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Reconstruction of equilibrium trajectories during whole-body movements.

The framework of the equilibrium-point hypothesis was used to reconstruct equilibrium trajectories (ETs) of the ankle, hip and body center of mass during quick voluntary hip flexions ('Japanese courtesy bow') by standing subjects. Different spring loads applied to the subject's back were used to introduce smooth perturbations that are necessary to reconstruct ETs based on a series of trials at the same task. Time patterns of muscle torques were calculated using inverse dynamics techniques. A second-order linear model was employed to calculate the instantaneous position of the spring-like joint or center of mass characteristic at different times during the movement. ETs of the joints and of the center of mass had significantly different shapes from the actual trajectories. Integral measures of electromyographic bursts of activity in postural muscles demonstrated a relation to muscle length corresponding to the equilibrium-point hypothesis.

Adult↗

Selective visual attention in a neurocomputational model of phase oscillators.

In order to understand the dynamic property of covert selective visual attention, which is different from the proposed mechanism of the spotlight metaphor, a two-layered network of phase oscillators was developed. The first layer is related to the hippocampus and controls attention focus formation. The second layer is related to the visual cortex, and each cortical oscillator in it simulates an assembly of cells coding for a particular stimulus in the sense of feature binding. Selective visual attention is interpreted as the result of the emergent synchronization of hippocampus oscillators and a part of cortical oscillators. Numerical experiments are presented to illustrate attention focus formation and attention shifting from one set of stimuli to another. From a neurocomputational point of view, our results demonstrate that attention is an emergent property of the dynamical cell assemblies responding to the whole visual field.

Attention↗

Neural network models of bilateral coordination.

Two mechanisms are described for controlling the movement of a pair of arms. The first is an engineered motion planner that finds solutions to the ill-posed problem of making noncolliding, goal-directed movements. The second uses neural networks that learn to emulate the coordinated behaviors of the motion planner using considerably less computational resources. Analysis of the networks shows in general terms how they work, and allows us to make testable predictions about some of the response properties that might be observed in the brain systems serving bilateral coordination.

Arm↗

Multiple-input, multiple-output system identification for characterization of limb stiffness dynamics.

This study presents time-domain and frequency-domain, multiple-input, multiple-output (MIMO) linear system identification techniques that can be used to estimate the dynamic endpoint stiffness of a multijoint limb. The stiffness of a joint or limb arises from a number of physiological mechanisms and is thought to play a fundamental role in the control of posture and movement. Estimates of endpoint stiffness can therefore be used to characterize its modulation during physiological tasks and may provide insight into how the nervous system normally controls motor behavior. Previous MIMO stiffness estimates have focused upon the static stiffness components only or assumed simple parametric models with elastic, viscous, and inertial components. The method presented here captures the full stiffness dynamics during a relatively short experimental trial while assuming only that the system is linear for small perturbations. Simulation studies were performed to investigate the performance of this approach under typical experimental conditions. It was found that a linear MIMO description of endpoint stiffness dynamics was sufficient to describe the displacement responses to small stochastic force perturbations. Distortion of these linear estimates by nonlinear centripetal and Coriolis forces was virtually undetectable for these perturbations. The system identification techniques were also found to be robust in the presence of significant output measurement noise and input coupling. These results indicate that the approach described here will allow the estimation of endpoint stiffness dynamics in an experimentally efficient manner with minimal assumptions about the specific form of these properties.

Algorithms↗

Identification of head motions by central vestibular neurons receiving linear and angular input.

Most naturally occurring displacements of the head in space, due to either an external perturbation of the body or a self-generated, volitional head movement, apply both linear and angular forces to the head. The vestibular system detects linear and angular accelerations of the head separately, but the succeeding control of gaze and posture often relies upon the combined processing of linear and angular motion information. Thus, the output of a secondary neuron may reflect the linear, the angular, or both components of the head motion. Although the vestibular system is typically studied in terms of separate responses to linear and angular acceleration of the head, many secondary and higher-order neurons in the vestibular system do, in fact, receive information from both sets of motion sensors. The present paper develops methods to analyze responses of neurons that receive both types of information, and focuses on responses to sinusoidal motions composed of a linear and an angular component. We show that each neuron has a preferred motion, but a single neuron cannot code for a single motion. However, a pair of neurons can code for a motion by the relative phases of firing-rate modulation. In this way, information about motion is enhanced by neurons combining information about linear and angular motion.

Animals↗

Delayed reverberation through time windows as a key to cerebellar function.

We present a functional model of the cerebellum comprising cerebellar cortex, inferior olive, deep cerebellar nuclei, and brain stem nuclei. The discerning feature of the model being time coding, we consistently describe the system in terms of postsynaptic potentials, synchronous action potentials, and propagation delays. We show by means of detailed single-neuron modeling that (i) Golgi cells can fulfill a gating task in that they form short and well-defined time windows within which granule cells can reach firing threshold, thus organizing neuronal activity in discrete 'time slices', and that (ii) rebound firing in cerebellar nuclei cells is a robust mechanism leading to a delayed reverberation of Purkinje cell activity through cerebellar-reticular projections back to the cerebellar cortex. Computer simulations of the whole cerebellar network consisting of several thousand neurons reveal that reverberation in conjunction with long-term plasticity at the parallel fiber-Purkinje cell synapses enables the system to learn, store, and recall spatio-temporal patterns of neuronal activity. Climbing fiber spikes act both as a synchronization and as a teacher signal, not as an error signal. They are due to intrinsic oscillatory properties of inferior olivary neurons and to delayed reverberation within the network. In addition to clear experimental predictions the present theory sheds new light on a number of experimental observation such as the synchronicity of climbing fiber spikes and provides a novel explanation of how the cerebellum solves timing tasks on a time scale of several hundreds of milliseconds.

Action Potentials↗

Exact digital simulation of time-invariant linear systems with applications to neuronal modeling.

An efficient new method for the exact digital simulation of time-invariant linear systems is presented. Such systems are frequently encountered as models for neuronal systems, or as submodules of such systems. The matrix exponential is used to construct a matrix iteration, which propagates the dynamic state of the system step by step on a regular time grid. A large and general class of dynamic inputs to the system, including trains of delta-pulses, can be incorporated into the exact simulation scheme. An extension of the proposed scheme presents an attractive alternative for the approximate simulation of networks of integrate-and-fire neurons with linear sub-threshold integration and non-linear spike generation. The performance of the proposed method is analyzed in comparison with a number of multi-purpose solvers. In simulations of integrate-and-fire neurons, Exact Integration systematically generates the smallest error with respect to both sub-threshold dynamics and spike timing. For the simulation of systems where precise spike timing is important, this results in a practical advantage in particular at moderate integration step sizes.

Animals↗

A model-based interpretation of the biphasic daily pattern of sleepiness.

We developed a thermoregulatory model of sleep control based on the hypothesis that non-rapid eye-movement sleep participates in homeostatic thermoregulation. This model successfully reproduced several qualitative features of human sleep/wake cycles during entrained as well as the internally desynchronized states. Among the reproduced features, generation mechanisms of the biphasic sleepiness distribution are studied here in the light of the model structure. Harmonic analysis is employed for this purpose. Through linearizations and confining the harmonics of the masking process to the fundamental component, a simplified representation of sleepiness is obtained. The simplified sleepiness is constructed with the fundamental circadian, the second harmonic components, and the constant (DC). The bimodality of the sleepiness is shown to be made by the second harmonic which is added to the fundamental component. The behavior of their amplitudes and phase positions are investigated under the varied sleep/wake durations and phase differences between the oscillators. Since the sleepiness generated by our model is roughly mimicked by the simplified representation under diverse conditions, this simplification can be regarded as adequate. From the behavior of the constituents of respective harmonic components, the fundamental component is shown to originate from the sleep/wake masking process and the circadian oscillators; the second harmonic from the multiplicative interactions between the circadian oscillators and the sleep/wake masking process. These results indicate that the rhythmic processes are principal constituents of the sleepiness, at least in the steady state.

Body Temperature Regulation↗

Nonlinear EEG analysis based on a neural mass model.

The well-known neural mass model described by Lopes da Silva et al. (1976) and Zetterberg et al. (1978) is fitted to actual EEG data. This is achieved by reformulating the original set of integral equations as a continuous-discrete state space model. The local linearization approach is then used to discretize the state equation and to construct a nonlinear Kalman filter. On this basis, a maximum likelihood procedure is used for estimating the model parameters for several EEG recordings. The analysis of the noise-free differential equations of the estimated models suggests that there are two different types of alpha rhythms: those with a point attractor and others with a limit cycle attractor. These attractors are also found by means of a nonlinear time series analysis of the EEG recordings. We conclude that the Hopf bifurcation described by Zetterberg et al. (1978) is present in actual brain dynamics.

Cybernetics↗

Recurrent V1-V2 interaction in early visual boundary processing.

A majority of cortical areas are connected via feedforward and feedback fiber projections. In feedforward pathways we mainly observe stages of feature detection and integration. The computational role of the descending pathways at different stages of processing remains mainly unknown. Based on empirical findings we suggest that the top-down feedback pathways subserve a context-dependent gain control mechanism. We propose a new computational model for recurrent contour processing in which normalized activities of orientation selective contrast cells are fed forward to the next processing stage. There, the arrangement of input activation is matched against local patterns of contour shape. The resulting activities are subsequently fed back to the previous stage to locally enhance those initial measurements that are consistent with the top-down generated responses. In all, we suggest a computational theory for recurrent processing in the visual cortex in which the significance of local measurements is evaluated on the basis of a broader visual context that is represented in terms of contour code patterns. The model serves as a framework to link physiological with perceptual data gathered in psychophysical experiments. It handles a variety of perceptual phenomena, such as the local grouping of fragmented shape outline, texture surround and density effects, and the interpolation of illusory contours.

Animals↗

Iterative manual control model of human operator.

In this paper, we present an iterative manual control model of a human operator performing some repetitive task. Various aspects of the model are discussed in detail. Experiments have been done to study the human capability to perform the tasks by learning iteratively. Results of the experiments show the ability of the human operator to perform the tracking of a desired trajectory for some unknown non-linear system with quite reasonable accuracy during the iteration process. It is concluded that the human operator performs the repetitive task by modifying his control action using error and error rate in each iteration. During the modification, the human operator assigns different weights to the error and error rate in each iteration. These results can be implemented in designing more efficient iterative learning control algorithms.

Adenosine Diphosphate↗

Numerical fourier transform spectroscopy of EMG half-waves: fragmentary-decomposition-based approach to nonstationary signal analysis.

A nonstationary signal analysis technique is introduced, which regards an oscillatory physiological signal as a sum of its fragments, presented in the form of a fragmentary decomposition (FD). The virtue of FD is that it is free of the necessity to choose a priori the basis functions intended for signal analysis or synthesis. FD uses an unchanged signal fragment between adjacent zero-crossings, as a natural basis function called the half-wave function (HWF). To show that such a function is a physically meaningful object, Fourier transform methods were employed, supported by the similar basis function (SBF) algorithm, which provides the means for numerical Fourier transform spectroscopy of separate half-waves and their frequency domain description in terms of both amplitude and phase. The application of this method to parameter identification of 751 EMG half-waves from the eye blink EMG records of ten normal subjects showed that HWF's frequency domain image represents a Gaussian distribution, which applies over a defined range of relative frequencies. This empirical evidence shows that HWFs are produced by a specific system of first-order nonlinear differential equations, whose dependency on a number of random factors is characteristic of deterministic chaos. The particular form of solutions indicates that statistical regularities relevant to the central limit theorem are likely to underlie the genesis of the mass potentials studied. FD shows potential utility in a range of nonstationary physiological signals.

Adolescent↗

Cooperative mechanism for improving the discriminating ability in the chemoreceptor neuron binomial case.

The discriminating ability (selectivity) of the chemoreceptor neuron is compared with that of its receptor proteins. The process of neuronal triggering is expected to be cooperative and threshold type in a sense that the neuron fires a spike if and only if the number of receptor proteins which are bound with odor molecules is above a definite threshold. The binomial distribution is utilized to estimate the firing probability if a definite odor is applied. It is established that a chemoreceptor neuron can have a much higher selectivity than its individual receptor proteins, provided that the chemical stimuli are presented at low concentrations. A possibility for the above mechanism to be valid in other sensory systems is discussed.

Animals↗

Impedance characteristics of a neuromusculoskeletal model of the human arm I. Posture control.

The mechanical impedance of neuromusculoskeletal models of the human arm is studied in this paper. The model analysis provides a better understanding of the contributions of possible intrinsic and reflexive components of arm impedance, makes clear the limitations of second-order mass-viscosity-stiffness models and reveals possible task effects on the impedance. The musculoskeletal model describes planar movements of the upper arm and forearm, which are moved by six lumped muscles with nonlinear dynamics. The motor control system is represented by a neural network which combines feedforward and feedback control. It is optimized for the control of movements or for posture control in the presence of external forces. The achieved impedance characteristics depend on the conditions during the learning process. In particular, the impedance is adapted in a suitable way to the frequency content and direction of external forces acting on the hand during an isometric task. The impedance characteristics of a model, which is optimized for movement control, are similar to experimental data in the literature. The achieved stiffness is, to a large extent, reflexively determined whereas the approximated viscosity is primarily due to intrinsic attributes. It is argued that usually applied Hill-type muscle models do not properly represent intrinsic muscle stiffness.

Adaptation, Physiological↗

Impedance characteristics of a neuromusculoskeletal model of the human arm II. Movement control.

The modulation of neuromusculoskeletal impedance during movements is analysed using a motor control model of the human arm. The motor control system combines feedback and feedforward control and both control modes are determined in one optimization process. In the model, the stiffness varies at the double movement frequency for 2-Hz oscillatory elbow movements and has high values at the movement reversals. During goal-directed two-degrees-of-freedom arm movements, the stiffness is decreased during the movement and may be increased in the initial and final phases, depending on the movement velocity. The stiffness has a considerable curl during the movement, as was also observed in experimental data. The dynamic stiffness patterns of the model can be explained basically by the alpha-gamma coactivation scheme where feedback gains covary with motor control signals. In addition to the modulation of the gain factors, it is argued that the variation of the intrinsic stiffness has a considerable effect on movement control, especially during fast movements.

Arm↗

Biomechanical properties and a kinetic simulation model of the smooth muscle I2 in the buccal mass of Aplysia.

The muscle I2 is a smooth muscle from the buccal mass of the marine mollusc Aplysia californica whose neural control, in vivo kinematics, and behavioral role have been extensively analyzed. In this study, we measured the activation and contractile dynamics of the muscle in order to construct a Hill-type kinetic model of the muscle. This is the first study to our knowledge, of Aplysia muscle contractile dynamics. The isometric force-frequency relationship of I2 had a frequency threshold of about 6-8 Hz, and its force output saturated at 20-25 Hz, properties that match the high frequency (20 Hz) bursts generated by the B31/B32 neurons that innervate it. Peak isometric force was generated at about 118% of the in situ relaxed length. These results and I2's estimated in vivo kinematics suggest that it generates maximum force at the onset of protraction. The muscle tension during iso-velocity lengthening and shortening was an asymmetric function of velocity. Short range stiffness and yielding responses were observed in lengthening, whereas muscle tension decreased smoothly in shortening. These visco-elastic properties suggest that the I2 muscle can serve to brake forceful retraction movements. A Hill-type model, parameterized from the measurements, captured many of the mechanical properties of I2. Our results provide a quantitative understanding of the biomechanical significance of the muscle's neural control and provide a basis for simulation studies of the control of feeding behavior.

Animals↗

Interaction of ON and OFF pathways for visual contrast measurement.

We propose a novel model of visual contrast measurement based on segregated On and Off pathways. Two driving forces have shaped our investigation: (1) establishing a mechanism selective for sharp local transitions in the luminance distribution; (2) generating a robust scheme of oriented contrast detection. Our starting point was the architecture of early stages in the mammalian visual system. We show that the circuit behaves as a soft AND-gate and analyze the scale-space selectivity properties of the model in detail. The theoretical analysis is supplemented by computer simulations in which we selectively investigate key functionalities of the proposed contrast detection scheme. We demonstrate that the model is capable of successfully processing synthetic as well as natural images, thus illustrating the potential of the method for computer vision applications.

Computer Simulation↗

Linear combinations of nonlinear models for predicting human-machine interface forces.

This study presents a computational framework that capitalizes on known human neuromechanical characteristics during limb movements in order to predict human-machine interactions. A parallel-distributed approach, the mixture of nonlinear models, fits the relationship between the measured kinematics and kinetics at the handle of a robot. Each element of the mixture represented the arm and its controller as a feedforward nonlinear model of inverse dynamics plus a linear approximation of musculotendonous impedance. We evaluated this approach with data from experiments where subjects held the handle of a planar manipulandum robot and attempted to make point-to-point reaching movements. We compared the performance to the more conventional approach of a constrained, nonlinear optimization of the parameters. The mixture of nonlinear models accounted for 79 +/- 11% (mean +/- SD) of the variance in measured force, and force errors were 0.73 +/- 0.20% of the maximum exerted force. Solutions were acquired in half the time with a significantly better fit. However, both approaches suffered equally from the simplifying assumptions, namely that the human neuromechanical system consisted of a feedforward controller coupled with linear impedances and a moving state equilibrium. Hence, predictability was best limited to the first half of the movement. The mixture of nonlinear models may be useful in human-machine tasks such as in telerobotics, fly-by-wire vehicles, robotic training, and rehabilitation.

Artificial Intelligence↗