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Steve Piazza
09-12-2008, 05:23 AM
Paolo de Leva makes several good points and asks some important questions
about the modeling results we described in our earlier post. We'll try to
provide a more detailed description of our model and the mechanism by which
short muscle moment arms increase forward impulse generation in the
simulation.

The model is a very simple: a 2-dof planar linkage with revolute joints at
the "ankle" and "toe" and two segments, a massless "foot" and a "body"
segment that incorporates a point mass atop a massless rod. There is a
single muscle that passes behind the ankle that we modeled as a Hill-type
muscle-tendon actuator with force that depended on fiber length and velocity
and an elastic tendon. We are interested in plantarflexor function, so we
gave the muscle force-generating properties that approximate the combined
triceps surae. An image of the model may be seen here:

http://www.biomechanics.psu.edu/research/spiazza/model.jpg

We simulated a sprint pushoff with the model in an initial configuration
like that seen in the picture and with the mass moving forward with some
initial velocity. The muscle was fully active throughout the
forward-dynamic simulation and the simulation ended when the vertical
constraint force at the toe joint ceased to act upward, signifying toe-off.
There were no constraints on the direction of the GRF and the muscle moment
arms were changed in two different ways: by keeping the heel-toe length
constant and moving the ankle, and by keeping the ankle-toe length constant
and changing the length of the heel (this choice did not appreciably affect
the simulation results).

With no muscle force and a massless foot, the force at the toe would be zero
and the simulation would end immediately; there is an upward vertical GRF
only as long as muscle force is being generated. A long muscle moment arm
(~60 mm) results in rapid muscle fiber shortening that reduces muscle force
to zero very quickly due to force-velocity effects and movement down the
ascending limb of the active force-length curve that occurs with
plantarflexion. Very short moment arms (
> You wrote:
>
> ..."the force-velocity-related benefits of having reduced shortening
> velocity result in contact being maintained with the ground for longer,
> thus
> enabling greater forward impulse generation."
>
> This is a surprising result, and I cannot guess the mechanism through which
> a shorter moment arm (with consequent reduced shortening velocity and
> higher
> force) produces a longer contact time, although I have read your abstract
> (http://www.asbweb.org/conferences/2005/pdf/0090.pdf).
>
> It is not as simple as it seems. With a fixed displacement (range of
> motion)
> in a given direction (e.g. "forward"), if you push harder in that direction
> throughout the pushoff, your time of force application (contact time)
> becomes smaller, and vice versa.
>
> Thus, one way to maintain contact "with the ground for longer" would be to
> push less hard throughout the pushoff (as if your leg were a spring with
> lower stiffness). But if you did so, even though the contact time would
> become longer, your impulse would become smaller (the increase in time of
> force application would not suffice to compensate for the decrease in
> force).
>
> Another way would be to change the range of motion: you would obtain a
> longer range of motion in the forward direction if your leg were more
> tilted
> forward at the end of the extension, or more flexed at the beginning of the
> extension (hip and knee flexion is limited, however, by "short term
> fatigue", otherwise everybody would jump from full squat...).
>
> A third way would be to push harder in the first part of the pushoff, and
> less hard in the second part. This may give a larger final velocity and a
> larger impulse, even with a fixed range of motion...
>
> Your abstract does not explain this mechanism. Do you have an explanation?
> Also, what are the simulation constraints? Was the orientation of the
> ground
> reaction force (GRF) fixed? And what about the moment arm of the GRF
> relative to the ankle rotation axis? Subjects with a longer arm for the
> muscle force and longer muscle fascicles may also have a longer arm for the
> GRF (i.e a longer foot). A longer foot would increase range of motion...
>
> Thank you,
>
> Paolo de Leva
> University of Rome - Foro Italico.
>
>
> -----Messaggio originale-----
> Da: * Biomechanics and Movement Science listserver
> [mailto:BIOMCH-L@NIC.SURFNET.NL] Per conto di Steve Piazza
> Inviato: Friday, September 05, 2008 5:15 PM
> A: BIOMCH-L@NIC.SURFNET.NL
> Oggetto: Re: Bolt
>
> At NACOB last month, we presented data that supports Ton's expectation that
> sprinters would benefit from having smaller moment arms. We measured
> tendon
> excursion with ultrasound to estimate the plantarflexion moment arms of the
> Achilles' tendon in collegiate sprinters and height-matched non-sprinters
> and found the sprinters' moment arms to be 25% smaller.
>
> Why smaller moment arms might confer an advantage to sprinters, and when
> that advantage occurs, is an interesting question. We made a simple (but
> anthropomorphic) 2-segment, 1-muscle model of a sprint pushoff and found
> that smaller moment arms conferred an advantage even at slower speeds
> consistent with the start of the race. The simulated "plantarflexion"
> moment is indeed lower when smaller moment arms are imposed, but the
> force-velocity-related benefits of having reduced shortening velocity
> result
> in contact being maintained with the ground for longer, thus enabling
> greater forward impulse generation.
>
> Steve Piazza
> Sabrina Lee
> Penn State University
>


--
Stephen Piazza, PhD
Associate Professor
Departments of Kinesiology, Mechanical Engineering,
and Orthopaedics & Rehabilitation
29 Recreation Building
The Pennsylvania State University
University Park, PA 16802