Harmonic Analysis and Lameness

by
James Rooney, D.V.M.

This little piece may well not be worth the time to post it, but I shall do so in any case. My resaon is that so many trials, tests, experiments, ideas are tried but do not work out, and most people never hear about them. I shoot down one of my own favorites here, not to make a big show but simply to describe a reasonable idea that did not work out, so that if someone comes up with this idea again, they can avoid a lot of unnecessary work.

The idea which will be rather opaque to many of you perhaps starts here: the movement of the leg or part thereof over time describes a curve something like that in Fig. 1 for the fetlock during one step. We know from other considerations that the 2-D curve produced during normal movement is part of a logarithmic spiral, a regular, defined curve. (Joint movement is always 3-D, but the records available are only for 2-D.

We subject that curve to harmonic analysis which is simply finding how many nice, regular sine curves are needed to reproduce that original curve. We find that only one sine curve is necessary and that is called the fundamental. My hypothesis, dearly held for too long, was that the movement curve of a lame horse might have harmonics in addition to the fundamental. That is, more than one sine curve would be needed to reproduce the original curve. This is all summarized in the fictitious harmonic analysis of Figure 2. The normal, lone fundamental is to the left and the proposed (but falsified) abnormal with two harmonics, below.

Now for the kicker, I copied curves of fetlock and coffin joint movement of sound and lame horses from the paper by Buchner etal and did the harmonic analysis (at least my Mathcad program did). The curves of the lame horses, in general, showed less displacement than the normal as is well-known. There was no evidence, however, of harmonics appearing as a result of or along with the changes in joint displacement.

The hypothesis, then, has been falsified.

Harmonic analysis is of no use in the detection or evaluation of the curves of displacement of the legs of lame horses.

Buchner et al. Limb movement adaptations in horses with experimentally induced fore- or hind limb lameness. Equine Veterinary Journal (1996) 28: 63-70.

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