Estimating conditional cell population associations across tumor density trajectory in three dimensional tissue images

Abstract Registered serial-section imaging preserves a depth coordinate that a single planar image cannot represent. We introduce ISPat-3D (Informed Spatially Aware Patterns in Three Dimensions), a framework that combines anisotropic Gaussian-process adjustment with multi-study factor analysis to separate smooth spatial variation from covariance shared across tumor-density zones and covariance specific to individual zones. Precision matrices summarize the adjusted structure as signed partial correlations, interpreted as conditional co-location or exclusion rather than physical contact, signaling, or causation. We analyze conditional associations among cell-type neighborhood-density variables across five relative tumor-burden strata in one colorectal-cancer CyCIF specimen and one HER2-positive breast-carcinoma IMC specimen. The workflow adjusts modeled smooth spatial variation with an anisotropic three-coordinate Gaussian process, fits shared and zone-specific factor covariance to the residuals, and converts each full zone covariance to signed partial correlations. To make the reported cell budgets feasible, the analysis uses a 15-neighbor Vecchia GP likelihood on spatially balanced anchors and a Gaussian-likelihood fit of the same factor covariance form from full residual covariance summaries. Controlled simulations, a matched section-wise planar comparison, and direct graphical-lasso sensitivity check the estimator. In CRC, positive T-cell and macrophage–stroma density associations show relatively high agreement across three sampling budgets. Breast pair signs are much less stable across budgets and remain exploratory, even though graphical lasso agrees on the same GP-adjusted residuals. A GP separates patterns by assumed spatial scale; a smooth field may contain meaningful biology and residual associations may contain noise or unmeasured effects. The two single-specimen analyses identify biologically plausible, zone-resolved conditional associations for replication, without establishing cellular contact, mechanism, or cohort-level reproducibility. Code release: https://github.com/sagnikbhadury/ISPAT-3D .