An application of mathematical morphology to analysis of the size and shape of nuclei in tissue sections of non‐Hodgkin's lymphoma

Abstract

Using principles from the theory of mathematical morphology, a semiautomatic analysis of the size and shape of cell nuclei on tissue sections was carried out on a Leitz Texture Analysis System (Leitz-TAS). The four parameters proposed here are more discriminatory than conventional shape evaluation by the form factor (FF), which is based on the ratio of perimeter squared to area. The parameters quantified, respectively, nuclear elongation (ND), narrow (R1) and wide (R2) irregularities, and the distribution of R1 and R2 along the nuclear contour (ID). The properties of these parameters were tested nucleus-by-nucleus on 24 nuclear models. The methodology was then illustrated by a study of lymph node nuclei in non-Hodgkin's lymphoma (NHL). Prior to analysis, 45 lymphomas were classified into five categories of nuclear size and shape according to the International Working Formulation (IWF). Two hundred nuclei were measured on each lymph node section. Statistical interpretation was based upon an analysis of the nuclear surface area on sections and upon the mean values of R1, R2, and ND, the standard deviations of R1 and R2, and the percentage of cleaved nuclei detected by ID. The mean value of R2 discriminated best between the two sets of populations with regular and irregular nuclear contours, respectively. Parameters R1, ND, and ID permitted the distinction of certain NHL cases among populations with irregular nuclei. Nuclear invaginations decreased in depth as the nuclear area became greater. The median surface area was well correlated to the IWF, and the skewness coefficient (third statistical moment of the nuclear surface area distribution) was related to the number of nuclear size or shape sub-populations.