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

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.