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

Abstract

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.

A Data Driven Experimental System for Individualized Brain Stimulation Design and Validation

“…Su et al explored the application of model predictive control in the closed-loop control of Parkinson's state on the model of basal ganglia computing model [33], and evaluated the tracking ability of proportional-integral (PI) controller to the dynamic beta oscillation reference signal [34]. Chang et al [35] and Chatterjee et al [36] explored the effects of nonlinear auto-regressive moving-average Volterra model predictive control and fractional-order model predictive control in epileptic seizure suppression based on common computational models. These studies provide potential impetus for the development and implementation of real-time closed-loop electrical neurostimulation.…”

Fractional cyber-neural systems -- a brief survey

“…In this brief survey, we focus our attention on neural behavior, which can be accurately represented by fractional-order systems (Baleanu et al, 2011;West et al, 2016;Moon, 2008;Lundstrom et al, 2008;Werner, 2010;Thurner et al, 2003;Teich et al, 1997). Fractional-order systems have also been explored in the context of neurophysiological networks constructed from electroencephalographic (EEG), electrocorticographic (ECoG), or blood-oxygenlevel-dependent (BOLD) data (Chatterjee et al, 2020;Magin, 2006).…”

“…For instance, within the purview of epileptic seizure mitigation using intracranial EEG data, the objective of the former is to suppress the overall length or duration of an epileptic seizure. Thus, the goal is steering the state of the neurophysiological system in consideration away from seizure-like activity, using a control strategy like model predictive control (Chatterjee et al, 2020).…”

Online Learning Koopman operator for closed-loop electrical neurostimulation in epilepsy

“…For instance, Siyuan Chang et al presented a nonlinear auto-regressive moving-average (NARMA) Volterra model to identify the relationship between the external input and the corresponding neuronal responses such as synthetic seizure-like waves, based on which the closed-loop MPC actuation strategy was implemented to optimize the stimulator's waveform [8]. Sarthak Chatterjee et al proposed a fractional-order model predictive control framework for real-time closed-loop electrical neurostimulation in epilepsy [9]. However, the MPC requires a decent model to predict the system dynamics, which is particularly challenging for seizure dynamics.…”

“…Some tools are available for modeling the seizure system dynamics using time-series EEG data. For example, auto-regressive moving-average model [8] and fractional-order system model [9] have been applied for seizure dynamics identification. With the advances of machine learning methods, data-driven models have shown great potentials as a system identification tool.…”