Spontaneous fast-ultradian dynamics of polymorphic interictal events in drug-resistant focal epilepsy.

OBJECTIVE: We studied the rate dynamics of interictal events occurring over fast-ultradian time scales, as commonly examined in clinics to guide surgical planning in epilepsy. METHODS: Stereo-electroencephalography (SEEG) traces of 35 patients with good surgical outcome (Engel I) were analyzed. For this we developed a general data mining method aimed at clustering the plethora of transient waveform shapes including interictal epileptiform discharges (IEDs) and assessed the temporal fluctuations in the capability of mapping the epileptogenic zone (EZ) of each type of event. RESULTS: We found that the fast-ultradian dynamics of the IED rate may effectively impair the precision of EZ identification, and appear to occur spontaneously, that is, not triggered by or exclusively associated with a particular cognitive task, wakefulness, sleep, seizure occurrence, post-ictal state, or antiepileptic drug withdrawal. Propagation of IEDs from the EZ to the propagation zone (PZ) could explain the observed fast-ultradian fluctuations in a reduced fraction of the analyzed patients, suggesting that other factors like the excitability of the epileptogenic tissue could play a more relevant role. A novel link was found between the fast-ultradian dynamics of the overall rate of polymorphic events and the rate of specific IEDs subtypes. We exploited this feature to estimate in each patient the 5 min interictal epoch for near-optimal EZ and resected-zone (RZ) localization. This approach produces at the population level a better EZ/RZ classification when compared to both (1) the whole time series available in each patient (p = .084 for EZ, p < .001 for RZ, Wilcoxon signed-rank test) and (2) 5 min epochs sampled randomly from the interictal recordings of each patient (p < .05 for EZ, p < .001 for RZ, 105 random samplings). SIGNIFICANCE: Our results highlight the relevance of the fast-ultradian IED dynamics in mapping the EZ, and show how this dynamics can be estimated prospectively to inform surgical planning in epilepsy.

Bifurcation structure determines different phase-amplitude coupling patterns in the activity of biologically plausible neural networks.

Phase-amplitude cross frequency coupling (PAC) is a rather ubiquitous phenomenon that has been observed in a variety of physical domains; however, the mechanisms underlying the emergence of PAC and its functional significance in the context of neural processes are open issues under debate. In this work we analytically demonstrate that PAC phenomenon naturally emerges in mean-field models of biologically plausible networks, as a signature of specific bifurcation structures. The proposed analysis, based on bifurcation theory, allows the identification of the mechanisms underlying oscillatory dynamics that are essentially different in the context of PAC. Specifically, we found that two PAC classes can coexist in the complex dynamics of the analyzed networks: 1) harmonic PAC which is an epiphenomenon of the nonsinusoidal waveform shape characterized by the linear superposition of harmonically related spectral components, and 2) nonharmonic PAC associated with "true" coupled oscillatory dynamics with independent frequencies elicited by a secondary Hopf bifurcation and mechanisms involving periodic excitation/inhibition (PEI) of a network population. Importantly, these two PAC types have been experimentally observed in a variety of neural architectures confounding traditional parametric and nonparametric PAC metrics, like those based on linear filtering or the waveform shape analysis, due to the fact that these methods operate on a single one-dimensional projection of an intrinsically multidimensional system dynamics. We exploit the proposed tools to study the functional significance of the PAC phenomenon in the context of Parkinson's disease (PD). Our results show that pathological slow oscillations (e.g. ß band) and nonharmonic PAC patterns emerge from dissimilar underlying mechanisms (bifurcations) and are associated to the competition of different BG-thalamocortical loops. Thus, this study provides theoretical arguments that demonstrate that nonharmonic PAC is not an epiphenomenon related to the pathological ß band oscillations, thus supporting the experimental evidence about the relevance of PAC as a potential biomarker of PD.

Analytical study of the acoustic field in a spherical resonator for single bubble sonoluminescence.

The acoustic field in the liquid within a spherical solid shell is calculated. The proposed model takes into account Stoke's wave equation in the viscous fluid, the membrane theory to describe the solid shell motion and the energy loss through the external couplings of the system. A point source at the resonator center is included to reproduce the acoustic emission of a sonoluminescence bubble. Particular calculations of the resulting acoustic field are performed for viscous liquids of interest in single bubble sonoluminescence. The model reveals that in case of radially symmetric modes of low frequency, the quality factor is mainly determined by the acoustic energy flowing through the mechanical coupling of the resonator. Alternatively, for high frequency modes the quality factor is mainly determined by the viscous dissipation in the liquid. Furthermore, the interaction between the bubble acoustic emission and the resonator modes is analyzed. It was found that the bubble acoustic emission produces local maxima in the resonator response. The calculated amplitudes and relative phases of the harmonics constituting the bubble acoustic environment can be used to improve multi-frequency driving in sonoluminescence.

Complex interplay between spectral harmonicity and different types of cross-frequency couplings in nonlinear oscillators and biologically plausible neural network models.

Cross-frequency coupling (CFC) refers to the nonlinear interaction between oscillations in different frequency bands, and it is a rather ubiquitous phenomenon that has been observed in a variety of physical and biophysical systems. In particular, the coupling between the phase of slow oscillations and the amplitude of fast oscillations, referred as phase-amplitude coupling (PAC), has been intensively explored in the brain activity recorded from animals and humans. However, the interpretation of these CFC patterns remains challenging since harmonic spectral correlations characterizing nonsinusoidal oscillatory dynamics can act as a confounding factor. Specialized signal processing techniques are proposed to address the complex interplay between spectral harmonicity and different types of CFC, not restricted only to PAC. For this, we provide an in-depth characterization of the time locked index (TLI) as a tool aimed to efficiently quantify the harmonic content of noisy time series. It is shown that the proposed TLI measure is more robust and outperforms traditional phase coherence metrics (e.g., phase locking value, pairwise phase consistency) in several aspects. We found that a nonlinear oscillator under the effect of additive noise can produce spurious CFC with low spectral harmonic content. On the other hand, two coupled oscillatory dynamics with independent fundamental frequencies can produce true CFC with high spectral harmonic content via a rectification mechanism or other post-interaction nonlinear processing mechanisms. These results reveal a complex interplay between CFC and harmonicity emerging in the dynamics of biologically plausible neural network models and more generic nonlinear and parametric oscillators. We show that, contrary to what is usually assumed in the literature, the high harmonic content observed in nonsinusoidal oscillatory dynamics is neither a sufficient nor necessary condition to interpret the associated CFC patterns as epiphenomenal. There is mounting evidence suggesting that the combination of multimodal recordings, specialized signal processing techniques, and theoretical modeling is becoming a required step to completely understand CFC patterns observed in oscillatory rich dynamics of physical and biophysical systems.

Two types of ictal phase-amplitude couplings in epilepsy patients revealed by spectral harmonicity of intracerebral EEG recordings.

OBJECTIVE: Spectral harmonicity of the ictal activity was analyzed regarding two clinically relevant aspects, (1) as a confounding factor producing 'spurious' phase-amplitude couplings (PAC) which may lead to wrong conclusions about the underlying ictal mechanisms, and (2) its role in how good PAC is in correspondence to the seizure onset zone (SOZ) classification performed by the epileptologists. METHODS: PAC patterns observed in intracerebral electroencephalography (iEEG) recordings were retrospectively studied during seizures of seven patients with pharmacoresistant focal epilepsy. The time locked index (TLI) measure was introduced to quantify the degree of harmonicity between frequency bands associated to the emergence of PAC during epileptic seizures. RESULTS: (1) Harmonic and non harmonic PAC patterns coexist during the seizure dynamics in iEEG recordings with macroelectrodes. (2) Harmonic PAC patterns are an emergent property of the periodic non sinusoidal waveform constituting the epileptiform activity. (3) The TLI metric allows to distinguish the non harmonic PAC pattern, which has been previously associated with the ictal core through the paroxysmal depolarizing shifts mechanism of seizure propagation. CONCLUSIONS: Our results suggest that the spectral harmonicity of the ictal activity plays a relevant role in the visual analysis of the iEEG recordings performed by the epileptologists to define the SOZ, and that it should be considered for the proper interpretation of ictal mechanisms. SIGNIFICANCE: The proposed harmonicity analysis can be used to improve the delineation of the SOZ by reliably identifying non harmonic PAC patterns emerging from fully recruited cortical and subcortical areas.

Cross-frequency couplings in non-sinusoidal dynamics of interacting oscillators: Acoustic estimation of the radial position and spatial stability of nonlinear oscillating bubbles.

In this work, the analysis of cross-frequency couplings (CFC) is introduced in the context of nonlinear acoustics related to the dynamics of bubble(s)-resonator systems. The results obtained from experiments specifically designed to untangle the causal connection between the CFC patterns observed at the signal level and the underlying physical processes, are discussed. It was found that "causal" amplitude-to-amplitude (AAC) and amplitude-to-phase (APC) couplings emerge in the system dynamics as a consequence of the bubble(s)-resonator mechanistic interaction in the oscillatory steady-state. In these CFC patterns, the amplitude of the fundamental frequency component (f0) effectively modulates the amplitude and relative phase of the harmonic components (Nf0). Moreover, these AAC and APC couplings give rise to "epiphenomenal" phase-to-amplitude (PAC) and phase-to-phase (PPC) couplings, in which the link between modulating and modulated parameters represents a correlation rather than a causal connection. It is shown that these CFC patterns can be exploited to determine the presence, spatial stability and radial position of nonlinear oscillating bubble(s) trapped within the acoustic chamber. Potential applications of the proposed techniques are also discussed. Substantial evidence is presented showing that CFC patterns emerging from quasi-periodic non-sinusoidal waveforms are informative on the interaction between underlying oscillators.

Experimental study of transient paths to the extinction in sonoluminescence.

An experimental study of the extinction threshold of single bubble sonoluminescence in an air-water system is presented. Different runs from 5% to 100% of air concentrations were performed at room pressure and temperature. The intensity of sonoluminescence (SL) and time of collapse (t(c)) with respect to the driving were measured while the acoustic pressure was linearly increased from the onset of SL until the bubble extinction. The experimental data were compared with theoretical predictions for shape and position instability thresholds. It was found that the extinction of the bubble is determined by different mechanisms depending on the air concentration. For concentrations greater than approximately 30%-40% with respect to the saturation, the parametric instability limits the maximum value of R(0) that can be reached. On the other hand, for lower concentrations, the extinction appears as a limitation in the time of collapse. Two different mechanisms emerge in this range, i.e., the Bjerknes force and the Rayleigh-Taylor instability. The bubble acoustic emission produces backreaction on the bubble itself. This effect occurs in both mechanisms and is essential for the correct prediction of the extinction threshold in the case of low air dissolved concentration.

Positional stability as the light emission limit in sonoluminescence with sulfuric acid.

We studied a single bubble sonoluminescence system consisting of an argon bubble in a sulfuric acid aq. solution. We experimentally determined the relevant variables of the system. We also measured the bubble position, extent of the bubble orbits, and light intensity as a function of acoustic pressure for different argon concentrations. We find that the Bjerknes force is responsible for the bubble mean position and this imposes a limitation in the maximum acoustic pressure that can be applied to the bubble. The Rayleigh-Taylor instability does not play a role in this system and, at a given gas concentration, the SL intensity depends more on the bubble time of collapse than any other investigated parameter.

Mechanisms for pattern specificity of deep-brain stimulation in Parkinson's disease.

Deep brain stimulation (DBS) has become a widely used technique for treating advanced stages of neurological and psychiatric illness. In the case of motor disorders related to basal ganglia (BG) dysfunction, several mechanisms of action for the DBS therapy have been identified which might be involved simultaneously or in sequence. However, the identification of a common key mechanism underlying the clinical relevant DBS configurations has remained elusive due to the inherent complexity related to the interaction between the electrical stimulation and the neural tissue, and the intricate circuital structure of the BG-thalamocortical network. In this work, it is shown that the clinically relevant range for both, the frequency and intensity of the electrical stimulation pattern, is an emergent property of the BG anatomy at the system-level that can be addressed using mean-field descriptive models of the BG network. Moreover, it is shown that the activity resetting mechanism elicited by electrical stimulation provides a natural explanation to the ineffectiveness of irregular (i.e., aperiodic) stimulation patterns, which has been commonly observed in previously reported pathophysiology models of Parkinson's disease. Using analytical and numerical techniques, these results have been reproduced in both cases: 1) a reduced mean-field model that can be thought as an elementary building block capable to capture the underlying fundamentals of the relevant loops constituting the BG-thalamocortical network, and 2) a detailed model constituted by the direct and hyperdirect loops including one-dimensional spatial structure of the BG nuclei. We found that the optimal ranges for the essential parameters of the stimulation patterns can be understood without taking into account biophysical details of the relevant structures.

Path suppression of strongly collapsing bubbles at finite and low Reynolds numbers.

We study, numerically and experimentally, three different methods to suppress the trajectories of strongly collapsing and sonoluminescent bubbles in a highly viscous sulfuric acid solution. A new numerical scheme based on the window method is proposed to account for the history force acting on a spherical bubble with variable radius. We could quantify the history force, which is not negligible in comparison with the primary Bjerknes force in this type of problem, and results are in agreement with the classical primary Bjerknes force trapping threshold analysis. Moreover, the present numerical implementation reproduces the spatial behavior associated with the positional and path instability of sonoluminescent argon bubbles in strongly gassed and highly degassed sulfuric acid solutions. Finally, the model allows us to demonstrate that spatially stationary bubbles driven by biharmonic excitation could be obtained with a different mode from the one used in previous reported experiments.

Energy concentration and positional stability of sonoluminescent bubbles in sulfuric acid for different static pressures.

In this study we report several experimental and numerical results on the influence of static pressure (P_{0}) over the main parameters in single bubble sonoluminescence (SBSL), using a sulfuric acid aqueous solution (SA) with low concentrations of argon gas dissolved. Bifrequency driving was used in the experiments to enhance spatial stability of the bubbles. The experimental results were compared with simulations provided by a numerical code that models the radial dynamics of the bubbles. The results showed that an increase on the static pressure of the system shifts the Bjerknes instability threshold, allowing the bubble to access higher acoustic pressures (P_{Ac}^{}). Furthermore, a decrease in the measured ambient radius R_{0} and the calculated relative gas concentration c_{∞}/c_{0} were observed. A notorious increment in the bubble collapse violence and energy focusing for P_{0} above 1 bar was achieved. These were mainly indicated by the growth of the bubble expansion ratio (R_{max}/R_{0}), the bubble mechanical energy density, and the maximum bubble wall velocity dR/dt. In agreement with the previous statement, the maximum temperature during the bubble collapse predicted by the model is augmented as well. The use of different harmonics in the ultrasound pressure field regarding energy focusing is also discussed. Finally, we analyzed the stability regions of the R_{0}-P_{Ac}^{} parameter space via numerical predictions for P_{0} above the measured, identifying the shape instabilities as the main limiting agent to obtain further energy concentration in SA systems at high static pressures.

Upscaling energy concentration in multifrequency single-bubble sonoluminescence with strongly degassed sulfuric acid.

Single-bubble sonoluminescence (SBSL) was explored under a variety of multifrequency excitations. In particular, biharmonic excitation was used to produce SBSL for unprecedented low dissolved noble gas concentrations in a sulfuric acid solution. Reducing the amount of dissolved noble gas makes it possible to reach higher acoustic pressures on the SL bubble, which otherwise are not attainable because of the Bjerknes instability. By using biharmonic excitation, we were able to experimentally trap and to spatially stabilize SL bubbles for xenon pressure overhead as low as 1 mbar. As a result, we have access to regions in phase space where the plasma temperatures are higher than the ones reached before for bubbles driven at ≈30 kHz.