View Full Version : Responses on original posting "Correlation Dimension of EMG "

Swie Yuniarto W
01-12-2006, 04:56 PM
Dear All,

As I received severals mail asking to post responses on my
original posting, below is the response I got.
Hope will be useful.

Yuniarto Swie/ UEC -JP

---------Original Posting---------------
Dear Experts,

I am doing Chaotic analysis to EMG by taking the
Correlation Dimension, and found in most case that the
Corr. Dimension increased as the increasing of the muscle

However in some case, it was observed that even the
contraction supposed to be weak (at least showed from the
EMG power), the Corr. Dim is relatively high (higher than
the relax stage). As noise has been removed, We consider
that there is underlying mechanism cause the high
Corr.Dimension in the relatively weak contraction.

Can anyone advise on such phenomenon and to share idea
onwhat happening behind.

RESPONSES : 3 postings (excluded mails requested to post
the responses in Biomch-L)
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\#1. Dear Yuniarto:

If you are analyzing raw EMG signals, then I would expect
these signals to be high dimensional. The signal itself
is an interference pattern generated by the interference
of the electrical output of a large number of individual
motor units (which may be from a few to a few hundred,
depending on the muscle you're looking at and the level of
activation). If one can think of each motor unit as a
"degree of freedom" in the underlying system, then the
true dimension could be quite high. This could cause you
problems, as the correlation dimension algorithm is not
very good at assessing such high dimensional systems
(i.e., d > about 4 or 5). You should be looking at the
entire correlation integral (not just the slope of the
curve) to see if you really are obtaining results that
will allow you to compute a valid correlation integral to
begin with. You should also see if/how these curves
change as you vary the embedding dimension. If they do
change substantially, this could be problematic.

Also, I don't know how you are filtering your data, but
standard frequency domain linear filters (e.g. Butterworth
low-pass filter) can substantially alter the nonlinear
properties (including correlation dimension) of inherently
nonlinear signals.

There's an excellent text that deals with these issues,
recently published in it's second edition, by Holger Kantz
& Thomas Schreiber. The book is called "Nonlinear Time
Series Analysis" and is published by Cambridge University
Press (2nd Ed., 2004). These authors also offer their
analysis software (the "TISEAN" package) via a
well-documented web site:

I hope this is helpful.

Good luck!
Jon Dingwell

/#2. F Borg/* wrote:
> Pax!
> I am afraid there are not too many experts on using
nonlinear time series analysis methods to EMG. I did
general survey of methdos some years back (available as
the first paper here -->
> www.netti.fi/~borgbros/bisoni ) and turned up only a
few devoted to EMG.
> Recurrence plot analysis seems to be one of the
favoured methods.However, if someone finds something like
correlation dimension to work that would be interesting. I
would expect fatigue would be the
natural phenomenon to investigate. In order to check your
results youwould have to map the correlation function C(x)
vs the scale parameter x (I guess
> you have used the Grassberger-Procaccia algorithm).
It is true that noise can drive up the *dimension*.
Denoising can also create artifacts.
> Only a closer view of your stuff would make it
possible to tell.
> Best regards

/# 3. Pax!

At low signal levels the system may play tricks. In a
recent mesurement
on the leg during quiet standing we found eg a perfect
match between
gastroc and tibialilis sEMG -- TA had a very weak signal
but it was a
sort of crosstalk from GA and when amplified and filtered
it matched
perfectly the GA sEMG!

One may also wonder what SVD filtering does to a weak
signal. (Does the
algorithm use relative thresholding and scaling?) Try to
leave out SVD
and use only LP and HP. I spotted a paper (Hu et al.,
Classification of
surface EMG signal with fractal dimension, Journal of
University 2005 6B(8): 844-848, www.zju.edu.cn/jzus )
where they found
that using just LP 350 Hz seemed to produce intelligible
results for D_c
calculations (D_c found to be around 1 - 3 -- forearm
supination/pronation) for the purpose of classification.

The connection between fatigue and synchronization makes
Recurrence quantification analysis (RQA) seems eg to show
an increase in
the so called %DET parameter for increasing fatigue (there
is a short
discusion in the book Merletti & Parker, Electromyography,
IEEE Press
2004, ch. 6). In order to study possible relations between
spectrum and
RQA maps and parameters I think one would have to run
simulations woth
various types of signals and then compare the results
obtained by the
different methods of analysis. As yet I have not come
accross (as far as
I remember) such a study although it would be quite
straightforward to
do (but requires some work).

Regards Frank

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