A model of feedback control for the charge-balanced suppression of epileptic seizures

Patient-Specific Network Connectivity Combined With a Next Generation Neural Mass Model to Test Clinical Hypothesis of Seizure Propagation

Dynamics underlying epileptic seizures span multiple scales in space and time, therefore, understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. In this view, mathematical models have been developed, ranging from single neuron to neural population. In this study, we consider a neural mass model able to exactly reproduce the dynamics of heterogeneous spiking neural networks. We combine mathematical modeling with structural information from non invasive brain imaging, thus building large-scale brain network models to explore emergent dynamics and test the clinical hypothesis. We provide a comprehensive study on the effect of external drives on neuronal networks exhibiting multistability, in order to investigate the role played by the neuroanatomical connectivity matrices in shaping the emergent dynamics. In particular, we systematically investigate the conditions under which the network displays a transition from a low activity regime to a high activity state, which we identify with a seizure-like event. This approach allows us to study the biophysical parameters and variables leading to multiple recruitment events at the network level. We further exploit topological network measures in order to explain the differences and the analogies among the subjects and their brain regions, in showing recruitment events at different parameter values. We demonstrate, along with the example of diffusion-weighted magnetic resonance imaging (dMRI) connectomes of 20 healthy subjects and 15 epileptic patients, that individual variations in structural connectivity, when linked with mathematical dynamic models, have the capacity to explain changes in spatiotemporal organization of brain dynamics, as observed in network-based brain disorders. In particular, for epileptic patients, by means of the integration of the clinical hypotheses on the epileptogenic zone (EZ), i.e., the local network where highly synchronous seizures originate, we have identified the sequence of recruitment events and discussed their links with the topological properties of the specific connectomes. The predictions made on the basis of the implemented set of exact mean-field equations turn out to be in line with the clinical pre-surgical evaluation on recruited secondary networks.

Epilepsy control using a fixed time integral super twisting sliding mode control for Pinsky-Rinzel pyramidal model through ion channels with optogenetic method

BACKGROUND AND OBJECTIVE

Epilepsy is a dynamic disease of neuronal networks and epileptic activity in the brain should be suppressed quickly in the shortest possible time with minimum control signal. Thus, a closed-loop feedback control by using the fixed-time integral super-twisting sliding-mode controller via an optogenetic method is employed for suppressing seizures in the Pinsky-Rinzel (PR) model as a dynamic model of the hippocampus CA3 region where epileptic seizures occur. The control signal is applied to the PR model through the ChR2 channel model in the form of light photons using the optogenetic method. The present study aimed to determine the controller robustness against parameter changes and disturbances in order to reduce the control time, approach the zero tracking error of the normal desired state in a fixed time, and finally, converge the epileptic state to the normal desired state.

METHOD

In order to apply the control signal to the Pinsky-Rinzel model in the optogenetic method, the dynamic model of the ion current generated by channelrhodopsin 2 (ChR2) as a light-sensitive protein model in the optogenetic method was first applied to the PR model. Then, a fixed-time integral super-twisting sliding-mode controller was designed for the system, which is the combination of PR and ChR2 models.

RESULTS

After applying the proposed controller, the simulation results indicated that the control signal was -0.7 mV, the tracking error of the normal desired state could reach zero within 1.5 milliseconds, and the problems of singularity and chattering were solved.

CONCLUSIONS

A reduction occurred in the control signal reduced regarding the objectives of the study and comparing the proposed controller with the classical sliding-mode controller. Thus, this method can produce a safe control input for brain. In addition, both types of sliding mode controllers are robust against the parameters variations and external disturbances. Thus, they are superior to non-robust and simple controllers. Finally, based on the results, the validity of the fixed-time integral super-twisting sliding mode controller is confirmed for epilepsy control.

Model-based robust suppression of epileptic seizures without sensory measurements

Uncontrolled seizures may lead to irreversible damages in the brain and various limitations in the patient's life. There exist experimental studies to stabilize the patient seizures. However, the experimental setups have many sensory devices to measure the dynamics of the brain cortex. These equipments prevent to produce small portable stabilizers for patients in everyday life. Recently, a comprehensive cortex model is introduced to apply model-based observers and controllers. However, this cortex model can be uncertain and have time-varying parameters. Therefore, in this paper, a robust Takagi-Sugeno (TS) controller and observer are designed to suppress the epileptic seizures without sensory measurements. The unavailable sensory measurements are provided by the designed nonlinear observer. The exponential convergence of the observer and controller is satisfied by the feedback parameter design using linear matrix inequalities. In addition, TS fuzzy observer-controller design has been compared with the conventional PID method in terms of control performance and design problem. The numerical computations show that the epileptic seizures are more effectively suppressed by the TS fuzzy observer-based controller under uncertain membrane potential dynamics.

Suppression of epileptic seizures via Anderson localization

Here we show that brain seizures can be effectively suppressed through random modulation of the brain medium. We use an established mesoscale cortical model in the form of a system of coupled stochastic partial differential equations. We show that by temporal and spatial randomization of parameters governing the firing rates of the excitatory and inhibitory neuron populations, seizure waves can be significantly suppressed. We find that the attenuation is the most effective when applied to the mean threshold potential. The proposed technique can serve as a non-invasive paradigm to mitigate epileptic seizures without knowing the location of the epileptic foci.

Suppressing epileptic activity in a neural mass model using a closed-loop proportional-integral controller

Closed-loop control is a promising deep brain stimulation (DBS) strategy that could be used to suppress high-amplitude epileptic activity. However, there are currently no analytical approaches to determine the stimulation parameters for effective and safe treatment protocols. Proportional-integral (PI) control is the most extensively used closed-loop control scheme in the field of control engineering because of its simple implementation and perfect performance. In this study, we took Jansen's neural mass model (NMM) as a test bed to develop a PI-type closed-loop controller for suppressing epileptic activity. A graphical stability analysis method was employed to determine the stabilizing region of the PI controller in the control parameter space, which provided a theoretical guideline for the choice of the PI control parameters. Furthermore, we established the relationship between the parameters of the PI controller and the parameters of the NMM in the form of a stabilizing region, which provided insights into the mechanisms that may suppress epileptic activity in the NMM. The simulation results demonstrated the validity and effectiveness of the proposed closed-loop PI control scheme.

Closed-loop feedback control and bifurcation analysis of epileptiform activity via optogenetic stimulation in a mathematical model of human cortex

Optogenetics provides a method of neuron stimulation that has high spatial, temporal, and cell-type specificity. Here we present a model of optogenetic feedback control that targets the inhibitory population, which expresses light-sensitive channelrhodopsin-2 channels, in a mean-field model of undifferentiated cortex that is driven to seizures. The inhibitory population is illuminated with an intensity that is a function of electrode measurements obtained via the cortical model. We test the efficacy of this control method on seizurelike activity observed in two parameter spaces of the cortical model that most closely correspond to seizures observed in patients. We also compare the effect of closed-loop and open-loop control on seizurelike activity using a less-complicated ordinary differential equation model of the undifferentiated cortex in parameter space. Seizurelike activity is successfully suppressed in both parameter planes using optimal illumination intensities less likely to have adverse effects on cortical tissue.

A probabilistic framework for a physiological representation of dynamically evolving sleep state

This work presents a probabilistic method for mapping human sleep electroencephalogram (EEG) signals onto a state space based on a biologically plausible mathematical model of the cortex. From a noninvasive EEG signal, this method produces physiologically meaningful pathways of the cortical state over a night of sleep. We propose ways in which these pathways offer insights into sleep-related conditions, functions, and complex pathologies. To address explicitly the noisiness of the EEG signal and the stochastic nature of the mathematical model, we use a probabilistic Bayesian framework to map each EEG epoch to a distribution of likelihoods over all model sleep states. We show that the mapping produced from human data robustly separates rapid eye movement sleep (REM) from slow wave sleep (SWS). A Hidden Markov Model (HMM) is incorporated to improve the path results using the prior knowledge that cortical physiology has temporal continuity.

Open loop optogenetic control of simulated cortical epileptiform activity

We present a model for the use of open loop optogenetic control to inhibit epileptiform activity in a meso scale model of the human cortex. The meso scale cortical model first developed by Liley et al. (2001) is extended to two dimensions and the nature of the seizure waves is studied. We adapt to the meso scale a 4 state functional model of Channelrhodopsin-2 (ChR2) ion channels. The effects of pulsed and constant illumination on the conductance of these ion channels is presented. The inhibitory cell population is targeted for the application of open loop control. Seizure waves are successfully suppressed and the inherent properties of the optogenetic channels ensures charge balance in the cortex, protecting it from damage.

A continuous mapping of sleep states through association of EEG with a mesoscale cortical model

Here we show that a mathematical model of the human sleep cycle can be used to obtain a detailed description of electroencephalogram (EEG) sleep stages, and we discuss how this analysis may aid in the prediction and prevention of seizures during sleep. The association between EEG data and the cortical model is found via locally linear embedding (LLE), a method of dimensionality reduction. We first show that LLE can distinguish between traditional sleep stages when applied to EEG data. It reliably separates REM and non-REM sleep and maps the EEG data to a low-dimensional output space where the sleep state changes smoothly over time. We also incorporate the concept of strongly connected components and use this as a method of automatic outlier rejection for EEG data. Then, by using LLE on a hybrid data set containing both sleep EEG and signals generated from the mesoscale cortical model, we quantify the relationship between the data and the mathematical model. This enables us to take any sample of sleep EEG data and associate it with a position among the continuous range of sleep states provided by the model; we can thus infer a trajectory of states as the subject sleeps. Lastly, we show that this method gives consistent results for various subjects over a full night of sleep and can be done in real time.