Title: Complex dynamics of excitable McKean-Vlasov dynamics and applications to Parkinson’s disease

Abstract: In this talk, I will present a few properties of McKean-Vlasov equations representing the dynamics of large networks of neurons. Neurons are typically described as excitable systems: each has a globally stable state corresponding to rest, but perturbations exceeding a threshold lead to transient large excursions away from the resting state. I will present here a combination of mathematical results, conjectures and computer simulations aimed at better understanding the dynamics of these excitable networks in various coupling regimes. From an applied perspective, I will present possible links with Parkinson’s disease, a neurodegenerative disorder associated with alterations of neural excitability and collective synchrony. Specifically, I will propose that a better understanding of excitable McKean-Vlasov dynamics allows exploring the mechanisms of action of chronic stimulation therapies (called Deep Brain Stimulation, DBS). Time allowing, I will conclude by presenting a new dataset that we collected on Parkinsonian patients implanted with DBS electrodes to test the theoretical hypothesis that DBS may act to restore information capability in patients.

This talk will cover joint works with Charlotte Piette, Laurent Venance, Bertrand Degos, Cristobal Quiñinao and Bard Ermentrout.