# Estimation of Respiratory Rate from Functional Near-Infrared Spectroscopy (fNIRS): A New Perspective on Respiratory Interference

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Pre-Processing

#### 2.2. RR Estimation

#### 2.2.1. Trough Detection

Algorithm 1 Localization of ${O}_{2}Hb$ signal troughs | |

Input: ${O}_{2}Hb$ signal $x\left(n\right)$, constants A, B | |

Output: Troughs, K | |

Initialisation $Th1\leftarrow $ 0, $Th2\leftarrow $ 0, $J\leftarrow $ [ ], $K\leftarrow $ [ ] | |

1: | $x\left(n\right)\leftarrow $ Normalize ($x\left(n\right)$) |

2: | $Th1\leftarrow $ A × Mean ($x\left(n\right)$) |

3: | for $i=2$ to $\mathrm{length}\left(x\right(n\left)\right)-1$ do |

4: | if $x\left(i\right)<x(i-1)\phantom{\rule{3.33333pt}{0ex}}\&\&\phantom{\rule{3.33333pt}{0ex}}x\left(i\right)<x(i+1)\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\&\&\phantom{\rule{3.33333pt}{0ex}}x\left(i\right)<Th1$ then |

5: | $J\leftarrow \left[J\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}i\right]$ |

6: | end if |

7: | end for |

8: | $z\left(n\right)\leftarrow $$x\left(J\right)$ |

9: | $Th2\leftarrow $ Mean ($z\left(n\right)$) + B × std ($z\left(n\right)$) |

10: | for $i=1$ to $\mathrm{length}\left(z\right(n\left)\right)$ do |

11: | if $z\left(i\right)>Th2$ then |

12: | $K=\left[K\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}i\right]$ |

13: | end if |

14: | end for |

15: | returnK |

#### 2.2.2. Forming the Baseline Wander Signal

#### 2.2.3. FFT for RR Estimation

Algorithm 2 Estimation of the RR from the ${O}_{2}Hb$ signal’s baseline wander | |

Input:${O}_{2}HB$ signal $x\left(n\right)$, Troughs of ${O}_{2}HB$ signal K, and the length of moving average
| |

filter L | |

Output:$RR$ | |

1: | $m\left(n\right)\leftarrow $ Spline (K, $x\left(K\right)$, 1 to length($x\left(n\right)$)) |

2: | $MA\leftarrow $$\frac{1}{L}\times $ ones(L,1) |

3: | $S\left(n\right)\leftarrow $ filtfilt($MA$,1,$m\left(n\right)$) |

4: | $G\left(n\right)\leftarrow $$m\left(n\right)-S\left(n\right)$ |

5: | $[P,F]\leftarrow $ FFT ($G\left(n\right)$) |

6: | $r\leftarrow $ find($P\left(F\right)\leftarrow $ Max($P\left(F\right)$)) |

7: | $RR\leftarrow $ r × 60 |

8: | return
$RR$ |

#### 2.3. Evaluation Criteria

## 3. Data

#### 3.1. Data Recording Protocol

#### 3.2. fNIRS Systems for Data Collection

#### 3.2.1. Dataset I

#### 3.2.2. Dataset II

## 4. Experimental Results

#### 4.1. Optimization of the Proposed Method’s Parameters

#### 4.1.1. Trough Detection

#### 4.1.2. The Length of MA Filtering

#### 4.1.3. Results of RR Estimation from Dataset I

#### 4.2. Results of RR Estimation from Dataset II

## 5. Discussion

#### 5.1. Significance and Robustness of the Proposed Method

#### 5.2. Comparison with State-of-the-Art Methods

#### 5.3. Directions for Future Work

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Paulmurugan, K.; Vijayaragavan, V.; Ghosh, S.; Padmanabhan, P.; Gulyás, B. Brain–Computer Interfacing Using Functional Near-Infrared Spectroscopy (fNIRS). Biosensors
**2021**, 11, 389. [Google Scholar] [CrossRef] [PubMed] - Ferrari, M.; Quaresima, V. A Brief Review on the History of Human Functional Near-Infrared Spectroscopy (fNIRS) Development and Fields of Application. NeuroImage
**2012**, 63, 921–935. [Google Scholar] [CrossRef] [PubMed] - Almajidy, R.K.; Mankodiya, K.; Abtahi, M.; Hofmann, U.G. A Newcomer’s Guide to Functional Near Infrared Spectroscopy Experiments. IEEE Rev. Biomed. Eng.
**2020**, 13, 292–308. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Scholkmann, F.; Kleiser, S.; Metz, A.J.; Zimmermann, R.; Pavia, J.M.; Wolf, U.; Wolf, M. A Review on Continuous Wave Functional Near-Infrared Spectroscopy and Imaging Instrumentation and Methodology. NeuroImage
**2014**, 85, 6–27. [Google Scholar] [CrossRef] [PubMed] - Chao, J.; Zheng, S.; Wu, H.; Wang, D.; Zhang, X.; Peng, H.; Hu, B. fNIRS Evidence for Distinguishing Patients With Major Depression and Healthy Controls. IEEE Trans. Neural Syst. Rehabil. Eng.
**2021**, 29, 2211–2221. [Google Scholar] [CrossRef] - Borgheai, S.B.; McLinden, J.; Zisk, A.H.; Hosni, S.I.; Deligani, R.J.; Abtahi, M.; Mankodiya, K.; Shahriari, Y. Enhancing Communication for People in Late-Stage ALS Using an fNIRS-Based BCI System. IEEE Trans. Neural Syst. Rehabil. Eng.
**2020**, 28, 1198–1207. [Google Scholar] [CrossRef] - Wang, Z.; Zhang, J.; Zhang, X.; Chen, P.; Wang, B. Transformer Model for Functional Near-Infrared Spectroscopy Classification. IEEE J. Biomed. Health Inform.
**2022**, 26, 2559–2569. [Google Scholar] [CrossRef] - Sommer, N.M.; Kakillioglu, B.; Grant, T.; Velipasalar, S.; Hirshfield, L. Classification of fNIRS Finger Tapping Data with Multi-Labeling and Deep Learning. IEEE Sens. J.
**2021**, 21, 24558–24569. [Google Scholar] [CrossRef] - Joshi, S.; Herrera, R.R.; Springett, D.N.; Weedon, B.D.; Ramirez, D.Z.M.; Holloway, C.; Dawes, H.; Ayaz, H. Neuroergonomic Assessment of Wheelchair Control Using Mobile fNIRS. IEEE Trans. Neural Syst. Rehabil. Eng.
**2020**, 28, 1488–1496. [Google Scholar] [CrossRef] - Pellegrini-Laplagne, M.; Dupuy, O.; Sosner, P.; Bosquet, L. Effect of Simultaneous Exercise and Cognitive Training on Executive Functions, Baroreflex Sensitivity, and Pre-frontal Cortex Oxygenation in Healthy Older Adults: A Pilot Study. GeroScience
**2022**, 1, 1–22. [Google Scholar] [CrossRef] - Germain, C.; Perrot, A.; Tomasino, C.; Bonnal, J.; Ozsancak, C.; Auzou, P.; Prieur, F. Effect of the Level of Physical Activity on Prefrontal Cortex Hemodynamics in Older Adults During Single- and Dual-Task Walking. J. Aging Phys. Act.
**2022**, 1, 1–9. [Google Scholar] [CrossRef] [PubMed] - Goenarjo, R.; Dupuy, O.; Fraser, S.; Berryman, N.; Perrochon, A.; Bosquet, L. Cardiorespiratory Fitness and Prefrontal Cortex Oxygenation During Stroop Task in Older Males. Physiol. Behav.
**2021**, 242, 113621. [Google Scholar] [CrossRef] [PubMed] - Koren, Y.; Mairon, R.; Sofer, I.; Parmet, Y.; Ben-Shahar, O.; Bar-Haim, S. Vision, Cognition, and Walking Stability in Young Adults. Sci. Rep.
**2022**, 12, 513. [Google Scholar] [CrossRef] [PubMed] - Bizzego, A.; Neoh, M.; Gabrieli, G.; Esposito, G. A Machine Learning Perspective on fNIRS Signal Quality Control Approaches. IEEE Trans. Neural Syst. Rehabil. Eng.
**2022**, 30, 2292–2300. [Google Scholar] [CrossRef] [PubMed] - Patashov, D.; Menahem, Y.; Gurevitch, G.; Kameda, Y.; Goldstein, D.; Balberg, M. fNIRS: Non-stationary Preprocessing Methods. Biomed. Signal Process. Control
**2023**, 79, 104110. [Google Scholar] [CrossRef] - Tachtsidis, I.; Scholkmann, F. False Positives and False Negatives in Functional Near-Infrared Spectroscopy: Issues, Challenges, and the Way Forward. Neurophotonics
**2016**, 3, 031405. [Google Scholar] [CrossRef] [Green Version] - Zhou, L.; Chen, C.; Liu, Z.; Hu, Y.; Chen, M.; Li, Y.; Hu, Y.; Wang, G.; Zhao, J. A Coarse/Fine Dual-Stage Motion Artifacts Removal Algorithm for Wearable NIRS Systems. IEEE Sens. J.
**2021**, 21, 13574–13583. [Google Scholar] [CrossRef] - Ivo, I.A.; Horschig, J.M.; Gerakaki, S.; Wanrooij, M.M.V.; Colier, W.N.J.M. Cerebral Oxygenation Responses to Head Movement Measured with Near-Infrared Spectroscopy. In Biophotonics in Exercise Science, Sports Medicine, Health Monitoring Technologies, and Wearables II; SPIE: Bellingham, WA, USA, 2021; Volume 11638, pp. 40–52. [Google Scholar]
- Zhang, F.; Cheong, D.; Khan, A.F.; Chen, Y.; Ding, L.; Yuan, H. Correcting Physiological Noise in Whole-Head Functional Near-Infrared Spectroscopy. J. Neurosci. Methods
**2021**, 360, 109262. [Google Scholar] [CrossRef] - Svinkunaite, L.; Horschig, J.; Floor-Westerdijk, M. Employing Cardiac and Respiratory Features Extracted From fNIRS Signals for Mental Workload Classification. In Biophotonics in Exercise Science, Sports Medicine, Health Monitoring Technologies, and Wearables II; SPIE: Bellingham, WA, USA, 2021; Volume 11638, pp. 53–61. [Google Scholar]
- Hakimi, N.; Jodeiri, A.; Mirbagheri, M.; Setarehdan, S.K. Proposing a Convolutional Neural Network for Stress Assessment by Means of Derived Heart Rate from Functional Near Infrared Spectroscopy. Comput. Biol. Med.
**2020**, 121, 103810. [Google Scholar] [CrossRef] - Izzetoglu, M.; Holtzer, R. Effects of Processing Methods on fNIRS Signals Assessed During Active Walking Tasks in Older Adults. IEEE Trans. Neural Syst. Rehabil. Eng.
**2020**, 28, 699–709. [Google Scholar] [CrossRef] - Bellissimo, G.; Leslie, E.; Maestas, V.; Zuhl, M. The Effects of Fast and Slow Yoga Breathing on Cerebral and Central Hemodynamics. Int. J. Yoga
**2020**, 13, 207–212. [Google Scholar] [CrossRef] [PubMed] - Bak, S.; Shin, J.; Jeong, J. Subdividing Stress Groups into Eustress and Distress Groups Using Laterality Index Calculated from Brain Hemodynamic Response. Biosensors
**2022**, 12, 33. [Google Scholar] [CrossRef] [PubMed] - Charlton, P.H.; Birrenkott, D.A.; Bonnici, T.; Pimentel, M.A.; Johnson, A.E.; Alastruey, J.; Tarassenko, L.; Watkinson, P.J.; Beale, R.; Clifton, D.A. Breathing Rate Estimation From the Electrocardiogram and Photoplethysmogram: A Review. IEEE Rev. Biomed. Eng.
**2018**, 11, 2–20. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Reddy, P.; Izzetoglu, M.; Shewokis, P.A.; Sangobowale, M.; Diaz-Arrastia, R.; Izzetoglu, K. Evaluation of fNIRS Signal Components Elicited by Cognitive and Hypercapnic Stimuli. Sci. Rep.
**2021**, 11, 23457. [Google Scholar] [CrossRef] - Pollonini, L.; Bortfeld, H.; Oghalai, J. PHOEBE: A Method for Real Time Mapping of Optodes-Scalp Coupling in Functional Near-Infrared Spectroscopy. Biomed. Opt. Express
**2016**, 7, 5104–5119. [Google Scholar] [CrossRef] [Green Version] - Sappia, M.S.; Hakimi, N.; Colier, W.N.J.M.; Horschig, J.M. Signal Quality Index: An Algorithm for Quantitative Assessment of Functional Near Infrared Spectroscopy Signal Quality. Biomed. Opt. Express
**2020**, 11, 6732–6754. [Google Scholar] [CrossRef] - Delpy, D.T.; Cope, M.; Zee, P.V.D.; Arridge, S.; Wray, S.; Wyatt, J. Estimation of Optical Pathlength Through Tissue from Direct Time of Flight Measurement. Phys. Med. Biol.
**1988**, 33, 1433. [Google Scholar] [CrossRef] [Green Version] - Lázaro, J.; Gil, E.; Bailón, R.; Laguna, P. Deriving Respiration From the Pulse Photoplethysmographic Signal. In 2011 Computing in Cardiology; IEEE: Piscataway, NJ, USA, 2011; pp. 713–716. [Google Scholar]
- Estañol, B.; Sentíes-Madrid, H.; Elías, Y.; Coyac, P.; Martínez-Memije, R.; Infante, Ó.; Tellez-Zenteno, J.F.; García-Ramos, G. Respiratory and Non-respiratory Oscillations of the Skin Blood Flow: A Window to the Function of the Sympathetic Fibers to the Skin Blood Vessels. Arch. Cardiol. México
**2008**, 78, 187–194. [Google Scholar] - Madhav, K.V.; Ram, M.R.; Krishna, E.H.; Komalla, N.R.; Reddy, K.A. Robust Extraction of Respiratory Activity From PPG Signals Using Modified MSPCA. IEEE Trans. Instrum. Meas.
**2013**, 62, 1094–1106. [Google Scholar] [CrossRef] - Hernando, A.; Pelaez, M.D.; Lozano, M.T.; Aiger, M.; Gil, E.; Lázaro, J. Finger and Forehead PPG Signal Comparison for Respiratory Rate Estimation based on Pulse Amplitude Variability. In Proceedings of the 2017 25th European Signal Processing Conference (EUSIPCO), Kos, Greece, 28 August–2 September 2017; pp. 2076–2080. [Google Scholar]
- Hernando, A.; Peláez-Coca, M.D.; Lozano, M.T.; Lázaro, J.; Gil, E. Finger and forehead PPG signal comparison for respiratory rate estimation. Physiol. Meas.
**2019**, 40, 095007. [Google Scholar] [CrossRef] [Green Version] - Tipton, M.J.; Harper, A.; Paton, J.F.R.; Costello, J.T. The Human Ventilatory Response to Stress: Rate or Depth? J. Physiol.
**2017**, 17, 5729–5752. [Google Scholar] [CrossRef] [PubMed] - Grassmann, M.; Vlemincx, E.; Leupoldt, A.; Mittelstädt, J.M.; Bergh, O. Respiratory Changes in Response to Cognitive Load: A Systematic Review. Neural Plast.
**2016**, 2016, 8146809. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Iqbal, T.; Elahi, A.; Ganly, S.; Wijns, W.; Shahzad, A. Photoplethysmography-Based Respiratory Rate Estimation Algorithm for Health Monitoring Applications. J. Med. Biol. Eng.
**2022**, 42, 242–252. [Google Scholar] [CrossRef] [PubMed] - Tong, Y.; Lindsey, K.P.; Frederick, B. Partitioning of Physiological Noise Signals in the Brain with Concurrent Near-Infrared Spectroscopy and fMRI. J. Cereb. Blood Flow Metab.
**2011**, 31, 2352–2362. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lühmann, A.; Li, X.; Müller, K.R.; Boas, D.A.; Yücel, M.A. Improved physiological noise regression in fNIRS: A multimodal extension of the General Linear Model using temporally embedded Canonical Correlation Analysis. NeuroImage
**2020**, 208, 116472. [Google Scholar] [CrossRef] [PubMed] - Charlton, P.H.; Bonnici, T.; Tarassenko, L.; Alastruey, J.; Clifton, D.A.; Beale, R.; Watkinson, P.J. Extraction of respiratory signals from the electrocardiogram and photoplethysmogram: Technical and physiological determinants. Physiol. Meas.
**2017**, 38, 669–690. [Google Scholar] [CrossRef]

**Figure 1.**The block diagram of the proposed method. It should be noted that for the sake of clarity, fNIRS signals are shown only for 10 s.

**Figure 3.**An example of the trough detection. The filtered ${O}_{2}Hb$ signal (

**a**), the selected troughs after employing $T{h}_{1}$ (

**b**), and $T{h}_{2}$ (

**c**).

**Figure 4.**The FFT of the baseline wander before (

**a**) and after (

**b**) employing the MA filtering. The red dot stands for dominant frequency in the FFT domain. Note that the reference RR is 0.4 Hz in this example.

**Figure 5.**Data recording protocol. It consists of a resting period for 60 s (

**A**), and two breathing control tasks lasting for 250 s (

**B**,

**D**), which are separated by a 30 s resting period (

**C**). Subsequently, the same blocks were repeated (

**E**–

**H**).

**Figure 7.**Regulation of constants for trough detection in terms of mean±std of the CSI. $T{h}_{1}$ (

**a**) and $T{h}_{2}$ (

**b**).

**Figure 8.**An example of the filtered ${O}_{2}Hb$ signal, the corresponding baseline wanders, and the reference respiratory signal.

MA Filter Length (s) | Average AE ± Std (BPM) |
---|---|

2 | 3.2 ± 1.9 |

2.5 | 3.1 ± 1.8 |

3 | 2.6 ± 1.3 |

3.5 | 2.7 ± 1.4 |

4 | 2.9 ± 1.9 |

4.5 | 2.9 ± 2.1 |

5 | 3.1 ± 2.2 |

Subjects | Average AE (BPM) |
---|---|

1 | 0.9 |

2 | 2.7 |

3 | 2.7 |

4 | 1.1 |

5 | 2.2 |

6 | 1.9 |

7 | 2.1 |

8 | 5.2 |

Subjects | Average AE (BPM) |
---|---|

1 | 1.7 |

2 | 0.3 |

3 | 0.3 |

4 | 0.5 |

5 | 1.8 |

6 | 0.8 |

7 | 1.5 |

8 | 2.7 |

9 | 2.1 |

10 | 0.3 |

11 | 0.4 |

12 | 0.7 |

13 | 3.6 |

14 | 0.5 |

15 | 1.8 |

16 | 1.8 |

17 | 0.4 |

18 | 2.1 |

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## Share and Cite

**MDPI and ACS Style**

Hakimi, N.; Shahbakhti, M.; Sappia, S.; Horschig, J.M.; Bronkhorst, M.; Floor-Westerdijk, M.; Valenza, G.; Dudink, J.; Colier, W.N.J.M.
Estimation of Respiratory Rate from Functional Near-Infrared Spectroscopy (fNIRS): A New Perspective on Respiratory Interference. *Biosensors* **2022**, *12*, 1170.
https://doi.org/10.3390/bios12121170

**AMA Style**

Hakimi N, Shahbakhti M, Sappia S, Horschig JM, Bronkhorst M, Floor-Westerdijk M, Valenza G, Dudink J, Colier WNJM.
Estimation of Respiratory Rate from Functional Near-Infrared Spectroscopy (fNIRS): A New Perspective on Respiratory Interference. *Biosensors*. 2022; 12(12):1170.
https://doi.org/10.3390/bios12121170

**Chicago/Turabian Style**

Hakimi, Naser, Mohammad Shahbakhti, Sofia Sappia, Jörn M. Horschig, Mathijs Bronkhorst, Marianne Floor-Westerdijk, Gaetano Valenza, Jeroen Dudink, and Willy N. J. M. Colier.
2022. "Estimation of Respiratory Rate from Functional Near-Infrared Spectroscopy (fNIRS): A New Perspective on Respiratory Interference" *Biosensors* 12, no. 12: 1170.
https://doi.org/10.3390/bios12121170