Koopman-Based Linearization of Preparatory EEG Dynamics in Parkinson's Disease During Galvanic Vestibular Stimulation

Maryam Kia^1,2Maryam S. Mirian²Saeed Soori³Saeed Saedi⁴Emad Arasteh⁵Mohammadhossein Faramarzi⁶Abhijit Chinchani²Soojin Lee²Artur Luczak¹Martin J McKeown^2*

• ¹University of Lethbridge, Lethbridge, Alberta, Canada
• ²University of British Columbia, Vancouver, British Columbia, Canada
• ³University of Toronto, Toronto, Ontario, Canada
• ⁴University of Tehran, Tehran, Tehran, Iran
• ⁵University Medical Center Utrecht, Utrecht, Netherlands, Netherlands
• ⁶Sharif University of Technology, Tehran, Tehran, Iran

Parkinson's Disease (PD) is a prevalent neurodegenerative disorder that impacts both motor and nonmotor functions. Complementary therapies, such as Galvanic Vestibular Stimulation (GVS), have shown potential as non-invasive alternatives or adjuncts to traditional Levodopa treatment; however, the mechanisms underlying their efficacy remain poorly understood. For instance, GVS may influence ongoing brain dynamics and/or activate underactive brain regions in PD, thereby enhancing motor function. In this study, we utilized a Deep Koopman model to analyze EEG data from healthy controls (n=18) and participants with PD (n=18) during the preparatory phase of an overlearned squeeze task. The task was performed under varying conditions, including medication states (off/on) and stimulation settings (Sham, GVS1, GVS2). The Koopman framework enabled linearization and dimensionality reduction of complex EEG signals, facilitating predictive modeling and control strategies within a simplified three-dimensional latent space. Our results demonstrated that the Koopman model effectively captured key EEG dynamics. Eigenvalue analyses revealed no significant differences in latent-space dynamics between the PD and control groups. However, examination of the transformation from the raw EEG data to the latent space identified distinct spatial pattern differences between groups. Notably, under GVS and medication conditions, the EEG patterns in PD participants shifted closer to those observed in healthy controls. Additionally, in PD subjects, a stronger alignment of spatial patterns during the preparatory phase with those of healthy controls was associated with faster subsequent movements. These group-specific spatial transformation patterns during motor planning are particularly relevant in PD, where voluntary movement pathways are disrupted due to basal ganglia dysfunction, with complex projections to scalp-based EEG recordings. Our findings support the hypothesis that GVS may activate brain regions typically underactive during motor preparation, potentially compensating for impaired neural circuits in PD. In addition, we demonstrate that a hypothetical Linear Quadratic Regulator (LQR) controller could be used to move PD-related dynamics toward that of healthy subjects. The Deep Koopman framework thus offers a robust approach for detecting EEG effects of non-invasive brain stimulation and for informing the design of targeted therapeutic interventions.