Metabolic connectivity alterations in amyotrophic lateral sclerosis: Individual network analysis based on Wasserstein distances.

Molecular connectivity analysis with positron emission tomography (PET) imaging offers a promising approach for characterising brain network alterations in neurodegenerative disorders. In this study, we introduce Wasserstein distance (WD) as an alternative to Kullback-Leibler divergence similarity estimation (KLSE) for constructing single-subject metabolic connectivity networks. Using ¹⁸F-FDG PET data from 167 individuals with amyotrophic lateral sclerosis (ALS), 36 healthy volunteers (HV), and 25 ALS mimics, we generated WD- and KLSE-based connectivity matrices across 77 atlas-defined brain regions and evaluated corresponding graph theory-based nodal metrics. WD- and KLSE-derived nodal measures were strongly correlated, indicating methodological consistency. Compared with HVs, age-matched subjects in the ALS group (ALS_amHV) showed significant alterations in frontal, temporal, cerebellar, and occipital network nodes, with WD-based metrics revealing differences across more brain regions than the KLSE-based approach. Support vector machine classification of ALS_amHV vs. HV demonstrated that both connectivity approaches matched voxel-wise PET performance with accuracy higher than 0.80 (yet significantly lower than voxel-wise data, $p<0.05$ ), while significantly outperforming image-based classification for ALS vs. ALS mimics ( $p<0.01$ ), with WD achieving the highest accuracy of 0.65 ( $p<0.001$ ). These findings support WD-based metabolic connectivity as a sensitive, data-efficient framework for detecting disease-related network alterations and motivate its application to a broader range of PET tracers and cohorts.