This well-illustrated text is the most comprehensive volume available on the applications of the modern stereology to biomedical research. Covered topics include the theory and practice of unbiased sampling; principles and applications of unbiased steroelogical probes; and a review of the stochastic geometry and probability theory underlying modern stereology. The book does not assume previous mathematical or statistical background beyond the college level.

Other highlights include:

• Written in clear English and a minimum of jargon
• Definitions and description of terminology
• Historical background for current techniques
• Detailed bibliography and up-to-date citations for important stereology references

CHAPTER 1: THE HISTORY OF STEREOLOGY

A broad review of the historical events leading to the current era of modern stereology. The term stereology was first introduced in 1961, and after a brief period of reliance on assumption- and model-based classical geometry, moved into assumption- and model free (theoretically unbiased) approaches to quantify 3-D objects of biological interest. The chronology of these developments provides insight into the rationale for modern stereological approaches.

CHAPTER 2: STEREOLOGICAL BIAS

Review of the assumptions and models that can add systematic error (bias) to estimates of biological structure. Stereological bias causes sample estimates to diverge from expected values for the parameter distribution. An important feature is that once present, stereological bias cannot be quantified, corrected, or removed. Understanding how to identify and avoid sources of stereological bias is the first step toward making theoretically unbiased estimates of structural parameters in biological tissue.

CHAPTER 3: SYSTEMATIC SAMPLING

Sampling in modern stereology is designed to sample all biological objects of interest in a theoretically unbiased and efficient manner. Sampling begins with unambiguous definition of a reference space, the three-dimensional unit of tissue that contains the biological objects of interest; the second step is sampling the reference space in an efficient manner. Systematic sampling provides an unbiased strategy to optimize sampling of biological tissue for maximum efficiency.

CHAPTER 4: GEOMETRIC PROBES

Weaknesses inherent to models, and assumptions, and correct-factors in morphometric methods stimulated stereologists to develop theoretically unbiased geometric probes to sample and estimate the expected (true) value of morphological parameters from the appearance of biological objects on tissue sections. Unbiased geometric probes are theoretically unbiased estimators of first-order stereological parameters and second-order stereological parameters. These geometric probes ensure that intersections between the probe and features of interest in the tissue are proportional to the expected value without the need for assumptions about the size, shape, or orientation of the biological objects.

CHAPTER 5: BIAS IN NUMBER ESTIMATION

Avoiding stereological bias inherent to the appearance of 3-D objects on 2-D sections is essential for the estimation of total object number in a defined reference space. Recognition and avoidance of these sources of bias requires a thorough understanding of bias introduced by assumptions, models, and correction factors. The goal of unbiased sampling and assumption-free stereology designs to estimate number is to overcome this and other sources of systematic error that can introduce systematic error into sample estimates.

CHAPTER 6: THE DISECTOR PRINCIPLE

The disector principle by D.C. Sterio in 1984 was the first theoretically unbiased method to estimate total object number per unit volume (numerical density, N_V) on tissue sections. In combination with methods to avoid edge effects and other sources of stereological bias, the disector method permits total numbers of cells to be estimated without assumptions, models, or correction factors. Practical applications of the disector principle include counting objects with two physical planes (physical disector), two optical planes (optical disector), and optical planes in conjunction with the fractionator sampling scheme (optical fractionator).

CHAPTER 7: VOLUME

Modern stereological methods for volume (size) estimation on tissue sections avoid assumption- and model-based estimators through theoretically unbiased sampling and geometric probes. These approaches allow for the estmation of expected values for regional (tissue) volumes and a variety of local size estimators for cells and other biological objects of interest.

CHAPTER 8: LENGTH AND SURFACE AREA

Based on Buffon needle problem, modern estimators of length and surface area use two dimensions (planes) and one dimension (lines), respectively, to estimate parameters of length (L) and surface area (S) of objects on tissue sections. These approaches apply to regional (tissue) parameters and local estimators of length density (L_V) and surface density (S_V) which are scaled to the total reference volume using either the two-stage method or fraction-based approach.

CHAPTER 9: NON-STEREOLOGICAL BIAS

A variety of non-stereological sources of bias, including a variety of tissue processing artifacts, poor stain penetration, nonspecific antigen-antibody binding, incorrect dilution, etc., can introduce systematic error into stereology results. While stereological bias cannot be measured, reduced, or eliminated once present, sources of non-stereological bias can be identified, removed and/or minimized, thus ensuring that sample estimates reflect the expected value of interest.

CHAPTER 10: ALL VARIATION CONSIDERED

Variation in sample estimates occur with the use of theoretically unbiased stereological approaches. With theoretically unbiased methods, however, this variation can be partitioned into two sources of bias: biological variation and sampling error. To focus sampling on biological (inter-individual) variation, the most efficient sampling strategy for stereology involves light sampling within a relatively large number of individuals until the majority of variation in the parameter has been captured. This approach is known colloquially as, "Do More Less Well".

CHAPTER 11: TYPICAL STEREOLOGY DESIGNS

Typical experimental designs are commonly repeated in the application of unbiased stereology to biological systems. Six designs given here provide the basis for unbiased stereology designs across a wide range of applications to biological tissue.

CHAPTER 12: FREQUENT QUESTIONS

Common questions that are frequently raised about theoretically unbiased stereology are presented and answered.

BIBLIOGRAPHY

Comprehensive, up-to-date reference list related to stereology and applications to biological systems. Index included.