skdh.gait.GaitSymmetryIndex

class skdh.gait.GaitSymmetryIndex

Assessment of the symmetry between steps during straight overground gait. It is computed for an entire bout. Values closer to 1 indicate higher symmetry, while values close to 0 indicate lower symmetry.

Methods

predict(*, fs, leg_length, gait, gait_aux)

Predict the bout level gait endpoint

Notes

If the minimum gait window time is less than 4.5 seconds, there may be issues with this endpoint for those with slow gait (those with stride lengths approaching the minimum gait window time).

GSI is computed using the biased autocovariance of the acceleration after being filtered through a 4th order 10Hz cutoff butterworth low-pass filter. [1] and [2] use the autocorrelation, instead of autocovariance, however subtracting from the compared signals results in a better mathematical comparison of the symmetry of the acceleration profile of the gait. The biased autocovariance is used to suppress the value at higher lags [1]. In order to ensure that full steps/strides are capture, the maximum lag for the autocorrelation is set to 4s, which should include several strides in healthy adults, and account for more than 2.5 strides in impaired populations, such as hemiplegic stroke patients [3].

With the autocovariances computed for all 3 acceleration axes, the coefficient of stride repetition (\(C_{stride}\)) is computed for lag \(m\) per

\[C_{stride}(m) = K_{AP}(m) + K_{V}(m) + K_{ML}(m)\]

where \(K_{x}\) is the autocovariance in the \(x\) direction - Anterior-Posterior (AP), Medial-Lateral (ML), or vertical (V). The coefficient of step repetition (\(C_{step}\)) is the norm of \(C_{stride}\)

\[C_{step}(m) = \sqrt{C_{stride}(m)} = \sqrt{K_{AP}(m) + K_{V}(m) + K_{ML}(m)}\]

Under the assumption that perfectly symmetrical gait will have step durations equal to half the stride duration, the GSI is computed per

\[GSI = C_{step}(0.5m_{stride}) / \sqrt{3}\]

where \(m_{stride}\) is the lag for the average stride in the gait bout, and corresponds to a local maximum in the autocovariance function. To find the peak corresponding to \(m_{stride}\) the peak nearest to the average stride time for the bout is used. GSI is normalized by \(\sqrt{3}\) in order to have a maximum value of 1.

References

[1] (1,2)

W. Zhang, M. Smuck, C. Legault, M. A. Ith, A. Muaremi, and K. Aminian, “Gait Symmetry Assessment with a Low Back 3D Accelerometer in Post-Stroke Patients,” Sensors, vol. 18, no. 10, p. 3322, Oct. 2018, doi: 10.3390/s18103322.

[2]

C. Buckley et al., “Gait Asymmetry Post-Stroke: Determining Valid and Reliable Methods Using a Single Accelerometer Located on the Trunk,” Sensors, vol. 20, no. 1, Art. no. 1, Jan. 2020, doi: 10.3390/s20010037.

[3]

H. P. von Schroeder, R. D. Coutts, P. D. Lyden, E. Billings, and V. L. Nickel, “Gait parameters following stroke: a practical assessment,” Journal of Rehabilitation Research and Development, vol. 32, no. 1, pp. 25–31, Feb. 1995.