One-stop stereology: the estimation of 3D parameters using isotropic rulers

The stereological estimation of second-order descriptors of spatial architecture appears to be inherently more time-consuming and labour-intensive than the estimation of first-order quantities (total quantities or ratios). Therefore, far fewer researchers tend to make use of second-order approaches in their stereological research projects. In this paper, we use a tutorial approach to illustrate how a desire for practical simplicity has provided us with a data collection method that can be used to simultaneously estimate both first-order and second-order properties of the microstructure of a defined anatomical feature of an organ. The approach does not rely on new results from theory, but nevertheless allows either isotropic uniform random or vertical uniform random sections to be used to make estimates of a comprehensive list of 10 microstructural parameters using relationships that are well known in the literature. The probe used in all cases is an isotropically distributed Ruler and the data collection protocol is easy to learn and apply. We illustrate the method on brain tissue but emphasize that the approach can also be applied to non-biological material.