Download - Symmetry
Symmetry
Definition: Both limbs are behaving identically
Measures of Symmetry Symmetry Index
Symmetry Ratio
Statistical Methods
Symmetry Index
SI when it = 0, the gait is symmetricalDifferences are reported against their average value. If a large asymmetry is present, the average value does not correctly reflect the performance of either limb
Robinson RO, Herzog W, Nigg BM. Use of force platform variables to quantify the effects of chiropractic manipulation on gait symmetry. J Manipulative Physiol Ther 1987;10(4):172–6.
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Symmetry Ratio
Limitations: relatively small asymmetry and a failure to provide info regarding location of asymmetry
Low sensitivity
Seliktar R, Mizrahi J. Some gait characteristics of below-knee amputees and their reflection on the ground reaction forces. Eng Med 1986;15(1):27–34.
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Statistical Measures of Symmetry
Correlation Coefficients Principal Component Analysis Analysis of Variance
•Use single points or limited set of points•Do not analyze the entire waveform
Sadeghi H, et al. Symmetry and limb dominance in able-bodied gait: areview. Gait Posture 2000;12(1):34–45.
Sadeghi H, Allard P, Duhaime M. Functional gait asymmetry in ablebodied subjects. Hum Movement Sci 1997;16:243–58.
The measure of trend symmetry utilizes eigenvectors to compare time-normalized right leg and left leg gait cycles in the following manner. Each waveform is translated by subtracting its mean value from every value in the waveform.
for every ith pair of n rows of waveform data
Eigenvector Analysis
Eigenvector Analysis
Translated data points from the right and left waveforms are entered into a matrix (M), where each pair of points is a row. The rectangular matrix M is premultiplied by its transpose (MTM) to form a square matrix S, and the eigenvectors are derived from the square matrix S. To simplify the calculation process, we applied a singular value decomposition (SVD) to the translated matrix M to determine the eigenvectors, since SVD performs the operations of multiplying M by its transpose and extracting the eigenvectors.
Eigenvector Analysis
Each row of M is then rotated by the angle formed between the eigenvector and the X-axis (u) so that the points lie around the X-axis (Eq. (2)):
Eigenvector Analysis
The variability of the points is then calculated along the X and Y-axes, where the Y-axis variability is the variability about the eigenvector, and the X-axis variability is the variability along the eigenvector. The trend symmetry value is calculated by taking the ratio of the variability about the eigenvector the variability along the eigenvector, and subtracting it from 1.0.
A value of 1.0 indicates perfect symmetry, and a value of 0.0 indicates asymmetry.
Eigenvector Analysis
We also calculated two additional measures of symmetry between waveforms.
Range amplitude ratio quantifies the difference in range of motion of each limb, and is calculated by dividing the range of motion of the right limb from that of the left limb.
Range offset, a measure of the differences in operating range of each limb, is calculated by subtracting the average of the right side waveform from the average of the left side waveform.
Eigenvector Analysis
Expressed as ratio of the variance about eigenvector to the variance along the eigenvectorTrend Symmetry: 0.948 Range Amplitude Ratio: 0.79, Range Offset:0
Eigenvector Analysis
Expressed as a ratio of the range of motion of the left limb to that of the right limbRange Amplitude Ratio: 2.0 Trend Symmetry: 1.0, Range Offset: 19.45
Eigenvector Analysis
Calculated by subtracting the average of the right side waveform from the average of the left side waveformRange Offset: 10.0 Trend Symmetry: 1.0, Range Amplitude Ratio: 1.0
Eigenvector Analysis
Trend Symmetry: 0.979 Range Amplitude Ratio: 0.77 Range Offset: 2.9°
Raw flexion/extension waveforms from an ankle
Eigenvector Analysis
Final Adjustment #1
Determining Phase Shift and the Maximum Trend Symmetry Index: Shift one waveform in 1-percent increments (e.g.
sample 100 becomes sample 1, sample 1 becomes sample 2…) and recalculate the trend similarity for each shift. The phase shift is determined by identifying the index at which the smallest value for trend similarity occurs. The maximum trend similarity value independent of original phase position is also identified in this process.
Final Adjustment #2
Modifications to Trend Symmetry Index to accommodate mirrored waveforms: Assign the sign of the eigenvector slope to the
TSI value. A modified TSI value of 1.0 indicates perfect symmetry in like oriented waveforms, while a TSI value of -1 indicates perfect symmetry in reflected waveforms. A TSI value of 0.0 still indicates asymmetry.
Symmetry Example
Hip Joint Trend Symmetry
Phase Shift (% Cycle
Max Trend Symmetry
Range Amplitude
Range Offset
95% CI 0.98 – 1.00 -3.1 – 2.9 0.99 – 1.00 0.88 - 1.16 -5.99 – 5.66
Unbraced 1.00 1 1.00 0.95 4.21
Braced 1.00 0 1.00 1.02 4.73
Amputee 1.00 -1 1.00 0.88 -0.72
Symmetry Example…Hip Joint
Braced AmputeeUnbraced
Knee Joint
Trend Symmetry
Phase Shift (% Cycle
Max Trend Symmetry
Range Amplitude
Range Offset
95% CI 0.97 – 1.00 -2.6 – 2.5 0.99 – 1.00 0.87 - 1.16 -8.95 - 10.51
Unbraced 1.00 0 1.00 1.03 5.28
Braced 1.00 -1 1.00 0.99 6.40
Amputee 0.98 -1 0.99 0.91 4.15
Symmetry Example…Knee Joint
Braced AmputeeUnbraced
Ankle Joint
Trend Symmetry
Phase Shift (% Cycle
Min Trend Symmetry
Range Amplitude
Range Offset
95% CI 0.94 – 1.00 -2.62 – 2.34 0.96 – 1.00 0.75 - 1.32 -6.4 – 7.0
Unbraced 0.98 -1 0.98 1.03 -2.96
Braced 0.73 -4 0.79 0.53 5.84
Amputee 0.58 4 0.61 1.27 0.48
Symmetry Example…Ankle Joint
Unbraced Braced Amputee
Normalcy Example
Hip Joint Trend Normalcy
Phase Shift (% Cycle
Max Trend Normalcy
Range Amplitude
Range Offset
95% CI 0.98 – 1.00 -3.1 – 2.9 0.99 – 1.00 0.88 - 1.16 -5.99 – 5.66
Right hip
Unbraced 1.00 2 1.00 0.85 -14.91
Braced 0.99 3 1.00 0.90 -14.20
Amputee 0.97 -4 1.00 0.92 -8.08
Left hip
Unbraced
Braced
Amputee
Unbraced Braced Amputee
Hip Joint Trend Normalcy
Phase Shift (% Cycle
Max Trend Normalcy
Range Amplitude
Range Offset
95% CI 0.98 – 1.00 -3.1 – 2.9 0.99 – 1.00 0.88 - 1.16 -5.99 – 5.66
Right hip
Unbraced
Braced
Amputee
Left hip
Unbraced 1.00 2 1.00 0.91 -19.28
Braced 0.99 4 1.00 0.91 -19.09
Amputee 0.99 -2 1.00 1.06 -7.52
Unbraced Braced Amputee
Knee Joint
Trend Normalcy
Phase Shift (% Cycle
Max Trend Normalcy
Range Amplitude
Range Offset
95% CI 0.97 – 1.00 -2.6 – 2.5 0.99 – 1.00 0.87 - 1.16 -8.95 – 10.51
Right knee
Unbraced 0.99 1 0.99 1.12 -11.89
Braced 0.98 3 0.99 1.07 -13.22
Amputee 0.96 -2 0.99 0.97 -7.45
Left knee
Unbraced
Braced
Amputee
Unbraced Braced Amputee
Knee Joint
Trend Normalcy
Phase Shift (% Cycle
Max Trend Normalcy
Range Amplitude
Range Offset
95% CI 0.97 – 1.00 -2.6 – 2.5 0.99 – 1.00 0.87 - 1.16 -8.95 – 10.51
Right knee
Unbraced
Braced
Amputee
Left knee
Unbraced 0.99 1 0.99 1.11 -16.35
Braced 0.97 4 0.99 1.10 -18.80
Amputee 0.98 -2 1.00 1.08 -10.78
Unbraced Braced Amputee
Ankle Joint
Trend Normalcy
Phase Shift (% Cycle
Max Trend Normalcy
Range Amplitude
Range Offset
95% CI 0.94 – 1.00 -2.62 – 2.34 0.96 – 1.00 0.75 - 1.32 -6.4 – 7.0
Right ankle
Unbraced 0.90 -2 0.94 1.48 1.33
Braced 0.65 -4 0.72 0.77 9.04
Amputee 0.80 -5 0.98 1.40 4.30
Left ankle
Unbraced
Braced
Amputee
Unbraced Braced Amputee
Ankle Joint
Trend Normalcy
Phase Shift (% Cycle
Max Trend Normalcy
Range Amplitude
Range Offset
95% CI 0.94 – 1.00 -2.62 – 2.34 0.96 – 1.00 0.75 - 1.32 -6.4 – 7.0
Right ankle
Unbraced
Braced
Amputee
Left ankle
Unbraced 0.93 -1 0.95 1.49 4.62
Braced 0.94 2 0.95 1.51 3.53
Amputee 0.11 -11 0.76 1.14 4.15
Unbraced Braced Amputee