Parameter Estimation in a Crossbridge Muscle Model

[+] Author and Article Information
David C. Lin

Departments of Biological Systems Engineering and Veterinary and Comparative Anatomy, Pharmacology, and Physiology, Washington State University, Pullman, WA 99163

T. Richard Nichols

Department of Physiology, Emory School of Medicine, Atlanta, GA 30322

J Biomech Eng 125(1), 132-140 (Feb 14, 2003) (9 pages) doi:10.1115/1.1537262 History: Received December 01, 2001; Revised August 01, 2002; Online February 14, 2003
Copyright © 2003 by ASME
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Grahic Jump Location
Block diagram of the experimental servo system which implemented force controlled perturbations. The dSpace board was a digital signal processing (DSP) board with analog to digital and digital to analog capabilities which implemented the blocks within the dotted outline. Fd(t) was the desired time-course of force which was generated by software. G1 and G2 are the gains of the force controller (see Eq. (1)), Ld(t) was the input to the length-servo, L(t) was the actual fiber length, and F(t) was the force generated by the muscle fiber.
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The staircase length perturbation which was used to record the F-L characteristics of a single fiber. Shown are the active and passive forces recorded from one fiber during the shortening (heavy line) and the lengthening (light line) perturbation. The active force was estimated by subtracting the force recorded in the passive trial from the force recorded in the active trial. Fiber lengths were normalized to the initial fiber length (Lo).
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The force ramp perturbation which was used to record the F-V characteristics of a single fiber. Shown are two trials from one fiber, one shortening (heavy line) and one lengthening (light line). The rates of the force ramp were ±1.5 Po/s. The active force was estimated by subtracting the force recorded in the passive trial from the force recorded in the active trial.
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The distribution-moment crossbridge model parameters. The solid line describes the attachment rate (f(x) in Eq. (4)) as a function of crossbridge position, and the dashed lines describe the detachment rate (g(x)). The constant “h” is often called the crossbridge reach.
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Averaged F-L data across all fiber data, plotted with standard deviation. The force data of each fiber were first normalized to the initial active isometric force (Fo) and then averaged across fibers.
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The F-V data of an individual fiber. Shown are the filtered experimental data (solid line) and the best fit of the hyperbolic Eqs. (2) and (3) (dashed-dot line).
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Averaged F-V data across all fiber data, plotted with standard deviation (dashed line). The F-V data of each fiber were first fitted to hyperbolic equations, the velocity evaluated at specific forces, and the velocities of all trials averaged at those forces.
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The averaged F-V data (solid line) of Fig. 7 overlaid with the DM model simulation (dashed line) with the best fitting parameters. The simplex algorithm minimized the sum of the squared velocity error difference between the simulation and experimental data.
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The distribution of parameter estimates calculated from the bootstrapping 100 different samples. Shown are the distributions which appear the most normal and the least normal.
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The mean normalized standard deviation of each parameter estimate, calculated by dividing the standard deviation by the mean of the parameter estimates derived from the bootstrapping method.



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