Outgrowing seizures in Childhood Absence Epilepsy: time delays and bistability

Impact of GABAA and GABAB Inhibition on Cortical Dynamics and Perturbational Complexity during Synchronous and Desynchronized States

“…All the details of the implementation of these currents are described by Compte et al (2003) , except for I KL and GABA B , which are described below. The GABA B current ( I GABAB ) is modeled as ( Destexhe et al, 1996 ; Liu et al, 2019 ), where r and s represent the GABA B -R and the gating variable, respectively. The transmitter concentration T is modeled as a square pulse of 0.5 m m during 3 ms.…”

Suppression of seizure in childhood absence epilepsy using robust control of deep brain stimulation: a simulation study

“…The topology of the three-coupled network is depicted in Fig. 1 , and the dynamics of the membrane voltage of the neurons are modeled with the following nonlinear first-order differential equations 8 , 25 : where in ( 1 ), μF cm −2 is the capacitance of the membrane of CT, TC, and RT neurons and , , and is the membrane voltage of the CT, TC, and RT neurons, respectively. The ionic membrane currents (μA cm −2 ) are denoted by , a leak current, , a transient voltage-gated current of Na + ions, , a transient voltage-gated current of K + ions, , a low-threshold current of Ca ++ ions for RT neuron, , a depolarization-activated current of K + ions, , a low-threshold current of Ca ++ ions for TC neuron, , a mixed Na + -K + current activated by hyperpolarization, , a slow current of K + ions, and, , , and , external currents of TC, CT, and RT neurons, respectively due to the input from other brain regions.…”

“…Destexhe 7 , 8 developed a conductance-based neuronal model of the thalamocortical circuit and emphasized the pivotal role of corticothalamic feedback and GABA receptors in hyper-synchronized oscillations and SWDs patterns. Motivated by this work, a 3-neuron pattern of CAE was formulated 25 . According to this model, long corticothalamic loop delay and low GABA A activity of thalamic relay cells are associated with CAE.…”

“…To overcome the aforementioned problems (asymptotic stability, chattering, and singularity of the controller and the knowledge of the plant dynamics), in this paper, a robust control technique based on adaptive fuzzy TSM control (AFTSMC) is developed for control of the oscillatory spiking pattern of the three-neuron pattern of CAE whereby the controller is not dependent on any knowledge of the dynamics of the system to be controlled. The main contributions of this work are as follows: To implement the proposed MIMO control algorithm, the dynamics of the membrane voltage of three-neuron CAE motif 8 , 25 should be represented and modeled as a three-input three-output nonlinear state delay model, and three continuous DBS pulses (control input) are designed to force the CAE pattern to track the normal state. This representation is based on the decomposition of the nonlinear dynamics of the current and delayed states of the CAE system 8 , 25 .…”

“…The main contributions of this work are as follows: To implement the proposed MIMO control algorithm, the dynamics of the membrane voltage of three-neuron CAE motif 8 , 25 should be represented and modeled as a three-input three-output nonlinear state delay model, and three continuous DBS pulses (control input) are designed to force the CAE pattern to track the normal state. This representation is based on the decomposition of the nonlinear dynamics of the current and delayed states of the CAE system 8 , 25 . Indeed, the continuous DBS pulses are automatically generated based on the MIMO model of the CAE motif.…”