Fig. 1

a The proposed multimodal framework, where dw-MRI network as a constraint is used to guide the regression of rs-fMRI BOLD time series to create fused brain connectivity network; b a sequence of brain networks with different sparsity are constructed to form integrated networks, which are prepared for subsequent graph filtration analysis to extract persistent homology measures; c each integrated network is converted to distance network, and persistent homology is applied to quantify the distance network by evaluating the persistence of connected components (PH-0) and cycles (PH-1); d statistical analysis is performed to capture the difference between APOE ε4 carriers and non-carriers. Also, we extract specific loop structures by identifying connectivity patterns using PH-1