Effects of maximal sodium and potassium conductance on the stability of Hodgkin-Huxley model

Active fault tolerant deep brain stimulator for epilepsy using deep neural network

Millions of people around the world are affected by different kinds of epileptic seizures. A deep brain stimulator is now claimed to be one of the most promising tools to control severe epileptic seizures. The present study proposes Hodgkin-Huxley (HH) model-based Active Fault Tolerant Deep Brain Stimulator (AFTDBS) for brain neurons to suppress epileptic seizures against ion channel conductance variations using a Deep Neural Network (DNN). The AFTDBS contains the following three modules: (i) Detection of epileptic seizures using black box classifiers such as Support Vector Machine (SVM) and K-Nearest Neighbor (KNN), (ii) Prediction of ion channels conductance variations using Long Short-Term Memory (LSTM), and (iii) Development of Reconfigurable Deep Brain Stimulator (RDBS) to control epileptic spikes using Proportional Integral (PI) Controller and Model Predictive Controller (MPC). Initially, the synthetic data were collected from the HH model by varying ion channel conductance. Then, the seizure was classified into four groups namely, normal and epileptic due to variations in sodium ion-channel conductance, potassium ion-channel conductance, and both sodium and potassium ion-channel conductance. In the present work, current controlled deep brain stimulators were designed for epileptic suppression. Finally, the closed-loop performances and stability of the proposed control schemes were analyzed. The simulation results demonstrated the efficacy of the proposed DNN-based AFTDBS.

HH model based smart deep brain stimulator to detect, predict and control epilepsy using machine learning algorithm

BACKGROUND

Epilepsy is the most common neurological disorder in the world. To control epilepsy, deep brain stimulation is one of the widely accepted treatment techniques. However, conventional deep brain stimulation technique provides continuous stimulation without optimizing the stimulation parameters, resulting in adverse side effects and unexpected death. Hence, understanding the dynamic behavior of brain neural networks at a cellular level is required for patient-specific epilepsy treatment. Considering the underlying mechanism of a single neuronal shift in the brain neural network, computational model-based techniques have a new face for healthcare, which aims to develop effective medical devices for preclinical investigations.

NEW METHOD

This paper discusses the design of a Smart Deep Brain Stimulator (SDBS) using the Hodgkin-Huxley (HH) conductance-based cellular model of brain neurons to automatically detect, predict and regulate epilepsy against patient-specific conditions. Epileptic activity is simulated as a spike train of action potential due to sodium and potassium channel conductance variations in the single-neuron HH model. The proposed SDBS consists of three components:- i) seizure detection using bagging and boosting-based ensemble machine learning classifiers, ii) channel conductance prediction using Long Short Term Memory-Recurrent Neural Network (LSTM-RNN) based Deep Neural Network (DNN) for updating model parameters of brain neuron, and iii) model-based intelligent control of epileptic seizure with Nonlinear Autoregressive Moving Average-L2 (NARMA-L2) Controller and Nonlinear Model Predictive Controller (NMPC).

RESULTS

For effective treatment, improving the overall accuracy and efficiency of SDBS is essential. For epilepsy detection, the ensemble bagging machine learning algorithm provides better accuracy of 92.7% compared to the ensemble boosting algorithm. LSTM-RNN deep neural network model with four layers predicts the variations in channel conductance with Root Mean Square Error (RMSE) of 0.00568 and 0.009081 for sodium and potassium channel conductance, respectively. From the closed-loop performances of SDBS with an intelligent control scheme, it is observed that SDBS with NMPC provides efficient and accurate stimulation with minimum energy consumption. From a stability point of view, SDBS with NMPC provides better stability than SDBS with NARMA-L2 Controller.

COMPARISON WITH EXISTING METHOD

The proposed SDBS is designed to generate accurate stimulation pulses for epilepsy patients with specific conditions depending on the neuronal activity of a single neuron. Moreover, it will also adapt to the dynamic condition of epilepsy patients. The existing deep brain stimulator continuously provides stimulation pulses without adapting to the patient's conditions.

CONCLUSION

The proposed SDBS could provide patient-specific treatment based on sodium/potassium channel conductance variations of brain neurons. It will help increase the use of deep brain stimulation techniques and reduce sudden death. Furthermore, the proposed technique will be extended to neural network models with larger neuronal populations to improve the practical feasibility.

Selective neural stimulation by leveraging electrophysiological differentiation and using pre-pulsing and non-rectangular waveforms

Efforts on selective neural stimulation have concentrated on segregating axons based on their size and geometry. Nonetheless, axons of the white matter or peripheral nerves may also differ in their electrophysiological properties. The primary objective of this study was to investigate the possibility of selective activation of axons by leveraging an assumed level of diversity in passive (C_m & G_leak) and active membrane properties (K_temp & G_namax). First, the stimulus waveforms with hyperpolarizing (HPP) and depolarizing pre-pulsing (DPP) were tested on selectivity in a local membrane model. The default value of membrane capacitance (C_m) was found to play a critical role in sensitivity of the chronaxie time (Chr) and rheobase (Rhe) to variations of all the four membrane parameters. Decreasing the default value of C_m, and thus the passive time constant of the membrane, amplified the sensitivity to the active parameters, K_temp and G_Namax, on Chr. The HPP waveform could selectively activate neurons even if they were diversified by membrane leakage (G_leak) only, and produced higher selectivity than DPP when parameters are varied in pairs. Selectivity measures were larger when the passive parameters (C_m & G_leak) were varied together, compared to the active parameters. Second, this novel mechanism of selectivity was investigated with non-rectangular waveforms for the stimulating phase (and HPP) in the same local membrane model. Simulation results suggest that Kt² is the most selective waveform followed by Linear and Gaussian waveforms. Traditional rectangular pulse was among the least selective of all. Finally, a compartmental axon model confirmed the main findings of the local model that Kt² is the most selective, but rank ordered the other waveforms differently. These results suggest a potentially novel mechanism of stimulation selectivity, leveraging electrophysiological variations in membrane properties, that can lead to various neural prosthetic applications.

A Potential Mechanism of Sodium Channel Mediating the General Anesthesia Induced by Propofol

General anesthesia has revolutionized healthcare over the past 200 years and continues to show advancements. However, many phenomena induced by general anesthetics including paradoxical excitation are still poorly understood. Voltage-gated sodium channels (Na_V) were believed to be one of the proteins targeted during general anesthesia. Based on electrophysiological measurements before and after propofol treatments of different concentrations, we mathematically modified the Hodgkin–Huxley sodium channel formulations and constructed a thalamocortical model to investigate the potential roles of Na_V. The ion channels of individual neurons were modeled using the Hodgkin–Huxley type equations. The enhancement of propofol-induced GABAa current was simulated by increasing the maximal conductance and the time-constant of decay. Electroencephalogram (EEG) was evaluated as the post-synaptic potential from pyramidal (PY) cells. We found that a left shift in activation of Na_V was induced primarily by a low concentration of propofol (0.3–10 μM), while a left shift in inactivation of Na_V was induced by an increasing concentration (0.3–30 μM). Mathematical simulation indicated that a left shift of Na_V activation produced a Hopf bifurcation, leading to cell oscillations. Left shift of Na_V activation around a value of 5.5 mV in the thalamocortical models suppressed normal bursting of thalamocortical (TC) cells by triggering its chaotic oscillations. This led to irregular spiking of PY cells and an increased frequency in EEG readings. This observation suggests a mechanism leading to paradoxical excitation during general anesthesia. While a left shift in inactivation led to light hyperpolarization in individual cells, it inhibited the activity of the thalamocortical model after a certain depth of anesthesia. This finding implies that high doses of propofol inhibit the network partly by accelerating Na_V toward inactivation. Additionally, this result explains why the application of sodium channel blockers decreases the requirement for general anesthetics. Our study provides an insight into the roles that Na_V plays in the mechanism of general anesthesia. Since the activation and inactivation of Na_V are structurally independent, it should be possible to avoid side effects by state-dependent binding to the Na_V to achieve precision medicine in the future.

Interaction of the Mechano-Electrical Feedback With Passive Mechanical Models on a 3D Rat Left Ventricle: A Computational Study

In this paper, we are investigating the interaction between different passive material models and the mechano-electrical feedback (MEF) in cardiac modeling. Various types of passive mechanical laws (nearly incompressible/compressible, polynomial/exponential-type, transversally isotropic/orthotropic material models) are integrated in a fully coupled electromechanical model in order to study their specific influence on the overall MEF behavior. Our computational model is based on a three-dimensional (3D) geometry of a healthy rat left ventricle reconstructed from magnetic resonance imaging (MRI). The electromechanically coupled problem is solved using a fully implicit finite element-based approach. The effects of different passive material models on the MEF are studied with the help of numerical examples. It turns out that there is a significant difference between the behavior of the MEF for compressible and incompressible material models. Numerical results for the incompressible models exhibit that a change in the electrophysiology can be observed such that the transmembrane potential (TP) is unable to reach the resting state in the repolarization phase, and this leads to non-zero relaxation deformations. The most significant and strongest effects of the MEF on the rat cardiac muscle response are observed for the exponential passive material law.

Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathology

A proposed model consisting of two coupled models (Hodgkin-Huxley and Yanagihara-Noma-Irisawa model) is considered as a description of the heart's action potential. System of ordinary differential equations is used to recreate pathological behaviour in the conducting heart's system such as double fire and the most common tachycardia: atrioventricular nodal reentrant tachycardia (AVNRT). Part of the population has an abnormal accessory pathways: fast and slow (Fujiki, 2008). These pathways in the atrioventricular node (AV node) are anatomical and functional contributions of supraventricular tachycardia. However, the appearance of two pathways in the AV node may be a contribution of arrhythmia, which is caused by coexistent conduction by two pathways (called double fire). The difference in the conduction time between these pathways is the most important factor. This is the reason to introduce three types of couplings and delay to our system in order to reproduce various types of the AVNRT. In our research, introducing the feedback loops and couplings entails the creation of waves which can correspond to the re-entry waves occurring in the AVNRT. Our main aim is to study solutions of the given equations and take into consideration the influence of feedback and delays which occur in these pathological modes. We also present stability analysis for both components, that is Hodgkin-Huxley and Yanagihara-Noma-Irisawa models, as well as for the final double-fire model.