Predicting Epileptic Seizures
In this chapter we will be interested in methods for anticipating seizures. It would, of course, be best if one could predict seizure occurrence with absolute accuracy and indefinitely into the future. But that is not likely to happen. One could reasonably hope to make such predictions in a fairly simple, nonchaotic, autonomous system. But the brain is not such a system. However, a more modest goal may be achievable. There is reason to believe that seizure prediction with reasonable confidence minutes to tens of minutes ahead may be possible, at least in some patients. Such an achievement would be a great boon to treatment and to the quality of life of patients with epilepsy. First, it would open up the possibility of interventive measures that might abort the seizure. But even if that were not possible, a few minutes warning could be invaluable. It would allow a patient with epilepsy to stop a potentially risky activity in which they were engaged, and find a safe situation in which to be when the seizure occurred.
KeywordsEpileptic Seizure Temporal Lobe Epilepsy Seizure Onset Seizure Focus Nonlinear Measure
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- 1.Although different time and length scales may give rise to qualitatively different effective dynamics, there may be, in principle, calculable relations among the effective dynamics over different length and time scales. One approach to computing these relationships is that of the renormalization group and related computational schemes. There is a large literature on this subject, but its discussion is beyond the scope of this chapter.Google Scholar
- 2.Note that these authors use D to refer to a correlation density. Other authors tpically use D to refer to a dimension.Google Scholar
- 3.Of course, it is possible that there simply is no pre-ictal change in epileptogenic brain; that the transition to the seizure state occurs, in general, within a few seconds of seizure onset. But this possibility is just too depressing to entertain.Google Scholar
- 4.Here and in the rest of this section we use attractor in an informal sense that includes those objects produced in a reconstruction space from data in a given window. Such an object may not, strictly speaking, be an attractor in a precise dynamical sense.Google Scholar
- 5.More detailed considerations of this system lead to a model of neural process that is driven by a bistability, and the one-dimensional driving force, which varies over time can be interpreted as the hopping probability between the two (bistable) states .Google Scholar
- 6.This statistical anaylsis was performed using a likelihood ratio test in the context of the model of bistability discussed in . It showed, with high statistical confidence, that the results on healthy subjects could be described by an autonomous version of that model, while the results on people with epilepsy required the inclusion of non-autonomous effects (R. Manuca, R. Savit and I. Drury, in preparation).Google Scholar
- 7.For example, in statistical mechanics or in field theory there is a complementarity between different descriptions of a physical system. A field theory can be described either in terms of a statistical ensemble of a sum over states, or in terms of stochastic differential equations. The two “theories” are mathematically equivalent, but are, in a sense, different ontologically.Google Scholar