Effective Brain Connectivity Extraction by Frequency-Domain Convergent Cross-Mapping (FDCCM) and its Application in Parkinson's Disease Classification

Objective: Inferring causal or <italic>effective connectivity</italic> between measured timeseries is crucial to understanding directed interactions in complex systems. This task is especially challenging in the brain as the underlying dynamics are not well-understood. This paper aims to introduce a novel causality measure called <italic>frequency-domain convergent cross-mapping</italic> (FDCCM) that utilizes frequency-domain dynamics through nonlinear state-space reconstruction. Method: Using synthesized chaotic timeseries, we investigate general applicability of FDCCM at different causal strengths and noise levels. We also apply our method on two resting-state Parkinson&#x0027;s datasets with 31 and 54 subjects, respectively. To this end, we construct causal networks, extract network features, and perform machine learning analysis to distinguish Parkinson&#x0027;s disease patients (PD) from age and gender-matched healthy controls (HC). Specifically, we use the FDCCM networks to compute the betweenness centrality of the network nodes, which act as features for the classification models. Result: The analysis on simulated data showed that FDCCM is resilient to additive Gaussian noise, making it suitable for real-world applications. Our proposed method also decodes scalp-EEG signals to classify the PD and HC groups with approximately 97&#x0025; leave-one-subject-out cross-validation accuracy. We compared decoders from six cortical regions to find that features derived from the left temporal lobe lead to a higher classification accuracy of 84.5&#x0025; compared to other regions. Moreover, when the classifier trained using FDCCM networks from one dataset was tested on an independent out-of-sample dataset, it attained an accuracy of 84&#x0025;. This accuracy is significantly higher than correlational networks (45.2&#x0025;) and CCM networks (54.84&#x0025;). Significance: These findings suggest that our spectral-based causality measure can improve classification performance and reveal useful network biomarkers of Parkinson&#x0027;s disease.