Instability detector of a fragile neural network: application to seizure detection in epilepsy.

It has recently been proposed that the epileptic cortex is fragile in the sense that seizures manifest through small perturbations in the synaptic connections that render the entire cortical network unstable. Therefore, one method for detecting seizures is to detect when the neuronal network has gone unstable. This is important for implementing a closed-loop therapy to suppress seizures. In this paper, we consider a widely used nonlinear stochastic model of a neuronal network, and assume that spiking dynamics during non-seizure periods correspond to certain synaptic connections that render its fixed point stable. We then apply a minimum energy perturbation theory we recently developed for networks to determine the changes in the most fragile node's synaptic connections that make the same fixed point unstable (our model during seizure). Then a detector is designed as follows. First a 2-state HMM is constructed (stable=state 1 and unstable=state 2) with fixed state transition probabilities, where the output observation is the firing rate of the most fragile node in the network. The output density functions are assumed to be Gaussian with parameters computed using maximum likelihood estimation on data generated from the nonlinear network model in each state. Then, to detect a transition from stable to unstable, spiking activity is simulated in all nodes from the nonlinear model. The detector first measures the firing rate of the fragile node, and computes the derivative of the cumulative likelihood ratio of the observed firing rate from the HMM's output distributions. When the derivative exceeds a certain threshold, a transition to the unstable state is detected. Various thresholds were tested when firing rate was computed by averaging over a different number of windows of different lengths. High performance was achieved and a tradeoff was found between the accuracy of the detector and the detection delay.