A simulator for the analysis of neuronal ensemble activity: application to reaching tasks
Introduction
The ability to study how the brain maps arrays of sensory inputs into a set of motor actions requires the analyses of the functional interactions of large and distributed populations of cortical and sub-cortical neurons. A central paradigm for studying these interactions is chronic, multi-site, neural ensemble recordings in behaving animals. One limitation of this technique, however, is that measurements are only possible at a limited number of sites. At present, it is not clear what information, if any, is lost due to sub-sampling and whether more optimal strategies for decoding the ensemble activity are possible. To assist in the interpretation of multi-site, spatiotemporal cortical ensemble patterns, we have developed a scalable, biologically based, multi-cortical model of reaching tasks whose output of neuronal spike trains can be directly related to recordings.
To make the model relevant to the problem of interest, several criteria were established. First, the model must be capable of learning three-dimensional reaching tasks through the movement of a virtual, multi-jointed arm with mass, damping, and spring constants. Second, the individual neurons within the model should have dynamics which are biologically based and be capable of generating noisy, spike train data. Next, the neurons should be assembled into a number of cortical areas that are large enough to study the effects of sampling (>1000). Finally, the neurons within the cortical areas should be connected by synapses with long-term dynamics amenable to learning that is not cortical specific.
In this paper, we present a preliminary model of a multi-cortical model of three-dimensional reaching tasks. The simulations demonstrate that the model, without pre-tuned neurons, learns to move a simple arm to a number of arbitrary targets within a three-dimensional space. The model is used to test the hypothesis that the ensemble spike train activity encodes the parameters of the arm model and that the individual neuronal responses are sensitive to the arm kinematics. The simulations also show that the ensemble activity reveals functional clustering after learning and that the spike trains can be used to predict arm movement directly.
Section snippets
Methods
The model consists of four cortical areas; association, motor, somatosensory, and visual, connected by both feed-forward and feedback connections. Feedback from the visual cortical area is used by the association cortical area to generate movement commands while feedback from the somatosensory cortical area is used by the motor cortical area to condition these movement commands. The output of the motor cortical is coupled to a muscle model to generate actual movement (Fig. 1).
The motor and
Results
To investigate ensemble activity during reaching, both a two-dimensional (2D) model and a three-dimensional (3D) models were developed. The 2D model uses five neurons in both the motor and somatosensory cortical areas while the 3D model uses 17 neurons in these areas. To train both models, the end of the arm is positioned at the origin and targets are presented to the model limited to the first quadrant. The pre-synaptic weights are initialized to random numbers which represent either
Discussion
The simulations presented here demonstrate that the multi-cortical model, without pre-tuned neurons, can learn to move a simple arm to a number of arbitrary targets within a three-dimensional space. The output of each neuron is a spike train which can be subsequently analyzed using existing algorithms. Although the model is a clear simplification it nevertheless demonstrates many behaviors that are consistent with those seen experimentally. First, the model is able to learn the task and can
Conclusion
We have developed a biologically based, multi-cortical model that uses neuronal ensembles to accomplish a reaching task. Our results show that even for a small network, the neurons exhibit directional tuning that is sensitive to changes in the arm model. The model also produces spike train outputs that can be analyzed using a variety of multivariate tools. xICA of randomized ensemble output was shown to identify the functional clusters within cortical areas. Such clustering was not identified
Acknowledgements
This work was supported by NSF grant IBN-99-80043 and a grant of computer resources from the North Carolina Supercomputing Center.
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Present address: The John B. Pierce Laboratory and Department of Neurobiology, Yale School of Medicine, New Haven, CT 06519, USA.