Abstract

A model of pulse oximetry is developed based on the three-dimensional photon diffusion theory. To test the applicability of the model, an in vitro assay was developed. Three different scattering levels and six different relative dye concentrations were analyzed. Average percent errors of 13.9% were obtained over the full range of the study. An in vivo clinical study of two pulse oximeter probes with different spectral characteristics was compared with results estimated by the model. The model correctly predicted the changes in pulse oximeter response resulting from the wavelength changes. A χ2 test gave a probability of 20% that the model fit the data. These results demonstrated the utility of the photon diffusion theory for the modeling of tissue optics.

© 1994 Optical Society of America

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  1. I. Yoshiya, Y. Shimada, K. Tanaka, “Spectrophotometric monitoring of arterial oxygen saturation in the fingertip,” Med. Biol. Eng. Comput. 18, 27–32 (1980).
    [CrossRef] [PubMed]
  2. Y. Shimada, I. Yoshiya, “Effects of multiple scattering and peripheral circulation on arterial oxygen saturation measured with a pulse-type oximeter,” Med. Biol. Eng. Comput. 22, 475–478 (1984).
    [CrossRef] [PubMed]
  3. D. R. Marble, P. W. Cheung, “Mathematical model of transmission pulse oximetry,” in Proceedings of the Tenth International Conference of the IEEE Engineering in Medicine and Biology Society (Institute of Electrical and Electronic Engineers, New York, 1988), Chap. 2, pp. 542–543.
    [CrossRef]
  4. L. O. Reynolds, “Optical diffuse reflectance and transmittance from an anisotropically scattering finite blood medium,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1975).
  5. S. Takatani, “On the theory and development of a noninvasive tissue reflectance oximeter,” Ph.D. dissertation (Case Western Reserve University, Cleveland, Ohio, 1978).
  6. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  7. Y. Kuga, “Laser light propagation and scattering in a dense distribution of spherical particles,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1983).
  8. K. Shimizu, “Remote sensing of microparticles by laser scattering for medical applications,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1979).
  9. J. M. Schmitt, “Optical measurement of blood oxygen by implantable telemetry,” Ph.D. dissertation (Stanford University, Palo Alto, Calif., 1986).
  10. O. W. van Assendelft, Spectrophotometry of Hemoglobin Derivatives (Royal van Gorcum, Assen, The Netherlands, 1970).
  11. J. M. Schmitt, “Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry,” IEEE Trans. Biomed. Eng. 38, 1194–1203 (1991).
    [CrossRef] [PubMed]
  12. Y. Mendelson, “Theory and development of a transcutaneous reflectance oximeter system for noninvasive measurements of arterial oxygen saturation,” Ph.D. dissertation (Case Western Reserve University, Cleveland, Ohio, 1983).
  13. D. P. Brown, “Evaluation of pulse oximeters using theoretical models and experimental studies,” M.S. thesis (University of Washington, Seattle, Wash., 1987).
  14. R. R. Anderson, J. Hu, J. A. Parrish, “Optical radiation transfer in the human skin and applicationsin in vivo remittance spectroscopy,” in Bioengineering and the Skin, R. Marks, P. A. Payne, eds. (MTP, Hingham, Mass., 1981), pp. 231–265.
  15. E. Bo, H. Saxberg, B. R. Kowalski, “Generalized standard addition method,” Anal. Chem. 51, 1031–1038 (1979).
    [CrossRef]
  16. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  17. R. C. Weast, ed., CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, Fla., 1983).
  18. K. Shimizu, “Experimental test of the reduced effective velocity of light in a diffuse medium,” Opt. Lett. 5, 205–207 (1980).
    [CrossRef] [PubMed]
  19. B. Chance, J. S. Leigh, H. Miyake, O. S. Smith, R. Greenfield, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and -unresolved measurements of deoxy-hemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
    [CrossRef] [PubMed]
  20. J. W. Severinghaus, K. H. Naifeh, S. O. Koh, “Errors in 14 pulse oximeters during profound hypoxia,” J. Clin. Monit. 5, 72–81 (1989).
    [CrossRef] [PubMed]
  21. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

1991 (1)

J. M. Schmitt, “Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry,” IEEE Trans. Biomed. Eng. 38, 1194–1203 (1991).
[CrossRef] [PubMed]

1989 (1)

J. W. Severinghaus, K. H. Naifeh, S. O. Koh, “Errors in 14 pulse oximeters during profound hypoxia,” J. Clin. Monit. 5, 72–81 (1989).
[CrossRef] [PubMed]

1988 (1)

B. Chance, J. S. Leigh, H. Miyake, O. S. Smith, R. Greenfield, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and -unresolved measurements of deoxy-hemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

1984 (1)

Y. Shimada, I. Yoshiya, “Effects of multiple scattering and peripheral circulation on arterial oxygen saturation measured with a pulse-type oximeter,” Med. Biol. Eng. Comput. 22, 475–478 (1984).
[CrossRef] [PubMed]

1980 (2)

I. Yoshiya, Y. Shimada, K. Tanaka, “Spectrophotometric monitoring of arterial oxygen saturation in the fingertip,” Med. Biol. Eng. Comput. 18, 27–32 (1980).
[CrossRef] [PubMed]

K. Shimizu, “Experimental test of the reduced effective velocity of light in a diffuse medium,” Opt. Lett. 5, 205–207 (1980).
[CrossRef] [PubMed]

1979 (1)

E. Bo, H. Saxberg, B. R. Kowalski, “Generalized standard addition method,” Anal. Chem. 51, 1031–1038 (1979).
[CrossRef]

Anderson, R. R.

R. R. Anderson, J. Hu, J. A. Parrish, “Optical radiation transfer in the human skin and applicationsin in vivo remittance spectroscopy,” in Bioengineering and the Skin, R. Marks, P. A. Payne, eds. (MTP, Hingham, Mass., 1981), pp. 231–265.

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

Bo, E.

E. Bo, H. Saxberg, B. R. Kowalski, “Generalized standard addition method,” Anal. Chem. 51, 1031–1038 (1979).
[CrossRef]

Brown, D. P.

D. P. Brown, “Evaluation of pulse oximeters using theoretical models and experimental studies,” M.S. thesis (University of Washington, Seattle, Wash., 1987).

Chance, B.

B. Chance, J. S. Leigh, H. Miyake, O. S. Smith, R. Greenfield, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and -unresolved measurements of deoxy-hemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Cheung, P. W.

D. R. Marble, P. W. Cheung, “Mathematical model of transmission pulse oximetry,” in Proceedings of the Tenth International Conference of the IEEE Engineering in Medicine and Biology Society (Institute of Electrical and Electronic Engineers, New York, 1988), Chap. 2, pp. 542–543.
[CrossRef]

Finander, M.

B. Chance, J. S. Leigh, H. Miyake, O. S. Smith, R. Greenfield, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and -unresolved measurements of deoxy-hemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Greenfield, R.

B. Chance, J. S. Leigh, H. Miyake, O. S. Smith, R. Greenfield, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and -unresolved measurements of deoxy-hemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Hu, J.

R. R. Anderson, J. Hu, J. A. Parrish, “Optical radiation transfer in the human skin and applicationsin in vivo remittance spectroscopy,” in Bioengineering and the Skin, R. Marks, P. A. Payne, eds. (MTP, Hingham, Mass., 1981), pp. 231–265.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

Kaufmann, K.

B. Chance, J. S. Leigh, H. Miyake, O. S. Smith, R. Greenfield, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and -unresolved measurements of deoxy-hemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Koh, S. O.

J. W. Severinghaus, K. H. Naifeh, S. O. Koh, “Errors in 14 pulse oximeters during profound hypoxia,” J. Clin. Monit. 5, 72–81 (1989).
[CrossRef] [PubMed]

Kowalski, B. R.

E. Bo, H. Saxberg, B. R. Kowalski, “Generalized standard addition method,” Anal. Chem. 51, 1031–1038 (1979).
[CrossRef]

Kuga, Y.

Y. Kuga, “Laser light propagation and scattering in a dense distribution of spherical particles,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1983).

Leigh, J. S.

B. Chance, J. S. Leigh, H. Miyake, O. S. Smith, R. Greenfield, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and -unresolved measurements of deoxy-hemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Levy, W.

B. Chance, J. S. Leigh, H. Miyake, O. S. Smith, R. Greenfield, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and -unresolved measurements of deoxy-hemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Marble, D. R.

D. R. Marble, P. W. Cheung, “Mathematical model of transmission pulse oximetry,” in Proceedings of the Tenth International Conference of the IEEE Engineering in Medicine and Biology Society (Institute of Electrical and Electronic Engineers, New York, 1988), Chap. 2, pp. 542–543.
[CrossRef]

Mendelson, Y.

Y. Mendelson, “Theory and development of a transcutaneous reflectance oximeter system for noninvasive measurements of arterial oxygen saturation,” Ph.D. dissertation (Case Western Reserve University, Cleveland, Ohio, 1983).

Miyake, H.

B. Chance, J. S. Leigh, H. Miyake, O. S. Smith, R. Greenfield, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and -unresolved measurements of deoxy-hemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Naifeh, K. H.

J. W. Severinghaus, K. H. Naifeh, S. O. Koh, “Errors in 14 pulse oximeters during profound hypoxia,” J. Clin. Monit. 5, 72–81 (1989).
[CrossRef] [PubMed]

Parrish, J. A.

R. R. Anderson, J. Hu, J. A. Parrish, “Optical radiation transfer in the human skin and applicationsin in vivo remittance spectroscopy,” in Bioengineering and the Skin, R. Marks, P. A. Payne, eds. (MTP, Hingham, Mass., 1981), pp. 231–265.

Reynolds, L. O.

L. O. Reynolds, “Optical diffuse reflectance and transmittance from an anisotropically scattering finite blood medium,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1975).

Saxberg, H.

E. Bo, H. Saxberg, B. R. Kowalski, “Generalized standard addition method,” Anal. Chem. 51, 1031–1038 (1979).
[CrossRef]

Schmitt, J. M.

J. M. Schmitt, “Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry,” IEEE Trans. Biomed. Eng. 38, 1194–1203 (1991).
[CrossRef] [PubMed]

J. M. Schmitt, “Optical measurement of blood oxygen by implantable telemetry,” Ph.D. dissertation (Stanford University, Palo Alto, Calif., 1986).

Severinghaus, J. W.

J. W. Severinghaus, K. H. Naifeh, S. O. Koh, “Errors in 14 pulse oximeters during profound hypoxia,” J. Clin. Monit. 5, 72–81 (1989).
[CrossRef] [PubMed]

Shimada, Y.

Y. Shimada, I. Yoshiya, “Effects of multiple scattering and peripheral circulation on arterial oxygen saturation measured with a pulse-type oximeter,” Med. Biol. Eng. Comput. 22, 475–478 (1984).
[CrossRef] [PubMed]

I. Yoshiya, Y. Shimada, K. Tanaka, “Spectrophotometric monitoring of arterial oxygen saturation in the fingertip,” Med. Biol. Eng. Comput. 18, 27–32 (1980).
[CrossRef] [PubMed]

Shimizu, K.

K. Shimizu, “Experimental test of the reduced effective velocity of light in a diffuse medium,” Opt. Lett. 5, 205–207 (1980).
[CrossRef] [PubMed]

K. Shimizu, “Remote sensing of microparticles by laser scattering for medical applications,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1979).

Smith, O. S.

B. Chance, J. S. Leigh, H. Miyake, O. S. Smith, R. Greenfield, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and -unresolved measurements of deoxy-hemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Takatani, S.

S. Takatani, “On the theory and development of a noninvasive tissue reflectance oximeter,” Ph.D. dissertation (Case Western Reserve University, Cleveland, Ohio, 1978).

Tanaka, K.

I. Yoshiya, Y. Shimada, K. Tanaka, “Spectrophotometric monitoring of arterial oxygen saturation in the fingertip,” Med. Biol. Eng. Comput. 18, 27–32 (1980).
[CrossRef] [PubMed]

van Assendelft, O. W.

O. W. van Assendelft, Spectrophotometry of Hemoglobin Derivatives (Royal van Gorcum, Assen, The Netherlands, 1970).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Yoshiya, I.

Y. Shimada, I. Yoshiya, “Effects of multiple scattering and peripheral circulation on arterial oxygen saturation measured with a pulse-type oximeter,” Med. Biol. Eng. Comput. 22, 475–478 (1984).
[CrossRef] [PubMed]

I. Yoshiya, Y. Shimada, K. Tanaka, “Spectrophotometric monitoring of arterial oxygen saturation in the fingertip,” Med. Biol. Eng. Comput. 18, 27–32 (1980).
[CrossRef] [PubMed]

Young, M.

B. Chance, J. S. Leigh, H. Miyake, O. S. Smith, R. Greenfield, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and -unresolved measurements of deoxy-hemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Anal. Chem. (1)

E. Bo, H. Saxberg, B. R. Kowalski, “Generalized standard addition method,” Anal. Chem. 51, 1031–1038 (1979).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

J. M. Schmitt, “Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry,” IEEE Trans. Biomed. Eng. 38, 1194–1203 (1991).
[CrossRef] [PubMed]

J. Clin. Monit. (1)

J. W. Severinghaus, K. H. Naifeh, S. O. Koh, “Errors in 14 pulse oximeters during profound hypoxia,” J. Clin. Monit. 5, 72–81 (1989).
[CrossRef] [PubMed]

Med. Biol. Eng. Comput. (2)

I. Yoshiya, Y. Shimada, K. Tanaka, “Spectrophotometric monitoring of arterial oxygen saturation in the fingertip,” Med. Biol. Eng. Comput. 18, 27–32 (1980).
[CrossRef] [PubMed]

Y. Shimada, I. Yoshiya, “Effects of multiple scattering and peripheral circulation on arterial oxygen saturation measured with a pulse-type oximeter,” Med. Biol. Eng. Comput. 22, 475–478 (1984).
[CrossRef] [PubMed]

Opt. Lett. (1)

Proc. Natl. Acad. Sci. USA (1)

B. Chance, J. S. Leigh, H. Miyake, O. S. Smith, R. Greenfield, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and -unresolved measurements of deoxy-hemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Other (14)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

R. C. Weast, ed., CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, Fla., 1983).

Y. Mendelson, “Theory and development of a transcutaneous reflectance oximeter system for noninvasive measurements of arterial oxygen saturation,” Ph.D. dissertation (Case Western Reserve University, Cleveland, Ohio, 1983).

D. P. Brown, “Evaluation of pulse oximeters using theoretical models and experimental studies,” M.S. thesis (University of Washington, Seattle, Wash., 1987).

R. R. Anderson, J. Hu, J. A. Parrish, “Optical radiation transfer in the human skin and applicationsin in vivo remittance spectroscopy,” in Bioengineering and the Skin, R. Marks, P. A. Payne, eds. (MTP, Hingham, Mass., 1981), pp. 231–265.

D. R. Marble, P. W. Cheung, “Mathematical model of transmission pulse oximetry,” in Proceedings of the Tenth International Conference of the IEEE Engineering in Medicine and Biology Society (Institute of Electrical and Electronic Engineers, New York, 1988), Chap. 2, pp. 542–543.
[CrossRef]

L. O. Reynolds, “Optical diffuse reflectance and transmittance from an anisotropically scattering finite blood medium,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1975).

S. Takatani, “On the theory and development of a noninvasive tissue reflectance oximeter,” Ph.D. dissertation (Case Western Reserve University, Cleveland, Ohio, 1978).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

Y. Kuga, “Laser light propagation and scattering in a dense distribution of spherical particles,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1983).

K. Shimizu, “Remote sensing of microparticles by laser scattering for medical applications,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1979).

J. M. Schmitt, “Optical measurement of blood oxygen by implantable telemetry,” Ph.D. dissertation (Stanford University, Palo Alto, Calif., 1986).

O. W. van Assendelft, Spectrophotometry of Hemoglobin Derivatives (Royal van Gorcum, Assen, The Netherlands, 1970).

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

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Figures (4)

Fig. 1
Fig. 1

Diagram of the system used for in vitro simulation of pulses by controlled stepwise absorbance changes.

Fig. 2
Fig. 2

Results of the in vitro study for 16.7% red dye and 83.3% green dye. The results of the theoretical model are shown by the curves. The experimental data are shown by squares. A, 50.0% nondairy creamer; B, 33.3% nondairy creamer; C, 12.5% nondairy creamer.

Fig. 3
Fig. 3

Experimental and theoretical results for pulse oximetry with a 660-nm red LED with no IR secondary peak.

Fig. 4
Fig. 4

Experimental and theoretical results for pulse oximetry with a 665-nm red LED with a 0.2% secondary peak at 880 nm.

Equations (16)

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( 2 - 3 Σ a Σ t r ) U d ( r ) = - Q 0 ( r ) ,
U d ( r ) - h z U d ( r ) + Q 1 ( r ) 2 π = 0             at z = 0 ,
U d ( r ) - h z U d ( r ) - Q 1 ( r ) 2 π = 0             at z = d ,
h = 2 3 Σ t r .
Q 0 ( r ) = 3 4 π Σ s ( Σ t + μ ¯ Σ a ) exp ( - r 2 / W 2 ) exp ( - Σ t z ) C 0 exp ( - r 2 / W 2 ) exp ( - Σ t z ) ,
Q 1 ( r ) = Σ s μ ¯ Σ t r exp ( - r 2 / W 2 ) exp ( - Σ t z ) C 1 exp ( - r 2 / W 2 ) exp ( - Σ t z ) .
U d ( r ) = V G ( r , r ) Q 0 ( r ) d V - 1 2 π h S G ( r , r ) Q 1 ( r ) d S .
G ( r , z ; r , z ) = 1 4 π 0 λ d λ γ J 0 ( λ r ) J 0 ( λ r ) { exp ( - γ z - z ) + g 11 exp [ - γ ( z + z ) ] + g 12 exp [ - γ ( z - z ) ] + g 21 exp [ γ ( z + z ) ] + g 12 exp [ γ ( z - z ) ] } ,
g 11 = ( h 2 γ 2 - 1 ) exp ( γ d ) Δ ,             g 12 = ( h γ - 1 ) 2 exp ( - γ d ) Δ , g 21 = ( h 2 γ 2 - 1 ) exp ( - γ d ) Δ ,
γ = ( λ 2 + 3 Σ a Σ t r ) 1 / 2 ,
Δ = ( h γ + 1 ) 2 exp ( γ d ) - ( h γ - 1 ) 2 exp ( - γ d ) .
I = exp ( - Σ t d ) + 2 π 0 a d λ γ J 1 ( λ a ) × exp ( - W 2 λ 2 / 4 ) [ C 0 2 A ( d ) + C 1 4 π h B ( d ) ] ,
A ( d ) = 1 + g 12 γ - Σ t [ exp ( - Σ t d ) - exp ( - γ d ) ] - g 11 γ + Σ t [ exp ( - 2 γ d - Σ t d ) - exp ( - γ d ) ] - g 12 γ + Σ t [ exp ( - Σ t d ) - exp ( γ d ) ] + g 21 γ - Σ t [ exp ( 2 γ d - Σ t d ) - exp ( γ d ) ] ,
B ( d ) = exp ( - Σ t d ) - exp ( - γ d ) + g 11 × [ exp ( - 2 γ d - Σ t d ) - exp ( - γ d ) ] + g 12 [ exp ( - Σ t d ) - exp ( - γ d ) ] + g 21 [ exp ( 2 γ d - Σ t d ) - exp ( γ d ) + g 12 [ exp ( - Σ t d ) - exp ( γ d ) ] .
S a O 2 = [ HbO 2 ] [ HbO 2 ] + [ Hb ] × 100 % = f ( ac / dc ratio ) ,
ac / dc / ratio = ( I red ac / I red dc ) ( I IR ac / I IR dc ) = ( I red max - I red min ) I IR max ( I IR max - I IR min ) I red max .

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