Joint kinetics

Power to the planes?

I’ve just noticed that my blog is still displaying its Christmas card which feels a bit poor as we move into February. Thought I’d reflect on an issue that came up just before Christmas when we were looking at some joint power data from a cohort of amputees. My colleague first presented the data in “components” in the different planes. I commented that I regarded this as wrong and asked her to plot out the total joint power. She came back to me a little later to say that she couldn’t see how to compute this directly within Visual3D.  This caused us to look at their wicki which appeared to confirm what she had found with an explanation that this is how joint power was presented in Move3D, the software out of which Visual3D evolved, and that this “has become common in the biomechanics community”. My initial reaction was that “common in the biomechanics community” does not necessarily correlate with “correct”. To do Visual3D justice, the wicki also points out that you can calculate total power from its “components” but not vice versa which at least makes sense, even if you question how appropriate it is to refer to these as “components” . (Rather bizarrely feedback from C-motion after publication of this post makes it clear that a JOINT POWER SCALAR function has been available in the software for quite a long time as well as the original calculation of “components” and it was the wicki that was/is misleading! The original wording of this paragraph has been modified in acknowledgement of this).

Knee power

The confusion is quite widespread. When Vicon first produced Polygon it only allowed a graphing of total power and then one day I noticed an option to plot the different “components”. I dropped them an e-mail pointing out the mistake and was told that it wasn’t a mistake but a feature that a number of their customers had requested. It was clear that consumer demand was a more important driver of product development than the rigour of the biomechanics!

So what is the issue? As defined in physics, power is what we call a scalar, it cannot be related to any particular direction or plane. Think of it as a bit like your age, another scalar, it doesn’t really make any sense to talk about having age in a particular direction or plane does it. Well, to the classically trained physicist (me!) then talking about sagittal plane power doesn’t make any more sense than talking about sagittal plane age!

Or is it that simple? The quantities in physics that are related to direction are called vectors (position, speed, acceleration are common examples in biomechanics). Vectors are generally represented as a set of three number which are the components in a particular direction. Thus speed (v) is written (vx, vy, vz) with vx representing the component of speed in the x-direction. Joint power is the product of two such vectors, moment (mx, my, mz) and angular velocity (ωx, ωy, ωz) and under the laws of vector multiplication this gives the equation:

P = m.ω = mx ωx+my ωy.+mz ωy

and, although the physicist doesn’t think it has any significance, it is clear that the total power does appear to be made of three separate terms that involve quantities measured along different directions. It is these three terms that have come to be known as the “components” of power. (Notice that throughout this article I’ve put putted inverted commas around “component” when I’ve used it differently to the conventional definition in physics).

So if it is very clear what the terms mean, does it matter if we just choose to use it even if the physicists don’t think we should? I think the answer to this is “yes, it does matter” (I would though, I’m trained as a physicist). To me the whole point of biomechanics is that it allows us to understand the way the body works using rules and relationships that have been developed in the context of wider physics and engineering and which we know are true in all practical circumstances. If we start using terms which are not part of that understanding, no matter how convenient, then we lose that guarantee that they relate to each other in any particular way. It may seem sensible when you set out, but sooner or later it will lead you into trouble.

Power, in this context for example, is the amount of energy generated in a given time. The “components” of power (e.g. mx ωx ) can be negative as well as positive so if, for example, the x “component” is positive and the y and z “components” are negative, then the amount of energy generated in a given time in the x plane (if this is how it is regarded) is greater than the total energy generated in all the planes. This just doesn’t make sense. Are we saying that power is being generated at a joint in one plane at the same time as it is being absorbed in the other planes?! I hope even the non-physicists who read this can appreciate the problem.

The problem with calculating and using “components” of joint powers is that we don’t know under what other circumstances they lead us to nonsensical conclusions. Stick to the rules of physics and we know our conclusions will always be valid (as long as we’ve applied them properly of course!)

One defence of “sagittal plane joint power” which I have a little sympathy with is that, because the components of both angular velocity and moment tend to be considerably greater in the sagittal plane than others, the “sagittal plane joint power” is generally quite a good approximation to the total joint power. Given that in the modern world all these numbers just pop out of the computer anyway though its not at all clear how this is useful. If you want to know the total joint power why not calculate the total joint power? You also need to be careful that if you justify “sagittal plane power” as a good approximation to total joint power, then all you can really say about the transverse and coronal “plane powers” is that they represent the error in this approximation. Attributing physical significance to poorly defined error terms in a calculation is always going to end in tears.

In passing it may be worth commenting that kinetic energy can also be defined as a product of two vectors,

KE = ½mv.v = vx vx+vy vy.+vz vy

but I’ve never heard anyone talking of kinetic energy having components in different directions!

Shockingly wrong?

Hi, sorry I’ve been away for so long. How very Australian of me to take all of January off!

We’ve started a new semester on the MSc programme its called “Healthy walking” and for this two weeks the students are working through my video series “Why we walk the way we do“. I’ve also been preparing some study material to support this. In doing this I’ve become even more convinced than ever that the conventional understanding of first double support as a phase of shock absorption is wrong.

Of course one of the old chestnuts that follow from that theory is that stance phase knee flexion is a mechanism to absorb the shock of impact. I’ve been thinking about this for sometime but it wasn’t until I was preparing this material last week that it struck me that it would be useful to look at the knee power graph. Why? – because if there is one thing that shock absorbers do it is absorb energy. You can make an argument that this is all they do. So if the knee is a shock absorber and we look at the knee power graph immediately after foot contact we should expect to see power absorption.Knee powerIf you look at the graph you’ll see quite the reverse. Immediately after foot contact the knee is generating power – this is not the action of a shock absorber.

In case anyone thinks this is just my data we can go to David Winter’s book (1991, figure 4.34b):

Winter knee

This is interesting because the early power generation peak is definitely there but Winter seems to ignore it. He starts numbering at the power absorption peak in late double support that extends into early single support (K1). Its almost as if he can’t bring himself to admit that it’s there – perhaps he was a shock absorption theorist and this didn’t fit in with his world view?

Kirtley (2006) admits the peak is there and even labels it Ko. He claims however that it is an artefact of the filtering. This claim is unreferenced but I think refers to the work of Bisseling and Hof (2006) which was drawn into a discussion on K0 on the old CGA web-site. I’m not convinced. I don’t think anyone doubts that the ground reaction is anterior to the knee in the first half of double support and the knee is clearly flexing at this point. The inevitable consequence of the combination of these two observations is that power (moment . joint velocity) must be generated. The knee is not acting as a shock absorber.

Putting it another way the knee moment graph clearly shows that the knee flexors are the dominant muscle group at the knee for the first half of double support whereas the knee extensors would have to be dominant for knee flexion to have the capacity to absorb shock.

Of course from about half-way through double support power is absorbed at the knee but this is about 50msec after foot contact which is too long after contact for this to be a consequence of a mechanical “shock” at the time of contact.

On the balance of evidence I’m more and more convinced that stance phase knee flexion is not a shock absorbing mechanism. But if it’s not to absorb shock – what is it for?

.

Bisseling, R. W., & Hof, A. L. (2006). Handling of impact forces in inverse dynamics. J Biomech, 39(13), 2438-2444.

Kirtley, C. (2006). Clinical gait analysis (1st ed.). Edinburgh: Elsevier.

Winter, D. (1991). The biomechanics and motor control of human gait: Normal, Elderly and Pathological (2nd ed.). Waterloo:: Waterloo Biomechanics.

Winter, D. A. (1992). Foot trajectory in human gait: a precise and multifactorial motor control task. Phys Ther, 72(1), 45-53; discussion 54-46.