Quantifying Asymmetry in Gait: The Weighted Universal Symmetry Index to Evaluate 3D Ground Reaction Forces

Abstract

Though gait asymmetry is used as a metric of functional recovery in clinical rehabilitation, there is no consensus on an ideal method for its evaluation. Various methods have been proposed to analyze single bilateral signals but are limited in scope, as they can often use only positive signals or discrete values extracted from timescale data as input. By defining five symmetry axioms, a framework for benchmarking existing methods was established and a new method was described here for the first time: the weighted universal symmetry index (wUSI), which overcomes limitations of other methods. Both existing methods and the wUSI were mathematically compared to each other and in respect to their ability to fulfill the proposed symmetry axioms. Eligible methods that fulfilled these axioms were then applied using both discrete and continuous approaches to ground reaction force (GRF) data collected from healthy gait, both with and without artificially induced asymmetry using a single instrumented elbow crutch. The wUSI with a continuous approach was the only symmetry method capable of identifying GRF asymmetry differences in different walking conditions in all three planes of motion. When used with a continuous approach, the wUSI method was able to detect asymmetries while avoiding artificial inflation, a common problem reported in other methods. In conclusion, the wUSI is proposed as a universal method to quantify three-dimensional GRF asymmetries, which may also be expanded to other biomechanical signals.

Sensitivity of discrete symmetry metrics: implications for metric choice

“…We represent a generic symmetry function as S ( x,y ). We assume that the inputs x and y are independent, normally distributed (an assumption made by many parametric tests), and have the same shape with a variability σ (e.g., group, condition): As noted by Alves et al (2020), a key characteristic of symmetry metrics is the relative difference between x and y , the ratio y / x . Therefore, Eqn.…”

“…Discrete symmetry metrics from eight previously published papers (Alves et al, 2020; Plotnik et al, 2005; Queen et al, 2020; Robinson et al, 1987; Rochester et al, 2014; Seliktar and Mizrahi, 1986; Vagenas and Hoshizaki, 1992; Zifchock et al, 2008) were included, based on presence in previous reviews, number of citations, or if recently proposed as improvements on previous metrics. Two metrics (Plotnik et al, 2005; Rochester et al, 2014) are defined with absolute values and solely assess asymmetry magnitude; to enable consistent comparisons between metrics, these two metrics were assessed with and without the absolute value applied.…”

“…Two metrics (Plotnik et al, 2005; Rochester et al, 2014) are defined with absolute values and solely assess asymmetry magnitude; to enable consistent comparisons between metrics, these two metrics were assessed with and without the absolute value applied. As well, Alves et al (2020) proposed a weighting factor for their metric based on the standard deviation of the input data; the weighted and unweighted metric were evaluated. The standard deviation used in the weighting factor was the σ value from the set of parameters for a given test, which will produce a best-case estimate of power, as the true standard deviation would not be known for real data.…”

“…Another metric was proposed by Zifchock et al (2008) to address issues of previous DSMs related to the choice of reference value (Robinson et al, 1987). Additionally, a research group from Newcastle University uses another metric on a number of spatiotemporal gait variables (Lord et al, 2013; Rochester et al, 2014), and two new DSM have been recently proposed by Queen et al (2020) and Alves et al (2020). Because the defining equations for all of these DSM are different, each metric produces unique numeric results which are not directly comparable (Patterson et al, 2010).…”

“…A power analysis known as “sensitivity power analysis” in G*Power (Faul et al, 2007) can analytically calculate power for many statistical tests given a significance criterion, sample size, and effect size. However, symmetry metric sensitivity cannot be assessed in this way because it remains unclear how a given underlying effect of asymmetry translates to standardized effect sizes for each symmetry metric (Alves et al, 2020). Additionally, the sensitivity of various symmetry metrics cannot be precisely assessed using (finite) experimental data as a reference effect of asymmetry because observed effect sizes have inherent error, as point estimates, which would propagate to estimates of sensitivity (Cohen, 1988).…”