UKF-based closed loop iterative learning control of epileptiform wave in a neural mass model

Adaptive fuzzy iterative learning control based neurostimulation system and in-silico evaluation

Closed-loop neural stimulation has been an effective treatment for epilepsy patients. Currently, most closed-loop neural stimulation strategies are designed based on accurate neural models. However, the uncertainty and complexity of the neural system make it difficult to build an accurate neural model, which poses a significant challenge to the design of the controller. This paper proposes an Adaptive Fuzzy Iterative Learning Control (AFILC) framework for closed-loop neural stimulation, which can realize neuromodulation with no model or model uncertainty. Recognizing the periodic characteristics of neural stimulation and neuronal firing, Iterative Learning Control (ILC) is employed as the primary controller. Furthermore, a fuzzy optimization module is established to update the internal parameters of the ILC controller in real-time. This module enhances the anti-interference ability of the control system and reduces the influence of initial controller parameters on the control process. The efficacy of this strategy is evaluated using a neural computational model. The simulation results validate the capability of the AFILC strategy to suppress epileptic states. Compared with ILC-based closed-loop neurostimulation schemes, the AFILC-based neurostimulation strategy has faster convergence speed and stronger anti-interference ability. Moreover, the control algorithm is implemented based on a digital signal processor, and the hardware-in-the-loop experimental platform is implemented. The experimental results show that the control method has good control performance and computational efficiency, which provides the possibility for future application in clinical research.

Exploration of interictal to ictal transition in epileptic seizures using a neural mass model

An epileptic seizure can usually be divided into three stages: interictal, preictal, and ictal. However, the seizure underlying the transition from interictal to ictal activities in the brain involves complex interactions between inhibition and excitation in groups of neurons. To explore this mechanism at the level of a single population, this paper employed a neural mass model, named the complete physiology-based model (cPBM), to reconstruct electroencephalographic (EEG) signals and to infer the changes in excitatory/inhibitory connections related to excitation-inhibition (E-I) balance based on an open dataset recorded for ten epileptic patients. Since epileptic signals display spectral characteristics, spectral dynamic causal modelling (DCM) was applied to quantify these frequency characteristics by maximizing the free energy in the framework of power spectral density (PSD) and estimating the cPBM parameters. In addition, to address the local maximum problem that DCM may suffer from, a hybrid deterministic DCM (H-DCM) approach was proposed, with a deterministic annealing-based scheme applied in two directions. The H-DCM approach adjusts the temperature introduced in the objective function by gradually decreasing the temperature to obtain relatively good initialization and then gradually increasing the temperature to search for a better estimation after each maximization. The results showed that (i) reconstructed EEG signals belonging to the three stages together with their PSDs can be reproduced from the estimated parameters of the cPBM; (ii) compared to DCM, traditional D-DCM and anti D-DCM, the proposed H-DCM shows higher free energies and lower root mean square error (RMSE), and it provides the best performance for all stages (e.g., the RMSEs between the reconstructed PSD computed from the reconstructed EEG signal and the sample PSD obtained from the real EEG signal are 0.33 ± 0.08, 0.67 ± 0.37 and 0.78 ± 0.57 in the interictal, preictal and ictal stages, respectively); and (iii) the transition from interictal to ictal activity can be explained by an increase in the connections between pyramidal cells and excitatory interneurons and between pyramidal cells and fast inhibitory interneurons, as well as a decrease in the self-loop connection of the fast inhibitory interneurons in the cPBM. Moreover, the E-I balance, defined as the ratio between the excitatory connection from pyramidal cells to fast inhibitory interneurons and the inhibitory connection with the self-loop of fast inhibitory interneurons, is also significantly increased during the epileptic seizure transition.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-023-09976-6.

Design of Closed-Loop Control Schemes Based on the GA-PID and GA-RBF-PID Algorithms for Brain Dynamic Modulation

Neurostimulation can be used to modulate brain dynamics of patients with neuropsychiatric disorders to make abnormal neural oscillations restore to normal. The control schemes proposed on the bases of neural computational models can predict the mechanism of neural oscillations induced by neurostimulation, and then make clinical decisions that are suitable for the patient's condition to ensure better treatment outcomes. The present work proposes two closed-loop control schemes based on the improved incremental proportional integral derivative (PID) algorithms to modulate brain dynamics simulated by Wendling-type coupled neural mass models. The introduction of the genetic algorithm (GA) in traditional incremental PID algorithm aims to overcome the disadvantage that the selection of control parameters depends on the designer's experience, so as to ensure control accuracy. The introduction of the radial basis function (RBF) neural network aims to improve the dynamic performance and stability of the control scheme by adaptively adjusting control parameters. The simulation results show the high accuracy of the closed-loop control schemes based on GA-PID and GA-RBF-PID algorithms for modulation of brain dynamics, and also confirm the superiority of the scheme based on the GA-RBF-PID algorithm in terms of the dynamic performance and stability. This research of making hypotheses and predictions according to model data is expected to improve and perfect the equipment of early intervention and rehabilitation treatment for neuropsychiatric disorders in the biomedical engineering field.

Closed-loop seizure modulation via extreme learning machine based extended state observer

Neuromodulation is a promising way in clinical treatment of epilepsy, but the existing methods cannot adjust stimulations according to patients' real-time reactions. Therefore, it is necessary to acquire a systematic and a scientific regulation method based on patients' real-time reactions. The linear active disturbance rejection control can adapt to complex epileptic dynamics and improve the epilepsy regulation, even if little model information is available, and various uncertainties and external disturbances exist. However, a linear extended state observer estimates the time-varying total disturbance with a steady-state error. To improve regulation, it is crucial to estimate the total disturbance in a more accurate manner. An extreme learning machine is capable of approximating any nonlinear function. Its initial parameter generation is more convenient, adjustable parameters are fewer, and learning speed is faster. Thus, a nonlinear time-varying function can be estimated more timely and accurately. Then, an extreme learning machine based extended state observer is proposed to get a more satisfactory total disturbance estimation and more desired closed-loop regulation. The convergence of the extreme learning machine based extended state observer is verified and the stability of the closed-loop system is analyzed. Numerical results show that the proposed extended state observer is much better than a linear extended state observer in estimating the total disturbance. It guarantees a more satisfied closed-loop neuromodulation.

Burster Reconstruction Considering Unmeasurable Variables in the Epileptor Model

Epilepsy is one of the most common brain disorders worldwide, affecting millions of people every year. Although significant effort has been put into better understanding it and mitigating its effects, the conventional treatments are not fully effective. Advances in computational neuroscience, using mathematical dynamic models that represent brain activities at different scales, have enabled addressing epilepsy from a more theoretical standpoint. In particular, the recently proposed Epileptor model stands out among these models, because it represents well the main features of seizures, and the results from its simulations have been consistent with experimental observations. In addition, there has been an increasing interest in designing control techniques for Epileptor that might lead to possible realistic feedback controllers in the future. However, such approaches rely on knowing all of the states of the model, which is not the case in practice. The work explored in this letter aims to develop a state observer to estimate Epileptor's unmeasurable variables, as well as reconstruct the respective so-called bursters. Furthermore, an alternative modeling is presented for enhancing the convergence speed of an observer. The results show that the proposed approach is efficient under two main conditions: when the brain is undergoing a seizure and when a transition from the healthy to the epileptiform activity occurs.

On disturbance rejection control of the epileptiform spikes

Epilepsy is a neurological disorder resulting from a sudden development of synchronous firing in a massive group of neurons. For the particularity of the epilepsy, a neural mass model (NMM) is commonly utilized to understand and simulate the mechanism and evolution of the epilepsy. In this paper, based on a multi-coupling NMM and real EEGs of an epileptic mouse, a computational epileptic model is established to simulate the abnormal discharges of a mouse during seizures. Thus, rather than make animal experiments directly, numerical tests can be performed first. It reduces risks and helps improve the closed-loop neuromodulation. In addition, considering that no epileptic model can be utilized for neuromodulation in clinic, and even if a model exists, it still cannot describe the dynamics of the epilepsy faithfully, a scalable observer bandwidth and phase leading active disturbance rejection control (SOB-PLADRC) is proposed. Accordingly, a timelier and more accurate total disturbance estimation can be obtained by a scalable observer bandwidth and phase leading extended state observer, and an expected closed-loop neuromodulation can be realized without an accurate epileptic model. Numerical simulations based on the established model also show that the SOB-PLADRC suppresses seizures best among the PI and other active disturbance rejection approaches. More powerful disturbance rejection ability and more satisfactory closed-loop neuromodulation make the SOB-PLADRC more promising in the seizure control.

An Efficient Approach to Define the Input Stimuli to Suppress Epileptic Seizures Described by the Epileptor Model

Epilepsy affects about 70 million people in the world. Every year, approximately 2.4 million people are diagnosed with epilepsy, two-thirds of them will not know the etiology of their disease, and 1% of these individuals will decease as a consequence of it. Due to the inherent complexity of predicting and explaining it, the mathematical model Epileptor was recently developed to reproduce seizure-like events, also providing insights to improve the understanding of the neural dynamics in the interictal and ictal periods, although the physics behind each parameter and variable of the model is not fully established in the literature. This paper introduces an approach to design a feedback-based controller for suppressing epileptic seizures described by Epileptor. Our work establishes how the nonlinear dynamics of this disorder can be written in terms of a combination of linear sub-models employing an exact solution. Additionally, we show how a feedback control gain can be computed to suppress seizures, as well as how specific shapes applied as input stimuli for this purpose can be obtained. The practical application of the approach is discussed and the results show that the proposed technique is promising for developing controllers in this field.

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.

Controlling mechanism of absence seizures by deep brain stimulus applied on subthalamic nucleus

Based on a classical model of the basal ganglia thalamocortical network, in this paper, we employed a type of the deep brain stimulus voltage on the subthalamic nucleus to study the control mechanism of absence epilepsy seizures. We found that the seizure can be well controlled by turning the period and the duration of current stimulation into suitable ranges. It is the very interesting bidirectional periodic adjustment phenomenon. These parameters are easily regulated in clinical practice, therefore, the results obtained in this paper may further help us to understand the treatment mechanism of the epilepsy seizure.

Particle swarm optimization algorithm based parameters estimation and control of epileptiform spikes in a neural mass model

This paper proposes an epilepsy detection and closed-loop control strategy based on Particle Swarm Optimization (PSO) algorithm. The proposed strategy can effectively suppress the epileptic spikes in neural mass models, where the epileptiform spikes are recognized as the biomarkers of transitions from the normal (interictal) activity to the seizure (ictal) activity. In addition, the PSO algorithm shows capabilities of accurate estimation for the time evolution of key model parameters and practical detection for all the epileptic spikes. The estimation effects of unmeasurable parameters are improved significantly compared with unscented Kalman filter. When the estimated excitatory-inhibitory ratio exceeds a threshold value, the epileptiform spikes can be inhibited immediately by adopting the proportion-integration controller. Besides, numerical simulations are carried out to illustrate the effectiveness of the proposed method as well as the potential value for the model-based early seizure detection and closed-loop control treatment design.