Browsing by Author "Malladi, Rakesh"

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    Inferring Spectral and Spatiotemporal Dependencies from Data and its Application to Epilepsy
    (2017-03-28) Malladi, Rakesh; Aazhang, Behnaam
    A fundamental problem in many science and engineering disciplines is inferring the characteristics of a physical or biological system from the dependencies in data recorded from the system. The dependencies in data, particularly in case of signals recorded from brain, are commonly believed to be nonlinear and the underlying model is often unknown. This thesis focusses on developing novel information-theoretic approaches to detect and quantify spectral and spatiotemporal dependencies from data in a data-driven manner and applies them to electrocorticographic (ECoG) recordings from epilepsy patients to unravel epileptic brain networks. Frequency components in a signal or between two signals, not necessarily at the same frequency, are spectrally dependent if they are not statistically independent. Two signals are temporally dependent if the past measurements at one decrease the uncertainty in predicting the other. First, we define a novel metric, mutual information in frequency, to detect spectral dependency and quantify it using a data-driven estimator. We then develop a data-driven estimator of mutual information between dependent data using mutual information in frequency. Next, we develop a model-based and a data-driven estimator of directed information to detect and quantify the temporal dependencies in data. Finally, we apply the proposed metrics to ECoG recordings from epilepsy patients to identify seizure onset zone (SOZ), to learn the spatiotemporal characteristics of seizures and to infer the cross-frequency coupling in SOZ. We observe that seizure onset zone drives the rest of brain to a seizure during pre-seizure and seizure periods, while it acts as a sink during post-seizure periods. In addition, high frequency coupling increases during seizures within an ECoG channel and between channels in the same anatomical region in SOZ, but not between different regions in SOZ. This suggests different anatomical regions in the SOZ are independently driving the seizure activity and any treatment should potentially target these regions simultaneously. Going forward, the dependencies unraveled by the proposed metrics should be further analyzed to optimize the parameters of closed-loop electrical stimulation based treatments for epilepsy.
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    Mutual Information in Frequency and Its Application to Measure Cross-Frequency Coupling in Epilepsy
    (IEEE, 2018) Malladi, Rakesh; Johnson, Don H.; Kalamangalam, Giridhar P.; Tandon, Nitin; Aazhang, Behnaam
    We define a metric, mutual information in frequency (MI-in-frequency), to detect and quantify the statistical dependence between different frequency components in the data, referred to as cross-frequency coupling and apply it to electrophysiological recordings from the brain to infer cross-frequency coupling. The current metrics used to quantify the cross-frequency coupling in neuroscience cannot detect if two frequency components in non-Gaussian brain recordings are statistically independent or not. Our MI-in-frequency metric, based on Shannon's mutual information between the Cramér's representation of stochastic processes, overcomes this shortcoming and can detect statistical dependence in frequency between non-Gaussian signals. We then describe two data-driven estimators of MI-in-frequency: One based on kernel density estimation and the other based on the nearest neighbor algorithm and validate their performance on simulated data. We then use MI-in-frequency to estimate mutual information between two data streams that are dependent across time, without making any parametric model assumptions. Finally, we use the MI-in-frequency metric to investigate the cross-frequency coupling in seizure onset zone from electrocorticographic recordings during seizures. The inferred cross-frequency coupling characteristics are essential to optimize the spatial and spectral parameters of electrical stimulation based treatments of epilepsy.