## Teach-in '98: Variability in Gait Analysis

Normal biological variation means that subjects never walk quite the same each time we analyse them. Coupled with this inherent variation, variability is also introduced by the measurement procedure:
• Environmental constraints (targeting the force platform etc.)
• Identification of bony landmarks and joint centres (e.g. knee axis in the Davis marker set)
• Skin movement artifact
• Marker wobble on the skin
• Calibration of the motion analysis system
It is, of course, impossible to separate these two sources of variation (true variation in the subject's gait and artifact from the measurement procedure). We therefore need some estimate of the variability to be expected. This is important when, for example, comparing a patient's data against normative standards - we need to know how much difference is significant.

One frequently used estimate of variation is the standard deviation, which is often drawn on gait curves as dotted lines around the mean. One problem with this, though, is that the SD is slightly different at each point in the cycle. It would be nice to summarise this information, to calculate an "average SD" for the parameter over the whole gait cycle. This is what is called the coefficient of variation (CV), and it is simply the average standard deviation in the gait parameter divided by the average mean (Winter, 1991):

Notice that the sign of the mean (X) is ignored since many gait curves are biphasic and would otherwise have a mean around zero, making the CV go to infinity. This is probably not strictly correct mathematically, but it seems reasonable intuitively.

### Coefficient of Variation of Gait Parameters

We measured the CVs of the gait measures recorded by a standard Vicon Clinical Manager (VCM) analysis in 10 young and 9 older subjects (full details here). Two separate analyses were performed on different days to assess day-to-day variation. Each session is the mean of three trials. All the subjects were pooled to obtain inter-subject variability.

As can be seen in the above figure, some measures (especially the temporal-spatial parameters) show relatively little variation, whilst some (the transverse-plane joint powers) show almost no consistency. Note also that ankle measurements seem to be, in general, more consistent than hip variables, and the knee parameters are least consistent. We expected this, because of the particular problems in determining the knee-joint axis in the Davis marker set. We also expected that the inter-subject results would be more variable than those for individual subjects, and results recorded on different days to be more variable than those from the same session.

### Effect of Maturity

Dr. Cho, in South Korea, has kindly donated his normal data on children to the CGA database. Here's what his results show:

Note that children's gait become more consistent as it matures. But note, also, that the pattern seen above is reversed, with ankle measurements more variable than hip, which is more variable than knee. The results of Dr.  Selber & Wagner de Godoy (for 44 children aged 8-16 y), in Brazil, confirm this trend (highest CVs at the ankle joint), as do published results from David Winter for both 2D and 3D analysis (although his 2D kinetic CVs seem to have been overestimated):

Sagittal-plane Coefficients of Variation (%)

 Joint Hip Knee Ankle Study Angle Moment Power Angle Moment Power Angle Moment Power Winter 2D Inter-subject 52 140 (121) 221 (170) 23 135 (108) 157 (127) 72 42 (32) 100 (71) Winter 2D Intra-subject 21 33 45 8 37 39 16 16 49 Winter 3D 37 70 70 79 28 49 Oxfd. Met.* 6 24 46 11 35 38 22 14 30 Dr. Cho~ 23 83 109 26 82 80 49 128 150 Dr.Selber' 37 40 89 HK young# 22 40 56 20 49 66 35 18 51 HK old# 20 46 62 27 63 83 39 19 50 HK all# 53 65 106 31 76 126 56 28 83
Winter inter-subject 2D moment and power values appear to have been overestimated - my corrected values in parentheses.
*Data supplied by Oxford Metrics with Vicon 370 (N=3).
~Data from Dr. Cho's 6 yo female Korean children (N=4).
'Data from Dr. Selber's 8-16 yo Brazilian children (N=44).
#Inter-subject data from our study (N=19).

### Questions

• How do you explain the differences in CVs (variability) at each joint?
• Why should the ankle have the highest CVs in the Winter, Cho & Selber studies?
• Why did we find the opposite (ankle least variable joint)?
• Do you routinely calculate CVs in your gait lab?
• How do your values compare with those above?
• Is Coefficient of Variation a good measure of variability in gait measurements?
• Are there any alternatives?

### References

Davis, RB III, Ounpuu, S, Tyburski, D, and Gage, JR (1991). A gait data collection and reduction technique. Human
Movement Sciences 10, 575-587.

Winter, DA (1991) The biomechanics & motor control of human gait: normal, elderly & pathological (2nd. ed.), univ. of Waterloo Press, Waterloo, Ont.., p. 9.

Eng J, Winter D (1995). Kinetic analysis of the lower limb during walking: What information can be gained from a
three-dimensional model? Journal of Biomechanics, 28:6, 753-758

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