Toward a Mathematical Representation of Pathological Diagnosis: A Weighted Coordinate Model for B-cell Lymphoid Lesions

Background: Current pathological diagnosis is based on the integration of morphological, immunophenotypic, molecular, and clinical findings. Although current disease classifications define characteristic features for individual diseases, the relative importance assigned to these features largely depends on the implicit judgment of pathologists, making it difficult to represent the diagnostic process explicitly and mathematically. Methods: In this study, we propose a weighted coordinate model for pathological diagnosis of B- cell lymphoid lesions. Morphological, immunophenotypic, molecular, and clinical information is retained as features constituting a common multidimensional observation space, and each case is positioned within this space based on its observed findings. Each disease is represented by an evaluation function that assigns different weights to individual features, and the degree of fit to each disease is assessed by applying these weights to the observed features. This framework enables the objective observational information to be represented separately from the interpretive process by which that information is evaluated in the context of disease concepts. Results: The model provides a unified framework for representing pathological findings without immediately assigning them to discrete diagnostic categories. Typical cases are represented by a high degree of fit to the characteristic evaluation pattern of each disease, whereas borderline or atypical cases can be described as occupying intermediate positions in the feature space or as deviations along specific feature dimensions. Furthermore, the model enables the diagnostic process to be represented mathematically and allows cases ranging from typical to borderline to be described continuously within a common observation space. Conclusions: The aim of this model is not to propose new diagnostic criteria, but to explicitly and quantitatively represent the importance that pathologists based on their experience assign to individual features as disease-specific weights. The weighted coordinate model provides a conceptual framework for representing pathological diagnosis not as the direct classification of cases into disease categories, but as the evaluation of cases within a common multidimensional observation space. Although this study demonstrates the model using B-cell lymphoid lesions, the model is based on the fundamental principle of separating observation from interpretation, which is common to pathological diagnosis, and may therefore be applicable to lymphoproliferative disorders more broadly and, ultimately, to other areas of pathological diagnosis. In the future, this framework may provide a theoretical basis for data-driven analyses and the investigation of disease structure using unsupervised learning.