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Optimal control of antagonistic muscle stiffness during voluntary movements.

This paper presents a study on the control of antagonist muscle stiffness during single-joint arm movements by optimal control theory with a minimal effort criterion. A hierarchical model is developed based on the physiology of the neuromuscular control system and the equilibrium point hypothesis. For point-to-point movements, the model provides predictions on (1) movement trajectory, (2) equilibrium trajectory, (3) muscle control inputs, and (4) antagonist muscle stiffness, as well as other variables. We compared these model predictions to the behavior observed in normal human subjects. The optimal movements capture the major invariant characteristics of voluntary movements, such as a sigmoidal movement trajectory with a bell-shaped velocity profile, an 'N'-shaped equilibrium trajectory, a triphasic burst pattern of muscle control inputs, and a dynamically modulated joint stiffness. The joint stiffness is found to increase in the middle of the movement as a consequence of the triphasic muscle activities. We have also investigated the effects of changes in model parameters on movement control. We found that the movement kinematics and muscle control inputs are strongly influenced by the upper bound of the descending excitation signal that activates motoneuron pools in the spinal cord. Furthermore, a class of movements with scaled velocity profiles can be achieved by tuning the amplitude and duration of this excitation signal. These model predictions agree with a wide body of experimental data obtained from normal human subjects. The results suggest that the control of fast arm movements involves explicit planning for both the equilibrium trajectory and joint stiffness, and that the minimal effort criterion best characterizes the objective of movement planning and control.

Arm↗

Realistic simulations of neurons by means of an ad hoc modified version of SPICE.

This paper describes an ad hoc modified version of the electrical circuit analysis program SPICE, which has been optimized for detailed simulations of the behaviour of neurons. An equivalent-circuit description of the simulation building blocks is provided, and the SPICE modifications are specified. These modifications, in contrast to previous uses of SPICE, allows one to simulate the behaviour of neurons of Hodgkin-Huxley type (excitable membrane) and of postsynaptic membranes without any approximations. Simulation results are reported and compared, both with data previously analysed in the literature by other authors and with experimental data recently obtained by coupling neurons to planar extracellular microelectrodes. Details of the circuit elements used in the simulations are reported. The improvements of our proposed model are discussed in comparison with a previous SPICE-based model described in the literature.

Action Potentials↗

In-phase and antiphase self-oscillations in a model of two electrically coupled pacemakers.

The dynamic behavior of a model of two electrically coupled oscillatory neurons was studied while the external polarizing current was varied. It was found that the system with weak coupling can demonstrate one of five stable oscillatory modes: (1) in-phase oscillations with zero phase shift; (2) antiphase oscillations with half-period phase shift; (3) oscillations with any fixed phase shift depending on the value of the external polarizing current; (4) both in-phase and antiphase oscillations for the same current value, where the oscillation type depends on the initial conditions; (5) both in-phase and quasiperiodic oscillations for the same current value. All of these modes were robust, and they persisted despite small variations of the oscillator parameters. We assume that similar regimes, for example antiphase oscillations, can be detected in neurophysiological experiments. Possible applications to central pattern generator models are discussed.

Animals↗

Space-variant models of visual acuity using self-adjoint integral operators.

The purpose of this paper is to outline a more general approach to visual acuity experiments than the classical methods borrowed from the optical sciences. A theory based on integral operators with symmetric kernels replaces the standard use of filters constructed from windowed sines and cosines. This more general approach allows greater latitude in the range of phenomena to be modelled. It also permits all the standard techniques used in Fourier expansion of a stimulus and response to be generalized to a space-variant system such as the human visual field.

Cybernetics↗

Time-frequency analysis of the electrocortical activity during maturation using wavelet transform.

In this study, we introduce the wavelet transform (WT) as a method for characterizing the maturational changes in electrocortical activity in 24 fetal lambs ranging from 110-144 days gestation (term 145 days). The WT, based on multiresolution signal decomposition, is free of assumptions regarding the characteristics of the signal. The approximation of the electrocortical activity at resolutions varying from 2j+1 to 2j can be extracted by decomposing the signal on a wavelet orthonormal basis of L2(R). We performed multiresolution decomposition for four sets of parameters D2j, where -1 < j < -4. The four series WT represent the detail signal band-widths: (1) 16-32 Hz, (2) 8-16 Hz, (3) 4-8 Hz, (4) 2-4 Hz. The data were divided into three groups according to gestational age: 110-122 days (early), 123-135 days (middle), and 136-144 days (late). In the early group, the power was highest in the fourth signal bandwidth, with relatively low power in the other bands. Increase in gestational age was characterized by increased power in all four bandwidths. Comparison of the cumulative distribution function of the power in the four wavelet bands confirmed the presence of two statistically different patterns in all three age groups. These two patterns correspond to the visually identified patterns of HVSA (high-voltage slow activity) and LVFA (low-voltage fast activity). The earliest development change occurred in HVSA, with progressive increase in power in the 2-8 Hz band. Later changes occurred in LVFA, with a significant increase in power in the 16-32 Hz band.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

On the computational architecture of the neocortex. II. The role of cortico-cortical loops.

This paper is a sequel to an earlier paper which proposed an active role for the thalamus, integrating multiple hypotheses formed in the cortex via the thalamo-cortical loop. In this paper, I put forward a hypothesis on the role of the reciprocal, topographic pathways between two cortical areas, one often a 'higher' area dealing with more abstract information about the world, the other 'lower', dealing with more concrete data. The higher area attempts to fit its abstractions to the data it receives from lower areas by sending back to them from its deep pyramidal cells a template reconstruction best fitting the lower level view. The lower area attempts to reconcile the reconstruction of its view that it receives from higher areas with what it knows, sending back from its superficial pyramidal cells the features in its data which are not predicted by the higher area. The whole calculation is done with all areas working simultaneously, but with order imposed by synchronous activity in the various top-down, bottom-up loops. Evidence for this theory is reviewed and experimental tests are proposed. A third part of this paper will deal with extensions of these ideas to the frontal lobe.

Animals↗

Trace feature map: a model of episodic associative memory.

An approach to episodic associative memory is presented, which has several desirable properties as a human memory model. The design is based on topological feature map representation of data. An ordinary feature map is a classifier, mapping an input vector onto a topologically meaningful location on the map. A trace feature map, in addition, creates a memory trace on that location. The traces can be stored episodically in a single presentation, and retrieved with a partial cue. Nearby traces overlap, which results in plausible memory interference behavior. Performance degrades gracefully as the memory is overloaded. More recent traces are easier to recall as are traces that are unique in the memory.

Association Learning↗

Evidence of hyperplanes in the genetic learning of neural networks.

Genetic Algorithms have been successfully applied to the learning process of neural networks simulating artificial life. In previous research we compared mutation and crossover as genetic operators on neural networks directly encoded as real vectors (Manczer and Parisi 1990). With reference to crossover we were actually testing the building blocks hypothesis, as the effectiveness of recombination relies on the validity of such hypothesis. Even with the real genotype used, it was found that the average fitness of the population of neural networks is optimized much more quickly by crossover than it is by mutation. This indicated that the intrinsic parallelism of crossover is not reduced by the high cardinality, as seems reasonable and has indeed been suggested in GA theory (Antonisse 1989). In this paper we first summarize such findings and then propose an interpretation in terms of the spatial correlation of the fitness function with respect to the metric defined by the average steps of the genetic operators. Some numerical evidence of such interpretation is given, showing that the fitness surface appears smoother to crossover than it does to mutation. This confirms indirectly that crossover moves along privileged directions, and at the same time provides a geometric rationale for hyperplanes.

Algorithms↗

From basis functions to basis fields: vector field approximation from sparse data.

Recent investigations (Poggio and Girosi 1990b) have pointed out the equivalence between a wide class of learning problems and the reconstruction of a real-valued function from a sparse set of data. However, in order to process sensory information and to generate purposeful actions living organisms must deal not only with real-valued functions but also with vector-valued mappings. Examples of such vector-valued mappings range from the optical flow fields associated with visual motion to the fields of mechanical forces produced by neuromuscular activation. In this paper, I discuss the issue of vector-field processing from a broad computational perspective. A variety of vector patterns can be efficiently represented by a combination of linearly independent vector fields that I call "basis fields". Basis fields offer in some cases a better alternative to treating each component of a vector as an independent scalar entity. In spite of its apparent simplicity, such a component-based representation is bound to change with any change of coordinates. In contrast, vector-valued primitives such as basis fields generate vector field representations that are invariant under coordinate transformations.

Animals↗

Vector field approximation: a computational paradigm for motor control and learning.

Recent experiments in the spinalized frog (Bizzi et al. 1991) have shown that focal microstimulation of a site in the premotor layers in the lumbar grey matter of the spinal cord results in a field of forces acting on the frog's ankle and converging to a single equilibrium position. These experiments suggested that the neural circuits in the spinal cord are organized in a set of control modules that "store" a few limb postures in the form of convergent force fields acting on the limb's end-point. Here, we investigate how such postural modules can be combined by the central nervous system for generating and representing a wider repertoire of control patterns. Our work is related to some recent investigations by Poggio and Girosi (1990a, b) who have proposed to represent the task of learning scalar maps as a problem of surface approximation. Consistent both with this view and with our experimental findings in the spinal frog, we regard the issue of generating motor repertoires as a problem of vector-field approximation. To this end, we characterize the output of a control module as a "basis field" (Mussa-Ivaldi 1992), that is as the vectorial equivalent of a basis function. Our theoretical findings indicate that by combining basis fields, the central nervous system may achieve a number of goals such as (1) the generation of a wide repertoire of control patterns and (2) the representation of these control patterns with a set of coefficients that are invariant under coordinate transformations.

Animals↗

Dynamic characteristics of the auditory cortex of guinea pigs observed with multichannel optical recording.

The spatiotemporal characteristics of neural activity in the guinea pig auditory cortex are investigated to determine their importance in neural processing and coding of the complex sounds. A multi-channel optical recording system has been developed for observing the cortical field of the mammalian brain in vivo. Using the voltage-sensitive dye: RH795, optical imaging was used to visualize neural activity in the guinea pig auditory cortex. Experimental results reveal a boomerang-shaped pattern of movement of activated neural cell regions for the evoked response to click as complex sounds. Parallel and sequential neural processing structure was observed. Although the exact frequency selectivities of single cells and tonotopical organization observed using microelectrode were not visible, the similar feature to the microelectrode evidences was imaged by extracting the strongly response field from the optical data.

Acoustic Stimulation↗

Two-dimensional coding of linear acceleration and the angular velocity sensitivity of the otolith system.

There exist otolith-sensitive vestibular nuclei neurons with spatio-temporal properties that can be described by two response vectors that are in temporal and spatial quadrature. These neurons respond to the component of a stimulus vector on a plane rather than a single axis. It is demonstrated here that these "two-dimensional" linear accelerometer neurons can function as one-dimensional angular velocity detectors. The two-dimensional property in both space and time allows these neurons to encode the component of the stimulus angular velocity vector that is normal to the plane defined by the two response vectors. The angular velocity vector in space can then be reconstructed by three populations of such neurons having linearly independent response planes. Thus, we propose that these two-dimensional spatio-temporal linear accelerometer neurons, in addition to participating in functions of the otolith system that are based on detection of linear acceleration, are also involved in the generation of compensatory ocular responses during off-vertical axis rotations.

Acceleration↗

Detection of rotating gravity signals.

It is shown in the preceding paper that neurons with two-dimensional spatio-temporal properties to linear acceleration behave like one-dimensional rate sensors: they encode the component of angular velocity (associated with a rotating linear acceleration vector) that is normal to their response plane. During off-vertical axis rotation (OVAR) otolith-sensitive neurons are activated by the gravity vector as it rotates relative to the head. Unlike "one-dimensional" linear accelerometer neurons which exhibit equal response magnitudes for both directions of rotation, "two-dimensional" neurons can be shown to respond with unequal magnitudes to clockwise and counterclockwise off-vertical axis rotations. The magnitudes of the sinusoidal responses of these neurons is not only directionally selective but also proportional to rotational velocity. Thus, responses from such "two-dimensional" neurons may represent the first step in the computations necessary to generate the steady-state eye velocity during OVAR. An additional step involving a nonlinear operation is necessary to transform the sinusoidally modulated output of these neurons into a signal proportional to sustained eye velocity. Similarly to models of motion detection in the visual system, this transformation is proposed to be achieved through neuronal operations involving mathematical multiplication followed by a leaky integration by the velocity storage mechanism. The proposed model for the generation of maintained eye velocity during OVAR is based on anatomical and physiological properties of vestibular nuclei neurons and capable of predicting the experimentally observed steady-state characteristics of the eye velocity.

Acceleration↗

Modeling the dishabituation hierarchy: the role of the primordial hippocampus.

We present a neural model for the organization and neural dynamics of the medial pallium, the toad's homolog of mammalian hippocampus. A neural mechanism, called cumulative shrinking, is proposed for mapping temporal responses from the anterior thalamus into a form of population coding referenced by spatial positions. Synaptic plasticity is modeled as an interaction of two dynamic processes which simulates acquisition and both short-term and long-term forgetting. The structure of the medial pallium model plus the plasticity model allows us to provide an account of the neural mechanisms of habituation and dishabituation. Computer simulations demonstrate a remarkable match between the model performance and the original experimental data on which the dishabituation hierarchy was based. A set of model predictions is presented, concerning mechanisms of habituation and cellular organization of the medial pallium.

Animals↗

Action potential refractory period in axonal demyelination: a computer simulation.

Axonal demyelination leads to an increase in the refractory period for propagation of the action potential. Computer simulations were used to investigate the mechanism by which changes in the passive properties of the internodal membrane increase the refractory period. The properties of the voltage dependent ion channels can be altered to restore conduction in demyelinated nerve fibers. The ability of these alterations to decrease the refractory period of demyelinated model nerve fibers was compared. The model nerve fiber contained six nodes. The action potential was stimulated at node one and propagated to node six. The internode between nodes three and four was demyelinated in a graded manner. The absolute refractory period for propagation of the action potential through the demyelinated internode increased as the number of myelin wraps was reduced to less than 25% of the normal value. The increase in refractory period was found to be due to a reduction in the rate or repolarization of the action potential at node three. The delay in repolarization reduced the rate of recovery of inactivated Na channels and slowed the closing of K channels. The rate of repolarization of node three was reduced by the conduction delay for the depolarization of node four caused by demyelination of the preceding internode. In these simulations the increase in refractory period due to demyelination was eliminated by slowing the onset of Na channel inactivation. A small reduction of the K conductance also decreased the refractory period. However, larger reductions eliminated this effect.

Action Potentials↗

Human control of a simple two-hand grasp.

We investigated how people control fast, accurate movements of a load using a simple two-hand grasp. By providing a clear instruction to several subjects, we isolated a single control strategy. The kinematics produced by this control strategy are nearly indistinguishable from those produced during singlehand movements, but the torques are quite different: one hand accelerates not only itself, but also the load and the other hand, while the other hand brakes the hand-load-hand system. As a result, the hands squeeze the load with a large force during the movement. The dynamics of the hand-load-hand system are of the same form as the dynamics of a single-hand system. Apparently, by taking advantage of this dynamic similarity and of the spring-like properties of muscle, the human motor control system can control the two-hand grasp system simply by modifying the muscle activation patterns used to control single-hand movements. The task dynamics of two-hand grasp do not require that the load be squeezed during the movement, and squeezing the load wastes torque that could be used to move more quickly. However, the human motor control system may choose this squeezing strategy because it reliably brakes the hand-load-hand system despite inherent variability in the braking of individual hands.

Acceleration↗

Oscillatory binocular system and temporal segmentation of stereoscopic depth surfaces.

A dynamical neural network model of binocular stereopsis is proposed to solve the problem of segmentation which remains ambiguous even when the problem of binocular correspondence is solved. Being compatible with the recent neurophysiological findings (Engel et al. 1991), the model assumes that neural cells show oscillatory activities and that segmentation into a coherent depth surface is coded by synchronization of activities. Employing appropriate constraints for segmentation, the present model shows proper segmentation of depth surfaces and also solves segmentational ambiguity caused by a gap. It is newly shown that binocularly-unmatched monocular cells are discriminated in temporal segmentation of monocular cells caused by recurrent interactions between monocular and binocular cells. Integrative interactions with the other visual components through temporal segmentation are also discussed.

Computer Simulation↗

Rapid synchronization through fast threshold modulation.

Synchronization properties of locally coupled neural oscillators were investigated analytically and by computer simulation. When coupled in a manner that mimics excitatory chemical synapses, oscillators having more than one time scale (relaxation oscillators) are shown to approach synchrony using mechanisms very different from that of oscillators with a more sinusoidal waveform. The relaxation oscillators make critical use of fast modulations of their thresholds, leading to a rate of synchronization relatively independent of coupling strength within some basin of attraction; this rate is faster for oscillators that have conductance-based features than for neural caricatures such as the FitzHugh-Nagumo equations that lack such features. Computer simulations of one-dimensional arrays show that oscillators in the relaxation regime synchronize much more rapidly than oscillators with the same equations whose parameters have been modulated to yield a more sinusoidal waveform. We present a heuristic explanation of this effect based on properties of the coupling mechanisms that can affect the way the synchronization scales with array length. These results suggest that the emergent synchronization behavior of oscillating neural networks can be dramatically influenced by the intrinsic properties of the network components. Possible implications for perceptual feature binding and attention are discussed.

Computer Simulation↗