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Volume 12
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10.3390/app12052654
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Article

A Computationally Efficient Musculoskeletal Model of the Lower Limb for the Control of Rehabilitation Robots: Assumptions and Validation

by
Nidal Farhat
1,
Pau Zamora
2,
David Reichert
3,
Vicente Mata
4,
Alvaro Page
2 and
Angel Valera
5,*
1
Department of Mechanical and Mechatronics Engineering, Birzeit University, Birzeit P.O. Box 14, Palestine
2
Instituto Universitario de Ingeniería Mecánica y Biomecánica, Universitat Politècnica de València, 46022 Valencia, Spain
3
Center for Medical Physics and Biomedical Engineering, Medizinische Universität Wien General Hospital Vienna, 1090 Vienna, Austria
4
Departamento de Ingeniería Mecánica y de los Materiales, Universitat Politècnica de València, 46022 Valencia, Spain
5
Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022 Valencia, Spain
*
Author to whom correspondence should be addressed.
Appl. Sci. 2022, 12(5), 2654; https://doi.org/10.3390/app12052654
Submission received: 31 January 2022 / Revised: 26 February 2022 / Accepted: 2 March 2022 / Published: 4 March 2022
(This article belongs to the Special Issue In-Silico Methods in Musculoskeletal Biomechanics and Biotribology Ⅱ)
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Abstract

We present and validate a computationally efficient lower limb musculoskeletal model for the control of a rehabilitation robot. It is a parametric model that allows the customization of joint kinematics, and it is able to operate in real time. Methods: Since the rehabilitation exercises corresponds to low-speed movements, a quasi-static model can be assumed, and then muscle force coefficients are position dependent. This enables their calculation in an offline stage. In addition, the concept of a single functional degree of freedom is used to minimize drastically the workspace of the stored coefficients. Finally, we have developed a force calculation process based on Lagrange multipliers that provides a closed-form solution; in this way, the problem of dynamic indeterminacy is solved without the need to use an iterative process. Results: The model has been validated by comparing muscle forces estimated by the model with the corresponding electromyography (EMG) values using squat exercise, in which the Spearman’s correlation coefficient is higher than 0.93. Its computational time is lower than 2.5 ms in a conventional computer using MATLAB. Conclusions: This procedure presents a good agreement with the experimental values of the forces, and it can be integrated into real time control systems.
Keywords: biomechanics; musculoskeletal model; knee biomechanics; musculoskeletal model; knee

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MDPI and ACS Style

Farhat, N.; Zamora, P.; Reichert, D.; Mata, V.; Page, A.; Valera, A. A Computationally Efficient Musculoskeletal Model of the Lower Limb for the Control of Rehabilitation Robots: Assumptions and Validation. Appl. Sci. 2022, 12, 2654. https://doi.org/10.3390/app12052654

AMA Style

Farhat N, Zamora P, Reichert D, Mata V, Page A, Valera A. A Computationally Efficient Musculoskeletal Model of the Lower Limb for the Control of Rehabilitation Robots: Assumptions and Validation. Applied Sciences. 2022; 12(5):2654. https://doi.org/10.3390/app12052654

Chicago/Turabian Style

Farhat, Nidal, Pau Zamora, David Reichert, Vicente Mata, Alvaro Page, and Angel Valera. 2022. "A Computationally Efficient Musculoskeletal Model of the Lower Limb for the Control of Rehabilitation Robots: Assumptions and Validation" Applied Sciences 12, no. 5: 2654. https://doi.org/10.3390/app12052654

APA Style

Farhat, N., Zamora, P., Reichert, D., Mata, V., Page, A., & Valera, A. (2022). A Computationally Efficient Musculoskeletal Model of the Lower Limb for the Control of Rehabilitation Robots: Assumptions and Validation. Applied Sciences, 12(5), 2654. https://doi.org/10.3390/app12052654

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