Controlling Seizure-Like Events by Perturbing Ion Concentration Dynamics with Periodic Stimulation

Abstract

We investigate the effects of adding periodic stimulation to a generic, conductance-based neuron model that includes ion concentration dynamics of sodium and potassium. Under conditions of high extracellular potassium, the model exhibits repeating, spontaneous, seizure-like bursting events associated with slow modulation of the ion concentrations local to the neuron. We show that for a range of parameter values, depolarizing and hyperpolarizing periodic stimulation pulses (including frequencies lower than 4 Hz) can stop the spontaneous bursting by interacting with the ion concentration dynamics. Stimulation can also control the magnitude of evoked responses to modeled physiological inputs. We develop an understanding of the nonlinear dynamics of this system by a timescale separation procedure that identifies effective nullclines in the ion concentration parameter space. Our results suggest that the manipulation of ion concentration dynamics via external or endogenous stimulation may play an important role in neuronal excitability, seizure dynamics, and control.

Minimal model of interictal and ictal discharges “Epileptor-2”

“…The first assumption has been partially validated by experimental observations from the literature [ 15 ]. It is also consistent with that from modeling studies [ 10 , 11 , 32 ]. For instance, it was concluded in the detailed modeling study that it is the coupled dynamics of sodium, potassium, and chloride ions play a critical role in the development and termination of seizures [ 32 ].…”

“…In fact, the extracellular potassium concentration increased during the initial phase of the ID and began to decrease before the end of the ID [ 4 , 8 , 14 ], whereas the intracellular sodium concentration increased until the actual end of the ID [ 15 ]. Some simulations showed a similar behavior of ionic concentrations [ 9 , 10 ]. Therefore, the ionic dynamics may be explained by the activation of the Na-K pump, and the consequent decrease in the extracellular potassium concentration may lead to ID termination [ 12 ].…”

“…Thus, the ID represents a burst of bursts of spikes. Previous biophysical seizure-modeling attempts that considered the ionic dynamics in a single neuron model [ 9 , 10 ] or a network [ 11 – 13 ] did not show this feature. The second observation suggested a crucial role of the Na-K pump in the termination of each ID.…”

Computational model of interictal discharges triggered by interneurons

“…Instead, the effect of chloride accumulation was taken into account in the form of V GABA depolarization. This approach is in contrast to very detailed consideration of ionic dynamics in the works of Kager et al [ 51 ], [ 52 ], [ 53 ], [ 54 ]. Their consideration proposes a detailed description of ionic dynamics for a single multi-compartmental neuron surrounded by extracellular medium and glia.…”

Parameter estimation of slow potassium dynamics in a neuron model for seizure-like activity via adaptive lag synchronization and unscented Kalman filter

“…7,8 Compared with membrane potentials, the macroscopic time scale of [K] o is relatively slow, but the influence of [K] o on the neural activity is almost instantaneous. 3,4,9 Therefore, it is of importance to estimate parameters of the slow dynamics of [K] o from membrane potentials, which in turn can be used to regulate the neural activity.…”