Detection and Control of Epileptiform Regime in the Hodgkin–Huxley Artificial Neural Networks via Quantum Algorithms

The problem of detection and the following suppression of epileptiform dynamics in artificial neural networks (ANN) still is a hot topic in modern theoretical and applied neuroscience. For the purpose of such modeling, the Hodgkin–Huxley (HH) elements are important due to the variety of their behavior such as resting, singular spikes, and spike trains and bursts. This dynamical spectrum of individual HH neurons can cause an epileptiform regime originated in the hyper-synchronization of the cell outcomes. Our model covers the detection and suppression of ictal behavior in a small ANN consisting of HH cells. The model follows our approach [Borisenok et al., 2018] for the HH neurons as a classical dynamical system driving the collective neural bursting, but here we use a quantum paradigm-based algorithm emulated with the pair of HH neurons. Such emulation becomes possible due to the complexity of the individual 4d HH dynamics. The linear chain of two HH neurons is connected to the rest of ANN and works autonomously. The first neuron plays a role of the detecting element for the hyper-synchronization in the ANN and the quantum algorithm emulator; while the second one works as a measuring element (emulation of the quantum measurement converting the signals into the classical domain) and the trigger for the feedback suppressing the epileptiform regime. We use here the speed gradient algorithm for controling the emulating neuron and discuss its pros and cons to compare with our classical model of epileptiform suppression.