Macular pigment density assessed by directional fundus reflectance

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Gorrand et al. Vol. 26, No. 8 /August 2009 /J. Opt. Soc. Am. A 1847

Macular pigment density assessed by directionalfundus reflectance

Jean-Marie Gorrand,1,* Michel Doly,1 and Franck Bacin1,2

1Université d’Auvergne, Biophysique des Handicaps Sensoriels, EA 2667, BP 38, Clermont-Ferrand, F-63001 France2CHU Clermont-Ferrand, Service d’Ophtalmologie, BP 69, Clermont-Ferrand, F-63003 France

*Corresponding author: [email protected]

Received December 5, 2008; revised April 25, 2009; accepted June 16, 2009;posted June 30, 2009 (Doc. ID 104910); published July 29, 2009

Light radiated from foveal photoreceptors was analyzed in the eye’s pupil at 470 nm and 532 nm. The reflec-tance of the inner limiting membrane was then measured at 6 deg from the fovea for the same wavelengths,allowing us to determine the macular pigment (MP) density Ddir using the directional reflectance technique. Inaddition we measured the MP density Dnd using the nondirectional reflectance technique (26 subjects). Themean values of Ddir and Dnd were 0.419±0.097 and 0.195±0.042 D.U., respectively (sample field of 2 deg). Theywere highly correlated �p�0.0001�. Comparison of Ddir and Dnd implies that 57±12% of the light reflected fromthe fovea comes from layers anterior to MP at 470 nm. The mean directionality factors � that we have mea-sured at 470 nm and 532 nm were equal to 0.239±0.028 and 0.210±0.028 mm−2, respectively. They were cor-related �p�0.0001� and followed the spectral dependence suggested by Marcos. © 2009 Optical Society ofAmerica

OCIS codes: 330.7326, 330.7331.

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. INTRODUCTIONhe optical density of macular pigment (MP) can be mea-ured by psychophysical or optical methods. For half aentury optical methods have been dominated by the re-ectometry technique, in which the reflectance spectrumf the retina at the fovea is compared with the reflectancepectrum at the perifovea. This method was first devel-ped in 1952 by Brindley and Willmer [1]. Yet reflectom-try estimates of macular pigment density (MPD) areower than those found by psychophophysical methods2–10]. MP is deposited preferentially in the photorecep-or axon and inner plexiform layers of the retina. Severaluthors have suggested that the small values of MPD pro-ided by reflectometry are caused by the anterior reflec-ions from the retinal nerve fiber layer (RNFL), the innerimiting membrane (ILM), and the ocular media [4,7]. De-ori et al. ([7], p. 1226) also suggested that “scattering ofight by Henle’s fibers contributes to the anterior reflec-ions as well as reducing the path through the MP to lesshan a double pass.” Different optical methods have beeneveloped to avoid these spurious internal reflectionshen measuring MPD. The autofluorescence technique ofelori et al. [7] takes advantage of the location of the fluo-

ophores behind MP. They measured an MPD of.48±0.16 D.U., compared with 0.23±0.07 D.U. with theeflectometry technique (in the same group of 159 sub-ects).

Another way to eliminate these effects from light re-ected by layers anterior to MP is to analyze the direc-ional component reflected by the fundus, a techniquealled directional reflectance spectroscopy [11]. Light ra-iated from photoreceptors passes twice through MP, but

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tray light, which does not show a directional dependence,s virtually eliminated in the analysis of the directionaleflectance. Recently Zagers et al. [12] designed the fovealeflection analyzer (FRA), which is capable of measuringoth the spectral and the directional aspects of fundus re-ectance in the wavelength range 420–790 nm. Using theodel of van de Kraats et al. [4] they could derive anPD of 0.560 D.U. in the aged group [11].Although most methods estimate the MPD from a den-

ity difference between foveal and perifoveal sites, allow-ng elimination of the influence of absorption in the ocular

edia, fundus reflectance spectroscopy provides MPDalues without the need of a reference spectrum at a pe-ipheral location. The model contains four free param-ters whose values are adjusted to produce a match with

full reflectance spectrum from 400 to 800 nm. Zagersescribes the spectral absorption of the lens by the sum ofwo functions, a “young” and an “aged” template. In a re-ned model, van de Kraats and van Norren [13] modifyhese two templates and add a third one, the “Rayleighcatter” template. They found an MPD of.391±0.156 D.U., lower than the estimate of Zagers0.560 D.U.�: such a difference arises from the criticalhoice of the templates for spectral lens absorption.

To avoid the problem of spectral absorption templates,e introduce a new procedure that eliminates the con-

ounding influence of these anterior scattering structuresy measuring the directional components in the fovea at70 and 532 nm, then the reflectance of the ILM at 6 degccentricity, also at 470 and 532 nm, so that we minimizehe influence of the spectral characteristics of the ocularedia and of the instrument (directional reflectance tech-

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ique). In addition we measure the MPD with the methodf Brindley and Willmer [1] (nondirectional reflectanceechnique).

. PRINCIPLES. Fundus Reflectancehe MPD is determined by measuring the spatial distri-ution in the eye’s pupil of light radiated from photorecep-ors. Figure 1(a) shows a foveal cone oriented toward theoint I of the pupil (whose center is O). Light enters theye through the entrance pupil (diameter 0.2 mm) cen-ered about a point J close to I. A large fraction of incom-ng light is guided along the myoid, ellipsoid, and outeregment. Light reflected by the posterior tip of the outeregment and/or the ellipsoid/outer segment junction isuided backward and radiated from the myoid toward theye’s pupil. A diffuse (nondirectional) component that uni-ormly fills the pupil is added to the directional compo-ent. Figure 1(b) presents the distribution of light in theupil. The arrow indicates the position where light entershe eye. The surfacic flux in the pupil (defined as the fluxer area unit) is described by the sum of a Gaussian func-ion (amplitude Q) and a constant (amplitude CF) [14,15].

ig. 1. Directional component (at the fovea). (a) Light is guidedackward along the photoreceptor and radiated from the myoidoward the eye’s pupil. In addition a diffuse component uniformlylls the pupil. O, center of the eye’s pupil; I, point where the pho-oreceptor axis intersects the pupil; J, center of the entrance pu-il. (b) Distribution of light in the eye’s pupil. The arrow indi-ates the position where light enters the eye. The surfacic flux inhe pupil is described by the sum of a Gaussian function (ampli-ude Q) and a constant (amplitude C ).
F
he amplitudes Q and CF will be used to calculate thePD by the directional and nondirectional reflectanceethods, respectively.At 6 deg from the fovea, we assume that the inner lim-

ting membrane (ILM) inside the sample field A is close tospherical mirror [Fig. 2(a)]. The beam coming from J il-

uminates the retina and is reflected by the ILM. Thisseudomirror forms an image J1 which is conjugate to J.he beam goes through the eye’s pupil in an area A2round J2. If we choose an entrance pupil far from thetiles–Crawford (S-C) peak, the guided modes cannot bexcited inside photoreceptors, and the distribution of lightn the eye’s pupil [Fig. 2(b)] comes from the ILM, the reti-al nerve fiber layer (RNFL), and the other nondirec-ional scattering layers. Light backscattered from theNFL has an extension that is smaller than the eye’s pu-il, but much larger than the area A2 of the ILM reflex16]; it remains roughly constant along A2. Consequentlye can determine the amplitude CP of the nondirectional

omponent and measure the flux Fspec carried by the ILMeflex. The parameters Fspec and CP will be used as refer-nces in the perifovea with the directional and nondirec-ional reflectance methods, respectively.

ig. 2. Specular reflection of the ILM (in the perifovea). (a) Wessume that the ILM is close to a spherical mirror inside the reti-al area A. The beam coming from J illuminates the retinal areaand is reflected by the ILM. This mirror forms an image J1 that

s conjugate to J. The beam goes through the eye’s pupil aroundhe point J2 (spot A2). (b) Distribution of light in the eye’s pupil.he arrow indicates the position where light enters the eye.ight backscattered from the RNFL has an extension which ismaller than the eye’s pupil, but much larger than the area A2 ofhe ILM reflex; it remains roughly constant along A2. CP, ampli-ude of the nondirectional component.

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. Directional Reflectance Method

. Foveahe surfacic flux in the eye’s pupil [Fig. 1(b)] is describedy a function SF that is the sum of a constant and aaussian function [14,15]:

SF�x,y,�� = CF�� + Q�� 10−��x − x0�2+�y − y0�2�, �1�

here x0 and y0 give the position of I in the eye’s pupilpositive x, temporal; positive y, superior), �� is the di-ectionality factor, and CF�� and Q�� are the amplitudesf the nondirectional and directional components, respec-ively.

The radiant flux carried by the directional components

Fdir = Q�� 10−��x2+y2�dxdy, �2�

Fdir =�

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Q��

��. �3�

efore reaching the photoreceptor layer, and after beingadiated, light is absorbed in the ocular media and theacular pigment. The spectral transmission TF��

hrough these media is expressed as [7]

TF�� = �2��10−2DF�460�Kmp��, �4�

ith �� the transmission factor of the ocular media,F�460� the MP density at 460 nm, and Kmp�� the extinc-

ion coefficient of MP relative to that at 460 nm.We define Rphot�� as the ratio between the flux radi-

ted backward from the myoid and the flux incident onhe photoreceptor (with J aligned to its axis). Such aodel predicts a radiant flux carried by the directional

omponent equal to

Fdir�� = Finc��TF��Rphot��, �5�

ith Finc�� the radiant flux incident on the eye (in a solidngle subtended by the sample field). Equating Eqs. (3)nd (5) gives

TF�� =�

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1

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��

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et �1 and �2 be two wavelengths in the high- and low-bsorption ranges of MP, respectively. Following Burns etl. [17] and Vohnsen et al. [18], who assume that Rphot��hows spectrally neutral behaviour, we obtain

TF��2�

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sing the expression of TF�� from Eq. (4), we can rear-ange Eq. (7) as

2�Kmp��1� − Kmp��2��DF�460�

= log��1�Q��2�

Q��1��2�+ log

Finc��1��1�

Finc��2��2�. �8�

. Perifoveahe surfacic flux in the eye’s pupil [Fig. 2(b)] is describedy a function SP which is the sum of three terms:

SP�x,y,�� = CP�� + Srnfl�x,y,�� + Sspec�x,y,��, �9�

here CP is the amplitude of the nondirectional compo-ent, Srnfl the surfacic flux backscattered from the RNFL,nd Sspec the surfacic flux reflected by the ILM. The func-ion Srnfl has an extension much larger than A2 and re-ains roughly constant along A2 [16]. Consequently Sspec

an be obtained by subtracting CP and the mean value ofrnfl around A2 from the function SP. The RNFL is noteutral, but this does not cause any error in the measure-ent of Sspec since it is determined by subtraction. Theux carried by the spot A2 is measured as

Fspec =�� Sspec�x,y,��dxdy. �10�

Let Rspec�� be the reflectance of the ILM [19]. The fluxarried by the spot A2 is predicted as

Fspec* �� = Finc��TP��Rspec��, �11�

here TP�� is the spectral transmission of light throughhe media at the perifovea,

TP�� = �2��10−2DP�460�Kmp��, �12�

ith DP�460� the MPD in the perifovea (at 6 deg in theemporal retina). Assuming that the spectral reflectancef the ILM is neutral, we obtain an equation similar toq. (7),

TP��2�

TP��1�=

Finc��1�

Finc��2�

Fspec* ��2�

Fspec* ��1�

. �13�

inally Eq. (13) is rearranged as

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Fspec* ��1�

+ logFinc��1��1�

Finc��2��2�. �14�

. Optical Density Ddiret Ddir=DF�460�−DP�460� be the MPD difference be-ween the fovea and the perifovea. Combination of Eqs.8) and (14) gives

Ddir =0.5

Kmp��1� − Kmp��2��logQ��2�

Q��1�

��1�

��2�− log

Fspec* ��2�

Fspec* ��1�� .

�15�

�� and �� are derived from the fit to Eq. (1), and*spec�� from Eq. (10).

. Nondirectional Reflectance Methodhe density difference Dnd between the fovea and theerifovea is derived from the amplitudes CF�� and CP��f the nondirectional components (Subsection 2.A). Thenalysis of Subsection 2.B remains effective if we replacehe directional flux �Q�� /�� by the background ampli-ude �C �� at the fovea, and the specular flux �F ��
F spec

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y the background amplitude �CP�� at the perifovea.herefore the density difference Dnd between the foveand the perifovea follows from Eq. (15), where such sub-titutions are made. Assuming that all the reflected lighthat is detected has been attenuated by MP, the densityifference Dnd is

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he amplitudes CF�� and CP�� are derived from Eqs. (1)nd (9), respectively.

. METHODS. Subjectshe study population consisted of 26 normal male sub-

ects in good health and free of ocular pathology (26 OD).hey were Caucasian of European descent, and nonsmok-rs. Their ages ranged from 45 to 55 (mean age9.0±3.1 years). Their visual acuity in all cases was cor-ectable to 20/20 or better. The tenets of the declarationf Helsinki were followed. All subjects gave informed con-ent to the protocol approved by an Institutional Reviewoard.

. Directional and Nondirectional Reflectanceshe distribution of light in the eye’s pupil was determinedy means of a dedicated reflectometer [20]. The measur-ng beam was provided by a 75 W xenon lamp (Oriel) fil-ered either by an interference filter at �1=470 nmFWHM 10 nm, Oriel) or an interference filter at �2532 nm (FWHM 10 nm, Oriel). The retinal illuminancesere 4.8 logTd and 5.5 logTd for the blue and green light,

espectively. Fixation was provided by a red 633 nme–Ne laser (Melles Griot). The surfacic flux in the pupilas measured with a CCD camera cooled by liquid nitro-en (Princeton Instruments). This camera had a reso-ution of 512�512 pixels with an image depth of 16 bits.he pixel size in the pupil was 0.0255 mm. We combinedreas of 2�2 pixels, giving a resolution of.051 mm/pixel. We chose an integration time of 4 s forach image.

The retina was illuminated in an area of 3 deg andampled in an area of 2 deg. The fixation target had a di-meter of 5 arcmin. The operator selected the retinal ec-entricity (either 0 or 6 deg) by rotating a mirror that wasonjugate to the eye’s pupil. Two stepping motors X and YNewport) allowed the center J of the entrance pupil to beositioned at the chosen location in the eye’s pupil (com-only so that J was aligned with photoreceptor axes). The

ead of the subject was stabilized by a bite bar fixed on ahree-dimensional positioner. The main optical compo-ents were mounted on a single plate which could behifted longitudinally, thus allowing focus adjustmentrom −12 D to +12 D of ametropia.

A computer controlled the shutter (Xe lamp light), thewo stepping motors, and the CCD camera.

. Experimental Conditionsach subject was tested in one experimental session. Theupil was dilated by application of 0.5% Mydriacyl to ainimum of 7 mm diameter. The eye was then aligned to

he reflectometer. With the subject looking at the fixationpot, the pupil was brought into focus and centered.

In the fovea we positioned the center J of the entranceupil successively at 2 mm nasal (N), 0, and 2 mm tem-oral (T) on the horizontal diameter of the eye’s pupil. Theeasurement was repeated three times for each position

f J and for the two wavelengths. The shutter was openednd the measuring green beam bleached the retina for aeriod of 15 s. Then 3�3 pupil images were captured at32 nm (integration time of 4 s) with an interval of 10 setween each one; they were followed by 3�3 pupil im-ges at 470 nm. Finally we could determine the locationf the S-C peak in the pupil, and acquire six more imagesith J aligned with photoreceptor axes (three images at32 nm, and three at 470 nm). Usually the alignmentith the photoreceptor axis involved a vertical shift. The

etinal illuminance (5.5 logTd) was high enough to pro-ide a full decomposition of the photopigment. Compari-on of successive images allowed us to verify that theleaching state of the retina was stationary.Similar to the foveal pupil images, at 6 deg T eccentric-

ty we recorded three images at 2 mmN, 0, and 2 mmT onhe horizontal diameter of the eye’s pupil for the twoavelengths.The safe times for exposure to these illuminances and

avelengths were well above the exposure times of thexperimental session [21].

. Data Analysishe experimental data consisted of the radiant flux val-es �m� (collected by areas of 51�51 �m2) at different po-itions �x ,y� in the eye’s pupil. These distributions of lightere processed using a MatLab program (vers. 7.5; Theathworks Inc.). Each image was processed separately.irst the pupil center and diameter were determined,

hen the dark level dl around the pupil was subtractednd the distribution normalized with the radiant flux rfntering the eye, thus giving �m= ��m� −dl� /rf.

Experimental data farther than 3 mm from the peakere rejected because the signal becomes very low at suchistances (1.6% of the maximum for a � value of.2 mm−2), so points farther away do not help to stabilizehe fits. In addition two masks were positioned to cut outhe fourth Purkinje image and backscattering from theens around the entrance pupil. Weighted least-squarests to the remaining data were used to determine the fivenknown parameters x0, y0, CF��, Q��, and �� of Eq.

1). We made use of a weight of 1/r, with r the distancerom the S-C peak to the data.

At 6 deg T eccentricity, the parameters CP�� [Eq. (9)]nd Fspec�� [Eq. (10)] were calculated according to therocedure explained in Subsection 2.B.2.The function Kmp�� was derived from the MP spectrumeasured by Bone et al. [22].We have pointed out that a mask had been used to cut

ut backscattering from the lens around the entrance pu-il. The subjects of this protocol were above 45 years ofge and so could present some lens scattering in blue

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ight. To get more reliable estimates of parametersF�470�, Q�470�, and ��470�, we have used the coordinates0 and y0 [S-C peak in Eq. (1)] that had been determinedor 532 nm when fitting the Gaussian function to the dis-ribution of light at 470 nm (three free parameters in-tead of five).

The Statistics Toolbox of MATLAB (vers. 7.5; Theathworks Inc.) was used for analysis. All results are

iven as mean±standard deviation (SD). Pearson correla-ion coefficients were calculated to investigate bivariateelationships. The three images in any configuration weresed to calculate the standard deviation in the param-ters as a measure of reproducibility (ratio between theD and the average value).

. RESULTS. Macular Pigment Densityacular pigment density Ddir determined by the direc-

ional reflectance method displays a large individual vari-bility. The mean value of Ddir is 0.419±0.097 D.U., theean of the reproducibility for the whole group being 9%.P density Dnd determined by the nondirectional reflec-

ance method in the same subjects has a mean value of.195±0.042 D.U., the mean of the reproducibility being3%. Figure 3 shows the density Dnd as a function of Ddiror the 26 subjects. Each point represents the average ofhree measurements. MPD estimates Ddir and Dnd areighly correlated with each other (r=0.787, p�0.0001).inear regression through the data gives Dnd=0.05300.338 Ddir (D in D.U.).

. Directionality Factorhe directionality factor �� of photoreceptors inside theample field �2 deg� defines the relative angular distribu-ion of light radiated from myoids toward the pupil. Aarge value of �� corresponds to a steep function SFround the point I [Eq. (1)]. The mean value of ��532� is.210±0.028 mm−2 and the mean value of ��470�.239±0.028 mm−2. Figure 4 shows the factor ��470� as a

ig. 3. Comparison of MPD estimates derived from the direc-ional �Ddir� and nondirectional �Dnd� reflectance methods (26ubjects). The solid curve represents a linear fit to the data.ample field, 2 deg.

unction of ��532� for the 26 subjects. Each point repre-ents the average of three measurements. The means ofhe reproducibility for the whole group are provided inable 1. There is a strong correlation between ��470� and�532� (r=0.853, p�0.0001). Linear regression throughhe data gives ��470�=0.0546+0.875 ��532� (� in mm−2).

. Directionality Factor and MPDe have observed a weak correlation between the direc-

ionality factor ��532� and the density Dnd (r=0.477, p0.014). But we could not find any correlation between�532� and Ddir (r=0.340, p=0.090), neither between�470� and Dnd �r=0.382� nor between ��470� and Ddir �r0.322�. Therefore the above relationship is probably co-

ncidentally significant.

. DISCUSSION. Macular Pigment Densityany MPD data have been presented in the literature

ince the early stages of optical methods. In Table 2 weompare our results with data from experiments onealthy subjects using similar sample fields (between 1.5nd 2 deg). Our D estimates are of the same order of

Table 1. Mean Parameters for the Groupof 26 Subjects

Parameter UnitMean±S.D.and (Range)

ReproducibilityMean and(Range)

Dnd D.U. 0.195±0.042 (0.113–0.268) 13% (7%–27%)Ddir D.U. 0.419±0.097 (0.230–0.588) 9% (3%–36%)

a/RP�470� 0.572±0.118��532� mm−2 0.210±0.028 (0.162–0.264) 3% (0%–8%)��470� mm−2 0.239±0.028 (0.187–0.281) 8% (2%–17%)

mm−2 0.110±0.066 mm−2 0.101±0.054

ig. 4. Directionality factor ��470� as a function of ��532� at theovea (26 subjects). Each point is the average of three measure-ents. Sample field, 2 deg.

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agnitude, although slightly smaller, as those deter-ined with the nondirectional reflectance technique

6–8]. Indeed most reflectometers were collecting an addi-ion of directional and nondirectional light. On the otherand, we have been careful to take account of the nondi-ectional component alone when we determine Dnd, sinceur reflectometer allows an accurate separation of the twoomponents.

The autofluorescence method that was proposed by De-ori and colleagues [7] is an optical method commonlysed today [23–26]. One of its advantages comes from the

ocation of the fluorophores in the RPE, behind MP. Tablepresents a few MP densities obtained with this method.ome studies measure high MPD values [7], but othersrrive at low MPDs [23,24]. A partial explanation for theow MPDs with a reference at 4 deg [24] could be that vane Kraats et al. found an MPD of almost 0.1 at thatccentricity [27].

Contrary to the above methods, which estimate the MPensity from a difference between foveal and perifovealites, fundus reflectance spectroscopy provides densityalues without the need of a reference spectrum at a

ig. 5. Model of a reflector anterior to MP. R*F is the nondirec-

ional reflectance that would be measured if there were no reflec-or anterior to MP. Ra is the reflectance of the layers anterior toP. The directional component passes twice through MP. O, cen-

er of the eye’s pupil; I, point where the photoreceptor axis inter-ects the pupil.

Table 2. Macular Pigm

First Author MethodaReferenc(degrees

Berendschot [6] ndRefl. 14Delori [7] ndRefl. 7

Wustemeyer [8] ndRefl. 7Present study ndRefl. 6

Delori [7] autofluor. 7Wüstemeyer [23] autofluor. 5

Delori [24] autofluor. 4

Zagers [11] dirSpectr. no ref.Berendschot [9] dirSpectr. no ref.an de Kraats [13] dirSpectr. no ref.

Kanis [30] dirSpectr. no ref.Present study dirRefl. 6

andRefl., nondirectional reflectance; autofluor., autofluorescence; dirSpectr., direcbn, number of subjects.

eripheral location [4,28,29]. The model contains N freearameters whose values are adjusted to produce a matchith a full reflectance spectrum. Separating the direc-

ional component allowed Berendschot, Zagers, van deraats, Kanis, and colleagues [9,11,13,30] to reduce N tovalue of 4. This method uses spectral absorption curves

or the ocular media and retinal layers as input to theodel. However the choice of the templates for spectral

ens absorption is critical, as can be seen in Table 2. Zag-rs described the spectral absorption of the lens by theum of two functions, a “young” and an “aged” template,hich gave MPDs of 0.56 and 0.53 D.U. [9,11]. Van deraats has modified these two templates, and added a

hird one, the “Rayleigh scatter” template, which pro-ided MPDs of 0.39 and 0.42 D.U. [13,30], i.e., smallerhan those of Zagers.

We have measured a mean density Ddir of.42±0.10 D.U., which is closer to the density obtainedith the templates of van de Kraats than to the densityerived from those of Zagers. Our method minimizes thenfluence of the spectral characteristics of the ocular me-ia and of the instrument. Its main assumption is that re-ection from photoreceptors, as well as specular reflectiony ILM, are neutral. More precisely the ratiosphot�470� /Rphot�532� and Rspec�470� /Rspec�532� have to bequal, where Rphot�� and Rspec�� are the reflectances ofhe photoreceptor and the ILM, respectively.

The MP density Dnd is highly correlated with Ddir (r0.787, p�0.0001), but less than half Ddir. Several au-

hors suggested that these small values of Dnd are due tohe anterior reflections by the RNFL, the ILM, and thecular media [4,6]. Delori et al. [7] have calculated the ef-ect of an anterior reflector on MPD estimates. Figure 5resents such a model. R*

F is the nondirectional reflec-ance that would be measured if there were no reflectornterior to MP. Ra�� is the reflectance of the layers ante-ior to MP. Let Dmp be the true MP density and RF theeflectance measured at the fovea. If we assume thata�532� /RF�532� is much smaller than Ra�470� /RF�470�,q. (21) of Delori et al. [7] can be rewritten as

Studies’ Comparison

nbField Diameter

(degrees)MPD(D.U.)

8 1.5 0.26134 2.0 0.23±0.0710 2.0 0.18±0.0226 2.0 0.19±0.04

134 2.0 0.48±0.16109 2.0 0.21±0.0739 2.0 0.22±0.06

16 1.9 0.56133 1.9 0.53±0.13102 1.5 0.39±0.1645 1.5 0.4226 2.0 0.42±0.10

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Ra�470�

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here D*nd is the MPD that one would estimate if Ra

ere ignored; the factor k is equal to 0.5/ �Kmp�470�Kmp�532��. Equation (17) can be rearranged as

Ra�470�

RF�470�= 1 − 10−�1/k��Dmp�460�−D

nd* �460��. �18�

aking Dmp=Ddir and D*nd=Dnd, we can apply Eq. (18) to

he individual data of all subjects. We obtain an anterioreflectance Ra�470� that represents 57.2±11.8% of the to-al foveal reflectance RF�470�. This percentage is close tohe values calculated by van de Kraats et al. [4] and De-ori et al. [7] (60% and 50%, respectively).

Another way to analyze the relationship between Dndnd Ddir is to determine the theoretical curve best fitted tour data. This theoretical curve derives from Eq. (17):

Dnd = Ddir + k log�1 −Ra�470�

Ra�470� + 10−��Ddir/k�−log �� ,

�19�

ith �=RF�532�RP�470� /RP�532� and RP�� the reflec-ance measured at the perifovea. The two free parametersf Eq. (19) (Ra and �) are adjusted to obtain the least-quares best-fitted curve. This curve is represented by therosses in Fig. 6. Let RF�470� be the mean foveal reflec-ance at 470 nm (26 subjects). We find a ratioa�470� /RF�470� of 0.567, i.e., very close to the ratio 0.572erived from individual data.

. Directionality Factorarcos and colleagues [31,32] proposed a model of photo-

eceptor reflectance where scattering as well asaveguides were included. The directionality factor of the

esultant Gaussian distribution had a wavelength depen-ence described by the function

ig. 6. Crosses represent the theoretical curve derived from theodel [Eq. (19)] and best fitted to the MPD data (26 subjects).ample field, 2 deg.

�� = + �532

�2

. �20�

heir experiments were limited to three subjects and twoavelengths, so Zagers et al. [33] made use of their FRA

Foveal Reflection Analyzer) to bring a confirmation ofhis theory (population of 21 subjects). They could evalu-te values of and equal to 0.077 mm−2 and.102 mm−2, respectively. We have measured the factor �t two wavelengths for a population of 26 subjects. We canhus derive the coefficients and from Eq. (20):

= �1/0.281��1.281��532� − ��470��,

= �1/0.281��470� − ��532��. �21�

Applying Eq. (21) to the individual data of all subjects,e obtain mean values of and equal to.110±0.066 mm−2 and 0.101±0.054 mm−2, respectively.hese estimations are close to those of Zagers et al. [33].Thus these measurements of the directionality factor at

wo wavelengths confirm the model of spectral depen-ence suggested by Marcos and colleagues.

. CONCLUSIONeatty et al. ([34], p. 483) pointed out that there existome “key questions on the methods of measuring MPensity in vivo, which have inherent and major limita-ions.” One of these limitations is that light reflected byhe RNFL, the ILM, and the ocular media gives rise to anrror in the estimation of MP density. Methods based onutofluorescence and directional reflectance bypass thisroblem since their source of reflection is behind the MP.oth the method of Zagers and van Norren [11] and ours

ake advantage of the characteristics of the directionalomponent radiated from foveal photoreceptors to the pu-il. Directional reflectance spectroscopy [11] provides MPensity without the need of a reference spectrum at a pe-ipheral location, but the choice of templates for spectralens absorption may be delicate; on the other hand, wese a reference in the perifovea (reflectance of the ILM)hat minimizes the influence of the spectral characteris-ics of the ocular media and of the instrument. These twoechniques are complementary and provide close estima-ions of MP density when the new templates of van deraats and van Norren [13] are taken into account. Theirectional reflectance method that we have developed isoninvasive and produces estimates of MP density thatorrelate highly with those derived from the nondirec-ional reflectance method. Comparison of MPD valuesrovided by the two techniques implies that 57±12% ofhe light reflected from the fovea comes from layers ante-ior to the macular pigment at 470 nm. We chose a subjectool that was very homogeneous (Caucasians of Europeanescent, mean age of 49±3 years), since ethnicity plays aole in MP density (MPD values being significantly loweror the group of white non-Hispanics than for the group offricans [26]). The reproducibility would of course beigher with younger subjects whose lens transmission isetter at 470 nm.

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The directionality factors that we measured at 470 nmnd 532 nm were slightly higher than those from previoustudies. They were strongly correlated and followed thepectral dependence suggested by Marcos et al. [31,32].

CKNOWLEDGMENTShis work was supported by the Centre National de la Re-herche Scientifique (CNRS) (France) and by a grant fromilège (France).

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Macular pigment density assessed by directional fundus reflectance