LAUSR

Stereological methods for estimating the 3D particle size and density from 2D projections are essential to many research fields. These methods are, however, prone to errors arising from undetected particle profiles due to sectioning and limited resolution, known as ‘lost caps’. A potential solution by Keiding et al. (1972) accounts for lost caps by quantifying the smallest detectable profiles in terms of their limiting section angle (ϕ). However, this simple solution has not been widely adopted nor validated. Rather, model-independent design-based stereological methods, which do not explicitly account for lost caps, have come to the fore. Here, we provide the first experimental validation of the Keiding model by quantifying ϕ of synaptic vesicles using electron-tomography 3D reconstructions. This analysis reveals a Gaussian distribution for ϕ rather than a single value. Nevertheless, curve fits of the Keiding model to the 2D diameter distribution accurately estimate the mean ϕ and 3D diameter distribution. While systematic testing using Monte Carlo simulations revealed an upper limit to determining ϕ, our analysis shows that mean ϕ can be used to estimate the 3D particle density from the 2D density under a wide range of conditions, and this method is potentially more accurate than minimum-size-based lost-cap corrections and disector methods. We applied the Keiding model to estimate the size and density of somata, nuclei and vesicles in rodent cerebella, where high packing density can be problematic for design-based methods.