# Does Curved Walking Sharpen the Assessment of Gait Disorders? An Instrumented Approach Based on Wearable Inertial Sensors

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Procedures

#### 2.3. Equipment

^{2}, and ±1500 deg·s

^{−1}of full-range scale, respectively). Two IMUs were located on the center of the sternum (S), and at L4/L5 level, slightly above the pelvis (P), and other two IMUs were positioned on both distal tibiae, slightly above the lateral malleoli. The upper-body units were used to assess the upper-body stability, whereas the tibiae-mounted ones for stride segmentation. The IMUs were positioned by two expert physiotherapists who securely fixed the devices following ad hoc instructions relying on specific anatomical landmarks. Each IMU was attached to the participants’ body with ad hoc Velcro straps.

#### 2.4. Data Processing

^{®}software (The MathWorks Inc., Natick, MA, USA). First, the two IMUs located on the upper body were verticalized through a rigid transformation applied during the static phase before each trial. This transformation was obtained using the accelerometer as an inclinometer and thus obtaining both IMUs inclination with respect to gravity. [26]. The resulting IMU axes were considered to approximate the antero-posterior (AP), medio-lateral (ML), and cranio-caudal (CC) anatomical axes. This procedure guaranteed identical starting conditions for all the participants as well as a reliable and repeatable system of reference for both sternum and pelvis IMUs.

- Average walking speed (WS): total distance/time to complete the test.
- Average stride duration (SD): time to complete the test/total number of strides.
- Stride frequency (SF) total number of strides/time to complete the test.
- Stability:
- (i)
- normalized Root Mean Square (nRMS) values of the measured accelerations at P and S levels, calculated by dividing the RMS obtained for the AP and ML components by the RMS of the CC component. As widely reported in the literature, the greater the nRMS values, the higher the amount of acceleration and, hence, the higher the instability [27];$$RM{S}_{j}K=\frac{1}{N}\sqrt{{{\displaystyle \sum}}_{i=1}^{N}{a}_{i}^{2}};nRM{S}_{j}K=\frac{RM{S}_{j}K}{RM{S}_{CC}K}$$
- (ii)
- attenuation coefficient (AC) [28] between P and S levels, for the acceleration component (j), defined as:$$ACP{S}_{j}=\left(1-\frac{RM{S}_{j}S}{RM{S}_{j}P}\right)\xb7100$$

- Symmetry: improved Harmonic Ratio (iHR) calculated for each acceleration component (j) measured at the pelvis level, as proposed by [29]. It was calculated as:$${\mathrm{iHR}}_{j}=\frac{\sum \mathrm{Power}\text{}\mathrm{of}\text{}\mathrm{intrinsic}\text{}\mathrm{harmonics}}{\sum \mathrm{Power}\text{}\mathrm{of}\text{}\mathrm{intrinsic}\text{}\mathrm{harmonics}+\sum \mathrm{Power}\text{}\mathrm{of}\text{}\mathrm{extrinsic}\text{}\mathrm{harmonics}}\xb7100$$
- Smoothness: SPectral ARC length (SPARC) [30] calculated for each acceleration component (j) measured at the P level. It estimates smoothness by calculating the arc length of the Fourier magnitude spectrum of a given signal profile within a defined frequency range. The calculation of SPARC has been performed, as follows:$$-{{\displaystyle \int}}_{0}^{{\stackrel{~}{\mathsf{\omega}}}_{\mathrm{c}}}[{(\frac{1}{{\stackrel{~}{\mathsf{\omega}}}_{\mathrm{c}}})}^{2}+{(\frac{\mathrm{d}\hat{\mathrm{A}}(\stackrel{~}{\mathsf{\omega}})}{\mathrm{d}\stackrel{~}{\mathsf{\omega}}}{)}^{2}]}^{\frac{1}{2}}\mathrm{d}\stackrel{~}{\mathsf{\omega}};\hat{\mathrm{A}}(\stackrel{~}{\mathsf{\omega}})=\frac{\mathrm{A}(\stackrel{~}{\mathsf{\omega}})}{\mathrm{A}\left(0\right)}$$$${\stackrel{~}{\mathsf{\omega}}}_{\mathrm{c}}=\mathrm{min}\{{{\stackrel{~}{\mathsf{\omega}}}_{\mathrm{c}}}^{\mathrm{max}},\mathrm{min}\{\stackrel{~}{\mathsf{\omega}},\hat{\mathrm{A}}\left(\mathrm{r}\right)<\overline{\mathrm{A}}\forall \mathrm{r}\stackrel{~}{\mathsf{\omega}}\}\}$$

#### 2.5. Statistical Analysis

## 3. Results

#### 3.1. Spatiotemporal Parameters

#### 3.2. Gait Quality Indices

## 4. Discussion

^{−1}during straight walking), differences in the spatiotemporal and gait quality-related parameters between straight and curved locomotion may become negligible [31].

^{−1}for the linear and curvilinear walking, respectively), likely as an expression of the motor deficit and to counteract the fear of falling, or because of post-traumatic parkinsonism features [32,33]. On the other hand, less severely affected patients displayed a median speed value of 1.15 m·s

^{−1}during straight walking, which is higher than the abovementioned threshold [31]. Similar to healthy adults, in fact, they exhibited different walking patterns when performing straight and curvilinear paths. Specifically, consistent with what has been reported in previous literature [31], the more challenging gait modality induces a decrease in walking speed, an increase in stride duration, and a decrease in the stride frequency, with respect to the straight path (Figure 2). This confirms that human subjects adapt their locomotor velocity to the radius of curvature of the path they are following, with the velocity that tends to increase when the trajectory becomes straighter and decrease when it becomes more curved [5].

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The Figure-of-8 Walk Test, adapted from [18].

**Figure 2.**Whisker’s plots reporting walking speed, stride frequency, and stride duration for both the 10 mWT and the F8WT in sTBI-VS, sTBI-S, and CG. In all subplots, the horizontal lines with asterisks indicate statistically significant differences.

**Figure 3.**Whisker’s plots reporting gait quality indices for both sTBI sub-groups (sTBI-VS and sTBI-S) and for CG in the 10 mWT (solid boxes) and F8WT (striped boxes). Panel (

**A**,

**B**): normalized RMS values (nRMS) for pelvis and sternum levels, respectively; Panel (

**C**): attenuation coefficients (AC); Panel (

**D**): improved Harmonic Ratio (iHR); Panel (

**E**): SPectral ARC length (SPARC). AP, antero-posterior; ML, medio-lateral; CC, cranio-caudal; P, pelvis; S. In all plots, the horizontal lines with asterisks indicate statistically significant differences.

**Table 1.**Demographic and anthropometric characteristics of very severe Traumatic Brain Injury (sTBI-VS), severe Traumatic Brain Injury (sTBI-S), and control group (CG). Median and interquartile (IQR) values are displayed. Groups were homogeneous in terms of age, body mass, and height (p > 0.05). sTBI-S and sTBI-VS did not show statistical differences in terms of time since trauma (p > 0.05).

sTBI-VS | sTBI-S | CG | |
---|---|---|---|

Nr. of participants | 11 | 9 | 20 |

Nr. of males | 7 | 5 | 12 |

Age (ears) | 32.0 (9.7) | 34.1 (9.1) | 33.6 (10.8) |

Time since trauma (days) | 504 (456) | 302 (178) | - |

Body mass (kg) | 72.0 (13.7) | 75.9 (16.2) | 78.3 (14.9) |

Body height (m) | 1.74 (0.02) | 1.73 (0.04) | 1.78 (0.05) |

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**MDPI and ACS Style**

Belluscio, V.; Bergamini, E.; Tramontano, M.; Formisano, R.; Buzzi, M.G.; Vannozzi, G.
Does Curved Walking Sharpen the Assessment of Gait Disorders? An Instrumented Approach Based on Wearable Inertial Sensors. *Sensors* **2020**, *20*, 5244.
https://doi.org/10.3390/s20185244

**AMA Style**

Belluscio V, Bergamini E, Tramontano M, Formisano R, Buzzi MG, Vannozzi G.
Does Curved Walking Sharpen the Assessment of Gait Disorders? An Instrumented Approach Based on Wearable Inertial Sensors. *Sensors*. 2020; 20(18):5244.
https://doi.org/10.3390/s20185244

**Chicago/Turabian Style**

Belluscio, Valeria, Elena Bergamini, Marco Tramontano, Rita Formisano, Maria Gabriella Buzzi, and Giuseppe Vannozzi.
2020. "Does Curved Walking Sharpen the Assessment of Gait Disorders? An Instrumented Approach Based on Wearable Inertial Sensors" *Sensors* 20, no. 18: 5244.
https://doi.org/10.3390/s20185244