Cross-spectral analysis of physiological tremor and muscle activity. I. Theory and application to unsynchronized EMG

We investigate the relationship between the extensor electromyogram (EMG) and tremor time series in physiological hand tremor by cross-spectral analysis. Special attention is directed to the phase spectrum and the effects of observational noise. We calculate the theoretical phase spectrum for a second order linear stochastic process and compare the results to measured tremor data recorded from subjects who did not show a synchronized EMG activity in the corresponding extensor muscle. The results show that physiological tremor is well described by the proposed model and that the measured EMG represents a Newtonian force by which the muscle acts on the hand.Comment: 9 pages, 6 figures, to appear in Biological Cybernetic

Estimation of time delay by coherence analysis

Using coherence analysis (which is an extensively used method to study the correlations in frequency domain, between two simultaneously measured signals) we estimate the time delay between two signals. This method is suitable for time delay estimation of narrow band coherence signals for which the conventional methods cannot be reliably applied. We show by analysing coupled R\"ossler attractors with a known delay, that the method yields satisfactory results. Then, we apply this method to human pathologic tremor. The delay between simultaneously measured traces of Electroencephalogram (EEG) and Electromyogram (EMG) data of subjects with essential hand tremor is calculated. We find that there is a delay of 11-27 milli-seconds ($ms$) between the tremor correlated parts (cortex) of the brain (EEG) and the trembling hand (EMG) which is in agreement with the experimentally observed delay value of 15 $ms$ for the cortico-muscular conduction time. By surrogate analysis we calculate error-bars of the estimated delay.Comment: 21 pages, 8 figures, elstart.cls file included. Accepted for publication in Physica

A noninvasive handheld assistive device to accommodate essential tremor: A pilot study

Background We explored whether a noninvasive handheld device using Active Cancellation of Tremor (ACT) technology could stabilize tremor‐induced motion of a spoon in individuals with essential tremor (ET). Methods Fifteen ET subjects (9 men, 6 women) performed 3 tasks with the ACT device turned on and off. Tremor severity was rated with the Fahn‐Tolosa‐Marin Tremor Rating Scale (TRS). Subjective improvement was rated by subjects with the Clinical Global Impression Scale (CGI‐S). Tremor amplitude was measured using device‐embedded accelerometers in 11 subjects. Results TRS scores improved with ACT on (versus off) in all 3 tasks: holding (1.00 ± 0.76 vs. 0.27 ± 0.70; P  = 0.016), eating (1.47 ± 1.06 vs. 0.13 ± 0.64; P  = 0.001), and transferring (1.33 ± 0.82 vs. 0.27 ± 0.59; P  = 0.001). CGI‐S improved with eating and transferring, but not the holding task. Accelerometer measurements demonstrated 71% to 76% reduction in tremor with the ACT device on. Conclusions This noninvasive handheld ACT device can reduce tremor amplitude and severity for eating and transferring tasks in individuals with ET. © 2013 International Parkinson and Movement Disorder SocietyPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106922/1/mds25796.pd

Can Zipf's law be adapted to normalize microarrays?

BACKGROUND: Normalization is the process of removing non-biological sources of variation between array experiments. Recent investigations of data in gene expression databases for varying organisms and tissues have shown that the majority of expressed genes exhibit a power-law distribution with an exponent close to -1 (i.e. obey Zipf's law). Based on the observation that our single channel and two channel microarray data sets also followed a power-law distribution, we were motivated to develop a normalization method based on this law, and examine how it compares with existing published techniques. A computationally simple and intuitively appealing technique based on this observation is presented. RESULTS: Using pairwise comparisons using MA plots (log ratio vs. log intensity), we compared this novel method to previously published normalization techniques, namely global normalization to the mean, the quantile method, and a variation on the loess normalization method designed specifically for boutique microarrays. Results indicated that, for single channel microarrays, the quantile method was superior with regard to eliminating intensity-dependent effects (banana curves), but Zipf's law normalization does minimize this effect by rotating the data distribution such that the maximal number of data points lie on the zero of the log ratio axis. For two channel boutique microarrays, the Zipf's law normalizations performed as well as, or better than existing techniques. CONCLUSION: Zipf's law normalization is a useful tool where the Quantile method cannot be applied, as is the case with microarrays containing functionally specific gene sets (boutique arrays)

Dynamic imaging of coherent sources reveals different network connectivity underlying the generation and perpetuation of epileptic seizures

The concept of focal epilepsies includes a seizure origin in brain regions with hyper synchronous activity (epileptogenic zone and seizure onset zone) and a complex epileptic network of different brain areas involved in the generation, propagation, and modulation of seizures. The purpose of this work was to study functional and effective connectivity between regions involved in networks of epileptic seizures. The beginning and middle part of focal seizures from ictal surface EEG data were analyzed using dynamic imaging of coherent sources (DICS), an inverse solution in the frequency domain which describes neuronal networks and coherences of oscillatory brain activities. The information flow (effective connectivity) between coherent sources was investigated using the renormalized partial directed coherence (RPDC) method. In 8/11 patients, the first and second source of epileptic activity as found by DICS were concordant with the operative resection site; these patients became seizure free after epilepsy surgery. In the remaining 3 patients, the results of DICS / RPDC calculations and the resection site were discordant; these patients had a poorer post-operative outcome. The first sources as found by DICS were located predominantly in cortical structures; subsequent sources included some subcortical structures: thalamus, Nucl. Subthalamicus and cerebellum. DICS seems to be a powerful tool to define the seizure onset zone and the epileptic networks involved. Seizure generation seems to be related to the propagation of epileptic activity from the primary source in the seizure onset zone, and maintenance of seizures is attributed to the perpetuation of epileptic activity between nodes in the epileptic network. Despite of these promising results, this proof of principle study needs further confirmation prior to the use of the described methods in the clinical praxis

Essential constraints for detecting deep sources in EEG - application to orthostatic tremor

The hypotheses that orthostatic tremor is generated by a central oscillator is been tested in this paper. In order to understand the mechanisms of the central network its sources need to be found. The cortical sources of both the basic and first “harmonic” frequency of orthostatic tremor are addressed in this paper. The Dynamic Imaging of Coherent Sources (DICS) was used to find the coherent sources in the brain. The three essential constraints for detecting deep sources in the brain using EEG data were tested by three model simulations. The optimal number of electrodes, length of the data and the signal to noise ratio required for error-free localization was tested. In all the orthostatic tremor patients the corticomuscular coherence was also present in the basic and the first harmonic frequency of the tremor. The basic frequency constituted a network of primary leg area, supplementary motor area, primary motor cortex, two pre-motor sources, diencephalon and cerebellum. The first harmonic frequency was in the region of primary leg area, supplementary motor area, primary motor cortex, diencephalon and cerebellum. Thus the generation of these two oscillations involves the same network structure and indicates the oscillation at double the tremor frequency is a harmonic of the basic tremor frequency. The orthostatic tremor could have the central oscillator in the brain