Differential Equations Seminar: Rachel Smith (Google Meet)

Abstract: Medically-refractory epilepsy (MRE) is a devastating neurological disease that is defined by recurrent and unprovoked seizures that are insufficiently controlled by anti-epileptic medication. Surgical resection of areas in the brain identified as the seizure onset zone (SOZ) can be a curative option for patients with well-localized (‘focal’) MRE, but localization of the SOZ heavily relies on visual inspection of intracranial electroencephalographic (iEEG) data and has historically resulted in surgical failure rates around 50%. In this talk, I will describe a study that aims to improve seizure onset localization by employing dynamical network models. Specifically, we have recorded iEEG data in MRE patients that have undergone extensive evaluation with single-pulse electrical stimulation (SPES), a technique recently used to probe functional brain networks such as language and motor cortices. We hypothesize that a dynamical quantification of the connectivity networks derived from the evoked responses induced by SPES could also be used to accurately localize the SOZ. We construct linear, time-invariant state-space models from the SPES data and calculate properties of the model that we believe may be clinically-relevant, such as the largest reachable state spacecovered by finite energy stimulation inputs. This denotes the “largest” network response attainable via stimulation. I will give an overview of these dynamical network techniques and describe their potential impact in the clinical treatment of medically-refractory epilepsy.