Arc-Length Re-Parametrization and Signal Registration to Determine a Characteristic Average and Statistical Response Corridors of Biomechanical Data

Abstract

A characteristic average and biofidelity response corridors are commonly used to represent the average behaviour and variability of biomechanical signal data for analysis and comparison to surrogates such as anthropometric test devices and computational models. However, existing methods for computing the characteristic average and corresponding response corridors of experimental data are often customized to specific types or shapes of signal and therefore limited in general applicability. In addition, simple methods such as point-wise averaging can distort or misrepresent important features if signals are not well aligned and highly correlated. In this study, an improved method of computing the characteristic average and response corridors of a set of experimental signals is presented based on arc-length re-parameterization and signal registration. The proposed arc-length corridor method was applied to three literature datasets demonstrating a range of characteristics common to biomechanical data, such as monotonic increasing force-displacement responses with variability, oscillatory acceleration-time signals, and hysteretic load-unload data. The proposed method addresses two challenges in assessing experimental data: arc-length re-parameterization enables the assessment of complex-shaped signals, including hysteretic load-unload data, while signal registration aligned signal features such as peaks and valleys to prevent distortion when determining the characteristic average response. The arc-length corridor method was shown to compute the characteristic average and response corridors for a wide range of biomechanical data, while providing a consistent statistical framework to characterize variability in the data. The arc-length corridor method is provided to the community in the freely available and open-source software package, ARCGen.