# Gait Asymmetry Post-Stroke: Determining Valid and Reliable Methods Using a Single Accelerometer Located on the Trunk

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## Abstract

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_{21}) = 0.98, respectively). Future research should test the responsiveness of this and other step asymmetry variables to quantify change during recovery and the effect of rehabilitative interventions for consideration as digital biomarkers to quantify gait asymmetry.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Design and Setting

#### 2.2. Participants

#### 2.3. Demographic and Clinical Measures

#### 2.4. Test Protocol

#### 2.5. Asymmetry Variables

#### 2.6. Description of Acceleration-Derived Variables

#### 2.6.1. Harmonic Ratio

#### 2.6.2. Autocorrelation

#### 2.6.3. Gait Symmetry Index

#### 2.6.4. Phase Plot Analysis

#### 2.6.5. Measures Indicative of Stability

#### 2.7. Statistical Analysis

_{21}), and limits of agreement (LoA) expressed as a percentage of the mean of the two variables and the 95% LoA. For all analyses, statistical significance was set at p < 0.05. Predefined acceptance ratings for ICC

_{21}were set at excellent (≥900, 0.0%–4.9%), good (0.750–0.899, 5.0%–9.9%), moderate (0.500–0.749, 10.0%–49.9%), and poor (50.0%) [1,34]. The selection for the most robust variable was based upon the variable with the highest Spearman rank correlation coefficient with the asymmetry variable obtained from the GaitRite while also recording an ICC

_{21}greater than 0.8 for test–retest reliability.

## 3. Results

#### 3.1. Concurrent Validity of the Asymmetry Variables

#### 3.2. Test–Retest Reliability of the Variables

_{21}of 0.98. Taken from the ICC

_{21}values, excellent reliability was achieved for 12 out of the 27 variables tested. These came from the majority of autocorrelation outputs except for step regularity (ML), stride regularity (AP), and autocorrelation symmetry (vertical acceleration (V) and medial lateral acceleration (ML)) direction, the GSI, the HR in the V and AP direction, Jerk RMS, and the short half-orbit segment angle form the phase plot analysis. Good reliability was achieved for a further five variables (stride regularity (AP), autocorrelation symmetry (V), relative orbit inclination, short half orbit eccentricity, and long half orbit eccentricity).

#### 3.3. Selection of the Most Robust Variable

_{21}greater than 0.8 for test–retest reliability. For the GaitRite variables of asymmetry, step regularity (V) achieved the highest concurrent validity due to its correlation with step time asymmetry (RHO = 0.87 and ICC

_{21}= 0.98 **). The second highest concurrent validity was the HR in the vertical direction, which correlated with swing time asymmetry (RHO = 0.73 and ICC

_{21}= 0.98 **).

## 4. Discussion

_{21}= 0.98). Since we did not assess control subjects, we could not determine the best measure to characterise gait post-stroke and highlight the compensatory mechanisms adopted relative to healthy controls. This is a broader aim for ongoing work. However, it has been previously highlighted that compensation strategies may be beneficial to increase gait ability, but this occurs at the compromise of stability. Thus, variables such as Acceleration and Jerk RMS should always be considered in addition to variables directly linked to asymmetry, aiming to provide a more holistic description of gait patterns [13,16]. Future research should explore this relationship so that a holistic, multivariate wearable approach can better assess gait strategies during recovery post-stroke. This potentially would quantify what movements are beneficial to gait, while also highlighting the impact of compensation strategies, consequently quantifying separate movements that can be targeted for rehabilitation.

#### 4.1. Limitations

#### 4.2. Applications

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Data Sharing

## Appendix A

#### Appendix A.1. Acceleration-Derived Variable Definitions

**Table A1.**Indication for the variables used from the signal-derived variables and their respective definitions.

Variable | Definition |
---|---|

Harmonic ratio (V, ML, AP) | The step-to-step symmetry within a stride from calculating a ratio of the odd and even harmonics of a signal following fast Fourier transformation. |

Step regularity (V, ML, AP) | Estimated as the normalized unbiased autocovariance for a lag of one step time. Thus, this feature reflects the similarity between subsequent steps of the acceleration pattern over a step. Values of this feature close to 1.0 (maximum possible value) reflect repeatable patterns between subsequent steps. |

Stride regularity (V, ML, AP) | Estimated as the normalized unbiased autocovariance for a lag of one stride time. Thus, this feature reflects the similarity between subsequent strides of the acceleration pattern over a stride cycle. |

Autocorrelation symmetry (V, ML, AP) | Difference between step and stride regularity designed to quantify the level of symmetry between them and indicative of symmetry during a straight walk. |

Gait symmetry index | Calculated based upon the concept of the summation of the biased autocorrelation from all three components of movement and a subsequent calculation of step and stride timing asymmetry. |

Orbit eccentricity (V) | Average eccentricity of all fully fitted ellipses. |

Relative orbit inclination (V) | Average angle subtended by alternating fitted ellipses within a bout of gait. |

Orbit width deviation (V) | Standard deviation of minor axes lengths of all fully fitted ellipses. Analogous to Principle Component Analysis (second component). |

Short half orbit eccentricity (V) | Difference in eccentricity of two ellipses fitted to each half-cycle of a full orbit in the phase plot. Averaged over all orbits in a bout’s phase plot. |

Short half orbit segment angle (V) | Difference in inclination of two ellipses fitted to each half-cycle of a full orbit in the phase plot. Averaged over all orbits in a bout’s phase plot. |

Long half orbit eccentricity (V) | Difference in eccentricity of two ellipses fitted to each half-cycle of a full orbit in the phase plot. Averaged over all orbits in a bout’s phase plot. |

Long half orbit segment angle (V) | Difference in inclination of two ellipses fitted to each half-cycle of a full orbit in the phase plot. Averaged over all orbits in a bout’s phase plot. |

Intra step correlation (V) | Average correlation of acceleration signal corresponding to step i with that of step i-1. I.e., a lag-1 autocorrelation where a single lag is one step cycle’s duration. |

Acceleration RMS (V, ML, AP) | The calculation of the root mean square of the acceleration signal. |

Jerk RMS (V, ML, AP) | The calculation of the root mean square of the first time derivative of the acceleration signal (jerk). |

#### Appendix A.2. Explanation and Equation for Each Acceleration Derived Variable for Asymmetry

#### Appendix A.2.1. Harmonic Ratio

#### Appendix A.2.2. Autocorrelation

#### Appendix A.2.3. Gait Symmetry Index (GSI)

#### Appendix A.2.4. Phase Plot Analysis

**Figure A3.**Indication of the different conic (ellipses) fitted to the major/minor axis and the first/second halves.

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**Figure 1.**Indication of the instrumentation and the protocol used to collect the acceleration signal and the asymmetry parameters from the GaitRite mat. Also pictured is the acceleration-derived asymmetry variables and the means for the calculation of asymmetry following the processing of the raw acceleration signal.

**Figure 2.**Indication of the correlation between the asymmetry variables quantified using a GaitRite mat and the variables proposed to measure asymmetry from the acceleration signals from the trunk. Black indicates a strong positive or negative correlation. * and ** denotes significance at the 0.05 and 0.01 level, respectively. V = Vertical acceleration, ML = Medial lateral acceleration, and AP = Anterior posterior acceleration.

Demographics (n = 23) | |

Gender (male/female) | 19/4 |

Age (years) | 63 ± 11 |

Body mass index | 26 ± 4 |

Stroke characteristics | |

Time since stroke (months) | 66 ± 48 (range 5–201) |

Stroke subtype (OCSP) | |

Total anterior circulation | 11 |

Partial anterior circulation | 6 |

Lacunar | 3 |

Posterior circulation | 3 |

Stroke impairment | |

NIHSS score (0–40) | 4 ± 3 (range 0–11) |

NIHSS lower limb score (0–4) | 1 ± 0.7 (range 0–3) |

Walking speed (m/s) | 0. 9 ± 0.4 |

Marked hemiplegia (Yes/No) | 15/8 |

Walking aid (number (%)) | 3 (13%) |

Push Aequi ankle foot orthosis (number (%)) | 4 (17%) |

Variables | Median (IQR) | Agreement | ||||
---|---|---|---|---|---|---|

T1 | T2 | Median Difference (%) | ICC_{21} | LOA % (95% LoA) | Rho | |

Harmonic ratio (V) | 1.71 (1.37) | 1.70 (1.23) | −0.01 | 0.98 ** | 1.94 (2.52, 1.36) | 0.92 ** |

Harmonic ratio (ML) | 1.38 (0.60) | 1.57 (0.72) | 0.14 | 0.71 ** | 1.56 (2.80, 0.31) | 0.71 ** |

Harmonic ratio (AP) | 1.26 (0.97) | 1.39 (0.92) | 0.10 | 0.92 ** | 1.54 (2.34, 0.73) | 0.91 ** |

Step regularity (V) | 0.53 (0.47) | 0.52 (0.54) | −0.02 | 0.98 ** | 0.51 (0.67, 0.34) | 0.96 ** |

Step regularity (ML) | 0.42 (0.20) | 0.44 (0.18) | 0.04 | 0.73 ** | 0.44 (0.69, 0.19) | 0.61 ** |

Step regularity (AP) | 0.51 (0.43) | 0.40 (0.49) | −0.20 | 0.92 ** | 0.37 (0.68, 0.07) | 0.87 ** |

Stride regularity (V) | 0.70 (0.25) | 0.68 (0.27) | −0.03 | 0.94 ** | 0.66 (0.85, 0.46) | 0.88 ** |

Stride regularity (ML) | 0.59 (0.14) | 0.66 (0.20) | 0.12 | 0.93 ** | 0.57 (0.78, 0.37) | 0.73 ** |

Stride regularity (AP) | 0.74 (0.18) | 0.75 (0.13) | 0.01 | 0.87 ** | 0.70 (0.92, 0.48) | 0.74 ** |

Autocorrelation symmetry (V) | 0.53 (0.26) | 0.52 (0.29) | 0.56 | 0.80 ** | 0.18 (0.40, −0.03) | 0.76 ** |

Autocorrelation symmetry (ML) | 0.10 (0.19) | 0.16 (0.25) | 0.09 | 0.59 * | 0.19 (0.44, −0.05) | 0.49 * |

Autocorrelation symmetry (AP) | 0.18 (0.15) | 0.19 (0.14) | 0.61 | 0.93 ** | 0.36 (0.62, 0.10) | 0.79 ** |

Gait symmetry index | 0.21 (0.37) | 0.35 (0.43) | −0.02 | 0.92 ** | 0.47 (0.70, 0.23) | 0.82 ** |

Orbit eccentricity | 7.79 (6.27) | 8.32 (15.13) | 0.00 | 0.72 ** | 0.97 (1.04, 0.91) | 0.70 ** |

Relative orbit inclination | 0.01 (0.01) | 0.01 (0.01) | 0.07 | 0.76 ** | 11.02 (28.02, −5.99) | 0.60 ** |

Orbit width deviation | 0.01 (0.02) | 0.00 (0.02) | −0.07 | 0.66 ** | 0.01 (0.05, −0.02) | 0.65 ** |

Short half orbit eccentricity | 5.32 (6.35) | 4.12 (5.31) | −0.38 | 0.73 ** | 0.02 (0.07, −0.03) | 0.87 ** |

Short half orbit segment angle | 0.02 (0.05) | 0.01 (0.04) | −0.23 | 0.95 ** | 7.74 (15.28, 0.20) | 0.57 ** |

Long half orbit eccentricity | 5.20 (10.73) | 5.61 (6.55) | −0.16 | 0.79 ** | 0.04 (0.13, −0.05) | 0.59 ** |

Long half orbit segment angle | 0.89 (0.41) | 0.88 (0.20) | 0.08 | 0.45 | 7.77 (26.32, −10.78) | 0.57 ** |

Intra step correlation | 1.05 (0.04) | 1.05 (0.04) | −0.01 | 0.58 * | 0.78 (1.29, 0.28) | 0.68 ** |

Acceleration RMS (V) | 0.18 (0.09) | 0.17 (0.06) | 0.00 | 0.03 | 1.03 (1.24, 0.83) | 0.41 |

Acceleration RMS (ML) | 0.25 (0.15) | 0.24 (0.15) | −0.06 | 0.90 ** | 0.17 (0.24, 0.10) | 0.68 ** |

Acceleration RMS (AP) | 8.53 (8.00) | 8.57 (7.47) | −0.04 | 0.20 | 0.26 (0.62, −0.10) | 0.21 |

Jerk RMS (V) | 6.29 (4.18) | 6.36 (4.15) | 0.01 | 0.96 ** | 9.32 (13.49, 5.14) | 0.93 ** |

Jerk RMS (ML) | 6.22 (4.89) | 6.42 (6.88) | 0.01 | 0.97 ** | 7.39 (10.67, 4.11) | 0.90 ** |

Jerk RMS (AP) | 1.71 (1.37) | 1.70 (1.23) | 0.03 | 0.96 ** | 7.26 (11.23, 3.28) | 0.92 ** |

**Table 3.**Indication of what wearable sensor variable recorded the highest Spearman’s rank correlation coefficient with each variable obtained by the GaitRite mat. The Spearman’s rank correlation coefficient between the two devices and the intraclass correlation coefficient is displayed for each variable.

GaitRite Variable | Acceleration Derived Variable | Spearman’s Rank Correlation Coefficient (RHO) | ICC_{21} (Test–Retest) | |
---|---|---|---|---|

Asymmetry | Step time (s) | Step regularity (V) | 0.87 | 0.98 ** |

Swing time (s) | Harmonic ratio (V) | 0.73 | 0.98 ** | |

Stance time (s) | Step regularity (V) | 0.72 | 0.98 ** | |

Step length (m) | Step regularity (V) | 0.65 | 0.98 ** |

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## Share and Cite

**MDPI and ACS Style**

Buckley, C.; Micó-Amigo, M.E.; Dunne-Willows, M.; Godfrey, A.; Hickey, A.; Lord, S.; Rochester, L.; Del Din, S.; Moore, S.A. Gait Asymmetry Post-Stroke: Determining Valid and Reliable Methods Using a Single Accelerometer Located on the Trunk. *Sensors* **2020**, *20*, 37.
https://doi.org/10.3390/s20010037

**AMA Style**

Buckley C, Micó-Amigo ME, Dunne-Willows M, Godfrey A, Hickey A, Lord S, Rochester L, Del Din S, Moore SA. Gait Asymmetry Post-Stroke: Determining Valid and Reliable Methods Using a Single Accelerometer Located on the Trunk. *Sensors*. 2020; 20(1):37.
https://doi.org/10.3390/s20010037

**Chicago/Turabian Style**

Buckley, Christopher, M. Encarna Micó-Amigo, Michael Dunne-Willows, Alan Godfrey, Aodhán Hickey, Sue Lord, Lynn Rochester, Silvia Del Din, and Sarah A. Moore. 2020. "Gait Asymmetry Post-Stroke: Determining Valid and Reliable Methods Using a Single Accelerometer Located on the Trunk" *Sensors* 20, no. 1: 37.
https://doi.org/10.3390/s20010037