During my PhD, apart from small ones I mainly studied two related problems: 1. the effect of the amplitude information on the estimation of phase locking value between Gaussian signals 2. development of a new measure to estimate functional connectivity in presence of cross-talk. Here is a 4 minute overview of my research:
A new measure in Presence of Cross-talk (ongoing project)
The rich temporal content of EEG/ MEG data allows us to study dynamic networks in the human brain. The main challenge with this data is its poor spatial resolution due to the volume conduction problem.
Say we want to measure interaction between two areas as shown on the cortex through the measurements acquired outside the head (see Fig. on the left). It is very likely that there will be a cross-talk between these sources. Measures including coherence and correlation may yield spurious interaction in this case. Imaginary coherence (Nolte 2004) and lagged coherence (Pasqual-Marqui -2007) are proposed to overcome this problem. Both of these metrics measure the non-instantaneous interaction between the signals since the cross-talk effect is thought to be instantaneous.
However, these two measures do not consider the interference from the external sources. Say in addition to a cross-talk between signals, there is an interference effect from the third source (see Fig. on right). In my research, I address this problem using a novel measure as an extension of lagged coherence. Now, I am in the process of writing up a journal paper out of this work.
Publications: S. Aydore, S. Ashrafulla, R. M. Leahy, Regularized Partial Lagged Coherence for Functional Connectivity Analysis in the Presence of Cross-talk, Human Brain Mapping (HBM), June 8-12, 2014, Hamburg, Germany. (submitted) S. Aydore, S. Ashrafulla, A. A. Joshi, R. M. Leahy, A Measure of Connectivity in the Presence of Crosstalk, Asilomar Conference on Signals, Systems and Computers, November 3-6, 2013, Pacic Grove, CA, USA. Phase Synchronization We need to represent the signals in time-frequency domain in order to investigate the interactions at the temporal and frequency range of interest.
The time-series are band-pass filtered so that the resulting signals are narrow-band. Hilbert transform is then applied to obtain amplitude and phase information. We could use Fourier or Wavelet transforms as well. Phase locking value (PLV) incorporates only the phase information and quantifies the relative phase consistency between the signals. Nonparametric estimation of PLV simply takes the average over trials and parametric approach assumes von Mises distribution of the relative phase. It can be shown that maximum likelihood estimation of parametric approach approximates to the nonparametric approach. In my work, I explored the relative phase distribution for Gaussian signals. We have shown that this distribution depends on the amplitude information of the signals. This finding indicates 1-1 relationship between coherence and PLV. In other words, PLV does not add information not contained in coherence. Publications: S. Aydore, D. Pantazis, R.M. Leahy, A Note on the Phase Locking Value and its Properties , Neuroimage 74, 231–244. doi: 10.1016/j.neuroimage.2013.02.008. S. Aydore, D. Pantazis, R. M. Leahy, Phase Synchrony in Multivariate Gaus- sian Data with Applications to Cortical Networks, ISBI 2012, Barcelona, Spain. S. Aydore, R. M. Leahy, The Partial Phase Locking Value for Circular Gaus- sian Processes, BIOMAG 2012, France. (Best PhD poster award). S. Aydore, D. Pantazis, R. M. Leahy, Measuring Partial Phase Locking Value to Detect Synchronization in Multivariate Gaussian Systems, NeuroInformatics 2011, Boston, MA, USA. S. Aydore, D. Pantazis, J. Mosher, R. M. Leahy, Statistical Analysis of Phase and Amplitude via Partial Coherence in Hilbert Transform Domain, Human Brain Mapping (HBM), June, 26-30, 2011, Quebec City, Canada.