Independent assessment of pattern and offset variability of time series waveforms

In quantitative gait analysis, two types of variability of kinematic waveforms with identifiably different sources may be distinguished: variability of the offset values (mean or DC values) of the waveforms and variability of the waveform patterns. Offset variability is influenced by the repeatability of the motor performance as well as by additional factors related to reliability and errors of measurement, such as individual differences in the mean posture chosen for the performance and factors related to the definition and measurement of the reference position for each angle. All of these factors may have a considerable effect on the coefficient of variation, a measure that is commonly employed to assess kinematic variability. Waveform pattern variability, in contrast, is more manifestly determined by the repeatability of the motor performance and is less subject to factors related to offset value. Hence, we propose that offset variability and pattern variability be evaluated separately and outline an approach to accomplish this by first removing the mean value of raw kinematic waveforms before averaging across trials or subjects. Independent measurement of pattern variability and offset variability is shown to yield values that are markedly different from the traditional coefficient of variation, which reflects all sources of variability in a single measure. The benefit of the procedures proposed here is that they help to differentiate among largely independent causes of variability of kinematic waveforms and to quantify their relative magnitudes. By way of illustration, in a group of subjects with low-arched feet, where waveform offsets are of particular interest, midfoot and ankle rotation angles showed smaller pattern variability and larger offset variability than normal.