The symmetry angle: A novel, robust method of quantifying asymmetry
Introduction
Quantifying differences in gait mechanics, strength, and anthropometrics between limbs is a common clinical and research objective. A single discrete measure describing the symmetry between sides is useful for characterizing the functional imbalance between limbs of an individual. Such measures have been used in the past to characterize normal levels of asymmetry in healthy individuals [1], [2]. Additionally, since asymmetry is often associated with pathology, comparisons of symmetry levels have been drawn between groups [3] and in the same group prior to and following an intervention [4].
The symmetry index (SI) [4] is one of the most common methods of quantifying asymmetry between discrete measures [1], [5], [6], [7]. A measurement of the percent difference between two limbs, the SI ascribes a single value to the level of asymmetry between two sides. Therefore, it quantifies the imbalance between the sides of an individual, or permits comparisons of asymmetry levels between groups. A general formula for SI is: SI = (Xside1 − Xside2)/(reference value) × 100%. Unfortunately, there are disadvantages to this measure. First, the SI must be normalized to a reference value. The choice of reference value is typically based upon the question being asked. For example, when comparing between injured and uninjured sides, the uninjured side may be the logical choice. However, if the injured side were chosen instead, the value of the SI could be quite different. Assessing asymmetry in a healthy population can be difficult where there is no obvious side to use as a reference; thus, the average of the two sides is often used. Zifchock et al. [3] compared asymmetry levels between subjects with a history of tibial stress fracture and healthy controls. These authors calculated the SI values of both groups using the average of their left and right sides as the reference value. While it may have been useful to calculate the SI values of the injured group using the uninjured side as the reference value, there was no clear choice for the healthy group. Averaging values can filter out differences between sides and may have limited the ability to compare asymmetry levels between two groups.
Another limitation of the SI is its potential for artificial inflation. This was highlighted in a paper by Herzog et al. [1] who described typical asymmetry values for ground reaction force data during walking. They reported SI values ranging from 4% to 13,000%. These inflated values can occur when a clinically irrelevant difference between sides is divided by a much smaller reference value. This was exemplified by Herzog et al. who showed that the difference between a positive value on one side and a negative value on the other may be referenced to the average of the two values, which will be close to zero.
Recently, Crenshaw and Richards [8] proposed a new method for assessing symmetry between two waveforms. This method is very useful for comparing curves over a period of time. However, it does not allow for the comparison of discrete values such as peak knee flexion or hip abduction strength. While the SI is a valuable method of assessing symmetry of discrete values, the previously discussed limitations underscore the need for a more robust method of quantification.
The current study proposes the use of the symmetry angle (SA) and compares its performance with the traditionally used SI. The objectives were to examine the limitations of the SI, define the SA, and compute the correlations between the two measures. Therefore, the first purpose was to identify whether the use of different reference values significantly alters the SI value. It was hypothesized that SI values would be significantly different when referenced to the right versus the left side. In addition, SI values referenced to the average of the right and left sides were expected to be smaller than values referenced to a given side. The second purpose was to assess the correlation between values calculated using the SA and the SI. These values were expected to be significantly correlated. To assess the applicability of these results to the types of biomechanical variables that are assessed in studies of gait, two kinetic, two kinematic, two structural, and two strength variables were analyzed for each aim.
Section snippets
Methods
An a priori power analysis (α = 0.05, β = 0.8, expected difference = 15%) was conducted using variability measures from previous literature and pilot data [3]. Results of the analysis suggested that 50 subjects would be needed to adequately power the study. Therefore, 52 volunteers (28 male, 24 female) were recruited to take part in the study. All participants were rearfoot strikers, 18–45 years of age, and were running at least 20 miles/week. All subjects were free from injury at the time of the
Results
The first analysis identified the proportion of subjects who exhibited at least a 15% difference between SI values referenced to either the left or right side. For all variables, the majority of subjects exhibited a difference of at least 15%. The proportion was significant for the kinetic and kinematic variables, as well as HIRr (Fig. 3). The second analysis compared SIleft to SIaverage. For six of the eight variables, SIaverage tended to be lower than SIleft (Fig. 4). For the two variables in
Discussion
Assessment of biomechanical asymmetry is useful in both clinical and research settings. However, it is important that the measurement tool is robust to problems of reference value and inflation. The purpose of this study was to examine the effect of reference value selection on SI values, and to compare SI values to a new method of quantifying asymmetry, the SA. The results of the first aim of this study suggested that quantification of gait asymmetry is influenced by the side chosen as the
Conflict of interest
None.
Acknowledgements
This work was supported by the American Society of Biomechanics Student Grant-In-Aid and the International Society of Biomechanics Matching Dissertation Grant.
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