Memristive Neural Networks for Predicting Seizure Activity.

The aim of the study is to assess the possibilities of predicting epileptiform activity using the neuronal activity data recorded from the hippocampus and medial entorhinal cortex of mice with chronic epileptiform activity. To reach this goal, a deep artificial neural network (ANN) has been developed and its implementation based on memristive devices has been demonstrated. Materials and Methods: The biological part of the investigation. Young healthy outbred CD1 mice were used in our study. They were divided into two groups: control (n=6) and the group with induced chronic epileptiform activity (n=6). Local field potentials (LFP) were recorded from the hippocampus and medial entorhinal cortex of the mice of both groups to register neuronal activity. The LFP recordings were used for deep ANN training. Epileptiform activity in mice was modeled by intraperitoneal injection of pilocarpine (280 mg/kg). LFP were recorded in the awake mice a month after the induction of epileptiform activity.Mathematical part of the investigation. A deep long short-term memory (LSTM) ANN capable of predicting biological signals of neuronal activity in mice has been developed. The ANN implementation is based on memristive devices, which are described by the equations of the redox processes running in the memristive thin metal-oxide-metal films, e.g., Au/ZrO2(Y)/TiN/Ti and Au/SiO2(Y)/TiN/Ti. In order to train the developed ANN to predict epileptiform activity, a supervised learning algorithm was used, which allowed us to adjust the network parameters and train LSTM on the described recordings of neuronal activity. Results: After training on the LFP recordings from the hippocampus and medial entorhinal cortex of the mice with chronic epileptiform activity, the proposed deep ANN has demonstrated high values of evaluation metric (root-mean-square error, RMSE) and successfully predicted epileptiform activity shortly before its occurrence (40 ms). The results of the numerical experiments have shown that the RMSE value of 0.019 was reached, which indicates the efficacy of proposed approach. The accuracy of epileptiform activity prediction 40 ms before its occurrence is a significant result and shows the potential of the developed neural network architecture. Conclusion: The proposed deep ANN can be used to predict pathological neuronal activity including epileptic seizure (focal) activity in mice before its actual occurrence. Besides, it can be applied for building a long-term prognosis of the disease course based on the LFP data. Thus, the proposed ANN based on memristive devices represents a novel approach to the prediction and analysis of pathological neuronal activity possessing a potential for improving the diagnosis and prognostication of epileptic seizures and other diseases associated with neuronal activity.

Bifurcation analysis of multistability of synchronous states in the system of two delay-coupled oscillators.

Systems of mutually coupled oscillators with delay coupling are of great interest for various applications in electronics, laser physics, biophysics, etc. Time delay usually originates from the finite speed of propagation of the coupling signal. In this paper, we present the results of detailed bifurcation analysis of two delay-coupled limit-cycle (Landau-Stuart) oscillators. First, we study the simplified case when the delay time is much smaller than the oscillation build-up time. When the coupling signal propagates between the two counterparts, it acquires a phase shift, which strongly affects the synchronization pattern. Depending on this phase shift, the system may demonstrate the behavior typical for either dissipative or conservative (reactive) coupling. We examine stability of the in-phase and anti-phase synchronous states and reveal the complicated pattern of the synchronization domains on the frequency mismatch-coupling strength parameter plane paying a special attention to the mechanisms of appearance and disappearance of the phase multistability. We demonstrate that taking into account reactive phase nonlinearity the coupling signal acquires an additional phase shift, which depends on the signal intensity. We also examine the more complicated case of finite delay time. The increase of the reactive nonlinearity parameter and the delay time leads to transformations of synchronization domains similar to those that occur when the phase shift increases. For the bifurcation analysis, we employ XPPAUT and DDEBifTool package and verify the results by direct numerical integration.