Joël M. H. Karel

Quantifying Neural Oscillatory Synchronization: A Comparison between Spectral Coherence and Phase-Locking Value Approaches

Synchronization or phase-locking between oscillating neuronal groups is considered to be important for coordination of information among cortical networks. Spectral coherence is a commonly used approach to quantify phase locking between neural signals. We systematically explored the validity of spectral coherence measures for quantifying synchronization among neural oscillators. To that aim, we simulated coupled oscillatory signals that exhibited synchronization dynamics using an abstract phase-oscillator model as well as interacting gamma-generating spiking neural networks. We found that, within a large parameter range, the spectral coherence measure deviated substantially from the expected phase-locking. Moreover, spectral coherence did not converge to the expected value with increasing signal-to-noise ratio. We found that spectral coherence particularly failed when oscillators were in the partially (intermittent) synchronized state, which we expect to be the most likely state for neural synchronization. The failure was due to the fast frequency and amplitude changes induced by synchronization forces. We then investigated whether spectral coherence reflected the information flow among networks measured by transfer entropy (TE) of spike trains. We found that spectral coherence failed to robustly reflect changes in synchrony-mediated information flow between neural networks in many instances. As an alternative approach we explored a phase-locking value (PLV) method based on the reconstruction of the instantaneous phase. As one approach for reconstructing instantaneous phase, we used the Hilbert Transform (HT) preceded by Singular Spectrum Decomposition (SSD) of the signal. PLV estimates have broad applicability as they do not rely on stationarity, and, unlike spectral coherence, they enable more accurate estimations of oscillatory synchronization across a wide range of different synchronization regimes, and better tracking of synchronization-mediated information flow among networks.

Implementing Wavelets in Continuous-Time Analog Circuits With Dynamic Range Optimization

Signal processing by means of analog circuits offers advantages from a power consumption viewpoint. A method is described to implement wavelets in analog circuits by fitting the impulse response of a linear system to the time-reversed wavelet function. The fitting is performed using local search involving an L2 criterion, starting from a deterministic starting point. This approach offers a large performance increase over previous Padé-based approaches and allows for the circuit implementation of a larger range of wavelet functions. Subsequently, using state-space optimization the dynamic range of the circuit is optimized. Finally, to illustrate the design procedure, a sixth-order L2-approximated orthonormal Gaussian wavelet filter using Gm-C integrators is presented.

Wavelet approximation for implementation in dynamic translinear circuits

Abstract For applications requiring low power consumption, signal processing in the analog domain is preferable. Approximate implementations of wavelet transforms in analog hardware can be achieved with dynamic translinear circuits. The quality of such implementations depends on the accuracy of the corresponding wavelet approximations. A design trade-off involves the approximation accuracy versus the complexity (model order) of the implemented filter. First we discuss the technique of Pade approximation for obtaining wavelet approximations. Then we present the technique of L 2 -approximation, which is conceptually more attractive but computationally more demanding. These techniques are compared by means of a worked example, involving Gaussian wavelet approximation and real measurements of an ECG signal. The L 2 -approximation approach is shown to exhibit superior performance.

Analog complex wavelet filters

This paper presents an analog implementation of the complex wavelet transform using both the complex first order system (CFOS) and the Pade approximation. The complex wavelet filter design is based on the combination of the real and the imaginary state-space descriptions that implement the respective transfer functions. In other words, a complex filter is implemented by an ordinary state-space structure for the real part and an extra C matrix for the imaginary part. Several complex wavelets, such as Gabor, Gaussian and Morlet complex wavelets, are obtained and simulations demonstrate excellent approximations to the ideal wavelets.

Systematic comparison of non-invasive measures for the assessment of atrial fibrillation complexity: a step forward towards standardization of atrial fibrillation electrogram analysis

AIMS To present a comparison of electrocardiogram-based non-invasive measures of atrial fibrillation (AF) substrate complexity computed on invasive animal recordings to discriminate between short-term and long-term AF. The final objective is the selection of an optimal sub-set of measures for AF complexity assessment. METHODS AND RESULTS High-density epicardial direct contact mapping recordings (234 leads) were acquired from the right and the left atria of 17 goats in which AF was induced for 3 weeks (short-term AF group, N = 10) and 6 months (long-term AF group, N = 7). Several non-invasive measures of AF organization proposed in the literature in the last decade were investigated to assess their power in discriminating between the short-term and long-term group. The best performing measures were identified, which when combined attained a correct classification rate of 100%. Their ability to predict standard invasive AF complexity measures was also tested, showing an average R(2) of 0.73 ± 0.04. CONCLUSION An optimal set of measures of the AF substrate complexity was identified out of the set of non-invasive measures analysed in this study. These measures may contribute to improve patient-tailored diagnosis and therapy of sustained AF.

SINGULAR SPECTRUM DECOMPOSITION: A NEW METHOD FOR TIME SERIES DECOMPOSITION

This study introduces singular spectrum decomposition (SSD), a new adaptive method for decomposing nonlinear and nonstationary time series in narrow-banded components. The method takes its origin from singular spectrum analysis (SSA), a nonparametric spectral estimation method used for analysis and prediction of time series. Unlike SSA, SSD is a decomposition method in which the choice of fundamental parameters has been completely automated. This is achieved by focusing on the frequency content of the signal. In particular, this holds for the choice of the window length used to generate the trajectory matrix of the data and for the selection of its principal components for the reconstruction of a specific component series. Moreover, a new definition of the trajectory matrix with respect to the standard SSA allows the oscillatory content in the data to be enhanced and guarantees decrease of energy of the residual. Through the numerical examples and simulations, the SSD method is shown to be able to accurately retrieve different components concealed in the data, minimizing at the same time the generation of spurious components. Applications on time series from both the biological and the physical domain are also presented highlighting the capability of SSD to yield physically meaningful components.

An L 2 -based approach for wavelet approximation

computation in the analog domain is very appealing from a power-consumption perspective. To implement a wavelet transform in an analog circuit, the wavelet function can be approximated by a linear system. An approach based on L2-approximation is presented, that enables largely automated approximation of wavelet functions by impulse responses of linear systems. Various continuous wavelet functions, such as the Gaussian wavelet and Daubechies wavelets of several orders, have been successfully approximated with this approach.

Multiwavelet Design for Cardiac Signal Processing

An approach for designing multiwavelets is introduced, for use in cardiac signal processing. The parameterization of the class of multiwavelets is in terms of associated FIR polyphase all-pass filters. Orthogonality and a balanced vanishing moment of order 1 are built into the parameterization. An optimization criterion is developed to associate the wavelets with different meaningful segments of a signal. This approach is demonstrated on the simultaneous detection of QRS-complexes and T-peaks in ECG signals

Singular spectrum analysis improves analysis of local field potentials from macaque V1 in active fixation task

Local field potentials (LFPs) represent the relatively slow varying components of the neural signal, and their analysis is instrumental in understanding normal brain function. To be properly analyzed, this signal needs to be separated in its fundamental frequency bands. Recent studies have shown that empirical mode decomposition (EMD) can be exploited to pre-process LFP recordings in order to achieve a proper separation. However, depending on the analyzed signal, EMD is known to generate components that may cover a too wide frequency range to be considered as narrow banded. As an alternative, we present here an improved version of the singular spectrum analysis (SSA) algorithm, validated by numerical simulations, and applied to LFP recordings in V1 of a macaque monkey exposed to simple visual stimuli. The components generated by the improved SSA algorithm are shown to be more meaningful than those generated by EMD, paving the way for its use in LFP analysis.

In-vivo evaluation of reduced-lead-systems in noninvasive reconstruction and localization of cardiac electrical activity

Noninvasive imaging of electrical activity of the heart has increasingly gained attention last decades. Heart-surface potentials are reconstructed from a torso-heart geometry and body-surface potentials recorded from tens to hundreds of body-surface electrodes. However, it remains an open question how many electrodes are needed to accurately reconstruct heart-surface potentials. In a canine model, we reconstructed epicardial electrograms and activation locations, investigating the use of a full-lead system, consisting of 169 well connected body-surface electrodes, and reduced-lead systems: using half or a third of the electrodes, or a minimalistic set of the default 12-lead ECG. Correlation coefficients indicate that the quality of the reconstructed electrograms remains stable to a third of the electrodes, and decreases with fewer electrodes. Similarly, the mismatch between the detected origin of a beat and known pacing location decreases when fewer body-surface electrodes are used. However, when only 9 or 10 electrodes are available for pacing localization, the median mismatch is 30mm, only marginally higher than when half of the electrodes are used, although with a significant error spread up to 65mm. These results indicate that for specific purposes (such as detecting the origin of an extrasystolic beat), a lower number of body-surface electrodes can provide noninvasive electrocardiographic imaging results that might still be useful for a clinical purpose.