Time-Dependent Statistical and Correlation Properties of Neural Signals during Handwriting Valery I. Rupasov 1 , Mikhail A. Lebedev 2 , Joseph S. Erlichman 3 , Stephen L. Lee 4 , James C. Leiter 5 , Michael Linderman 6 * 1 Department of Basic Research, Norconnect Inc., Ogdensburg, New York, United States of America, 2 Department of Neurobiology, Duke University, Durham, North Carolina, United States of America, 3 Department of Biology, St. Lawrence University, Canton, New York, United States of America, 4 Department of Neurology, Dartmouth Medical School, Lebanon, New Hampshire, United States of America, 5 Department of Physiology and Neurobiology, Dartmouth Medical School, Lebanon, New Hampshire, United States of America, 6 Department of Neuroethics, Norconnect Inc., Ogdensburg, New York, United States of America Abstract To elucidate the cortical control of handwriting, we examined time-dependent statistical and correlational properties of simultaneously recorded 64-channel electroencephalograms (EEGs) and electromyograms (EMGs) of intrinsic hand muscles. We introduced a statistical method, which offered advantages compared to conventional coherence methods. In contrast to coherence methods, which operate in the frequency domain, our method enabled us to study the functional association between different neural regions in the time domain. In our experiments, subjects performed about 400 stereotypical trials during which they wrote a single character. These trials provided time-dependent EMG and EEG data capturing different handwriting epochs. The set of trials was treated as a statistical ensemble, and time-dependent correlation functions between neural signals were computed by averaging over that ensemble. We found that trial-to-trial variability of both the EMGs and EEGs was well described by a log-normal distribution with time-dependent parameters, which was clearly distinguished from the normal (Gaussian) distribution. We found strong and long-lasting EMG/EMG correlations, whereas EEG/EEG correlations, which were also quite strong, were short-lived with a characteristic correlation durations on the order of 100 ms or less. Our computations of correlation functions were restricted to the b spectral range (13–30 Hz) of EEG signals where we found the strongest effects related to handwriting. Although, all subjects involved in our experiments were right-hand writers, we observed a clear symmetry between left and right motor areas: inter-channel correlations were strong if both channels were located over the left or right hemispheres, and 2–3 times weaker if the EEG channels were located over different hemispheres. Although we observed synchronized changes in the mean energies of EEG and EMG signals, we found that EEG/EMG correlations were much weaker than EEG/EEG and EMG/EMG correlations. The absence of strong correlations between EMG and EEG signals indicates that (i) a large fraction of the EEG signal includes electrical activity unrelated to low-level motor variability; (ii) neural processing of cortically-derived signals by spinal circuitry may reduce the correlation between EEG and EMG signals. Citation: Rupasov VI, Lebedev MA, Erlichman JS, Lee SL, Leiter JC, et al. (2012) Time-Dependent Statistical and Correlation Properties of Neural Signals during Handwriting. PLoS ONE 7(9): e43945. doi:10.1371/journal.pone.0043945 Editor: Natasha M. Maurits, University Medical Center Groningen UMCG, The Netherlands Received April 19, 2012; Accepted July 27, 2012; Published September 11, 2012 Copyright: ß 2012 Rupasov et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was supported by National Science Foundation (www.nsf.gov) grants 0848523 (IIP), 1048430 (RAHSS), 1048428 (RET) (Principal investigator: ML), and by a National Instruments (www.ni.com) grant. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: ML is paid employee and the owner of Norconnect Inc., and VIR is an employee of Norconnect Inc. ML is going to develop products from this and future research. He is the author of pending patents with United States Patent Office. Recordation of handwriting and hand movement using electromyography 11640954, Handwriting EMG for Medical Diagnosis 61108603, Method and Apparatus for Biomedical Analysis Using EEG, and EMG signals 13341465. ML has 88% stock ownership in Norconnect Inc. and is the board chairman at Norconnect Inc. This research was supported by research grant #0848523 to Norconnect from National Science Foundation and a National Instruments grant. There are no further patents, products in development or marketed products to declare. This does not alter the authors’ adherence to all the PLoS ONE policies on sharing data and materials, as detailed online in the guide for authors. * E-mail: mlinderman@acm.org Introduction Since the first publication by D. Walter [1], the coherence method, developed for the analysis of stationary random data in linear systems (see, e.g., [2]), has been employed in hundreds of papers dealing with the analysis of neural signals such as EEGs and EMGs. In these publications, the level of coherence was used as a measure of coupling between the processes generating neural signals and of the functional association between neuronal structures [3–6]. This analysis of relationships between neural signals is based on computations of the coherence and phase of the two signals. For Fourier harmonics, X (v) and Y (v), of two time-dependent signals X (t) and Y (t), the coherence is defined as the square of the modulus, C(v)~DP(v)D 2 , and the phase is defined as W(v)~arctan½Im P(v)=Re P(v), of the complex coherence function P(v)~ X (v)Y  (v) ½X (v)X  (v) 1=2 ½Y (v)Y  (v) 1=2 ð1Þ PLOS ONE | www.plosone.org 1 September 2012 | Volume 7 | Issue 9 | e43945