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

TL;DR

This paper analyzes the mathematical properties of neural fragility, a model used to localize epileptogenic zones in epilepsy patients, providing bounds on its behavior based on the underlying system and noise.

Contribution

It offers the first theoretical analysis of neural fragility, establishing bounds and conditions for its well-definedness given a good system estimator.

Findings

Neural fragility is well-defined with a good linear system estimator.

Bounds on neural fragility depend on the underlying system and noise.

Provides theoretical insights into the numerical properties of neural fragility.

Abstract

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.