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Theoretical Analysis of a Spectrophotometric Technique for
Measuring Oxygen Saturation in Retinal Vessels
M. Üzümcü1, F.M. Vos1, A.M. Vossepoel1, G.L. van der Heijde2
1. Pattern Recognition Group, Department of Applied Physics, Delft University of Technology,
Lorentzweg 1, 2628 CJ Delft, The Netherlands
2. Depts. of Ophthalmology and Clinical Physics and Informatics, Academic Hospital of the Vrije
Universiteit, De Boelelaan 1117, 1081 HV Amsterdam, The Netherlands
e-mail: {mehmet, albert, frans}@ph.tn.tudelft.nl
Keywords: Retinal oximetry, spectrophotometric methods, optical density, image processing.
Abstract that hypoxia has a stimulating effect on
Diabetes mellitus patients often suffer from neovascularisation [1], the formation of pathological
diabetic retinopathy (DRP), a disease that new vessels [2]. Such new vessels block sensitive
reduces vision significantly. The main cause areas of the retina and can cause bleeding in the eye,
of this disease is probably hypoxia, lack of retinal detachment or glaucoma, which are major
oxygen. In this paper a precision analysis of causes of visual loss.
a non-invasive method to calculate the At present DRP is diagnosed clinically by fundoscopy
oxygen saturation in the retina in order to and fluorescence angiography. In this method a
diagnose DRP is presented. Simulations fluorescent dye is injected in the patient, which
show that this approach is promising. spreads all over the body through the blood vessels.
Upon excitation of the fluorophore, the vessels in the
retina can be visualised using a fundus camera (see
1. Introduction figure 1.2) and newly formed vessels show a
characteristic leaking pattern.
1.1 Diabetic retinopathy Unfortunately no information is obtained on risk areas
where new vessels might start forming. If the oxygen
The retina is one of the posterior layers of the human
saturation is known to be low in a certain region, the
eye. Here the cones and rods are situated, that make
formation of new vessels may be prevented by
the eye sensitive to brightness and colour. Figure 1.1
targeted laser treatment, by which the pathologically
is a schematic of the eye in which the retina is
active regions of the retina are ablated with the
depicted.
intention to reduce the oxygen consumption in that
area.
Figure 1.1: schematic of the retina
When the flow of blood in the retina is reduced, the
retinal tissue lacks oxygen. Eventually this may cause
diabetic retinopathy (DRP), the most common of
ischaemic retinal diseases. It has been demonstrated Figure 1.2: fluorescence angiography picture
1.2 Spectrophotometry 2. Theory
To determine the oxygen saturation of retinal blood A three-wavelength model was developed by Pittman
Delori [3] has developed a three wavelength & Duling [4,5] and Delori [3]. This method is based
spectrophotometric model. The principle of this on the difference in light absorption of oxygenated
technique is reflection oximetry (see section 2). haemoglobin (HbO2) and deoxygenated haemoglobin
To do non-invasive measurements, the retina is (Hb). Figure 2.1 shows the difference in absorption of
illuminated from outside the eye through the pupil. HbO2 and Hb.
This causes a number of problems. As various layers For blood containing a mixture of Hb and HbO2, the
of the human eye – such as the cornea, the lens, etc. - specific extinction coefficient at a known O2sat and a
will absorb, reflect and scatter some of the light. measuring optical wavelength (λ) is given by:
These effects are not accounted for in the three-
wavelength model. To compensate for these effects Eλ = Eo ,λ ⋅ O2 sat + Er ,λ ⋅ (1 − O2 sat ) (2.1)
the introduction of several extra parameters is
necessary. Then the question arises, however,
Which can be rewritten as:
whether it is possible to estimate the extra variables.
Calculations that we have done, show that these extra
parameters cannot be estimated with significant Eλ = Er,λ + ∆λ • O2sat (2.2)
precision.
Earlier attempts to determine the retinal oxygen In these formulas Eλ is the specific extinction
saturation were purely empirical. In this paper we will coefficient for a mixture of HbO2 and Hb
describe an elaborate evaluation of a three-parameter (cm2/µmole), Eo,λ is the specific extinction coefficient
six-wavelength model, including an error analysis. of HbO2 (cm2/µmole), Er,λ is the specific extinction
This paper is organised as follows. In section 2 the coefficient of Hb (cm2/µmole) and ∆λ≡Eo,λ-Er,λ.
theoretic model is explained. This is followed by
details about the used equipment and several settings For wavelengths between 500 and 600 nm the optical
of the peripherals in section 3. Section 4 describes the density depends on the specific extinction coefficient
method that we use to calculate the parameters. The of blood as follows:
Dλ = S + sCd (E r ,λ + ∆ λ ⋅ O2 sat )
results of these calculations and a noise analysis are
presented in section 5. Finally in section 6 some (2.3)
conclusions are presented.
where Dλ is the optical density, C the total
haemoglobin concentration (µmole/cm3), d the path
16
14
specific extinction coefficient (cm /µmole)
12
3
10
HbO2
Hb
8
6
4
522 548 558 569 577 586
2
0
500 505 510 515 520 525 530 535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640
wavelength (λ)
Figure 2.1: absorption spectra of Hb and HbO2
length (cm), S and s wavelength independent capture the images. This camera is connected to an 8-
parameters that describe the light scattering by red bit analogue to digital converter (ADC or digitiser),
blood cells (RBC’s). which is located in a personal computer (Pentium 90
These parameters cannot be measured directly. The with 128 MB RAM).
parameters that can be measured are the intensities of With this set-up six 8-bit grey value images of the
light reflected at the vessels and the background. retina can be made within 0.25 seconds. Figure 3.2
With these intensities the optical density can be shows such an image.
determined as follows:
V
Dλ = − log (2.4)
B
where V is the intensity of the reflection at the vessel
and B is the same for the background.
This method requires measurements of the optical
density at at least three wavelengths to solve the three
unknown parameters: S, the product of sCd and, most
importantly, O2sat.
3. Hardware
3.1 Equipment
In our experimental set-up (see figure 3.1), that is
developed by the department of Clinical Physics and
Figure 3.2: 8-bit grey value image of the retina.
Informatics of the VU academic hospital, images of
An area of 3 x 3 mm2 is shown.
the retina are acquired using a modified Zeiss fundus
camera.
3.2 Safety
If the retina is not properly illuminated or if it is
illuminated with high intensities of light, it can be
severely damaged. In our case, for short irradiance
duration (<1 sec.), only thermal damage might occur,
when the intensity of the light is too high. Blue light
damage can be ruled out, because our measuring
wavelengths are all above 500 nm.
To make sure that there is no thermal damage to the
retina, intensity measurements were done at several
Figure 3.1: Schematic of experimental set-up. The settings of the light source.
unlabeled elements represent lens systems of the fundus A light sensor (Tektronix J16 Digital Photometer) was
camera. placed in the hotspot of the fundus camera, which is
the focus point of the illumination beam. To
A fundus camera is a tool, which provides a magnified determine the maximum intensity of the light, the
image of the retina. To be able to get a view, filter that transmits most light was selected in the filter
illumination of the retina is necessary and to this end a wheel. The intensity in the hotspot was measured at
xenon light source (Storz xenon 300) is used. The several settings of the light source.
light exiting the source is coupled through glass fibre Results are shown in the following table.
to a filter wheel, which contains six filters of different
wavelengths (see figure 2.1).
After filtering, the monochromatic light is coupled
into the fundus camera to illuminate the retina.
An Adimec MX12 CCD-camera with a resolution of
1024x1024 pixels is mounted on the fundus camera to
Light source (%) I (W/m2) coefficients of oxygenated hemoglobin and reduced
5 456 hemoglobin is zero, the so called isobestic
wavelengths. This placement of the filters was chosen
10 711 originally to simplify the calculation of the model.
25 1411 16
50 2725
14
Table 3.1: Intensities on retina (I) as function of light source
specific extinction coefficient
12
setting
10
HbO2
According to a report of the “Gezondheidsraad” 8
Hb
(Dutch Health Council) [6] thermal damage occurs at
a retinal intensity of 105 W/m2. To acquire images of 6
the retina a setting of 25% of the light source is used, 4
which corresponds with an intensity of 1411 W/m2. 2
To rule out retinal damage, shutters have been
installed in the filter wheel. These shutters 0
500 505 510 515 520 525 530 535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640
automatically close when the light source is set higher wavelength (λ)
than 40% or when one of the filters breaks and Figure 5.1: extinction curve with filters positioned at new
transmits intensity more than 2200 W/m2. Also in wavelengths.
case of a malfunction, e.g. an electrical failure, the
shutters will close. One might imagine, however, if it’s not more efficient
– with present computing power and non-linear
4. Method parameter estimation methods – to place all of the
Measurements at six wavelengths are performed to filters at wavelengths of maximal difference in
calculate the three unknown parameters in the model, specific extinction coefficients, i.e. at 532 nm, 542
explained in section 2. These wavelengths are nm, 555 nm, 565 nm, 577 nm and 592 nm. In figure
depicted in figure 2.1. 5.1 these new wavelengths are depicted. To explore
An algorithm to solve the equations numerically is this possibility an experimental design study has been
implemented. This algorithm is based on the done.
Levenberg-Marquardt [7] method, which is an
iterative method that uses the forward difference
approximation of the Jacobian of the set of equations 5. Results
to estimate the solution of the unknown parameters by The result of a simulated noise analysis, in which
means of a least squares fit. The standard deviations noise with varying levels is added to the calculated
of these estimated parameters (σ) can be calculated as data, was that a noise level of 3 on a scale of 0 to 255
follows, using the known Jacobian [8] : on the grey values of vessel and background results in
a precision of 8% in O2sat.
SSres In the test-images of retinas the noise per pixel is
C= ⋅ ( J T J ) −1 (4.1) approximately 20 grey values. Averaging over a
n− p number of pixels reduces the noise significantly. To
obtain a noise level of 3 grey values for which σO2sat =
with C the covariance matrix, SSres the residual sum of 0.08, averaging must take place over at least 49 pixels.
squares, J the Jacobian, n the number of equations and Figure 5.2 shows the relation between the standard
p the number of unknown parameters. The diagonal deviation in the oxygen saturation (O2sat) and the
of C consists of the squares of the standard deviations number of pixels used for averaging.
of the parameters. In this case n=6 and p=3, so the Although simulations with noise at the new
system has three degrees of freedom. wavelengths showed a slight decrease in the standard
deviations of the estimated parameters at high noise
As shown in section two, six filters at distinct levels, in the region that we are interested in (σ <
wavelengths are used to acquire images of the retina. 0.10), there is no significant improvement in the
Four of these filters are placed at wavelengths, where precision of the parameters. The result of the
the difference between the specific extinction
experimental design, therefore, is that there is no [4] Pittman RN, Duling BR. A new method for the
necessity to change the present filters. measurement of percent oxyhemoglobin. J Appl
Physiol 1975; 38:315-20
0.45
0.40 [5] Pittman RN, Duling BR. Measurement of percent
standard deviation in O2sat
0.35 oxyhemoglobin in the microvasculature. J Appl
0.30 Physiol 1975; 38:321-7
0.25
0.20
[6] Optische straling; Rapport Gezondheidsraad 1993:
0.15
Gezondheidskundige advieswaarden voor
new filters
0.10 old filters
blootstelling aan elektromagnetische straling met
0.05
golflengten tussen 100nm en 1mm (Report of the
Dutch Health Council on optical radiation)
0.00
0.00 0.00 0.01 0.10 1.00
1 / #pixels (on log scale) [7] Press WH, Teukolsky SA, Vetterling WT,
Flannery BP, Numerical Recipes in C. Cambridge
Figure 5.2: standard deviation in O2sat as function of University Press, 1996.
1/#pixels for present situation (old filters) and experimental
design situation (new filters). [8] Bates DM, Watts DG, Nonlinear regression and its
applications. New-York, Wiley, 1988.
6. Conclusions
It was demonstrated that the error in the retinal
oxygen saturation will be less than 8% when
averaging over 49 pixels. The simulations also
demonstrate that it is not necessary to use filters at
non-isobestic wavelengths.
Further experiments and error analysis are necessary,
however, to determine the effects of poor focussing,
orientation of the eye, pigmentation, etc.
Acknowledgement
We would like to thank Dr. I. van Stokkum (dept. of
Physics, VU Amsterdam) for his help on the
parameter estimation and experimental design study.
References
[1] Tiedeman JS, Kirk SE, Srinivas S, Beach JM.
Retinal oxygen consumption during hyperglycaemia
in patients with diabetes without retinopathy.
Ophthalmology 1988; 105:31-36
[2] Hogeboom van Buggenum IM, Van der Heijde
GL, Tangelder GJ, Reichert-Thoen JWM. Ocular
oxygen measurement. British journal of
Ophthalmology 1996; 80:567-573
[3] Delori FC. Non-invasive technique for oximetry
of blood in retinal vessels. Applied Optics 1988;
27:1113-25
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