Wicksell and the Corpuscle problem

The following has been claimed about Wicksell’s paper published in 1925.
The work of S.D. Wicksell in the early 20th century (Wicksell, 1925) demonstrated the Corpuscle Problem — the number of profiles per unit area in 2-D observed on histological sections does not equal the number of objects per unit volume in 3-D; i.e., NA ≠ NV.

Is that what Wicksell published? No.

Wicksell was asked to assist in a problem where some anatomical shapes were seen as profiles on sections. What Wicksell solved was how to relate discs to the balls from which they were sliced. He related what was seen on slices to the original objects. The term ball is used here since that is the structure, which is not a sphere. Also, the profiles were observed to be discs, not circles.

In doing this he makes a number of important statements concerning the applicability of the mathematics to the problem at hand. He covers issues such as the size distribution of balls. He covers the issue of the position distribution.

In 1926 he reports that the solution he provides only works for a set of spheres. It does not work for ellipsoidal forms.

The corpuscle problem relates the distribution and numbers of profiles to the numbers of density of objects in the original material. The corpuscle problem is not useful in biology, but is used  in other fields such as geology, metallurgy, and studies of cements and roads.

To relate the corpuscle problem to the issue of the numerical density per unit area being not the same as the numerical density per unit volume simply shows a lack of understanding of Wicksell and his work.

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One Response to “Wicksell and the Corpuscle problem”

  1. Peter Mouton Says:

    Again, you miss the point. Of course Wicksell did not publish Na ≠ Nv. However, his work does provide a theoretical foundation for understanding why simply counting the number of 2-D cell profiles per unit area on sections through tissue might lead to an assumption and model-based (biased) estimate of the number of 3-D cells per unit volume of tissue, i.e., Na ≠ Nv. The sources of bias related to the Corpuscle Problem include size, shape, and orientation of the biological objects relative to the direction of sectioning.

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