Stereological length estimation using spherical probes

Lineal structures in biological tissue support a wide variety of physiological functions, including membrane stabilization, vascular perfusion, and cell-to-cell communication. In 1953, Smith and Guttman demonstrated a stereological method to estimate the total length density (Lv) of linear objects based on random intersections with a two-dimensional sampling probe. Several methods have been developed to ensure the required isotropy of object-probe intersections, including isotropic-uniform-random (IUR) sections, vertical-uniform-random (VUR) slices, and isotropic virtual planes. The disadvantages of these methods are the requirements for inconvenient section orientations (IUR, VUR) or complex counting rules at multiple focal planes (isotropic virtual planes). To overcome these limitations we report a convenient and straightforward approach to estimate Lv and total length, L, for linear objects on tissue sections cut at any arbitrary orientation. The approach presented here uses spherical probes that are inherently isotropic, combined with unbiased fractionator sampling, to demonstrate total L estimation for thin nerve fibres in dorsal hippocampus of the mouse brain.