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Model-Based Sensorimotor Integration for Multi-Joint Control: Development of a Virtual Arm Model

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Abstract

An integrated, sensorimotor virtual arm (VA) model has been developed and validated for simulation studies of control of human arm movements. Realistic anatomical features of shoulder, elbow and forearm joints were captured with a graphic modeling environment, SIMM. The model included 15 musculotendon elements acting at the shoulder, elbow and forearm. Muscle actions on joints were evaluated by SIMM generated moment arms that were matched to experimentally measured profiles. The Virtual MuscleTM (VM) model contained appropriate admixture of slow and fast twitch fibers with realistic physiological properties for force production. A realistic spindle model was embedded in each VM with inputs of fascicle length, gamma static (γstat) and dynamic (γdyn) controls and outputs of primary (Ia) and secondary (II) afferents. A piecewise linear model of Golgi Tendon Organ (GTO) represented the ensemble sampling (Ib) of the total muscle force at the tendon. All model components were integrated into a Simulink block using a special software tool. The complete VA model was validated with open-loop simulation at discrete hand positions within the full range of α and γ drives to extrafusal and intrafusal muscle fibers. The model behaviors were consistent with a wide variety of physiological phenomena. Spindle afferents were effectively modulated by fusimotor drives and hand positions of the arm. These simulations validated the VA model as a computational tool for studying arm movement control. The VA model is available to researchers at website http://pt.usc.edu/cel.

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Acknowledgments

The materials of this paper are based on the work supported by a grant from the NSF (IBN-0352117). The authors appreciate the assistance of Mr. Nayar in this project, the useful suggestions from Dr. Mileunsic. The authors wish to thank Dr. Murray for providing elbow muscle moment arm data, and Dr. Davoodi for programming MMS. Part of the shoulder/thorax complex in this model was obtained from Stanford University with permission.

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Authors and Affiliations

  1. Department of Biomedical Engineering, University of Southern California, Los Angeles, CA, 90089, USA

    D. Song & G. E. Loeb

  2. Department of Biokinesiology and Physical Therapy, University of Southern California, Los Angeles, CA, 90089, USA

    N. Lan & J. Gordon

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  1. D. Song
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  2. N. Lan
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  3. G. E. Loeb
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Corresponding author

Correspondence to N. Lan.

Appendix A

Appendix A

The muscle architectural parameters of each of the 15 muscles in the VA model were tuned step by step as described in Methods, Section “Virtual Muscle Model Parameters”. The physiological constraint for this tuning process is the fascicle length operating range within \( 0.45 \le \ifmmode\expandafter\bar\else\expandafter\=\fi{L}_{{{\text{ce}}}} \le 1 \) (See Fig. 6). At the same time, there has been a wide range of literature reports on muscle peak force (F 0), optimal fascicle length (L ce0), and tendon slack length (L ses). We compared the values of our VM parameters with those of experimental measurements and previous modeling approaches here in Table 5 on F 0, Table 6 on L ce0 and Table 7 on L ses. There is a large variability in the literature on each of the three sets of parameters due to the possible differences in experimental preparations and specimen size.17,18,20,24,33,39 However, our model parameters fall generally within the range of physiological values, and the VA model reproduces the realistic force generating capability of human arm muscles.

Table 5 comparison of muscle peak forces with literature values
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Table 6 Comparison of optimal fascicle lengths with literature values
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Table 7 Comparison of tendon slack length with literature values
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Song, D., Lan, N., Loeb, G.E. et al. Model-Based Sensorimotor Integration for Multi-Joint Control: Development of a Virtual Arm Model. Ann Biomed Eng 36, 1033–1048 (2008). https://doi.org/10.1007/s10439-008-9461-8

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