(373g) Modeling Interictal and Preictal Seizure States Using Stochastic Differential Equations

Epilepsy is a neurological disorder that affects approximately 3 million Americans [1]. Presently, there is no method for the early detection of the event (known as the ictal state) [2]. If there is a mathematical model capable of predicting the events reliably, then the model can be used for early detection. In the last ten years, three types of mathematical models describing the interictal (in-between events) and preictal (prior to event) states have been developed: Hodgkin-Huxley type conductance-based models and chaos theory, probabilistic prediction methods based on EEG training, and spectral transforms of a training EEG signal used to determine changes in criticality (the sudden change from interictal to preictal state). The use of these models has led to anticipation of an epileptic seizure rather than early detection, as these methods only yield a high probability window of when the seizure is going to occur. Generally, this window is 60 to 80 minutes prior to the predicted event. Early detection 1 to 2 minutes prior to a seizure would be even more useful for two reasons. First, a patient can take immediate precautionary measures to minimize risk of injury. Second, new therapies, such as responsive cortical neurostimulation or topical anticonvulsant drug delivery might be effectively used if reliable, early warning is available.

The purpose of this work is to provide early detection by interpreting the EEG signals using stochastic differential equations with stochastic impulse inputs to model the interictal and preictal states. For instance, Iasemidis et al. [3] used the convergence and divergence of short-term maximum Lyapunov exponents to determine the dynamic transition toward a seizure. The average warning time in the study was 71.7 min. We intend to construct a state estimator capable of early detection of an impending epileptic attack with low false positive and negative rates. Since the system is highly dependent on the patient, the number of states modeled from individual EEG signals will vary. This can be done off-line, similar to the training done in previous works to refine the model. Thus, the bulk of the numerical computations are done prior to on-line operation. The on-line portion of the algorithm, the state estimator, can therefore be more efficiently run on an implantable microchip.

References

1. Epilepsy Foundation. Prevalence and Incidence. 2008. Available from: http://www.epilepsyfoundation.org/about/

2. Jerger, K. K., and T. I. Netoff, J. T. Francis, T. Sauer, L. Pecora, S. L. Weinstein, and S. J. Schiff. Early Seizure Detection. Journal of Clinical Neurophysiology, 2001. 18(3):p. 259-268.

3. Iasemidis, L. D., and D-S Shiau, W. Chaovalitwongse, J. C. Sackellares, P. M. Pardalos, J. C. Principe, P. R. Carney, A. Prasad, B. Veeramani, and K. Tsakalis. Adaptive Epileptic Seizure Prediction System. IEEE Transactions on Biomedical Engineering, 2003. 50(5): p. 616-627.