Characterization of Neuroimage Coupling Between EEG and FMRI Using Within-Subject Joint Independent Component Analysis

The purpose of this dissertation was to apply joint independent component analysis (jICA) to electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) to characterize the neuroimage coupling between the two modalities. EEG and fMRI are complimentary imaging techniques which have been used in conjunction to investigate neural activity. Understanding how these two imaging modalities relate to each other not only enables better multimodal analysis, but also has clinical implications as well. In particular, Alzheimer’s, Parkinson’s, hypertension, and ischemic stroke are all known to impact the cerebral blood flow, and by extension alter the relationship between EEG and fMRI. By characterizing the relationship between EEG and fMRI within healthy subjects, it allows for comparison with a diseased population, and may offer ways to detect some of these conditions earlier. The correspondence between fMRI and EEG was first examined, and a methodological approach which was capable of informing to what degree the fMRI and EEG sources corresponded to each other was developed. Once it was certain that the EEG activity observed corresponded to the fMRI activity collected a methodological approach was developed to characterize the coupling between fMRI and EEG. Finally, this dissertation addresses the question of whether the use of jICA to perform this analysis increases the sensitivity to subcortical sources to determine to what degree subcortical sources should be taken into consideration for future studies. This dissertation was the first to propose a way to characterize the relationship between fMRI and EEG signals using blind source separation. Additionally, it was the first to show that jICA significantly improves the detection of subcortical activity, particularly in the case when both physiological noise and a cortical source are present. This new knowledge can be used to design studies to investigate subcortical signals, as well as to begin characterizing the relationship between fMRI and EEG across various task conditions

Deterministic and stochastic sampling of two coupled Kerr parametric oscillators

The vision of building computational hardware for problem optimization has spurred large efforts in the physics community. In particular, networks of Kerr Parametric Oscillators (KPOs) are envisioned as simulators for finding the ground states of Ising Hamiltonians. It was shown, however, that KPO networks can feature large numbers of unexpected solutions that are difficult to sample with the existing deterministic (i.e., adiabatic) protocols. In this work, we experimentally realize a system of two coupled KPOs and find good agreement with the predicted mapping to Ising states. We then introduce a protocol based on stochastic sampling of the system and show how the resulting probability distribution can be used to identify the ground state of the corresponding Ising Hamiltonian. This method is akin to a Monte-Carlo sampling of multiple out-of-equilibrium stationary states and is less prone to become trapped in local minima than deterministic protocols

EEG and fMRI Coupling and Decoupling Based on Joint Independent Component Analysis (jICA)

Background Meaningful integration of functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) requires knowing whether these measurements reflect the activity of the same neural sources, i.e., estimating the degree of coupling and decoupling between the neuroimaging modalities. New method This paper proposes a method to quantify the coupling and decoupling of fMRI and EEG signals based on the mixing matrix produced by joint independent component analysis (jICA). The method is termed fMRI/EEG-jICA. Results fMRI and EEG acquired during a syllable detection task with variable syllable presentation rates (0.25–3 Hz) were separated with jICA into two spatiotemporally distinct components, a primary component that increased nonlinearly in amplitude with syllable presentation rate, putatively reflecting an obligatory auditory response, and a secondary component that declined nonlinearly with syllable presentation rate, putatively reflecting an auditory attention orienting response. The two EEG subcomponents were of similar amplitude, but the secondary fMRI subcomponent was ten folds smaller than the primary one. Comparison to existing method FMRI multiple regression analysis yielded a map more consistent with the primary than secondary fMRI subcomponent of jICA, as determined by a greater area under the curve (0.5 versus 0.38) in a sensitivity and specificity analysis of spatial overlap. Conclusion fMRI/EEG-jICA revealed spatiotemporally distinct brain networks with greater sensitivity than fMRI multiple regression analysis, demonstrating how this method can be used for leveraging EEG signals to inform the detection and functional characterization of fMRI signals. fMRI/EEG-jICA may be useful for studying neurovascular coupling at a macro-level, e.g., in neurovascular disorders

Extracting the lifetime of a synthetic two-level system

The Kerr Parametric Oscillator (KPO) is a nonlinear resonator system that is often described as a synthetic two-level system. In the presence of noise, the system switches between two states via a fluctuating trajectory in phase space, instead of following a straight path. The presence of such fluctuating trajectories makes it hard to establish a precise count or even a useful definition, of the “lifetime” of the state. Addressing this issue, we compare several rate counting methods that allow to estimate a lifetime for the levels. In particular, we establish that a peak in the Allan variance of fluctuations can also be used to determine the levels’ lifetime. Our work provides a basis for characterizing KPO net- works for simulated annealing where an accurate determination of the state lifetime is of fundamental importance.ISSN:0003-6951ISSN:1077-311

Extracting the lifetime of a synthetic two-level system

The Kerr Parametric Oscillator (KPO) is a nonlinear resonator system that is often described as a synthetic two-level system. In the presence of noise, the system switches between two states via a fluctuating trajectory in phase space, instead of following a straight path. The presence of such fluctuating trajectories makes it hard to establish a precise count or even a useful definition, of the “lifetime” of the state. Addressing this issue, we compare several rate counting methods that allow to estimate a lifetime for the levels. In particular, we establish that a peak in the Allan variance of fluctuations can also be used to determine the levels’ lifetime. Our work provides a basis for characterizing KPO net- works for simulated annealing where an accurate determination of the state lifetime is of fundamental importance.ISSN:0003-6951ISSN:1077-311