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Research Papers

A Highly Efficient Semiphenomenological Model of a Half-Sarcomere for Real-Time Prediction of Mechanical Behavior

[+] Author and Article Information
Xing Chen

Robotics Institute,
State Key Laboratory of Mechanical System and Vibration,
Shanghai Jiao Tong University,
R. 301, Mechanical Building B,
800 Dong Chuan Road,
Shanghai 200240, China
e-mail: sing@sjtu.edu.cn

Yue Hong Yin

Robotics Institute,
State Key Laboratory of Mechanical System and Vibration,
Shanghai Jiao Tong University,
R. 914, Mechanical Building A,
800 Dong Chuan Road,
Shanghai 200240, China
e-mail: yhyin@sjtu.edu.cn

1Corresponding author.

Manuscript received April 22, 2014; final manuscript received September 2, 2014; accepted manuscript posted September 11, 2014; published online October 15, 2014. Assoc. Editor: Tammy L. Haut Donahue.

J Biomech Eng 136(12), 121001 (Oct 15, 2014) (9 pages) Paper No: BIO-14-1177; doi: 10.1115/1.4028536 History: Received April 22, 2014; Revised September 02, 2014; Accepted September 11, 2014

With existent biomechanical models of skeletal muscle, challenges still exist in implementing real-time predictions for contraction statuses that are particularly significant to biomechanical and biomedical engineering. Because of this difficulty, this paper proposed a decoupled scheme of the links involved in the working process of a sarcomere and established a semiphenomenological model integrating both linear and nonlinear frames of no higher than a second-order system. In order to facilitate engineering application and cybernetics, the proposed model contains a reduced number of parameters and no partial differential equation, making it highly concise and computationally efficient. Through the simulations of various contraction modes, including isometric, isotonic, successive stretch and release, and cyclic contractions, the correctness and efficiency of the model, are validated. Although this study targets half-sarcomeres, the proposed model can be easily extended to describe the larger-scale mechanical behavior of a muscle fiber or a whole muscle.

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Figures

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Fig. 1

The mechanical configuration of a half-sarcomere in the proposed model

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Fig. 2

Activation kinetics represented by the isometric force of muscle. (a) The tension development and relax transients of a muscle under FES (functional electrical stimulation) of various frequencies. The dashed curves represent the smoothed trends. (b) The relationship between the stimulus frequency and the steady state isometric force. Here, the fitting parameter p is 5.77. The plots of all the experimental data are modified from Ref. [23].

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Fig. 3

Schematic representation of the second-order system characterizing the activation kinetics

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Fig. 4

(a) Schematic representation of the two-state cross-bridge model; (b) the bias of the distribution of P(x, t) and the mean deformation of a myosin motor under various sliding velocities

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Fig. 5

Schematic representation of the fluctuation kinetics of the AE's force

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Fig. 6

(a) The FaV relationships and FextV relationships under various activation degrees. The values of the parameters describing the FextV relationship at β = 1 are: a = 0.333, b = −0.333, A = 0.75, q = 15, and bc = 0.1; (b) The viscoelastic force of P1 under the sinusoidal length change as indicated by the inset. The parameters involved are: c1 = 0.04, c2 = 2.4, c3 = 2, and L1 = 2.6.

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Fig. 7

Simulation of the force transients under the isometric stimulations of various intensities. All the stimuli are applied at the start and stopped at 0.4 s.

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Fig. 8

(a) The length transients of the half-sarcomere under the isotonic contractions with various magnitudes of force steps; (b) the comparison of the FextV relationships between the simulated results and the experimental curve

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Fig. 9

The force response of the half-sarcomere under the successive stretch and release at constant velocities during activation. The arrows indicate the time when the length ramps are applied or finished. The plot of experimental data is modified from Ref. [25].

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Fig. 10

(a) The transients of f, β, Fext, and L during five cycles of stimulus with the phase of 10.4%; (b) the force–length orbits under the stimulus phase of 10.4%, 33%, −24%, and −4%, respectively. (c) The experimental force–length orbits under the stimulus phase of 18%, 33%, −24%, and −4%. The plots are modified from [41].

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Fig. 11

The cybernetic architecture of the proposed model for the force-control mode, wherein the insets (a)–(d) represent the force–velocity relationship, the force–length relationship, the passive force of titin, and the response of drag force, respectively

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Fig. 12

The form of G(L) that characterizes the isometric force–length relationship of a half-sarcomere

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