Fractional-order model predictive control as a framework for electrical neurostimulation in epilepsy

Objective. Electrical neurostimulation is an increasingly adopted therapeutic methodology for neurological conditions such as epilepsy. Electrical neurostimulation devices are commonly characterized by their limited sensing, actuating, and computational capabilities. However, the sensing mechanisms are often used only for their detection potential (e.g. to detect seizures), which automatically and dynamically trigger the actuation capabilities, but ultimately deploy prespecified stimulation doses that resulted from a period of manual (and empirical) calibration. The potential information contained in the measurements acquired by the sensing mechanisms is, therefore, considerably underutilized, given that this type of stimulation strategy only entails an event-triggered relationship between the sensors and actuators of the device. Such stimulation strategies are suboptimal in general and lack theoretical guarantees regarding their performance. Approach. In order to leverage the aforementioned information, harvested during normal sensing-actuating operation, we must consider a real-time feedback (closed-loop) strategy. More precisely, the stimulation signal itself should automatically adapt based upon the state of the neurophysiological system at hand, estimated from data collected in real-time through sensors in the device. Main results. In this work, we propose a model-based approach for (real-time) closed-loop electrical neurostimulation, in which the evolution of the system is captured by a fractional-order system (FOS). More precisely, we propose a model predictive control (MPC) approach with an underlying FOS predictive model, due to the ability of fractional-order dynamics to more accurately capture the long-term dependence present in biological systems, compared to the standard linear time-invariant models. Furthermore, MPC offers, by design, an additional layer of robustness to compensate for system-model mismatch, which the more traditional strategies lack. To establish the potential of our framework, we focus on epileptic seizure mitigation by computational simulation of our proposed strategy upon seizure-like events. Lastly, we provide evidence of the effectiveness of our method on seizures simulated by commonly adopted models in the neuroscience and medical community present in the literature, as well as real seizure data as obtained from subjects with epilepsy. Significance Our study thus paves the way for the development and implementation of robust real-time closed-loop electrical neurostimulation which can then be used for the construction of more effective devices for epileptic seizure mitigation.