We present an in vivo study of the reduced scattering coefficient of normal skin and of common melanocytic nevi in Caucasian subjects. The spectral shape of the reduced scattering coefficient is described well by a power-law dependence on the wavelength, in accordance with previous studies of light scattering by biological tissues. We investigate statistical variations in the scattering spectrum slope and also identify an inherent correlation between scattering intensity and scattering spectral slope, observed mainly in normal skin. In addition, we do not find any significant differences between the scattering properties of normal skin and common melanocytic nevi. Finally, we also provide a short review of previously published studies reporting on the light scattering properties of human skin both in vivo and in vitro.
© 2009 Optical Society of America
Light scattering properties of skin can provide valuable information regarding its biochemical composition and microarchitecture. This information can be obtained with the additional advantages of non-invasiveness and real-time monitoring and can be very useful for skin characterization as well as for the diagnosis of a wide range of pathologic conditions and diseases. One of the simplest ways to probe skin light scattering properties is through the study of diffusely reflected light.
The light scattering properties of the skin have been studied in the visible and near-infrared regions of the spectrum by various researchers, both in vitro and in vivo [1-17]. However, almost all of these studies were of initial and exploratory nature and as a result, the skin light scattering properties remain largely unexplored, especially in vivo. Thus, it appears that there is plenty of room for further investigations, particularly of various skin lesions and pathologic conditions.
In this article, we set out for a more detailed and systematic investigation of the light scattering properties of normal human skin and common melanocytic nevi in Caucasian volunteers. In particular, by employing a simple implementation of diffuse reflectance spectroscopy through a fiber optic probe, we investigate the biological variability of skin scattering properties in vivo and identify a correlation between the scatterer density and scatterer size in normal skin. We also investigate the scattering properties of benign pigmented lesions (melanocytic nevi i.e. common skin moles) and show that the presence of melanin does affect the average scattering properties of skin as measured by diffuse reflectance.
2.1 Experimental setup
The experimental setup employed a compact CCD spectrophotometer (Ocean Optics, USB2000-VIS-NIR). Light delivery and collection was by means of a fiber optic probe (Ocean Optics, R200-7) consisting of six 200 μm core diameter optical fibers for delivery of light and a single 200 μm core optical fiber for diffuse reflectance collection, with the six illumination fibers placed around the central collection fiber in a circular manner. The numerical aperture of the optical fibers was equal to 0.22. Illumination was provided by a tungsten-halogen light source (Ocean Optics, HL-2000). All spectra were calibrated on a diffuse reflectance standard (Ocean Optics, WS-1); calibration spectra on the standard were routinely measured prior to data acquisition. Calibration spectra were measured by placing the probe at a fixed distance from the reflectance standard (5.0 mm) such that a calibration scale could be established in accordance with the calibration scale established previously on tissue phantoms . Spectra were collected in the 450-900 nm range with spectral resolution approximately equal to 1.5 nm and typical signal to noise ratio greater than 100:1. Typical integration time for data acquisition was 80 ms.
2.2 In vivo data
Data were collected on the skin of three healthy adult volunteers with Fitzpatrick skin type III (Caucasian descent). Measurements were conducted on normal skin of the volar forearm and on melanocytic nevi located on the arms and trunk of the same volunteers with typical nevi diameter smaller than 5 mm. In general, a few spectra were measured on different sites on each nevus, depending on nevus size. In all cases, diffuse reflectance data were collected by gently placing the probe in contact with the skin, with zero pressure applied.
2.3 Reflectance model
with R(λ) the diffuse reflectance spectrum, μa(λ), μ′s(λ) the absorption and reduced scattering coefficients, respectively, and k 1 =0.025 mm-1, k 2 =0.057 two constants which are determined with a one-time calibration on tissue phantoms . These constants depend, in general, on the geometrical characteristics of the probe.
2.4 Skin absorption
Several chromophores absorb light in skin. However, the only chromophores affecting the reflectance spectra in the 450-900 nm wavelength range are melanin and hemoglobin. Thus, the absorption coefficient of skin, μa (λ), can be expressed as follows:
In Eq. (2), c Hb1 is the oxyhemoglobin concentration, c Hb2 is the deoxyhemoglobin concentration, cm is the melanin concentration, ε Hb1(λ) and ε Hb2(λ) are the absorption spectra of oxyhemoglobin and deoxyhemoglobin, respectively , and λ0=400 nm is a constant.
The melanin absorption spectrum is described by an exponential dependence on the wavelength; this is supported by numerous in vitro studies (please see  for a short review) as well as by our recent in vivo studies [19,20]. This remarkable property of melanin, uncharacteristic of any other biological chromophore, permits description of its absorption spectrum with a single parameter i.e. the exponential decay constant, km. Melanin absorption generally affects the reflectance spectra over the entire wavelength range used in this study, while hemoglobin absorption shows two characteristic dips at approximately 540 and 580 nm.
2.5 Skin scattering
The reduced scattering coefficient of skin, μ′s(λ), is described by Eq. (3) i.e. it is assumed to exhibit a power law dependence on the wavelength
with λs = 1000 nm a constant. This functional dependence is supported by numerous experimental studies and is widely accepted and used in biomedical optics, even though no rigorous theoretical model has established its general validity. Nevertheless, several biological tissue scattering models that have been proposed, ranging from simple Mie theory models [21,22] (i.e. scattering of light by spherical microparticles) to other more sophisticated models [23,24], do predict the power law dependence described by Eq. (3). The exponent γ (which sometimes is also called scattering power [25,26]) is restricted by both theoretical predictions and experimental results in the range 0.20 < γ < 4.0. Small values of γ correspond to larger scatterer sizes in tissue i.e. up to one order of magnitude larger than the wavelength of light (e.g. cells, cell nuclei) while at the other extreme, higher values of γ (up to γ=4.0) are due to smaller scatterer sizes. For γ=4 we have the case of Rayleigh scattering with scatterer sizes typically smaller than an order of magnitude than the wavelength of light. Using a simple Mie theory model, it is possible to establish a relationship between average scatterer size diameter and γ [21,22]. Fig. 1 illustrates this dependence of γ on scatterer size. To produce this figure, Mie theory [27,28] was used to calculate μ′s(λ) spectra in the 400-900 nm range for ensembles of scatterers with sizes following a Gaussian distribution with FWHM equal to 20% of the corresponding peak scatterer size value. The resulting μ′s (λ) spectra were fitted to Eq. (3) and thus the exponent γ was determined; each data point in Fig. 1 was calculated in this way. The continuous line represents an empirical fit to the data; we found that a Lorentzian cumulative function, described by Eq. (4), fits the data well:
with a 1= 0.3518, a 2 = 4.561, a 3 =0.1364, a 4 = −0.091 and d the spherical scatterer diameter in microns. In all the above Mie calculations, the scatterer refractive index was assumed equal to 1.42 and a background refractive index was assumed equal to 1.36; both are reasonable assumptions for soft biological tissues, including skin [21,23,29]. Note that Fig. 1 is in very good agreement with similar results reported by Mourant et al using narrower Gaussian distributions of scatterer sizes . It is also important to note that the data shown in Fig. 1 and described by Eq. (4) are only indicative and they are not supposed to represent a rigorous and detailed relationship between tissue scatterer size and γ, for biological tissue in general. Another noteworthy point is that γ asymptotically approaches the value of approximately 0.35 for scatterer sizes greater than a few microns. This has also been noted theoretically before , but lower experimental values of γ down to at least γ ≃ 0.2 have been reported for breast tissue .
One additional interesting point we should stress is the fact that Eq. (3) may be well approximated by a linear dependence on wavelength for low values of γ, e.g. in the range 0.2 < γ < 1.0. We have successfully employed such an approximation for modeling skin scattering before with good results [17,19,20,31,32] and, in addition, this linear dependence has also been noted by other researchers previously . To express this linear approximation we have used Eq. (5)
with c 1 parameter describing the slope of the reduced scattering spectrum and λ1 = 400 nm and λ2 = 800 nm two constants. Fig. 2 shows how Eqs. (3) and (5) compare for two different values of γ; γ=0.3 and γ=0.6. As can be seen, different values of γ correspond to different values of the c 1 parameter; c1 =0.19 and c1 =0.35, respectively. The agreement between Eqs. (3) and (5) is reasonable over the 450-900 nm range while for higher values of γ, Eq. (5) is not such good approximation to Eq. (3) anymore. For skin, a wide range of γ values has been reported in the literature; for a short review please see Section 3 below. However, as we will show further below, our in vivo measurements yield low values of γ, typically γ < 1.0 for which general good agreement with the linear approximation described by Eq. (5) may be achieved.
2.6 Data analysis
Data were analyzed by fitting the experimental data to Eq. (1) with the optical coefficients described by Eqs. (2) and (3). Thus, fitting produced a set of six parameters characteristic for each skin spectrum:c Hb1, c Hb2, cm, km, μ′s(λs), and γ. Fitting was performed using the Levenberg-Marquardt minimization method offered by the MERLIN optimization environment . This method is in general very robust for minimizing functions expressed as the sum of squares. In all cases, there were no bounds imposed on the parameters and the fitting produced positive reasonable parameter values. In addition to automated fitting, a chi-square analysis was conducted on selected spectra, by varying the fit parameters and by evaluating the corresponding goodness-of-fit (chi-square). In all cases, this analysis showed that the optimization software identified the global minimum, ensuring that a unique set of six parameters existed for each spectrum yielding the best agreement between the experimental data and the model.
3. Literature review
We present here a brief review of the scattering properties of skin as reported in the literature. We limit the review to human skin only (excluding breast and head) and we include both in vivo and in vitro results. Table 1 presents a summary of the available results.
The main observation is the wide range of reported values for γ starting from γ=0.50 and going all the way up to γ=3.70. This is an indication that, according to Fig. 1, the average scatterer size may change by an order of magnitude from approximately 0.5 μm down to approximately 0.05 μm (almost reaching the Rayleigh scattering regime). It is not obvious that this variation may be attributed to biological variability, so additional effects may be responsible for it. First, the value of γ may change depending on the penetration depth of the technique used to perform the measurements. This mainly applies to in vivo measurements; one can normally assume that as penetration depth increases, scattering becomes more affected by the dermis which is rich in dense connective tissue, where average scatterer size may be smaller than that of the highly cellular epidermal layer. Second, for the in vitro measurements, there may be in vitro artifacts at play resulting in higher values of γ, unlikely to be observed in vivo. In addition, the epidermal layer contribution may be minimal for the in vitro measurements and there may also be errors and inaccuracies related to the reflectance and transmission measurements and the use of integrating sphere techniques . Finally, it is worth noting that all three in vitro studies [1-3] reporting high values of γ used the same technique (adding-doubling ) for calculation of skin optical properties.
Two of the aforementioned in vitro studies assumed a considerable presence of Rayleigh scattering to explain the high values of γ [1,2,35]. However, we believe this to be highly speculative because it is possible to model the data using Mie theory only, without having to resort to Rayleigh scattering. This is because the Rayleigh scattering cross section is weak and would require an unrealistically high density of scatterers in order to significantly affect skin light scattering properties. In addition, Rayleigh scattering would significantly reduce the scattering anisotropy factor g, something that is not observed experimentally [14,36].
The reported γ values are generally lower in vivo, with 0.50 < γ < 1.70 for Caucasian skin. The only exception to this is a single study reporting an average value of γ=2.45 for black African skin . This result is quite interesting since it may indicate that the scattering properties of skin are affected by melanosomes and melanin. However, the aforementioned study  found differences mainly in γ and smaller differences in the overall values of the reduced scattering coefficient. Confocal microscopy also reveals that scattering due to melanin provides strong contrast in skin  and some authors generalize these observations by stating that “melanin is a major contributor to epidermal scattering” . However, as we will show below, we have found no dramatic differences in light scattering between pigmented and normal skin using diffuse reflectance spectroscopy, which is in agreement with at least a couple of previous in vivo studies [11,39]. One possible explanation for this apparent discrepancy may be related to the detailed geometry employed by the different techniques. More specifically, confocal microscopy observes singly scattered light in the backscattered direction and focuses on a relatively small skin volume while diffuse reflectance spectroscopy measures multiply forward-scattered light, probes larger skin volume, and it is also affected by a wide range of scattering centers in skin besides melanin and melanosomes. All the above observations and arguments clearly call for more detailed studies and investigations.
Finally, we should make a comment on the absolute value of the reduced scattering coefficient. All in vivo studies report values in the 0.5-3.0 mm-1 range which are reasonable for soft epithelial tissues and quite consistent with our own results as we will show below. However, the in vitro studies report higher values up to 11 mm-1. These values seem unlikely to be observed in vivo, but again more detailed and conclusive studies are needed to confirm or rule out this.
4. Results and discussion
Figure 3 shows typical spectra measured on normal skin and melanocytic nevi together with model fits to Eq. (1). The model fits are excellent, indicating that the model does a very good job in describing the data. The main and noteworthy features of the spectra shown in Fig. 3 are as follows.
In the normal skin spectrum, a linear dependence of the reflectance on the wavelength is apparent in the 600-900 nm range. This is actually a power-low dependence but with a low γ value (γ=0.70) such that it appears linear by visual inspection (see also Fig. 2). In the same wavelength range, the reflectance spectrum is only affected by scattering. Absorption due to characteristic hemoglobin absorption bands is evident in the 500-600 nm region and overall melanin absorption effects are negligible because spectra were measured in the inner forearm, an untanned skin area with quite low melanin concentration. Contrary to the normal skin spectrum, melanin absorption drastically affects the two melanocytic nevi spectra. Both nevi spectra exhibit the characteristic monotonic reduction in intensity towards shorter wavelengths, due to melanin absorption. Note that melanin absorption effects become evident below 700 nm for spectrum (A) while they affect the entire spectrum up to 900 nm for spectrum (B). The principal difference between the two spectra is in melanin concentration. Due to lower melanin concentration in spectrum (A), scattering effects dominate in the 700-900 nm range. In fact, in this wavelength range the linear dependence of reflectance on the wavelength is clearly observed, just like in the normal skin spectrum, thus suggesting that scattering properties of melanocytic nevi and normal skin are similar, at least in that wavelength range. In both nevi spectra, hemoglobin absorption dips are less pronounced as compared with the normal skin spectrum. This is because of the layered structure of skin; hemoglobin lies in the dermis below melanin and it is thus optically shielded by melanin. Finally, there is an inherent overall difference in scattering intensity between spectra (A) and (B). This is most evident at the long wavelength end of the spectrum (around 900 nm) where melanin absorption is minimal. Also, the normal skin spectrum is characterized by higher scattering intensity than both nevi spectra.
Figure 4 shows the distribution of the γ parameter values for normal skin (Fig. 4(a)) and melanocytic nevi (Fig. 4(b)). Notably, γ values are quite variable and they generally lie in the range 0.2 < γ < 1.2. Their statistical distributions for both normal skin and melanocytic nevi exhibit similar general characteristics, with the melanocytic nevi distribution being generally broader. These results are in good general agreement with results reported previously for in vivo skin as is evident by inspection of Table 1.
Figure 5 shows plots of μ′s(λs) as a function of γ for normal skin (Fig. 5(a)) and melanocytic nevi (Fig. 5(b)). For normal skin, a clear correlation is observed between the two parameters while a similar correlation also appears present in melanocytic nevi data, even though it is much less pronounced in the latter. It would be very interesting to explore the origins of this correlation which indicates that higher values of the scattering coefficient (and hence scatterer density) are inversely correlated with scattering slope (and hence average scatterer size). One likely explanation could be related to probe pressure; in fact a similar effect has been reported for animal muscle tissue due to probe pressure . However, even though we were able to observe a small similar effect by varying probe pressure in skin, we could not fully reproduce this correlation by just varying probe pressure in our experiments. In addition, all data shown here were measured with zero probe pressure. Another potential explanation may have to do with an inherent scattering anisotropy that has been observed in skin [41,42]. Clearly, the aforementioned correlation deserves further investigation.
Finally, we should briefly discuss the major approximation employed by the model i.e. the one-layer approximation. Skin consists of several layers that are distinctly different in their morphology and biochemical composition. However, it has been shown previously by many other research groups and also by us that the one-layer assumption is a reasonable approximation when it comes to studying epithelial tissues with reflectance spectroscopy. Furthermore, the short delivery-collection geometry reduces the dependence of the light penetration depth on the tissue optical properties and limits light penetration to the top layers of skin i.e. epidermis and dermis. The larger deviation from the one-layer approximation is noted for hemoglobin which lies in the dermis, typically a few hundred microns below the skin surface. Accurate assessment of hemoglobin is though beyond the scope of the present work and does not seem to affect assessment of melanin and scattering properties. Distribution of melanin, in particular, conforms much better to the one-layer approximation since it is reasonable to assume that in a melanocytic nevus melanin is more or less evenly distributed throughout the top layers of the skin, which are being interrogated in this study. Similar arguments apply to skin scattering properties; they vary much less across the spectrum compared to melanin and hemoglobin, and in essence, what we measure is an average scattering property in the top millimeter of skin or so.
We have presented an investigation of the light scattering properties of normal skin and common melanocytic nevi in vivo. Our main observations can be summarized as follows.
- Skin scattering properties are in general agreement with previous studies. Both the absolute values of the reduced scattering coefficient and the spectral slope γ agree well with previously reported in vivo studies. This means that one can expect, in general, γ<1 for in vivo skin with the reduced scattering coefficient being described very well by the power-law dependence of Eq. (3) or even by the linear approximation of Eq. (5).
- Melanin does not appear to affect skin scattering properties significantly. We have not observed any significant differences between the scattering properties of normal skin and common melanocytic nevi. This means that melanin mainly affects the diffuse reflectance spectra through absorption. It also suggests that Rayleigh scattering due to melanin which has been observed in vitro  is negligible compared to both melanin absorption and scattering from the remaining morphological microstructures of skin. It is noteworthy that our observations are in agreement with a previous in vivo study which also did not find any differences in the reduced scattering coefficient between normal skin and melanocytic nevi at 633 nm .
- Scattering intensity and spectral slope appear correlated, particularly in normal skin. The correlation is much less pronounced for melanocytic nevi which indicates a possible intrinsic differentiation between the scattering properties of melanocytic nevi and normal skin, perhaps in contrast to observation (b) just above. Scattering by melanosomes could be responsible here; it would definitely be quite interesting to further investigate the origins of this effect. In addition, it would be interesting to further investigate probe pressure effects  as well as inherent inhomogeneities in the scattering properties of the skin [41,42] in relation to the aforementioned observed effects.
- Scattering slope γ is not very high in vivo. For most of our data, we observed γ<1 in agreement with previously published in vivo data [9-13]. This leaves the high γ values reported by in vitro studies [1-3] largely unexplained and also questions the relatively high contribution of Rayleigh scattering that has been employed to justify these high γ in vitro values.
- Power-law dependence on wavelength provides an excellent description for the reduced scattering coefficient over a broad wavelength range. This is in agreement with a wide range of observations for various types of soft biological tissues and biological cells. It is quite fortunate that such a reliable description for the reduced scattering coefficient exists, albeit largely empirical in nature. Small deviations from the power law dependence can be observed though and they can prove useful in the development of more sophisticated and potentially more rigorous and accurate models of light scattering by biological tissue [23,24]; or they can be helpful in identifying particular morphological microstructures responsible for light scattering in tissue .
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