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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LR

LR

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XXSI

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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XSR

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