Second‐order stereology of benign and malignant alterations of the human mammary gland

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Abstract
Summary: The purpose of the present study was a quantitative characterization of the three‐dimensional arrangement of the epithelial component of benign and malignant alterations of the female breast by combining stereology with stochastic geometry. Twenty cases of fibrous mastopathy and 20 cases of invasive ductal mammary cancer were studied at the light microscopic level. Segmentation of the epithelial tissue component was performed with an image analyser. From the resulting binary images, unbiased estimates of the covariance C(r) and the intensity Vv of the epithelial volume component were obtained automatically by computer. From these data, estimates of the correlation function k(r), of the pair correlation function g(r), of the radial distribution function RDF(r) and of the reduced second moment function K(r) of epithelial volume were determined. The estimates of C(r) and RDF(r) differed between groups, but these functions depend on spatial pattern and Vv. As carcinomas showed a significantly higher epithelial volume density Vv than mastopathies, estimation of C(r) and RDF(r) alone did not permit a safe distinction between possibly different types of spatial arrangement of epithelium in the benign and malignant lesions. Analysis of the estimates of k(r), g(r) and K(r), which are not influenced by Vv, showed definite interaction between epithelial volume elements, with clustering at short distances and repulsion at long distances. In both groups, the null hypothesis of purely random arrangement of epithelium had to be rejected. The clearest distinction between groups was obtained by estimation of g(r), which showed that short‐range, tubular pattern as well as long‐range, lobular architecture are better preserved in benign than in malignant lesions. The low interindividual scatter of k(r), g(r) and K(r) indicates a high biological significance of spatial pattern, which is presumably under strict genetic control. Potential uses of the method are: (i) the identification of biomathematical models which could contribute to a better understanding of the growth processes involved, (ii) conditional simulation of the underlying three‐dimensional structures by computer, and (iii) supporting the diagnosis of mammary lesions with borderline histopathological appearance.