Formation and Dynamics of Waves in a Cortical Model of Cholinergic Modulation

Acetylcholine (ACh) is a regulator of neural excitability and one of the neurochemical substrates of sleep. Amongst the cellular effects induced by cholinergic modulation are a reduction in spike-frequency adaptation (SFA) and a shift in the phase response curve (PRC). We demonstrate in a biophysical model how changes in neural excitability and network structure interact to create three distinct functional regimes: localized asynchronous, traveling asynchronous, and traveling synchronous. Our results qualitatively match those observed experimentally. Cortical activity during slow wave sleep (SWS) differs from that during REM sleep or waking states. During SWS there are traveling patterns of activity in the cortex; in other states stationary patterns occur. Our model is a network composed of Hodgkin-Huxley type neurons with a M-current regulated by ACh. Regulation of ACh level can account for dynamical changes between functional regimes. Reduction of the magnitude of this current recreates the reduction in SFA the shift from a type 2 to a type 1 PRC observed in the presence of ACh. When SFA is minimal (in waking or REM sleep state, high ACh) patterns of activity are localized and easily pinned by network inhomogeneities. When SFA is present (decreasing ACh), traveling waves of activity naturally arise. A further decrease in ACh leads to a high degree of synchrony within traveling waves. We also show that the level of ACh determines how sensitive network activity is to synaptic heterogeneity. These regimes may have a profound functional significance as stationary patterns may play a role in the proper encoding of external input as memory and traveling waves could lead to synaptic regularization, giving unique insights into the role and significance of ACh in determining patterns of cortical activity and functional differences arising from the patterns.     

Expression of Hemispheric Asymmetry and Psychological Type in the EEG Traveling Wave

Spontaneous EEG patterns were recorded from 16 derivations in the parieto-occipital area over 2 min for subjects in the resting state with the eyes closed. Further, computer analysis of the current pattern of EEG phase relationships between all derivations was conducted, followed by visualization in real time of the trajectory and velocity of the traveling EEG wave as a computerized animation over the contour of the head. On the basis of visual observations and objective statistical analysis, we found consistent individual characteristics of the time course and trajectory of the traveling wave, which were compared to the results of psychological testing of the subjects. Most characteristic were modulations of the electric activity (traveling) in the transverse direction (from left to right and from right to left) and along the diagonal from the left anterior to the right posterior areas. Distinct groups of subjects were found with the predominance of one or the other trajectory type. The specific direction of the diagonal traveling was significantly correlated with the level of extroversion of the subject: extroverts were characterized by traveling of electric waves from the occiput forward to the vertex along the diagonal indicated, whereas for introverts, traveling from the vertex to the occiput was typical.     

Refinement and Pattern Formation in Neural Circuits by the Interaction of Traveling Waves with Spike-Timing Dependent Plasticity

Traveling waves in the developing brain are a prominent source of highly correlated spiking activity that may instruct the refinement of neural circuits. A candidate mechanism for mediating such refinement is spike-timing dependent plasticity (STDP), which translates correlated activity patterns into changes in synaptic strength. To assess the potential of these phenomena to build useful structure in developing neural circuits, we examined the interaction of wave activity with STDP rules in simple, biologically plausible models of spiking neurons. We derive an expression for the synaptic strength dynamics showing that, by mapping the time dependence of STDP into spatial interactions, traveling waves can build periodic synaptic connectivity patterns into feedforward circuits with a broad class of experimentally observed STDP rules. The spatial scale of the connectivity patterns increases with wave speed and STDP time constants. We verify these results with simulations and demonstrate their robustness to likely sources of noise. We show how this pattern formation ability, which is analogous to solutions of reaction-diffusion systems that have been widely applied to biological pattern formation, can be harnessed to instruct the refinement of postsynaptic receptive fields. Our results hold for rich, complex wave patterns in two dimensions and over several orders of magnitude in wave speeds and STDP time constants, and they provide predictions that can be tested under existing experimental paradigms. Our model generalizes across brain areas and STDP rules, allowing broad application to the ubiquitous occurrence of traveling waves and to wave-like activity patterns induced by moving stimuli.     

Three people can synchronize as coupled oscillators during sports activities

We experimentally investigated the synchronized patterns of three people during sports activities and found that the activity corresponded to spatiotemporal patterns in rings of coupled biological oscillators derived from symmetric Hopf bifurcation theory, which is based on group theory. This theory can provide catalogs of possible generic spatiotemporal patterns irrespective of their internal models. Instead, they are simply based on the geometrical symmetries of the systems. We predicted the synchronization patterns of rings of three coupled oscillators as trajectories on the phase plane. The interactions among three people during a 3 vs. 1 ball possession task were plotted on the phase plane. We then demonstrated that two patterns conformed to two of the three patterns predicted by the theory. One of these patterns was a rotation pattern (R) in which phase differences between adjacent oscillators were almost 2π/3. The other was a partial anti-phase pattern (PA) in which the two oscillators were anti-phase and the third oscillator frequency was dead. These results suggested that symmetric Hopf bifurcation theory could be used to understand synchronization phenomena among three people who communicate via perceptual information, not just physically connected systems such as slime molds, chemical reactions, and animal gaits. In addition, the skill level in human synchronization may play the role of the bifurcation parameter.     

A method for the estimation of functional brain connectivity from time-series data

A central issue in cognitive neuroscience is which cortical areas are involved in managing information processing in a cognitive task and to understand their temporal interactions. Since the transfer of information in the form of electrical activity from one cortical region will in turn evoke electrical activity in other regions, the analysis of temporal synchronization provides a tool to understand neuronal information processing between cortical regions. We adopt a method for revealing time-dependent functional connectivity. We apply statistical analyses of phases to recover the information flow and the functional connectivity between cortical regions for high temporal resolution data. We further develop an evaluation method for these techniques based on two kinds of model networks. These networks consist of coupled Rössler attractors or of coupled stochastic Ornstein–Uhlenbeck systems. The implemented time-dependent coupling includes uni- and bi-directional connectivities as well as time delayed feedback. The synchronization dynamics of these networks are analyzed using the mean phase coherence, based on averaging over phase-differences, and the general synchronization index. The latter is based on the Shannon entropy. The combination of these with a parametric time delay forms the basis of a connectivity pattern, which includes the temporal and time lagged dynamics of the synchronization between two sources. We model and discuss potential artifacts. We find that the general phase measures are remarkably stable. They produce highly comparable results for stochastic and periodic systems. Moreover, the methods proves useful for identifying brief periods of phase coupling and delays. Therefore, we propose that the method is useful as a basis for generating potential functional connective models.     

Spatial and temporal coupling between slow waves and pendular contractions

In contrast to the mechanisms of segmental and peristaltic contractions in the small intestine, not much is known about the mechanism of pendular contractions. High-resolution electrical and mechanical recordings were performed from isolated segments of the rabbit ileum during pendular contractions. The electrical activities were recorded with 32 extracellular electrodes while motility was assessed simultaneously by video tracking the displacements of 20-40 serosal markers. The electrical activities consisted of slow waves, followed by spikes, that propagated in either the aboral or oral direction. The mechanical activity always followed the initial electrical activity, describing a contraction phase in one direction followed by a relaxation phase in the opposite direction. Pendular displacements were always in rhythm with the slow wave, whereas the direction of the displacements was dictated by the origin of the slow wave. If the slow wave propagated aborally, then the pendular displacement occurred in the oral direction, whereas if the slow wave propagated in the oral direction, then the displacement occurred in the aboral direction. In the case of more complex propagation patterns, such as in the area of pacemaking or collision, direction of displacements remained always opposite to the direction of the slow wave. In summary, the direction and pattern of propagation of the slow wave determine the rhythm and the direction of the pendular motility. The well-known variability in pendular movements is caused by the variability in the propagation of the underlying slow wave.     

Synchronization of delayed coupled neurons in presence of inhomogeneity

In principle, two directly coupled limit cycle oscillators can overcome mismatch in intrinsic rates and match their frequencies, but zero phase lag synchronization is just achievable in the limit of zero mismatch, i.e., with identical oscillators. Delay in communication, on the other hand, can exert phase shift in the activity of the coupled oscillators. In this study, we address the question of how phase locked, and in particular zero phase lag synchronization, can be achieved for a heterogeneous system of two delayed coupled neurons. We have analytically studied the possibility of inphase synchronization and near inphase synchronization when the neurons are not identical or the connections are not exactly symmetric. We have shown that while any single source of inhomogeneity can violate isochronous synchrony, multiple sources of inhomogeneity can compensate for each other and maintain synchrony. Numeric studies on biologically plausible models also support the analytic results.     

Transient coordinated activity within the developing brain��s default network

The concept of a brain default network postulates that specific brain regions are more active when a person is engaged in introspective mental activity. Transient functional coordination between groups of neurons is thought to be necessary for information processing. Since children develop introspection as they mature, regions of the default network may establish increasing functional coordination with age, resulting in fewer fluctuations in synchronization patterns. We investigated the transient coordinated activity in regions of the default network in seventeen children aged 11 months to 17 years of age using EEG recordings while subjects were resting quietly with eyes closed. The temporal and spatial fluctuations in the phase synchrony patterns were estimated across sites associated with the default network pattern and compared to other regions. Lower variability of the spatio-temporal patterns of phase synchronization associated with the default network was observed in the older group as compared to the younger group. This indicates that functional coordination increases among regions of the default network as children develop.     

Intracellular calcium waves accompany neutrophil polarization,formylmethionylleucylphenylalanine stimulation,and phagocytosis: a high speed microscopy study

Using high sensitivity fluorescence imaging with shutter speeds approximately 600,000 times faster than those of video frames, we have characterized Ca2+ waves within cells in exquisite detail to reveal Ca2+ signaling routes. Polarized neutrophils exhibited a counterclockwise rotating ryanodine-sensitive juxtamembrane Ca2+ wave during temporal calcium spikes. During stimulation with fMLP, a chemotactic factor, two Ca2+ waves traveling in opposite directions around the perimeter of the cell emanated from sites of stimulation (the clockwise wave is verapamil sensitive). Phagocytosed targets exhibit counterclockwise Ca2+ waves traveling about their periphery originating from the plasma membrane. This study: 1) outlines the technology to observe Ca2+ signaling circuitry within small living cells; 2) shows that extracellular spatial information in the form of a chemotactic factor gradient is transduced into intracellular chemical patterns, which provides fresh insights in signaling; 3) suggests that a line of communication exits between the cell surface and phagosomes; and 4) suggests that spatiotemporal Ca2+ patterns contribute to drug actions.     

Thrombin Activity Propagates in Space During Blood Coagulation as an Excitation Wave

Injury-induced bleeding is stopped by a hemostatic plug formation that is controlled by a complex nonlinear and spatially heterogeneous biochemical network of proteolytic enzymes called blood coagulation. We studied spatial dynamics of thrombin, the central enzyme of this network, by developing a fluorogenic substrate-based method for time- and space-resolved imaging of thrombin enzymatic activity. Clotting stimulation by immobilized tissue factor induced localized thrombin activity impulse that propagated in space and possessed all characteristic traits of a traveling excitation wave: constant spatial velocity, constant amplitude, and insensitivity to the initial stimulation once it exceeded activation threshold. The parameters of this traveling wave were controlled by the availability of phospholipids or platelets, and the wave did not form in plasmas from hemophilia A or C patients who lack factors VIII and XI, which are mediators of the two principal positive feedbacks of coagulation. Stimulation of the negative feedback of the protein C pathway with thrombomodulin produced nonstationary patterns of wave formation followed by deceleration and annihilation. This indicates that blood can function as an excitable medium that conducts traveling waves of coagulation.     

Characterization of ovarian follicular wave dynamics in women

A wave phenomenon of ovarian follicular development in women has recently been documented in our laboratory. The objective of the present study was to characterize follicular waves to determine whether women exhibit major and minor wave patterns of follicle development during the interovulatory interval (IOI). The ovaries of 50 women with clinically normal menstrual cycles were examined daily using transvaginal ultrasonography for one IOI. Profiles of the diameters of all follicles >or=4 mm and the numbers of follicles >or=5 mm were graphed during the IOI. Major waves were defined as those in which one follicle grew to >or=10 mm and exceeded all other follicles by >or=2 mm. Minor waves were defined as those in which follicles developed to a diameter of <10 mm and follicle dominance was not manifest. Blood samples were drawn to measure serum concentrations of estradiol-17beta, LH, and FSH. Women exhibited major and minor patterns of follicular wave dynamics during the IOI. Of the 50 women evaluated, 29/34 women with two follicle waves (85.3%) exhibited a minor-major wave pattern of follicle development and 5 women (14.7%) exhibited a major-major wave pattern. Ten of the 16 women with three follicle waves (62.5%) exhibited a minor-minor-major wave pattern, 3 women (18.8%) exhibited a minor-major-major wave pattern, and 3 women (18.8%) exhibited a major-major-major wave pattern. Documentation of major and minor follicular waves during the menstrual cycle challenges the traditional theory that a single cohort of antral follicles grows only during the follicular phase of the menstrual cycle.     

Detection of Cochlear Amplification and Its Activation

The operation of the mammalian cochlea relies on a mechanical traveling wave that is actively boosted by electromechanical forces in sensory outer hair cells (OHCs). This active cochlear amplifier produces the impressive sensitivity and frequency resolution of mammalian hearing. The cochlear amplifier has inspired scientists since its discovery in the 1970s, and is still not well understood. To explore cochlear electromechanics at the sensory cell/tissue interface, sound-evoked intracochlear pressure and extracellular voltage were measured using a recently developed dual-sensor with a microelectrode attached to a micro-pressure sensor. The resulting coincident in vivo observations of OHC electrical activity, pressure at the basilar membrane and basilar membrane displacement gave direct evidence for power amplification in the cochlea. Moreover, the results showed a phase shift of voltage relative to mechanical responses at frequencies slightly below the peak, near the onset of amplification. Based on the voltage-force relationship of isolated OHCs, the shift would give rise to effective OHC pumping forces within the traveling wave peak. Thus, the shift activates the cochlear amplifier, serving to localize and thus sharpen the frequency region of amplification. These results are the most concrete evidence for cochlear power amplification to date and support OHC somatic forces as its source.     

Detection of Cochlear Amplification and Its Activation

The operation of the mammalian cochlea relies on a mechanical traveling wave that is actively boosted by electromechanical forces in sensory outer hair cells (OHCs). This active cochlear amplifier produces the impressive sensitivity and frequency resolution of mammalian hearing. The cochlear amplifier has inspired scientists since its discovery in the 1970s, and is still not well understood. To explore cochlear electromechanics at the sensory cell/tissue interface, sound-evoked intracochlear pressure and extracellular voltage were measured using a recently developed dual-sensor with a microelectrode attached to a micro-pressure sensor. The resulting coincident in vivo observations of OHC electrical activity, pressure at the basilar membrane and basilar membrane displacement gave direct evidence for power amplification in the cochlea. Moreover, the results showed a phase shift of voltage relative to mechanical responses at frequencies slightly below the peak, near the onset of amplification. Based on the voltage-force relationship of isolated OHCs, the shift would give rise to effective OHC pumping forces within the traveling wave peak. Thus, the shift activates the cochlear amplifier, serving to localize and thus sharpen the frequency region of amplification. These results are the most concrete evidence for cochlear power amplification to date and support OHC somatic forces as its source.     

Soliton behaviour in a bistable reaction diffusion model

We analyze a generic reaction-diffusion model that contains the important features of Turing systems and that has been extensively used in the past to model biological interesting patterns. This model presents various fixed points. Analysis of this model has been made in the past only in the case when there is only a single fixed point, and a phase diagram of all the possible instabilities shows that there is a place where a Turing-Hopf bifurcation occurs producing oscillating Turing patterns. In here we focus on the interesting situation of having several fixed points, particularly when one unstable point is in between two equally stable points. We show that the solutions of this bistable system are traveling front waves, or solitons. The predictions and results are tested by performing extensive numerical calculations in one and two dimensions. The dynamics of these solitons is governed by a well defined spatial scale, and collisions and interactions between solitons depend on this scale. In certain regions of parameter space the wave fronts can be stationary, forming a pattern resembling spatial chaos. The patterns in two dimensions are particularly interesting because they can present a coherent dynamics with pseudo spiral rotations that simulate the myocardial beat quite closely. We show that our simple model can produce complicated spatial patterns with many different properties, and could be used in applications in many different fields.      

Pattern formation in a spatial plant-wrack model with tide effect on the wrack

Spatial patterns are a subfield of spatial ecology, and these patterns modify the temporal dynamics and stability properties of population densities at a range of spatial scales. Localized ecological interactions can generate striking large-scale spatial patterns in ecosystems through spatial self-organization. Possible mechanisms include oscillating consumer–resource interactions, localized disturbance–recovery processes, and scale-dependent feedback. However, in this paper, our main aim is to study the effect of tide on the pattern formation of a spatial plant-wrack model. We discuss the changes of the wavelength, wave speed, and the conditions of the spatial pattern formation, according to the dispersion relation formula. Both the mathematical analysis and numerical simulations reveal that the tide has great influence on the spatial pattern. More specifically, typical traveling spatial patterns can be obtained. Our obtained results are consistent with the previous observation that wracks exhibit traveling patterns, which is useful to help us better understand the dynamics of the real ecosystems.     

Fractal Gait Patterns Are Retained after Entrainment to a Fractal Stimulus

Previous work has shown that fractal patterns in gait can be altered by entraining to a fractal stimulus. However, little is understood about how long those patterns are retained or which factors may influence stronger entrainment or retention. In experiment one, participants walked on a treadmill for 45 continuous minutes, which was separated into three phases. The first 15 minutes (pre-synchronization phase) consisted of walking without a fractal stimulus, the second 15 minutes consisted of walking while entraining to a fractal visual stimulus (synchronization phase), and the last 15 minutes (post-synchronization phase) consisted of walking without the stimulus to determine if the patterns adopted from the stimulus were retained. Fractal gait patterns were strengthened during the synchronization phase and were retained in the post-synchronization phase. In experiment two, similar methods were used to compare a continuous fractal stimulus to a discrete fractal stimulus to determine which stimulus type led to more persistent fractal gait patterns in the synchronization and post-synchronization (i.e., retention) phases. Both stimulus types led to equally persistent patterns in the synchronization phase, but only the discrete fractal stimulus led to retention of the patterns. The results add to the growing body of literature showing that fractal gait patterns can be manipulated in a predictable manner. Further, our results add to the literature by showing that the newly adopted gait patterns are retained for up to 15 minutes after entrainment and showed that a discrete visual stimulus is a better method to influence retention.     

Traveling-wave pattern generator controls movement and organization of sensory feedback in a spinal cord model

 A traveling wave in a two-dimensional spinal cord model constitutes a stable pattern generator for quadruped gaits. In the context of the somatotopic organization of the spinal cord, this pattern generator is sufficient to generate stable locomotive limb trajectories. The elastic properties of muscles alone, providing linear negative feedback, are sufficient to stabilize stance and locomotion in the presence of perturbative forces. We further show that such a pattern generator is capable of organizing sensory processing in the spinal cord. A single-layer perceptron was trained to associate the sensory feedback from the limb (coding force, length, and change of length for each muscle) with the two-dimensional activity profile of the traveling wave. This resulted in a well-defined spatial organization of the connections within the spinal network along a rostrocaudal axis. The spinal network driven by peripheral afferents alone supported autonomous locomotion in the positive feedback mode, whereas in the negative feedback mode stance was stabilized in response to perturbations. Systematic variation of a parameter representing the effect of gamma-motor neurons on muscle spindle activity in our model led to a corresponding shift of limb position during stance and locomotion, resulting in a systematic displacement alteration of foot positions. Received: 30 July 2001 / Accepted in revised form: 17 April 2002 Correspondence to: A. Kaske (e-mails: alexander.kaske@mtc.ki.se, alexander.kaske@vglab.com)     

Cranial morphometry of early hominids: facial region

We report here on early hominid facial diversity, as part of a more extensive morphometric survey of cranial variability in Pliocene and early Pleistocene Hominidae. Univariate and multivariate techniques are used to summarise variation in facial proportions in South and East African hominids, and later Quaternary groups are included as comparators in order to scale the variation displayed. The results indicate that "robust" australopithecines have longer, broader faces than the "gracile" form, but that all australopithecine species show comparable degrees of facial projection. "Robust" crania are characterised by anteriorly situated, deep malar processes that slope forwards and downwards. Smaller hominid specimens, formally or informally assigned to Homo (H. habilis, KNM-ER 1813, etc.), have individual facial dimensions that usually fall within the range of Australopithecus africanus, but which in combination reveal a significantly different morphological pattern; SK 847 shows similarly hominine facial proportions, which differ significantly from those of A. robustus specimens from Swartkrans. KNM-ER 1470 possesses a facial pattern that is basically hominine, but which in some respects mimics that of "robust" australopithecines. Early specimens referred to H. erectus possess facial proportions that contrast markedly with those of other Villafranchian hominids and which suggest differing masticatory forces, possibly reflecting a shift in dietary niche. Overall the results indicate two broad patterns of facial proportions in Hominidae: one is characteristic of Pliocene/basal Pleistocene forms with opposite polarities represented by A. boisei and H. habilis; the other pattern, which typifies hominids from the later Lower Pleistocene onwards, is first found in specimens widely regarded as early representatives of H. erectus, but which differ in which certain respects from the face of later members of that species.     

Structure and Dynamics of Minke Whale Surfacing Patterns in the Gulf of St. Lawrence,Canada

Animal behavioral patterns can help us understand physiological and ecological constraints on animals and its influence on fitness. The surfacing patterns of aquatic air-breathing mammals constitute a behavioral pattern that has evolved as a trade-off between the need to replenish oxygen stores at the surface and the need to conduct other activities underwater. This study aims to better understand the surfacing pattern of a marine top predator, the minke whale (Balaenoptera acutorostrata), by investigating how their dive duration and surfacing pattern changes across their activity range. Activities were classified into resting, traveling, surface feeding and foraging at depth. For each activity, we classified dives into short and long dives and then estimated the temporal dependence between dive types. We found that minke whales modified their surfacing pattern in an activity-specific manner, both by changing the expression of their dives (i.e. density distribution) and the temporal dependence (transition probability) between dive types. As the depth of the prey layer increased between activities, the surfacing pattern of foraging whales became increasingly structured, going from a pattern dominated by long dives, when feeding at the surface, to a pattern where isolated long dives were followed by an increasing number of breaths (i.e. short dives), when the whale was foraging at depth. A similar shift in surfacing pattern occurred when prey handling time (inferred from surface corralling maneuvers) increased for surface feeding whales. The surfacing pattern also differed between feeding and non-feeding whales. Resting whales did not structure their surfacing pattern, while traveling whales did, possibly as a way to minimize cost of transport. Our results also suggest that minke whales might balance their oxygen level over multiple, rather than single, dive cycles.