An integrated geometric quantification and shape analysis framework for axillary lymph node metastasis in breast cancer patients

📅 2026-09-28
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This study addresses the limitations of surface topological defects in CT-reconstructed lymph nodes and the inability of conventional descriptors to capture beyond global morphology. We propose an integrated analytical framework that combines topology-aware mesh repair with multi-resolution spherical harmonic analysis, coupled with a family-specific hybrid-resolution model. This approach enables multiscale quantification of both local and global geometric features while preserving geometric fidelity and interpretability. Experimental results demonstrate that the proposed framework achieves an AUC of 0.918 for lymph node metastasis assessment, significantly outperforming baseline methods. Furthermore, validation on independent datasets confirms its superior cross-center generalization capability.
📝 Abstract
Quantitative characterization of lymph node morphology is important for assessing axillary lymph node metastasis in breast cancer. However, surfaces reconstructed from computed tomography (CT) segmentation may contain geometric and topological defects that compromise subsequent analysis, while conventional shape descriptors predominantly characterize global morphology. To address these issues, we developed an integrated framework combining topology-aware surface processing with multi-resolution spherical harmonic (SH) analysis of CT-derived axillary lymph nodes. The processing pipeline produced topology-valid genus-0 surfaces with improved mesh quality, which were then represented at multiple SH degrees and characterized using 20 predefined geometric feature families. Geometric fidelity increased with SH degree, whereas predictive performance peaked at intermediate resolutions. Preferred SH degree also differed across feature families. A family-specific mixed-resolution model achieved an AUC of 0.918, compared with 0.884 for the conventional PyRadiomics Shape14 baseline, corresponding to an improvement of 0.0344. Controlled perturbation experiments showed that higher SH degrees transmitted more fine-scale geometric variation and yielded lower stability of curvature-based predictions. Representative geometric descriptors provided interpretable characterization of metastasis-associated surface morphology. Independent validation further supported the framework's transportability: label-free replication in a multicenter lymph node cohort reproduced the family-specific resolution effects, while a labeled LIDC-IDRI lung-nodule experiment reproduced the resolution-dependent relationship between SH degree and predictive performance. Altogether, the framework provides a topology-valid basis for quantitative characterization of lymph node morphology and metastasis-associated imaging phenotypes.
Problem

Research questions and friction points this paper is trying to address.

axillary lymph node metastasis
breast cancer
surface reconstruction defects
shape analysis
morphological quantification
Innovation

Methods, ideas, or system contributions that make the work stand out.

Spherical Harmonics
Topology-aware Surface Processing
Multi-resolution Shape Analysis
Geometric Quantification
Lymph Node Metastasis
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Z
Zixi Yi
School of Mathematics and Statistics, Central South University, Changsha, Hunan, China
L
Limeng Qu
Department of General Surgery, The Second Xiangya Hospital, Central South University, Changsha, Hunan, China; Clinical Research Center for Breast Disease in Hunan Province, Changsha, Hunan, China
Gary P. T. Choi
Gary P. T. Choi
Vice-Chancellor Assistant Professor, Department of Mathematics, The Chinese University of Hong Kong
Applied MathematicsComputational GeometryMathematical ModelingMetamaterialsMedical Imaging