Tonic-clonic seizures can be devastating to a patient with epilepsy. While there is evidence that DBS can reduce seizures, no clinical application has been found to be fully effective in truncating seizures. It is well known in oscillatory models that periodic forcing of a network of oscillators can synchronize or phase disperse the oscillators (Glass and Mackey, 1988
; Elbert et al., 1994
; Kaplan et al., 1996
). It has previously been proposed that this may be used to control seizures (Milton and Jung, 2003
). In a recent paper, we proposed that this may be involved in treating Parkinsonian symptoms (Wilson et al., 2011
). In this paper we use similar periodic stimulation theory to affect the tonic and clonic phases of a seizure in a computational model we have recently developed (Beverlin et al., 2011
). Recently we proposed that the shift from the desynchronized tonic phase to the synchronous clonic phase occurs as the neuronal firing rate adapts over the duration of the seizure. At the high firing rates, the model neurons do not synchronize, but as the firing rates slow down, the cells become more sensitive to synaptic inputs and the network synchronizes. The change in spike rate is modeled by gradually decreasing the current drive to the neurons along with depressing synapses.
In this paper, we have added periodic stimulation to the tonic-clonic model to determine if periodic stimulation could be used to affect the duration of the seizure phases. We analyzed the effects of stimulus frequency and amplitude on the population synchrony at the tonic phase and again at the clonic phase. Depending on the stimulus frequency we were able to synchronize neurons during the asynchronous tonic phase, or desynchronize neurons in the synchronous clonic phase. Periodic stimulation at integer ratios of the stimulus frequency to the natural frequency was found to entrain and thereby synchronize the population. Conversely, periodic stimulation just slightly slower than the firing rates (and at some frequencies, faster than the firing rates of the neurons) could desynchronize the population. Our findings can be explained with PRC theory, which we previously used to explain the effects of the stimulus at different frequency amplitudes and its effect on population synchrony (Beverlin et al., 2011
). The effect of firing rate shifting the peak of the PRC to the left in response to excitatory inputs is generally true and should therefore not be heavily model dependent (Gutkin et al., 2005
; Fink et al., 2011
). We chose the M–L model because it is one of the simplest conductances based neuronal models that can demonstrate this effect.
Periodic stimulation of a network during a seizure with a fixed period would have a mixed effect; synchronizing at some phases of the seizure and desynchronizing at others, as the neurons are constantly changing their firing rate. However, the ratio of stimulus frequency to neuronal firing rate that entrains or desynchronizes the population is relatively consistent. Therefore, we created a closed-loop control system that adjusts the stimulus frequency to desynchronize or synchronize the population, holding the stimulus at a fixed rate relative to the neuronal firing rate. In this case the tonic phase of the seizure could effectively be shortened by applying a stimulus at the same frequency of the neurons, while the tonic phase could be prolonged by applying a stimulus frequency that is slightly slower than the firing rate of the neurons, effectively preventing the synchronization of the population.
This model illustrates the principle that periodic stimulation at certain ratios to the measured firing rate of neurons can be used to promote or decrease synchrony and this principle may be used in a closed-loop feedback system for seizure suppression. We are not suggesting that this model is an accurate model of the actual physiology in the brain. Instead, if PRCs can be measured during seizures, our theory may be tested experimentally. We plan to test these hypotheses in brain slice experiments in the near future.
In addition, the complicated structure and function of real neurons in real tissue are beyond the scope of this paper. Here we have investigated the applicability of DBS in a model network; naturally, there may be real world complications when implementing these protocols depending on the location of the electrode(s) and stimulus parameters. In addition, clinical applications of DBS thus far are typically less than 200 Hz. For example the SANTE trials studying the treatment of refractory epilepsy used a stimulation of 145 Hz (Fisher et al., 2010
). Some of the frequencies in our model presented here exceed these typical frequencies, but the relative frequency between the stimulus and the neuronal firing rate is what we consider important. Our model is not designed to produce realistic firing rates, so we do not suggest based on this model that these are realistic stimulation frequencies for all brain regions that should be used clinically.
There are many aspects of this simulation which are not physiologically realistic which could be improved in future studies. First, the neurons are modeled as oscillators. Generally, neurons do not fire periodically. However, at the onset of a seizure with high rate of synaptic asynchronous synaptic inputs, neurons may fire close to periodically. All the neurons are also modeled as oscillators with the same parameters and the same firing rate, while it would be more realistic to model the neurons with a distribution of parameters and firing rates. Furthermore, in this model the stimulus was applied uniformly to all the neurons. In a real neuronal network there is geometry to the position of the neurons and a stimulus electrode will not uniformly stimulate all the neurons. All of these aspects of the model could be improved to make it more realistic, and will be the focus of further investigation, but we do not feel will change the fundamental approach we present here to desynchronizing populations.
How might this algorithm be implemented in practice, such as in a brain slice model of seizures and eventually in humans? First, a stimulation electrode and a recording electrode are needed. Then, it is necessary to determine the optimal stimulus frequency ratio with respect to the neuronal frequency. This can be determined from the neuron's PRC to the stimulus. The PRC is measured by open-loop stimulation at random intervals that are on average much longer than the period of the neuron on average. The phase of the oscillation is measured before and after the stimulation to estimate the phase advance of each stimulus. Generally, some model representing the phase advance as a function of the stimulus phase is fit to the resulting data. PRCs would need to be measured at different firing rates or phases of the seizure. From the measured PRCs the Lyapunov Exponents (LEs) of the population response at is estimated different stimulus amplitudes and frequencies (Wilson et al., 2011
). Stimulus parameters are selected that maximize the LE to desynchronize the population, or minimize the LE to synchronize. To implement the algorithm, the recording electrode would be used to measure the firing rate of neurons in the population; the measured firing rate would then be used to modulate the frequency of the stimulating electrode.
An interesting finding is that the closed-loop controller could affect the duration of the tonic phase with equal efficacy at one quarter the stimulus amplitude than the open-loop control. This indicates that a simple measure of the neuronal firing rate may significantly improve the efficacy of DBS.
It is important to note that we do not propose that it is best to synchronize and shorten the duration of the tonic phase of the seizure, or to prolong it. We consider that the restructuring of the neuronal network by induction of synaptic plasticity by high firing rates of neurons during seizures may ultimately be the long term deleterious effect if seizures. The goal of the therapy may be to minimize the plasticity changes during a seizure. If neurons fire synchronously, plasticity may be greater than when neurons fire asynchronously. In this case, maximizing the tonic phase of the seizure and minimizing the clonic phase may result in less plasticity changes. However, if the synchronization of the population is integral to the termination of the seizure promoting synchrony may terminate the seizure earlier (Schindler et al., 2007a
). For example, if seizures are sustained by recurrent excitation, increasing synchrony may decrease the excitable pool of neurons, thereby decreasing the likelihood of re-entry and terminating seizures earlier. Using a stimulus that can modulate the duration of the tonic phase may help us determine whether synchrony is just a network behavior that occurs at the termination of the seizure or whether it is integral to the termination.
HFOs are population oscillations that are seen between seizures. Suppressing these oscillations may be considered a target for DBS stimulation. The hope would be that disrupting these pathological oscillations may suppress epileptogenesis. The same approach used in this paper might be used to design a stimulus to suppress HFOs. HFOs might be a good target because they are observed to increase prior to a seizure in human and animal models (Worrell et al., 2004
), and are thought to arise from synchronous bursts of neurons that occur in an epileptic focus (Bragin et al., 1999
; Ibarz et al., 2010
). There is also strong experimental evidence that synchrony amongst cortical regions is increased in epileptic patients (Bullock et al., 1995
; Towle et al., 1999
; Ben-Jacob et al., 2007
; Schevon et al., 2007
; Prusseit and Lehnertz, 2008
; Zaveri et al., 2009
) and that this synchrony changes in the lead up to a seizure (Lehnertz and Elger, 1995
; Chavez et al., 2003
; Le Van Quyen et al., 2005
). In contrast, other evidence suggests that synchrony may decrease prior to a seizure (Mormann et al., 2003
). We hypothesize that tuning DBS stimulators to desynchronize prominent pathological oscillations relevant to the generation of seizures interictally suppress seizures. However, we are not aware of any direct evidence that DBS affects these oscillations.