The volume of a slab divided by it’s surface will give it’s mean width or thickness. This simple idea has been used to estimate, for example, the width of the cortical ribbon (Karlsen and Pakkenberg, 2011) and the width of blood vessel walls (Mühlfeld, 2014, Introduction, Morphometric parameters related to vasculature, surface area, last paragraph). Counting intersections of line-segments with the surface is used to estimate surface area, and points are used to estimate volume. For surface estimation, if the objects themselves are not isotropic, then some combination of the probe and the tissue must be. In the example given for estimating the width of the cortex, it was pointed out that another study (Oster, et al., 1993) has shown that the cortex is ninety-seven per-cent isotropic (Karlsen and Pakkenberg, pg. 2, second column, second paragraph, last sentence).
For information on how to estimate the width or thickness of a slab directly, please see Orthogonal Intercepts.
Karlsen, A.S. and B. Pakkenberg (2011) Total Numbers of Neurons and Glial Cells in Cortex and Basal Ganglia of Aged Brains with Down Syndrome — A Stereological Study. Cerebral Cortex, 21, 2519 – 2524.
Mühlfeld, C. (2014) Quantitative Morphology of the Vascularisation of Organs: A Stereological Approach Illustrated Using the Cardiac Circulation. Ann Anat., 196, 12 – 19.
Oster, S., Christoffersen, P., Gundersen, H.J., Nielsen, J.O., Pakkenberg, B., and C. Pedersen (1993) Cerebral Atrophy in AIDS: a Stereological Study. Acta Neuropathol., 85. 617 – 622.