Simon:

You wrote:

<<"......stability, that much overburdened word with an unstabilised
definition." Bellman, R.: Stability theory of differential equations. McGraw
Hill Book Co., New York, 1953


A while back we talked about definitions of "stability". I was scanning a
book on cybernetics today (Ashby, W.R: An introduction to
cybernetics.Chapman & Hall Ltd. London, 1973). The author, W. Ross Ashby
M.A., M.D., D.P.M. seems to have been a podiatrist? A chapter of the book is
devoted to stability and he offers an interesting definition which I think
may also be applicable to the problem of defining excessive pronation:

Stability: "...that although the system is passing through a series of
changes, there is some aspect that is unchanging; so some statement can be
made that, in spite of the incessant changing, is true unchangingly. Thus,
if we take a cube that is resting on one face and tilt it by 5 degrees and
let it go, a whole series of changes in position follow. A statement such as
"it's tilt is 1degree" may be true at one moment but it is false at the
next. On the other hand, the statement "its tilt does not exceed 6 degrees"
remains true permanently. This truth is invariant for the system. Next
consider a cone stood on its point and released, like the cube, from a tilt
of 5 degrees. The statement "its tilt does not exceed 6 degrees" is soon
falsified, and (if we exclude reference to other subjects) so are the
statements with wider limits. This inability to put a bound to the system's
states along some trajectory corresponds to "instability".

So can we make an invariant statement for the foot or its joints during
gait? What in spite of incessant changing, is true unchangingly?>>

Stability is a difficult word to deal with in foot biomechanics, as we have
mentioned before in previous postings on the same subject.  I have been
doing some thinking about this subject in response to one of Eric Fuller's
postings and/or lectures recently in which he stated that stability would be
difficult to measure in a foot.

I think that the problem of measuring frontal plane foot stability in the
foot in relaxed bipedal stance could be overcome by using a simple device
which applies given magnitudes of external forces to the foot which would
tend to cause either inversion or eversion moments on the foot.   By then
measuring the kinematic response of the foot to those externally generated
moments, a ratio of Newtons of force to degrees of rotational movement of
the foot could be measured and used as a method of quantifying frontal plane
foot stability.

This would be analogous to assessing the stability of a tall building to
wind load.  The more stable the structure, the less deflection of the
building per unit of wind velocity.  The less stable the structure, the more
deflection of the building per unit of wind velocity.  I see no reason why
the frontal plane stability of the foot couldn't be measured in a similar
manner so that further analysis of the mechanical factors of the foot and
lower extremity which contribute to the frontal plane stability of the foot
could be made.

Cheers,

Kevin

********************************************
Kevin A. Kirby, DPM
Assistant Clinical Professor of Biomechanics
California College of Podiatric Medicine

Private Practice:
2626 N Street
Sacramento, CA  95816  USA

Voice: (916) 456-4768   Fax: (916) 451-6014
E-mail: [log in to unmask]
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