Fig. 7.5 DSPS (Pi(Df)) obtained in measurement times of 0.4, 0.8, 1.6, and 3.2 s from 0.1% suspension of polystyrene spheres in water ßowing through a 200-mm-internal-

diameter glass capillary tube. The precision of Pi(Df) at each Df increases with the measurement time (Adapted from Riva et al. [13] with permission from the Publisher)

s is the standard deviation, T the measurement time, and Dν the resolution bandwidth of the spectrum analyzer. The linear relationship expressed by Eq. 7.12 has been veriÞed with excellent accuracy for the recordings shown in Fig. 7.5 [13].

7.2.7The DSPS for RBCs Moving in a Retinal Vessel

7.2.7.1 Multiple Scattering of Blood

Equation 7.10 is based on a model that assumes single scattering of the incident laser light by the RBCs. The validity of this assumption, however, may be questionable in view of previous studies that demonstrate a predominance of multiple scattering when visible light interacts with whole blood. Thus, in a blood layer of 100 mm, the photon mean free path length at a wavelength ® = 0.6328 mm is only 7 mm [22], and multiple scattering of light by the RBCs is expected to be important [23]. Therefore, for blood vessels with diameters typically between 50 and 200 mm, photons would be expected to

have undergone a great number of scattering events and, consequently, of Doppler shifts before being detected.

7.2.7.2 DSPS from RBCs Flowing in a Glass Capillary Tube

Four DSPS from whole blood (hematocrit, 41%) ßowing at a maximum speed of 1.44 cm/s through a glass capillary tube with a 200-mm internal diameter are shown in Fig. 7.6. The expected Dfmax was 5.9 kHz. Clearly, the DSPS obtained in 51.2 s does not exhibit the rectangular shape of the DSPS predicted for a dilute suspension of latex spheres (Fig. 7.5). There is no discernible cutoff at the expected Dfmax but a rather a monotonic decrease in the amplitude at the higher frequencies. The spectral power beyond 5.9 kHz is most likely the result of multiple scattering as the laser light penetrates into and exits from the ßowing medium [2, 24]. The DSPS obtained in 3.2 s has essentially the same characteristics. However, since the measurement time is much shorter, the statistical ßuctuations in Pi (Df ) are increased, as expected. One also observes that the DSPS obtained in 0.4 s exhibits a greater increase in the

0.2

0.8

f (KHz)

Fig. 7.7 DSPS from a human retinal vein obtained in 0.1, 0.2, and 0.8 s, demonstrating the effect of decreasing the measurement time. With a short measurement time, the cutoff frequency Dfmax can be more precisely detected (Adapted from Riva et al. [13] with permission from the Publisher)

multiple scattering of light by the RBCs. The detected light is depolarized, and the corresponding DSPS does not present a sharp cutoff but rather has a smoothly declining shape (Fig. 7.8), which does not vary with the scattering angle. Such DSPS conform to the model of Bonner and Nossal when multiple scattering is the dominant process [26].

7.2.8Computer Modeling of the

DSPS for Automatic Determination of Äfmax

In the early days of retinal blood velocity recordings by LDV, the photocurrent was fed to a tape recorder, and a loudspeaker and the DSPS were recorded during playback. Typically, for veins and arteries during diastole and often during systole, the frequencies of the DSPS are in the audio range. Therefore, during playback, only those portions of the tape were analyzed for which a clearly identiÞable pulsatile pitch (for arteries) or a monotonous, high-frequency pitch (for veins) could be heard [28]. The DSPS were obtained with a hardware spectrum analyzer, one pair at a time, and successively displayed on an oscilloscope screen. An examiner visually deter-

mined the Dfmax, one channel at a time, by moving a cursor along the frequency axis to the

frequency value where a sharp decline in the power spectral density and variance was identiÞable. Each estimate of Dfmax (mean and standard deviation) was based on 10Ð20 pairs of DSPS. Such a procedure was time-consuming, especially for retinal arteries, for which several Dfmax were measured at different phases of the heart cycle to obtain average Vmax during the heart cycle. In addition, masking of the examiner with respect to the type of patient and experimental protocol to eliminate possible bias was an additional time-consuming procedure.

Fig. 7.8 Left: DSPS obtained from a vein in the tapetal region of the cat retina. The tapetum is a highly light reßecting layer. For the upper DSPS, the scattered light was detected in the same plane of polarization (//) as the incident light. For the lower DSPS, these polarizations were perpendicular (//). Light transmitted through the blood is highly reßected and some of it retransmitted through the blood. This double transmission represents predominantly multiply scattered light. Right: DSPS from

a vein in the pigmented (highly absorbing) region of the fundus. Notice the disappearance of the spectral power when the polarization of the scattered light was perpendicular (^) to that of the incident light. For vessels above the pigment, only the light backscattered by the blood column reaches the detector. The light transmitted through this column is totally absorbed by the pigment behind the vessel (Adapted from Riva et al. [22] with permission from the Publisher)

Later, to automate the analysis, a computer algorithm to calculate Vmax based on the aforementioned rectangular shape model of the DSPS was implemented on a NeXT computer [29]. It includes data acquisition, eye blink rejection, power spectrum analysis, and display of the Vmax data and of its change during the heart cycle.

More recently, a digital signal processor (DSP)-based approach, which addresses the need for higher temporal resolution of Vmax, combined with blink rejection, was reported [30]. In brief, blink rejection is based on the fact that because the laser light is out of focus at the pupil plane, closing the lid scatters much less laser light back to the detector than does the fundus. This results in a markedly reduced DC value of the photocurrent. Whenever the DC value of the Doppler signal falls below a user-adjustable threshold, the

data is automatically excluded from further analysis and presentation.

7.2.9Instrumentation

A bidirectional retinal laser Doppler velocimeter (RLDV) consists basically of distinct optical systems with the functions of: (1) aiming a laser beam (red or near-infrared) at a main retinal vessel; (2) collecting and detecting some of the light scattered by the blood in the vessel along two directions of scattering;

(3) observing the eye fundus and the laser beam; and (4) providing a pinpoint fixation target to be observed by the eye being tested in order to precisely aim the laser at the desired site [13].