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Collective topological dynamics in the frenkel-kontorova chains

Topological dynamics of an array of harmonically coupled damped dc-driven nonlinear oscillators are studied by introducing a dynamical contraction factor and a deviation factor. Different dynamical transitions are identified, and topological changes for these transitions are studied. A bifurcation from the kink state to the kink-antikink-pair state is found, which relates the topological change to the spatiotemporal dynamics of the system. The presence of antikinks leads to the extension of the localized kink, and collisions of kinks and antikinks induce strong oscillations of the topology of the array.

Journal Article↗

Slow Ca2+ dynamics in pharyngeal muscles in Caenorhabditis elegans during fast pumping.

The pharyngeal muscles of Caenorhabditis elegans are composed of the corpus, isthmus and terminal bulb from anterior to posterior. These components are excited in a coordinated fashion to facilitate proper feeding through pumping and peristalsis. We analysed the spatiotemporal pattern of intracellular calcium dynamics in the pharyngeal muscles during feeding. We used a new ratiometric fluorescent calcium indicator and a new optical system that allows simultaneous illumination and detection at any two wavelengths. Pumping was observed with fast, repetitive and synchronous spikes in calcium concentrations in the corpus and terminal bulb, indicative of electrical coupling throughout the muscles. The posterior isthmus, however, responded to only one out of several pumping spikes to produce broad calcium transients, leading to peristalsis, the slow and gradual motion needed for efficient swallows. The excitation-calcium coupling may be uniquely modulated in this region at the level of calcium channels on the plasma membrane.

Animals↗

Coupled maps with local and global interactions.

A coupled map lattice model with both local and global couplings is studied as a simple example of hierarchical pattern dynamics with different length scales of interactions. Several phases are classified according to domain structures, degree of chaotic dynamics, distribution function, and power spectra. In particular, a cascade process of formation and collapse of bubbles is found in some parameter regime. The state is characterized by spatiotemporal power-law correlation and few positive Lyapunov exponents. In a two-dimensional case, the state leads to a characteristic spatiotemporal pattern that may be regarded as a dynamic extension of a Turing pattern. The possible relevance to natural patterns is also discussed. (c) 2000 American Institute of Physics.

Journal Article↗

Spatiotemporal visualization of neuromagnetic data.

We describe the development of a computer visualization tool that displays topographic maps of neuromagnetic data on realistic head shapes. Two topographic display modes are implemented--a raw mode that depicts the actual position, orientation, and corresponding magnetic field data of each detection coil with respect to the head shape, and an interpolated mode, where the magnetic data are smoothly interpolated over the scalp. False coloration is used to represent magnetic field strength. The topographic displays are coupled with wave form displays in order to integrate spatial and temporal visualization of the data. The X Window system is used to write device independent, network-transparent computer code.

Brain Mapping↗

Performance of locomotion and foot grasping following a unilateral thoracic corticospinal tract lesion in monkeys (Macaca mulatta).

Six adult monkeys (Macaca mulatta) received a unilateral lesion of the lateral corticospinal tract (CST) in the thoracic spinal cord. Prior to surgery, the animals were trained to perform quadrupedal stepping on a treadmill, and item retrieval with the foot. Whole body kinematics and electromyogram (EMG) recordings were made prior to, and at regular intervals over a period of 12 weeks after the CST lesion. After 1 week of recovery, all monkeys were able to walk unaided quadrupedally on the treadmill. The animals, however, dragged the hindpaw ipsilateral to the lesion along the treadmill belt during the swing phase and showed a significant reorganization of the spatiotemporal pattern of hindlimb (HL) and forelimb (FL) displacements. The inability to appropriately trigger the swing phase resulted in an increase in the cycle duration and stride length of both HLs. The stance duration decreased in the ipsilateral HL, and increased in the contralateral HL and both FLs. Consequently, there was a dramatic disruption of interlimb and intralimb coupling that was reflected in the limb kinematic and EMG patterns. The CST lesion completely abolished the ability of the monkeys to retrieve items with the foot ipsilateral to the lesion and significantly disrupted the level of performance of the contralateral HL during the first 2 weeks post-lesion. Interestingly, selected HL muscles remained almost quiescent when the monkeys attempted to retrieve items, but were unsuccessful with the affected foot at 1 week post-lesion, whereas the capacity to activate the same muscles was preserved, although reduced, during stepping. Spatial and temporal parameters of gait, kinematics, and EMG patterns recorded during locomotion generally converged toward control values over time, but significant differences persisted up to 12 weeks post-lesion. Although some control was recovered over the distal foot musculature, fine foot grasping remained significantly impaired at the end of the testing period. These findings demonstrate that the CST pathway from the brain normally makes an important contribution to interlimb and intralimb coordination during basic locomotion, and to muscle activation to produce dexterous foot digit movements in the monkey. Furthermore, the present study indicates that the primate has the ability to rapidly accommodate locomotor performance, and to a lesser degree fine foot motor skills, to a reduction in supraspinal control. Identification of the neural substrates mediating the rapid recovery of motor function following injury to the primate spinal cord could provide insight into developing repair strategies to augment functional recovery from neuromotor impairments.

Animals↗

Imaging optical reflectance in rodent barrel and forelimb sensory cortex.

Novel neuroimaging techniques are extending the scope for studying dynamic brain function. We have developed a system which enables the repeatable imaging of rapid function in rodent primary somatosensory cortex (S-I), based on activity-related changes in its optical reflectance (intrinsic signals). The S-I cortices of anesthetized male Sprague-Dawley rats were exposed. Images were acquired with a slow-scan, cooled, charge-coupled device camera (CCD) through filters at 550, 610, and 850 nm before, during, and after contralateral stimulation (vibrissal deflection or forepaw stimulation). Images were divided by prestimulus controls and then averaged across 9-27 trials to produce maps of stimulus-related reflectance change. Optical activity had magnitude 10(-3) of baseline reflectance and consistently comprised two distinct spatiotemporal components over cortex, depending on paradigm. The diffuse signal at 610 nm begins 0.5-1 s after stimulus onset and has a duration of 4-5 s. The second signal is macrovenous and is delayed by 1 s. Similar response patterns were observed at 550 and 850 nm. Evoked potentials, recorded at sites inside and outside the zone of optical activity, confirmed the functional nature of these signals. Using a CCD we have imaged functional reflectance changes over rodent S-I which commence, peak, and extinguish over a time scale of seconds. This optical activity is consistent with the etiologies of microvascular recruitment and chromophore redox change.

Afferent Pathways↗

Manipulation of surface reaction dynamics by global pressure and local temperature control: a model study.

Specific catalyst design and external manipulation of surface reactions by controlling accessible physical or chemical parameters may be of great benefit for improving catalytic efficiencies and energetics, product yield, and selectivities in the field of heterogeneous catalysis. Studying a realistic spatiotemporal one-dimensional model for CO oxidation on Pt(110) we demonstrate the value and necessity of mathematical modeling and advanced numerical methods for directed external multiparameter control of surface reaction dynamics. At the model stage we show by means of optimal control techniques that species coverages can be adjusted to desired values, aperiodic oscillatory behavior for distinct coupled reaction sites can be synchronized, and overall reaction rates can be optimized by varying the surface temperature in space and time and the CO and O2 gas phase partial pressure with time. The control aims are formulated as objective functionals to be minimized which contain a suitable mathematical formulation for the deviation from the desired system behavior. The control functions pCO(t) (CO partial pressure), pO2(t) (O2 partial pressure), and T(x,t) (surface temperature distribution) are numerically computed by a specially tailored optimal control method based on a direct multiple shooting approach which is suitable to cope with the highly nonlinear unstable mode character of the CO oxidation model.

Journal Article↗

Texture formation under phase ordering and phase separation in polymer-liquid crystal mixtures.

Computational modeling of texture formation in coupled phase separation-phase ordering processes in polymer/liquid crystal mixtures is performed using a unified model based on the nematic tensor order parameter and gradient orientation elasticity. The computational methods are able to resolve defect nucleation, defect-defect interactions, and defect-particle interactions, as well as global and local morphological features in the concentration and order parameter spatiotemporal behavior. Biphasic structures corresponding to polymer dispersed liquid crystals (PDLCs), crystalline filled nematic (CFNs), and random filled nematics (RFNs) are captured and analyzed using liquid crystal defect physics and structure factors. Under spinodal decomposition due to concentration fluctuations, the PDLC structure emerges, and the nucleation and repulsive interaction of defects within nematic droplets leads to bipolar nematic droplets. Under spinodal decomposition due to ordering fluctuations, the CFNs structure emerges, and the stable polymer droplet crystal is pinned by a lattice of topological defects. For intermediate cases, where the mixture is unstable to both concentration and nematic order fluctuations, the RFN structure emerges, and polymer droplets and fibrils are pinned by a defect network, whose density increases with the curvature of the polymer-liquid crystal interface. The simulations provide an information of the role of topological defects on phase separation-phase ordering processes in polymer-liquid crystal mixtures.

Journal Article↗

ICA-based spatiotemporal approach for single-trial analysis of postmovement MEG beta synchronization.

The extraction of event-related oscillatory neuromagnetic activities from single-trial measurement is challenging due to the non-phase-locked nature and variability from trial to trial. The present study presents a method based on independent component analysis (ICA) and the use of a template-based correlation approach to extract Rolandic beta rhythm from magnetoencephalographic (MEG) measurements of right finger lifting. A single trial recording was decomposed into a set of coupled temporal independent components and corresponding spatial maps using ICA and the reactive beta frequency band for each trial identified using a two-spectrum comparison between the postmovement interval and a reference period. Task-related components survived dual criteria of high correlation with both the temporal and the spatial templates with an acceptance rate of about 80%. Phase and amplitude information for noise-free MEG beta activities were preserved not only for optimal calculation of beta rebound (event-related synchronization) but also for profound penetration into subtle dynamics across trials. Given the high signal-to-noise ratio (SNR) of this method, various methods of source estimation were used on reconstructed single-trial data and the source loci coherently anchored in the vicinity of the primary motor area. This method promises the possibility of a window into the intricate brain dynamics of motor control mechanisms and the cortical pathophysiology of movement disorder on a trial-by-trial basis.

Adult↗

Kinematic optimization of spatiotemporal patterns in paretic arm training with stroke patients.

The effect of rhythmic cueing on spatiotemporal control of sequential reaching movements of the paretic arm was studied in 21 hemispheric stroke patients. Reaching movements were studied with and without rhythmic metronome cuing in a counterbalanced design. Metronome frequencies were entrained to the naturally selected frequency of the patient. Results indicate statistically significant (P<0.05) improvements of spatiotemporal arm control during rhythmic entrainment. Variability of timing and reaching trajectories were reduced significantly. Time series analysis of sequential movement repetitions showed an immediate reduction in variability of arm kinematics during rhythmic entrainment within the first two to three repetitions of each trial. Rhythm also produced significant increases in angle ranges of elbow motion (P<0.05). Analysis of acceleration and velocity profiles of the wrist joint showed significant kinematic smoothing during rhythmic cuing. The link between rhythmic sensory timing and spatiotemporal motor control was investigated using a mathematical optimization model with minimization of peak acceleration as criterion. Rhythmically cued acceleration profiles fit the predicted model data significantly closer (P<0.01) than the self-paced profiles. Since velocity and acceleration are mathematical derivatives of position-time trajectories, the model data suggest that enhanced timing precision via temporal phase and period coupling of the motor pattern to the rhythmic time timekeeper enhances the brain's computational ability to optimally scale movement parameters across time.

Aged↗

Growing correlation length on cooling below the onset of caging in a simulated glass-forming liquid.

We present a calculation of a fourth-order, time-dependent density correlation function that measures higher-order spatiotemporal correlations of the density of a liquid. From molecular dynamics simulations of a glass-forming Lennard-Jones liquid, we find that the characteristic length scale of this function has a maximum as a function of time which increases steadily beyond the characteristic length of the static pair correlation function g(r) in the temperature range approaching the mode coupling temperature from above. This length scale provides a measure of the spatially heterogeneous nature of the dynamics of the liquid in the alpha-relaxation regime.

Journal Article↗

Recent developments in oximetry and perfusion-based mapping techniques and their role in the surgical treatment of neocortical epilepsy.

Detailed understanding of neurovascular coupling during epilepsy is critical for the interpretation of various perfusion-based imaging techniques, such as positron emission tomography, single-photon-emission computed tomography, and functional magnetic resonance imaging, which are used to guide surgical therapy. We used high-resolution intrinsic signal- and voltage-sensitive dye imaging, as well as oxygen-sensitive electrodes, to map the precise spatiotemporal relationship between excitatory and inhibitory neuronal activity, cerebral blood volume, and oximetry during epilepsy. We observed a rapid focal decrease in tissue oxygenation and an increase in deoxygenated hemoglobin in association with both interictal and ictal events. This "epileptic dip" in oxygenation lasts several seconds following both interictal and ictal events, implying that for a period, cerebral blood flow is inadequate to meet metabolic demand. We also observed a rapid focal increase in cerebral blood volume that soon spread to adjacent nonepileptic gyri. Likewise, a diffuse decrease in deoxygenated hemoglobin, related to the blood oxygen level-dependent signal recorded with functional magnetic resonance imaging, spread to adjacent gyri and was poorly localized.

Animals↗

Cellular calcium imaging: so, what's new?

The ability to uncover the fine details of intracellular Ca(2+) signals has improved remarkably in recent years, largely as a result of developments in methods for reporting Ca(2+), coupled with great improvements in measurement instrumentation. The cell biologist wishing to image intracellular Ca(2+) has a range of options to consider. These include the use of photoproteins, commercially available fluorescent indicators or the new generation of fluorescent protein Ca(2+) probes. Molecular biology and biophysics are now joining forces to bring major advances in the art of deciphering the complexity of spatiotemporal Ca(2+) signals.

Animals↗

Effects of time-delayed interactions on dynamic patterns in a coupled phase oscillator system.

We investigate the effects of time delayed interactions in the network of neural oscillators. We perform the stability analysis in the vicinity of a synchronized state at vanishing time delay and present a related phase diagram. In the simulations it is shown that time delay induces various phenomena such as clustering where the system is spontaneously split into two phase locked groups, synchronization, and multistability. Time delay effects should be considered both in the natural and artificial neural systems whose information processing is based on the spatiotemporal dynamic patterns.

Journal Article↗

Scattering coherent and partially coherent space-time pulses through few-mode optical systems.

We consider the spatiotemporal behavior of coherent and partially coherent, pulsed, few-mode optical systems. It is shown that there is some set of orthogonal space-time pulses at the input reference surface that maps in one-to-one correspondence with some set of orthogonal space-time pulses at the output reference surface; we call these pulses eigenfields. The spectrum of the coupling coefficients determines the amount of information that can be transmitted within a given period of time. The eigenfields are unique for a given system and can be used to propagate a field that is in any state of spatial and temporal coherence. They can also be used to account for the spatial and temporal coherence of internally generated noise and to calculate the powers, fluctuations, and correlations that would be recorded by multimode detectors. Our technique is ideal for modeling the behavior of pulsed imaging arrays and interferometers.

Journal Article↗

Trapped to free: a mechanism to spatiotemporal chaos.

We further investigate the crisis-induced transition from temporal chaos (TC) to spatiotemporal chaos (STC) due to collision between the unstable orbit of a carrier saddle steady wave (SSW) and the attractor of its perturbation wave (PW) [Kaifen He, Phys. Rev. Lett. 80, 696 (1998)]. In the present work, the influence of the SSW on its PW is studied in different dimensions. It is found that in our case, as a result of mode-mode couplings only one dimension becomes crucial in the onset of crisis. The state transition of the PW mode phase in this dimension at the crisis is emphasized. Before the crisis, all the PW partial waves are trapped in the SSW state. After the crisis, the PW partial wave in this dimension is free from the trapping of the SSW partial wave; it experiences on-off resonance with the latter, which is responsible for the transition to STC.

Journal Article↗

Dynamic inositol trisphosphate-mediated calcium signals within astrocytic endfeet underlie vasodilation of cerebral arterioles.

Active neurons communicate to intracerebral arterioles in part through an elevation of cytosolic Ca(2+) concentration ([Ca(2+)](i)) in astrocytes, leading to the generation of vasoactive signals involved in neurovascular coupling. In particular, [Ca(2+)](i) increases in astrocytic processes ("endfeet"), which encase cerebral arterioles, have been shown to result in vasodilation of arterioles in vivo. However, the spatial and temporal properties of endfoot [Ca(2+)](i) signals have not been characterized, and information regarding the mechanism by which these signals arise is lacking. [Ca(2+)](i) signaling in astrocytic endfeet was measured with high spatiotemporal resolution in cortical brain slices, using a fluorescent Ca(2+) indicator and confocal microscopy. Increases in endfoot [Ca(2+)](i) preceded vasodilation of arterioles within cortical slices, as detected by simultaneous measurement of endfoot [Ca(2+)](i) and vascular diameter. Neuronal activity-evoked elevation of endfoot [Ca(2+)](i) was reduced by inhibition of inositol 1,4,5-trisphosphate (InsP(3)) receptor Ca(2+) release channels and almost completely abolished by inhibition of endoplasmic reticulum Ca(2+) uptake. To probe the Ca(2+) release mechanisms present within endfeet, spatially restricted flash photolysis of caged InsP(3) was utilized to liberate InsP(3) directly within endfeet. This maneuver generated large amplitude [Ca(2+)](i) increases within endfeet that were spatially restricted to this region of the astrocyte. These InsP(3)-induced [Ca(2+)](i) increases were sensitive to depletion of the intracellular Ca(2+) store, but not to ryanodine, suggesting that Ca(2+)-induced Ca(2+) release from ryanodine receptors does not contribute to the generation of endfoot [Ca(2+)](i) signals. Neuronally evoked increases in astrocytic [Ca(2+)](i) propagated through perivascular astrocytic processes and endfeet as multiple, distinct [Ca(2+)](i) waves and exhibited a high degree of spatial heterogeneity. Regenerative Ca(2+) release processes within the endfeet were evident, as were localized regions of Ca(2+) release, and treatment of slices with the vasoactive neuropeptides somatostatin and vasoactive intestinal peptide was capable of inducing endfoot [Ca(2+)](i) increases, suggesting the potential for signaling between local interneurons and astrocytic endfeet in the cortex. Furthermore, photorelease of InsP(3) within individual endfeet resulted in a local vasodilation of adjacent arterioles, supporting the concept that astrocytic endfeet function as local "vasoregulatory units" by translating information from active neurons into complex InsP(3)-mediated Ca(2+) release signals that modulate arteriolar diameter.

Animals↗

Synchronization from disordered driving forces in arrays of coupled oscillators.

The effects of disorder in external forces on the dynamical behavior of coupled nonlinear oscillator networks are studied. When driven synchronously, i.e., all driving forces have the same phase, the networks display chaotic dynamics. We show that random phases in the driving forces result in regular, periodic network behavior. Intermediate phase disorder can produce network synchrony. Specifically, there is an optimal amount of phase disorder, which can induce the highest level of synchrony. These results demonstrate that the spatiotemporal structure of external influences can control chaos and lead to synchronization in nonlinear systems.

Action Potentials↗