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 S₀–S₃. In the primary absolute-correlation analysis, persistent entropy of H₂ 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.