## Adaptive pulse oximeter with dual-wavelength based on wavelet transforms |

Optics Express, Vol. 21, Issue 20, pp. 23058-23067 (2013)

http://dx.doi.org/10.1364/OE.21.023058

Acrobat PDF (1147 KB)

### Abstract

Pulse oximeter is widely used in the monitoring of blood oxygen in clinic for its convenience and efficiency. However, synchronizing light source flashing with data collecting is required, otherwise the separation of the data from different LEDs will fail. More importantly, synchronous acquisition makes the pulse oximetry system vulnerable. Meanwhile, the pulse waveform extraction is a crucial procedure in the measurement. Hence, in this paper, an asynchronous acquisition pulse oximetry system based on wavelet transform has been built. PhotoPlethysmoGraph (PPG) and photoelectric detection technology are applied in our homemade system. The adaptive soft-threshold de-noising is realized by Stein's Unbiased Risk Estimate (SURE). The principle and system configuration are described. The preliminary experiment results from wavelet transforms and Fourier transforms are compared. The results show that our homemade system is adaptive, accurate, robust and simple.

© 2013 Optical Society of America

## 1. Introduction

3. P. S. Addison and J. N. Watson, “A novel time–frequency-based 3D Lissajous figure method and its application to the determination of oxygen saturation from the photoplethysmogram,” Meas. Sci. Technol. **15**(11), L15–L18 (2004). [CrossRef]

## 2. Description of pulse oximeter

### 2.1 The theoretical basis of blood oxygen measurements

*ΔA*and

_{1}*ΔA*from the original data.

_{2}### 2.2 System configuration

### 2.3 Original signal explanation

## 3. Principles of signal processing

### 3.1 WT method

*s(t)*is the signal of a single LED, the discrete wavelet transform (DWT) can be express aswithwhere

*j*is scale factor,

*k*is time shifting,

*φ*is the mother wavelet,

*WT*is the wavelet coefficient sequence of each resolution level (stratified according to scale factor

_{s}(j,k)*j*).

9. C. M. Stein, “Estimation of the mean of a multivariate normal distribution,” Ann. Stat. **9**(6), 1135–1151 (1981). [CrossRef]

*WT*is the original wavelet coefficients,

*σ*is the variance of

^{2}*WT*,

*p(WT)*is an estimator of pulse’s wavelet coefficients from

*WT*,

*g*is the estimator of the wavelet coefficients of noise which is denote as the difference between

*p(WT)*and

*WT*,

*p(WT)*which meanswhere

*pulse*stands for the wavelet coefficients of actual pulse signal which cannot be obtained directly. However, based on Eq. (6), the MSE of

*p(WT)*can be computed by

*p(WT)*independently. Therefore, minimizing the risks in

*p(WT)*to obtain the adaptive threshold value [10

10. D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” J. Am. Stat. Assoc. **90**(432), 1200–1224 (1995). [CrossRef]

*WT*). Assuming

*ST*is the threshold of a single resolution level, the soft-threshold method can be denoted aswhere

*η(WT)*is the wavelet coefficients after thresholding,

*sgn(x)*is the sign function. After this, the reconstruction of the wavelet coefficients is conducted as followingwhere

*f(t)*is the ideal signal. Figure 4 shows the signal processing procedure by DWT.

### 3.2 FT method

*s(t)*denote the signal of a single LED, the discrete Fourier transform (DFT) can be expressed aswhereis an N

^{th}root of unity. Pulse wave and noises are converted into frequency spectrum. Therefore, it is convenient to conduct the band-pass filtering. The frequency ranges from 0.5 Hz to 2 Hz is selected to rebuild the signal. Assuming

*F*is the frequency spectrum which contains the target frequency, and then the reconstruction can be expressed aswhere

*f*is the pulse waveform. Figure 5 shows the signal processing procedure by FT.

## 4. Experiment

*ΔA*and

_{1}*ΔA*) is desired.

_{2}*ΔA*and

_{1}*ΔA*are normalized to eliminate the detector’s different response between each wavelength and the changes of the arterial perfusion caused by pressure variation. The normalization can be expressed aswhere

_{2}*AC*is the difference between the wave peaks and troughs in the same pulse wave cycle,

*DC*is the baseline of the same cycle. Then Eq. (2) can be re-written aswhere the subscript 1 and 2 represent the red and infrared LED, respectively. The system parameters are obtained by calibration as a = 103.5 and b = −9.42. Five pulse fluctuation cycles were taken into the computation by the least square method in order to eliminate the influence of random factors.

*SaO*values [11

_{2}11. J. A. Dempsey and P. D. Wagner, “Exercise-induced arterial hypoxemia,” J. Appl. Physiol. **87**(6), 1997–2006 (1999). [PubMed]

## 5. Discussion

*SaO*, FT obtains smaller

_{2}*SaO*value than WT. This is because the reduction of the amplitude shown in Fig. 10. To figure out the relationship between

_{2}*SaO*value and amplitude, the total differential of Eq. (13) is performed aswhere

_{2}*d(SaO*is the variation of

_{2})*SaO*,

_{2}*d(AC*and

_{1})*d(AC*are the amount of the amplitude reduction of red and infrared respectively. Because the same band-pass filter is applied in both red and infrared signals, the amount of the amplitude reduction of each signal can be regarded as the same which means

_{2})*d(AC*) =

_{1}*d(AC*). Therefore, Eq. (14) can be simplified asUpon our careful study and experiment, the value of

_{2}*AC*is found less than 1,

_{2}*b*and

*d(AC*are both negative values while

_{1})*DC*,

_{2}*AC*and

_{2}*DC*are all positive values. Hence, the variation of

_{1}*SaO*(

_{2}*d(SaO*) is negative which means the

_{2})*SaO*is reduced as a result of the slight reduction of the pulse wave amplitude caused by FT. Therefore, a slight reduction of the pulse wave amplitude will lead to a lower level of SaO

_{2}_{2}value which reduces the accuracy of the pulse oximetry system.

## 6. Conclusion

_{2}values computed from WT and FT, respectively, are compared. The preliminary experimental results show that the measuring result with WT is more accurate than that with FT.

## Acknowledgments

## References and links

1. | T. Aoyagi, M. Kishi, K. Yamaguchi, and S. Watanabe, “Improvement of the earpiece oximeter,” in |

2. | S. A. Wilber, “Blood constituent measuring device and method,” U.S. Patent No. 4,407,290, Washington, DC: U.S. Patent and Trademark Office (1983). |

3. | P. S. Addison and J. N. Watson, “A novel time–frequency-based 3D Lissajous figure method and its application to the determination of oxygen saturation from the photoplethysmogram,” Meas. Sci. Technol. |

4. | Y. S. Yan and Y. T. Zhang, “An efficient motion-resistant method for wearable pulse oximeter,” IEEE Trans. Inf. Technol. Biomed. |

5. | F. U. Dowla, P. G. Skokowski, and R. R. Leach, Jr., “Neural networks and wavelet analysis in the computer interpretation of pulse oximetry data,” in |

6. | S. Lee, B. L. Ibey, W. Xu, M. A. Wilson, M. N. Ericson, and G. L. Coté, “Processing of pulse oximeter data using discrete wavelet analysis,” IEEE Trans. Biomed. Eng. |

7. | Y. Yong-sheng, C. Y. Poon Carmen, and Z. Yuan-ting, “Reduction of motion artifact in pulse oximetry by smoothed pseudo Wigner-Ville distribution,” J. NeuroEng. Rehabil. |

8. | X. U. Kexin, G. A. O. Feng, and Z. H. A. O. Huijuan, |

9. | C. M. Stein, “Estimation of the mean of a multivariate normal distribution,” Ann. Stat. |

10. | D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” J. Am. Stat. Assoc. |

11. | J. A. Dempsey and P. D. Wagner, “Exercise-induced arterial hypoxemia,” J. Appl. Physiol. |

**OCIS Codes**

(000.3110) General : Instruments, apparatus, and components common to the sciences

(230.0230) Optical devices : Optical devices

(230.3670) Optical devices : Light-emitting diodes

(220.1080) Optical design and fabrication : Active or adaptive optics

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: June 24, 2013

Revised Manuscript: September 10, 2013

Manuscript Accepted: September 12, 2013

Published: September 23, 2013

**Citation**

Shengjia Wang, Zhan Gao, Guangyu Li, and Ziang Feng, "Adaptive pulse oximeter with dual-wavelength based on wavelet transforms," Opt. Express **21**, 23058-23067 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23058

Sort: Year | Journal | Reset

### References

- T. Aoyagi, M. Kishi, K. Yamaguchi, and S. Watanabe, “Improvement of the earpiece oximeter,” in Abstracts of the Japanese Society of Medical Electronics and Biological Engineering (Japanese Society of Medical Electronics and Biological Engineering, Tokyo, 1974), pp. 90–91.
- S. A. Wilber, “Blood constituent measuring device and method,” U.S. Patent No. 4,407,290, Washington, DC: U.S. Patent and Trademark Office (1983).
- P. S. Addison and J. N. Watson, “A novel time–frequency-based 3D Lissajous figure method and its application to the determination of oxygen saturation from the photoplethysmogram,” Meas. Sci. Technol.15(11), L15–L18 (2004). [CrossRef]
- Y. S. Yan and Y. T. Zhang, “An efficient motion-resistant method for wearable pulse oximeter,” IEEE Trans. Inf. Technol. Biomed.12(3), 399–405 (2008). [CrossRef] [PubMed]
- F. U. Dowla, P. G. Skokowski, and R. R. Leach, Jr., “Neural networks and wavelet analysis in the computer interpretation of pulse oximetry data,” in Proceedings of IEEE Conference on Neural Networks for Signal Processing (IEEE Signal Processing Society Workshop, Kyoto, 1996), pp. 527–536. [CrossRef]
- S. Lee, B. L. Ibey, W. Xu, M. A. Wilson, M. N. Ericson, and G. L. Coté, “Processing of pulse oximeter data using discrete wavelet analysis,” IEEE Trans. Biomed. Eng.52(7), 1350–1352 (2005). [CrossRef] [PubMed]
- Y. Yong-sheng, C. Y. Poon Carmen, and Z. Yuan-ting, “Reduction of motion artifact in pulse oximetry by smoothed pseudo Wigner-Ville distribution,” J. NeuroEng. Rehabil.2(3), 9 (2005).
- X. U. Kexin, G. A. O. Feng, and Z. H. A. O. Huijuan, Biomedical Photonics, 2nd ed. (Science Press, 2010), p. 182.
- C. M. Stein, “Estimation of the mean of a multivariate normal distribution,” Ann. Stat.9(6), 1135–1151 (1981). [CrossRef]
- D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” J. Am. Stat. Assoc.90(432), 1200–1224 (1995). [CrossRef]
- J. A. Dempsey and P. D. Wagner, “Exercise-induced arterial hypoxemia,” J. Appl. Physiol.87(6), 1997–2006 (1999). [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.