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EMD cont.

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  • EMD cont.

    Dear Readers

    It seems most people agree there is something to the electromechanical
    delay (EMD). The concept itself betrays its engineering origin where it
    used to mean the delay of electromagnetic/mechanic switches (relays).
    [Has anyone tracked the history of EMD in biomechanics?] Thinking of the
    muscle as an actuator controlled via motor neurons easily provokes the
    analogy with the relays. No one doubts there is sort of a turn-on-time
    and a turn-off-time for the muscle. The questions are whether they can
    be measured and defined in robust ways, and whether they are of any
    physiological interest. For instance, i hit upon the paper

    Corcos et al., Electromechanical delay: An experimental artifact (J
    Electrmyogr Kinesiol, 2, 2, 1992, 59-68)

    where is stated that "published values of electromechanical delay are
    all so severely influenced by unknown factors of the apparatus on which
    they are made that the published record is void of physiological
    significance" (67). Their conclusion about the irrelevance of EMD may
    apply if one uses their methodology for "measuring" it. Indeed, they
    define EMD as the time from onset of DETECTABLE changes in EMG to the
    onset of DETECTABLE changes in force, and what is "detectable" naturally
    depends on the resolution etc; i.e., becomes device dependent. If one
    adapts the threshold level (they call it T) close to the noise level,
    instead of say some fraction of MVC or standard deviation of EMG and
    force, the results will most likely vary with the resolution, as they
    demonstrate experimentally.

    Corcos et alii thus raise a valid point about the importance of how one
    tries to extract parameters from data, and to what extent we obtain
    intrinsic values, or values that mostly reflects properties of the
    measuring device. Adopting the threshold idea for determining EMD the
    authors obtain, for a simple dash-pot model, the approximative expression

    t_f = sqrt {2*(T/R)* B* (1 + K_d/K_s)}

    for the time t_f "to generate detectable changes in force". T is the
    detection threshold; R is the rate of force development of the muscle
    (one assumes that Force(t) of the contractile element grows with time t
    as R*t; i.e., a linear ramp); B is the viscosity parameter of the muscle
    (corresponding to the velocity term in the Hill-model); K_s is the
    spring constant of the muscle SEC; K_d is the spring constant of the
    measuring device (e.g. a hand grip). This expression presupposes an over
    damped muscle (viscosity term dominates); indeed, the over-damped case
    leads to an equation of the form dx/dt = a*t from which one obtains the
    above expression setting x(0) = 0 and x(t_f) = T.

    Incidentally, a recent paper

    Isabelle et al., Electromechanical assessment of ankle stability (Eur J
    Appl Physiol 88, 2003, 558-564)

    demonstrates a method for measuring EMD of the peroneal muscles (PL)
    using supramaximal electrical stimulation while the participant was
    standing on a force plate. The EMD was defined as the time from onset of
    PL EMG activity to the onset of the lateral ground reaction force (GRF).
    For healthy people (no functional ankle instability, FAI) they obtained
    10.5 ± 0.7 ms for bipedal stance, and 8.7 ± 0.6 ms for monopedal stance.
    These numbers could makes sense, but we are not informed how exactly the
    onsets are determined, leaving it open to the criticism of Corcos et
    alii. The lower EMD value for monopedal stance is interpreted as a
    consequence of "higher SEC stiffness" which would be in line with the
    expression for t_f (which decreases with increasing K_d).´The effect of
    mechanical coupling could have been tested making also measurement with
    compliant foam between the feet and the force plate. Isabelle et alii
    note the variations in the EMD values obtained by various groups but
    they seem unaware of the points raised by Cocos et alii.

    One would certainly expect EMG-to-force models to address the EMD-issue
    as well. One example is

    Lloyd & Besier, An EMG-driven musculoskeletal model to estimate muscle
    forces and knee
    joint moment in vivo (J Biom 36, 2003, 765-776).

    They too go back to the "critically damped linear second-order
    differential system" which they render as a discrete IIR-filter. This
    filter involves a delay d which they set to 40 ms and refer to as EMD
    and which they employ because it "improves the synchronization between
    activation and the force production". Referring to the paper by Cocos et
    alii they think d should be reduced to 10 ms in future models "by
    modelling the delay of force production within the musculotendon unit".
    So the quantity seems model-dependent, but this is not a problem but a
    basic condition of the physical sciences in general. While the use of
    black box models (such as based on neural networks etc) and system
    identification methods may have important uses they turn a blind eye on
    the physiological interpretations of the parameters.

    Finally, the cross-correlation analysis of EMG-force has been up, and it
    does proved a measure of phase shift between EMG and force, but its
    relation to turn-on and turn-off times is probably quite convoluted,
    necessitating a physical (tailored) model to make a headway on that (a
    problem i am interested in).

    Regards Frank Borg


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