Skin Melanin, Hemoglobin, and Light Scattering Properties can be Quantitatively Assessed In Vivo Using Diffuse Reflectance Spectroscopy
2001; Elsevier BV; Volume: 117; Issue: 6 Linguagem: Inglês
10.1046/j.0022-202x.2001.01577.x
ISSN1523-1747
AutoresGeorge Zonios, Julie L. Bykowski, Nikiforos Kollias,
Tópico(s)Spectroscopy Techniques in Biomedical and Chemical Research
ResumoNoninvasive and real-time analysis of skin properties is useful in a wide variety of applications. In particular, the quantitative assessment of skin in terms of hemoglobin and melanin content, as well as in terms of its light scattering properties, is a challenging problem in dermatology. We present here a technique for examining human skin, based on the in vivo measurement of diffuse reflectance spectra in the visible and near-infrared ranges of the electromagnetic spectrum. Spectra were measured by means of a fiber optic probe, and they were analyzed using an analytical model of light diffusion in the skin. The results of the analysis indicate that it is possible to obtain quantitative information about hemoglobin and melanin content, as well as basic information regarding the scattering properties of the skin. Noninvasive and real-time analysis of skin properties is useful in a wide variety of applications. In particular, the quantitative assessment of skin in terms of hemoglobin and melanin content, as well as in terms of its light scattering properties, is a challenging problem in dermatology. We present here a technique for examining human skin, based on the in vivo measurement of diffuse reflectance spectra in the visible and near-infrared ranges of the electromagnetic spectrum. Spectra were measured by means of a fiber optic probe, and they were analyzed using an analytical model of light diffusion in the skin. The results of the analysis indicate that it is possible to obtain quantitative information about hemoglobin and melanin content, as well as basic information regarding the scattering properties of the skin. The optical properties of human skin have been the subject of numerous investigations (Edwards and Duntley, 1939Edwards E.A. Duntley S.Q. The pigment and color of human skin.Am J Anat. 1939; 65: 1-33Crossref Scopus (136) Google Scholar;Anderson and Parrish, 1981Anderson R.R. Parrish J.A. The optics of human skin.J Invest Dermatol. 1981; 77: 13-19Crossref PubMed Scopus (1919) Google Scholar;van Gemert et al., 1989van Gemert M.J.C. Jacques S.L. Sterenborg H.J.C.M. Star W.M. Skin optics.IEEE Trans Biomed Eng. 1989; 36: 1146-1154https://doi.org/10.1109/10.42108Crossref PubMed Scopus (651) Google Scholar;Graaff et al., 1993Graaff R. Dassel A.C.M. Koelink M.H. de Mul F.F.M. Aarnoudse J.G. Zijlstra W.G. Optical properties of human dermis in vitro and in vivo.Appl Opt. 1993; 32: 435-447Crossref PubMed Scopus (169) Google Scholar). Interest in skin optics stems from the fact that useful information about the skin physiology, morphology, and composition can be obtained in a noninvasive manner and in real time using an optical method of analysis. One such optical method is diffuse reflectance spectroscopy, which has already been widely used in the study of skin, especially in the study of hemodynamics and inflammation (Kollias et al., 1994Kollias N. Baqer A. Sadiq I. Minimum erythema dose determination in individuals of skin type V and VI with diffuse reflectance spectroscopy.Photodermatol Photoimmunol Photomed. 1994; 10: 249-254PubMed Google Scholar;Merschbrock et al., 1994Merschbrock U. Hoffman J. Caspary L. Huber J. Schmickaly U. Lubbers D.W. Fast wavelength scanning reflectance spectrophotometer for noninvasive determination of hemoglobin oxygenation in human skin.Int J Microcirc. 1994; 14: 274-281Crossref PubMed Scopus (30) Google Scholar;Svaasand et al., 1995Svaasand L.O. Norvang L.T. Fiskerstrand E.J. Stopps E.K.S. Berns M.W. Nelson J.S. Tissue parameters determining the visual appearance of normal skin and port-wine stains.Lasers Med Sci. 1995; 10: 55-65Crossref Scopus (156) Google Scholar) and skin pigmentation (Kollias and Baqer, 1986Kollias N. Baqer A. On the assessment of melanin in human skin in vivo.Photochem Photobiol. 1986; 43: 49-54Crossref PubMed Scopus (82) Google Scholar;Marchesini et al., 1991Marchesini R. Brambilla M. Clemente C. et al.In vivo spectrophotometric evaluation of neoplastic and non-neoplastic skin pigmented lesions – I. Reflectance measurements.Photochem Photobiol. 1991; 53: 77-84Crossref PubMed Scopus (76) Google Scholar). In this work, we examine human skin in vivo using an analytical model of diffuse reflectance that provides quantitative information in a more direct and potentially more accurate and reliable manner (Zonios et al., 1999Zonios G. Perelman L.T. Backman V. Manoharan R. Fitzmaurice M. Van Dam J. Feld M.S. Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo.Appl Opt. 1999; 38: 6628-6637Crossref PubMed Scopus (480) Google Scholar). Diffuse reflectance probes the scattering and absorption properties of skin. Light is absorbed by the various skin chromophores (Edwards and Duntley, 1939Edwards E.A. Duntley S.Q. The pigment and color of human skin.Am J Anat. 1939; 65: 1-33Crossref Scopus (136) Google Scholar;Young, 1997Young A.R. Chromophores in human skin.Phys Med Biol. 1997; 42: 789-802Crossref PubMed Scopus (229) Google Scholar) and scattering arises because of the refractive index fluctuations on a microscopic level (Schmitt and Kumar, 1996Schmitt J.M. Kumar G. Turbulent nature of refractive-index variations in biological tissue.Opt Lett. 1996; 21: 1310-1312Crossref PubMed Scopus (272) Google Scholar). In the visible range, the main chromophores of human skin are hemoglobin and melanin. Hemoglobin is found in the microvascular network of the dermis, typically 50–500 μm below the skin surface. In contrast, melanin is located in the epidermis, which occupies the top 50–100 μm. Human skin is characterized by variable concentration in melanin, ranging from very low in light complexioned Caucasian skin (type I), to very high in black African skin (type VI) (Young, 1997Young A.R. Chromophores in human skin.Phys Med Biol. 1997; 42: 789-802Crossref PubMed Scopus (229) Google Scholar). Melanin and hemoglobin strongly absorb light in the ultraviolet (UV) and visible ranges and they present low absorption in the near-infrared range. Melanin in particular has a photoprotective action because of its light absorption properties (Kollias et al., 1991Kollias N. Sayre R.M. Zeise L. Chedekel M.R. Photoprotection by melanin.J Photochem Photobiol B. 1991; 9: 135-160Crossref PubMed Scopus (337) Google Scholar). We have measured diffuse reflectance spectra from skin sites located on the forearm and on the back of healthy volunteers by means of a fiber optic probe. The goal of this work was to investigate the potential to obtain quantitative information regarding the absorption and scattering properties through the use of an analytical model of diffuse reflectance. The model has been previously extensively tested and successfully applied to the analysis of diffuse reflectance from human colon tissue in vivo (Zonios et al., 1999Zonios G. Perelman L.T. Backman V. Manoharan R. Fitzmaurice M. Van Dam J. Feld M.S. Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo.Appl Opt. 1999; 38: 6628-6637Crossref PubMed Scopus (480) Google Scholar). In this study, the model was extended and applied to the diffuse reflectance from skin. To perform this task, melanin was introduced as an absorber in addition to hemoglobin. Furthermore, it was assumed that the reduced scattering coefficient of skin exhibits a linear dependence on the wavelength of light. This approximation is well supported by scattering theory as will be discussed further below. The ability of the model to measure the absorption and scattering properties of tissue has already been established on tissue phantoms (Zonios et al., 1999Zonios G. Perelman L.T. Backman V. Manoharan R. Fitzmaurice M. Van Dam J. Feld M.S. Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo.Appl Opt. 1999; 38: 6628-6637Crossref PubMed Scopus (480) Google Scholar). To evaluate the utility of the model for measuring melanin and hemoglobin content in skin, we studied skin sites with variable melanin and hemoglobin content. Skin sites with variable melanin content were studied on individuals with different skin types and, in addition, UVB irradiation was used to produce skin pigmentation at various levels. Variable hemoglobin content was studied by blocking blood flow in the arm of human volunteers with a pressure cuff and by inducing reactive hyperemia immediately after the release of pressure. The results of the analysis indicate that the model can be successfully used for the analysis of diffuse reflectance spectra from skin, as well as for the quantitative assessment of the melanin and hemoglobin content. This model-based approach to the analysis of diffuse reflectance spectra of skin presents a potential improvement over previously employed empirical or semiempirical diffuse reflectance models for data analysis. Diffuse reflectance spectra were measured on skin sites (2.5 cm2 area) located on the back of 10 volunteers, with a range of skin types, from very light Caucasian (type II), to black African (type V). In five out of 10 volunteers, skin sites were irradiated with UVB radiation (280–320 nm) to produce pigmentation at various levels and therefore obtain a wider and more continuous range of melanin concentration. Spectra were measured on these skin sites in 10 d following UVB irradiation. Irradiation was performed on a total of 12 skin sites on every volunteer at six different UVB doses (two sites per dose) with the starting dose set at 18 mJ per cm2 and with subsequent dose increments of approximately 40%. UVB radiation was provided at a fluence rate of 0.5 mW per cm2 by a lamp (UVB-HO-90, Elder Pharmaceuticals, Bryan, OH) located 30 cm away from the skin. In a separate group of seven volunteers with skin type II or III, a pressure cuff was used to block completely arterial and venous blood flow (occlusion) in the arm by inflating at a pressure 50 mmHg higher than the systolic arterial pressure. This pressure was maintained for 4 min and then the pressure cuff was released. The arm of each volunteer was placed on an armrest such that the pressure cuff was not in contact with the body when inflated. The volunteers were allowed to equilibrate at ambient conditions for 20 min before measurements were made. The fiber optic probe was attached to the ventral forearm with adhesive tape prior to the inflation of the pressure cuff. Diffuse reflectance spectra were measured as a function of time, before, during, and after occlusion. Prior to the study, IRB approval was obtained from the Subcommittee for Human Studies of the Massachusetts General Hospital and informed consent was obtained from all volunteers. The instrumentation employed for measurement of diffuse reflectance has been described in detail elsewhere (Knoefel et al., 1996Knoefel W.T. Kollias N. Rattner D.W. Nishioka N.S. Warshaw A.L. Reflectance spectroscopy of pancreatic microcirculation.J Appl Physiol. 1996; 80: 116-123PubMed Google Scholar). Briefly, a spectrophotometer (HP-8452, Hewlett-Packard, Palo Alto, CA) was used consisting of a CW white light source, a spectrograph, and a diode array detector. Light delivery and collection was by means of a fiber optic probe consisting of multiple, tightly packed together, randomly arranged optical fibers with 30 µm core diameter providing a total delivery/collection spot diameter of 2.5 mm. Diffuse reflectance spectra were measured in the range 460–820 nm. Prior to data acquisition, a reference spectrum was measured on a BaSO4 diffuse reflectance standard and all skin spectra were subsequently divided by this reference spectrum to ensure proper data calibration. Skin color measurements were made with a chromameter device (CR-200, Minolta, Japan) and skin color parameters were recorded in the Commission International d'Eclairage L*a*b* colorimetric system (Billmeyer and Saltzman, 1981Billmeyer F.W. Saltzman M. Principles of Color Technology. 2nd edn. Wiley-Interscience, New York1981Google Scholar;Weatherall and Coombs, 1992Weatherall I.L. Coombs B.D. Skin color measurements in terms of CIELAB color space values.J Invest Dermatol. 1992; 99: 468-473Abstract Full Text PDF PubMed Google Scholar). Data were analyzed by means of an analytical diffuse reflectance model that has been described in detail previously, including testing and calibration on tissue phantoms (Farrell et al., 1992Farrell T.J. Patterson M.S. Wilson B.C. A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the non-invasive determination of tissue optical properties.Med Phys. 1992; 19: 879-888Crossref PubMed Scopus (1289) Google Scholar;Zonios et al., 1999Zonios G. Perelman L.T. Backman V. Manoharan R. Fitzmaurice M. Van Dam J. Feld M.S. Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo.Appl Opt. 1999; 38: 6628-6637Crossref PubMed Scopus (480) Google Scholar). Data analysis produced a set of five parameters for every skin spectrum: three absorption parameters (total hemoglobin concentration cHb*, hemoglobin oxygen saturation α, melanin concentration cmel) and two scattering parameters [the maximum value of the reduced scattering coefficient μs′(λmin) and the effective scatterer size ds]. Technical details regarding the implementation of the model can be found in the appendix. Figure 1 shows representative model fits to three diffuse reflectance spectra measured on the back of three volunteers with three different skin types, prior to UVB irradiation (normal unirradiated skin sites). The model described the reflectance spectra with very good accuracy over the entire wavelength range, for all three skin types. The agreement between the model and the experimental data was particularly good in the 600–800 nm range where the reflectance spectral features were mainly affected by scattering. At wavelengths shorter than 600 nm, absorption by melanin and hemoglobin played a key role. Effects of light absorption by these two chromophores were increasingly evident by the lower intensity of the spectra in the short wavelength range, especially for darker skin types. Table I summarizes the model parameter values obtained by analyzing the reflectance spectra measured on the back of the 10 volunteers before UVB irradiation. Hemoglobin and scattering parameters exhibited small variations among volunteers, with no correlation among different tissue types, whereas melanin content exhibited a clear correlation with tissue type.Table IModel parametersVolunteer number (skin type)Melanin content cmel (× 10-7 mmol per dl)Hemoglobin content cHb* (mg per dl)Hemoglobin oxygen saturation αReduced scattering coefficient μs′(λmin) (per mm)Scatterer size ds (µm)1 (type V)1182.80.661.270.782 (type IV)673.50.761.310.883 (type IV)472.20.781.820.624 (type IV)353.10.651.770.635 (type III)243.70.781.650.616 (type III)173.30.761.310.597 (type III)152.90.641.570.448 (type III)143.90.681.610.479 (type II)4.54.10.711.440.5110 (type II)2.72.50.741.690.44 Open table in a new tab To assess the ability of the model to measure the melanin content of the skin, the characteristic angle α was calculated independently usingα=tan−1(L*−50b*)(1) from the L*a*b* measurements performed with the chromameter. This parameter has been empirically shown to correlate well with the color appearance of the skin (Chardon et al., 1991Chardon A. Cretois I. Hourseau C. Skin colour typology and suntanning pathways.Int J Cosm Sci. 1991; 13: 191-208Crossref PubMed Scopus (174) Google Scholar). Figure 2 shows the melanin content on UVB-irradiated skin sites on the back of the five volunteers (skin types II-IV), as measured by the model, plotted against the corresponding values of the characteristic angle α. Also included in Figure 2 are the normal unirradiated skin sites before UVB irradiation for these five volunteers. A total of 14 skin sites are shown for each volunteer (two skin sites for six different UVB doses, plus two unirradiated sites). In these UVB-exposed sites, melanin was distributed throughout the epidermis. The correlation between the two parameters was very good (r = - 0.96, p <0.001), which confirmed the ability of the model to measure melanin content. The lowest correlation was observed for the individual with type II skin whose skin had very low melanin concentration (even after UVB irradiation). This made it more difficult to obtain a better correlation between the two parameters. Figure 3(a) shows diffuse reflectance spectra measured on the arm of one volunteer (skin type III) immediately following release of the pressure cuff (reactive hyperemia). The sudden influx of oxyhemoglobin is evident, due to the strong presence of the characteristic absorption bands of oxyhemoglobin at 542 and 577 nm. Figure 3(b) shows the concentration of oxyhemoglobin and deoxyhemoglobin as a function of time, obtained by analyzing the corresponding diffuse reflectance spectra with the model, before, during, and after occlusion. During occlusion, deoxyhemoglobin concentration increased and oxyhemoglobin decreased, as expected. Immediately after the release of the pressure cuff, there was a dramatic increase in the oxyhemoglobin concentration and a drop in the deoxyhemoglobin concentration, followed by an eventual return back to the initial levels (before occlusion occurred) for both oxyhemoglobin and deoxyhemoglobin concentrations. Similar results were obtained for all the volunteers studied. We have presented an analytical model for the study of diffuse reflectance spectra from skin. The model provides quantitative information for the hemoglobin and melanin contents, which are the dominant chromophores of skin in the visible range. In addition, it provides information about the light scattering properties of the skin. The technique described here is promising for the analysis and evaluation of human skin in vivo, in a rapid and noninvasive way, and the information obtained is potentially useful in the assessment and diagnosis of numerous pathologic conditions. For example, measurement of the melanin content in skin is essential in the study of conditions such as hyperpigmentation or hypopigmentation (Gniadecka et al., 1996Gniadecka M. Wulf H.C. Mortensen N.N. Poulsen T. Photoprotection in vitiligo and normal skin. A quantitative assessment of the role of stratum corneum, viable epidermis and pigmentation.Acta Derm Venereol. 1996; 76: 429-432PubMed Google Scholar) as well as in the assessment of skin appearance. Another important application is the quantitative assessment of inflammation, erythema, and occlusion, by means of hemoglobin content and oxygen saturation evaluation (Merschbrock et al., 1994Merschbrock U. Hoffman J. Caspary L. Huber J. Schmickaly U. Lubbers D.W. Fast wavelength scanning reflectance spectrophotometer for noninvasive determination of hemoglobin oxygenation in human skin.Int J Microcirc. 1994; 14: 274-281Crossref PubMed Scopus (30) Google Scholar;Svaasand et al., 1995Svaasand L.O. Norvang L.T. Fiskerstrand E.J. Stopps E.K.S. Berns M.W. Nelson J.S. Tissue parameters determining the visual appearance of normal skin and port-wine stains.Lasers Med Sci. 1995; 10: 55-65Crossref Scopus (156) Google Scholar). Finally, knowledge of the scattering properties can reveal information about the morphology and architecture of skin, such as the arrangement and density of the collagen fibers in the dermis (Ferdman and Yannas, 1993Ferdman A.G. Yannas I.V. Scattering of light from histologic sections: a new method for the analysis of connective tissue.J Invest Dermatol. 1993; 100: 710-716Abstract Full Text PDF PubMed Google Scholar). This information could be useful in the assessment of burn damage or in the examination of skin resurfacing conditions. We have found that the melanin content of the skin, as evaluated through the model, shows a good correlation with independent measurements performed using a standard chromameter device. This is an important finding, as it opens the way for direct, quantitative, noninvasive, assessment of the melanin content in human skin. The hemoglobin content as measured by the model on the back of the volunteers was found to be consistent among different volunteers, and the average concentration was lower than in previous studies that measured the average concentration of hemoglobin in the capillary network of the colon mucosa (Zonios et al., 1999Zonios G. Perelman L.T. Backman V. Manoharan R. Fitzmaurice M. Van Dam J. Feld M.S. Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo.Appl Opt. 1999; 38: 6628-6637Crossref PubMed Scopus (480) Google Scholar). This is reasonable, because the skin of the volunteers studied was under normal conditions and no inflammation or other abnormality related to increased hemoglobin content was clinically observed. In the case of forearm arterial and venous blood flow occlusion, the typical hemodynamic response of the anticipated reactive hyperemia was observed, immediately after the release of the pressure cuff. These results are in good agreement with previous studies (Hampson and Piantadosi, 1988Hampson N.B. Piantadosi C.A. Near infrared monitoring of human skeletal muscle during forearm ischemia.J Appl Physiol. 1988; 64: 2449-2457PubMed Google Scholar). The scattering properties of skin were found to be in general agreement with existing reports, with the average scatterer size being in the range 0.4 < ds < 1.5 µm (Mourant et al., 1998Mourant J.R. Freyer J.P. Hielscher A.H. Eick A.A. Shen D. Johnson T.M. Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics.Appl Opt. 1998; 37: 3586-3593Crossref PubMed Scopus (573) Google Scholar;Zonios et al., 1999Zonios G. Perelman L.T. Backman V. Manoharan R. Fitzmaurice M. Van Dam J. Feld M.S. Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo.Appl Opt. 1999; 38: 6628-6637Crossref PubMed Scopus (480) Google Scholar). A very weak correlation was observed between the scattering properties of skin and the tissue type, with the average scatterer size being slightly larger in volunteers with higher melanin content. This could be an indication that scattering from melanin, which has not been explicitly taken into account in the model, possibly contributes to the skin scattering properties as already reported (Jacques and McAuliffe, 1991Jacques S.L. McAuliffe D.J. The melanosome: threshold temperature for explosive vaporization and internal absorption coefficient during pulsed laser irradiation.Photochem Photobiol. 1991; 53: 769-775Crossref PubMed Scopus (219) Google Scholar;Rajadhyaksha et al., 1995Rajadhyaksha M. Grossman M. Esterowitz D. Webb R.H. Anderson R.R. In vivo confocal scanning laser microscopy of human skin: melanin provides strong contrast.J Invest Dermatol. 1995; 104: 946-952Crossref PubMed Scopus (900) Google Scholar). Nevertheless, this is an observation that requires further investigation, in which we are currently engaged. Another point requiring additional investigation is the multilayered structure of skin. The model employed in this work assumes a one-layer skin geometry, but the two major absorbers found in skin, hemoglobin and melanin, reside in different skin layers, with the melanin found in the top layer (epidermis) and the hemoglobin found in the capillary network of the second layer (dermis). For skin that is not very dark, our results show that the single-layer approximation is applicable and yields reasonable results. For very dark skin types (type V and above), however, which we did not study in detail, the applicability of the model remains to be investigated. Finally, in this work, hemoglobin and melanin were assumed to be the only skin chromophores. Other chromophores may be present in the skin though, especially in pathologic conditions. In such a case, the present model could be enhanced to include these chromophores. One such example is bilirubin, which has a broad absorption band at 460 nm (Hannemann et al., 1979Hannemann R.E. Dewitt D.P. Hanley E.J. Schreiner R.L. Bonderman P. Determination of serum bilirubin by skin reflectance: effect of pigmentation.Pediatr Res. 1979; 13: 1326-1329Crossref PubMed Scopus (13) Google Scholar) and gives skin the characteristic yellow color of jaundice. We thank Mabet Alora and Takeshi Sakamaki for help with the UVB irradiation of skin sites. This work was supported in part by L'OREAL Recherche, Clichy, France. According to the model, the diffuse reflectance R(λ) is given byR(λ)=R0μs′μs′+μa{exp(μz0)+exp[−(1+(4A/3))μz0]−z0exp(−μr1′)r1′−(1+(4A/3))z0exp(−μr2′)r2′}(A.1) withr1′=(z02+rc2)1/2r2′=[z02(1+(4A/3))2+rc2]1/2μ=[3μa(μa+μs′)]1/2, z0=1μs′.μs′(λ) and μa(λ) are the reduced scattering and absorption coefficients, respectively, and A is a parameter that depends on the refractive index of skin. We have assumed n = 1.4 for the skin refractive index, which yields A = 2.8 (Zonios et al., 1999Zonios G. Perelman L.T. Backman V. Manoharan R. Fitzmaurice M. Van Dam J. Feld M.S. Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo.Appl Opt. 1999; 38: 6628-6637Crossref PubMed Scopus (480) Google Scholar). The parameters R0 and rc are empirically determined by measuring the diffuse reflectance spectra of polystyrene bead suspensions as explained further below and elsewhere (Zonios et al., 1999Zonios G. Perelman L.T. Backman V. Manoharan R. Fitzmaurice M. Van Dam J. Feld M.S. Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo.Appl Opt. 1999; 38: 6628-6637Crossref PubMed Scopus (480) Google Scholar). Absorption in skin was assumed to be due to hemoglobin and melanin. Thus, the absorption coefficient μa(λ) was written as the sum of the oxy/deoxy hemoglobin (van Assendelft, 1970van Assendelft O.W. Spectrophotometry of Haemoglobin Derivatives. C C Thomas, Springfield, IL1970: 355-359Google Scholar) and melanin (Crippa et al., 1978Crippa R.P. Christofoletti V. Romeo N. A band model for the melanin deduced from optical absorption and photoconductivity experiments.Biochim Biophys Acta. 1978; 538: 164-170Crossref PubMed Scopus (114) Google Scholar) absorptions as follows:μa(λ)=cHb*[αεHbO2(λ)+(1−α)εHb(λ)]+cmelεmel(λ)(A.2) whereα=cHbO2cHbO2+cHbis the hemoglobin oxygen saturation parameter, cHbO2 and cHb are the concentrations of oxyhemoglobin and deoxyhemoglobin, respectively, and cHb* = cHbO2 + cHb is the total concentration of hemoglobin. The molecular extinction coefficient spectra of oxyhemoglobin, deoxyhemoglobin, and melanin are εHbO2(λ), εHb(λ), and εmel(λ), respectively, and are shown in Figure A1. Note the characteristic absorption bands of oxyhemoglobin (415, 542, and 577 nm) and deoxyhemoglobin (430 and 555 nm), as well as the relatively smooth and featureless absorption spectrum of melanin. Scattering was modeled by assuming skin scatterers to be a homogeneous collection of microspheres (Zonios et al., 1999Zonios G. Perelman L.T. Backman V. Manoharan R. Fitzmaurice M. Van Dam J. Feld M.S. Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo.Appl Opt. 1999; 38: 6628-6637Crossref PubMed Scopus (480) Google Scholar), and μs′(λ) was assumed to exhibit a linear dependence on wavelength. This is an approximation supported by Mie scattering theory (Born and Wolf, 1975Born M. Wolf E. Principles of Optics. Pergamon Press, New York1975Google Scholar;Wiscombe, 1979Wiscombe W.J. NCAR Technical Note. National Center for Atmospheric Research, Boulder, Colorado1979Google Scholar) as illustrated in Figure A2(a), which shows μs′(λ) for a collection of homogeneous spherical scatterers with Gaussian distribution (with width σ) in the scatterer diameter. The reduced scattering coefficient for three different distributions is shown with average scatterer sizes ds = 0.4, 1.0, and 2.0 µm, and σ= 0.1 µm. As can be seen, μs′(λ) has an approximately linear dependence on wavelength in the 460–820 nm range, with a slope depending on the scatterer size. Furthermore, the slope of μs′(λ) was not found to have a significant dependence on the width of the Gaussian distribution. Thus, μs′(λ) was written as follows:μs′(λ)=(1−scλ−λminλmax−λmin)μs′(λmin)(A.3) where sc is the spectral slope, which is a function of the characteristic scatterer size ds, and λmax = 820 nm and λmin = 460 nm are the maximum and minimum wavelengths, respectively. Figure A2(b) shows the dependence of sc on ds as calculated by Mie theory in the range 0.3 < ds < 2.0 µm. In this range, this dependence can be expressed bysc≈14ds1/2(A.4) with ds in µm. An average “effective” scatterer size can thus be assigned to a given scattering spectrum, from the value of the scattering slope sc. In the above Mie theory calculations, a refractive index of ns = 1.40 was assumed for the scatterers, and n0 = 1.36 for the surrounding material (Perelman et al., 1998Perelman L.T. Backman V. Wallace M. et al.Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution.Phys Rev Lett. 1998; 80: 627-630https://doi.org/10.1103/physrevlett.80.627Crossref Google Scholar;Zonios et al., 1999Zonios G. Perelman L.T. Backman V. Manoharan R. Fitzmaurice M. Van Dam J. Feld M.S. Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo.Appl Opt. 1999; 38: 6628-6637Crossref PubMed Scopus (480) Google Scholar). Determination of rc and R0 was performed as explained in detail elsewhere (Zonios et al., 1999Zonios G. Perelman L.T. Backman V. Manoharan R. Fitzmaurice M. Van Dam J. Feld M.S. Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo.Appl Opt. 1999; 38: 6628-6637Crossref PubMed Scopus (480) Google Scholar). Briefly, the procedure followed is outlined here. A polystyrene bead suspension was used with bead diameter 1.0 µm and the bead density was adjusted such that the diffuse reflectance signal intensity was made comparable to that of skin. The reduced scattering spectrum of the beads was calculated using Mie theory and equation (A.1) was fitted to the actual measured bead reflectance spectrum to determine the optimal value of rc. Fitting was performed by minimizing the χ2 difference between the diffuse reflectance spectrum of the bead suspension and equation (A.1), using the Levenberg-Marquardt nonlinear iterative minimization method (Press et al., 1992Press W.H. Teukolsky S.A. Vetterling W.T. Flannery B.P. Numerical Recipes in C. 2nd edn. Cambridge University Press, 1992: 681-699Google Scholar). Once rc = 4.0 mm and R0 =0.70 were determined in this way, they were kept fixed throughout the entire data analysis of the skin spectra. Diffuse reflectance spectra from skin were analyzed by fitting to equation (A.1). Fitting was carried out by minimizing the χ2 difference between the model and the experimental data for the entire wavelength range using the Levenberg-Marquardt minimization method (Press et al., 1992Press W.H. Teukolsky S.A. Vetterling W.T. Flannery B.P. Numerical Recipes in C. 2nd edn. Cambridge University Press, 1992: 681-699Google Scholar).
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