Alexander V. Lukashin

A dynamical neural network model for motor cortical activity during movement: population coding of movement trajectories

As a dynamical model for motor cortical activity during hand movement we consider an artificial neural network that consists of extensively interconnected neuron-like units and performs the neuronal population vector operations. Local geometrical parameters of a desired curve are introduced into the network as an external input. The output of the model is a time-dependent direction and length of the neuronal population vector which is calculated as a sum of the activity of directionally tuned neurons in the ensemble. The main feature of the model is that dynamical behavior of the neuronal population vector is the result of connections between directionally tuned neurons rather than being imposed externally. The dynamics is governed by a system of coupled nonlinear differential equations. Connections between neurons are assigned in the simplest and most common way so as to fulfill basic requirements stemming from experimental findings concerning the directional tuning of individual neurons and the stabilization of the neuronal population vector, as well as from previous theoretical studies. The dynamical behavior of the model reveals a close similarity with the experimentally observed dynamics of the neuronal population vector. Specifically, in the framework of the model it is possible to describe a geometrical curve in terms of the time series of the population vector. A correlation between the dynamical behavior of the direction and the length of the population vector entails a dependence of the “neural velocity” on the curvature of the tracing trajectory that corresponds well to the experimentally measured covariation between tangential velocity and curvature in drawing tasks.

Modeling motor cortical operations by an attractor network of stochastic neurons

Understanding the neural computations performed by the motor cortex requires biologically plausible models that account for cell discharge patterns revealed by neurophysiological recordings. In the present study the motor cortical activity underlying movement generation is modeled as the dynamic evolution of a large fully recurrent network of stochastic spiking neurons with noise superimposed on the synaptic transmission. We show that neural representations of the learned movement trajectories can be stored in the connectivity matrix in such a way that, when activated, a particular trajectory evolves in time as a dynamic attractor of the system while individual neurons fire irregularly with large variability in their interspike intervals. Moreover, the encoding of trajectories as attractors ensures high stability of the ensemble dynamics in the presence of synaptic noise. In agreement with neurophysiological findings, the suggested model can provide a wide repertoire of specific motor behaviors, whereas the number of specialized cells and specific connections may be negligibly small if compared with the whole population engaged in trajectory retrieving. To examine the applicability of the model we study quantitatively the relationship between local geometrical and kinematic characteristics of the trajectories generated by the network. The relationship obtained as a result of simulations is close to the ‘2/3 power law’ established by psychophysical and neurophysiological studies.

A simulated actuator driven by motor cortical signals

One problem in motor control concerns the mechanism whereby the central nervous system translates the motor cortical command encoded in cell activity into a coordinated contraction of limb muscles to generate a desired motor output. This problem is closely related to the design of adaptive systems that transform neuronal signals chronically recorded from the motor cortex into the physiologically appropriate motor output of multijoint prosthetic limbs. In this study we demonstrated how this transformation can be carried out by an artificial neural network using as command signals the actual impulse activity obtained from recordings in the motor cortex of monkeys during the performance of a task that required the exertion of force in different directions. The network receives experimentally measured brain signals and recodes them into motor actions of a simulated actuator that mimics the primate arm. The actuator responds to the motor cortical commands with surprising fidelity, generating forces in close quantitative agreement with those exerted by trained monkeys, in both the temporal and spatial domains. Moreover, we show that the time-varying motor output may be controlled by the impulse activity of as few as 15 motor cortical cells. These results outline a potentially implementable computation scheme that utilizes raw neuronal signals to drive artificial mechanical systems.

Directional operations in the motor cortex modeled by a neural network of spiking neurons

A neural network with realistically modeled, spiking neurons is proposed to model ensemble operations of directionally tuned neurons in the motor cortex. The model reproduces well directional operations previously identified experimentally, including the prediction of the direction of an upcoming movement in reaching tasks and the rotation of the neuronal population vector in a directional transformation task.

Modeling of directional operations in the motor cortex: a noisy network of spiking neurons is trained to generate a neural-vector trajectory

Abstract A fully connected network of spiking neurons modeling motor cortical directional operations is presented and analyzed. The model allows for the basic biological requirements stemming from the results of experimental studies. The dynamical evolution of the networks output is interpreted as the sequential generation of neuronal population vectors representing the combined directional tendency of the ensemble. Adding these population vectors tip-to-tail yields the neural-vector trajectory that describes the upcoming movement trajectory. The key point of the model is that the intra-network interactions provide sustained dynamics, whereas external inputs are only required to initiate the population. The network is trained to generate neural-vector trajectories corresponding to basic types of two-dimensional movements (the network with specified connections can store one trajectory). A simple modification of the simulated annealing algorithm enables training of the network in the presence of noise. Training in the presence of noise yields robustness of the learned dynamical behaviors. Another key point of the model is that the directional preference of a single neuron is determined by the synaptic connections. Accordingly, individual preferred directions as well as tuning curves are not assigned, but emerge as the result of interactions inside the population. For trained networks, the spiking behavior of single neurons and correlations between different neurons as well as the global activity of the population are discussed in the light of experimental findings.

A neural network learns trajectory of motion from the least action principle

This paper considers the problem of training layered neural networks to generate sequences of states. Aiming at application for situations when an integral characteristic of the process is known rather than the specific sequence of states we put forward a method in which underlying general principle is used as a foundation for the learning procedure. To illustrate the ability of a network to learn a task and to generalize algorithm we consider an example where a network generates sequences of states referred to as trajectories of motion of a particle under an external field. Training is grounded on the employment of the least action principle. In the course of training at restricted sections of the path the network elaborates a recurrent rule for the trajectory generation. The rule proves to be equivalent to the correct equation of motion for the whole trajectory.