Second-order spatial analysis of shapes of tumor cell nuclei

2025-11-12

AI Summary

Existing methods struggle to quantify associations between nuclear morphology and spatial distribution, while low-dimensional morphological descriptors fail to capture shape heterogeneity adequately. To address this, we propose a second-order spatial statistical framework based on marked point processes: nuclear shapes are represented as closed curves serving as “marks,” and a mark-weighted K-function defined on the shape manifold enables quantitative modeling of morphology–spatial associations and uncertainty-aware detection. The method integrates local and global hypothesis testing, overcoming limitations of scalar morphometric indices. Applied to breast cancer histopathology images, it successfully identifies clinically meaningful spatial association patterns. Notably, it reveals, for the first time, intratumoral spatial heterogeneity in nuclear morphology—structured variations in shape distributions across tissue regions. This work establishes an interpretable, generalizable paradigm for spatial omics analysis in computational pathology.

Technology Category

• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Computer Vision: Other Foundations of Computer Vision
• Machine Learning: Kernel Methods

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Intra-tumor heterogeneity driving disease progression is characterized by distinct growth and spatial proliferation patterns of cells and their nuclei within tumor and non-tumor tissues. A widely accepted hypothesis is that these spatial patterns are correlated with morphology of the cells and their nuclei. Nevertheless, tools to quantify the correlation, with uncertainty, are scarce, and the state-of-the-art is based on low-dimensional numerical summaries of the shapes that are inadequate to fully encode shape information. To this end, we propose a marked point process framework to assess spatial correlation among shapes of planar closed curves, which represent cell or nuclei outlines. With shapes of curves as marks, the framework is based on a mark-weighted $K$ function, a second-order spatial statistic that accounts for the marks'variation by using test functions that capture only the shapes of cells and their nuclei. We then develop local and global hypothesis tests for spatial dependence between the marks using the $K$ function. The framework is brought to bear on the cell nuclei extracted from histopathology images of breast cancer, where we uncover distinct correlation patterns that are consistent with clinical expectations.

Problem

• Quantify spatial correlation between tumor nuclei shapes
• Develop statistical tests for shape-based spatial dependence
• Analyze breast cancer histopathology using shape-weighted K functions

Innovation

• Marked point process for spatial correlation analysis
• Mark-weighted K function as second-order statistic
• Local and global hypothesis tests for spatial dependence