light reflection spectra as a diagnostic tool for the structural and biophysical parameters of skin

ISSN 0030-400X, Optics and Spectroscopy, 2008, Vol. 104, No. 2, pp. 300–307. © Pleiades Publishing, Ltd., 2008.Original Russian Text © A.P. Ivanov, V.V. Barun, 2008, published in Optika i Spektroskopiya, 2008, Vol. 104, No. 2, pp. 344–351.

300

INTRODUCTION

The reflection spectrum of human skin coverdepends on the structure of the tissue and on the absorb-ing and scattering components contained in it. There-fore, there is a fundamental possibility of determiningcertain characteristics of skin from the spectral reflec-tion coefficients. However, mathematically, the prob-lem indicated is ill-posed; i.e., it cannot be rigorouslysolved. The necessary condition for obtaining a solu-tion is the knowledge of the true absorption and scatter-ing spectra of the components of skin and of the varia-tion in the macrostructure of skin with depth, as well asthe application of adequate methods of the theory of thepropagation of light in such a medium. The availableinformation on these three questions is frequentlyincomplete and ambiguous. Therefore, the diagnosticproblem formulated in this study does not pretend to becompletely solved at this stage. Here, we will only givesome recommendations on the choice of spectralranges and discuss the sensitivity aspects. The soughtparameters are the volume concentrations of melaninand capillaries, the thickness of epidermis, the averagediameter of capillaries, and the degree of blood oxygen-ation.

THE STRUCTURE, COMPOSITION,AND OPTICAL CHARACTERISTICS OF SKIN

The Structure and Component Composition

The composition, the structure [1–3], and the opticalcharacteristics [1, 3–7] of human skin have been stud-ied sufficiently completely. Usually, a layered model ofskin is used, in which the properties of the skin vary

only along one of the coordinates, the depth

z

. Themodel includes three basic layers—stratum corneum,epidermis, and dermis [1, 3, 5]. Their thicknesses varywithin 0.01–0.02, 0.04–0.15 and 1–4 mm, respectively.These layers will be denoted below by indices 1, 2, and3. The diameter of capillaries

D

varies from a fewmicrometers to tens of micrometers. Clearly, such astructure is rather simplified. In reality, there are neitherclear-cut interfaces between the layers nor clearly pro-nounced differences in their refractive indices.

We assume that each of these three layers has a basictissue (a bloodless tissue base) [5]. In epidermis, thebasic tissue contains a pigment, melanin, while thebasic tissue of dermis contains randomly distributedblood vessels (capillaries). Also, skin has water, but itsabsorption in the visible and near-IR ranges is too lowto be considered in the estimation of the diffuse reflec-tion coefficient. The thickness of the stratum corneumwill be fixed at 0.02 mm. (Subsequent calculationsshowed that this layer plays an insignificant role in thereflection of light by skin because of its small opticalthickness.) The characteristics of the other two layersare varied and are objects for diagnostics. Melanindetermines the color of skin. Its volume concentration

f

(the amount of melanin per unit volume of epidermis)is varied from a few percent for fair skin to dozens ofpercent in the course of dark skin [5]. The volume con-centration of capillaries

c

is usually as high as severalpercent. Blood is considered as a mixture of oxyhemo-globin and deoxyhemoglobin with the variable degreeof oxygenation

S

(the ratio of the amount of oxyhemo-globin to the amount of the entire hemoglobin).

GEOMETRICAL AND APPLIED OPTICS

Light Reflection Spectra As a Diagnostic Tool for the Structural and Biophysical Parameters of Skin

A. P. Ivanov and V. V. Barun

Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, 220072 Belarus

Received March 12, 2007; in final form, August 2, 2007

Abstract

—The calculation scheme and the diagnostic algorithm for diagnosing the structural and biophysicalparameters of skin from the spectrum of reflected radiation are constructed. The sought parameters are deter-mined from the solution of the spectroscopic problem under conditions of multiple scattering. The method pre-sented is based on the previously proposed model of the spectral properties of a tissue and on the engineeringapproaches to the solution of the transfer equation. The sought parameters are the volume concentrations ofmelanin and capillaries, the thickness of epidermis, the average diameter of capillaries, and the degree of bloodoxygenation. In order to optimize the algorithm with respect to wavelength and to elaborate the experimentaldiagnostic scheme, the sensitivity of the reflection spectrum to the sought parameters is studied. The procedureof their successive restoration is proposed.

PACS numbers: 42.62.Be

DOI:

10.1134/S0030400X08020252

OPTICS AND SPECTROSCOPY

Vol. 104

No. 2

2008

LIGHT REFLECTION SPECTRA AS A DIAGNOSTIC TOOL 301

The Optical Characteristics

The optical characteristics of skin are determinedvia the corresponding properties of its components andtheir concentrations. For elementary volumes of thethree layers of skin, we have

(1)

(2)

where

k

is the absorption coefficient, and

ε

is thereduced extinction coefficient (

ε

=

ε

'(1 –

g

),

where

ε

'

isthe extinction coefficient,

g

is the average cosine of thephase function;

g

1, 2, 3

= 0.62 + 0.00029

λ

, where

λ

is thewavelength in nm [1, 3]). The indices

t

,

m

, and

b

pertainto the basic tissue, melanin, and blood, respectively.The correction coefficient

α

takes into account local-ized absorption of light by blood vessels [8–10]. Thisparameter will be considered below. In turn, the valueof

k

b

is determined by the absorption coefficients ofoxyhemoglobin (

HbO

2

) and deoxyhemoglobin (Hb),

(3)

where

H

is the hematocrit (the volume fraction of eryth-rocytes in the blood), and

f

H

is the volume fraction ofhemoglobins in the erythrocytes. It is seen from (2) and(3) that the expression for the absorption of blood con-tains the product

cHf

H

rather than these quantities sep-arately. Therefore, only this product can be found fromoptical experiments. In what follows, we assume that

H

= 0.4 and

f

H

= 0.25 [7]. The used spectra of theabsorption and extinction coefficients of skin are pre-sented in Fig. 1 from [1].

The Localized Absorption of Light by Blood Vessels

Formula (1) introduces the effect of the localizedabsorption of light by blood vessels [8–10] via the cor-rection coefficient

α

. Let us clarify its meaning. Usu-ally, the concentration of light-absorbing capillaries inbiological tissues is small. This suggests that such aninhomogeneity in the medium may cause the sieve (orhole) effect [12], as a result of which a large amount oflight will pass through less absorbing regions of themedium, making the total transmission greater than itwould be in the case of a uniform absorption ability ofa unit volume. In [10], the following analytical formulawas proposed for the parameter

α

in the case of ran-domly distributed capillaries with typical values of

k

b

D

(where

D

is the average capillary diameter):

(4)

k1 kt, k2 f km 1 f–( )kt,+= =

k3 cαkb 1 c–( )kt,+=

ε1 εt, ε2 1 f–( )εt, ε3 cεb 1 c–( )εt,+= = =

kb H f H SkHbO21 S–( )kHb+[ ],=

α 2 31 –πkbD 1 0.043kbD–( )/ 2 3( )[ ]exp–

πkbD-----------------------------------------------------------------------------------------------.=

The calculations by formula (4) were compared in[10] with the numerical integration in [8] and with theMonte Carlo simulation in [9], and good agreementbetween all these data was obtained. As is seen,

α

depends only on the product

k

b

D

, and the inequality

α

≤

1

always holds. At

k

b

D

�

1

, the coefficient

α

= 1.This is equivalent to the fact that the absorption abilityin the entire elementary volume is constant. What arethe consequences of this effect for the diagnostic prob-lem under consideration? In the blue-green range,where blood strongly absorbs light, the product

k

b

D

isof the order of unity or greater, so that the absorptioncoefficient of the elementary volume of dermis dependson the diameter

D

. In principle, this opens possibilitiesfor determining

D

from the characteristics of lighttransmitted through tissue. This question will be dis-cussed below. Note also that, since the absorption ofblood at

λ

> 600 nm is weak, the coefficient

α

is prac-tically equal to unity for real capillary diameters; there-fore,

D

does not affect the absorption coefficient.

ANALYTICAL DESCRIPTION OF THE SPECTRAL DIFFUSE REFLECTION

COEFFICIENT OF SKIN

Let skin be illuminated by a directed beam of light.The propagation of this beam can schematically be rep-resented as follows. Initially, the skin surface with thereflection coefficient

r

reflects a fraction of the incidentflux. Since the optical thicknesses of the upper two lay-ers are small and because their phase functions arestrongly elongated forward, the light passing throughthe skin surface is incident on the three successive lay-ers as a directed beam. Then, as a result of scattering orreflection, the radiation becomes virtually diffuse. Mul-tiple rereflections between the layers occur. Finally, acertain light flux emerges from the surface. The ratio ofthe emerged flux to the incident one is the diffusereflection coefficient R of skin. The scheme consideredimplies that the spectral values of R(λ) depend on the

0.5

0.4

0.3

0.2

R

800600400λ, nm

1

2

Fig. 1. Calculated spectra of the diffuse reflection coeffi-cient of a test skin sample at D = (1) 5 and (2) 40 µm.

302

OPTICS AND SPECTROSCOPY Vol. 104 No. 2 2008

IVANOV, BARUN

transmission and reflection coefficients of the directedand diffuse light by the stratum corneum and epidermis,as well as on the coefficients of reflection of thedirected and diffuse light by the dermis. Therefore,below, we will present the formulas for the transmis-sion and reflection coefficients of the directed and dif-fuse radiations by the corresponding layers. The quan-tities pertaining to the diffuse light are asterisked. Aswas noted, the optical thicknesses of the stratum cor-neum and epidermis are rather small; therefore, thepropagation of the directed radiation in these layers isdescribed using the small-angle approximation of [13]of the transport theory, whereas the propagation of thediffuse radiation is described in terms of the asymptoticapproximation of [13, 14]. The latter approximation isexact even for optically thin layers if the angular distri-butions of the incident diffuse radiation and of the lightin the bulk regime of the medium coincide [13, 14]. Weassume that this condition is satisfied. At the same time,the dermis is the optically thick layer, which can bewell described by the asymptotic approximation. Notethat, optically, the dermis is considered as a semi-infi-nite scattering and absorbing medium.

Transmission and Reflection of Light by Stratum Corneum and Epidermis

The coefficients of transmission and reflection oflight (T and R with the corresponding indices) of stra-tum corneum and epidermis illuminated along a normalhave the form [13]

(5)

where τ is the optical thickness (τ = ε'd, where d is thegeometric thickness of the stratum corneum or epider-mis), Λ is the photon survival probability (single scat-tering albedo) Λ = (ε' – k)/ε', F is the fraction of the lightscattered forward (at scattering angles 0°–90°) withrespect to the total scattered flux (F = 1 – (1 – g)/3[13]), and µ is the cosine of the scattering angle. Upondiffuse illumination [13, 14],

(6)

where β = is the bulk extinction coefficient of thecorresponding layer.

T1 2, τ1 2, 1 Λ1 2, F1 2,–( )–[ ],exp=

R1 2, Λ1 2,1 F1 2,–

1 F1 2, Λ1 2,–-----------------------------=

× 1 –τ1 2, 1 Λ1 2, F1 2,–( )1 µ+µ

------------exp–⎩ ⎭⎨ ⎬⎧ ⎫

µ,d

0

1

∫

T1 2,*4 k1 2, / 3ε1 2,( )[ ]sinh

d1 2, β1 2, 4 k1 2, / 3ε1 2,( )+[ ]sinh----------------------------------------------------------------------------,=

R1 2,*d1 2, β1 2,( )sinh

d1 2, β1 2, 4 k1 2, / 3ε1 2,( )+[ ]sinh----------------------------------------------------------------------------,=

3εk

Reflection of Light by Dermis

Upon directional illumination of dermis along a nor-mal [13, 14],

(7)

Upon diffuse illumination [13, 14],

(8)

which is analogous to (6) at d ∞.

The Diffuse Reflection Coefficient of Skin

The values of the light fluxes multiply rereflectedfrom skin layers form an infinitely decreasing geomet-ric progression. It is easy to find its sum and obtain thediffuse reflection coefficient of skin

(9)

where r = 0.04, r* = 0.2 is the reflection coefficient ofthe skin surface illuminated from within by the diffuseflux, and R123 and are the reflection coefficients ofthe three-layer “pie” (stratum corneum (1), epidermis(2), and dermis (3)) without the outer boundary (theskin surface) in the cases of the directed and diffuseilluminations, respectively. The coefficients R123 and

can be found similarly to (9) by summing the cor-responding geometric progressions,

(10)

where, as in (9) and (10), R23 and are determinedby the sums of the geometric progressions,

(11)

The transmission and reflection coefficients in (9)–(11) are given by formulas (5)–(8). It should be notedthat expressions (9)–(11) are similar to each other, tak-ing into account that (1 – r) and (1 – r*) are the trans-mission coefficients of the skin surface upon directedand diffuse illuminations, respectively. It is seen fromthe expressions presented that the diffuse reflectioncoefficient R is governed by the structural and biophys-ical parameters of skin. It is necessary to find theseparameters.

OPTIMAL WAVELENGTHSFOR THE DIAGNOSTIC OF THE SKIN

PARAMETERS: THEORETICAL INVESTIGATIONS

The first stage of the solution of the inverse problemposed was to study the sensitivity of the spectral diffuse

R3 36/7( ) k3/ 3ε3( )–[ ].exp=

R3* 4 k3/ 3ε3( )–[ ],exp=

R r1 r–( ) 1 r*–( )R123

1 r*R123*–----------------------------------------------,+=

R123*

R123*

R123 = R1

T1T1*R23

1 R1*R23*–------------------------, R123*+ = R1*

T1*( )2R23*

1 R1*R23*–------------------------,+

R23*

R23 = R2

T2T2*R3

1 R2*R3*–-----------------------, R23*+ = R2*

T2*( )2R3*

1 R2*R3*–-----------------------.+



reflection coefficient to the sought parameters of skin.A skin cover with f = 0.04, c = 0.02, d2 = 100 µm, D =5 or 40 µm, and S = 0.75 was chosen as a test sample.By substituting these values into (1)–(4), one can findall the optical characteristics of the elementary volumesof skin layers, which describe the radiation transfer.Then, by using expressions (5)–(11), we obtain thesought spectrum of the diffuse reflection coefficient.The calculations showed that the optimization proce-dure described below weakly depends on particular val-ues of the parameters indicated above if these values arewithin the limits typical for real skin. Below, the sensi-tivity was studied based on the calculated spectra of Rshown in Fig. 1 for two values of the capillary diameter,D = 5 and 40 µm.

The differences between curves 1 and 2 in Fig. 1demonstrate that the diffuse reflection coefficient in theblue-green range depends on D. Analytically, thisdependence is given by formula (9), taking into account(1) and (4). As was noted above, the stronger reflectionat D = 40 µm than at D = 5 µm is caused by a smallereffective volume fraction of blood involved into lightabsorption. It is this fact that physically accounts for theeffect of the capillary diameter on the reflection of skin.Below, based on theoretical and experimental grounds,we will present the quantitative estimates of the possi-bility for the restoration of D (as well as of the otherparameters). Here, we only stress that, as follows fromFig. 1, the fundamental possibility exists of determin-ing the diameter from the spectrum R(λ). Whether thequantitative differences in the diffuse reflection coeffi-

cient of skin suffice for the practical estimation of theaverage capillary diameter and how this can be done arethe questions that we will discuss below.

Reconstruction of the Volume Concentrationof Capillaries and of the Product of the Melanin

Concentration by the Epidermis Thickness

We calculated the diffuse reflection coefficient ofthe test sample of skin in relation to the volume concen-tration c of capillaries for several wavelengths at differ-ent values of fd2 typical for real skin. Note that thisproduct is the physical equivalent of the optical thick-ness of epidermis τ2. The corresponding plots areshown in Fig. 2 at λ = (a) 400, (b) 500, (c) 570, and(d) 800 nm. Since these wavelengths are approximateisosbestic points of the absorption spectra of hemoglo-bins, the diffuse reflection coefficient at these pointsdoes not depend on the degree of oxygenation of blood.Figure 2 shows that, at the wavelengths λ = 500, 570,and 800 nm, the diffuse reflection coefficient is practi-cally determined by only the product fd2, rather than bythe separate values of f and d2. (We neglect small differ-ences in the values of the diffuse reflection coefficientat λ = 500 and 570 nm at comparatively large volumeconcentrations of capillaries (at approximately c >0.04), because such concentrations are not typical forthe majority of skin covers.) At the same time, the dif-fuse reflection coefficient in the blue range (Fig. 2a)separately depends on f and d2. These features are

0.20

0.16

0.12

R (a)

0.35

(b)

0.30

0.25

0.20

0.35R (c)

0.15

0.25

642 c, %

0.55

(d)

0.50

0.45

642 c, %

Fig. 2. Dependence of the spectral diffuse reflection coefficient of skin on the capillary volume concentration c at λ = (a) 400,(b) 500, (c) 570, and (d) 800 nm and at f = (�) 0.04, (�) 0.08, and (�) 0.16.

304


IVANOV, BARUN

explained as follows. In the long-wavelength range ofthe spectrum, because the absorption of blood is rela-tively small, the reflection of skin is mainly determinedby dermis. The contribution of melanin to the totalreflection coefficient R manifests itself only through thetransmission coefficient of epidermis, the expressionfor which contains the product fd2. In the blue range,the epidermis reflects more light than the dermis does,and the reflection coefficient of the epidermis dependsnot only on fd2, but also on f (through Λ2). Such a spec-tral behavior of the diffuse reflection coefficient is aphysical premise for the reconstruction of c and fd2 inthe green–near-IR range and for the subsequent deter-

mination of f and d2 from the diffuse reflection coeffi-cient in the blue range.

Let us consider the procedure of the reconstructionof c and fd2. Analytical expressions (5)–(11) contain theoptical characteristics of skin in the explicit form viarelations (1)–(3). By solving two transcendental equa-tions for the diffuse reflection coefficient of skin at twowavelengths, we find the sought values of c and fd2.Figure 3 illustrates the procedure of the graphic solu-tion of the above transcendental equations. This figureshows pairs of values of c and fd2 that ensure the “mea-sured” diffuse reflection coefficient at λ = 500, 570, and800 nm (Fig. 1). Naturally, the curves intersect at a sin-gle point, which corresponds to the specified values ofc and fd2 for the test sample, namely, c = 0.02 and fd2 =4 µm. This point yields the “sought” parameters of theskin. However, it is seen that the curves for 500 and800 nm practically coincide near the intersection point,so that it is hardly possible to localize this point takinginto account the measurement errors and unavoidabledifferences between the model used and the real skin. Inorder to more precisely determine experimentally c andfd2, it is more practical to use light at a wavelength of570 nm (curve 2) instead of 800 nm. In this case, theslope of curve 1 relative to curve 2 is greater than theslope of curve 1 relative to curve 3. Therefore, thewavelengths 500 and 570 nm are recommended fordetermining the values of c and fd2 from the spectrumof the diffuse reflection coefficient.

Reconstruction of the Average Capillary Diameter and the Melanin Concentration

Having determined the values of c and fd2, we canfind the average capillary diameter D and the volumeconcentration f of melanin. As was already said, the dif-fuse reflection coefficient depends on D if the opticaldiameter kbD of the vessel is sufficiently large. Other-wise, α is approximately equal to unity; therefore, theabsorption coefficient k3 of dermis and, therefore, dif-fuse reflection coefficient of skin do not depend on D.The maximal values of the optical diameter lie in theblue spectral range, where blood strongly absorbs light.Therefore, the diffuse reflection coefficient is maxi-mally sensitive to D in the range λ = 400–450 nm. Letthe wavelengths 400 and 450 nm be chosen for thereconstruction of D and f. Although, strictly speaking,these wavelengths are not isosbestic points of theabsorption spectra of hemoglobins, the calculationsshow that the sensitivity of the diffuse reflection coeffi-cient to the degree of oxygenation S of blood in the bluespectral range is very low, which makes R practicallyindependent of S.

As above, we solve two transcendental equationswith respect to the parameters D and f, with the valuesof c and fd2 being known. The solution is illustrated byFig. 4. It is seen (as was expected from the estimatespresented above) that the pairs of the values of f and D

8

4

0

c, %

1

2

3

f d2, µm4321

Fig. 3. Pairs of the values of c and fd2 yielding the “mea-sured” diffuse reflection coefficient of skin at (1) 500,(2) 570, and (3) 800 nm at D = 5 µm.

7

5

3

f, %

20 40 60D, µm

8642

1

2

D, µm

Fig. 4. Pairs of the values of f and D yielding the “mea-sured” diffuse reflection coefficient of skin at (1) 400 and(2) 450 nm at D = (thin curves, the lower abscissa scale)5 µm and (thick curves, the upper abscissa scale) 40 µm.



that yield the “measured” diffuse reflection coefficientat 400 and 450 nm at D = 5 µm (the thin curves) prac-tically coincide. Therefore, in practice, it is hardly pos-sible to reconstruct f and D from the experimental databecause the optical diameter kbD of the vessels is small.At the same time, the thick curves for D = 40 µm inter-sect at a sufficiently large angle and ensure a highersensitivity of the diffuse reflection coefficient of skin tothe values of D and f. Therefore, the use of two addi-tional wavelengths at 400 and 450 nm (along with 500and 570 nm indicated above) theoretically allows one toreconstruct D and f (and, therefore, the thickness of theepidermis).

Reconstruction of the Degree of Blood Oxygenation

Above, we theoretically reconstructed four parame-ters of skin, c, d2, f, and D. The sought degree of bloodoxygenation S can be found as a solution of one equa-tion with one unknown. Initially, we will consider thespectral sensitivity of the diffuse reflection coefficient(η = dR/dS) of the test sample to values of S. Curve 1 inFig. 5 yields the corresponding dependence. As is seen,the maximum of the sensitivity is at λ about 600 nm.For wavelengths shorter than 500 nm (not shown), thesensitivity is very low because epidermis with stronglyabsorbing melanin shields the vessels and because theabsorption of the dermis itself is high. The zeros of thesensitivity correspond to the isosbestic points of theabsorption spectra of hemoglobins. Note that, in gen-eral, the sensitivity of the measurement of the diffusereflection coefficient to S is low (even at the maximum).For the experimental absolute error in R equal to 1%, itis possible, at best, to distinguish only the increments inS about 10%. It seems that, to reconstruct the degree ofblood oxygenation from optical experiments, it is nec-essary to use another approach, for example, the mea-surement of the diffusely reflected flux at some distancefrom the illumination point [15]. Evidently, the sensi-tivity in this case will be higher because the light passesa greater “effective” optical path through the hemoglo-bin-containing dermis.

At the last stage, we calculated the diffuse reflectioncoefficient of skin at a wavelength of 600 nm as a func-tion of S (curve 2 in Fig. 5) and found that S = 0.75. Thiscompletes the simulation of the problem for diagnosticsof structural and biophysical parameters of skin.

Estimation of the Reconstruction Errorsof the Skin Parameters

With the help of the analytical formalism for thesimulation of the spectra of the diffuse reflection coef-ficient of skin, one can easily estimate the errors ofreconstruction of the sought parameters. These errorsare presented in Table 1. The second row shows thewavelengths used for the reconstruction. It turned outthat, for two specified levels of the relative error ofmeasurement of the diffuse reflection coefficient, δ =±1 and ±2%, the error of determination of the capillarydiameter is rather large (up to 50% for comparativelylarge (20 µm) vessels and more than 50% for small cap-illaries). To reconstruct D, higher measurement accu-racy is required. Therefore, the errors in Table 1 werecalculated without taking into account the effect of thediameter D on the diffuse reflection coefficient or, inother words, we assumed that capillaries are small anddo not affect the diffuse reflection coefficient of skin.

EXPERIMENTAL

It was interesting to experimentally test the methodproposed. We measured the spectra of the diffusereflection coefficient of the thumb of four volunteers.

0.08

0.04

0

η

0.5 0.7 0.9S

0.40

0.36

0.32

0.28

R

600 700 800λ, µm

1

2

Fig. 5. Spectral sensitivity (curve 1, the left ordinate scaleand the lower abscissa scale) of the diffuse reflection coef-ficient of a test skin sample to the degree of blood oxygen-ation and diffuse reflection coefficient of skin (curve 2, theright ordinate scale) as a function of S (the upper abscissascale) at a wavelength of 600 nm.

Table 1. Simulated relative errors (in percent) of the reconstruction of the structural and biophysical parameters of a skin testsample with c = 0.02, f = 0.04, d2 = 100 µm, and S = 0.75

δ, %c fd2 f d2 S

λ = 500 and 570 nm λ = 400 or 450 nm λ = 400 or 450 nm λ = 600 nm

±1 ±10 –4, +8 ±10 ±10 –4, +8

±2 –13, +18 ±10 ±20 ±20 –10, +20

306


IVANOV, BARUN

They were four male persons with fair skin of the mid-dle and elderly ages. The experiments were performedusing a spectrophotometer with an integrating sphere.The results of measurements are presented in Fig. 6.From these spectra, we took the values of the diffusereflection coefficient at 400, 450, 500, 570, and 600 nmfor each volunteer and processed them according to themethod described above. As was noted, the averagecapillary diameter was excluded for the reconstructionprocedure because of a low measurement accuracy ofthe diffuse reflection coefficient. Table 2 presents thevalues of c, fd2, f, d2, and S, as well as two wavelengths(400 and 450 nm) used in determining f (and, therefore,d2). The degree of blood oxygenation was found fromthe value of the diffuse reflection coefficient at 600 nminvolving the data for f and d2 reconstructed at thepreceding stage from the diffuse reflection coefficientat 400 and 450 nm. Therefore, Table 2 contains two val-ues of S.

It is seen from Fig. 6 that the four spectra do notshow any feature specific to a particular volunteer andare close to each other. Nevertheless, the reconstructed

structural and biophysical parameters are different andhave reasonable values characteristic of normal fairskin. It seems that comparatively large changes in themelanin concentration f and in the epidermis thicknessd2 that occur upon reconstruction of these parametersfrom the values of the diffuse reflection coefficient at400 and 450 nm are connected with the assumption thatthe capillary diameter is small or that the localizedabsorption of light has no effect on the extinction coef-ficient of the dermis. Nevertheless, even in such anunfavorable case, the estimates of f and d2 are fre-quently acceptable for practice. The data on the recon-structed degree of blood oxygenation are somewhatunexpected. The obtained values of S are reasonableand nearly do not depend on the wavelength used fordetermining f. Unfortunately, independent methods forverifying the reconstructed parameters, for example,biochemical medical procedures, were unavailable atthis stage.

CONCLUSIONS

We showed how five structural and biophysicalparameters of skin (the volume concentrations of mela-nin and blood vessels, the thickness of epidermis, theaverage capillary diameter, and the degree of bloodoxygenation) can be reconstructed by a theoretical sim-ulation based on the measured spectrum of the diffusereflection coefficient. At this stage, we failed to experi-mentally determine the average capillary diameter. Oneof the reasons for this is an insufficiently high measure-ment accuracy of the diffuse reflection coefficient. Tosuccessfully reconstruct this parameter, the relativeerror should be as small as fractions of percent. How-ever, the fundamental possibility for determining Ddoes exist. The remaining four parameters have reason-able values. The method proposed can be useful forbiologists and medics studying the skin and its dis-eases. The reconstructed parameters of skin can be usedin determining the light penetration depth into tissuesand in estimating the required irradiation dose uponlaser therapy and hyperthermia.

0.6

0.4

0.2

R

λ, nm600500400

1

2

3

4

Fig. 6. Measured spectra of the diffuse reflection coefficientof the thumb skin of four volunteers.

Table 2. Structural and biophysical parameters of the skin of four volunteers reconstructed from the measured spectra of thediffuse reflection coefficient

Volunteer c, % fd2, µm f, % d2, µm S (600 nm)

1 2.1 4.4 4.8 (400 nm) 92 0.91 (400 nm)

3.2 (450 nm) 135 0.94 (450 nm)

2 2.8 3.3 5.7 (400 nm) 58 0.63 (400 nm)

8.2 (450 nm) 40 0.63 (450 nm)

3 1.7 4 3.8 (400 nm) 105 0.94 (400 nm)

2.8 (450 nm) 143 0.94 (450 nm)

4 2.6 3.75 4.8 (400 nm) 78 0.86 (400 nm)

4 (450 nm) 94 0.87 (450 nm)



ACKNOWLEDGMENTSThis study was supported by the Belarussian Foun-

dation for Fundamental Research, project no. F05K-025. We are grateful to T.V. Ol’shanskaya for perform-ing the measurements. We acknowledge the participa-tion in experiments of collaborators of the Laboratoryof Optics of Scattering Media at the Institute of Phys-ics, National Academy of Sciences of Belarus, Minsk,as volunteers.

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Translated by V. Rogovoœ

light reflection spectra as a diagnostic tool for the structural and biophysical parameters of skin

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