Discontinuous Galerkin finite element method for solving population density functions of cortical pyramidal and thalamic neuronal populations.

Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons.

Suppression of acute seizures by theta burst electrical stimulation of the hippocampal commissure using a closed-loop system.

This study investigated the effects of electrical stimulation with theta burst stimulation (eTBS) on seizure suppression. Optimal parameters of eTBS were determined through open-loop stimulation experiments and then implemented in a close-loop seizure control system. For the experiments, 4-aminopyridine (4-AP) was injected into the right hippocampus of Sprague-Dawley rats to induce an acute seizure. eTBS was applied on the ventral hippocampal commissure and the effects of eTBS with different combinations of burst frequency and number of pulses per burst were analyzed in terms of seizure suppression. A closed-loop seizure control system was then implemented based on optimal eTBS parameters. The efficiency of the closed-loop eTBS was evaluated and compared to that of high frequency stimulation. The results show that eTBS induced global suppression in the hippocampus and this was sustained even after the application of eTBS. The optimal parameter of eTBS in the open-loop stimulation experiments was a burst frequency at 100Hz with nine pulses in a burst. The eTBS integrated with the on-off control law yielded less actions and cumulative delivered charge, but induced longer after-effects of seizure suppression compared to continuous high frequency stimulation (cHFS). To conclude, eTBS has suppressive effects on 4-AP induced seizure. A closed-loop eTBS system provides a more effective way of suppressing seizure and requires less effort compared to cHFS. eTBS may be a novel stimulation protocol for effective seizure control.

On-off control of burst high frequency electrical stimulation to suppress 4-AP induced seizures.

OBJECTIVE: The goal of this study was to investigate, using model simulations and animal experiments, the efficiency and the side effects of burst high frequency stimulation combined with on-off control in seizure suppression. APPROACH: A modified mathematical hippocampal seizure model was created to provide evidence of the eligibility of this approach. In the experimental setup, two recording electrodes were inserted into bilateral septal CA1 of the hippocampus, and a stimulation electrode was placed on the ventral hippocampal commissure of a rat. After seizures had been induced by 4-aminopyridine treatment, on-off control stimulation was used to suppress the seizures at 20 s intervals. The stimulation time, cumulative charge and post-stimulation suppression were used to assess the effects of burst duration. MAIN RESULTS: The results showed that burst stimulation could suppress the seizures during the control period and burst stimulation of a shorter duration could keep the seizure suppressed with less effort. By decreasing the burst duration, the cumulative stimulation time became shorter, the delivered cumulative charge became lower, and the cumulative time of post-stimulation suppression became longer. SIGNIFICANCE: The on-off control stimulation not only prolonged the duration of suppression but also avoided the side effects of the conversion of seizure patterns. In particular, decreasing the specified burst duration increased the efficiency of the burst stimulation.

Model analyses of visual biofeedback training for EEG-based brain-computer interface.

The primary goal of this study was to construct a simulation model of a biofeedback brain-computer interface (BCI) system to analyze the effect of biofeedback training on BCI users. A mathematical model of a man-machine visual-biofeedback BCI system was constructed to simulate a subject using a BCI system to control cursor movements. The model consisted of a visual tracking system, a thalamo-cortical model for EEG generation, and a BCI system. The BCI system in the model was realized for real experiments of visual biofeedback training. Ten sessions of visual biofeedback training were performed in eight normal subjects during a 3-week period. The task was to move a cursor horizontally across a screen, or to hold it at the screen's center. Experimental conditions and EEG data obtained from real experiments were then simulated with the model. Three model parameters, representing the adaptation rate of gain in the visual tracking system and the relative synaptic strength between the thalamic reticular and thalamo-cortical cells in the Rolandic areas, were estimated by optimization techniques so that the performance of the model best fitted the experimental results. The serial changes of these parameters over the ten sessions, reflecting the effects of biofeedback training, were analyzed. The model simulation could reproduce results similar to the experimental data. The group mean success rate and information transfer rate improved significantly after training (56.6 to 81.1% and 0.19 to 0.76 bits/trial, respectively). All three model parameters displayed similar and statistically significant increasing trends with time. Extensive simulation with systematic changes of these parameters also demonstrated that assigning larger values to the parameters improved the BCI performance. We constructed a model of a biofeedback BCI system that could simulate experimental data and the effect of training. The simulation results implied that the improvement was achieved through a quicker adaptation rate in visual tracking gain and a larger synaptic gain from the visual tracking system to the thalamic reticular cells. In addition to the purpose of this study, the constructed biofeedback BCI model can also be used both to investigate the effects of different biofeedback paradigms and to test, estimate, or predict the performances of other newly developed BCI signal processing algorithms.