CENTERED CONTACT DENSITY-FUNCTIONS FOR THE STATISTICAL-ANALYSIS OF RANDOM SETS - A STEREOLOGICAL STUDY ON BENIGN AND MALIGNANT GLANDULAR TISSUE USING IMAGE-ANALYSIS

Real structures investigated in the material and biological sciences, such as minerals or tissues, can often be reduced to two phases, In a stochastic approach, the components of such binary structures map be c onsidered as the union of grains - random sets implanted with their ce ntres at random points - and their complementary space, which is calle d the pore spare, The simplest stochastic germ-grain model is the Bool ean model of random sets, which we use here instrumentally as a null m odel (reference model) for comparison with our biological material, Af ter a brief review of basic properties of the Boolean model and relate d statistical methods, we introduce centred contact functions as a new approach, Empirical contact functions are estimated from the empirica l contact distribution functions with an image analyser by dilation of the grain phase, Theoretical contact density functions are then predi cted from a set of image parameters, under the assumption that the Boo lean model holds. A centred contact density function is the difference between the estimated and the predicted contact density function, Apa rt from a random error term, centred contact density functions amount to zero irrespective of the area fraction of the grain phase, when the germ-grain model is Boolean, As a section of a spatial Boolean model is a planar Boolean model, the method is also applicable in stereologi cal studies where digitized images are obtained from sections of a thr ee-dimensional structure, Centred contact density functions were deter mined for mastopathic tissue as compared to mammary cancer, and for tu mour-free prostatic tissue as compared to prostatic cancer, For each c ategory of specimens, twenty cases with 10 images each were analysed, Benign and malignant glandular tissue of the aforementioned types devi ates significantly from the Boolean model, Centred contact density fun ctions show that malignant transformation is connected with profound g eometric remodelling of the pore space.