# Gait Symmetry Assessment with a Low Back 3D Accelerometer in Post-Stroke Patients

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## Abstract

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_{L3}). GSI

_{L3}was evaluated with 16 post stroke patients and nine healthy controls in the Six-Minute-Walk-Test (6-MWT). Discriminative power was evaluated with Wilcoxon test and the effect size (ES) was computed with Cliff’s Delta. GSI

_{L3}estimated during the entire 6-MWT and during a short segment straight walk (GSI

_{L3straight}) have comparable effect size to one another (ES = 0.89, p < 0.001) and to the symmetry indices derived from feet sensors (|ES| = [0.22, 0.89]). Furthermore, while none of the indices derived from feet sensors showed significant differences between post stroke patients walking with a cane compared to those able to walk without, GSI

_{L3}was able to discriminate between these two groups with a significantly lower value in the group using a cane (ES = 0.70, p = 0.02). In addition, GSI

_{L3}was strongly associated with several symmetry indices measured by feet sensors during the straight walking cycles (Spearman correlation: |ρ| = [0.82, 0.88], p < 0.05). The proposed index can be a reliable and cost-efficient post stroke gait symmetry assessment with implications for research and clinical practice.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Acquisition

#### 2.2. Gait Symmetry Assessment with Two Feet Sensors

#### 2.2.1. Symmetry of Spatiotemporal Gait Parameters

#### 2.2.2. Symmetry of Foot Pitch Angular Velocity

_{left}(n) and ω

_{right}(n) of cycle n [19]. The gait symmetry between the left and the right signals was assessed for each cycle based on (a) Pearson correlation coefficient (denoted by GSI

_{corr}) and (b) the normalized sample distance (denoted by GSI

_{dist}). GSI

_{dist}was the mean absolute difference between each left and right signal sample of cycle n divided by the mean range of the signals in the cycle (Equation (2)). Mean values of GSI

_{corr}and GSI

_{dist}of all straight walking cycles in the entire 6-MWT were calculated. The detection of gait cycle and the selection of straight walking cycles were based on the same algorithms mentioned in Section 2.2.1:

#### 2.3. Gait Symmetry Assessment with a Single 3D Accelerometer at the Low Back

_{v}), frontal (AR

_{f}) and lateral (AR

_{l}) accelerations at the low back were computed as the function of time lag (t), respectively. The biased form of autocorrelation was used to suppress the amplitude of the coefficients while t increased [23]. The maximum time lag was 4 s (400 samples), which is about 2.5 times a single stride duration in post hemiplegic stroke patients [24]. This window length was chosen to capture the repetition of stride cycles in very slow walking. Coefficient of stride cycle repetition (C

_{stride}) was the sum of positive autocorrelation coefficients of the three axes as a function of t (Equation (3)). Coefficient of step repetition (C

_{step}) was the norm of autocorrelation coefficients as a function of t (Equation (4)). One stride time (T

_{stride}) equals to t, when C

_{stride}had the maximum value. The hypothesis was that, in a perfect symmetric gait pattern, two consecutive steps have the same step duration of 0.5 * T

_{stride}. The maximum value of C

_{step}was $\sqrt{3}$ when autocorrelation coefficient of each acceleration axis was 1 at zero-lag (t = 0). The gait symmetry index (GSI

_{L3}) was C

_{step}(0.5 * T

_{stride}) normalized to its value at zero-lag (Equation (5)), so that the maximum value of GSI

_{L3}was 1 in a perfect symmetric gait pattern:

#### 2.4. Statistical Analysis

_{corr}, GSI

_{dist}and GSI

_{L3}(estimated by the low back accelerometer) were computed for each post-stroke patient and each healthy control. For SI, GSI

_{corr}and GSI

_{dist}, mean values over all gait cycles during straight walking in the entire 6-MWT assessment period were computed. GSI

_{L3}was computed for the entire 6-MWT assessment period and for the first straight course of the assessment (GSI

_{L3straight}). Given the small sample size in this study, non-parametric statistics were applied for the analyses. Wilcoxon rank sum test was used to test whether there are significant differences in various sensor-derived gait symmetry indices between post-stroke patients and control group. In addition, effect size (ES) calculator Cliff’s Delta was used to determine the discriminating power of various symmetry indices [25]. Cliff’s Delta calculates the proportion of non-overlapped samples in the groups. ES = 1 or −1 indicates the two groups have no overlap. Whereas, ES = 0 means the two groups are not separable. According to a study by Romano et al., ES less than 0.147 is negligible, between 0.147 and 0.33 is small, between 0.33 and 0.474 is medium, and more than 0.474 is a large effect [26]. The correlations between the low back sensor derived symmetry indices (GSI

_{L3}and GSI

_{L3straight}) and the feet sensor based symmetry indices (SI, GSI

_{corr}and GSI

_{dist}) were analyzed with Spearman rank correlation coefficient (ρ).

## 3. Results

#### 3.1. Discriminative Power of Gait Symmetry as Measured by Various Indices

_{stride}and C

_{step}as illustrated in Figure 2. The healthy control (a) had a shorter stride duration (ca. 1.05 s at maximum C

_{stride}) compared to the post-stroke patient (b) (ca. 1.90 s). The coefficient of step repetition (C

_{step}) of the healthy control at half stride time was higher than that in the post-stroke patient, which indicated a higher gait symmetry.

_{dist}had the largest effect size. Gait symmetry measured with the low back accelerometer was significantly lower in post-stroke patients during the entire 6-MWT and during the shorter straight walk of the assessment. The effect size was the same as GSI

_{dist}, the best spatiotemporal parameter derived from the feet angular velocity signals. Boxplots in Figure 3 show the differences in various symmetry indices between post-stroke patients walking with and without a cane. Interestingly, GSI

_{L3}was significantly lower in post-stroke patients walking with a cane compared to those able to walk without. There were no significant differences between GSI

_{L3straight}and any symmetry estimates provided by the feet sensors.

#### 3.2. Correlations between Gait Symmetry Measured with Low Back Accelerometry and That Measured with Two Feet Sensors

_{LiftOffAng,}ρ = 0.87 with SI

_{corr}and ρ = −0.82 with GSI

_{dist}). Gait symmetry derived from the low back accelerometer when the participants walked through a short straight path (GSI

_{L3straight}) were significantly correlated with feet sensor based symmetry measures as well (ρ = −0.84 with SI

_{LiftOffAng,}ρ = 0.80 with GSI

_{corr}and ρ = −0.79 with GSI

_{dist}).

## 4. Discussion

_{L3}, is a measure of the repetitiveness of the gait cycles. Thus, the more symmetric the gait is, the higher the index value. On the contrary, the symmetry indices based on the spatiotemporal gait parameters with the feet sensors, SI, are measures of the degree of difference in the bilateral movement. The value decreases when the difference decreases as in symmetric gaits. Thus, SI has a negative correlation with GSI

_{L3}. This is also the case for the gait symmetry measured with angular velocity signal profile GSI

_{dist}using the feet sensors, as GSI

_{dist}measures the difference between the bilateral foot angular velocity signals. GSI

_{corr}with the feet sensors measures the correlation between the bilateral foot angular velocity signals. Its value increase when signals have higher correlation as in symmetric gaits. Hence, GSI

_{corr}has a positive correlation with GSI

_{L3}. More importantly, GSI

_{L3}has good discriminative power comparable to symmetry indices based on spatiotemporal parameters derived from two feet sensors. GSI

_{L3}has several advantages in technical implementation and clinical practice.

#### 4.1. Advantages in Technical Implementation

_{L3}) is based on analysis of acceleration signals’ repetitiveness quantified by autocorrelation coefficients. In addition, the computation is both easier and more robust than the morphology-based signal processing provided by the spatiotemporal gait parameter estimations. Compared to symmetry indices estimated with two feet sensors, GSI

_{L3}is easier for technical implementation as only a single sensor is required. The computation of GSI

_{L3}is based on the norm of autocorrelation coefficients rather than analysis of individual axis as presented in two studies [12,23]. Different from these studies, the proposed estimation of GSI

_{L3}does not rely on detection of step alternation, which can be unreliable in people with poorly symmetric gaits as shown in Figure 2b. The biased autocorrelation coefficients decreases while time lag increases, which allows the reliable detection of the immediate next stride. In addition, estimation of GSI

_{L3}during the entire 6-MWT as presented in this study has comparable discriminative power as those estimations using cleaned data (only straight walking cycles) with two feet sensors as shown in the results summarized in Table 2. Ultimately, GSI

_{L3}requires less computation and it may be more feasible and robust than feet sensor based gait symmetry measures in semi- or unsupervised assessment.

#### 4.2. Advantages in Clinical Practice

#### 4.3. Limitations

_{L3}should be evaluated to determine the minimum detectable change using the developed index. Another limitation is with the selection of the maximum time lag for autocorrelation analysis. Four-second lag was chosen based on reported data in previous stroke study. A longer window is unlikely to affect the stride time detection. However, a shorter window may not accurately detect the stride repetition in extremely impaired stroke patients with very slow walking. A systematic examination using different window length will be required to determine the optimized configuration for computation with a patient group exhibiting large functional variations. In addition, the sample size in this study was small, yet our findings did reach statistical significance with effect sizes that suggest the sample was sufficient to support our conclusion. Still, it must be noted that age differences between the post-stroke and the control group may introduce some bias into the effect sizes of the various symmetry indices.

#### 4.4. Future Studies

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Synchronized pitch angular velocity signals from feet sensors and 3D acceleration signals from low back sensor. (

**a**) Synchronized signals from a healthy control. (

**b**) Synchronized signals from a post-stroke patient. Upper plot shows foot pitch angular velocity on the left (red) and right (blue) side during walking. Lower plot shows lower back acceleration on the vertical (blue), frontal (yellow) and lateral (red) axis. The dotted vertical lines indicate of each gait cycles detected by the feet sensors. In (

**a**), time phases of foot-flat, push-up, swing and loading in one cycle of the left foot are indicated in the pitch angular velocity signal. Axes of the accelerometer at the low back are illustrated next to the acceleration signals.

**Figure 2.**Autocorrelation coefficients of 3D acceleration of lower back. (

**a**) Coefficients of a healthy control. (

**b**) Coefficients of a post-stroke patient. Autocorrelation coefficients in vertical (blue), lateral (red) and frontal (yellow) axis are computed with increased lag from 0 to 400 samples (4 s). C

_{stride}(dotted black line) and C

_{step}(solid black line) in the bottom plot are computed as a function of time lag.

**Figure 3.**Boxplots of various gait symmetry indices measured in post-stroke patients with (w Cane) or without (w/o Cane) using cane. Effect size (ES) is measured with Cliff’s Delta and p value is determined by Wilcoxon rank sum test. * indicates p < 0.05. (

**a**) Comparison and effect size of SI

_{LiftOffAng}. (

**b**) Comparison and effect size of GSI

_{dist}. (

**c**) Comparison and effect size of GSI

_{L3}. (

**d**) Comparison and effect size of GSI

_{L3straight}.

**Figure 4.**Correlation between gait symmetry measured with the low back accelerometer and symmetry measured with two feet sensors. Association is estimated with Spearman correlation. *** indicates p < 0.0001.

Parameter [Unit] | Description |
---|---|

Spatial | |

PathLength [% stride length] | Ratio between the length of the real path of the foot in 3D space (including both stride length and width) and stride length of one cycle. |

StrikeAng [deg] | Angle between the foot and the ground at heel strike in sagittal plane. |

LiftOffAng [deg] | Angle between the foot and the ground at toe off in sagittal plane. |

MaxAngVel [deg/s] | Maximum pitch foot angular velocity during swing phase. |

Temporal | |

StanceRatio [%] | Percentage of the gait cycle during which the foot is in stance phase. |

LoadRatio [%] | Percentage of the stance corresponding to loading phase defined as the time between heel strike and toe strike |

FootFlatRatio [%] | Percentage of the stance corresponding to the foot-flat phase |

PushRatio [%] | Percentage of the stance corresponding to push phase defined as the time between heel off and toe off. |

**Table 2.**Mean ± standard deviation and effect size (ES) as estimated by Cliff’s Delta of various symmetry indices.

Symmetry Index (SI) | Control Group | Post-stroke | ES |
---|---|---|---|

Gait symmetry based on spatiotemporal gait parameter | |||

PathLength | 0.54 ± 0.07 | 4.30 ± 5.69 | −0.85 *** |

StrikeAng | 8.50 ± 4.53 | 35.78 ± 30.85 | −0.79 ** |

LiftOffAng | 3.78 ± 1.33 | 42.80 ± 37.27 | −0.88 *** |

MaxAngVel | 6.31 ± 3.78 | 44.86 ± 39.23 | −0.81 ** |

StanceRatio | 3.06 ± 2.27 | 12.19 ± 8.06 | −0.79 ** |

LoadRatio | 22.36 ± 9.42 | 32.36 ± 22.06 | −0.22 |

FootFlatRatio | 5.99 ± 2.28 | 7.18 ± 4.98 | −0.13 |

PushRatio | 6.88 ± 3.67 | 25.76 ± 25.57 | −0.71 ** |

Gait symmetry based on feet angular velocity signal profile | |||

$\mathit{G}\mathit{S}{\mathit{I}}_{\mathit{c}\mathit{o}\mathit{r}\mathit{r}}$ | 0.97 ± 0.01 | 0.76 ± 0.24 | 0.85 *** |

$\mathit{G}\mathit{S}{\mathit{I}}_{\mathit{d}\mathit{i}\mathit{s}\mathit{t}}$ | 6.84 ± 1.23 | 16.87 ± 7.70 | −0.89 *** |

Gait symmetry based on low back accelerometry | |||

$GS{I}_{L3}$ | 0.74 ± 0.06 | 0.35 ± 0.22 | 0.89 *** |

$GS{I}_{L3straight}$ | 0.69 ± 0.09 | 0.36 ± 0.19 | 0.89 *** |

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## Share and Cite

**MDPI and ACS Style**

Zhang, W.; Smuck, M.; Legault, C.; Ith, M.A.; Muaremi, A.; Aminian, K.
Gait Symmetry Assessment with a Low Back 3D Accelerometer in Post-Stroke Patients. *Sensors* **2018**, *18*, 3322.
https://doi.org/10.3390/s18103322

**AMA Style**

Zhang W, Smuck M, Legault C, Ith MA, Muaremi A, Aminian K.
Gait Symmetry Assessment with a Low Back 3D Accelerometer in Post-Stroke Patients. *Sensors*. 2018; 18(10):3322.
https://doi.org/10.3390/s18103322

**Chicago/Turabian Style**

Zhang, Wei, Matthew Smuck, Catherine Legault, Ma A. Ith, Amir Muaremi, and Kamiar Aminian.
2018. "Gait Symmetry Assessment with a Low Back 3D Accelerometer in Post-Stroke Patients" *Sensors* 18, no. 10: 3322.
https://doi.org/10.3390/s18103322