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Kclowers
10-17-2001, 06:15 AM
Dear Group,

Thanks to all of those who replied to my original posting (see below). Here is
the summary of your responses.

Part of the problem seen with the force-velocity curve when modeling eccentric
components is a mathematical one. The eccentric hyperbola has an asymptote,
which changes to infinity. "One solution would be to extend the hyperbola to
infinity with a linear slope, this however increases force with velocity but
the muscles usually don't operate at that high velocities that this would
matter." (Harald Boehm, German Sport University) Furthermore, “The
Force-Velocity curve is then limited to a value of about 1.2 to 1.8 times the
force.” (At Hof, a.l.hof@med.rug.nl) Ton van den Bogert
(bogert@bme.ri.ccf.org ) also added that, “In simulation work (with Van Soest)
they used a muscle model in which the eccentric force-velocity curve at large
stretching velocities approached a straight line with non-zero slope. This is
done because in forward dynamics you need to have a velocity at each level of
force. You can't have a horizontal
asymptote. You can make the slope of the line arbitrarily small but not zero.”

All of the responses included references that addressed this topic and they
are listed below. Again, thanks for the information.

Reference:

Aubert, X., Roquet, M.L. and Van der Elst, J. (1951). The tension-length
diagram of the frog’s sartorius muscle. Arch. Intern. Physiol., 59, 239-241.

Bloom, W., and Fawcett, D.W. (1968). A Textbook of Histology (9th ed).
Saunders, Philadelphia.

Cole GK, van den Bogert AJ, Herzog W, Gerritsen KG.
Modelling of force production in skeletal muscle undergoing stretch.
J Biomech 1996 Aug;29(8):1091-104.

Edman, K. A. P. (1970). The rising phase of the active state in single
skeletal muscle fibers of the frog. Acta Physiol. Scand., 79, 167-173.

Edman, K. A. P., and Hwang, J. C. (1977). The force-velocity relationship in
vertebrate muscle fibers at varied tonicity of the extracellular medium.
J.Phyiol., 269, 255.

Eisenbeg, E., Hill, T. L. and Chen, Y. (1980). Crossbridge model of muscle
contraction: Quantitative analysis. Biophys. J., 29, 195-227.

Ford, L. E., Huxley, A. F., and Simmons, R.M. (1977). Tension responses to
sudden length change in simulate frog muscle fibers near slack length. J.
Physiol., 269, 441-515.

Gordon, A. M., Huxley, A. F., and Julian, F.J. (1966). The variation in
isometric tension with sarcomere length in vertebrate muscle fibers. J.
Physiol., 184, 170-192.

Herzog, W. (2001). History dependent force properties of skeletal muscle: in
vitro, in situ and in vivo considerations. In XVIII ISB congress (ed. R.
Mueller, H. Gerber and A. Stacoff). Zuerich: Lab. Biomechanics, ETH Zurich

Hill, A.V. (1938). The heat of shortening and the dynamic constants of muscle.
Proc. R. Soc, London B, 126, 136-195.

Hof, A. L., 1990. Effects of muscle elasticity in walking and running. In: J.
L. Winters and S. L.-Y. Woo (eds) Multiple muscle
systems.,Springer,New York, pp. 591-
607.

Hof, A. L. (2001). Muscle mechanics and neuromuscular control. ( Keynote
lecture). In ISB 2001 Congress (ed. A. Stacoff). Zurich.

Hof, A. L., Zandwijk, J. P. v. and Bobbert, M. F. ,2001. Mechanics of human
triceps surae muscle in walking. running and jumping. Acta Physiol. Scand. in
press,

Huxley, A. F. (1957). Muscle structure and theories of contraction. Prog.
Biophys. Biophys. Chem., 7, 255-318.

Huxley, A. F. (1974). Muscular Contraction. J. Physiol., 243, 1-43.

Huxley, A. F., and Simmons, R. M. (1971). Mechanical properties of the
cross-bridge of frog striated muscle. J. Physiol., 218, 59-60P.

Jewell, B. R., and Wilkie, D. R. (1958). An analysis of the mechanical
components in frog’s striated muscle. J. Physiol., 143, 515-540.

Julian, F. J., and Moss, R. L. (1980). Sarcomere length-tension relations of
frog skinned muscle fibers at lengths above the optimum. J. Physiol., 304,
529-539.

Mackean, D. G, (1962). Introduction to Biology. Murray, London.

McMahon, T. A. (1984). Muscles, Reflexes, and Locomotion. Princeton University
Press, Princeton, N.J.

Nigg, B. and Herzog, W. (1994). Biomechanics of the musculo-skeltal system.
Chichester: John Wiley & sons.

Squire, J. (1981). The Structural Basis of Muscular Contraction. Plenum Press,
New York.

Zandwijk, J. P. v., Bobbert, M. F., Harlaar, J. and Hof, A. L. ,1998. From
twitch to tetanus for human muscle: experimental data and model predictions
for triceps surae. Biol. Cybernetics 79, 121 - 130.


**ORIGINAL POSTING**

Dear Group

I am a graduate student at the University of Tennessee in biomechanics. I am
currently working on my thesis. I am trying to develop a muscle model for the
triceps surae muscle-tendon complex applied to landing. I am using Maarten
Bobbert's paper as a guide. However I am having difficulty with the eccentric
component of the model. When graphing out the Force-velocity curve much like
Nigg and Herzogg did in their book, the eccentric component of the graph is
quite strange. Thus, my question and call for help is to anyone who could
give
me a lead on some literature dealing with this problem.

Sincerely,

Kurt

Kurt Clowers
Biomechanics
The University of Tennessee
1914 Andy Holt Drive
Knoxville, TN 37996
865-974-8768

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