Brain-computer interfaces (BCIs) are an emerging technology that are capable of turning brain electrical activity into commands for an external device. Motor imagery (MI)—when a person imagines a motion without executing it—is widely employed in BCI devices for motor control because of the endogenous origin of its neural control mechanisms, and the similarity in brain activation to actual movements. Challenges with translating a MI-BCI into a practical device used outside laboratories include the extensive training required, often due to poor user engagement and visual feedback response delays; poor user flexibility/freedom to time the execution/inhibition of their movements, and to control the movement type (right arm vs. left leg) and characteristics (reaching vs. grabbing); and high false positive rates of motion control. Solutions to improve sensorimotor activation and user performance of MI-BCIs have been explored. Virtual reality (VR) motor-execution tasks have replaced simpler visual feedback (smiling faces, arrows) and have solved this problem to an extent. Hybrid BCIs (hBCIs) implementing an additional control signal to MI have improved user control capabilities to a limited extent. These hBCIs either fail to allow the patients to gain asynchronous control of their movements, or have a high false positive rate. We propose an immersive VR environment which provides visual feedback that is both engaging and immediate, but also uniquely engages a different cognitive process in the patient that generates event-related potentials (ERPs). These ERPs provide a key executive function for the users to execute/inhibit movements. Additionally, we propose signal processing strategies and machine learning algorithms to move BCIs toward developing long-term signal stability in patients with distinctive brain signals and capabilities to control motor signals. The hBCI itself and the VR environment we propose would help to move BCI technology outside laboratory environments for motor rehabilitation in hospitals, and potentially for controlling a prosthetic.
Hebbian theory proposes that ensembles of neurons form a basis for neural processing. It is possible to gain insight into the activity patterns of these neural ensembles through a binary analysis, regarding neurons as either active or inactive. The framework of permitted and forbidden sets, introduced by Hahnloser, Seung, and Slotine (2003), is a mathematical model of such a binary analysis: groups of coactive neurons can be permitted or forbidden depending on the network's structure. In order to widen the applicability of the framework of permitted sets, we extend the permitted set analysis from the original threshold-linear regime. Specifically, we generalize permitted sets to firing rate models in which Φ is a nonnegative continuous piecewise C1 activation function. In our framework, the focus is shifted from a neuron's firing rate to its responsiveness to inputs; if a neuron's firing rate is sufficiently sensitive to changes in its input, we say that the neuron is responsive. The algorithm for categorizing a neuron as responsive depends on thresholds that a user can select arbitrarily and that are independent of the dynamics. Given a synaptic weight matrix W, we say that a set of neurons is permitted if it is possible to find a stimulus where those neurons, and no others, remain responsive. The main coding property we establish about PΦ(W), the collection of all permitted sets of the network, is that PΦ(W) is a convex code when W is almost rank one. This means that PΦ(W) in the low-rank regime can be realized as a neural code resulting from the pattern of overlaps of receptive fields that are convex.
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