TY - JOUR

T1 - Filtering affects the calculation of the largest Lyapunov exponent

AU - Raffalt, Peter C.

AU - Senderling, Benjamin

AU - Stergiou, Nick

N1 - Publisher Copyright: © 2020 Elsevier Ltd

PY - 2020

Y1 - 2020

N2 - The calculation of the largest Lyapunov exponent (LyE) requires the reconstruction of the time series in an N-dimensional state space. For this, the time delay (Tau) and embedding dimension (EmD) are estimated using the Average Mutual Information and False Nearest Neighbor algorithms. However, the estimation of these variables (LyE, Tau, EmD) could be compromised by prior filtering of the time series evaluated. Therefore, we investigated the effect of filtering kinematic marker data on the calculation of Tau, EmD and LyE using several different computational codes. Kinematic marker data were recorded from 37 subjects during treadmill walking and filtered using a low pass digital filter with a range of cut-off frequencies (23.5–2Hz). Subsequently, the Tau, EmD and LyE were calculated from all cut-off frequencies. Our results demonstrated that the level of filtering affected the outcome of the Tau, EmD and LyE calculations for all computational codes used. However, there was a more consistent outcome for cut-off frequencies above 10 Hz which corresponded to the optimal cut-off frequency that could be used with this data. This suggested that kinematic data should remain unfiltered or filtered conservatively before calculating Tau, EmD and LyE.

AB - The calculation of the largest Lyapunov exponent (LyE) requires the reconstruction of the time series in an N-dimensional state space. For this, the time delay (Tau) and embedding dimension (EmD) are estimated using the Average Mutual Information and False Nearest Neighbor algorithms. However, the estimation of these variables (LyE, Tau, EmD) could be compromised by prior filtering of the time series evaluated. Therefore, we investigated the effect of filtering kinematic marker data on the calculation of Tau, EmD and LyE using several different computational codes. Kinematic marker data were recorded from 37 subjects during treadmill walking and filtered using a low pass digital filter with a range of cut-off frequencies (23.5–2Hz). Subsequently, the Tau, EmD and LyE were calculated from all cut-off frequencies. Our results demonstrated that the level of filtering affected the outcome of the Tau, EmD and LyE calculations for all computational codes used. However, there was a more consistent outcome for cut-off frequencies above 10 Hz which corresponded to the optimal cut-off frequency that could be used with this data. This suggested that kinematic data should remain unfiltered or filtered conservatively before calculating Tau, EmD and LyE.

KW - Biomechanics

KW - Cut-off frequency

KW - Nonlinear analysis

KW - Smoothing

KW - Walking

U2 - 10.1016/j.compbiomed.2020.103786

DO - 10.1016/j.compbiomed.2020.103786

M3 - Journal article

C2 - 32479345

AN - SCOPUS:85085242845

VL - 122

JO - Computers in Biology and Medicine

JF - Computers in Biology and Medicine

SN - 0010-4825

M1 - 103786

ER -