Stereological estimation of the mean and variance of nuclear volume from vertical sections

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Abstract
The application of assumption-free, unbiased stereological techniques for estimation of the volume-weighted mean nuclear volume, nuclear v̄V, from vertical sections of benign and malignant nuclear aggregates in melanocytic skin tumours is described. Combining sampling of nuclei with uniform probability in a physical disector and Cavalieri's direct estimator of volume, the unbiased, number-weighted mean nuclear volume, nuclear v̄N, of the same benign and malignant nuclear populations is also estimated. Having obtained estimates of nuclear volume in both the volume-and number distribution of volume, a detailed investigation of nuclear size variability is possible. Benign and malignant nuclear populations show approximately the same relative variability with regard to nuclear volume, and the presented data are compatible with a simple size transformation from the smaller benign nuclei to the larger malignant nuclei. Finally, the variance in the volume distribution of nuclear volume is estimated by shape-independent estimates of the volume-weighted second moment of the nuclear volume, ***v̄2v, using both a manual and a computer-assisted approach. The working procedure for the description of 3-D size variability within benign and malignant nuclear populations can for all practical purposes be reduced to 2-D measurement of nuclear profile areas. These new powerful stereological estimators of nuclear volume and nuclear size variability provide an attractive approach to quantitative and reproducible malignancy grading of cancers.