# Can Data-Driven Supervised Machine Learning Approaches Applied to Infrared Thermal Imaging Data Estimate Muscular Activity and Fatigue?

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Experimental Protocol

#### 2.3. Electromyography Recording and Preprocessing

_{i}is is the EMG power spectrum at the ith frequency bin, and N is the number of frequency bins. In this study, the power spectrum of the EMG signal was extracted through Welch’s method [36] and N was set at the next power of 2 from the length of EMG time-domain signal [37].

#### 2.4. Infrared Thermal Imaging Recording and Preprocessing

#### 2.5. Features Extraction and Machine Learning Procedures

- Mean value (MeanTemp): average value of the thermal signal T over a temporal window of 10 s after the end of the exercise defined as:$$MeanTemp=\frac{1}{N}{\displaystyle \sum}_{i=1}^{N}Ti$$
- Standard deviation (STD): standard deviation of the thermal signal T over a temporal window of 10 s after the end of the exercise defined as:$$\mathrm{STD}=\sqrt{\frac{1}{N-1}{\displaystyle \sum}_{i=1}^{N}{({T}_{i}-MeanTemp)}^{2}}$$
- Mean value of the power spectral density (MeanPSD) of the thermal signal T over a temporal window of 10 s after the end of the exercise. The PSD is defined as the Fourier transform of the autocorrelation matrix ${R}_{x}\left(\tau \right)$ of a random process $X\left(\tau \right)$:$${S}_{X}\left(f\right)=F\left\{{R}_{x}\left(\tau \right)\right\}={\displaystyle {\int}_{-\infty}^{+\infty}}{R}_{x}\left(\tau \right){e}^{-2j\pi f\tau}d\tau $$
- Kurtosis (Kurt): fourth standardized moment, and it is evaluated as follows:$$K=\frac{1}{N}\frac{\sqrt{{{\displaystyle \sum}}_{i=1}^{N}{({T}_{i}-MeanTemp)}^{4}}}{{\mathrm{STD}}^{4}}$$
- Skewness (Skew): third standardized moment, and it is evaluated as follows:$$S=\frac{1}{N}\frac{\sqrt{{{\displaystyle \sum}}_{i=1}^{N}{({T}_{i}-MeanTemp)}^{3}}}{{\mathrm{STD}}^{3}}$$
- 90th percentile (90th P): it is the temperature value below which the 90% of all temperature frequency distribution are comprised.
- Sample Entropy (SampEn): it is defined as the negative natural logarithm of the conditional probability that signals that the subseries of length m (pattern length) that match pointwise within a tolerance r (similarity factor) also match at the m + 1 point. SampEn of a time series {t
_{1},…,t_{N}} of length N is computed employing the following set of equations:$$SampEn\left(m,r,N\right)=-\mathrm{ln}\left[\frac{{U}^{m+1}\left(r\right)}{{U}^{m}\left(r\right)}\right]\phantom{\rule{0ex}{0ex}}{U}^{m}\left(r\right)={\left[N-m\tau \right]}^{-1}{\displaystyle \sum}_{i=1}^{N-m\tau}{C}_{i}^{m}\left(r\right)\phantom{\rule{0ex}{0ex}}{C}_{i}^{m}\left(r\right)=\frac{{B}_{i}}{N-\left(m+1\right)\tau}\phantom{\rule{0ex}{0ex}}{B}_{i}=numberofjwhered\left|{T}_{i},{T}_{j}\right|\le r\phantom{\rule{0ex}{0ex}}{T}_{i}=\left({t}_{i},{t}_{i+\tau},\dots ,{t}_{i+\left(m-1\right)\tau}\right)\phantom{\rule{0ex}{0ex}}{T}_{j}=\left({t}_{j},{t}_{j+\tau},\dots ,{t}_{j+\left(m-1\right)\tau}\right)\phantom{\rule{0ex}{0ex}}i\le j\le N-m\tau ,j\ne i$$

- Where U is the subseries vector considered and Cm(r) is the probability that any vector Um(j) is within r of Um(i).
- Spatial gradient (Grad): it is evaluated as follow:
- $\mathrm{Grad}=\nabla T=\frac{\partial T}{\partial x}\widehat{\u0131}+\frac{\partial T}{\partial y}\widehat{\u0237}$
- Delta (Δ): difference between the average of the signal in the first 2 s and in the last 2 s of a temporal window of 10 s after the end of the exercise.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic overview of the testing session. The figure is created with BioRender.com, EMG: electromyography; IRI: infrared thermal imaging; ML: machine learning.

**Figure 2.**(

**a**) A representative participant’s thermogram and ROI placement over the VM. Specifically, the blue, green, and red circles are the ROI1, ROI2, and ROI3, respectively. (

**b**) The time course of the average temperature of each ROI during the experiment, obtained through a video tracking algorithm.

**Figure 3.**F-tests scores associated to each thermal feature computed for each ROI evaluated for the ARV (

**a**) and MDF (

**b**) estimation.

**Figure 4.**Correlation plot (

**a**) and the Bland–Altman plot (

**b**) associated to the performance of the Gaussian model developed to estimate the ARV.

**Figure 5.**Correlation plot (

**a**) and the Bland–Altman plot (

**b**) associated to the performance of the Gaussian model developed to estimate the MDF.

**Table 1.**Correlation coefficients (r) computed between the ARV and MDF and the IRI features used as input to the ML algorithms.

ROI | IRI Feature | r (ARV) | r (MDF) |
---|---|---|---|

1 | MeanTemp | 0.607 (p = 0.001) | 0.067 (p = 0.749) |

STD | −0.213 (p = 0.306) | −0.160 (p = 0.444) | |

Δ | 0.202 (p = 0.331) | 0.240 (p = 0.248) | |

MeanPSD | 0.5966 (p = 0.002) | 0.106 (p = 0.615) | |

Kurt | −0.167 (p = 0.426) | −0.122 (p = 0.563) | |

Skew | −0.015 (p = 0.942) | 0.257 (p = 0.214) | |

90th P | 0.5856 (p = 0.002) | 0.049 (p = 0.818) | |

SampEn | −0.293 (p = 0.155) | −0.160 (p = 0.446) | |

Grad | 0.034 (p = 0.870) | −0.004 (p = 0.986) | |

2 | MeanTemp | 0.490 (p = 0.013) | 0.192 (p = 0.357) |

STD | −0.052 (p = 0.804) | −0.102 (p = 0.629) | |

Δ | 0.256 (p = 0.217) | 0.264 (p = 0.203) | |

MeanPSD | 0.505 (p = 0.010) | 0.195 (p = 0.350) | |

Kurt | −0.161 (p = 0.441) | −0.257 (p = 0.216) | |

Skew | 0.082 (p = 0.699) | 0.270 (p = 0.192) | |

90th P | 0.487 (p = 0.014) | 0.194 (p = 0.354) | |

SampEn | −0.270 (p = 0.196) | −0.088 (p = 0.675) | |

Grad | 0.248 (p = 0.231) | 0.211 (p = 0.312) | |

3 | MeanTemp | 0.541 (p = 0.005) | 0.196 (p = 0.349) |

STD | −0.117 (p = 0.579) | −0.151 (p = 0.473) | |

Δ | 0.040 (p = 0.849) | −0.064 (p = 0.761) | |

MeanPSD | 0.540 (p = 0.005) | 0.210 (p = 0.314) | |

Kurt | 0.068 (p = 0.746) | −0.159 (p = 0.449) | |

Skew | −0.166 (p = 0.427) | 0.232 (p = 0.264) | |

90th P | 0.518 (p = 0.008) | 0.186 (p = 0.375) | |

SampEn | −0.247 (p = 0.235) | −0.116 (p = 0.581) | |

Grad | 0.020 (p = 0.924) | 0.121 (p = 0.563) |

**Table 2.**Results of the regression obtained by the several ML approaches considered to estimate the ARV from the thermal metrics. Notably, the performance of the model was expressed as root-mean-square error (RMSE) computed on the normalized (z-score) values and the correlation coefficient (r) between the gold standard (EMG-based ARV) and the predicted metric (IRI-based ARV). The best model is highlighted with an asterisk.

Model | ROI | RMSE | r |
---|---|---|---|

LR | 1 | 0.869 | 0.453 (p = 0.023) |

SVR (Linear) | 1 | 0.933 | 0.421 (p = 0.036) |

SVR (Gaussian) | 1 | 0.959 | 0.711 (p = 6.75·10^{−5}) |

Ensemble | 1 | 0.824 | 0.545 (p = 0.005) |

Gaussian | 1 | 0.902 | 0.414 (p = 0.040) |

LR | 2 | 0.926 | 0.327 (p = 0.111) |

SVR (Linear) | 2 | 1.004 | 0.412 (p = 0.041) |

SVR (Gaussian) | 2 | 0.969 | 0.555 (p = 0.004) |

Ensemble | 2 | 0.821 | 0.550 (p = 0.004) |

Gaussian | 2 | 0.877 | 0.451 (p = 0.024) |

LR | 3 | 1.051 | 0.377 (p = 0.063) |

SVR (Linear) | 3 | 0.980 | 0.356 (p = 0.081) |

SVR (Gaussian) | 3 | 0.977 | 0.457 (p = 0.022) |

Ensemble | 3 | 0.833 | 0.529 (p = 0.007) |

Gaussian | 3 | 0.456 * | 0.886 (p = 3.91·10^{−9}) * |

**Table 3.**The regression results obtained from the various ML approaches considered for estimating the MDF from thermal metrics. Notably, the model’s performance was expressed as the root mean square error (RMSE) calculated on the normalized (z-score) values and the correlation coefficient (r) between the gold standard (EMG-based MDF) and the predicted metric (IRI-based MDF). The best model is highlighted with an asterisk.

Model | ROI | RMSE | r |
---|---|---|---|

LR | 1 | 1.094 | 0.368 (p = 0.063) |

SVR (Linear) | 1 | 1.114 | 0.271 (p = 0.239) |

SVR (Gaussian) | 1 | 0.981 | 0.447 (p = 0.025) |

Ensemble | 1 | 1.041 | 0.382 (p = 0.059) |

Gaussian | 1 | 0.854 | 0.509 (p = 0.009) |

LR | 2 | 1.077 | 0.319 (p = 0.121) |

SVR (Linear) | 2 | 0.994 | 0.528 (p = 0.007) |

SVR (Gaussian) | 2 | 1.016 | 0.498 (p = 0.011) |

Ensemble | 2 | 0.993 | 0.420 (p = 0.037) |

Gaussian | 2 | 1.017 | 0.464 (p = 0.020) |

LR | 3 | 1.085 | 0.364 (p = 0.074) |

SVR (Linear) | 3 | 0.775 | 0.623 (p = 8.85·10^{−4}) |

SVR (Gaussian) | 3 | 1.026 | 0.335 (p = 0.102) |

Ensemble | 3 | 1.039 | 0.442 (p = 0.027) |

Gaussian | 3 | 0.751 * | 0.661 (p = 3.21·10^{−4}) * |

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**MDPI and ACS Style**

Perpetuini, D.; Formenti, D.; Cardone, D.; Trecroci, A.; Rossi, A.; Di Credico, A.; Merati, G.; Alberti, G.; Di Baldassarre, A.; Merla, A.
Can Data-Driven Supervised Machine Learning Approaches Applied to Infrared Thermal Imaging Data Estimate Muscular Activity and Fatigue? *Sensors* **2023**, *23*, 832.
https://doi.org/10.3390/s23020832

**AMA Style**

Perpetuini D, Formenti D, Cardone D, Trecroci A, Rossi A, Di Credico A, Merati G, Alberti G, Di Baldassarre A, Merla A.
Can Data-Driven Supervised Machine Learning Approaches Applied to Infrared Thermal Imaging Data Estimate Muscular Activity and Fatigue? *Sensors*. 2023; 23(2):832.
https://doi.org/10.3390/s23020832

**Chicago/Turabian Style**

Perpetuini, David, Damiano Formenti, Daniela Cardone, Athos Trecroci, Alessio Rossi, Andrea Di Credico, Giampiero Merati, Giampietro Alberti, Angela Di Baldassarre, and Arcangelo Merla.
2023. "Can Data-Driven Supervised Machine Learning Approaches Applied to Infrared Thermal Imaging Data Estimate Muscular Activity and Fatigue?" *Sensors* 23, no. 2: 832.
https://doi.org/10.3390/s23020832