Abstract

The spatial organization of cells within tissues encodes critical information about biological function, disease progression, and therapeutic response. Advances in spatial transcriptomics, multiplexed imaging, and digital pathology now enable unprecedented characterization of tissue architecture. However, a fundamental statistical challenge remains: how can spatially resolved measurements be transformed into interpretable representations of cellular interactions, molecular regulation, and tissue function?

We present an integrated computational and statistical framework for learning the spatial language of tissue by combining spatial graph representations, functional data analysis, multimodal learning, and quantum information-inspired modeling. First, we introduce the Proximogram, a representation of tissue organization that captures spatial relationships among cellular populations and their local microenvironments. Building on this foundation, SPIFEE extends conventional spatial graphs by representing cellular relationships through spatially varying functions rather than scalar proximity measures, enabling the characterization of multiscale interactions and context-dependent tissue organization. These representations provide a foundation for statistical modeling of tissue architecture and its associations with biological and clinical phenotypes.

Next, we demonstrate how integrating hematoxylin and eosin (H&E) histopathology with spatial transcriptomics can connect observable tissue morphology to underlying molecular programs. This multimodal approach provides a means to investigate which aspects of molecular organization are recoverable from routine histology, identify biologically meaningful morphology–molecular associations, and characterize regions where morphological and molecular evidence diverge.

Finally, we explore quantum information-inspired approaches, including Hamiltonian-based generative models and information-theoretic representations, for modeling higher-order cellular dependencies and structured interactions within tissue ecosystems. These methods offer a mathematical framework for investigating complex dependencies that may not be adequately represented by pairwise spatial associations alone.

Together, these approaches motivate a unified statistical perspective on spatial biology, progressing from mapping cellular distributions to characterizing functional interactions and generating testable hypotheses about tissue organization. We discuss opportunities and challenges involving statistical identifiability, sample complexity, uncertainty quantification, and the integration of heterogeneous spatial measurements. Our broader objective is to develop interpretable and statistically principled representations that connect tissue architecture to biological mechanisms and clinically relevant outcomes.