Abstract

A new model based on ray tracing was developed to estimate power spectral properties in laser Doppler velocimetry of retinal vessels and to predict the effects of laser beam size and eccentricity as well as absorption of laser light by oxygenated and reduced hemoglobin. We describe the model and show that it correctly converges to the traditional rectangular shape of the Doppler shift power spectrum, given the same assumptions, and that reduced beam size and eccentric alignment cause marked alterations in this shape. The changes in the detected total power of the Doppler-shifted light due to light scattering and absorption by blood can also be quantified with this model and may be used to determine the oxygen saturation in retinal arteries and veins. The potential of this approach is that it uses direct measurements of Doppler signals originating from moving red blood cells. This may open new avenues for retinal vessel oximetry.

© 2005 Optical Society of America

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References

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  1. C. E. Riva, B. Ross, and G. B. Benedek, "Laser Doppler measurements of blood flow in capillary tubes and retinal arteries," Invest. Ophthalmol. 11, 936-944 (1972).
    [PubMed]
  2. G. T. Feke and C. E. Riva, "Laser Doppler measurements of blood velocity in human retinal vessels," J. Opt. Soc. Am. 68(4), 526-531 (1978).
    [CrossRef] [PubMed]
  3. C. E. Riva, G. T. Feke, B. Eberli, and V. Benary, "Bidirectional LDV system for absolute measurement of blood speed in retinal vessels," Appl. Opt. 18, 2301-2306 (1979).
    [CrossRef] [PubMed]
  4. C. E. Riva, J. E. Grunwald, S. H. Sinclair, and B. L. Petrig, "Blood velocity and volumetric flow rate in human retinal vessels," Invest. Ophthalmol. Vis. Sci. 26, 1124-1132 (1985).
    [PubMed]
  5. B. L. Petrig and C. E. Riva, "Retinal laser Doppler velocimetry: towards its computer-assisted clinical use," Appl. Opt. 27, 1126-1134 (1988).
    [CrossRef] [PubMed]
  6. E. Logean, L. F. Schmetterer, and C. E. Riva, "Velocity profile of red blood cells in human retinal vessels using confocal scanning laser Doppler velocimetry," Laser Phys. 13, 45-51 (2003).
  7. B. L. Petrig and L. Follonier, "New ray tracing model for the estimation of power spectral properties in laser Doppler velocimetry of retinal vessels," ARVO Abstract (2005).
  8. S. Wolfram, Mathematica Book, 5th ed. (Wolfram Media, Inc., 2003).
  9. D. U. Fluckiger, R. J. Keyes, and J. H. Shapiro, "Optical autodyne detection: theory and experiment," Appl. Opt. 26, 318-325 (1987).
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  10. C. E. Riva, B. L. Petrig, and J. E. Grunwald, "Retinal blood flow," in Laser-Doppler blood flowmetry, A. P. Shepherd and P. A. Oberg, eds., pp. 349-383 (Kluwer Academic Publishers, 1989).
  11. J. B. Lastovka, "Light mixing spectroscopy and the spectrum of light scattered by thermal fluctuations in liquids," Ph.D. thesis, Massachusetts Institute of Technology (1967).
  12. C. E. Riva and G. T. Feke, "Laser Doppler velocimetry in the measurement of retinal blood flow," in The Biomedical Laser: Technology and Clinical Applications, L. Goldman, ed., pp. 135-161 (Springer, New York, New York, NY, USA, 1981).
  13. O.W. van Assendelft, Spectrophotometry of hemoglobin derivatives (C.C. Thomas, Springfield, IL, USA, 1990).
  14. D. Schweitzer, M. Hammer, J. Kraft, E. Thamm, E. K¨onigsd¨orffer, and J. Strobel, "In vivo measurement of the oxygen saturation of retinal vessels in healthy volonteers," IEEE Trans. Biomed. Eng. 46, 1451-1465 (1999).
    [CrossRef]
  15. A. Ishimaru, Wave Propagation and Scattering in Random Media, vol. II (Academic Press, New York, 1978).
  16. C. E. Riva, J. E. Grunwald, and B. L. Petrig, "Laser Doppler measurement of retinal blood velocity: validity of the single scattering model," Appl. Opt. 24, 605-607 (1985).
    [CrossRef] [PubMed]
  17. A. Harris, R. B. Dinn, L. Kagemann, and E. Rechtman, "A review of methods for human retinal oximetry," Ophthal. Surg. Las. Im. 34, 152-164 (2003).
  18. F. C. Delori, "Noninvasive technique for oximetry of blood in retinal vessels," Appl. Opt. 27, 1113-1125 (1988).
    [CrossRef] [PubMed]
  19. B. Khoobehi, J. M. Beach, and H. Kawano, "Hyperspectral imaging for measurement of oxygen saturation in the optic nerve head," Invest. Ophthalmol. Vis. Sci. 45, 1464-1472 (2004).
    [CrossRef] [PubMed]

Appl. Opt. (5)

IEEE Trans. Biomed. Eng. (1)

D. Schweitzer, M. Hammer, J. Kraft, E. Thamm, E. K¨onigsd¨orffer, and J. Strobel, "In vivo measurement of the oxygen saturation of retinal vessels in healthy volonteers," IEEE Trans. Biomed. Eng. 46, 1451-1465 (1999).
[CrossRef]

Invest. Ophthalmol. (1)

C. E. Riva, B. Ross, and G. B. Benedek, "Laser Doppler measurements of blood flow in capillary tubes and retinal arteries," Invest. Ophthalmol. 11, 936-944 (1972).
[PubMed]

Invest. Ophthalmol. Vis. Sci. (2)

C. E. Riva, J. E. Grunwald, S. H. Sinclair, and B. L. Petrig, "Blood velocity and volumetric flow rate in human retinal vessels," Invest. Ophthalmol. Vis. Sci. 26, 1124-1132 (1985).
[PubMed]

B. Khoobehi, J. M. Beach, and H. Kawano, "Hyperspectral imaging for measurement of oxygen saturation in the optic nerve head," Invest. Ophthalmol. Vis. Sci. 45, 1464-1472 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Laser Phys. (1)

E. Logean, L. F. Schmetterer, and C. E. Riva, "Velocity profile of red blood cells in human retinal vessels using confocal scanning laser Doppler velocimetry," Laser Phys. 13, 45-51 (2003).

Laser-Doppler blood flowmetry (1)

C. E. Riva, B. L. Petrig, and J. E. Grunwald, "Retinal blood flow," in Laser-Doppler blood flowmetry, A. P. Shepherd and P. A. Oberg, eds., pp. 349-383 (Kluwer Academic Publishers, 1989).

Ophthal. Surg. Las. Im. (1)

A. Harris, R. B. Dinn, L. Kagemann, and E. Rechtman, "A review of methods for human retinal oximetry," Ophthal. Surg. Las. Im. 34, 152-164 (2003).

Ph.D. thesis (1)

J. B. Lastovka, "Light mixing spectroscopy and the spectrum of light scattered by thermal fluctuations in liquids," Ph.D. thesis, Massachusetts Institute of Technology (1967).

The Biomedical Laser: Technology and Cli (1)

C. E. Riva and G. T. Feke, "Laser Doppler velocimetry in the measurement of retinal blood flow," in The Biomedical Laser: Technology and Clinical Applications, L. Goldman, ed., pp. 135-161 (Springer, New York, New York, NY, USA, 1981).

Other (4)

O.W. van Assendelft, Spectrophotometry of hemoglobin derivatives (C.C. Thomas, Springfield, IL, USA, 1990).

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

B. L. Petrig and L. Follonier, "New ray tracing model for the estimation of power spectral properties in laser Doppler velocimetry of retinal vessels," ARVO Abstract (2005).

S. Wolfram, Mathematica Book, 5th ed. (Wolfram Media, Inc., 2003).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Cartesian coordinate system for model calculations with origin at the retina. (b) Vessel axis is on x-axis with blood velocity vector pointing in the direction of the positive x-axis. The y-axis is tangential to the retina, z-axis goes through center of eye. Laser beam axis is in the direction of the negative z-axis intersecting the y-axis at eccentricity y 0 from the vessel axis. Detector axis lies in a plane parallel to the xz-plane at y 0 (dashed rhombus) and makes an angle α 1 with the laser axis.

Fig. 2.
Fig. 2.

Model calculations of Doppler signal power spectral shapes in a round vessel (radius R = 50μm). Laser illumination (670 nm) is either uniform (traditional LDV, dashed line) or has a Gaussian shape with beam radii w = 5, 2, 1, 0.5, 0.2 and 0.1R. Laser beam and vessel axes are in the same plane, perpendicular to each other. Scattered beam angle: α 1 = 10°.

Fig. 3.
Fig. 3.

Power spectral shapes in a round vessel (R = 50μm) for a truncated Gaussian beam (radius w = 0.2R) as a function of eccentricity y 0 between laser beam and vessel axes. Scattered beam angle: α 1 = 10°.

Fig. 4.
Fig. 4.

Power spectral shapes in a round vessel (R = 50μm) for a truncated Gaussian beam (radius w = 0.2R) as a function of wavelength (532, 569, 670, 810 nm), with or without taking into account wavelength-dependent absorption of light by oxy- or deoxyhemoglobin. Laser beam and vessel axes intersect at the origin. Scattered beam angle: α 1 = 10°.

Fig. 5.
Fig. 5.

Specific absorption coefficient spectrum of oxy- and deoxyhemoglobin. The four wavelengths calculated in our model are shown as vertical dash-dotted lines, two of them (569 and 810 nm) are isobestic points. Data are taken from van Assendelft [13].

Equations (15)

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v ( r ) = ( 1 r 2 R 2 ) V max ,
I 1 ( ρ ) = I 0 exp ( 2 ρ 2 w 2 ) ,
f ( r ) = ( 1 2 π ) [ v ( r ) · ( k s k i ) ] ,
f ( r ) = v ( r ) sin ( α 1 ) n λ ,
I sc ( r ) = γ x min x max y min ( x ) y max ( x ) I 1 x y l arc y r d y d x ,
I sc ( r ) = γ x min x max y min ( x ) y max ( x ) I 1 x y exp [ μ a ( λ ) d ( y ) ] l arc y r y d x ,
d ( y ) = { 2 [ ( R 2 y 2 ) 1 2 ( r 2 y 2 ) 1 2 ] z 0 , 2 [ ( R 2 y 2 ) 1 2 + ( r 2 y 2 ) 1 2 ] z < 0 .
I sc ( f ) = λ R 2 2 n sin ( α 1 ) V max I sc ( r ) r .
DSPS ( f ) = β ( λ ) 2 SS lo I lo I sc ( f ) ,
P Hb O 2 . sh . 532 P HbO 2 . sh . 810 = k 0 ( 0.125 ) ,
P Hb . sh . 532 P Hb . sh . 810 = k 1 ( 0.25 ) .
P sh . 532 = α P Hb O 2 . sh . 532 + ( 1 α ) P Hb . sh . 532 .
P Hb O 2 . sh . 810 = P Hb . sh . 810 = P sh . 810
SO 2 =α* 100 % = k 1 P sh . 810 P sh . 532 ( k 1 k 0 ) P sh . 810 * 100 % ,
SO 2 =α* 100 % = k 1 P sh . 810 k 2 P sh . 532 ( k 1 k 0 ) P sh . 810 * 100 % ,

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