# Assessment of Biomechanical Response to Fatigue through Wearable Sensors in Semi-Professional Football Referees

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Subjects

#### 2.2. Experimental Procedures

- A 5 min warm-up phase of jogging on treadmill at fixed speed (i.e., 10 km/h);
- Pre-fatigue acquisition, in which MIMUs were placed on the participant’s body using elastic bands, and the athlete performed one series of 5 CMJs separated by a 10 s of rest time (at the end of this acquisition sensors were removed to facilitate the following phase);
- Fatigue phase induced in athletes by using the YYIR1 (which consisted of 2 × 20 m shuttle runs at increasing speeds, with a 10 s period of active recovery, allowing us to quantify the individual’s capacity to perform repeated intense exercise and to examine changes in performance [20]);
- Post-fatigue acquisitions in which the same CMJ test conducted in the pre-fatigue acquisition (i.e., 5 CMJs separated by a 10 s of rest time) was repeated after 5 min from the end of fatigue exercises.

#### 2.3. Segmentation of the Jump

- The start of the eccentric phase was identified by analysing the acceleration curve and automatically finding when it goes below a specific threshold (i.e., mean +3 standard deviations of the first 100 samples);
- The end of the eccentric phase corresponds to the zero crossing of the velocity (second red line in Figure 2);
- The end of the concentric jump coincides with the peak in the acceleration curve of the foot sensor. The peak of the curve was automatically detected by finding the maximum value of the acceleration.

#### 2.4. Measurements

- Displacement parameters: the mean displacement of the centre of mass during the eccentric phase (i.e., jump depth) is analysed in this work. In our opinion, monitoring the mean position of the barycentre could be useful to understand how much the athlete is loading the jump due to fatigue.
- Power and energy parameters: allow us to quantify the lower-limb explosive ability, resulting in extremely important indicators for fatigue detection. An in-depth analysis of the scientific literature allowed us to find the following parameters [5,17,24]: minimum and maximum relative power exerted, mean relative power over time, mean power velocity (MPV), mean and minimum energy.
- Time parameters [17,24]: allow us to pinpoint specific events in time during the execution of the exercise (i.e., when the maximum power is exerted or how long the athlete stays in contact with the ground). Therefore, negative power peak time (NPPT), positive power peak time (PPPT) and the total duration of the entire eccentric phase (${t}_{ecc}$) were reported in this study.

## 3. Results

#### 3.1. Fatigue Group

#### 3.2. PAP Group

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Segmentation of the jump from acceleration and velocity of the body centre of mass. ${t}_{ecc}$ and ${t}_{conc}$ are the eccentric and concentric phases duration, respectively. The red dotted lines limit the eccentric phase of the jump, while the black one delimits the concentric phase. (

**b**) Acceleration traces of the right foot, which is characterized by a peak in correspondence to the take off. The two negative peaks in the acceleration trace correspond to an extension movement of the foot immediately after the take off and before the landing, respectively. In particular, the first movement is the consequence of the boost phase that precedes the take-off, while the second one is an anticipatory movement carried out by the athlete for better landing on the ground.

**Figure 3.**Difference between relative eccentric power (in blue) and modified relative eccentric power (in orange), from which the aforementioned parameters were estimated.

**Figure 4.**Power traces of a fatigued group (

**a**) and Post-Activation Potentiation (PAP) group (

**b**) participants.

**Figure 5.**Normalized variations for all the parameters of the fatigued group. MPV = mean power velocity, VNPP = velocity at negative power peak, VPPP = velocity at positive power peak, AFV = area under the force-velocity curve, NPPT = negative power peak time, PPPT = positive power peak time, TSI = temporal symmetry index.

Physical Quantities | MIMU |
---|---|

Measured quantity | ${a}_{INERTIAL}={a}_{MIMU}-g$ |

$\mathrm{Velocity}\text{}(v\left(t\right))$ | $v\left(t\right)={\displaystyle \int}{a}_{INERTIAL}*dt$ |

$\mathrm{Relative}\text{}\mathrm{power}\text{}(\frac{P\left(t\right)}{m})$ $m=mass$ | $\frac{P\left(t\right)}{m}={a}_{INERTIAL}*v\left(t\right)$ |

$\mathrm{Mean}\text{}\mathrm{relative}\text{}\mathrm{power}\text{}\mathrm{over}\text{}\mathrm{time}\text{}({\left(\frac{P\left(t\right)}{m}\right)}_{mean})$ $m=mass$ | ${(\frac{P\left(t\right)}{m})}_{mean}=\frac{\frac{P\left(t\right)}{m}}{{t}_{ecc}}$ |

$\mathrm{Mean}\text{}\mathrm{power}\text{}\mathrm{velocity}\text{}{\left({v}_{p}\right)}_{mean}$ | ${\left({v}_{p}\right)}_{mean}=mean(\frac{d}{dt}\frac{P\left(t\right)}{m})$ |

$\mathrm{Relative}\text{}\mathrm{energy}\text{}(\frac{U\left(t\right)}{m})$ $m=mass$ | $\frac{U\left(t\right)}{m}={\displaystyle \int}\frac{P\left(t\right)}{m}*dt$ |

$\mathrm{Distance}\text{}(x\left(t\right))$ | $x\left(t\right)={\displaystyle \int}{\displaystyle \int}{a}_{INERTIAL}*d{t}^{2}$ |

$\mathrm{Angular}\text{}\mathrm{velocities}\text{}({w}_{FE})$ | ${w}_{FE}=\frac{d}{dt}{\theta}_{FE}$ |

TSI | $TSI=\left|\frac{{t}_{conc}-{t}_{ecc}}{{t}_{conc}+{t}_{ecc}}\right|$ |

Eccentric % | ${\%}_{ecc}=\left|\frac{{t}_{ecc}}{{t}_{conc}+{t}_{ecc}}\right|$ |

Parameters | PRE | POST | Wilcoxon Signed Rank Test Significance | Normalized Variations (%) | FAI Spearman Coefficient | Cliff’s Delta ES |
---|---|---|---|---|---|---|

$\mathit{M}\mathit{e}\mathit{d}\mathit{i}\mathit{a}\mathit{n}\left(\mathit{i}\mathit{q}\mathit{r}\right)$ | $\mathit{M}\mathit{e}\mathit{d}\mathit{i}\mathit{a}\mathit{n}\left(\mathit{i}\mathit{q}\mathit{r}\right)$ | $\mathit{M}\mathit{e}\mathit{d}\mathit{i}\mathit{a}\mathit{n}\left(\mathit{i}\mathit{q}\mathit{r}\right)$ | ||||

Mean distance $\left(\mathrm{m}\right)$ | −1.85 (0.54) | −1.76 (0.46) | 0.04 * | −4.27 (4.80) | 0.12 | 0.19 (T↓) |

$\mathrm{Minimum}\text{}\mathrm{power}\text{}(\mathrm{W}\xb7\mathrm{k}{\mathrm{g}}^{-1})$ | −4.92 (5.42) | −3.33 (3.30) | <0.01 ** | −34.4 (19.76) | 0.98 ** | 0.38 (M↓) |

$\mathrm{Maximum}\text{}\mathrm{power}\text{}(\mathrm{W}\xb7\mathrm{k}{\mathrm{g}}^{-1})$ | 5.42 (5.85) | 3.84 (4.56) | <0.01 ** | −26.4 (28.8) | 0.93 ** | −0.34 (M↓) |

$\mathrm{Mean}\text{}\mathrm{power}\text{}\mathrm{over}\text{}\mathrm{time}\text{}(\mathrm{W}\xb7{\mathrm{s}}^{-1})$ | 0.26 (0.62) | 0.15 (0.34) | <0.01 ** | −29.8 (38.2) | 0.90 ** | −0.38 (M↓) |

$\mathrm{MPV}\text{}(\mathrm{W}\text{}\xb7{\mathrm{s}}^{-1})$ | −28.3 (39.0) | −15.5 (21.4) | <0.01 ** | −44.3 (28.0) | 0.86 ** | 0.47 (M↓) |

Mean energy ($\mathrm{J}\xb7\mathrm{k}{\mathrm{g}}^{-1}$) | −3.57 (0.62) | −2.93 (0.74) | <0.01 ** | −21.9 (18.3) | 0.98 ** | 0.37 (M↓) |

Minimum energy ($\mathrm{J}\xb7\mathrm{k}{\mathrm{g}}^{-1}$) | −7.88 (5.12) | −5.97 (5.00) | <0.01 ** | −22.1 (19.1) | 0.95 ** | 0.34 (M↓) |

$\mathrm{Minimum}\text{}\mathrm{velocity}\text{}(\mathrm{m}\xb7{\mathrm{s}}^{-1})$ | −1.24 (0.18) | −1.08 (0.44) | <0.01 ** | −12.7 (11.3) | 0.95 ** | 0.34 (M↓) |

$\mathrm{Mean}\text{}\mathrm{velocity}\text{}(\mathrm{m}\xb7{\mathrm{s}}^{-1})$ | −0.70 (0.16) | −0.64 (0.22) | <0.01 ** | −11.1 (9.84) | 0.98 ** | 0.44 (M↓) |

$\mathrm{VNPP}\text{}(\mathrm{m}\xb7{\mathrm{s}}^{-1})$ | −0.91 (0.38) | −0.82 (0.36) | <0.01 ** | −8.37 (14.7) | 0.74 * | 0.28 (S↓) |

$\mathrm{VPPP}\text{}(\mathrm{m}\xb7{\mathrm{s}}^{-1})$ | −0.82 (0.38) | −0.64 (0.34) | <0.01 ** | −17.2 (12.9) | 0.95 ** | 0.31 (M↓) |

$\mathrm{AFV}\text{}(\mathrm{N}\xb7\mathrm{m}\xb7{\mathrm{s}}^{-1}\xb7\mathrm{k}{\mathrm{g}}^{-1})$ | −15.00 (15.9) | −10.10 (11.4) | <0.01 ** | −26.0 (27.2) | 0.90 ** | 0.34 (M↓) |

NPPT ($\mathrm{m}\mathrm{s}$) | 20.25 (5.44) | 23.25 (3.38) | 0.04 * | 14.2 (19.98) | −0.19 | 0.5 (L↑) |

PPPT ($\mathrm{m}\mathrm{s}$) | 47.75 (15.8) | 57.75 (15.9) | <0.01 ** | 9.53 (14.4) | −0.88 ** | 0.25 (S↑) |

${t}_{ecc}$ ($\mathrm{m}\mathrm{s}$) | 55.00 (15.8) | 60.00 (16.1) | <0.01 ** | 7.32 (17.8) | −0.98 ** | 0.28 (S↑) |

Knee mean angular velocity (deg/s) | 113.9 (31.8) | 107.8 (29.2) | 0.02 * | −7.23 (9.20) | 0.79 * | −0.39 (M↓) |

Hip mean angular velocity (deg/s) | 114.7 (56.2) | 101.9 (28.2) | 0.02 * | −16.2 (13.2) | 0.21 | −0.55 (L↓) |

TSI | 0.419 (0.10) | 0.488 (0.18) | 0.02 * | 6.04 (18.5) | −0.57 | 0.43 (M↑) |

Eccentric % | 0.711 (0.04) | 0.744 (0.08) | 0.02 * | 1.51 (5.04) | −0.43 | 0.43 (M↑) |

Parameters | Weight | Muscular Mass |
---|---|---|

Maximum power | - | 0.83 * |

Minimum energy | 0.79 * | 0.88 ** |

Minimum velocity | 0.79 * | 0.88 ** |

VPPP | - | 0.82 * |

VNPP | 0.86 * | 0.83 ** |

Parameters | PRE | POST | Wilcoxon Signed Rank Test Significance | Normalized Variations (%) | Cliff’s Delta ES |
---|---|---|---|---|---|

$\mathrm{Mean}\text{}\mathrm{distance}\text{}\left(\mathrm{m}\right)$ | −1.27 (0.30) | −1.31 (0.32) | 0.08 | 7.98 (13.8) | −0.19 (T↑) |

Minimum power (W) | −2.77 (1.38) | −4.34 (1.96) | <0.01 ** | 66.4 (52.6) | −0.78 (L↑)) |

Maximum power (W) | 3.47 (1.26) | 4.66 (1.74) | <0.01 ** | 36.3 (44.2) | 0.72 (L↑) |

$\mathrm{Mean}\text{}\mathrm{power}\text{}\mathrm{over}\text{}\mathrm{time}\text{}(\mathrm{W}\xb7\mathrm{d}{\mathrm{t}}^{-1})$ | 0.16 (0.08) | 0.34 (0.20) | <0.01 ** | 94.8 (57.0) | 0.72 (L↑) |

$\mathrm{MPV}\text{}(\mathrm{W}\xb7\mathrm{d}{\mathrm{t}}^{-1})$ | −14.37 (6.80) | −28.83 (14.0) | <0.01 ** | 91.6 (56.6) | −0.81 (L↑) |

Mean energy ($\mathrm{J}$) | −2.02 (0.66) | −2.49 (0.378) | <0.01 ** | 39.4 (42.6) | −0.62 (L↑) |

Minimum energy ($\mathrm{J}$) | −4.36 (1.62) | −5.43 (1.76) | <0.01 ** | 37.8 (50.4) | −0.59 (L↑) |

$\mathrm{Minimum}\text{}\mathrm{velocity}\text{}(\mathrm{m}\xb7{\mathrm{s}}^{-1})$ | −0.92 (0.18) | −1.03 (0.16) | <0.01 ** | 16.9 (20.8) | −0.59 (L↑) |

$\mathrm{Mean}\text{}\mathrm{velocity}\text{}(\mathrm{m}\xb7{\mathrm{s}}^{-1})$ | −0.54 (0.08) | −0.58 (0.10) | <0.01 ** | 16.2 (14.9) | −0.69 (L↑) |

$\mathrm{VNPP}\text{}(\mathrm{m}\xb7{\mathrm{s}}^{-1})$ | −0.71 (0.16) | −0.78 (0.12) | <0.01 ** | 13.9 (28.8) | −0.58 (L↑) |

$\mathrm{VPPP}\text{}(\mathrm{m}\xb7{\mathrm{s}}^{-1})$ | −0.60 (0.14) | −0.67 (0.16) | <0.01 ** | 18.5 (42.0) | −0.63 (L↑) |

$\mathrm{AFV}\text{}(\mathrm{N}\xb7\mathrm{m}\xb7{\mathrm{s}}^{-1})$ | −9.55 (3.06) | −13.13 (4.64) | <0.01 ** | 43.6 (52.2) | −0.84 (L↑) |

NPPT ($\mathrm{m}\mathrm{s}$) | 20.38 (3.76) | 17.38 (4.50) | 0.02 * | −17.0 (11.1) | −0.56 (L↓) |

PPPT ($\mathrm{m}\mathrm{s}$) | 44.50 (6.76) | 38.88 (11.0) | <0.01 ** | −12.9 (9.96) | −0.40 (M↓) |

${t}_{ecc}$ ($\mathrm{m}\mathrm{s}$) | 50.88 (0.08) | 45.25 (10.0) | <0.01 ** | −9.92 (5.66) | −0.34 (M↓) |

Knee mean angular velocity (°/sec) | 108.5 (20.5) | 124.6 (29.6) | <0.01 ** | 27.1 (33.4) | 0.81 (L↑) |

Hip mean angular velocity (°/sec) | 108.7 (22.8) | 131.8 (38.4) | <0.01 ** | 27.0 (27.2) | 0.68 (L↑) |

TSI | 0.486 (0.08) | 0.407 (0.12) | <0.01 ** | −14.5 (15.6) | −0.50 (L↓) |

Eccentric % | 0.743 (0.04) | 0.691 (0.80) | <0.01 ** | −5.48 (5.54) | −0.56 (L↑) |

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**MDPI and ACS Style**

Truppa, L.; Guaitolini, M.; Garofalo, P.; Castagna, C.; Mannini, A.
Assessment of Biomechanical Response to Fatigue through Wearable Sensors in Semi-Professional Football Referees. *Sensors* **2021**, *21*, 66.
https://doi.org/10.3390/s21010066

**AMA Style**

Truppa L, Guaitolini M, Garofalo P, Castagna C, Mannini A.
Assessment of Biomechanical Response to Fatigue through Wearable Sensors in Semi-Professional Football Referees. *Sensors*. 2021; 21(1):66.
https://doi.org/10.3390/s21010066

**Chicago/Turabian Style**

Truppa, Luigi, Michelangelo Guaitolini, Pietro Garofalo, Carlo Castagna, and Andrea Mannini.
2021. "Assessment of Biomechanical Response to Fatigue through Wearable Sensors in Semi-Professional Football Referees" *Sensors* 21, no. 1: 66.
https://doi.org/10.3390/s21010066