Ultrasound-Informed State Estimation of Wrist Tremor Dynamics via Koopman Operator for Personalized Sensory Peripheral Nerve Stimulation.

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Tremor is among the most disabling motor symptoms in Parkinson's disease and essential tremor, yet current pharmacological and surgical therapies remain limited by side effects, invasiveness, and inconsistent efficacy. Sensory peripheral nerve stimulation (sPNS) has emerged as a non-invasive alternative, but its optimization requires computational models that integrate ultrasound-informed state estimation of tremor dynamics and adapt to individual variability. Here, we introduce a data-driven modeling framework that leverages ultrasound sensing within a Koopman operator approach for state estimation to capture wrist tremor dynamics. In a study of six individuals with Parkinsonian or essential tremor, ultrasound-informed models significantly improved accuracy, reducing time-domain prediction error from 38.1% to 21.3% and enhancing frequency-domain measures, including tremor frequency and power ratio. Modal input analysis revealed that ultrasound-derived features from flexor and extensor muscles accounted for > 60% of model sensitivity, while intermuscular latency among sPNS parameters contributed most strongly (31.6%), consistent with the physiological principle of out-of-phase stimulation. The framework also proved resilient to sensor dropout, preserving dominant tremor frequency and temporal features via data-driven interpolation. In a pilot human-validation study involving one Parkinsonian tremor participant and one essential tremor participant, the model-informed protocols selected by the proposed framework produced the strongest suppression among the tested stimulation conditions, achieving mean suppression ratios of 28.3% and 45.1%, respectively. These findings establish ultrasound-informed modeling as a novel state-estimation and modeling strategy for tremor characterization, while also providing initial prospective support for model-guided personalization of sPNS parameters.

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