Conditional entropy as an indicator of pleomorphism in astrocytic tumors

The entropies of nuclear arrangements as an indicator of pleomorphism are assessed using a morphometric method. Sixty astrocytic tumors (grades I, II, III and IV; 15 cases each) were reviewed and analyzed. All slides were stained with HE and MIB-1 antibody. The MIB-1 labeling index (LI) was assessed by counting nuclei under a microscope. Images of HE-stained slides were digitized and segmented using the watershed algorithm. Then, six nuclear parameters were measured automatically: (i) the number of total nuclei in the image, (ii) percentage of total nuclear area in the image, (iii) the mean area of the nucleus, (iv) the standard deviation of the area of the nucleus, (v) the entropy of nuclear arrangement (Entropysimple), and (vi) conditional entropy of nuclear arrangement (Entropyconditional). Entropysimple was defined according to the area of the nucleus and Entropyconditional was defined according to both the area of the nucleus and the area of its neighboring nuclei. Image processing and image analysis were performed with public domain software developed in the laboratory. Segmentation of the images resulted in inappropriate segmentation in a few percent of the images. The measurements obtained for each parameter were classified using discriminant analysis. The percentage of correct classification with Entropyconditional was 62%, which was the highest value among all the measurements. Classification based on the combination of all measurements resulted in a rate of correct classification of 88%. Thus, conditional entropy of nuclear arrangement is useful for grading of astrocytic tumors and it is proposed as an indicator of pleomorphism.