The representation of the flow of information between neurons in the brain based on their activity is termed thecausal functional connectome. Such representation incorporates the dynamic nature of neuronal activity and causal interactions between them. In contrast to connectome, the causal functional connectome is not directly observed and needs to be inferred from neural time series. A popular statistical framework for inferring causal connectivity from observations is thedirected probabilistic graphical modeling. Its common formulation is not suitable for neural time series since it was developed for variables with independent and identically distributed static samples. In this work, we propose to model and estimate the causal functional connectivity from neural time series using a novel approach that adapts directed probabilistic graphical modeling to the time series scenario. In particular, we develop theTime-Aware PC(TPC) algorithm for estimating the causal functional connectivity, which adapts the PC algorithm—a state-of-the-art method for statistical causal inference. We show that the model outcome of TPC has the properties of reflecting causality of neural interactions such as being non-parametric, exhibits thedirected Markovproperty in a time-series setting, and is predictive of the consequence of counterfactual interventions on the time series. We demonstrate the utility of the methodology to obtain the causal functional connectome for several datasets including simulations, benchmark datasets, and recent multi-array electro-physiological recordings from the mouse visual cortex.

Peaks signify important events in a signal. In a pair of signals how peaks are occurring with mutual correspondence may offer us significant insights into the mutual interdependence between the two signals based on important events. In this work we proposed a novel synchronization measure between two signals, called peak synchronization, which measures the simultaneity of occurrence of peaks in the signals. We subsequently generalized it to more than two signals. We showed that our measure of synchronization is largely independent of the underlying parameter values. A time complexity analysis of the algorithm has also been presented. We applied the measure on intracranial EEG signals of epileptic patients and found that the enhanced synchronization during an epileptic seizure can be modeled better by the new peak synchronization measure than the classical amplitude correlation method.

Functional connectivitybetween brain regions is known to be altered in Alzheimer's disease and promises to be a biomarker for early diagnosis. Several approaches for functional connectivity obtain an un-directed network representing stochastic associations (correlations) between brain regions. However, association does not necessarily imply causation. In contrast, Causal Functional Connectivity (CFC) is more informative, providing a directed network representing causal relationships between brain regions. In this paper, we obtained the causal functional connectome for the whole brain from resting-state functional magnetic resonance imaging (rs-fMRI) recordings of subjects from three clinical groups: cognitively normal, mild cognitive impairment, and Alzheimer's disease. We applied the recently developed Time-aware PC (TPC) algorithm to infer the causal functional connectome for the whole brain. TPC supports model-free estimation of whole brain CFC based on directed graphical modeling in a time series setting. We compared the CFC outcome of TPC with that of other related approaches in the literature. Then, we used the CFC outcomes of TPC and performed an exploratory analysis of the difference in strengths of CFC edges between Alzheimer's and cognitively normal groups, based on edge-wisep-values obtained by Welch'st-test. The brain regions thus identified are found to be in agreement with literature on brain regions impacted by Alzheimer's disease, published by researchers from clinical/medical institutions.

(1) Background: Alterations in brain functional connectivity (FC) precede clinical symptoms of Alzheimer’s disease (AD) by decades, presenting opportunities for early diagnosis. However, conventional FC analyses measure correlations between brain regions and do not provide insights into directional, causal interactions. Causal functional connectivity (CFC), which infers directed interactions between regions, addresses this limitation. This study aims to identify disrupted CFC networks in AD compared to cognitively normal (CN) individuals. (2) Methods: The recently developed Time-aware PC (TPC) algorithm was employed to infer directed CFC from functional magnetic resonance imaging (fMRI) data. These results were compared with traditional correlation-based FC obtained via sparse partial correlation. Network-based Statistics (NBS) for directed networks was used to identify altered CFC sub-networks, with corrections for multiple comparisons applied at the 5% significance level. (3) Results: Key causal networks, including the inferior frontal gyrus, superior temporal gyrus, middle temporal gyrus, and cerebellum, showed significantly reduced strength in AD compared to CN (p = 0.0299; NBS corrected). Instead of detecting disruptions at the level of individual edges, this study identifies network-level alterations, revealing systemic disruptions in brain connectivity. (4) Conclusions: This study demonstrates the utility of CFC analysis in uncovering network-level disruptions in AD. The identified disrupted networks align with published medical literature and provide a framework for future studies with larger datasets.