joint kinematics

Just a minute

During a meeting of the CMAS standards meeting last week there was some discussion about how repeatable our measurements need to be. I was struck by  a comment from Rosie Richards from the Royal National Orthopaedic Hospital at Stanmore that six degrees is the angle represented by one minute on a clock (apparently the idea originally came from her colleague Matt Thornton). Her point was that this doesn’t feel like a very big angle and that if we are are working to this sort of accuracy then we are doing pretty well. I’d agree with her and think if there is ever any discussion of just how accurate gait analysis is then using this as an illustration is really powerful.

Corn Exchange clock, Bristol. This clock actually has two second hands. The red one records GMT and the black one the local time in Bristol which is 190 km west of London and thus nine seconds behind! (C) Rick Crowley, Creative commons licence.

The evidence supports this. In our systematic review, Jenny McGinley and I suggested that measurement variability of more than 5 degrees was concerning and showed that most repeatability studies for most joint angles report variability of less than this. They are thus also, of course, within the one minute limit as well.

It’s also interesting to note that the variability within normal gait is generally less than 6 degrees. I’ve tabulated the standard deviations from our recent comparison of normative data below. Hip rotation at one centre pushes above the limit (but this is almost certainly a consequence of measurement error). The only other variable that exceeds this is foot progression (which I’ll return to below). This should be of interest to those who think that they should be able to use differences in gait pattern as a biometric to identify people. To do this successfully would require variability within the 1 minute limit to distinguish between people.  Personally, I think this is a big ask from the CCTV camera footage that the biometricians would like to base their analysis upon.

Average standard deviations across gait cycles for different gait variables

This doesn’t mean we should be  complacent, however. In the figure below I’ve compared Verne  in the average normal pose at the instant of foot contact (grey outline) and then increased his leading hip flexion by 6 degrees (and adjusted the trailing foot pitch to bring the foot into contact with the ground again while all the other joint angles remain the same). You can see that this has increased step length by over 10%. If there was an additional 6 degree increase in trailing hip extension as well then this would double. The additive effect of such variability may help explain why foot progression in the table above is a little higher than the other measures in that it can be considered as a combination of the transverse plane rotations at pelvis, hip, knee and ankle rather than a “single” joint angle.

Effect on step length of increasing leading hip flexion by six degrees

In summary the one minute limit seems an extremely useful way of describing how accurate our measurement systems are and we should take considerable confidence from this. On the other hand we shouldn’t be complacent as variability of this level in specific joint parameters can have quite substantial impacts on the biomechanics of walking.

Readers outside the UK may not fully appreciate the title to this blog which is a reference to one of the oldest comedy shows on BBC radio which has been broadcast regularly since 1967. It is one of the purest and most exuberant celebrations of the English language that I know. Episodes are not being broadcast at present but when they are they can be listened to internationally (I think) through the BBC i-player

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Lost in translation

Before I start just to note the typo in the last post Elsevier make a profit of £700 million (roughly $1 billlion) each year not £700,000 as I first wrote! Also like to say that I’ve now got a Twitter account @RichardBakerUS. Not sure exactly how I’m going to use it but it is useful for correcting mistakes like these. Now back to biomechanics …

I thought I might share one particular issue that I’ve never really understood to see if anyone can help me. The issue is how we describe joint translations. If you look at the original ISB recommendations  for joint co-ordinate systems (JCS) they propose a system for describing translations as well as rotations. Co-ordinate systems (CS) are chosen in the proximal and distal segments in such a way that, in the joint’s neutral position, the origins of these two systems are coincident. Translation is then defined as the movement of the distal CS origin in the CS of the proximal segment. The ISB suggested that this should be described in terms of three components along the axes of the joint co-ordinate system (rather than the co-ordinate system of either segment).

The problem with this that I don’t think I’ve ever read any discussion of (maybe people think it obvious) is that the measured translations will depend critically on the point chosen for the CS origin. Take the sagittal plane view of the femur (above) and consider the movement of the tibia relative to this. Let’s assume that the tibia rotates about a fixed point within the distal femur (don’t worry too much about whether it does or not in reality as this example is merely to illustrate a point). It makes sense to choose this fixed point as the origin of the CS for both the femur and the tibia. By definition there is then no translation of the joint. But then look at the blue point on the articular surface of the tibia and you can see that this is clearly translating with respect to the femur. No translation of the joint centre – considerable translation at the articular surfaces.

If we look in the transverse plane things become even more perplexing. Here I’m assuming that we have pure internal and external rotation of the tibia on the femur about a  point fixed in both bones. Again, mathematically, there is no joint translation, but again at the joint surface there is considerable translation of points on the articular surface. Not only is there considerable translation but this varies with the distance from the joint centre. You can even see that the green point on the medial side of the joint translates in the opposite direction to the yellow point on the lateral side.

This final example takes things one stage further and demonstrates how the translations depend on the location of the joint centre. The small transverse plane rotations of the knee that do occur (I’ve exaggerated the range of movement in these illustrations for clarity) are probably about a point in the centre of the medial epicondyle as in the figure above. If this is the case then you’ll see that there is virtually no translation at the green point close to that centre of rotation but there is even more translation on the yellow point on the lateral epicondyle.

Use your imagination to scale these up to three dimensional examples and you can see that although there will be a mathematical relationship between the translation at the articular surface and that of the coordinate systems this is extremely complex and dependent on the size and anatomy of the joint. In short although you can measure joint translation using the ISB  proposal it is extremely difficult to interpret what the measurements mean. As a simple minded gait analyst I’ve given up at this point and decided that I’ll stick to the 3 degree of freedom (DoF) joints that my mind can cope with rather than worry about 6 DoF movements that some biomechanists claim we can measure. Measure maybe but make useful clinical inferences from – I’m not so sure.

PS if you want to see a practical application of this you can look at a paper we published quite a long time ago that suggested that wear rates in total hip prostheses can be associated with the pattern of movement of points on the femoral head over acetabulum.