Virtual Spectral Decomposition with Dendritic Tile Selection: An Explainable AI Framework for Multimodal Tissue Composition Analysis and Immune Phenotyping Across Pancreatic, Lung, and Breast Cancer

BackgroundCurrent deep learning models in computational pathology, radiology, and digital pathology produce opaque predictions that lack the explainable artificial intelligence (xAI) capabilities required for clinical adoption. Despite achieving radiologist-level performance in tasks from whole-slide image (WSI) classification to mammographic screening, these models function as black boxes: clinicians cannot trace predictions to specific biological features, verify outputs against established morphological criteria, or integrate AI reasoning into precision oncology workflows and tumor board decision-making. MethodsWe present Virtual Spectral Decomposition (VSD), a modality-agnostic, interpretable-by-design framework that decomposes medical images into six biologically interpretable tissue composition channels using sigmoid threshold functions--the same mathematical structure as CT windowing. Unlike post-hoc xAI methods (Grad-CAM, SHAP, LIME) applied to black-box deep learning models, VSD channels have pre-defined biological meanings derived from tissue physics, providing inherent explainability without sacrificing quantitative rigor. For whole-slide image (WSI) analysis in digital pathology, we introduce the dendritic tile selection algorithm, a biologically-inspired hierarchical architecture achieving 70-80% computational reduction while preferentially sampling the tumor immune microenvironment. VSD is validated across three cancer types and imaging modalities: pancreatic ductal adenocarcinoma (PDAC) on CT imaging, lung adenocarcinoma (LUAD) on H&E-stained pathology slides using TCGA data, and breast cancer on screening mammography. Composition entropy of the six-channel vector is computed as a visual Biological Entropy Index (vBEI)--an imaging biomarker quantifying the diversity of active biological defense systems. ResultsIn pancreatic cancer, the fat-to-stroma ratio (a novel CT-derived radiomics biomarker) declines from >5.0 (normal) to <0.5 (advanced PDAC), enabling early detection of desmoplastic invasion before mass formation on standard imaging. In lung cancer, composition entropy from H&E whole-slide images correlates with tumor immune microenvironment markers from RNA-seq (CD3: {rho}=+0.57, p=0.009; CD8: {rho}=+0.54, p=0.015; PD-1: {rho}=+0.54, p=0.013) and predicts overall survival (low entropy immune-desert phenotype: 71% mortality vs 29%, p=0.032; n=20 TCGA-LUAD), providing immune phenotyping for checkpoint immunotherapy patient selection from a $5 H&E slide without molecular assays. In breast cancer, each lesion type produces a characteristic six-channel fingerprint functioning as an interpretable computer-aided diagnosis (CAD) system for quantitative BI-RADS assessment and subtype classification (IDC vs ILC vs DCIS vs IBC). A five-level xAI audit trail provides complete traceability from clinical decision support output to specific biological structures visible on the original images. ConclusionVSD establishes a unified, interpretable-by-design mathematical framework for explainable tissue composition analysis across imaging modalities and cancer types. Unlike black-box deep learning and post-hoc xAI approaches, VSD provides inherently interpretable, clinically verifiable cancer detection and immune phenotyping from standard clinical imaging at existing costs--without requiring foundation model infrastructure, specialized hardware, or molecular assays. The open-source pipeline (Google Colab, Supplementary Material) enables immediate reproducibility and extension to additional cancer types across the pan-cancer TCGA atlas.