Analysis of Neural Fragility: Bounding the Norm of a Rank-One Perturbation Matrix

Over 15 million epilepsy patients worldwide do not respond to drugs and require surgical treatment. Successful surgical treatment requires complete removal, or disconnection of the epileptogenic zone (EZ), but without a prospective biomarker of the EZ, surgical success rates vary between 30%-70%. Neural fragility is a model recently proposed to localize the EZ. Neural fragility is computed as the l2 norm of a structured rank-one perturbation of an estimated linear dynamical system. However, an analysis of its numerical properties have not been explored. We show that neural fragility is a well-defined model given a good estimator of the linear dynamical system from data. Specifically, we provide bounds on neural fragility as a function of the underlying linear system and noise.