Phase Synchronization of Two Tremor-Related Neurons B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u Sunghan Kim Biomedical Signal Processing Laboratory Electrical and Computer Engineering Department Portland State University E LECTRICAL & C OMPUTER E NGINEERING
Background B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u • Physiological Tremors of Neurons � Fluctuation of an instantaneous firing rate of neurons � Recorded through a microelectrode recorder � Not amplitude-modulated signals like limb’s tremor recordings � Several studies on the interaction between neuron’s tremors and limb’s tremors � Few studies on the interaction between neurons’ tremors � Phase-locking analysis between tremor-related neurons is critical to the study of the tremor control mechanism in the central nerve system E LECTRICAL & C OMPUTER 2 E NGINEERING
Problem Introduction B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u • Limitations of Temporal Correlation Methods � Coherence analysis in frequency domains � Crosscorrelogram analysis in time domains � Both methods based on the stationarity assumption of signals � Most tremor signals such as MER, EMG, and EEG are not stationary � Current methods detect both phase and amplitude correlations � Instantaneous phase analysis method is required to study the phase-locking between nonstationary signals E LECTRICAL & C OMPUTER 3 E NGINEERING
Objectives B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u • Phase-locking Analysis of Two Tremor Spike Trains Extracted from a Single Microelectrode Recording � Instantaneous analysis � Only focuses on the phase coherence between two oscillatory signals, not amplitude correlation � Hypothesis test of two tremor’s independency E LECTRICAL & C OMPUTER 4 E NGINEERING
Methodology B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u • Overview � Building spike trains out of two-unit tremor MER � Constructing phase evolution series (core step) � Building instantaneous frequency series � Estimating the distribution of phase coherence between two independent tremor signals � Appling the result to a phase-locking index series of two tremor signals extracted from a single MER E LECTRICAL & C OMPUTER 5 E NGINEERING
Methodology - Step 1 B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u • Building Two Spike Trains out of Two-Unit Tremor MER E LECTRICAL & C OMPUTER 6 E NGINEERING
Methodology - Step 1 B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u • Histogram of All Peaks in a MER Signal E LECTRICAL & C OMPUTER 7 E NGINEERING
Methodology - Step 1 B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u • Histogram of All Peaks in a MER Signal E LECTRICAL & C OMPUTER 8 E NGINEERING
Methodology - Step 1 B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u • Building Two Spike Trains out of Two-Unit Tremor MER E LECTRICAL & C OMPUTER 9 E NGINEERING
Methodology - Step 2 B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u • Constructing Phase Evolution Series � Bandpass filter the spike trains to extract oscillatory components of the spike trains � 3~8 Hz is the typical essential tremor (ET) frequency range E LECTRICAL & C OMPUTER 10 E NGINEERING
Methodology - Step 2 B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u � Normalized Gabor representation of the oscillatory component time series through Hilbert transformation � Hilbert transformation where is the oscillatory component time series � This new representation is in a complex domain � Normalized Gabor representation of the time series � Its unwrapped phase is the phase evolution series of the oscillatory component time series � This process is equivalent to projecting the time series onto a unit circle in a complex domain E LECTRICAL & C OMPUTER 11 E NGINEERING
Methodology - Step 3 B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u • Building Instantaneous Frequency Series � Instantaneous frequency is equal to the derivative of the unwrapped phase evolution E LECTRICAL & C OMPUTER 12 E NGINEERING
Methodology - Step 4 B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u • Hypothesis Test for a Phase-Locking Index � Phase coherence as a phase-locking index � where is the phase difference between two phase evolution series � When two correlated signals’ phases are locked, the phase- locking index becomes large � However, the large phase-locking index does not necessarily mean the correlation of two tremor signals � The instantaneous frequency series of two independent tremor signals may look synchronized, i.e. phase-locked, over a certain period of time E LECTRICAL & C OMPUTER 13 E NGINEERING
Methodology - Step 4 B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u � Estimate the distribution of the phase coherence between two independent tremor signals to test a null hypothesis � Ho: two signals are independent � Model a tremor spike train as a quasi-Poisson process � Event occurring probability changes over time in a quasi Poisson process � Generate the ensembles of two independent tremor signals based on the model � Estimate the distribution of the phase coherence between these two independent synthetic tremor signals E LECTRICAL & C OMPUTER 14 E NGINEERING
Methodology - Step 4 B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u � If two tremor signals’ phases are truly locked its phase coherence should be greater than 95 th or 99 th percentile of the estimated distribution of the phase coherence between two independent tremor signals � The 99 th percentile of the estimated distribution vs. the length of time window for the phase coherence index E LECTRICAL & C OMPUTER 15 E NGINEERING
Result B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u • Applied This Method to the Tremor Signals Extracted from the Two-Unit Tremor MER � Two tremor signals’ instantaneous frequency series � Phase coherence vs. time E LECTRICAL & C OMPUTER 16 E NGINEERING
Discussion B I O M E D I C A L S I G N A L P R O C E S S I N G L A B b s p . p d x . e d u • The hypothesis test can be applied once to determine whether two tremor signals are phase-locked during a specific period of time • It cannot be applied to the sequential segments of two tremor signals because they are not independent • The 99 th percentile of the estimate distribution of the phase coherence was much greater than the phase coherence between two real tremor signals � It may indicate that two real tremor signals are not phase- locked at all � Or, the real tremor spike trains are quite different from the model tremor spike train E LECTRICAL & C OMPUTER 17 E NGINEERING
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