Ultrasound-Enhanced Data-Driven Modeling for Characterizing Natural Wrist Tremor Dynamics

The complex interplay of neural and muscular activity underlying involuntary rhythmic wrist tremors poses significant challenges for effective symptom management, particularly with identifying key tremor characteristics such as dominant frequency and amplitude. This study introduces an ultrasound (US)-enhanced data-driven modeling framework that uses wrist angle kinematics as state variables, which are augmented with muscle-specific ultrasound data inputs. We explore three modeling configurations: a wrist kinematics-only baseline model, a fixed-parameter US-augmented model, and a real-time adaptive US-enhanced model updated using a recursive least squares (RLS) algorithm. Comprehensive validation using time- and frequency-domain analyses was conducted using experimental data from six patients with tremor. Results show that integrating US input improves modeling specificity and accuracy by capturing internal muscle dynamics and temporal evolution patterns that are not accessible through IMU alone. Specifically, the time-domain modeling error (nRMSE) decreased substantially from 49.36% in the baseline model to 24.53% in the US-augmented model. The adaptive model further reduced the error to 0.48%, demonstrating its ability to account for the variability of tremor behaviors dynamically. Moreover, this work introduces, for the first time in tremor research, a comprehensive eigenvalue analysis of the data-driven model to extract clinically relevant tremor characteristics. The method enables accurate estimation of dominant tremor frequencies (average across patients nRMSE = 12.7%), quantification of dominant state contributions (mean $\Delta _{\text{dominance}}$ = 18.73%), and reliable tremor event detection (F1-score = 0.796). These findings highlight the framework's ability to not only reproduce tremor trajectories but also uncover how tremor behavior evolves over time in response to underlying neuromuscular activity. This work establishes a foundation for real-time tremor tracking and model-based control strategies, such as closed-loop afferent stimulation. By leveraging the unique sensing capabilities of ultrasound, the proposed framework offers a promising path toward personalized tremor modeling and intervention.