2.1.

Optical System

The device consists of five optical systems (Fig. 2): green illumination of the ONH, observation of the ONH, Schlieren LDF unit, projection of a fixation point coupled with the projection of a two wavelengths flicker illumination of the fovea and its surroundings and dedicated illumination, and observation of the eye pupil, which is not shown in Fig. 2. Observation of the ONH, fixation and flicker for the fovea and Schlieren LDF are the identical optical systems (lenses $L_{o1}=L_{f1}$, $L_{o2}=L_{f2}=L_{s2}$) with a magnification of 2.27 from the fundus to the last image. Conjugate pupils are labeled as $P_x$ and conjugate images as $I_x$.

Fig. 2

Optical system with the illumination (ONH and fovea for the flicker light), observation and LDF system. Indices $o$, $f$, and $s$ stand, respectively, for the pathes of observation, fixation/flicker and detection, and $i$ for intermediate. $I$ and $P$ stand for images and pupils conjugate planes, respectively. The illumination and observation of the eye pupil are not shown here.

Illumination of the ONH: A two lens system images a diffusing light source (505 nm, 20 nm full width at half maximum) onto the ONH with a field limitation of $\pm 3\mathrm{deg}$. The light pathway is separated from the other optical systems.

Observation of the ONH: Lenses $L_{o1}$ and $L_{o2}$ image the fundus $I$ onto a charge coupled device camera (B&W camera, $659\times 494$, imaging source) placed at $I_1$. An example of a fundus image is given in Fig. 3. In the eye pupil, light footprints of the illumination and observation are separated by 3 mm in order to avoid back-reflection from the illumination into the observation path.

Fig. 3

Example of an image of the fundus is taken by the instrument. The probing beam can be seen in the middle of the image.

Schlieren LDF unit: Probing light, located in the plane $I_4$, is delivered by a laser diode at 785 nm with a power of 90 μW at the eye pupil, which conforms to the American National Standard Institutes for laser safety.¹² The beam-splitter ${\mathrm{BS}}_o$ reflects near-infrared (NIR) and an absorption filter $F$ ensures that only the probing light is detected at $I_3$ by an avalanche photodiode (C5460-1, Hamamatsu, Japan). An aperture stop of 2.4-mm diameter at $P_3$ limits the probing laser beam and an annulus aperture (from 2.4 to 8 mm in diameter) at $P_2$ limits the detected light. This avoids reflected laser light at the eye pupil ($P$). Pupils $P_2$ and $P_3$ are placed on the faces of the polarizing beam-splitter PBS. The Schlieren arrangement consists of an annulus field stop (from 45 to 300 μm in diameter) in the detection plane $I_3$ and of a point source at the probing light source plane $I_4$.

Fixation point and flicker illumination of the fovea: Optical axis of the fixation and the observation build an angle of 15 deg. The fixation point in plane $I_2$, which can be moved perpendicularly to the optical axis, consists of a 670-nm laser diode of 1.2 μW at the eye pupil $P$. By asking the subject to look at this point located in the foveola, the probing beam can be placed on the desired location on the ONH for an LDF recording. Along the optical path to the fovea, a dichroic beam-splitter ${\mathrm{BS}}_f$ placed at a conjugate pupil plane reflects light coming from two LEDs (470 and 525 nm) modulated at 10 Hz, which illuminates the fovea and its surroundings ($\pm 6\mathrm{deg}$) with an intensity of 4 μW. When one of these LEDs is turned on, the intensity of the illumination of the ONH is also modulated in phase and in frequency with the flicker illumination.

The entrance position of the probing beam into the eye, which defines the angle of the incidence of the probing beam onto the ONH and thus the Doppler frequency shift, should remain the same from one measurement to the other. To ensure this, a second camera points to the eye pupil, which is illuminated by a dedicated NIR light. Thus the entrance position of the probing beam within the eye pupil can be checked and if necessary the head of the subject can be adjusted.

2.2.

Signal Analysis

Bonner and Nossal¹³ proposed a theoretical model, which was primarily intended for scattering tissues such as skin, but not the eye fundus. Based on this model, a fast Fourier transform computer implementation for measuring blood flow in the ONH was used.¹⁴ Using the same analysis technique, a new code was written in LabView and first tested with a MATLAB procedure. Substantial automatic analysis based on noise level, signal amplitude, and power spectrum level were implemented and explained below. In this theory, a probabilistic model is postulated for the interaction between photons and red blood cells. The relation between power spectrum of Doppler-shifted light $\mathrm{PS}(f)$ and laser Doppler perfusion parameters volume, Vol, in arbitrary units and velocity, Vel, in Hertz can be established quantitatively as

The power spectrum $P(f)$ of the detector output current (or, accordingly, the one of the digital signal $x[n]$) is not equal to or proportional to the Doppler-shifted light spectrum $\mathrm{PS}(f)$, but is also influenced by a nonzero DC and by a shot-noise.^13,15 In order to estimate Vel and Vol, the following quantities are computed:

As mentioned above, the software performs and analyzes the Fourier transform of the photocurrent $i(t)$ with a bandwidth of 120 kHz at a rate of 14.7 acquisitions per second. It automatically removes data when a sudden change in the blood volume occurs, which is mainly due to microsaccades, if power spectrums are too low, i.e., close to the noise level and if the DC of the data is outside a range of $\pm 10\%$ of the most probable value of the whole recording.

Due to the fact that back-scattering is a function of the optical properties of the eye (cornea, lens, vitreous, ONH tissue) and the angle of the incident and collecting beams, only changes in LDF perfusion parameters Vol, Vel, and BF are relevant. The absolute values cannot be compared between subjects.

3.1.

Linearity

A simulator, consisting of a single lens (20-mm focal length) and a rotating Teflon^© wheel, is used to produce Doppler shifts. All teflon scattering particles move approximately with the same velocity. Frequency shifts of light increase with the multiple scattering and in turn decrease as it decreases. With the chosen geometry, the induced power spectrum is close, but not identical, to that obtained from the human eye, i.e., Vol and Vel have similar values. Because the amount of back-scattered light is independent of the rotating speed, Vol should be constant, Vel is expected to be linear with the rotating speed and consequently BF, too. The speed of the surface of the wheel, which scatters light, is proportional to the rotating frequency $f$.

3.2.

Sensitivity

The minimum statistically significant change in an LDF parameter that can be detected with the device for a given experiment with $N$ subjects is defined as

3.3.

Response to Flicker

The pupil of the fixator eye of each subject was dilated with one drop of tropicamide 0.5%. After a rest of 20 min, the subject was asked to look at the fixation point and the probing laser was directed to the temporal superior field of the ONH in the tissue, where there were no vessels (Fig. 3). A continuous recording of 80 s was started. After 20 s, the 10 Hz flicker light was applied for 40 s. Statistical changes of BF were analyzed with a programming language $R$ ( www.r-project.org) and SPSS statistics. Data were analyzed using the mixed models procedure. (LDF parameters were defined as repeated measures, flicker was defined as a fixed effect during the 20- to 60-s period, and subject was defined as random effect.) The entire flicker period was selected to quantify the BF, Vel, and Vol changes.

4.1.

Linearity

The rotating wheel does not simulate a perfused tissue, but produces a power spectrum similar to those of ONH (Fig. 4).

Fig. 4

Blood flow parameters for the cohort of 12 subjects at the baseline and the 17 measurements done at different rotating speeds give similar results. The thick line within the box is the median, the box height represents the first quantile of the data and the upper and lower lines are 1.5 interquartile distance.

With $U$ the applied voltage on the motor, we found that the rotating frequency $f$ of the motor is a linear function of $U$: $f=(0.250\pm 0.001\mathrm{Hz}/\mathrm{V})$ $U-(0.036\pm 0.008\mathrm{Hz})$.

Therefore, in the following, the flow parameters are expressed as a function of the voltage $U$.

As expected, Vel is highly linearly dependent of $U$ ($\mathrm{Vel}=233·U+341$; $R^2=0.87$; $p<0.0001$). Vol, which should be independent, exhibits a slight increase over the whole span of the voltage used for that experiment ($\mathrm{Vol}=408·U+1032$; $R^2=0.66$; $p<0.0001$). Finally, BF is also linearly dependent of the voltage [$\mathrm{BF}=656·U+93$; $R^2=0.98$; $p<0.0001$, see Fig. 5(a)].

Fig. 5

(a) Calculated flow as a function of the speed of the wheel. (b) Power spectrum of the wheel at rest, which is about $100\times$ lower when the wheel is rotating. (c) Power spectrum at the lowest (black) and the highest (gray) speeds. A power spectrum obtained from the human eye is very similar.

4.2.

Sensitivity

Within the flicker experiment, we considered the baseline as two recordings of 10 s. For the 12 subjects, we found a sensitivity at $p=0.05$ of 5.3%, 12.4%, and 7.6% for Vel, Vol, and BF, respectively.

4.3.

Response to Flicker

Twelve healthy caucasian subjects were included [$30.0\pm 2.3$ (SEM) years old, $-0.8\pm 0.3$ diopters, nine men and three women]. During flicker stimulation, the increase of blow flow ($17.8\pm 12.9\%$, $p<0.001$) was concomitant with the rise of velocity ($+17.4\pm 12.7\%$, $p<0.001$). Volume did not significantly change ($p=0.16$).

Linear fits between Vol or Vel and DC give coefficients of determination $R^2$ smaller than 0.19. A larger value ($R^2=0.42$) is found between Vel and Vol. A Pearson’s correlation gives slightly higher values (0.27 and 0.59).