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J Theor Biol. 2010 Feb 21;262(4):634-43. doi: 10.1016/j.jtbi.2009.10.028. Epub 2009 Oct 28.

The expression of the skeletal muscle force-length relationship in vivo: a simulation study.

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Biomechanics Laboratory, The Pennsylvania State University, University Park, PA 16802, USA.


The force-length relationship is one of the most important mechanical characteristics of skeletal muscle in humans and animals. For a physiologically realistic joint range of motion and therefore range of muscle fibre lengths only part of the force-length curve may be used in vivo, i.e. only a section of the force-length curve is expressed. A generalised model of a mono-articular muscle-tendon complex was used to examine the effect of various muscle architecture parameters on the expressed section of the force-length relationship for a 90 degrees joint range of motion. The parameters investigated were: the ratio of tendon resting length to muscle fibre optimum length (L(TR):L(F.OPT)) (varied from 0.5 to 11.5), the ratio of muscle fibre optimum length to average moment arm (L(F.OPT):r) (varied from 0.5 to 5), the normalised tendon strain at maximum isometric force (c) (varied from 0 to 0.08), the muscle fibre pennation angle (theta) (varied from 0 degrees to 45 degrees) and the joint angle at which the optimum muscle fibre length occurred (phi). The range of values chosen for each parameter was based on values reported in the literature for five human mono-articular muscles with different functional roles. The ratios L(TR):L(F.OPT) and L(F.OPT):r were important in determining the amount of variability in the expressed section of the force-length relationship. The modelled muscle operated over only one limb at intermediate values of these two ratios (L(TR):L(F.OPT)=5; L(F.OPT):r=3), whether this was the ascending or descending limb was determined by the precise values of the other parameters. It was concluded that inter-individual variability in the expressed section of the force-length relationship is possible, particularly for muscles with intermediate values of L(TR):L(F.OPT) and L(F.OPT):r such as the brachialis and vastus lateralis. Understanding the potential for inter-individual variability in the expressed section is important when using muscle models to simulate movement.

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