Histologic disorderliness in the arrangement of tumor cells as an objective measure of tumor differentiation

Histologic tumor grading requires assessments on a continuum of morphologic alterations for which objective measuring tools may not be as easily developed as for laboratory tests. As a consequence, some subjectivity cannot be avoided, and issues such as inter-observer variability and lack of reproducibility are frequently identified as limits to the prognostic and predictive values of grading[1-5]. Various methods have been suggested to resolve these issues, employing not only conventional semi-quantitative sche mes but also relatively new approaches such as entropy- based texture analysis and fractal dimension analysis[6-12]. Although the specific criteria used for tumor grading vary by type of cancer, the strategy behind histologic grading is based primarily on the degree of tumor differentiation or the extent to which a tumor resembles the normal tissue counterpart. In this study, we hypothesized that the amount of histologic disorderliness in the arrangement of tumor cells may be quantified by adopting the concept of entropy, and that the quantified measurements would correlate with degree of differentiation. Here, by modifying the statistical thermodynamic definition of entropy that is often taken to be a measure of disorderliness in a physical system, we develop a novel mathematical formula to compute the relative degree of histologic disorderliness of tumor cells. We then apply the formula to colorectal adenocarcinomas with varying degrees of differentiation and determine whether disorderliness is a useful feature for grading cancer.