Counting sectioned cells via mathematical reconstruction

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Abstract
A new method for determining the number of neurons in sectioned tissue is presented. The method does not involve identification of subcellular structures; rather, it uses estimates of the mean diameters of sections of the neuronal somata (with or without nuclei). All such sections are termed profiles. A mathematical model is developed to reconstruct the cell population from a size histogram of the profiles. Although the model is simple, the calculations are numerous and best done on a computer. A program that performs these calculations is provided. We discuss the idealizations on which the model is based and test the method in various ways: on hand‐ and computer‐generated data in which imaginary spheres of known size were sectioned; on two small samples of real cells for which both cell and profile size histograms were available; and on a sample of potatoes, sliced by hand. In every case the estimate was within 10% of the actual number of cells (or potatoes). The method is robust in that it is relatively insensitive to section thickness, sample size, somal morphology, and observer error with respect to missing the small or thin profiles from any given cell. Results from the present model are compared to those obtained by using other cell count correction schemes that are currently employed. We call our method recursive translation.