Quantifying the architectural complexity of microscopic images of histology specimens

Tumour grade (a measure of the degree of cellular differentiation of malignant neoplasm) is an important prognostic factor in many types of cancer. In general, poorly differentiated tumours are characterized by a higher degree of architectural irregularity and complexity of histological structures. Fractal dimension is a useful parameter for characterizing complex irregular structures. However, one of the difficulties of estimating the fractal dimension from microscopic images is the segmentation of pathologically relevant structures for analysis. A commonly used technique to segment structures of interest is to apply a pixel intensity threshold to convert the original image to binary and extract pixel outline structures from the binary representation. The difficulty with this approach is that the value of the threshold required to segment the histological structures is highly dependent on the staining technique chosen and imaging conditions (i.e., illumination time, intensity, and uniformity) of the microscopic system. In this work, we present a method for finding the optimal intensity threshold by maximizing the corresponding fractal dimension. This method results in the segmentation of histological structures and the estimation of their fractal dimension (independent of imaging conditions). We applied our technique to 164 prostate histology sections from 82 prostate core biopsy specimens (two serial sections from each of the 63 benign prostate tissues and 19 high grade prostate carcinoma). We stained one of the serial sections with conventional hemotoxylin and eosin (H&E) and the other with pan-keratin, and found that the difference in mean fractal dimension between the two groups was statistically significant (p < 0.0001) for both stains. However, using receiver operating characteristics (ROC) analysis, we conclude that our fractal dimension method applied to the images of pan-keratin stained sections provides greater classification performance (benign versus high grade) than with those stained with H&E when compared to the original histological diagnosis. The sensitivity and specificity achieved with the pan-keratin images were 89.5% and 90.5%, respectively.