Session: MSNDC-06-02: Nonlinear and Computational Dynamics Aspects in Biomechanics

Paper Number: 97753

97753 - An Opensim Closed-Loop Forward-Dynamics Model to Simulate Pathological Hand Tremors 

An OpenSim Closed-Loop Forward-Dynamics Model to Simulate Pathological Hand Tremors

Wellington Cassio Pinheiro, Maria Claudia Ferrari de Castro, Luciano Luporini Menegaldo*

Biomedical Engineering Program, Federal University of Rio de Janeiro, Brazil

*Presenting author, e-mail lmeneg@peb.ufrj.br

Introduction

Pathological tremors are involuntary oscillatory, nonlinear and non-stationary movements present in Parkinson’s disease (PD), essential tremor (ET), and parkinsonism, among other syndromes. Such tremors significantly affect voluntary movement diminishing individual autonomy on daily tasks. We present a 2-DOF (flexion and pronation) wrist tremor model, based on a previous OpenSim model [1], associated with an endogenous nonlinear Central Pattern Generator. A closed-loop controller stabilizes the wrist in a neutral position, allowing for forward-dynamics analyses. The model is intended to control tunning and test patient-specific rehabilitation devices based on closed-loop Functional Electrical Stimulation (FES).

Methods

A Matlab-OpenSim interface was adapted from [2], allowing forward dynamics simulations to be performed using OpenSim’s API from within Matlab, returning model dynamic states at each time step. Transfer functions from muscle excitation to torque and torque to position were identified. An H_∞ feedback controller was designed using the mixed-sensitive technique to generate the excitations driving the muscles. A simplified reciprocal inhibition model was implemented to switch between the agonistic and antagonistic muscles for each DOF. A disturbance, based on the Matsuoka oscillator, was added to the controller output to simulate the CNS oscillatory drive [3]. Five subjects (four PD and one ET) were selected to compare their hand tremor patterns with the model simulations. The study was approved by the Institution Ethics Committee. Patients’ hand tremor was assessed by an Inertial Measurement Unity (IMU), and the model oscillator central driving frequency was tuned for each subject. Simulation and experimental output kinematics were compared using Kullback-Leibler Divergence (D_KL) and spectrograms.

Results

Obtained D_KL values (average ± SD) were: central tremor frequency 1.85±0.86; flexion angle 0.26±0.12, angular velocity 0.51±0.55; pronation-supination angle 0,89±0,79, angular velocity 0.69±0.60. The figure below shows two subjects’ experimental (left) and simulated (center) spectrograms for flexion-extension angle. The right column shows the histograms based on maximum energy frequency in 1-sec windows; amplitude was normalized to one (red-experimental, blue-model).

Discussion

D_KL measures the loss of information between voluntary and simulated tremors based on their probability distributions and was low for all kinematic variables across the voluntaries. Other variables, such as peak-to-peak amplitudes, phase-portraits and time-series patterns, were also similar. It has been shown that the proposed model was able to reproduce both mean tremor frequency and its variability. In future works, patient-specific tuning should be performed by numerical optimization.

Acknowledgments: The authors are acknowledged to FAPERJ, CNPq, FINEP, FAPESP and CAPES for financial support.

References

[1] K. R. Saul et al., Benchmarking of dynamic simulation predictions in two software platforms using an upper limb musculoskeletal model, Computer Methods Biomech. Biomed. Eng. 18, 1445–1458, 2015.

[2] M. Millard, et a., Flexing computational muscle: modeling and simulation of musculotendon dynamics, J. Biomech. Eng., 135, no. 2, 021005, 2013.

[3] D. Zhang and K. Zhu, Computer simulation study on central pattern generator: From biology to engineering, Int. J. Neural Syst. 16, 405–422, 2006.

Presenting Author: Luciano Menegaldo Federal University of Rio de Janeiro

Presenting Author Biography: L.L. Menegaldo is B.Sc. and M.Sc. in Mechanical Engineering from the State University of Campinas (1994, 1997), Ph.D. in Mechanical Engineering from the University de São Paulo (2001), with a post-doc at Università degli Studi Roma Tre, Italy (2008). He is currently a full professor at the Biomedical Engineering Program, Federal University of Rio de Janeiro, the Graduate Program Coordinator and Biomechanics Lab Coordinator. He has experience in Mechanical and Biomedical Engineering, focusing on Biomechanics, Dynamics and Control.

Authors:

Wellington Pinheiro Federal University of Rio de Janeiro
Maria Claudia Castro Centro Universitário FEI
Luciano Menegaldo Federal University of Rio de Janeiro