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A Geometric Analysis of Time Varying Electroencephalogram Vectors

Thakkar, Kairavee K
http://orcid.org/0000-0003-1397-486X
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1613745734396658

Abstract Details

2020, MS, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
Electroencephalogram (EEG) records the time-varying electrical activity of the brain. EEG can carry non-uniform noise, thereby making it a complex signal to analyze. In this thesis, we consider a set of two discrete, time-varying EEG vectors of the left and right hemispheres of brain. We develop dynamic models of EEG vectors based on different assumptions that pertain to the properties of a recorded EEG signal. These assumptions are primarily related to the amplitude, frequency, phase shift, and noise content of the two EEG vectors. For every model, we analyze this two-dimensional EEG vector in its phase plane based on the defined geometric properties of the phase plane portrait. For all models in this thesis, we show that the geometric properties are functions of the phase shift between two given signals. Moreover, by analyzing the geometric properties of two given EEG vectors with unknown amplitude and frequency, we can extract a relative phase shift between the given EEG vectors. A limitation in this study is an extracted value of phase shift between two signals is not highly accurate. One of the factors contributing to the low accuracy of an extracted phase shift is the minimizing numerical algorithm that is implemented to compute the geometric properties of the phase plane portrait of two EEG vectors. Other factors may include high noise content in EEG signals. An estimation of a phase shift between two EEG signals by geometrically analyzing their phase plane portrait can allow us to infer about the synchronization of two regions of brain from where the EEG signals are recorded.
Benjamin Vaughan, Ph.D. (Committee Chair)
Deeptankar DeMazumder, M.D. Ph.D. (Committee Member)
Donald French, Ph.D. (Committee Member)
76 p.
Mathematics
electroencephalogram; ellipse; eccentricity; phase plane; rotational angle

Recommended Citations

Citations

  • Thakkar, K. K. (2020). A Geometric Analysis of Time Varying Electroencephalogram Vectors [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1613745734396658

    APA Style (7th edition)

  • Thakkar, Kairavee. A Geometric Analysis of Time Varying Electroencephalogram Vectors. 2020. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1613745734396658.

    MLA Style (8th edition)

  • Thakkar, Kairavee. "A Geometric Analysis of Time Varying Electroencephalogram Vectors." Master's thesis, University of Cincinnati, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1613745734396658

    Chicago Manual of Style (17th edition)

ucin1613745734396658
142
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This open access ETD is published by University of Cincinnati and OhioLINK.