An exploratory persistent-homology analysis of resting-state fMRI functional connectivity under Ayahuasca

Psychedelic states offer a useful setting for studying changes in large-scale brain organization. Here, we applied Topological Data Analysis (TDA) to resting-state fMRI functional connectivity from nine participants scanned before and after Ayahuasca ingestion. Vietoris–Rips filtrations were constructed from correlation-derived dissimilarity matrices, and persistent entropy was used to quantify the distribution of persistence lifetimes across homology dimensions S 0 – S 3 . In the primary absolute-correlation analysis, persistent entropy of H 2 features showed a nominal pre/post decrease ( W = 4 . 0 , p = 0 . 027 , rank-biserial correlation = 0 . 822 ). This effect did not survive correction across the four tested homology dimensions ( q FDR = 0 . 109 ) and was not reproduced when signed correlations were preserved using d ( i , j ) = 1 − r ( i , j ) . Exploratory signal-complexity analyses using Lempel–Ziv complexity and sample entropy showed descriptive but statistically non-significant increases in temporal complexity. These results should therefore be interpreted as preliminary and hypothesis-generating, particularly given the small sample size, lack of placebo control, availability of only GSR-preprocessed connectivity data, and sensitivity to the distance definition. The study suggests that persistent homology may provide a useful framework for studying psychedelic-associated changes in the higher-dimensional topology induced by functional connectivity, but replication in larger placebo-controlled datasets is required.