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Research Papers

Influence of Uncertainty in Selected Musculoskeletal Model Parameters on Muscle Forces Estimated in Inverse Dynamics-Based Static Optimization and Hybrid Approach

[+] Author and Article Information
Magdalena Żuk, Celina Pezowicz

Faculty of Mechanical Engineering,
Wrocław University of Science and Technology,
Wrocław 50-370, Poland

Małgorzata Syczewska

Department of Paediatric Rehabilitation,
The Children's Memorial Health Institute,
Warsaw 04-730, Poland

1Corresponding author.

Manuscript received September 22, 2017; final manuscript received July 3, 2018; published online September 25, 2018. Assoc. Editor: Tammy L. Haut Donahue.

J Biomech Eng 140(12), 121001 (Sep 25, 2018) (12 pages) Paper No: BIO-17-1422; doi: 10.1115/1.4040943 History: Received September 22, 2017; Revised July 03, 2018

The purpose of the current study was to investigate the robustness of dynamic simulation results in the presence of uncertainties resulting from application of a scaled-generic musculoskeletal model instead of a subject-specific model as well as the effect of the choice of simulation method on the obtained muscle forces. The performed sensitivity analysis consisted of the following multibody parameter modifications: maximum isometric muscle forces, number of muscles, the hip joint center location, segment masses, as well as different dynamic simulation methods, namely static optimization (SO) with three different criteria and a computed muscle control (CMC) algorithm (hybrid approach combining forward and inverse dynamics). Twenty-four different models and fifty-five resultant dynamic simulation data sets were analyzed. The effects of model perturbation on the magnitude and profile of muscle forces were compared. It has been shown that estimated muscle forces are very sensitive to model parameters. The greatest impact was observed in the case of the force magnitude of the muscles generating high forces during gait (regardless of the modification introduced). However, the force profiles of those muscles were preserved. Relatively large differences in muscle forces were observed for different simulation techniques, which included both magnitude and profile of muscle forces. Personalization of model parameters would affect the resultant muscle forces and seems to be necessary to improve general accuracy of the estimated parameters. However, personalization alone will not ensure high accuracy due to the still unresolved muscle force sharing problem.

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Figures

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Fig. 1

Diagram showing model perturbation process and data analysis. M1–M23 modified models, M24 simplified model, SO dynamic simulation using static optimization with different criteria (sum of a2 (SO1), a5 (SO2), and a3 (SO3), where a is the activation level), computed muscle control (CMC) dynamic simulation using computed muscle control algorithm.

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Fig. 2

Comparison of muscle forces estimated for the initial and modified models using different dynamic simulation methods

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Fig. 3

Sensitivity analysis results for static optimization for subject 1. MAV values calculated between muscle forces estimated for the initial model (M0s1) and modified models (M1s1–M24s1) as well as MAVs calculated for static optimization with default criterion (M0s1) and other criteria (M0s2, M0s3) or CMC method (M0cmc). MAVs were calculated for each right lower-limb muscle in the model.

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Fig. 4

Sensitivity analysis results for static optimization for subject 2. MAV values calculated between muscle forces estimated for the initial model (M0s1) and modified models (M1s1–M24s1) as well as MAVs calculated for static optimization with default criterion (M0s1) and other criteria (M0s2, M0s3) or CMC method (M0cmc). MAVs were calculated for each right lower-limb muscle in the model.

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Fig. 5

Sensitivity analysis results for CMC algorithm for subject 1. MAV values calculated between muscle forces estimated for the initial model (M0cmc) and modified models (M1cmc1–M24cmc1) as well as MAVs calculated for CMC results (M0cmc) and static optimization with different criteria (M0s1, M0s2, M0s3). MAVs were calculated for each right lower limb muscle in the model.

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Fig. 6

Sensitivity analysis results for static optimization for subject 1. Values of Pearson correlation coefficients calculated between muscle forces estimated for the initial model (M0s1) and modified models (M1s1–M24s1) as well as correlation coefficients calculated for static optimization with default criterion (M0s1) and other criteria (M0s2, M0s3) or CMC method (M0cmc).

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Fig. 7

Sensitivity analysis results for static optimization for subject 2. Values of Pearson correlation coefficients calculated between muscle forces estimated for the initial model (M0s1) and modified models (M1s1–M24s1) as well as correlation coefficients calculated for static optimization with default criterion (M0s1) and other criteria (M0s2, M0s3) or CMC method (M0cmc).

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Fig. 8

Sensitivity analysis results for CMC algorithm for subject 1. Values of Pearson correlation coefficients calculated between muscle forces estimated for the initial model (M0cmc) and modified models (M1cmc1-M24cmc1) as well as correlation coefficients calculated for CMC results (M0cmc) and static optimization with different criteria (M0s1, M0s2, M0s3).

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