# Koopman-based linearization of preparatory EEG dynamics in Parkinson’s disease during galvanic vestibular stimulation

## TL;DR

This study uses a Deep Koopman model to show that Galvanic Vestibular Stimulation (GVS) helps restore normal brain activity patterns in Parkinson’s disease patients, improving motor preparation.

## Contribution

The novel use of a Deep Koopman framework to linearize and analyze EEG dynamics in Parkinson’s disease during GVS, revealing its impact on cortical activity.

## Key findings

- GVS and medication reduce deviations in PD EEG patterns toward healthy controls during motor preparation.
- Closer alignment of PD EEG patterns with controls correlates with improved motor performance metrics.
- LQR control simulations show PD neural dynamics can be guided toward healthy trajectories using the Deep Koopman framework.

## Abstract

Parkinson’s disease (PD) impairs motor preparation due to basal ganglia dysfunction, contributing to motor deficits. Galvanic Vestibular Stimulation (GVS), a non-invasive neuromodulation technique, shows promise in enhancing motor function in PD, but its underlying neural mechanisms are poorly understood. This study employs a Deep Koopman model to linearize and analyze preparatory EEG dynamics in PD, hypothesizing that GVS restores cortical activity patterns critical for motor planning.

EEG data from 18 PD participants (on/off medication) and 18 healthy controls were collected during a preparatory phase of a motor task under three conditions: sham, GVS1 (50–100 Hz multi-sine), and GVS2 (100–150 Hz multi-sine). A Deep Koopman framework mapped EEG signals into a three-dimensional latent space for linear dynamical analysis. Temporal dynamics were assessed via eigenvalue analysis, spatial contributions via regression-based scalp mapping, and motor performance correlations via Pearson’s coefficients. A Linear Quadratic Regulator (LQR) simulated control of PD dynamics toward healthy patterns.

The Deep Koopman model accurately captured EEG dynamics, with eigenvalue analysis showing no significant temporal dynamic differences across groups. Spatial contribution analysis revealed that PD-Off sham conditions deviated most from healthy control EEG patterns, while GVS and medication significantly reduced these deviations, aligning PD patterns closer to controls. Closer alignment correlated with improved motor performance metrics, including reduced reaction and squeeze times. LQR control effectively guided PD neural dynamics toward healthy trajectories in the latent space.

GVS enhances motor preparation in PD by restoring healthy cortical EEG patterns, with additive benefits from dopaminergic medication. The Deep Koopman framework offers a powerful approach for dissecting complex EEG dynamics and designing targeted neuromodulation strategies. These findings elucidate GVS’s therapeutic mechanisms and highlight its potential for personalized PD interventions, warranting further exploration in larger cohorts and varied stimulation protocols.