ISPAT-3D: Spatially Varying Conditional Volumetric Network Estimation for 3D Tumor Imaging

The spatial organization of the tumor microenvironment shapes immune function and disease progression, yet existing methods for cell-type interaction networks from multiplexed tissue images operate in two dimensions and ignore spatial auto-correlation. We introduce ISPat-3D (Informed Spatially Aware Patterns in 3D), a hierarchical Bayesian framework that recovers spatially varying, zone-specific interaction networks from 3D multiplexed cancer imaging data. The method partitions the tissue volume into tumor intensity zones, fits an anisotropic Gaussian process per cell type and zone with separate lengthscales for the tissue plane and axial direction, decomposes the residuals via multi-study factor analysis, and extracts partial correlation networks from the resulting precision matrices. Simulations demonstrate accurate recovery of shared and zone-specific structure with high power and controlled FDR. We apply ISPat-3D to two 3D datasets: the colorectal cancer atlas (CRC1) 3D CyCIF specimen and a HER2-positive ductal breast carcinoma (BC) specimen from a 3D IMC. In CRC1, zone-specific networks reveal a T cell module intensifying with tumor burden, with the dominant regulatory association shifting from CD4 ⁺ ↔Treg at intermediate density to CD8 ⁺ ↔Treg at maximal density, consistent with cytotoxic suppression at the tumor core. In BC, the shared network shows near-perfect conditional coupling between cancer-associated fibroblasts and the myoepithelial layer, while zone-specific networks reveal CAF↔endothelial co-localisation at intermediate and high burden, consistent with angiogenic remodeling, and a B cell↔CAF association confined to high-density zones, consistent with tertiary lymphoid structure formation. Across both tumors, ISPat-3D identifies volumetric spatial conditional interactions not recoverable from 2D sections.