Persistent Homology as a Detection Axis Complementary to Intensity-Based Methods for Comparative MALDI Mass...

Comparing spatial molecular distributions across mass spectrometry imaging (MSI) sections is complicated by intersection shape differences, intensity variation, and the blindness of intensity-based tests to spatial organization. Persistent homology (PH) with per-section z-score normalization and 1-Wasserstein (W1) distance between persistence diagrams provides an alignment-free framework for quantifying spatial dissimilarity. We applied this pipeline to the public positive-mode MALDI-MSI lung lipidomics data set of Stevens et al. (2025): 12 mice (6 female, 6 male; 3 saline (SFA) and 3 HDM + O3 per sex). For each sex, 1000 m/z channels were screened across 15 pairwise comparisons and prioritized by 9/9 directional consistency (all 9 cross-group distances exceeding the within-group mean). The female cohort yielded 16 PH candidates (∼15 putative species), of which 8 have strong Moran's I support (HO3/SFA Moran ratio ≥2 with absolute HO3Moran ≥0.20); the male cohort yielded 1 candidate, consistent with the expected sex-specificity. The Kolmogorov-Smirnov and Earth Mover's Distance baselines applied to the same pair structure returned 9 and 29 female candidates with zero overlap with the PH set at the main parameters (KS was a complete subset of EMD); the overlap becomes partial at coarser binning. A control analysis applying EMD to z-scored pixel distributions returned 92 female candidates, of which only 5 overlapped with PH and 3 with raw-EMD, localizing the detection-domain separation primarily to the topology/W1 step rather than to z-score preprocessing alone. Within this positive-mode data set PH acts as a detection axis partially orthogonal to intensity-based screening; candidates are reported as prioritization targets requiring targeted MS/MS for identification.