A multivariate solution for cyclic data, applied in modelling locomotor forces

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Abstract
The variability in dependent biological data (measured as forces at the human foot during pedalling) was reduced, by principal components analysis, to two major components which, combined, accounted for 46% of the variability observed in sets of 26 observations per cycle. On the basis of weighting over the cycle, the components were interpreted as due to Power Production and to Phase Switch from powergeneration to recovery. Force measurements were made for three frequencies of leg pedalling (1.00, 1.66, and 2.33 Hz at 10 N ergometer resistance). For each principal component, the mean (or summed) deviation over 75 consecutive cycles was found to increase linearly (p<0.05) with velocity of leg movement, by 7% and 85% respectively. Analysis of autocorrelations over cycles of movement showed that, in contrast to the strong interconnections of force measures within a cycle of movement, between-cycle dependence was very low. The statisticaltechnique described provides a useful descriptive and inferential method for analyzing dependent cyclic data. The resulting model of the locomotor forces generated at the foot implies that control of power output is substantially for one cycle of a limb and that variability of force increases at the point when the leg switches from power-generation to recovery.