OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 26 — Dec. 26, 2005
  • pp: 10642–10651
« Show journal navigation

Ray tracing model for the estimation of power spectral properties in laser Doppler velocimetry of retinal vessels and its potential application to retinal vessel oximetry

Benno L. Petrig and Lysianne Follonier  »View Author Affiliations


Optics Express, Vol. 13, Issue 26, pp. 10642-10651 (2005)
http://dx.doi.org/10.1364/OPEX.13.010642


View Full Text Article

Acrobat PDF (114 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

1. Introduction

Analysis of Doppler signals detected from red blood cells (RBCs) flowing in retinal vessels by laser Doppler velocimetry (LDV) was traditionally based on the following model. Assuming a parabolic blood velocity profile and uniform illumination of a cylindrical section of the vessel by laser light, one can show that the theoretical shape of the Doppler shift power spectrum (DSPS) is rectangular [1

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

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]

]. I.e., the DSPS is constant for all frequencies up to the “cutoff” frequency, fmax, which corresponds to the maximum velocity at the center of the vessel, Vmax. This cutoff was determined either by visual inspection of the DSPS using a spectrum analyzer [3

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

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]

], or automatically by a curve fitting algorithm using a computer [5

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]

].

Several factors contribute, however, to alter this theoretical shape. If the laser beam diameter is much smaller than the vessel size, as for example in a confocal system [6

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 ).

], only part of the blood column is illuminated, and thus, some streamlines are missed. The intensity profile may not be uniform but Gaussian, thus not all RBCs are illuminated equally. Absorption of light by hemoglobin and scattering by RBCs also cause non-uniformity of laser illumination, depending on the wavelength and the total path length in blood.

To quantify the relative contributions of all these factors and their combined effects on the DSPS, we have developed a new theoretical model, which allows the estimation of the power spectral shape more precisely using various geometrical and other parameters describing different configurations of the LDV paradigm [7

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 ).

]. In this paper, we describe this model in detail and apply it to predict the effects of varying relative laser beam versus retinal vessel size, eccentricity of beam intersection with the vessel, and differences in the absorption of laser light between oxy- and deoxyhemoglobin at various wavelengths. A potential application to retinal vessel oximetry is discussed.

2. Materials and Methods

2.1. New LDV model

The new LDV model consists of two main components, the blood vessel lumen containing the moving RBCs and the incident laser beam. The intersection of these two ‘rods’, i.e., the homogeneous collection of those RBCs that are illuminated by laser light, is defined as the ‘measuring volume’. We assume that the detector ‘sees’ all the light coming towards it from the entire measuring volume and that the laser and detector are relatively far away from the point of measurement.

This model keeps track of the path length of the laser light inside the measuring volume to take into account light absorption by hemoglobin contained in RBCs as a function of distance traveled within the blood column. The laser wavelength is also taken into account because of the spectral differences in the absorption coefficient between oxy- and deoxyhemoglobin. Power spectral shapes can thus be predicted for various available laser lines using wavelengths located either at isobestic points (same absorption coefficient) or at points with a large difference in absorption coefficients.

Because of the complexity of the required model calculations, we have used Mathematica 5 (Wolfram Research, Champaign, IL, USA), which provides the tools to evaluate the non-linear relationships that apply in this model and to perform the calculations necessary for numerical integration [8

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

].

2.1.1. Coordinate system

In a first approximation, the human retina (and thus the portions of retinal arteries and veins outside the optic disc) can be thought of as lying on a sphere. Our model uses a Cartesian coordinate system, whose origin is on this sphere at the ’point of measurement’ (Fig. 1(a)), where the x-axis is tangential to the sphere and coincides with the blood vessel axis (Fig. 1(b)). The y-axis is also tangential to the sphere, thus the z-axis goes through its center.

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.

2.1.2. Blood vessel model

The blood vessel lumen is considered circular in this model. The positive x-axis is in the direction of the RBCs flowing through the vessel (Fig. 1(b)). The vessel radius is held constant in all calculations presented here (R = 50μm).

The velocity profile, assumed to be parabolic (laminar flow) and symmetric about the x-axis, is given by the following equation

v(r)=(1r2R2)Vmax,
(1)

where r is the distance from the x-axis and Vmax is the centerline blood velocity.

Although the velocity profile normally can show temporal variation (especially in arteries, due to the cardiac cycle), this is not considered further in this model. We assume that blood flow pulsatility does not alter the spectral shapes, but affects only the scale of the Doppler shift frequency, as long as the profile remains parabolic and the scattering characteristics of the RBCs are constant within the range of velocity fluctuations during the heart beat.

2.1.3. Laser beam model

The laser beam is modeled as parallel light at a wavelength λ with a Gaussian beam intensity profile given by

I1(ρ)=I0exp(2ρ2w2),
(2)

where ρ is the distance from the beam axis, I 0 = 2P 0/πw 2 is the on-axis laser beam intensity, P 0 is the total power of the incident beam, and w is the distance from the beam axis, at which the intensity falls to 1/e 2. In our model, P 0 is a fixed value (unity) and the laser beam intensity profile is truncated at w, (i.e.,I 1(ρ) =0 for ρ >w). So the total power in the beam is the same for all beam sizes.

The wave vector k i, of the incident laser beam is assumed to be parallel to the z-axis, and the laser axis is modeled to go through a point y 0 on the y-axis. This simplifies the calculation of the incident laser light intensity I 1 (x,y, z) at any given point using Eq. (2).

2.1.4. Detector model

The detector is located on an axis defined by the wave vector k s, which goes through the same point y 0 where the laser axis intersects the y-axis. This axis also lies in a plane parallel to the xz-plane and makes an angle α 1 (= 10°) with the laser axis (Fig. 1(b)). The portion of the light scattered towards the detector coming from moving RBCs is very small compared to that coming from the static vessel wall, which is not Doppler-shifted and acts like a local oscillator that can be used for heterodyne mixing spectroscopy [9

9 . D. U. Fluckiger , R. J. Keyes , and J. H. Shapiro , “ Optical autodyne detection: theory and experiment ,” Appl. Opt. 26 , 318 – 325 ( 1987 ). [CrossRef] [PubMed]

, 10

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 ).

]. In this model, the intensity of the local oscillator on the detector surface is assumed to be constant.

We are assuming a square-law detector that produces an output current, which is proportional to the square of the two interfering incident optical fields, integrated over the coherence area at the photocathode. Thus the photocurrent is proportional to the intensity of the incident light. The power spectral density function of this photocurrent, the DSPS, is then calculated following the procedure of Lastovka [11

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 ).

] as described in detail elsewhere [12

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

].

2.2. Ray tracing approach

In this model we consider only the so-called ’pseudo single backscattering’ mode [9

9 . D. U. Fluckiger , R. J. Keyes , and J. H. Shapiro , “ Optical autodyne detection: theory and experiment ,” Appl. Opt. 26 , 318 – 325 ( 1987 ). [CrossRef] [PubMed]

]. This means that the laser light eventually reaching the detector is thought to have undergone many forward scattering events without any change in the angle of k i, (imparting no Doppler shift) and one single large-angle backscattering event in the direction of the detector, i.e., of wave vector k s, (imparting a Doppler shift once).

But most of the incident light is in fact lost, because it is either scattered away from the detector by the RBCs or absorbed by hemoglobin. Because only a very small fraction γ of the light incident at any given location within the measuring volume is scattered towards the detector, a large portion of the light (1-γ) is lost due to scattering, which in whole blood is mostly forward. We assume here that this probability γ is constant and uniform throughout the measuring volume.

The basic approach we have taken is to calculate the local intensity of the incident and back-scattered laser light, along with the Doppler shift frequency, for an infinitesimal volume element placed at a given locus within the measuring volume. In its general form, the Doppler shift frequency at a radius r from the vessel axis is defined by the scalar product:

f(r)=(12π)[v(r)·(kski)],
(3)

where v(r) is the blood velocity vector. For the scattering geometry used in this model and with |k s|=|k i|= 2πn/λ this becomes a simple product:

f(r)=v(r)sin(α1)nλ,
(4)

where n is the index of refraction of the flowing medium.

We first integrate over all loci that produce the same Doppler shift, which yields one single point on the DSPS curve. In our model, this corresponds to RBCs moving at the same velocity in a “flow tube”, which has a radius r = (y 2 +z 2)1/2 around the vessel axis and an infinitesimal annular “wall” of thickness dr. In general, for a nonuniform laser beam, this integral is not simply proportional to the circumference and length of this flow tube, but has to be evaluated for all loci, because the incident laser intensity varies with position around the annulus as well as along the tube.

Thus, we must first calculate the total intensity scattered towards the detector by the RBCs flowing in the portion of flow tube of radius r that is “cut out” by the truncated laser:

Isc(r)=γxminxmaxymin(x)ymax(x)I1xylarcyrdydx,
(5)

In order to take into account light absorption, we calculate for each locus on the flow tube the path length of the incident (di) and scattered (ds) light and apply the Beer-Lambert law (I = I 1 exp [-μa(λ)d]; with absorption coefficient μa(λ) and path length d = di + ds), before and after the single backscattering event. With ds = di/cos(α 1) and for a small angle α 1, we get d≈ 2di, and Eq. (5) can be rewritten as

Isc(r)=γxminxmaxymin(x)ymax(x)I1xyexp[μa(λ)d(y)]larcyrydx,
(6)

where the total path length for loci above and below the xy-plane is given by:

d(y)={2[(R2y2)12(r2y2)12]z0,2[(R2y2)12+(r2y2)12]z<0.
(7)

The complete spectrum of the scattered intensity is obtained by evaluating Eq. (6) for all r, but only to the extent that the corresponding points lie within the measuring volume defined above. Then the intensity spectrum of the light scattered by moving RBCs is converted from r-space to f-space (see [1

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]

], Appendix II) as follows:

Isc(f)=λR22nsin(α1)VmaxIsc(r)r.
(8)

Finally, the DSPS (the Doppler-shifted portion of the detected photocurrent [10

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 ).

]) is obtained from

DSPS(f)=β(λ)2SSloIloIsc(f),
(9)

where β(λ) is the responsivity of the photodetector. S is the illuminated photocathode area, Slo and Ilo are the coherence area and the intensity of the local oscillator at the photocathode, respectively, which are held constant in the present model.

3. Results

3.1. Convergence to the traditional model

We first validated our model by defining its parameters such that they approach the traditional LDV configuration. To achieve this, we made the laser beam radius much larger than the vessel radius (w = 100R), which results in all flow tubes being illuminated over approximately the same length. Vessel and laser axes intersect at the origin, and the laser intensity at each point is uniform, without taking into account absorption. Figure 2 shows indeed the expected rectangular shape (dashed line).

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°.

3.2. Effect of laser beam size

The other curves of Fig. 2 show the power spectral shapes for laser beam radii of w = 5,2,1,0.5,0.2 and 0.1R. Vessel and laser axes still intersect at the origin, but now the laser intensity has a truncated Gaussian shape, as defined above. The DSPS curves are normalized for equal power at fmax. As the laser beam radius gets progressively smaller than the vessel radius, power is lost at the low frequency end of the DSPS, because the laser beam misses more and more of the outer streamlines.

3.3. Effect of laser beam eccentricity

The effect of eccentric placement of a small laser beam on the vessel is shown in Fig. 3. It should be noted that there is a marked flattening in the shape of the DSPS with increasing eccentricity, not only a scaling of the frequency axis, as more and more of the streamlines near the center are missed.

3.4. Effect of light absorption by blood

Figure 4 shows DSPS shapes for a small Gaussian laser beam (w = 0.2R) at various wavelengths (λ = 532, 569, 670 and 810 nm). Three different absorption coefficients were modeled (none, oxy- and deoxyhemoglobin), for the latter two using the wavelength-dependent coefficients shown in Fig. 5.

Note that absorption plays no or only a small role at the two longer wavelengths (810 and 670 nm), for which the model was calculated, regardless of oxygen saturation. At the shorter wavelengths (569 and 532 nm), the model predicts a considerable reduction in power when absorption is taken into account. Furthermore, at 532 nm, the power for oxyhemoglobin is reduced to about half of that for deoxyhemoglobin. At the isobestic wavelength of 569 nm, the model predicts the same power reduction for oxy- and deoxyhemoglobin, as expected.

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. 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°.

3.5. Potential application to laser Doppler oximetry

From Fig. 4, we can see that at 532 nm the model predicts a total power under the DSPS curve for deoxy- and oxyhemoglobin of about 25 % and 12.5 %, respectively, when compared to the total power that would be predicted without absorption (dashed line). Since this total shifted power without absorption is unknown, the measured total Doppler-shifted power, Psh.λ, must be calibrated in a different way to obtain the oxygen saturation (SO 2) of blood. A possible calibration procedure could be achieved as follows.

Again referring to Fig. 4, we note that the predicted total power of the shifted light at 810 or 670 nm is the same or very similar for oxy- and deoxyhemoglobin and that there is no or very little absorption compared to 532 nm. Therefore, the power of the shifted light measured, for example at 810 nm, represents a reference value (100 %) for the measurements at 532 nm. Thus, we can calculate the ratio of total shifted power predicted for pure oxy- and deoxyhemoglobin, respectively:

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].
PHbO2.sh.532PHbO2.sh.810=k0(0.125),
(10)
PHb.sh.532PHb.sh.810=k1(0.25).
(11)

Now, for a given mixture of the two pigments [α oxyhemoglobin, (1 - α) deoxyhemoglobin], the total shifted power measured at 532 nm, P sh.532, will fall somewhere between those two end-points and, therefore, we can write

Psh.532=αPHbO2.sh.532+(1α)PHb.sh.532.
(12)

Exploiting the isobestic condition (same absorption coefficient for either pigment) we get

PHbO2.sh.810=PHb.sh.810=Psh.810
(13)

and, thus, solving Eq. (12) for α and inserting Eqs. (10), (11) and (13), we obtain the following formula for SO 2

SO2=α*100%=k1Psh.810Psh.532(k1k0)Psh.810*100%,
(14)

where k 0 and k 1 are the theoretical values taken from Eq. (10) and (11) of the LDV model, and P sh.532, P sh are the measured values of total Doppler-shifted power at each wavelength (area under each DSPS).

Since the power of the two lasers incident on the vessel is likely not the same, the measured photodetector direct current (DC) could be used to compensate for this. The DC represents the non-shifted light scattered by the vessel wall, which is proportional to the incident laser power. Therefore, the power of the shifted light at 532 nm must be scaled by the ratio of the respective DC powers to adjust for uneven incident laser power.

SO2=α*100%=k1Psh.810k2Psh.532(k1k0)Psh.810*100%,
(15)

where k 2 = P dc.810/P dc.532.

4. Discussion

This new model provides a basis for improving future LDV analysis algorithms and to study the effect of various model parameters to gain a better understanding of the LDV paradigm in retinal vessels, by comparing the theoretical shapes of the DSPS predicted by the model with those actually measured.

The model calculations shown here demonstrate that the shape of the DSPS differs markedly from a rectangle if a highly focused Gaussian laser beam is used, if the beam is not centered on the vessel and if absorption of light by the blood column is considered. The use of an eye-tracking device would minimize the effects of eccentricities due to eye motion.

We made some simplifying assumptions to limit the already high complexity of the model presented here. With new generations of software it may become feasible to allow variations in additional parameters, such as asymmetric velocity profiles near vessel junctions or a non-circular vessel lumen that may be expected in retinal veins. And a detector aperture conjugated to the retinal plane could be added to the model.

In the present model, γ, the probability of single backscattering of light towards the detector by moving RBCs, was held constant in Eqs. (5) and (6). A spatially non-uniform distribution or a wavelength dependency of this probability, γ(x,y, z, λ), could be introduced with a future extension of the model and placed inside the double integral. This could include a possible dependency on RBC velocity, as shown for reflectometry [14

14 . D. Schweitzer , M. Hammer , J. Kraft , E. Thamm , E. Königsdörffer , 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]

].

In general, the Beer-Lambert law for light propagation in a tissue layer of thickness d states that the total light attenuation by absorption and scattering is given by I(d) = I 0 exp(- [μa + μs]d), where μa and μs are the absorption and scattering coefficients, respectively. In whole blood, where the mean free pathlength between two scattering events is comparable to the RBC size, any detected Doppler-shifted light must have undergone many scattering events, and light is scattered predominantly in the forward direction (mean cosine of the scattering angle > 0.99 [15

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

]). Therefore, we assumed for the purpose of this model that all of the incident light at any given point inside the vessel lumen is scattered forward at zero angle from k i, except for a very small portion γ that is scattered towards the detector in a single backscattering event [16

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]

]. All remaining incident light (1 - γ) that has completely traversed the blood column is considered lost for detection, accounting for all the scattering losses at that point. After having been backscattered towards the detector, that portion of the light is taken to be scattered forward again, at zero angle from k s. Because γ is assumed to be very small compared to the absorption coefficient, we did not consider this attenuation due to backscattering inside the integral of Eq. (6) as we did for absorption. This could, however, be taken into account more precisely in a future extension of the model, as stated above.

Changes in the backscattering properties of unshifted light from the vessel wall (e.g., as a function of location: front vs. back, center vs. sides) were not modeled explicitly here. The intensity of the local oscillator Ilo at the detector is presently included in Eq. (9) as a constant. One could possibly model the tube of the vessel wall in a similar fashion as it was done with the RBCs inside the vessel and determine the variations of the local oscillator intensity as a function of wavelength and location within the vessel wall. However, to introduce it into the model, i.e., from Eq. (9) inside the integrals of Eqs. (5) and (6), this intensity would have to be expressed with respect to the locus of the Doppler-shifted light intensity Ilo(x,y,z,λ), which it is associated with.

In the data shown here, the DSPS curves for the different absorption coefficients were normalized to the DSPS curve without light absorption in a medium size retinal vessel of 100 μm diameter. The results show that compared to the 670 nm laser, the signal-to-noise ratio at 532 nm needs to be approximately 10 times higher, which should be achievable with a higher laser power delivered over a shorter time. Using an eye-tracking device and turning the probing laser on for only a few seconds would allow measurements with a minimum of light exposure. If needed, light exposure could be further reduced by measuring sequentially, turning only one probing laser on at a time.

Even though 670 nm is not an isobestic point, Fig. 4 shows that the total shifted power for oxy- and deoxyhemoglobin differs only by a few percents, because the absorption coefficient is already very small compared to 532 nm. Therefore, as a compromise, a 670 instead of 810 nm laser may be used as a reference for Eq.(15).

If the scattering properties at the above wavelengths (532 vs. 810 or 670 nm) turn out to be too different for the calibration by the DC to be accurate (i.e., if γ or the local oscillator depends strongly on wavelength), then an isobestic point close to 532 nm, for example 569 or even 548 nm, could be chosen instead. In that case, it should be noted that the total shifted power for oxyhemoglobin at 569 and 548 nm is similar to that at 532 nm (Fig. 4), requiring a comparable signal-to-noise ratio of the detector system.

Inexpensive diode lasers are available today at 532, 670 and 810 nm, but not yet at 548 or 569 nm. However, electro-optics technology is advancing rapidly and new laser lines may soon become available near 569 or 548 nm. Or a tunable, although more expensive, laser may be employed instead.

Previously developed techniques of retinal vessel oximetry (for a review see [17

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 ).

]) were mostly based on ocular fundus reflectance measurements, either using discrete wavelengths [18

18 . F. C. Delori , “ Noninvasive technique for oximetry of blood in retinal vessels ,” Appl. Opt. 27 , 1113 – 1125 ( 1988 ). [CrossRef] [PubMed]

], or by spectrometry over the whole visible spectrum [14

14 . D. Schweitzer , M. Hammer , J. Kraft , E. Thamm , E. Königsdörffer , 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]

, 19

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]

]. The potential of retinal vessel oximetry based on Doppler-shifted light is that this light necessarily originates from RBCs moving within the blood column, which could open new avenues for retinal vessel oximetry.

Acknowledgements

This work was supported in part by the Loterie Suisse Romande.

References and links

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 ). [CrossRef] [PubMed]

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 Bio-medical 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. Königsdörffer , 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]

OCIS Codes
(170.1460) Medical optics and biotechnology : Blood gas monitoring
(170.3340) Medical optics and biotechnology : Laser Doppler velocimetry
(170.4470) Medical optics and biotechnology : Ophthalmology

ToC Category:
Research Papers

Virtual Issues
Vol. 1, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Benno L. Petrig and Lysianne Follonier, "Ray tracing model for the estimation of power spectral properties in laser Doppler velocimetry of retinal vessels and its potential application to retinal vessel oximetry," Opt. Express 13, 10642-10651 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-26-10642


Sort:  Journal  |  Reset  

References

  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). [CrossRef] [PubMed]
  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]

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.

CrossCheck Deposited