Spatiotemporal Wave Research Articles

Physiology in Phylogeny: Modeling of Mechanical Driving Forces in Cardiac Development

This article explores the heart phylogeny, the development of the heart from embryonic to adult shape. For the shape change from tubular to four-chamber to be initiated, a mechanical twist needs to be present in the embryonic heart tube. The helical shape of the muscle fibers in the embryonic heart is a necessary but not a sufficient condition for the transformation to occur. It is also necessary for the excitation pattern to be in the form of a spatiotemporal wave. Such a combination, while producing twist, does not negatively impact the heart's ability to work as a pump.

Numerical investigation of the properties of nonlinear acoustical vortices through weakly heterogeneous media

Acoustical vortices (AV) are the acoustical equivalent of optical vortices (OV) that are a key feature in the discipline of singular optics. For linear waves, OV and AV possess the same properties. But as nonlinearities are different in optics and acoustics, the nonlinear behavior of these structures has to be different. In this paper, a numerical investigation of the three-dimensional (3D) nonlinear propagation of acoustical vortices through homogeneous or heterogeneous media is reported. First, an original numerical method is described and compared to existing ones. Then, it is used to study the dynamics of AV in a nonlinear regime. The nonlinear properties of acoustical vortices in a homogeneous medium are investigated. It is shown that shock waves can be produced during propagation, leading to an interesting spatiotemporal wave field with an azimuthal shock. The dynamics of the topological charge, intrinsic property of AV or OV, is studied in the nonlinear regime through different focusing lenses. Inversion of the topological charge is observed if the AV propagates through a 1D focusing medium (cylindrical lens), while the charge remains constant if the medium is 2D (spherical lens). These last results already observed in linear optics are generalized here to the nonlinear behavior through the investigation of harmonics which show the same behavior as the fundamental with respect to inversion.

Event-related wave activity in the EEG provides new marker of ADHD

Objective This study examines the utility of new measures of event-related spatio-temporal waves in the EEG as a marker of ADHD, previously shown to be closely related to the P3 ERP in an adult sample. Methods Wave activity in the EEG was assessed during both an auditory Oddball and a visual continuous performance task (CPT) for an ADHD group ranging in age from 6 to 18 years and comprising mostly Combined and Inattentive subtypes, and for an age and gender matched control group. Results The ADHD subjects had less wave activity at low frequencies (∼1 Hz) during both tasks. For auditory Oddball targets, this effect was shown to be related to smaller P3 ERP amplitudes. During CPT, the ∼1 Hz wave activity in the ADHD subjects was inversely related to clinical and behavioral measures of hyperactivity and impulsivity. CPT wave activity at ∼1 Hz was seen to “normalise” following treatment with stimulant medication. Conclusions The results identify a deficit in low frequency wave activity as a new marker for ADHD associated with levels of hyperactivity and impulsivity. Significance The marker is evident across a range of tasks and may be specific to ADHD. While lower ∼1 Hz activity partly accounts for reduced P3 ERPs in ADHD, the effect also arises for tasks that do not elicit a P3. Deficits in behavioral inhibition are hypothesized to arise from underlying dysregulation of cortical inhibition.

Spatial and spatiotemporal solitary waves and their stabilization in nonlinear negative index materials

Starting from a simple dispersion relation for negative index materials and a heuristic nonlinear Klein-Gordon-type extension, we derive the evolution equations for the envelopes of beams and spatiotemporal pulses in nonlinear dispersive negative index media. Using existing numerical methods, based on fast Fourier-Bessel transforms, we study the stability of the solitary wave solutions. Nonlinearity and dispersion management are then incorporated to find stable solutions of the underlying partial differential equations.

Dynamical evolution of spatiotemporal patterns in mammalian middle cortex

The spatiotemporal structure of brain oscillations are important in understanding neural function. We analyze oscillatory episodes from isotropic preparations from the middle layers of a mammalian cortex which display irregular and chaotic spatiotemporal wave activity, within which spontaneously emerge spiral and plane waves. The dimensionality of these dynamics shows a consistent decrease during the middle of these episodes, regardless of the presence of simple spiral or plane waves. It is important to define the relevant biological order parameters which govern these dynamical bifurcations.

Dynamical Evolution of Spatiotemporal Patterns in Mammalian Middle Cortex

The spatiotemporal structure of brain oscillations are important in understanding neural function. We analyze oscillatory episodes from isotropic preparations from the middle layers of a mammalian cortex which display irregular and chaotic spatiotemporal wave activity, within which spontaneously emerge spiral and plane waves. The dimensionality of these dynamics shows a consistent decrease during the middle of these episodes, regardless of the presence of simple spiral or plane waves. It is important to define the relevant biological order parameters which govern these dynamical bifurcations.

Accelerating finite energy Airy beams

We investigate the acceleration dynamics of quasi-diffraction-free Airy beams in both one- and two-dimensional configurations. We show that this class of finite energy waves can retain their intensity features over several diffraction lengths. The possibility of other physical realizations involving spatiotemporal Airy wave packets is also considered.

The contribution of apolipoprotein E alleles on cognitive performance and dynamic neural activity over six decades

Neuroimaging shows brain-functional differences due to apolipoprotein E ( APOE) polymorphisms may exist decades before the increased risk period for Alzheimer's disease, but little is known about their effect on cognition and brain function in children and young adults. This study assessed 415 healthy ɛ2 and ɛ4 carriers and matched ɛ3/ɛ3 controls, spanning ages 6–65, on a range of cognitive tests. Subjects were also compared on a new dynamical measure of EEG activity during a visual working memory task using alphabetical stimuli. ɛ4 subjects had better verbal fluency compared to ɛ3, an effect that was strongest in 51–65 year-olds. No ɛ4 deficits in cognition were found. In 6–15 year-olds, there were differences in total spatio-temporal wave activity between ɛ3 and ɛ4 subjects in the theta band, approximately 200 ms post-stimulus. Differences in brain function in younger ɛ4 subjects and superior verbal fluency across the entire age range suggest that the APOE ɛ4 allele is an example of antagonistic pleiotropy.

Arrhythmogenesis in the heart: Multiscale modeling of the effects of defibrillation shocks and the role of electrophysiological heterogeneity.

The mechanisms of initiation of ventricular arrhythmias as well as those behind the complex spatiotemporal wave dynamics and its filament organization during ventricular fibrillation (VF) are the topic of intense research and debate. Mechanistic inquiry into the various mechanisms that lead to arrhythmia initiation and VF maintenance is hampered by the inability of current experimental techniques to resolve, with sufficient accuracy, electrical behavior confined to the depth of the ventricles. The objective of this article is to demonstrate that realistic 3D simulations of electrical activity in the heart are capable of bringing a new level of understanding of the mechanisms that underlie arrhythmia initiation and subsequent organization. The article does this by presenting the results of two multiscale simulation studies of ventricular electrical behavior. The first study aims to uncover the mechanisms responsible for rendering the ventricles vulnerable to electric shocks during a specific interval of time, the vulnerable window. The second study focuses on elucidating the role of electrophysiological heterogeneity, and specifically, differences in action potential duration in various ventricular structures, in VF organization. Both studies share common multiscale modeling approaches and analysis, including characterization of scroll-wave filament dynamics.

Dispersion-compensated beam-splitting of femtosecond light pulses: Wave optics analysis

Recently, using parageometrical optics concepts, a hybrid, diffractive-refractive, lens triplet has been suggested to significantly improve the spatiotemporal resolution of light spots in multifocal processing with femtosecond laser pulses. Here, we carry out a rigorous wave-optics analysis, including the spatiotemporal nature of the wave equation, to elucidate both the spatial extent of the diffractive spots and the temporal duration of the pulse at the output plane. Specifically, we show nearly transform-limited behavior of diffraction maxima. Moreover, the temporal broadening of the pulse is related to the group velocity dispersion, which can be pre-compensated for in practical applications. Finally, some numerical simulations of the spatiotemporal wave field at the output plane in a realistic case are provided.

Low-complexity distributed parallel processor for 2D IIR broadband beam plane-wave filters

Real-time systolic-array-based implementations of VLSI two-dimensional (2D) infinite-impulse-response (IIR) frequency-planar beam plane-wave filters have potentially wide applications in the filtering of spatio-temporal RF broadband plane waves based on their directions of arrival (DOAs). Distributed-parallel-processor (DPP) implementations of the systolic arrays allow synchronous sampling of the 2D input signal array, but because of the direct-form structure they have high circuit complexity. To address the high-complexity problem, the differential-form 2D z-domain transfer function is employed here to obtain a novel DPP systolic-array-based filter architecture. Differential operators are obtained by applying elemental predistortion to the passive LR prototype filter network using series-connected negative-resistance elements. The proposed systolic 2D IIR architecture is implemented on a single Xilinx Virtex-4 Xc4v Sx35-10ff668 FPGA chip. Two examples of broadband plane-wave filtering supporting N = 32 and N = 64 sensors are reported. On-chip test results are achieved using stable real-time tests at frame sample frequencies of up to 90MHz as well as stepped hardware cosimulation in conjunction with a parallel-operating MATLAB/Simulink simulation.

Optical nonlinearity and existence conditions for quasi-steady-state photorefractive solitons

Generalizing soliton description using spatiotemporal wave variables, we identify and experimentally validate the nonlinearity supporting quasi-steady-state solitons in biased photorefractive crystals for the one-dimensional case, the transient counterpart of the explicit one-dimensional screening soliton theory. The approach leads to a non-Kerr-like spatially local exponential nonlinearity and explicitly provides soliton existence conditions. These find quantitative agreement with a series of experiments in potassium lithium tantalate niobate and reproduce previously described transient behavior.

Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion

The nonlinear dynamics of $1.6\text{\ensuremath{-}}\mathrm{\ensuremath{\mu}}\mathrm{m}\phantom{\rule{0.2em}{0ex}}\mathrm{fs}$ laser pulses propagating in fused silica is investigated by employing a full-order dispersion model. Different from the x-wave generation in normally dispersive media, a few-cycle spatiotemporally compressed soliton wave is generated with the contrary contributions of anomalous group velocity dispersion (GVD) and self-phase-modulation. However, at the tailing edge of the pulse forms a shock wave which generates separate and strong supercontinuum peaked at $670\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. It is also the origin of conical emission formed both in time and frequency domain with the contribution of normal GVD at visible light.

Spacetime Causality in the Study of the Hankel Transform

We study Hilbert space aspects of the Klein-Gordon equation in two-dimensional spacetime. We associate to its restriction to a spacelike wedge a scattering from the past light cone to the future light cone, which is then shown to be (essentially) the Hankel transform of order zero. We apply this to give a novel proof, solely based on the causality of this spatio-temporal wave propagation, of the theorem of de Branges and V. Rovnyak concerning Hankel pairs with a support property. We recover their isometric expansion as an application of Riemann’s general method for solving Cauchy-Goursat problems of hyperbolic type.

Measurement of phase gradients in the EEG

Previous research has shown that spatio-temporal waves in the EEG are generally of long spatial wavelength and form smooth patterns of phase gradients at particular time-samples. This paper describes a method to measure smooth phase gradients of long spatial wavelength in the EEG. The method depends on the global pattern of phase at a given frequency and time and is therefore robust to variations, over time, in phase-lag between particular sites. Phases were estimated in the EEG signal using wavelet or short time-series Fourier methods. During an auditory oddball task, phases across the scalp tend to fall within a limited circular range, a range that is not indicative of phase-synchrony nor waves with multiple periods. At times the phases tended to maintain a spatially and temporally ordered relationship. The relative phases were analysed using three phase gradient basis functions, providing a measure of the amount of variance explained, across the electrodes, by smooth changes in relative phase from a single minimum or single maximum. The data from 586 adult subjects were analysed and it was found that the probability of phase gradient events varies with time and frequency in the stimulus-locked average, and with task demands. The temporal extent of spatio-temporal waves was measured by detecting smoothly changing patterns of phase latencies across the scalp. The specific spatial pattern and timing of phase gradients correspond closely to the latency distributions of certain ERPs.

EEG MARKERS FOR COGNITIVE DECLINE IN ELDERLY SUBJECTS WITH SUBJECTIVE MEMORY COMPLAINTS

New treatments for Alzheimer's disease require early detection of cognitive decline. Most studies seeking to identify markers of early cognitive decline have focused on a limited number of measures. We sought to establish the profile of brain function measures which best define early neuropsychological decline. We compared subjects with subjective memory complaints to normative controls on a wide range of EEG derived measures, including a new measure of event-related spatio-temporal waves and biophysical modeling, which derives anatomical and physiological parameters based on subject's EEG measurements. Measures that distinguished the groups were then related to cognitive performance on a variety of learning and executive function tasks. The EEG measures include standard power measures, peak alpha frequency, EEG desynchronization to eyes-opening, and global phase synchrony. The most prominent differences in subjective memory complaint subjects were elevated alpha power and an increased number of spatio-temporal wave events. Higher alpha power and changes in wave activity related most strongly to a decline in verbal memory performance in subjects with subjective memory complaints, and also declines in maze performance and working memory reaction time. Interestingly, higher alpha power and wave activity were correlated with improved performance in reverse digit span in the subjective memory complaint group. The modeling results suggest that differences in the subjective memory complaint subjects were due to a decrease in cortical and thalamic inhibitory gains and slowed dendritic time-constants. The complementary profile that emerges from the variety of measures and analyses points to a nonlinear progression in electrophysiological changes from early neuropsychological decline to late-stage dementia, and electrophysiological changes in subjective memory complaint that vary in their relationships to a range of memory-related tasks.

3-D IIR filtering using decimated DFT-polyphase filter bank structures

Two three-dimensional (3-D) under-decimated uniform discrete Fourier transform polyphase filter bank structures are proposed along with two applications: first, the sub-pixel motion discrimination of two-dimensional spatial objects moving with approximately constant local velocity in a noisy 3-D spatio-temporal image sequence and, second, the selective filtering of 3-D spatio-temporal broad-band plane waves based on their directions of arrival. The desired 3-D filter passband shapes are realized utilizing combinations of highly selective first-order 3-D infinite-impulse response frequency-planar filters in each band between the analysis and synthesis sections. Measured spatio-temporal performance confirms the high-quality broad-band transmission of passband signals, high directional selectivity and low computational complexity.

Stabilization of inhomogeneous patterns in a diffusion–reaction system under structural and parametric uncertainties

Many phenomena such as neuron firing in the brain, the travelling waves which produce the heartbeat, arrythmia and fibrillation in the heart, catalytic reactions or cellular organization activities, among others, can be described by a unifying paradigm based on a class of nonlinear reaction–diffusion mechanisms. The FitzHugh–Nagumo (FHN) model is a simplified version of such class which is known to capture most of the qualitative dynamic features found in the spatiotemporal signals. In this paper, we take advantage of the dissipative nature of diffusion–reaction systems and results in finite dimensional nonlinear control theory to develop a class of nonlinear feedback controllers which is able to ensure stabilization of moving fronts for the FHN system, despite structural or parametric uncertainty. In the context of heart or neuron activity, this class of control laws is expected to prevent cardiac or neurological disorders connected with spatiotemporal wave disruptions. In the same way, biochemical or cellular organization related with certain functional aspects of life could also be influenced or controlled by the same feedback logic. The stability and robustness properties of the controller will be proved theoretically and illustrated on simulation experiments.

Complex-periodic spiral waves in confluent cardiac cell cultures induced by localized inhomogeneities

Spatiotemporal wave activities in excitable heart tissues have long been the subject of numerous studies because they underlie different forms of cardiac arrhythmias. In particular, understanding the dynamics and the instabilities of spiral waves have become very important because they can cause reentrant tachycardia and their subsequent transitions to fibrillation. Although many aspects of cardiac spiral waves have been investigated through experiments and model simulations, their complex properties are far from well understood. Here, we show that intriguing complex-periodic (such as period-2, period-3, period-4, or aperiodic) spiral wave states can arise in monolayer tissues of cardiac cell culture in vitro, and demonstrate that these different dynamic states can coexist with abrupt and spontaneous transitions among them without any change in system parameters; in other words, the medium supports multistability. Based on extensive image data analysis, we have confirmed that these spiral waves are driven by their tips tracing complex orbits whose unusual, meandering shapes are formed by delicate interplay between localized conduction blocks and nonlinear properties of the culture medium.

Observation of synchronized spatiotemporal reaction waves in coupled electrochemical oscillations of an NDR type

The coupling of spatiotemporal reaction waves was investigated by the use of current oscillations of an NDR type, appearing in H 2O 2 reduction on platinum (Pt) electrodes. For two Pt-ring working electrodes located side by side, the oscillatory coupling gave rise to various synchronized waves, such as spatially homogeneous waves (HW’s) in an in-phase mode, HW’s in an anti-phase mode, and a standing wave or a traveling wave synchronized with a HW, depending on the applied potential and the relative position of the reference electrode. The results are explained in terms of a combination of positive local coupling and negative global coupling effects.