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.

Hi Richard. As I understand it, the knee joint center is defined in the Helen Hayes model as the same point on both the femur and the tibia. Do you have any feeling for how the actual displacement between these points (as in your first diagram) affects joint angle accuracy when you are assuming (as with Vicon Plug-in-Gait) that there is no displacement between them? Do you think it is negligible?

John,

I’ll dodge the question a bit by saying that I think the relative translation of the fixed points in the tibia and femur axis systems that move least with respect to each other move less than soft-tissue artefact allows us to measure. I know this is a bit of a cop out and I also realise that I’ve got absolutely no data to back it up (except perhaps Tsai et al. 2009 and Akbarshahi et al. 2010 who both show that the lateral knee marker moves between 20 and 30mm in relation to the underlying bone over the gait cycle – note that this is masked a little in the tabulated data in both studies which report the RMS value rather than the range of movement).

Tsai, T.-Y., Lu, T.-W., Kuo, M.-Y., & Hsu, H.-C. (2009). Quanitfication of three-dimensional movement of skin markers realtive to the underlying bones during functional activities. Biomedical Engineering: Applications, Basis and Communications, 21(3), 223-232.

Akbarshahi, M., Schache, A. G., Fernandez, J. W., Baker, R., Banks, S., & Pandy, M. G. (2010). Non-invasive assessment of soft-tissue artifact and its effect on knee joint kinematics during functional activity. Journal of Biomechanics, 43(7), 1292-1301.

Hi Richard

So this is complex stuff – but how about this as a broad theoretical construct? Given many cycles of steady state data – divide it into bins of say 15-30 degrees of movement. Then calculate a functional joint centre for each bin of data than minimises the translational elements. Finally look at the trajectory of the set of rotation centres as an estimate of joint translation through the cycle. This value would seem intuitively close to the clinical meaning of say an anterior drawer test at the knee – maybe?