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These methods are, however, prone to errors arising from undetected particle profiles due to sectioning and limited resolution, known as \u2018lost caps\u2019. A potential solution developed by Keiding, Jensen, and Ranek in 1972, which we refer to as the Keiding model, accounts for lost caps by quantifying the smallest detectable profile in terms of its limiting \u2018cap angle\u2019 (\u03d5), a size-independent measure of a particle\u2019s distance from the section surface. However, this simple solution has not been widely adopted nor tested. 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 comparing the size and density of particles estimated from 2D projections with direct measurement from 3D EM reconstructions of the same tissue. We applied the Keiding model to estimate the size and density of somata, nuclei and vesicles in the cerebellum of mice and rats, where high packing density can be problematic for design-based methods. Our analysis reveals a Gaussian distribution for \u03d5 rather than a single value. Nevertheless, curve fits of the Keiding model to the 2D diameter distribution accurately estimate the mean \u03d5 and 3D diameter distribution. While systematic testing using simulations revealed an upper limit to determining \u03d5, our analysis shows that estimated \u03d5 can be used to determine 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. Our results show the Keiding model provides an efficient means of accurately estimating the size and density of particles from 2D projections even under conditions of a high density.<\/jats:p>","DOI":"10.1371\/journal.pone.0277148","type":"journal-article","created":{"date-parts":[[2023,3,17]],"date-time":"2023-03-17T13:32:11Z","timestamp":1679059931000},"page":"e0277148","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":3,"title":["Validation of a stereological method for estimating particle size and density from 2D projections with high accuracy"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3036-2291","authenticated-orcid":true,"given":"Jason Seth","family":"Rothman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carolina","family":"Borges-Merjane","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Noemi","family":"Holderith","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Jonas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R. 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