Neural Stimulation Reconstruction from EEG Using Fractional-Order Networks Towards Predictive Model Validation in Clinical Applications

Effective therapeutic neurostimulation requires predictive models that can reliably map how neural activity responds to specific stimuli. While recent advances in closedloop neurostimulation devices show promise for treating neurological disorders, most modeling approaches neglect the crucial relationship between stimulation input and neural response. A fundamental test of model predictive capability remains unaddressed: given baseline electroencephalographic (EEG) data and subsequent neural responses to stimulation, can we accurately reconstruct information about the injected stimuli? Furthermore, can such reconstruction remain valid across different stimulation parameters and electrode configurations, reflecting the diverse electrode placements required in clinical practice? In this paper, we demonstrate that input reconstruction is achievable using discrete-time linear fractional-order dynamical networks, which capture the rich temporal dependencies characteristic of neural systems. We present a novel minimization-minimization algorithm that generalizes expectation-maximization principles to learn both system parameters and unknown inputs. Through both a pedagogical example and extensive validation on a clinical dataset of simultaneous high-density EEG and intracerebral stimulation recordings, we show successful reconstruction of therapeutic biphasic pulses across varying stimulation locations, intensities, and electrode configurations. Our results demonstrate consistent reconstruction performance using different sizes and locations of electrode arrays, suggesting the robustness of our approach for practical neurostimulation applications.