Classifying the variability in impact and active peak vertical ground reaction forces during running using DFA and ARFIMA models

Abstract

The vertical ground reaction force (VGRF) during rear-foot striking running typically exhibits peaks referred to as the impact peak and the active peak; their timings and magnitudes have been implicated in injury. Identifying the structure of time-series can provide insight into associated control processes. The purpose here was to detect long-range correlations associated with the time from first contact to impact peak (TIP) and active peak (TAP); and the magnitudes of impact (IPM) and active peaks (APM) using a Detrended Fluctuation Analysis, and Auto-Regressive Fractionally Integrated Moving Average models. Twelve subjects performed an 8min trial at their preferred running speed on an instrumented treadmill. TIP, TAP; IPM, and APM were identified from the VGRF profile for each footfall. TIP and TAP time-series did not demonstrate long-range correlations, conversely IPM and APM time-series did. Short range correlations appeared as well as or instead of long range correlations for IPM. Conversely pure powerlaw behaviour was demonstrated in 11 of the 24 time series for APM, and long range dependencies along with short range correlations were present in a further 9 time series. It has been hypothesised that control mechanisms for IPM and APM are different, these results support this hypothesis.