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

Background: Inter-observer and intra-observer variation in histologic tumor grading are well documented. To determine whether histologic disorderliness in the arrangement of tumor cells may serve as an objective criterion for grading, we tested the hypothesis the degree of disorderliness is related to the degree of tumor differentiation on which tumor grading is primarily based. Methods: Borrowing from the statistical thermodynamic definition of entropy, we defined a novel mathematical formula to compute the relative degree of histologic disorderliness of tumor cells. We then analyzed a total of 51 photomicrographs of normal colorectal mucosa and colorectal adenocarcinoma with varying degrees of differentiation using our formula. Results: A one-way analysis of variance followed by post hoc pairwise comparisons using Bonferroni correction indicated that the mean disorderliness score was the lowest for the normal colorectal mucosa and increased with decreasing tumor differentiation. Conclusions: Disorderliness, a pathologic feature of malignant tumors that originate from highly organized structures is useful as an objective tumor grading proxy in the field of digital pathology.