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Kirtley, Christopher
01-26-2004, 08:07 AM
Dear Ton/Jonas,

I'm glad that you are supporting the decomposition of joint powers. I think this makes a lot of clinical sense as well as being biomechnically correct.

As far as I understood it, though, the objection some have raised is that power is a scalar quantity, so it makes no mathematical sense to break it up into components. I'd be interested in your comments on this - Ton's suggestion that flexion/extension should be treated as a seperate joint to abduction/adduction is a nice way of getting around this problem, but it isn't really convincing - I mean, the same physical joint at the hip is responsible for both motions.

Chris
--
Dr. Chris Kirtley MD PhD
Associate Professor
Dept. of Biomedical Engineering
Catholic University of America
620 Michigan Ave NE, Washington, DC 20064
Tel. 202-319-6134, fax 202-319-4287
Email: kirtley@cua.edu
http://faculty.cua.edu/kirtley

-----Original Message-----
From: Biomechanics and Movement Science listserver on behalf of Ton van den Bogert
Sent: Mon 1/26/2004 4:16 PM
To: BIOMCH-L@NIC.SURFNET.NL
Cc:
Subject: Re: [BIOMCH-L] 3D Joint Power

Jonas Rubenson wrote:

> Power = [Mx,My,Mz] . [wx ,wy,wz].

Which leads to: Power = Mx.wx + My.wy + Mz.wz

> But perhaps this will lead to an underestimate of the true muscle powe

I think this is very well possible. For example, if you have hip
extensors and abductors active, during a movement that is a combination
of flexion and abduction, the extensors will do negative work and the
abductors will do positive work. If extensors and abductors are
different muscles (which is an approximation, see below), some muscle
work would not be seen if you add the three terms, because positive
and negative terms are partially canceling.

To some extent, the three degrees of freedom of the hip are separate
joints. You would never add hip and ankle power, and for the same
reason you should not add hip extension power and hip abduction power,
if different muscles are involved.

Of course many muscles span two or three joints. There are muscles
that are at the same time a hip extensor and hip abductor, just as there
are muscles that are a knee flexor and hip extensor. In those cases,
you may see positive power at one joint and negative power at another
joint, when there may not be any muscle power at all! This is a reason
for adding two joint powers, but only to the extent that they have
a common source.

But, for consistency, if you keep knee and hip separate, you should
also keep the degrees of freedom within each joint separate. This is
the standard way of reporting joint power, see, for example

Ferber R, Davis IM, Williams DS (2003) Gender differences in lower
extremity mechanics during running. Clin Biomech 18: 350-357.

In the knee, the ab-adduction power will include elastic energy
storage and release in ligaments and cartilage. It would not be correct
to add this to the flexion-extension power, which has a completely
muscular origin.

The correct way to account for muscle work is to calculate power for
each muscle as a product of force and shortening velocity. But
in the real world, we don't know individual muscle forces.

> the joint powers themselves. Some time ago I recall that one of the
> list members suggested to calculate the components of the joint power
> from the product of the joint moments expressed in the joint coordinate
> system (rather than the anatomical fixed coordinate systems) and the
> euler anglular velocities. If one is to calculate a net power from all
> three planes will this approach still be valid given that the joint
> coordinate system is non-orthogonal?

I am the one who suggested this, a few weeks ago.

Good question. Intuitively it should be valid, but I have no quick proof.
If a joint has three degrees of freedom, it should not matter for a total
power calculation whether the joint is modeled as a ball and socket joint
(with a vector moment and vector angular velocity) or as a cardanic
mechanism with three scalar moments and three scalar angular velocities.
Maybe someone else can respond to this...

Ton van den Bogert

--

A.J. (Ton) van den Bogert, PhD
Department of Biomedical Engineering
Cleveland Clinic Foundation
9500 Euclid Avenue (ND-20)
Cleveland, OH 44195, USA
Phone: (216)444-5566
Fax: (501)665-1506

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