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At least 1,135 records · Page 63Linked to original sources
PubMed1994

Uncovering the synchronization dynamics from correlated neuronal activity quantifies assembly formation.

Synchronous network excitation is believed to play an outstanding role in neuronal information processing. Due to the stochastic nature of the contributing neurons, however, those synchronized states are difficult to detect in electrode recordings. We present a framework and a model for the identification of such network states and of their dynamics in a specific experimental situation. Our approach operationalizes the notion of neuronal groups forming assemblies via synchronization based on experimentally obtained spike trains. The dynamics of such groups is reflected in the sequence of synchronized states, which we describe as a renewal dynamics. We furthermore introduce a rate function which is dependent on the internal network phase that quantifies the activity of neurons contributing to the observed spike train. This constitutes a hidden state model which is formally equivalent to a hidden Markov model, and all its parameters can be accurately determined from the experimental time series using the Baum-Welch algorithm. We apply our method to recordings from the cat visual cortex which exhibit oscillations and synchronizations. The parameters obtained for the hidden state model uncover characteristic properties of the system including synchronization, oscillation, switching, background activity and correlations. In applications involving multielectrode recordings, the extracted models quantify the extent of assembly formation and can be used for a temporally precise localization of system states underlying a specific spike train.

Algorithms↗
PubMed1994

Generation of periodic and chaotic bursting in an excitable cell model.

There are interesting oscillatory phenomena associated with excitable cells that require theoretical insight. Some of these phenomena are: the threshold low amplitude oscillations before bursting in neuronal cells, the damped burst observed in muscle cells, the period-adding bifurcations without chaos in pancreatic beta-cells, chaotic bursting and beating in neurons, and inverse period-doubling bifurcation in heart cells. The three variable model formulated by Chay provides a mathematical description of how excitable cells generate bursting action potentials. This model contains a slow dynamic variable which forms a basis for the underlying wave, a fast dynamic variable which causes spiking, and the membrane potential which is a dependent variable. In this paper, we use the Chay model to explain these oscillatory phenomena. The Poincaré return map approach is used to construct bifurcation diagrams with the 'slow' conductance (i.e., gK, C) as the bifurcation parameter. These diagrams show that the system makes a transition from repetitive spiking to chaotic bursting as parameter gK, C is varied. Depending on the time kinetic constant of the fast variable (lambda n), however, the transition between burstings via period-adding bifurcation can occur even without chaos. Damped bursting is present in the Chay model over a certain range of gK, C and lambda n. In addition, a threshold sinusoidal oscillation was observed at certain values of gK, C before triggering action potentials. Probably this explains why the neuronal cells exhibit low-amplitude oscillations before bursting.

Computer Simulation↗
PubMed1993

The contribution of muscle properties in the control of explosive movements.

Explosive movements such as throwing, kicking, and jumping are characterized by high velocity and short movement time. Due to the fact that latencies of neural feedback loops are long in comparison to movement times, correction of deviations cannot be achieved on the basis of neural feedback. In other words, the control signals must be largely preprogrammed. Furthermore, in many explosive movements the skeletal system is mechanically analogous to an inverted pendulum; in such a system, disturbances tend to be amplified as time proceeds. It is difficult to understand how an inverted-pendulum-like system can be controlled on the basis of some form of open loop control (albeit during a finite period of time only). To investigate if actuator properties, specifically the force-length-velocity relationship of muscle, reduce the control problem associated with explosive movement tasks such as human vertical jumping, a direct dynamics modeling and simulation approach was adopted. In order to identify the role of muscle properties, two types of open loop control signals were applied: STIM(t), representing the stimulation of muscles, and MOM(t), representing net joint movements. In case of STIM control, muscle properties influence the joint moments exerted on the skeleton; in case of MOM control, these moments are directly prescribed. By applying perturbations and comparing the deviations from a reference movement for both types of control, the reduction of the effect of disturbances due to muscle properties was calculated. It was found that the system is very sensitive to perturbations in case of MOM control; the sensitivity to perturbations is markedly less in case of STIM control. It was concluded that muscle properties constitute a peripheral feedback system that has the advantage of zero time delay. This feedback system reduces the effect of perturbations during human vertical jumping to such a degree that when perturbations are not too large, the task may be performed successfully without any adaptation of the muscle stimulation pattern.

Computer Simulation↗
PubMed1993

Operation Everest II: an indication of deterministic chaos in human heart rate variability at simulated extreme altitude.

It has been shown that fluctuation of human heartbeat intervals (heart rate variability, HRV) reflects variations in autonomic nervous system activity. We studied HRV at simulated altitudes of over 6000 m from Holter electrocardiograms recorded during the Operation Everest II study (Houston et al. 1987). Stationary, approximately 30-min segments of HRV data from six subjects at sea level and over 6000 m were supplied to (1) spectral analysis to evaluate sympathetic and parasympathetic nervous system (SNS, PNS) activity, (2) the analysis of Poincaré section of the phase space trajectory reconstructed on a delayed coordinate system to evaluate whether there was fluctuation with deterministic dynamics, (3) the estimation of the correlation dimension to evaluate a static property of putative attractors, and (4) the analysis of nonlinear predictability of HRV time series which could reflect a dynamic property of the attractor. Unlike HRV at sea level, the recordings at over 6000 m showed a strong periodicity (period of about 20 s) with small cycle-to-cycle perturbation. When this perturbation was expressed on a Poincaré section, it seemed to be likely that the perturbation itself obeyed a deterministic law. The correlation dimensions of these recordings showed low dimensional values (3.5 +/- 0.4, mean +/- SD), whereas those of the isospectral surrogates showed significantly (P < 0.05) higher values (5.3 +/- 0.5) with embedding dimensions of 5.6 +/- 0.9.(ABSTRACT TRUNCATED AT 250 WORDS)

Altitude↗
PubMed1993

The relationship between smoothness and economy during walking.

The purpose of this study was to test a theoretical model (Stein et al. 1986) which suggested that minimizing the rate of metabolic energy consumption (VO2) is related to minimizing jerk (third derivative of position) during human movement. At a given speed of walking, VO2 has been shown to increase curvilinearly as stride length (SL) is varied from freely chosen stride length (FCSL). It was hypothesized that the jerk-cost, or JC (area under squared jerk curve), would exhibit similar behavior. Subjects (n = 24) walked (1.75 m.s-1) on a treadmill at FCSL, and at SL derivations at +/- 10 and +/- 20% of leg length from FCSL until steady-state VO2 was attained. Videotaping (60 Hz) in the sagittal plane and subsequent digitizing of relevant markers produced position coordinates which were smoothed and normalized in both distance and time before calculating the third time derivative to obtain two-dimensional JC values. The expected response of VO2 to deviations in SL was found (minimum at FCSL), but JC increased with SL except at the two longest SL conditions. A weak but statistically significant negative correlation was found between VO2 and JC, suggesting that smoothness and economy are not complementary performance criteria during walking.

Biomechanical Phenomena↗
PubMed1993

Modelling of direct motor program learning in fast human arm motions.

We propose and simulate a new paradigm for organization of motor control in fast and accurate human arm motions. We call the paradigm "direct motor program learning" since the control programs are learned directly without knowing or learning the dynamics of a controlled system. The idea is to approximate the dependence of the motor control programs on the vector of the task parameters rather than to use a model of the system dynamics. We apply iterative learning control and scattered data multivariate approximation techniques to achieve the goal. The advantage of the paradigm is that the control complexity depends neither on the order nor on the nonlinearity of the system dynamics. We simulate the direct motor program learning paradigm in the task of point-to-point control of fast planar human arm motions. Simulation takes into account nonlinear arm dynamics, muscle force dynamics, delay in low-level reflex feedback, time dependence of the feedback gains and coactivation of antagonist muscles. Despite highly nonlinear time-variant dynamics of the controlled system, reasonably good motion precision is obtained over a wide range of the task parameters (initial and final positions of the arm). The simulation results demonstrate that the paradigm is indeed viable and could be considered as a possible explanation for the organization of motor control of fast motions.

Algorithms↗
PubMed1996

Third-order reverse correlation analysis of muscle spindle primary afferent fiber responses to random muscle stretch.

The response of primary muscle spindle afferent fibers to muscle stretch is nonlinear. Now spindle responses (trains of action potentials) to band-limited Gaussian white noise length perturbations of the gastrocnemius muscles (input signal) are described in cats. The input noise upper cutoff frequency was clearly above the frequency range of physiological length changes in cat hindleg muscles. The input-output relation was analyzed by means of peri-spike averages (PSAs), which could be shown to correspond to the kernels of Wiener's white noise approach to systems identification. The present approach (the reverse correlation analysis) was applied up to the third order. An experiment consisted of two recordings: one (the source recording) to determine PSAs and the other (the test recording) to provide an input signal for predicting responses. The predictions of different orders were compared with the actual neuronal response (the observation) of the test recording. Four different approximation procedures were developed to adapt prediction and observation and to determine weighting factors for the predictions of different orders. The approximations also yielded the value of the power density P of the input noise signal: at a variety of stimulus parameters, P from approximations had the same magnitude as P determined directly from the input signal amplitude spectrum. The prediction of a sequence of action potentials improved the higher the order of components. 37 of 42 action potentials of a test recording (the observation) could be confidently predicted from PSAs or kernels. Compared with the size of the linear first-order prediction curve, the relative sizes of the second and third-order prediction curves were: 1.0:0.47:0.26.

Action Potentials↗
PubMed1996

Extending the HKB model of coordinated movement to oscillators with different eigenfrequencies.

We study the dynamics of a system of coupled nonlinear oscillators that has been used to model coordinated human movement behavior. In contrast to earlier work we examine the case where the two component oscillators have different eigenfrequencies. Problems related to the decomposition of a time series (from an experiment) into amplitude and phase are discussed. We show that oscillations at multiples of the main frequency of the oscillator system may occur in the phase and amplitude due to the choice of a coordinate system and how these oscillations can be eliminated. We derive an explicit equation for the dynamics of the relative phase of the oscillator system in phase space that enables a direct comparison between theory and experiment.

Cybernetics↗
PubMed1996

Synchronized oscillations in the visual cortex--a synergetic model.

We present an oscillator network model for the synchronization of oscillatory neuronal activity underlying visual processing. The single neuron is modeled by means of a limit cycle oscillator with an eigenfrequency corresponding to visual stimulation. The eigenfrequency may be time dependent. The mutual coupling strengths are unsymmetrical and activity dependent, and they scatter within the network. Synchronized clusters (groups) of neurons emerge in the network due to the visual stimulation. The different clusters correspond to different visual stimuli. There is no limitation of the number of stimuli. Distinct clusters do not perturb each other, although the coupling strength between all model neurons is of the same order of magnitude. Our analysis is not restricted to weak coupling strength. The scatter of the couplings causes shifts of the cluster frequencies. The model's behavior is compared with the experimental findings. The coupling mechanism is extended in order to model the influence of bicucullin upon the neural network. We additionally investigate repulsive couplings, which lead to constant phase differences between clusters of the same frequency. Finally, we consider the problem of selective attention from the viewpoint of our model.

Animals↗
PubMed1996

Coordination dynamics of trajectory formation.

The present study aims to understand the neurally based coordination dynamics (multistability, loss of stability, transitions, etc.) of trajectory formation in a simple task. Six subjects produced two spatial patterns of coordination in the xy plane by alternating the abduction-adduction and flexion-extension motions of their right index finger. Each pattern was characterized by a unique temporal ratio between the x and y directions of motion: (1) a figure zero, a 1:1 temporal pattern; and (2) a figure eight, a 2:1 temporal pattern. The patterns were produced rhythmically and movement frequency was scaled across ten frequency plateaus, with ten cycles of motion per step. As movement frequency increased, switching from a figure eight to a figure zero was observed at critical cycling frequencies. The switch from pattern (2) to pattern (1) was identified in the spatial trajectory and power spectra of x(t) and y(t). En route to the transition, enhancement of fluctuations was observed in the Fourier amplitudes of x(t) and y(t), specifically at f0 (the metronome frequency) and 2f0 (the first harmonic of f0). Interestingly, there was no difference in the spatial variability of the two patterns. Overall, the data demonstrate that spatial patterns of coordination can be characterized in terms of the temporal relationship between the spatial components of the trajectory itself. We discuss the experimental findings in relation to other end-point planning and multijoint control strategies, as well as the much more general problem of temporal synchronization in many interlimb and intralimb coordination tasks.

Adult↗
PubMed1996

Determination of the precision of spike timing in the visual cortex of anaesthetised cats.

Neuronal cortical spike trains contain precisely replicating patterns whose presence cannot be accounted for by change production. A comparison of the number of triplets of spikes present two times with the number of doublets replicated three times in the same window duration gives a frequency-insensitive measure of this type of fine temporal organisation. By varying the tolerance with which such precisely replicating patterns are detected, one can evaluate the accuracy of spike timing in spike trains. In the sample of data here analysed, it was found that replicating patterns were best seen in the precision range 0.4-1.4 ms (a result evidently at variance with a simple 'integrate and fire' model of neurons). Surprisingly, the fine temporal structure of spike trains thus evidenced was stronger at relatively low firing rate discharges and was present in both the 'spontaneous' and 'evoked' responses.

Action Potentials↗
PubMed1996

Dynamics control of semantic processes in a hierarchical associative memory.

A neural mechanism for control of dynamics and function of associative processes in a hierarchical memory system is demonstrated. For the representation and processing of abstract knowledge, the semantic declarative memory system of the human brain is considered. The dynamics control mechanism is based on the influence of neuronal adaptation on the complexity of neural network dynamics. Different dynamical modes correspond to different levels of the ultrametric structure of the hierarchical memory being invoked during an associative process. The mechanism is deterministic but may also underlie free associative thought processes. The formulation of an abstract neural network model of hierarchical associative memory utilizes a recent approach to incorporate neuronal adaptation. It includes a generalized neuronal activation function recently derived by a Hodgkin-Huxley-type model. It is shown that the extent to which a hierarchically organized memory structure is searched is controlled by the neuronal adaptability, i.e. the strength of coupling between neuronal activity and excitability. In the brain, the concentration of various neuromodulators in turn can regulate the adaptability. An autonomously controlled sequence of bifurcations, from an initial exploratory to a final retrieval phase, of an associative process is shown to result from an activity-dependent release of neuromodulators. The dynamics control mechanism may be important in the context of various disorders of the brain and may also extend the range of applications of artificial neural networks.

Cybernetics↗
PubMed1996

High-order behaviour in learning gate networks with lateral inhibition.

In this work we present a neural network model incorporating activity-dependent presynaptic facilitation with multidimensional inputs. The processing unit used is based on a slightly simplified version of the Learning Gate Model proposed by Ciaccia et al. (1992). The network topology integrates a well-known biological neural circuit with a lateral inhibition connection subnet. By means of simulation experiments, we show that the proposed networks exhibit basic and high-order features of associative learning. In particular, overshadowing and blocking are reproduced in the presence of both noise-free and noisy inputs. The role of noise in the development of high-order learning capabilities is also discussed.

Animals↗
PubMed1996

Electro-geometrical coupling in non-uniform branching dendrites. Consequences for relative synaptic reflectiveness.

The relationships between somatofugal electronic voltage spread, somatopetal charge transfer and non-uniform geometry of the neuronal dendrites were studied on the basis of the linear cable theory. It is demonstrated that for the dendritic arborization of arbitrary geometry, the path distribution of the relative effectiveness of somatopetal synaptic charge transfer defined as in Barrett and Crill (1974) is identical to that of the somatofugal steady electronic voltage normalized to the voltage at the soma. The features of both distributions are determined by breaks in the voltage gradient (the slope of monotonic voltage decay) at the sites of local non-uniformity of the dendritic geometry, such as abrupt change in diameter and asymmetric branching. If the membrane- and cytoplasm-specific electrical parameters are assumed as uniform and the branch diameter as piece-wise uniform, then at any site of step change the square reciprocal ratio of the pre- and poststep diameters determines the ratio of the pre- and poststep electronic gradients. At branching points this ratio is modulated by partition of the core current between the daughter branches in proportion to their input conductances depending on global geometries of the daughter subtrees originating there. Thus, simply computed steady somatofugal voltages provide a physiologically meaningful estimation of the relative influence of synaptic inputs in different parts of the dendritic arborization on the output of the neuron.

Cell Size↗
PubMed1995

Analysis of kinematic invariances of multijoint reaching movement.

There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joint angle or intrinsic space in the general condition of joint redundancy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate systems. We show that the cartesian trajectory can be planned based on the task parameters (target coordinates, etc.) prior to and independently of angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in cartesian and angular spaces simultaneously is proposed. Due to joint redundancy, each cartesian trajectory corresponds to a family of angular trajectories which can account for the substantial variability of the latter. A set of strategies for multijoint motor control following from this model is considered; one of them coincides with the frog wiping reflex model and resolves the kinematic inverse problem without inversion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, straight end-point paths, bell-shaped tangential velocity profiles, speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajectory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb configuration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian space. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control used in planning. All the results are given analytically and, in order to compare the model with experimental results, by computer simulations.

Animals↗
PubMed1995

Open-loop simulations of the primate saccadic system using burst cell discharge from the superior colliculus.

Saccade-related burst neurons (SRBNs) in the monkey superior colliculus (SC) have been hypothesized to provide the brainstem saccadic burst generator with the dynamic error signal and the movement initiating trigger signal. To test this claim, we performed two sets of open-loop simulations on a burst generator model with the local feedback disconnected using experimentally obtained SRBN activity as both the driving and trigger signal inputs to the model. First, using neural data obtained from cells located near the middle of the rostral to caudal extent of the SC, the internal parameters of the model were optimized by means of a stochastic hill-climbing algorithm to produce an intermediate-sized saccade. The parameter values obtained from the optimization were then fixed and additional simulations were done using the experimental data from rostral collicular neurons (small saccades) and from more caudal neurons (large saccades); the model generated realistic saccades, matching both position and velocity profiles of real saccades to the centers of the movement fields of all these cells. Second, the model was driven by SRBN activity affiliated with interrupted saccades, the resumed eye movements observed following electrical stimulation of the omnipause region. Once again, the model produced eye movements that closely resembled the interrupted saccades produced by such simulations, but minor readjustment of parameters reflecting the weight of the projection of the trigger signal was required. Our study demonstrates that a model of the burst generator produces reasonably realistic saccades when driven with actual samples of SRBN discharges.

Algorithms↗
PubMed1991

Markovian neural networks.

The neural network that efficiently and nearly optimally solves difficult optimization problems is defined. The convergence proof for the Markovian neural network that asynchronously updates its neurons' states is also presented. The comparison of the performance of the Markovian neural network with various combinatorial optimization methods in two domains is described. The Markovian neural network is shown to be an efficient tool for solving optimization problems.

Cybernetics↗