A novel quantitative measurement method for irregular tubules in breast carcinoma

Abstract Tubule detection is very crucial and is one of the important criterions for tubule formation assessment in breast carcinoma. The output of tubule formation is essential to determine the grade of breast carcinoma based on the Nottingham Histological Grading (NHG) system. Very few studies have been done on the tubule quantification in breast carcinoma. In this study, the geometrical pattern and regularity measurement in tubule and non-tubule were investigated. Spatial Angle (SA), Distribution (D), and Harmonic Mean ( H M κ ) indices were proposed to quantify the tubule and non-tubule. The information of the spatial angle and distribution of neighborhood nuclei surrounding the central lumen were considered in the proposed measurements. The main advantage of the proposed measurements over the other existing findings is that the proposed measurements provide a clear geometrical meaning for the irregular tubule. The proposed Harmonic Mean Index ( H M κ ) was found significant in discriminating the tubule and non-tubule (p value