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Reiner Beck (zebris)
09-03-2002, 05:45 PM
Dear List Members,

one week ago I posted following question:

I just learned that some people recently do use PDM (Pressure Distribution
Platforms) to perform balance and equilibrium tests on people. The persons
centre of gravity is calculated from the pressure distribution caused by the
person standing on the platform. The position of the centre of gravity is
recorded over time while the person stands on the platform eyes closed.
As a part of the evaluation a confidential ellipsis is approximated. This
ellipsis is containing the positions of the centre of gravity during the
test. Here comes my question:
How is this ellipsis interpreted ? Do the parameter of the ellipsis (length
major axis, length minor axis, ratio of this lengths, orientation, position
to feet) have a described indication ?

The following responses have been very helpful, many thanks to those who
contributed !!

Pax!

Perhaps this can be of some help to your query about the confidence
ellipse in posturology.

The force plate records the movements of the centre of pressure
(COP). The data consists of points with x-coordinates (medial-lateral
direction) and y-coordinates (posterior-anterior direction). In
calculating the confidence ellipse one first subtractes the averages
form x and y, then rotates the coordinate systems till the coordinates x'
and y' in the new coordinate system become uncorrelated, corr( x', y') =
0. (If we let x' and y' denote the vectors consisting of the dat points
x'[k] and y'[k], then the new coordinate axes are obtained as the
eigenvectors of the 2x2-matrix C with C[1][1] = x'*x', C[1][2] = C[2][1] =
x'*y', C[2][2] = y'*y' .) It's now supposed that x' and y' are statistically
indpendent. Next, if the standard deviation of x' and y' are stdx and
stdy, one assumes that the normalized variables x'' = x'/stdx, y'' =
y'/stdy are gaussian with zero mean and standard deviation = 1.
Finally, define the variable z = x''^2+y''2. According to our assumptions
of gaussian distribution this will have a chi-square distribution of
degree 2. For instance (looking up a table),

Prob(z < 5.995) = 0.95

which means that the 95% confidence ellipse will be a circle of radius
sqrt(5.995) in the x'',y''-system, and an ellipse with minor and major
axes of length sqrt(5.995)*stdx and sqrt(5.995)*stdy in the original
coordinate system. If the data points are approximately gaussian
distributed it means that ca 95% of the points are inside this ellipse.
The main parameters obtained from this ellipse is its area [units mm2]
and the inclination of the major axis. The area is e.g. used in
caluclating the Romberg quotient: QR = 100*S_ec/S_eo; where S_ec is
the area of the ellipse in case of eyes closed, S_eo the area in case of
eyes open. The 90% confidence ellipse is also commonly used
(replace 5.995 by 4.605 above).

One traditional test is to measure balance during quiet standing first
with eyes open, then with eyes closed, and compare the areas. So the
area is a basic parameter. Basically the tests consists of a
measurement under *normal* conditions, followed by a test with
altered conditions that might influence the balance control mechanism.

Also important is the spectrum of the x and y time series which may
reveal subtle changes in swaying. Odd pekas in the spectrum may
show some pathological condition. I have worked on an experimental
software for force plates and have thus become familiar with a number
of different posturological parameters in use and I am testing some
new ones. You might find this website useful (papers and documents):

http://perso.club-internet.fr/pmgagey/Index.htm

mantained by one of the masters in the field, P-M Gagey.

Regards

Frank B

===================================
Frank Borg
Chydenius Institute/ Jyväskylä Univ.

PB 567
Pitkänsillankatu 1-3
FIN-67701 Kokkola
Finland
frank.borg@chydenius.fi

====================================




Dear colleague,
as far as I know, different methods are used in the computation of the COP
during postural assesments. In the case you'll use the one mentioned in your
e-mail (which analyzes the ellipses), I think you should consider only the
90% of the total measured area. One of the most precise method I know is the
Principal Component Analysis (PCA), but I'm sorry I can't explain exactly
how it works here.
Good luck for your work.

Best wishes,

Federico Formenti


-------------------------------------
Federico Formenti

University of Verona
Department of Sport and Exercise Sciences
e-mail: fformenti@univr.it
off: 0039 045 895 26 33
fax: 0039 045 895 26 31



The clinical interpretation is complex. Some studies have
demonstrated clinical utility without trying to use it as an explicit
marker of a specific (uni-dimensional) biomechanical impairment.

From first principles the use of the ellipsoid is difficult to
interpret in isolation.

In my opinion the excursion of the FP (Force platform) data is not
independent of the level of compensation or control strategy the
subject uses. For example I did some work on sitting balance in
individuals with spinal cord injury. What I found was that
individuals with paraplegia had greater ellipsoid area (95%tile CI)
when compared to individuals with quadriplegia. This would seem
paradoxial since individuals with the higher lesion have poor sitting
balance.... however what we were seeing was a highly controlled
attempt by the individuals with poorer sitting balance. [This is
necessary because if they move away from their safe equilibrium
posture they have no capacity to save themselves]. The individuals
with paraplegia were much more comfortable to sit without support and
therefore did not need to have such a high frequency of control.

The sway paths lengths were the same and [as demonstrated by
frequency analysis] therefore the frequency content of the
Quadriplegic was significantly higher.

I have see this in individuals with brain injury and also in other
"stability" tests.

Cheers
GTA.

p.s Lord et al has used a modified excursion assessment as a factor
in prediction of falls in the elderly.


A long time ago I use the area of the ellipsoid, sway path length and
the frequency content. I chose these after a long look at the
literature. These may not be the best choices. [I have to do the
fourier transformation in excel on a computer which at the time had
1Mb RAM and was the best computer at the school:-)].

The area of the ellipsoid is the one option - of course how do you
fit the ellipsoid? I determined the 95%tile limits of the AP and ML
axes and then multiplied them - a scaling factors provides a real
translation to the area but statistically the data are the same. (4pi)

You may wish to translate the data around the axes to optimise the
fitting of the actual ellipsoid.

I suppose you have to decide if you use linear excursions in the ML
and AP directions or combine them for a 2D (planar estimate). The
difference probably depends on the foot position and control
strategies etc and your hypotheses.

Some people look at the frequency content and see if there is a lot
of power at the higher frequencies (peaks rather than median) -
suggesting a higher than average "frequency of control" evidence in
Brain injured individuals trying to maintain balance and people with
more specific neurological disorders such a Parkinson's Disease.

With the digital filtering capacities these days you could look at
combinations of the sway path length at frequencies higher than say
0.5Hz. and 1Hz , etc...


Comments from my side:

There is to differ between tests performed on force plates (FP, such as
AMTI) and pressure distribution measurement platforms (PDMs). The reason for
this is a big difference in the sampling rate between the systems (FP > 1000
Hz, PDM < 100 Hz). As a consequence things can only be compared and
transferred with great caution !



Many thanks !

Cheers
Reiner

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