Multivariate discriminant analysis for branching classification of colonic tubular adenoma glands

Many morphologic findings of histology can be translated into mathematically computerized data, and identifying important parameters is primarily pathologists' task as users. Shape-specific parameters based on computational geometry properties of glands can be used in the field of pathology. We evaluated the diagnostic utility of three shape-specific parameters: the chord intersection ratio, convexity ratio, and maximum concave area ratio for branching classification of glands.

Seven cases of tubular adenoma were studied. After image analysis, segmented neoplastic glands were classified into nonbranching, mild branching, and moderate branching. Using image analysis formulae for the three shape-specific parameters, we compared the values of the parameters with the branching classification results for colonic tubular adenoma.

Multivariate discriminant analysis was used to classify the branching groups. Classification accuracies of nonbranching, mild branching, and moderate branching group based on the three shape-specific parameters were 98, 94, and 95%, respectively. More branching growth exhibited a higher chord intersection ratio and maximum concave area ratio but lower convexity ratio. We found a statistically significant difference in chord intersection ratio, maximum concave area ratio, and convexity ratio between mild, moderate, and nonbranching groups. Among the three features, the chord intersection ratio was the most significant parameter.

Shape-based parameters of chord intersection ratio, convexity ratio, and maximum concave area ratio are valid assessment parameters for irregular branching structures. For the understanding of spatial relationships of histology, the holistic geometric approach using shape-based parameters can be useful.