joint kinetics

All you ever wanted to know about the conventional gait model but were afraid to ask

cdcover

What seems an awfully long time ago now (2003!), Jill Rodda and I gave a tutorial on the Conventional Gait Model (Davis, Newington, Helen Hayes, Kadaba, VCM, PiG – whatever you want to call it) to the Gait and Clinical Movement Analysis Society in Wilmington, Delaware. For it I prepared a CD-ROM (cover picture above) with an interactive multi-media presentation on as many aspects of the model that I could think of. This includes:

  • Description of how the different segments are defined anatomically.
  • Guidelines on marker placement.
  • Practical guidance on coping with larger people, defining the coronal plane of the femur and deformed feet.
  • An analysis of the effects of misplacing various markers
  • Limitations of the model and suggestions for the future.

Some of it appears a little dated (the future is now for instance) but for anyone who is still using the CGM (and many people are) there is still a lot of material that will be useful.

The reason that I’m posting this is that I’ve now uploaded the files to our institutional repository where they can now be freely downloaded by anyone. Click here to access the files. Extract the files to a folder somewhere on your PC, go to the sub-folder PolygonViewer and double click on the folder PolygonViewer.exe. (Which reminds me that this is probably still one of the world’s longest Polygon reports!) Once you are in the presentation I think everything should be quite intuitive.

The video above shows two clips from the presentation illustrating the equivalence of Cardan angles and the joint angles as specified using the joint coordinate system (see this paper for a more comprehensive description).

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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!

Normalising kinetics

There were a few things that struck me as odd when I was writing my book. Things that we’ve always done in a particular way in clinical gait analysis but which just don’t make sense. One of these is the way we typically “normalise” kinetic data by dividing through by mass only. Moments are a product of force and length and are thus likely to be influenced both by a person’s weight and their size. It just doesn’t make sense to normalise data by dividing through by weight only. There are similar, but slightly more complex, issues with joint power. Differences in adult height between individuals, expressed as a percentage, tend to be reasonably small (SD < 10%) even disregarding gender, so the effects of not normalising to height in adults are unlikely to be that important. Clinical gait analysis, however, has always had a considerable focus on children where differences in height are much larger. It just seems so obvious that we should normalise to height as well as weight. In my book I see that I actually commented, “Quite why this is not standard practice in gait analysis is unclear.”

A simple explanation may be that no-one has ever tested this assumption. So one of my colleagues (Ornella Pinzone) has performed a comparison of conventional normalisation (dividing moments and powers by mass only) and non-dimensional normalisation (dividing moments by mass and leg length and powers using a slightly more complex formula). We based it on data made available by Mike Schwartz from Gillette as their data are so well formatted for a study like this. The paper has just been published in Gait and Posture and if you use this link before 29th January then you should be able to view and download a copy of the article for free.

Pinzone

Coefficients of determination for relationship between a range of temporal, spatial and kinetic parameters and age amongst children across an age range from 4 to 18 years. Dashed line shows threshold for statistical significance at p<0.05.

The results are quite conclusive. About 80% of the associations between the conventionally normalised parameters and age, height and weight, were statistically significant (p<0.05) and for all of those parameters where the association was significant it was substantially reduced by non-dimensional normalisation (only just over 20% were statistically significant and most only marginally exceeded the p<0.05 threshold). The results have dispelled any lingering doubts in my mind as to the superiority of non-dimensional normalisation and when we next revise our normative dataset we’ll be using this as standard.

This isn’t quite the whole story, however, because even when you remove the systematic effects of height and weight (this is the primary purpose of normalisation) there is still a lot of scatter in the data. The figure below shows the relationship of peak knee extensor moment with leg length for conventional (top) and non-dimensional (bottom) normalisation. The slope on the line of regression is reduced to almost zero with non-dimensional normalisation but there is minimal effect on the scatter of data points about this line.

Pinzone2

Peak knee extensor moment plotted against leg length for conventional (top) and non-dimensional (bottom) normalisation.

It is difficult to compare this variability with that present in kinematic data because the nature of the data is so different but the impression I get is that the variability in the kinetic data is even greater than that in the kinematic data. I’ve commented in two earlier posts (here and here) that I think the assumption that we all walk similarly, an assumption on which all clinical gait analysis is based, needs to be re-examined. The most obvious conclusion from this dataset is that many of us, even in the absence of pathology, walk very differently.

Choosing your moment

Hi, sorry its been so long since I posted but I’ve been reinvigorated by this year’s ESMAC conference here in Heidelberg. Earlier in the week I had the pivilege of sitting in on a session of the ESMAC gait course. Julie Stebbins had arranged a short quiz to start people thinking on Wednesday morning and the last question caught my attention. It’squite simple. There are four sets of kinematics along the top and four of kinetics along the bottom labelled A to D. What order do the kinetic datasets need to be arranged in to match the kinematic graphs (and why)? (You should be able to get a bigger view by double clicking on the picture.

choosing your moment

Push off push-off

Sheila from Dundee dropped me an e-mail: 

In your meanderings around the subject of gait have you come across any definitive descriptions of push-off i.e. at what time in the cycle does it start? Or do you have any thoughts on the matter yourself?

Having replied it struck me that others may be interested in this topic.

As far as I’m aware “push-off” is only used loosely to describe a phase of the gait cycle. I’ve never seen a definition in terms of where it starts and where it ends. My preference is to describe the phases based on single and double support and swing (with single support and swing divided into three equal parts). This intentionally avoids labelling any particular phase as having any particular function (push-off, shock-absorption etc.) partly because people often get these functions wrong when describing walking and partly because patients may not achieve such functions at the same phase of the gait cycle as the able-bodied.

“Push-off” is particularly problematic. How usefully it describes the late stance phase depends both on whether you are considering the whole body or just the leg and the direction you are talking about. During late stance the centre of mass is moving downwards and forwards. The downward motion is being resisted. From this perspective late stance is a phase of deceleration and the term “push-off” is inappropriate. The segments in the limb however are moving in different directions, the foot, ankle and tibia are being “pushed up” whereas the femur is actually moving downwards with the centre of mass.

Looking in the horizontal direction both the centre of mass and the limb are being accelerated forwards. There is a relatively small acceleration of the centre of mass (but this affects a large mass) and a rapid acceleration of the limb (which has a much smaller mass). In this context “push-off”  does appear an appropriate descriptor at first.

Focussing first on the centre of mass movement though – if you model the whole body as an inverted pendulum with mass and leg length matching the human body you find that the entirely passive mechanism (no muscle activity) develops an anterior component of a ground reaction in late stance that is very similar in magnitude to that of the ground reaction at this phase of healthy walking. This force arises because of the relative alignment of the centre of mass, limb and foot and suggests that the muscles need only preserve this alignment to generate it. “Push-off” suggests something much more active and may be misleading.

If we focus on the limb – there has been a debate for nearly 200 years about whether it is being pushed forwards by the action of the plantarflexors pushing against the ground or pulled forwards by the hip flexors. I think it very likely that both are important. It’s tempting to think that some insight into this can be gained from looking as the joint power graphs. They show power generation at both hip and ankle which tends to confirm that both are important. Power, however, is a scalar quantity (it is not associated with any particular direction) representing the rate at which energy is supplied to or removed from the whole body by the muscles acting across a particular joint. Given this it is very difficult to come to any rigorous conclusions about the relationship between the power generated at the joints and the movement in a particular direction of the segments of the limb being “pushed-off”  (to say nothing of complications when power may actually be being generated by muscles spanning more than one joint). To answer the problem categorically would require some form of induced acceleration analysis as to what particular muscles are acting to accelerate the segments during late stance. I’m not aware of anyone having done this (perhaps readers can let me know if they are).

Going back to the original question. I’d maintain my suggestion that we avoid “push-off” as a term. It’s an easy label to apply that makes us think we understand something that many of us don’t (and I’d include myself in this).