Basic quantitative morphological methods applied to the central nervous system

Generating numbers has become an almost inevitable task associated with studies of the morphology of the nervous system. Numbers serve a desire for clarity and objectivity in the presentation of results and are a prerequisite for the statistical evaluation of experimental outcomes. Clarity, objectivity, and statistics make demands on the quality of the numbers that are not met by many methods. This review provides a refresher of problems associated with generating numbers that describe the nervous system in terms of the volumes, surfaces, lengths, and numbers of its components. An important aim is to provide comprehensible descriptions of the methods that address these problems. Collectively known as design-based stereology, these methods share two features critical to their application. First, they are firmly based in mathematics and its proofs. Second and critically underemphasized, an understanding of their mathematical background is not necessary for their informed and productive application. Understanding and applying estimators of volume, surface, length or number does not require more of an organizational mastermind than an immunohistochemical protocol. And when it comes to calculations, square roots are the gravest challenges to overcome. Sampling strategies that are combined with stereological probes are efficient and allow a rational assessment if the numbers that have been generated are "good enough." Much may be unfamiliar, but very little is difficult. These methods can no longer be scapegoats for discrepant results but faithfully produce numbers on the material that is assessed. They also faithfully reflect problems that associated with the histological material and the anatomically informed decisions needed to generate numbers that are not only valid in theory. It is within reach to generate practically useful numbers that must integrate with qualitative knowledge to understand the function of neural systems.