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

Zixi Yi; Limeng Qu; Gary P. T. Choi

q-bio.QMSep 28, 2026

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

Authors: Zixi Yi, Limeng Qu, Gary P. T. Choi

Organizations: School of Mathematics and Statistics, Central South University, Changsha, Hunan, China · 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 · Department of Mathematics, The Chinese University of Hong Kong, Hong Kong SAR, China

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.

Figures & tables

Figure 1 : Overview of the proposed geometric processing workflow. The pipeline comprises initial context-aware smoothing, adaptive voxelization with strict topology correction, geometry-constrained adaptive smoothing, and local artifact detection and repair. The post-repair validation criteria ensure that the output surfaces are connected, closed, consistently oriented genus-

0

surfaces for the subsequent spherical analysis.

Figure 2 : Qualitative comparison of surface smoothing stages. Representative lymph node surface meshes are shown before smoothing, after context-aware (CA) smoothing, and after adaptive Laplacian–Taubin smoothing.

Figure 3 : Qualitative examples of local artifact detection using three complementary filtering strategies. From left to right: ray-based inward-fold detection, local small-hole detection, and CT-informed geometric screening. The top row shows the location of each detected region on the complete surface, and the bottom row shows the corresponding enlarged mesh patch.

Figure 4 : Local artifact excision and surface-reconstruction workflow. (A) Artifact excision. (B) Initial triangulation and conforming subdivision. (C) Quadratic reference-surface estimation. (D) Constrained cotangent bi-Laplacian fairing. (E) Final reconstructed surface after local Taubin smoothing.

Feature family	Main descriptors	$n$
Convexity	Convex-hull measures	6
Radial morphology	Radial-distance statistics	15
Reflection symmetry	Principal-plane reflection errors	9
Mean curvature	Mean-curvature statistics	26
Gaussian curvature	Gaussian-curvature statistics	13
Shape Index and Curvedness	Local shape and bending measures	28

Table 1 : Feature families used in the multi-resolution SH analysis.

Criterion	Original	Processed	Change (pp)
Strict topology pass	1383/1769 (78.18%)	1769/1769 (100.00%)	+21.82
Single-component surface	1531/1769 (86.55%)	1769/1769 (100.00%)	+13.45
Genus- $0$ topology	1537/1769 (86.89%)	1769/1769 (100.00%)	+13.11
Outward orientation	1560/1769 (88.19%)	1769/1769 (100.00%)	+11.81

Table 2: Topological validity before and after geometric processing.

Measure	Original	Processed	Median paired change (95% CI)	FDR-adjusted $P$
Triangle quality (5th percentile)	0.7274	0.7787	+0.0453 (0.0413–0.0506)	$2.29\times 10^{-54}$
Normal jump (95th percentile, degrees)	38.7617	4.6759	$-33.3190$ ( $-33.9196$ – $-32.7360$ )	$5.06\times 10^{-83}$

Table 3: Downstream computational surface quality before and after geometric processing (internal cohort). Values are medians across 500 paired surfaces.

Figure 5 : Changes in univariate discrimination of conventional PyRadiomics shape descriptors across SH representations. For each descriptor and SH degree,

\Delta\mathrm{AUC}

was calculated relative to the corresponding descriptor extracted from the original surface. Positive values indicate higher discrimination after SH reconstruction, whereas negative values indicate lower discrimination.

Figure 6 : Degree-wise spectral discrimination across the SH spectrum. Folded univariate AUC is shown for relative spectral energy at each harmonic degree, summarizing discrimination irrespective of the direction of association. Discrimination was strongest at intermediate degrees and declined toward chance level at the highest degrees.

Figure 7 : Divergence between geometric fidelity and predictive performance across SH degrees. (A) Composite geometric fidelity increased monotonically with reconstruction degree. (B) AUC of the fixed-resolution 366-feature models increased from low resolution to intermediate degrees but declined at degree

34

. Error bars denote 95% confidence intervals.

Figure 8 : Feature-family-specific SH degree selection. (A) Selection frequencies are shown across the locked outer cross-validation folds for ten representative feature families; degree selection was performed for all 20 predefined feature families. (B) Distinct descriptor families favored different SH reconstruction degrees, demonstrating that a single common resolution was not uniformly optimal across geometric measurements.

Figure 9 : Resolution-dependent perturbation robustness across SH degrees. (A) Geometric perturbation transmission ratio

T_{L}

. (B) Cumulative retained perturbation energy

R_{L}

. (C) Perturbation-to-clean spectral energy ratio

Q_{\ell}

. (D) Perturbation-induced change in AUC. Complementary predictive-stability measures included the mean absolute probability shift

\Delta p_{L}

and clean–perturbed prediction correlation.

Feature family	Preferred $L$	Alternative $L$	Features	Composite median	95% CI	Positive lymph nodes (%)	One-sided $P$	Holm-adjusted $P$
Convexity	5	10	6	0.116	0.110–0.122	98.6	$<0.001$	$<0.001$
Convexity	5	34	6	0.223	0.213–0.232	99.2	$<0.001$	$<0.001$
Mean curvature	10	5	26	0.216	0.210–0.220	98.8	$<0.001$	$<0.001$
Mean curvature	10	34	26	0.970	0.943–1.004	99.7	$<0.001$	$<0.001$
Central asymmetry	34	5	10	0.166	0.154–0.174	79.4	$<0.001$	$<0.001$
Central asymmetry	34	10	10	0.024	0.021–0.028	65.4	$<0.001$	$<0.001$

Table 8: External replication of internally specified family-specific degree preferences. Composite contrasts were direction-aligned using feature-specific directions defined in the internal cohort and scaled using internal median absolute deviations. Positive values support the internally preferred degree relative to the alternative degree. Confidence intervals were obtained using 10,000 nonparametric bootstrap resamples of lymph nodes. Positive lymph nodes are those with a direction-aligned composite greater than zero. One-sided

P

values were adjusted across the six prespecified family–contrast tests using the Holm procedure.

Feature family	Highest observed degree	AUC (95% CI)	Paired $\Delta$ AUC (95% CI)
Convexity	${L=5}$	${0.853}$ (0.731–0.945)	0.013 (-0.073–0.093)
Mean curvature	${L=40}$	${0.883}$ (0.788–0.964)	0.063 (-0.012–0.142)
Central asymmetry	${L=30}$	${0.745}$ (0.606–0.879)	0.002 (-0.034–0.042)

Table 9: Observed family-specific SH-degree performance in the LIDC-IDRI cross-organ experiment. Values are shown as AUC with 95% confidence intervals. Paired

\Delta

AUC values denote the differences between the highest and second-highest observed AUCs and were calculated using the same out-of-fold predictions.

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