biomechanics

Torquing the tibia

A small group of us are currently trying to tidy up certain aspects of the Conventional Gait Model (Newington, Helen Hayes, Davis, Kadaba, PiG, VCM) in such a way as to address a number of known problems but also preserves its strengths. We’ve had quite a bit of discussion about tibial torsion recently which flags a number of different issues. Looking back at my book, I see I spent quite a bit of space discussing how different degrees of femoral anteversion affect gait data but not quite so long on tibial torsion.

Tibial torsion is the twist along the shaft of the tibia. If you were to look along the long axis of the bone and imagine where the knee joint axis is in relation to the proximal tibia (in black in the picture below) and the ankle joint axis (trans-malleolar axis) in relation to the distal tibia (grey) then the angle between them is the tibial torsion (20° in this example).

Tibial torsion

At birth tibial torsion, thus defined, is small (<5° on average) and normally increases with age to about 15-20° at adolescence after which it remains constant. (Note that this is different to femoral anteversion which starts off large and reduces over time). There is, however, considerable variability between individuals.

The importance of tibial torsion clinically and to biomechanical modelling is fundamentally that it means that the distal tibia is pointing in a different direction to the proximal tibia. In other words your knee points in a different direction to your ankle. This is particularly important for understanding gait problems in the transverse plane – if for example you want to know why someone is walking with internal foot progression (pigeon-toed in old language).

PiG, the current Vicon implementation of the Conventional Gait Model, deals with the issue by defining both a proximal and distal tibial segment differing only in a rotation about the long axis of the tibia. The proximal tibial segment is used for most measures of knee kinematics and kinetics and the distal tibial segment is used for the ankle kinematics and kinetics (and knee kinematics when generating outputs from the static trial, for some reason!).

At one level this is quite logical but it has several disadvantages:

  • There are two segments but only one bone!
  • The way tibial torsion is incorporated in the model is quite different to the way femoral anteversion is incorporated and this leads to confusion about both. (This is a particular issue as one of the principal advantages of the CGM is that it is inherently quite easy to understand).
  • Tibial torsion becomes an implicit feature of the gait graphs rather than an explicit feature. Thus if you want to consider what factors are affecting transverse plane alignment  from the gait graphs you cannot do so without also knowing the value of tibial torsion that has been used. (This is particularly important if the value of tibial torsion has been calculated with the use of a medial malleolar marker placed for the static trial but not reported along with the gait data). There are a number of ways around this but it would be better if the information was explicit in the graphs.

I much prefer the way we do things when using Visual3D which is to use only the distal tibia. Knee rotation (transverse plane) is then defined pretty much as in the diagram above except the knee axis is taken as the transepicondylar axis in the femur. The measurement is thus the combination of tibial torsion and any true rotation in the knee joint (subject to soft-tissue artefact of course, but that’s another story). What makes things even nicer is that we plot joint angles from the static trial along with our consistency plots (see graph below).

Knee rotation.png

Thus the data in black is knee rotation from 5 walking trials showing a range  between about 12° and 22° internal rotation which indicates that the ankle joint axis (in the tibia) is internally rotated with respect to the the knee joint axis (in the femur). The solid red line is knee rotation measured during the static trial which is by definition equal to the torsion that the system measures in the tibia. It is clear that the (very) abnormal knee rotation is almost entirely explained by torsion within the tibia (and you can then sit around and debate whether the remaining signal is real or a consequence of soft tissue artefact – yes rigid clusters are vulnerable to STA as skin markers it is just that the artefact is different!).

Another nice feature about this approach is that if you have measured tibial torsion clinically then you can compare that measurement with that which the system has made (the static trial measurement) and very easily think through the clinical consequences of any difference, by thinking how your interpretation might change if the solid red line were higher or lower.

Final paragraph for the advanced reader!

Just when we thought we’d considered all the issues and agreed a sensible way forwards someone mentioned kinetics. PiG expresses joint moments in the coordinate system of the distal segment by default and it really doesn’t make any sense to report the knee joint moment about a coordinate system defined by the ankle joint axis! Perhaps this is the reason that the two tibial reference frames were defined in the first place. A much simpler solution, however, is to express the joint moments in the coordinate system of the proximal segment (until now I’ve generally considered this an arbitrary choice but, as result of reflecting on this issue, I’ve now convinced myself that if you are going to define rotation of segments about their long axis by distal landmarks or functional axes and want to use an orthogonal axis system then you have no real choice but to use the proximal segment). The other solution which I actually prefer is to express the joint moments as projections of the total moment vector onto the axes of the joint coordinate system (as recommended by Anthony Schache and myself in this paper). At first glance reporting “components” of a vector about a non-orthogonal axis system appears quite offensive to any self-respecting engineer but this is actually more appropriate if you want to interpret those moments clinically in the context of the requirement of different muscle groups to exert moments about the axes that we regard movement as occurring.

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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).

Coping with maternity leave

How do you ensure that staff going on maternity or paternity leave do not get deskilled during their period away from gait analysis?

Here’s an idea to provide a regular knowledge update. The Verne mobile consists of  6 fully articulated Verne‘s allowing the user to set them in any desired pose. They are arranged in a circle to reinforce the importance of cyclic movement patterns. Comes complete with a customised worksheet* of cyclic gait patterns for the user to re-create. Choose three from the following list to suit any laboratory or clinic:

Made in attractive colours to blend in with the decor of any nursery.

Congratulations Julie on the birth of William

* it doesn’t really – this bit’s a joke – but I was fascinated at the wide variety of gait patterns that we now have some form of kinematic data for (the mobile is real though!).

Where’s the hip joint?

Most biomechanical models used in gait analysis require an estimate of where the hip joint is within the pelvis. The quest for the best equations to do this has become something of a Holy Grail within the gait analysis community. Andriacchi et al. (1980)  and Tylkowski (1982) were probably the first to propose methods for estimating its location and Bell, Brand and Peterson (1986) combined these in a method that they claimed predicted the joint centre to within 2.6cm with 95% certainty. At about the same time (1981) a different model was developed from x-ray studies at Newington Children’s Hospital which was incorporated into their clinical gait analysis software (finally published by Davis et al. in 1991).

ct-scans

Some time later Leardini et al. (1991) compared the Bell and Davis models against roentgen stereophotogrammetry and functional methods and found that the models differed quite significantly. Rather than choose one or the other he proposed a new set of equations. A little later Harrington et al. (2007) used MRI scans of a range of healthy children (14) and adults (8) and children with diplegic cerebral palsy (10) and generated another set of equations. A number of validation studies have suggested that those equations perform considerably better than the Davis equations  in healthy adults (Sangeux et al., 2011, Sangeux et al. 2014) and children with cerebral palsy (Peters et al., 2012). These have also suggested that Harrington’s equations generally work as well, or better, than modern functional methods.

One of the problems of the methods (highlighted by Sangeux last year) was that the equations scale the hip joint centre to measures of pelvic width (from one ASIS to the other) and depth (from the ASIS to the PSIS). Errors in measuring these, which can be particularly tricky in more obese subjects, can propagate to the hip joint centre estimates. It would be much better to scale to a measure that could be made more accurately such as clinical leg length.

Morgan (Sangeux) discovered that the Victorian Institute for Forensic Medicine had a repository of CT scans which we could access to investigate how well such scaling would work. He and PhD student Reiko Hara found scans of 37 children and 120 adults who had died without any signs of musculoskeletal injury or other abnormality and from which they were able determine the location of the hip joint centre relative to the anatomical landmarks on the pelvis as a function of leg length. As we published last week they found a set of linear functions of leg length that determine the hip joint location as well as the Harrington equations with a mean absolute error of 5.2mm or less in any single direction.

Interestingly (to me) the study showed that despite known differences in general pelvic morphology between males and females there were no appreciable differences in the location of the hip joint centres with respect to the anatomical landmarks (once scaled to leg length) and that age had only a small effect.

The method also means that we have an estimate of the size of the pelvis based on leg length that give us information that we can use when trying to locate where it is in relation to the ASIS and PSIS markers which could be particularly useful in people with higher BMI values.

Morgan has now made the data visible through a new data visualisation resource called Tableau. You can view it there using this link.

Electing a representative

One of the aspects of gait analysis that I didn’t cover in any particular depth in my book was how to select data from a number of trials that is in someway representative of the patient. I think one of the reasons for this is because I couldn’t easily get my hands on any data that illustrated the issues well. In some ways this speaks for itself – in my experience large inter-trial variability, larger enough to affect how we interpret data, is actually quite rare in clinical practice. If the variability is small then it doesn’t really matter what technique you choose.

representative-trial

My personal preference is to avoid the issue altogether by overplotting data from multiple trials on the same graphs (similar to the graphs on the left above but with data from the other side plotted in a different colour as well). In this way you can take into account both the general pattern and the variability when interpreting the data. Some people object that using this technique it can be difficult to appreciate subtle features in individual traces, but there is a real question as to whether you should be even looking at such features if they are not consistent from trace to trace.

Now I’ve started annotating graphs with symbols to identify specific features in the data, however, I find that the combination of symbols and multiple curves can be a bit too messy and have resorted to looking to a single trace that can be taken of as representative. Although alternatives have been proposed I use the average trace. It leads to a little smoothing of the data – which isn’t perfect – but none of the other techniques are perfect either. It was interesting last week to come across a patient’s data that illustrated beautifully the problems of doing this.

You can see the knee and hip traces here with the individual traces overlaid on the left and the averaged data plotted on the right. The problem is with the left knee. You can see that the patient exhibits two distinct patterns of knee movement in early stance (but remarkable repeatability elsewhere in the gait cycle). She either walks with full knee extension in early stance or with quite marked knee flexion. In the fully extended pattern her knee is more posterior and so there is increased hip extension as well (there is an effect on ankle dorsiflexion as well which I haven’t plotted). The average trace for the knee, however, falls well within normal limits and if you only ever looked at that trace you would never know that there was anything wrong with the knee.

None of the methods that are commonly used to generate a representative trace whether they be through picking one particular trace or providing some sort of averaging (mean or median) will result in something that represents the patient. The fundamental reason these don’t work is that this person’s gait is not characterised by one gait pattern, but by two, which she alternates between. It is not possible to understand her walking on a single curve, you need to look at multiple trials.

So although such issues don’t arise very often we don’t have a good way dealing with them in how we plot out or mark-up our data. What is needed is not a way of selecting single trace but a means of indicating that any single trace is unrepresentative. The broad semi-transparent bands on the right hand graphs are supposed to indicate that the trace cannot be appropriately interpreted without referring to the multiple trial data. I’ve now added them to the list of symbols that we use for marking up our graphs.

(PS The idea for a symbol to indicate underlying variability in the multiple trial data was first suggested to me by Sheila Gibbs in Dundee during an early consultation on the Impairment Focussed Interpretation methodology I outline in my book.)

(PPS if you do feel a need to select a representative trace and want to do this systematically then a robust method is presented by Morgan Sangeux in this recent paper. It is however worth noting that in the example he gives in Figure 1 the trace chosen as most representative overall does not give a good indication of the underlying data for either pelvic tilt or foot rotation despite the rigour of the technique.)