes that we could use 143:3-45. to map a path back to the genome. Gundersen H.J.G. (1988) The nucleator. J . Microsc., 151:3-21.

CONCLUDING COMMENTS In preparing for the future, we need to ask hard questions about the value of biological stereology-not only to ourselves, but to the larger scientific community as

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