View Full Version : Electromagnetic delay - turn on/off times

06-14-2005, 09:27 PM
Dear readers

I am linking another EMD-discussion thread w/ Chris Kirtley into this
forum, e.g. the refs popping up may be of interest to you fellows too.
For convenince i have arranged the stuff in chronological order,
starting w/ first response etc.

Best regards

Frank Borg
Biosignals project
Jyväskylä University, Chydenius Institute


Indeed, i have been brooding over the EMD the last weeks while preparing
a manuscript. In our measurements of Gastroc. (GA) EMG and Center of
pressure (COP, anterior-posterior [A/P]) during quiet standing we obtain
a consistent time lag between EMG-envelope and COP around 300 ms. This
delay is the time by which one must shift the EMG-envelope forward in
order to match the COP. Part of this may be attributed to EMD which is
often quoted to be about 100 ms. Now, EMD is not a single value - one
has the latency (time from onset of EMG to the onset of
force/contraction (meaning of *onset* is up to a particular
definition), and the time from cessation of EMG to the cessation of
force, plus perhaps variation w/ dynamical conditions (isometric vs
non-isometric etc). Such delays are expected due to physiological
processes in the muscle (Ca-dynamics, cross-bridge processes, etc).
Winter (Biomechanics, 2005 ed) does indeed quote twitch times but how
that might be related to EMD is not investigated. Indeed, there might be
a delay from the onset of EMG to the onset of the twitch. Winter
mentions (p 210) the *turn-off* times of muscle about 300 ms, this
turn-off being that which is usually referred to as EMD.

Loram and Lakie (J Physiol 564.1 2005 281-293) have recently used
ultrasound to measure changes in GA muscle length during quiet standing,
and they report an average time lag of about 110 ms between
GA-EMG-envelope (RMS, 100 ms window) and muscle length using
cross-correlation analysis. To this they add half of the RMS-window,
obtaining a final average value of 110+50 = 160 ms. We have used a
zero-lag filter computing the EMG-envelope obtaining a good correlation
w/ A/P COP [which is proportional to the plantar flexor torque] if
adding a time lag around 300 ms, as already mentioned. Using
RMS-envelope we get similar values without the *window-correction*
indicating that RMS+*correction* may be an insecure method. (Loram
informs that they will redo the calculations using 0-lag filters.) It is
not yet clear how to factor this 300 ms into EMD and something else.

EMD must however be part of any EMG-to-force model. As you mention the
*rather arbitrary result* of EMD this seems to be a thing associated
with all filters which add phase shifts. In a classic paper Soechting &
Roberts (J. Physiol (Paris) 70 1975 779-793) proposed a 2nd order low
pass filter with cutoff 2.5 Hz for obtaining force from rectified EMG.
Their data was based on feedback measurements involving biceps brachii
and isometric condition. Extracting data points from their paper i have
verified that the filter works quite well. We made the interesting
finding that this filter works well for GA-EMG vs COP too if one uses
the cutoff f_c = 1 Hz. Moreover, with this cut-off value the filter is
able to account for the time lag also since the time shift of the filter
will be around 1 / (PI*f_c) := 318 ms in the relevant band-width. So,
there arises an interesting question how this simple mathematical filter
(corresponding to a 2nd order critically damped system) may relate to
the physiology.

Commonly when one measures force in biomechanics it may be the result of
several muscles + tendon in which case the EMG-(effective)force lag is
affected by more factors than the basic EMD. Hof is known i.a. for his
studies on the influence of muscle-tendon properties on the force
output. Muscle-tendon compliance may add something like 10 - 20 ms to
the delay of the force onset (latency) in case of GA. If we consider
feedback loops involving stretch receptors and Golgi (GTO) we get
additional *impedance* effects with characteristic times of the order
B/K where B is the muscle viscosity factor and K the active stiffness.
As is already apparent, many factors contribute to the observed time
lags and i think that one will have to use intelligent mathematical
models (perhaps each
applicable only to a limited setup/situation) plus measurement data in
order to untangle them.

Ok, these were some rapid responses to the EMD-issue which will no doubt
deserve a

thorough study.

Regards frank borg

Thanks Frank.

I agree with most of what you say. It seems to me that the delay is a
purely artificial concept due to people using inappropriate envelopes -
if they use 2.5 Hz (or actually that determined by the twitch time, as
described by Soechting/Winter - actually I think it might have been
Miller who first proposed it) they won't see any time delay between EMG
envelope and force. But for some reason EMG worker's rarely seem to
understand this logic - I think it is really an aesthetic issue -
they just like seeing spikes!



True, the Soechting-Roberts filter appears in connection w/ EMG earlier
e.g. in Milner-Brown et al (J Physiol 228/2 1973 285-306) in a somewhat
different context. They measure the EMG from single MU (following
Basmaijan) in dorsal interosseus + gross isometric force (index finger
toward thumb) and investigate the gain (EMG-to-force) vs frequency. For
the mean cut-off they obtain 2.4 Hz. However, they do not investigate
the phase shift or delay and how it relates to the filter. (Their work
seems to be directed toward understanding postural tremor, still a
pretty foggy area i think.)

Two general remarks about delay may be added. First, in recent years the
importance of delay in physiological and physical feedback systems has
been recognized. Secondly, in prosthetics and control the role of delay
might become quite important too.

Regards frank b

Chris Kirtley wrote:'
P.S.: I actually did my PhD on closed-loop control of muscle for
FES-orthotics, so I know all about the control implications!



I had a quick browse at your paper [note: p 3 seems missing - Dokument
nicht gefunden!], quite interesting. How well do such systems work, can
plegic people walk and stand using FES+feedback? Quiet standing would
be the *simplest* case - there is also the debate whether feedback
control suffices in this case (a somewhat foggy area too). Back to EMD
it seems in control applications to get hidden away since, as has been
noticed, (causal) filters may cover it. By the way, Winter's terminology
of turn-on and turn-off times may be more revealing than *EMD*.

I recently got the new book en electromyography by Merletti & Parker,
eds., (Wiley 2004) and i was expecting to see something interesting
about EMD, but nope ... Anyway, i think a general study of the various
time scales/characteristic times in biological system, in which e.g. EMD
may be one case, is of interest. Correct timing is surely quite
essential, and knowing how that might be achieved in a *wet system*.
Millions of years of evolution has probably produced subtle and robust
*optimal* solutions+redundancy.

Dear Frank,

Sorry about p3 - not sure where that went. Will have to scan it again
when I have time. It was really an academic exercise, in that FES
systems were then, and largely remain, based on simple open-loop on/off
control. It really hasn't advanced in the last 20 years. There are big
obstacles - partly the control but mainly the fatigue because it is a
tetanic stimulation which is very inefficient and non-physiological. We
had complete paraplegics walking in the mid-80s though - it's not
difficult to do. But it's not much use to the patients in their daily
lives. I've just sent another response on the delay question - I think
it would be nice if you sent your comments to the list too



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