Estimation of melanin and hemoglobin in skin tissue using multiple regression analysis aided by Monte Carlo simulation

Izumi Nishidate; Yoshihisa Aizu; Hiromichi Mishina

doi:10.1117/1.1756918

1 July 2004 Estimation of melanin and hemoglobin in skin tissue using multiple regression analysis aided by Monte Carlo simulation

Izumi Nishidate, Yoshihisa Aizu, Hiromichi Mishina

Author Affiliations +

Journal of Biomedical Optics, Vol. 9, Issue 4, (July 2004). https://doi.org/10.1117/1.1756918

Abstract

To estimate the concentrations of melanin and blood and the oxygen saturation in human skin tissue, we propose a method using a multiple regression analysis aided by a Monte Carlo simulation for diffuse reflectance spectra from the skin tissue. By using the absorbance spectrum as a response variable and the extinction coefficients of melanin, oxygenated hemoglobin, and deoxygenated hemoglobin as predictor variables, the multiple regression analysis gives regression coefficients. The concentrations of melanin and blood are determined from the regression coefficients using conversion vectors that are estimated numerically in advance, while the oxygen saturation is obtained directly from the regression coefficients. Numerical and experimental investigations were performed for layered skin tissue models and phantoms. Measurements of human skin were also carried out to monitor variations in the melanin and blood contents and oxygenation during cuff occlusion. The results confirmed the usefulness of the proposed method.

1. Introduction

Various optical methods¹ ² ³ ⁴ ⁵ ⁶ have been reported for effective and noninvasive medical diagnostics of living human skin tissue. Quantitative estimation of the melanin and blood concentrations and blood oxygenation is important for detecting various skin diseases, including cancers; monitoring health status and tissue metabolism; and evaluating convalescence. The major chromophores in the superficial skin layer are melanin, oxygenated hemoglobin, and deoxygenated hemoglobin, which show distinctive optical absorption properties in the visible wavelength range. If the concentration of each chromophore varies, then the corresponding change may be visible in light diffusely reflected from the skin tissue in this wavelength range. Therefore, analysis of the diffuse reflectance spectra may provide us with useful information on tissue activities that are related to melanin and hemoglobin. On the other hand, the diffuse reflectance spectra also depend on the light scattering that is due to the structures of tissues and cells, such as collagen fibers and other cellular structures. Thus, estimation of the melanin and hemoglobin concentrations requires knowledge of the scattering properties of light in skin tissue as well as its absorption properties.

A number of spectroscopic methods have been studied for noninvasive determination of the scattering and absorption properties in living tissues, including time-resolved measurements,⁷ a frequency-domain method,⁸ and spatially resolved measurements.⁹ ¹⁰ ¹¹ ¹² ¹³ Chemometrics is generally known as a useful means for data analysis in spectroscopy. Some methods using this approach have been studied for skin tissue spectroscopy also to evaluate absorbing components in the tissue. Tsumura et al.;¹⁴ proposed a method using an independent component analysis of color images for visualizing the spatial distributions of melanin and hemoglobin in human skin. Shimada et al.;¹⁵ reported a method for predicting absorption spectra of skin tissue using multiple regression analysis based on the modified Lambert-Beer law. This method is simple and seems to be promising for routine assessments of melanin and hemoglobin concentrations in skin tissue because of assuming the modified Lambert-Beer law. However, reliable and absolute measurements are still difficult with this method because of the nonlinearity between the absorbance and the concentration of chromophores. Owing to this problem, the measurable range of concentration changes is limited and an estimation of oxygen saturation has not yet been made using their method.

In this paper we propose a different approach to using multiple regression analysis to estimate the concentrations of melanin and hemoglobin together with the oxygen saturation in skin tissue. In the proposed method, the nonlinearity between the absorbance of skin tissue and the concentration of each chromophore is compensated by conversion vectors derived in advance from a number of absorbance spectra simulated by the Monte Carlo method for various values of the melanin and hemoglobin concentrations. The possibility of this method was numerically investigated for absorbance spectra generated with typical optical parameters of human skin. Experiments with two-layered skin tissue phantoms and in vivo measurements for human skin during cuff occlusion were performed to confirm the usefulness of the method.

2. Theory

2.1.

Multiple Regression Analysis

In multiple regression analysis, a relationship between two variable sets y_k(k=1,2,…,p) and x_jk(j=1,2,…,q) is assumed to be given by the following linear equation,

Eq. (1)

y_{k} = α_{0} + \sum_{j = 1}^{q} α_{j} \times x_{j k} + e_{k},

where y_k and x_jk represent response variables and predictor variables, respectively, α₀ is a constant component, and e_k expresses unknown error components. In this multiple regression model, p is the number of sample data being analyzed and q is that of predictor variables. The regression coefficients α_j(j=0,1,2,… ,q) are unknown values that are estimated by the method of least-squares in the analysis. Let us denote the estimated regression coefficients by α^_j; then the corresponding multiple regression equation is expressed as

Eq. (2)

{\hat{y}}^{k} = {\hat{α}}_{0} + \sum_{j = 1}^{q} a^{j} \times x_{j k},

Eq. (3)

y_{k} = {\hat{y}}_{k} + r_{k}

where y^_k are the response variables estimated using α^_j, and r_k is the residual. A measure for suitability of the regression equation is given by the parameter R², which is defined as the square of the multiple correlation coefficient R, that is,

Eq. (4)

R^{2} = {[\frac{Σ_{k} (y_{k} - \bar{y_{k}}) ({\hat{y}}_{k} - \bar{{\hat{y}}_{k}})}{\sqrt{Σ_{k} {(y_{k} - \bar{y_{k}})}^{2}} \sqrt{Σ_{k} {({\hat{y}}_{k} - \bar{{\hat{y}}_{k}})}^{2}}}]}^{2},

where y¯_k and y^¯_k denote the average of y_k and y^_k, respectively, over the p number of data. The value of R is the correlation coefficient between y_k and y^_k. The value of R² ranges from 0 to 1, and the linear approximation becomes better as R² approaches 1.

2.2.

Multiple Regression Model for Modified Lambert-Beer Law

Figure 1 shows a flow chart of the proposed method. For a semi-infinite scattering medium such as human skin, an absorbance spectrum A(λ) is defined as

Eq. (5)

A (λ) = - {log}_{10} D (λ),

where D(λ) is a reflectance spectrum obtained from the medium and λ is its wavelength. According to the modified Lambert-Beer law,¹⁶ ¹⁷ the absorbance spectrum of a homogeneous scattering medium containing an absorber is expressed as

Eq. (6)

A (λ) = C \times \bar{l} (λ, C) \times ε (λ) + S (λ),

where C and ε(λ) are the molar concentration and molar extinction coefficient of the absorber, respectively, l¯(λ,C) is the mean path length, and S(λ) is attenuation that is due to scattering. Considering that the upper part of the skin tissue mainly consists of epidermis containing the melanin and dermis containing the oxygenated and deoxygenated hemoglobin, the absorbance spectrum may be given by the sum of the absorbance of epidermis, A_epi(λ), that of dermis, A_der(λ), and attenuation by scattering, S(λ) as the following equation:¹⁶ ¹⁷

Eq. (7)

A (λ) = A_{e p i} (λ) + A_{d e r} (λ) + S (λ) .

Using Eq. (6), Eq. (7) is rewritten as

Eq. (8)

A (λ) = C_{m} \times {\bar{l}}_{e p i} (λ, C_{m}) \times ε_{m} (λ) + C_{o h} \times {\bar{l}}_{d e r} (λ, C_{o h}, C_{d h}) \times ε_{o h} (λ) + C_{d h} \times {\bar{l}}_{d e r} (λ, C_{o h}, C_{d h}) \times ε_{d h} (λ) + S (λ),

where the subscripts m, oh, and dh for C and ε(λ) denote the melanin, oxygenated hemoglobin, and deoxygenated hemoglobin, respectively. The two functions l¯_epi(λ,C_m) and l¯_der(λ,C_oh,C_dh) are the mean path length in epidermis and dermis, respectively. For light diffusely reflected from a semi-infinite medium containing absorbers, it is generally known¹⁶ ¹⁷ that the mean path length becomes shorter as the concentration of absorbers increases, while the attenuation by scattering has no change. There are also some other chromophores such as bilirubin in skin tissue, but their contribution to the absorbance spectrum is considered to be small in comparison with those of the three chromophores given here. Then we assume that the effect of other chromophores is included in S(λ) of Eq. (8).

Figure 1

Flow chart of the estimation process.

By using the absorbance spectrum as a response variable and the molar extinction coefficients of the three chromophores as predictor variables, the multiple regression model given by Eq. (1) can be applied to Eq. (8) as¹⁵

Eq. (9)

A (λ_{k}) = a_{m} \times ε_{m} (λ_{k}) + a_{o h} \times ε_{o h} (λ_{k}) + a_{d h} \times ε_{d h} (λ_{k}) + a_{0} + e (λ_{k}),

where a_m, a_oh, a_dh, and a₀ are the regression coefficients, e(λ_k) is an error component, and λ_k indicates discrete values in the wavelength range treated in the analysis. By executing the multiple regression analysis for one sample of the absorbance spectrum consisting of a p number of discrete wavelengths, one set of the four regression coefficients is obtained. When they are denoted by a^_m, a^_oh, a^_dh, and a^₀, the resultant regression equation is written as

Eq. (10)

\hat{A} (λ_{k}) = {\hat{a}}_{m} \times ε_{m} (λ_{k}) + {\hat{a}}_{o h} \times ε_{o h} (λ_{k}) + {\hat{a}}_{d h} \times ε_{d h} (λ_{k}) + {\hat{a}}_{0},

where A^(λ_k) is the estimated absorbance spectrum. In this case, the regression coefficient a^₀ is expressed by applying the relation of Eqs. (2) and (3) to Eqs. (9) and (10), as

Eq. (11)

{\hat{a}}_{0} = \bar{A} - \bar{ε_{m}} \times {\hat{a}}_{m} - \bar{ε_{o h}} \times {\hat{a}}_{o h} - {\bar{ε}}_{d h} \times {\hat{a}}_{d h},

where A¯, ε¯_m, ε¯_oh, and ε¯_dh are the averages of A(λ_k), ε_m(λ_k), ε_oh(λ_k), and ε_dh(λ_k) over the wavelength range, or k=1 to p. In this paper, we denote this part of the multiple regression analysis, MRA1.

The regression coefficients, a^_m, a^_oh, and a^_dh describe the degree of contribution of each molar extinction coefficient to the absorbance spectrum and thus the three regression coefficients are closely related to the concentrations C_m, C_oh, and C_dh, respectively. Then, in Eq. (11), the value of a^₀ is also related to the three concentrations. As seen from the first terms in Eqs. (8) and (10), however, the regression coefficient a^_m includes a factor of the mean path length in epidermis, l¯_epi(λ,C_m) and the value of a^_m is nonlinearly related to that of C_m. This discussion applies also in the cases of a^_oh and a^_dh for dermis. Moreover, the regression coefficient a^_m depends on the concentrations of oxygenated hemoglobin C_oh and deoxygenated hemoglobin C_dh in dermis, and a^_oh and a^_dh depend on C_m as well. As illustrated in Fig. 2, light incident on the skin’s surface is propagated into epidermis and dermis under the scattering and absorption. Then some portion of the scattered light comes back from the dermis to the epidermis and finally is emitted from the surface. Therefore, the increase in A_der according to C_oh and C_dh causes a decrease in the light scattered back to the epidermis and thus results in a decrease in A_epi. Similarly, an increase in A_epi according to C_m may result in a decrease in A_der. In this way, the absorbance effects in epidermis and dermis are interdependent and their contributions cannot be separated. Therefore, the absolute values of C_m, C_oh, and C_dh are not accurately determined only from a^_m, a^_oh, and a^_dh, respectively. For this problem, Shimada et al.;¹⁵ have proposed the use of relative changes in the absorbance spectra as the predictor variable. But the effects of nonlinearity and interdependence mentioned above still remain in their results,¹⁶ ¹⁷ and their method is limited to a small range of the change in each concentration.

Figure 2

Two-layered skin tissue model.

The oxygen saturation of hemoglobin in dermis, SO ₂, is defined by the concentrations of oxygenated and deoxygenated hemoglobin as

Eq. (12)

{SO}_{2} = \frac{C_{o h}}{C_{o h} + C_{d h}} = \frac{C_{o h}}{C_{t h}},

where C_th=C_oh+C_dh is the concentration of total hemoglobin. Using the regression coefficients in Eq. (10), the estimated oxygen saturation SO ₂ may be given by

Eq. (13)

{SO}_{2} = \frac{{\hat{a}}_{o h}}{{\hat{a}}_{o h} + {\hat{a}}_{d h}} = \frac{{\hat{a}}_{o h}}{{\hat{a}}_{t h}},

where a^_th=a^_oh+a^_dh. The values of a^_oh and a^_dh contain the above-mentioned effects. However, it is considered that those effects on the value of SO ₂ are expected to be small, because the oxygen saturation is given by a ratio of the two coefficients in Eq. (13).

2.3.

Compensation for the Nonlinearity

To compensate for the effects of nonlinearity and interdependence in MRA1, it is necessary to know the mean path length functions l¯_epi(λ,C_m) and l¯_der(λ,C_oh,C_dh). However, they are generally unknown and thus it is necessary to estimate the relation between the regression coefficients a^_m, a^_oh, a^_dh, and a^₀ and the three concentration values, C_m, C_oh, and C_dh. There are some general methods for treating an estimation problem like this, including a neural network and multiple regression analysis using higher-order terms. A neural network usually gives relatively good estimates, but it is rather difficult to find appropriate parameters. As described in the previous section, we employed a multiple regression analysis to evaluate the absorption spectra because of its simplicity. To keep the effective use of this method, we apply a multiple regression analysis also to the estimation of the nonlinear relation.

When the oxygen saturation is obtained by Eqs. (12) or (13), it is enough to obtain the concentration of total hemoglobin, C_th, instead of both C_oh and C_dh. Thus the multiple regression model in this case is expressed by the following two equations:

Eq. (14)

C_{m}^{i} = b_{m} \times {\hat{a}}^{i} + e_{m}^{i},

Eq. (15)

C_{t h}^{i} = b_{t h} \times {\hat{a}}^{i} + e_{t h}^{i},

Eq. (16)

{\hat{a}}^{i} = {[1, {\hat{a}}_{m}^{i}_{}, {\hat{a}}_{}^{i}_{t h}, {\hat{a}}_{0}^{i}, {\hat{a}}_{m}^{i} \times {\hat{a}}_{t h}^{i}, {\hat{a}}_{m}^{i} \times {\hat{a}}_{0}^{i}, \dots higher order terms \dots]}^{t},

Eq. (17)

b_{m} = [b_{m}^{0}, b_{m}^{1}, b_{m}^{2}, \dots, b_{m}^{z - 1}],

Eq. (18)

b_{t h} = [b_{t h}^{0}, b_{t h}^{1}, b_{t h}^{2}, \dots, b_{t h}^{z - 1}],

where C_m ⁱ and C_th ⁱ (=C_oh ⁱ+C_dh ⁱ) denote the concentrations of melanin and total hemoglobin, respectively, in the medium from which the i’th absorbance spectrum sample is obtained, and e_m ⁱ and e_th ⁱ are error components. In Eq. (16), […]^t represents the transposition of the vector. Here, a^ ⁱ expresses the vector that contains the regression coefficients estimated by MRA1 for the i’th absorbance spectrum and their higher-order terms. The number of components in this vector is assumed to be z. In Eqs. (14) and (15), b _m×a^ ⁱ and b _th×a^ ⁱ are the scalar product. Two coefficient vectors b _m and b _th are unknown, but they can be estimated by the multiple regression analysis in which C_m ⁱ and C_th ⁱ are treated as response variables and vector components of a^ ⁱ as predictor variables. When the estimated coefficient vectors are denoted as b^ _m and b^ _th,

Eq. (19)

{\hat{C}}_{m}^{i} = {\hat{b}}_{m} \times {\hat{a}}^{i},

Eq. (20)

{\hat{C}}_{t h}^{i} = {\hat{b}}_{t h} \times {\hat{a}}^{i},

Eq. (21)

{\hat{b}}_{m} = [{\hat{b}}_{m}^{0}, {\hat{b}}_{m}^{1}, {\hat{b}}_{m}^{2}, \dots, {\hat{b}}_{m}^{z - 1}],

Eq. (22)

{\hat{b}}_{t h} = [{\hat{b}}_{t h}^{0}, {\hat{b}}_{t h}^{1}, {\hat{b}}_{t h}^{2}, \cdot\cdot\cdot, {\hat{b}}_{t h}^{z - 1}],

where C^_m ⁱ and C^_th ⁱ are the estimated values of C_m ⁱ and C_th ⁱ, respectively. We call this multiple regression analysis MRA2 in this paper.

To perform MRA2, we need a number of datasets that contain various concentrations of melanin C_m and total hemoglobin C_th, and the corresponding absorbance spectra. To prepare these data sets, we employed a Monte Carlo simulation for the layered skin tissue model.¹⁸ This process, including the Monte Carlo calculation, is shown as the preparation work in Fig. 1 and its details are described in the next section. The coefficients b^ _m and b^ _th obtained from MRA2 imply vectors that convert the regression coefficients obtained in MRA1 to the concentrations of melanin and total hemoglobin, respectively, and thus we refer to them as the conversion vectors in this study. Once we determine the conversion vectors b^ _m and b^ _th in MRA2 for necessary ranges of the melanin and hemoglobin concentrations, the values of C^_m and C^_th can easily be obtained by Eqs. (19) and (20) from the regression coefficients in MRA1 without the Monte Carlo simulation.

3. Derivation of the Conversion Vectors

3.1.

Method

To derive the conversion vectors numerically, we first calculated diffuse reflectance spectra at intervals of 10 nm in the wavelength range from 400 to 700 nm by Monte Carlo simulation for the layered skin tissue model shown in Fig. 2. In this model, we assumed that melanosomes containing melanin and blood, including hemoglobin, are homogeneously distributed over the epidermis and dermis, respectively. The actual human skin overlies a fatty layer and muscle tissue, which have their own optical properties. The light reflected from the skin tissue is probably affected by these subcutaneous layers. However, the diffuse reflectance spectrum in the visible wavelength range is primarily governed by the epidermis and upper part of the dermis, although the near-infrared light probes those deeper layers. Thus, we mainly paid attention to the contribution of the two upper layers in the present simulation. A more realistic model that includes the subcutaneous layers should be used in the next study of this method.

We used the Monte Carlo code developed by Wang et al.;,¹⁸ in which the diffuse reflectance from multilayered tissue is calculated. This code uses the Henyey-Greenstein phase function.¹⁹ The Monte Carlo simulation requires that each layer be characterized by the scattering coefficient μ_s(λ) cm ⁻¹, absorption coefficient μ_a(λ) cm ⁻¹, anisotropy factor g(λ), refractive index n(λ), and thickness d cm in the above-mentioned wavelength range. The absorption coefficient μ_a(λ) generally changes as the concentration of melanin or hemoglobin varies according to physiological conditions, whereas the other parameters may not substantially do so. Thus, values of the scattering coefficient μ_s(λ), anisotropy factor g(λ), refractive index n(λ), and thickness d were assumed to be known in the present model. In actual calculations, we input typical published values for μ_s(λ) ²⁰ of dermis and g(λ) ²¹ to both epidermis and dermis, which are provided as a function of wavelength. For a proper simulation, different values of μ_s(λ) should be used for the epidermis and dermis. However, the scattering coefficient of the epidermis was not available in the literature for the analyzed wavelength range. Thus, the same values were used for both epidermis and dermis.

It is said²⁰ ²¹ that the difference in the scattering coefficient between epidermis and dermis is not large, although there actually is some. The effects of such a difference on the analysis should be investigated in the future when the estimation accuracy is studied. The refractive index n(λ) is fixed to be 1.4 for the two layers over the wavelength range of 400 to 700 nm and thus is denoted simply by n in this paper. The thickness values d of epidermis and dermis were set to be 0.006 and 0.494 cm, respectively.

The absorption coefficient of the epidermis depends on the volume concentration of melanosome in epidermis, C_mel. We assumed that the absorption coefficient of a simple melanosome given in the literature²² corresponds to that of epidermis in the case of C_mel=100. Then we derived the corresponding absorption coefficients of epidermis for ten different concentrations of C_mel=1 to 10 at intervals of 1, by simply proportioning it to that for C_mel=100. The absorption coefficient of dermis depends both on the volume concentration C_b and oxygen saturation SO ₂ of blood in dermis. In the same way as described earlier, the generally known absorption coefficients of oxygenated (SO ₂=100) and deoxygenated (SO ₂=0) blood having a 45 hematocrit were assumed to be that of dermis in the case of C_b=100.

Then the absorption coefficients of dermis were derived for five different concentrations of C_b=0.2, 0.4, 0.6, 0.8, and 1.0 in both cases of SO ₂=0 and 100. These derivations were made on 31 wavelength points at 400 to 700 nm at 10-nm intervals. In this way the combination of C_mel, C_b, and SO ₂ took 100 different cases, from which 100 reflectance spectra were calculated. Taking into account our previous study²³ concerning the error of simulated results and calculation time, the number of incident photons was set to be 10⁵ for each wavelength. The calculation time for one spectrum ranging from 400 to 700 nm with 31 wavelength points was roughly 30 min, using the Athlon CPU, 1.4 GHz. Then all the reflectance spectra were converted into the absorbance spectra by Eq. (5).

Performing MRA1 for all the absorbance spectra, 100 sets of the regression coefficients a^_m, a^_oh, a^_dh, and a^₀ were obtained. Although the absorbance spectra were calculated in the range of 400 to 700 nm, we employed the spectral data only in the range of 500 to 600 nm for MRA1 because the spectral features of melanin and hemoglobin notably appear in this wavelength range. In fact, the mean value of the proportion R² for 100 absorbance spectra was 0.98±0.01, which means a good regression. In addition, the correlation between the molar extinction coefficient of oxygenated hemoglobin, ε_oh(λ), and that of deoxygenated hemoglobin, ε_dh(λ), is lower at 500 to 600 nm than in the other ranges, 400 to 500 and 600 to 700 nm. Thus, the multiple regression analysis may give a good separation between ε_oh(λ) and ε_dh(λ) as predictor variables. With this possibility, we expect that the oxygen saturation SO ₂ may be estimated from the values of a^_oh(λ) and a^_dh(λ) by Eq. (13).

Finally, we performed MRA2 to obtain the conversion vectors for estimating the volume concentrations, C_mel and C_b, of melanosome and blood, respectively. In the analysis, the values of C_mel ⁱ and C_b ⁱ input into the i’th Monte Carlo simulation were used as the i’th response variables, while the regression coefficients a^_m ⁱ, a^_th ⁱ, and a^₀ ⁱ obtained from the absorbance spectrum by the i’th Monte Carlo simulation were used as the i’th predictor variables. The number of datasets was 100, that is, i=1 to 100. From our preliminary estimations, it was reasonable to use components of the first and third order in the vector a^ ⁱ of Eq. (16) and thus the number z of components was 14. It is noted that the treatment in this section is not essentially different from the use of molar concentrations as described in the previous sections because the molar concentrations of melanin and hemoglobin are proportional to the volume concentrations of melanosome and blood, respectively. Table 1 lists components of the two conversion vectors b^ _mel and b^ _b which originally correspond to b^ _m and b^ _th in Eqs. (19) and (20), respectively. Two resultant regression equations using these vectors are expressed as

Table 1

Components of the conversion vectors b^ mel and b^ b obtained from MRA2.
z	a^ _i	b^ _mel		b^ _b
1	1	b^_m 0	−6.428E−01	b^_th 0	−5.489E−02
2	a^_m i	b^_m 1	1.692E+04	b^_th 1	−6.050E+01
3	a^_th i	b^_m 2	−4.542E+04	b^_th 2	1.778E+04
4	a^_0 i	b^_m 3	7.356E+00	b^_th 3	5.264E−01
5	a^_m i ³	b^_m 4	2.172E+10	b^_th 4	1.015E+09
6	a^_th i ³	b^_m 5	−1.212E+16	b^_th 5	−1.731E+14
7	a^_0 i ³	b^_m 6	2.340E+01	b^_th 6	1.453E+01
8	a^_m i⋅a^_th i⋅a^_0 i	b^_m 7	5.523E+09	b^_th 7	1.585E+09
9	a^_m i ²⋅a^_th i	b^_m 8	−1.647E+11	b^_th 8	−6.486E+11
10	a^_m i ²⋅a^_0 i	b^_m 9	5.766E+07	b^_th 9	2.952E+06
11	a^_th i ²⋅a^_m i	b^_m 10	−3.080E+14	b^_th 10	−3.072E+10
12	a^_th i ²⋅a^_0 i	b^_m 11	5.298E+11	b^_th 11	1.441E+11
13	a^_0 i ²⋅a^_m i	b^_m 12	2.132E+03	b^_th 12	−1.500E+04
14	a^_0 i ²⋅a^_th i	b^_m 13	−6.203E+06	b^_th 13	−1.682E+06

Eq. (23)

{\hat{C}}_{m e l}^{i} = {\hat{b}}_{m e l} \times {\hat{a}}^{i},

Eq. (24)

{\hat{C}}_{b}^{i} = {\hat{b}}_{b} \times {\hat{a}}^{i} .

These equations with the values in Table 1 were used for the following numerical and experimental investigations in this paper.

3.2.

Numerical Investigation

Before our experiments, we performed a numerical investigation to verify the feasibility of the proposed method using the conversion vectors. Instead of measurements, we calculated newly diffuse reflectance spectra by using the Monte Carlo simulation as test samples. For the volume concentrations, C_mel and C_b, of melanosomes in epidermis and blood, respectively, having a 45 hematocrit in dermis, the same values as those used in Sec. 3.1 were again employed. With ten values of C_mel and five values of C_b, we had 50 different combinations. The oxygen saturation SO ₂ of blood was set to be 60 for all 50 combinations. Other conditions for the simulation were fixed to be the same as those in Sec. 3.1. In this way we obtained 50 diffuse reflectance spectra and then converted them into the absorbance spectra by using Eq. (5). Figure 3 demonstrates typical absorbance spectra measured on the finger surface of a Japanese adult and calculated by the Monte Carlo simulation for C_mel=3.0, C_b=0.2, and SO ₂=60. Measurements were made by using a multichannel spectrometer under the illumination of a halogen lamp light. In Fig. 3, the measured result shows relatively high absorbance in the shorter wavelength range, has a slight increase around 550 nm, and decreases again in the longer wavelength range. This distinctive curve is due to the well-known light-absorption properties²⁴ ²⁵ of melanin and hemoglobin, which are characterized by their molar extinction coefficients. The same spectral characteristics as in the measured result are seen also in the simulated one. This comparison indicates that the present calculation model is suitable for numerically simulating the diffuse reflectance spectra from human skin tissue.

Figure 3

Typical absorbance spectra obtained from human skin tissue and the Monte Carlo simulation.

Then by performing MRA1 for each absorbance spectrum, 50 sets of a^_m, a^_oh, a^_dh, and a^₀ were obtained. The mean value of the proportion R² was again 0.98±0.01 for 50 absorbance spectra. At this point in time, the oxygen saturation SO ₂ was calculated for each spectrum from Eq. (13). The mean value of SO ₂ was 59.7±1.24, which gives good agreement with the original value of 60. To check reliability for the estimation of oxygen saturation, we performed the same investigation as above on the absorbance spectra that were calculated under the conditions of SO ₂=0 and 100. The mean values of SO ₂ were evaluated to be 8.5±1.98 and 87.0±2.90 for the original values of 0 and 100, respectively. This discrepancy for both cases may result from the distortion of absorbance spectra, which is due to the loss of reflection by the wavelength-dependent light scattering in the tissue. As a consequence, the absorbance spectra for SO ₂=0 become not fully independent of the molar extinction coefficient ε_oh(λ), although the oxygenated hemoglobin is not included in the simulation. Thus, the regression coefficient a^_oh becomes not zero, but a certain small value in MRA1. The same discussion can be applied to the case of SO ₂=100. These errors of SO ₂ possibly suggest the limits of abilities of MRA1 for estimating oxygen saturation.

Figures 4(a) and 4(b) show the values of a^_m and a^_th(=a^_oh+a^_dh) versus the volume concentrations, C_mel and C_b, of melanosomes and blood, respectively. In Fig. 4(a), the value of a^_m increases nonlinearly with an increase in C_mel. This indicates the nonlinear relation between the absorbance of epidermis, A_epi, and the concentration of melanosome, C_mel, as described in Sec. 2.2. Moreover, the value of a^_m decreases with an increase in C_b. The same tendency is also seen in the results of a^_th shown in Fig. 4(b). These properties indicate that the absorbance of epidermis, A_epi, and that of dermis, A_der, are interdependent. On the other hand, the value of a^₀ (not shown here) increased with increases in both C_mel and C_b. Therefore it is clear that the volume concentrations of melanin and blood are not accurately determined by using only MRA1, although the regression coefficients a^_m, a^_th, and a^₀ are related to those concentrations.

Figure 4

Regression coefficients (a) a^ _m and (b) a^ _th versus their concentrations obtained from multiple regression analysis, MRA1.

We next substituted the regression coefficients a^_m, a^_th, and a^₀ into the regression equations [Eqs. (23) and (24)] obtained in advance by MRA2 and then estimated the volume concentrations C_mel and C_b for each of 50 absorbance spectra, respectively. Figure 5 shows a comparison between the estimated and original values of the volume concentrations C_mel for melanosomes and C_b for blood. In both Figs. 5(a) and 5(b), the estimated values well agree with the original ones in given concentration ranges of C_mel and C_b. These results indicate the effectiveness of the method for compensation of the nonlinearity in the multiple regression analysis for skin tissue spectroscopy.

Figure 5

Comparison of the estimated and original concentrations for (a) melanosomes and (b) blood.

4. Experiments with Skin Tissue Phantom

4.1.

Skin Tissue Phantom

To confirm the usefulness of the proposed method, we performed experiments using skin tissue phantoms. The phantom consists of an epidermis and a dermis layer. We prepared agar solution by diluting agar powder (Ina Food Industrial Inc., Japan) with saline at a weight ratio of 0.8. To make the scattering condition, Intralipid 10 solution (Fresenius Kabi AB, Sweden) was added to the agar solution. The resultant solution was used as the base material for epidermis and dermis layers. The volume ratio of Intralipid 10 solution to the agar solution was one to ten. A coffee solution was introduced as a substitute for melanin into the base material, and this mixture was used to make an epidermis layer. An oxygenated dermis layer was made by adding a small amount of fully oxygenated horse blood having a 44 hematocrit to the base material, while a deoxygenated dermis layer was prepared by sufficiently dropping a Na ₂ S ₂ O ₄ -added saline solution on the surface of the oxygenated dermis layer. All these layers were hardened in various molds having the required thickness and size by being cooled at about 5.5 °C for 30 min.

The thicknesses of epidermis and dermis layers were made to be 0.1 and 0.5 cm, respectively, while the area of each layer was 2.6×4.5 cm ². The 0.1-cm thickness of the epidermis phantom is an order of magnitude greater than the actual epidermal thickness. In this study, however, it was difficult to make a layer thinner than 0.1 cm. To reduce the expected effects of this thickness on experimental results, then, the scattering and absorption coefficients of the epidermis phantom were controlled so that the absorbance spectrum became close to that of human skin shown in Fig. 3. The volume concentration of a coffee solution in the epidermis layer was set to be C_c=5.0, 10, and 20, while that of horse blood in the dermis layer was C_b=0.2, 0.4, and 0.6. The subscript c for the coffee concentration corresponds to mel for melanosome in the previous section. The oxygen saturations of blood in the oxygenated and deoxygenated dermis layers were assumed to be SO ₂=100 and 0, respectively, because both the oxygenation and deoxygenation were fully made in the above process. Finally, we built two-layered skin tissue phantoms by putting the epidermis layer on the dermis layer as the test sample.

4.2.

Method

As preparation measurements, we first determined the absorption coefficient μ_a(λ) and scattering coefficient μ_s(λ) in 500 to 600 nm of each layer that makes up the phantoms, because μ_a(λ) and μ_s(λ) are necessary for the Monte Carlo simulation, and μ_a(λ) is also required to calculate the volume concentrations of coffee and blood. For this purpose, we measured diffuse reflectance and total transmittance spectra of each layer individually. Figure 6 schematically shows experimental setups for measuring diffuse reflectance spectra and total transmittance spectra. A halogen lamp light (150 W), which covers the visible wavelength range from 400 to 700 nm, illuminates the phantom layer via a light guide and lens with a spot diameter of 0.4 cm. The diameter and focal length of the lens are 5.4 and 10 cm, respectively. The layer was placed between two glass slides having a thickness of 1.0 mm and fixed at the sample holder of an integrating sphere (Labsphere Inc., RT-060-SF). The detected area of the layer was circular, with a diameter of 2.2 cm. Light diffusely reflected or transmitted from this area was received at the input face of an optical fiber probe having a diameter of 400 μm placed at the detector port of the sphere. The fiber transmits the received light into a multichannel spectrometer (Ocean Optics Inc., SD-2000), which measures reflectance or transmittance spectra in the visible wavelength range under the control of a personal computer (PC).

Figure 6

Experimental setups for (a) diffuse reflectance measurements and (b) total transmittance measurements.

To determine μ_a(λ) and μ_s(λ) from measured spectra, we employed the inverse Monte Carlo method.²⁶ In the present study, the Monte Carlo calculation of reflectance and transmittance spectra was iterated for varying values of μ_a(λ) and μ_s(λ) until the difference between the simulated and measured spectral values decreased below a predetermined threshold. The values used in the last step of iteration were adopted as the final results. This process was carried out at intervals of 10 nm from 500 to 600 nm, and wavelength-dependent properties of μ_a(λ) and μ_s(λ) were obtained for each layer. A spectral curve for one layer was determined by averaging the results of five runs. In these calculations, the refractive index n was assumed to be 1.33 for all the layers in the whole wavelength range, and the published values²⁷ were used for the anisotropy factor g(λ) of Intralipid 10. The absorption coefficient μ_a(λ) varies according to the concentration of coffee or blood in each layer. Then we calculated the coefficient for a 100 volume concentration by making a linear fitting of various absorption coefficients obtained under the different concentrations given to the skin tissue phantoms. Figure 7(a) shows the resultant properties for the absorption coefficients of coffee solution μ_a ^c(λ), oxygenated blood μ_a ^ob(λ), and deoxygenated blood μ_a ^db(λ), and Fig. 7(b) shows the scattering coefficient μ_s(λ). The scattering coefficient in Fig. 7(b) is the average value for epidermis and dermis layers.

Figure 7

Properties of (a) absorption coefficients and (b) scattering coefficient for the skin tissue phantoms used in experiments.

We also need to have the conversion vectors for the skin tissue phantoms used in this study because the results of Table 1 were obtained with human skin conditions and thus were unavailable for the phantoms. We generated diffuse reflectance spectra ranging from 500 to 600 nm by using a Monte Carlo simulation with conditions of the phantoms. For this simulation, the volume concentration C_c of the coffee solution in the epidermis layer, that of blood in the dermis layer, C_b, and the oxygen saturation SO ₂ of blood were set to be the same as those used for the phantoms. We thus obtained 18 different reflectance spectra from the combination of C_c, C_b, and SO ₂, and then converted them into absorbance spectra by Eq. (5). Performing MRA1 and MRA2 as described in Sec. 3.1, we derived the conversion vectors and the corresponding regression equations for estimating the volume concentrations, C_c and C_b, of coffee solution and blood, respectively. The molecular weights of coffee and horse blood used for the phantoms were unknown and their molar extinction coefficients were accordingly unavailable. However, the absorption coefficient is proportional to the molar extinction coefficient. In MRA1, therefore, the absorption coefficients μ_a ^c(λ), μ_a ^ob(λ), and μ_a ^db(λ) shown in Fig. 7(a) were used as the predictor variables instead of the molar extinction coefficients. The mean value of the proportion R² was 0.98±0.01 for the 18 absorbance spectra.

4.3.

Results and Discussion

Although we made both oxygenated and deoxygenated dermis layers for the skin tissue phantom, we did not use the latter because its deoxygenated state was unstable and the optical properties of the epidermis layer may have been affected by permeation of Na ₂ S ₂ O ₄ into the dermis layer through the epidermis layer. Hence, nine different kinds of two-layered skin tissue phantoms were made from the combination of C_c and C_b with SO ₂=100. Using the setup of Fig. 6(a), we measured the diffuse reflectance spectra of skin tissue phantoms in the range of 400 to 700 nm and then converted them into the absorbance spectra by Eq. (5). Figure 8 shows typical absorbance spectra measured from the phantoms having different volume concentrations of the coffee solution. In Fig. 8, as the value of C_c becomes larger, the absorbance in a shorter wavelength range increases significantly in comparison with that in a longer wavelength range. This is due to the large absorption property of coffee solution in the shorter wavelength range, as expected from Fig. 7(a). The three absorbance spectra also reveal the well-known characteristic spectral curve of oxygenated blood, as shown in Fig. 7(a). These absorbance spectra of the phantom are similar to those of human skin shown in Fig. 3. Thus we conclude that the 0.1-cm thickness of the epidermis phantom had no significant effect on the present analysis, and that these skin tissue phantoms could be used successfully in our experiments.

Figure 8

Typical absorbance spectra obtained from the two-layered skin tissue phantoms.

Performing MRA1 for each absorbance spectrum measured from the skin tissue phantom, nine sets of a^_c, a^_b(=a^_ob+a^_db), and a^₀ were obtained. Here the subscripts c, b, ob, and db correspond to m, th, oh, and dh described in Sec. 2.2, respectively. The mean value of the proportion R² was 0.96±0.01 for the nine absorbance spectra. That of SO ₂ was 87.4±7.07, which resulted in underestimation with a relatively large variation. However, considering the numerical result for SO ₂=100 discussed in Sec. 3.2, this experimental result is reasonable at present. Substituting the regression coefficients a^_c, a^_b, and a^₀ into the regression equations obtained by the MRA2 analysis for the skin tissue phantom in Sec. 4.2, we estimated the volume concentrations, C_c and C_b, of coffee solution and blood for each phantom, respectively. Figure 9 shows the comparison between the estimated and original values of the volume concentrations for C_c and C_b. In Fig. 9(a), the estimated value agrees with the original one for each value of C_b. The agreement between the estimated and original values is also shown in Fig. 9(b). Hence the feasibility of this method was verified by the phantom experiments. These results also demonstrate the usefulness of the skin tissue phantoms developed for this study.

Figure 9

Comparison of the estimated and original concentrations for (a) coffee solution and (b) blood.

5. Experiments with Human Skin Tissue

5.1.

Method

To confirm the applicability of the present method to an in vivo situation, we performed time series measurements of melanin and hemoglobin on human skin tissue during cuff occlusion. A brachial cuff of a mercury sphygmomanometer (Kenzmedico Co., Ltd., Japan) was fixed around the upper arm of a Japanese adult male and pressure up to 200 mmHg was applied. Using the setup shown in Fig. 6(a), we conducted time series measurements of diffuse reflectance spectra from the surface of the forearm. Measurements were made at 2-s intervals for 14 min. One spectrum was obtained by averaging eight runs, in which one run was made in 250 ms. We converted all the diffuse reflectance spectra into the absorbance spectra, performed MRA1 for each spectrum, and obtained time series sets of a^_m, a^_th, and a^₀. The mean value of the proportion R² was 0.96±0.01 for all the absorbance spectra. The volume concentration of melanosomes, C_mel, that of blood, C_b, and the oxygen saturation SO ₂ were estimated from Eqs. (23), (24), and (13), respectively, together with the conversion vectors listed in Table 1. Since these vectors were used for deriving experimental results, it should be noted that the assumptions for the scattering coefficient, anisotropy factor, refractive index, and thickness in Sec. 3.1 were applied to these human measurements.

5.2.

Results and Discussion

Figure 10 shows the time course of C_mel, C_b, and SO ₂ during the cuff occlusion test. Each temporal variation is plotted at every 10 sec. Before the cuff occlusion (between −140 and 0 s), the oxygen saturation ranges from 51.6 to 60.3, which agrees with the results reported in the literatures.³ ⁴ ⁶ The mean value of C_b is 0.24±0.01, which is fairly close to a general example of the volume concentration of blood in dermis, C_b=0.2, assuming that the blood is uniformly distributed. Typical ranges for the volume concentration of melanosomes in epidermis have been reported:²⁸ C_mel=1 to 3 for light-skinned Caucasians, 11 to 16 for Mediterranean types, and 18–43 for darkly pigmented Africans. Considering that the subject in this experiment was a relatively light-skinned Japanese, the mean value of C_mel=4.6±0.02 is acceptable.

Figure 10

Time course of concentration of melanosomes, C_mel, blood, C_b, and oxygen saturation SO ₂, during the cuff occlusion.

During the cuff occlusion (between 0 and 370 s), the value of SO ₂ shows the well-known deoxygenation curve in which the oxygen saturation falls exponentially and approaches zero. On the other hand, the value of C_b increases slowly. This change in C_b probably has a physiological cause in that during the occlusion the venous outflow is reduced more than the arterial inflow. After the cuff was released (between 370 and 700 s), both SO ₂ and C_b increased sharply and then gradually returned to the values before the occlusion. These changes in SO ₂ and C_b may be due to the postocclusion reactive hyperemia and oxygenation, and recovery of blood circulation. In spite of the dramatic change in SO ₂ and C_b, the value of C_mel remains almost unchanged during measurements. This constancy of C_mel indicates that the interdependence between the absorbance of epidermis and that of dermis is effectively compensated by the present method. In this way, physiological conditions of human skin tissue were successfully monitored in vivo by using the proposed method.

However, this method requires different conversion vectors because the target tissue will have different scattering properties and thicknesses. Therefore, alternative conversion vectors must be prepared by Monte Carlo simulation whenever a target with different conditions is measured. In such a case, it may take about 12 h to generate 100 samples of reflectance spectra and to determine the conversion vectors by means of the Athlon CPU, 1.4 GHz, for example. There may be a possible approach to reduce this computational burden. Reflectance spectra of 100 samples are calculated in advance with typical scattering, absorbing, and geometric conditions. In using the present method, they are referenced as the standard set of spectra and may be modified according to deviations from the original (typical) values in those conditions when a new target tissue is measured, instead of recalculations of reflectance spectra. We consider that this approach is worth studying in future work. In addition, the problem of estimation errors for SO ₂=0 and 100 described in Sec. 3.2 still remains unsolved. These errors may be reduced if the value of SO ₂ is calculated, not from the values of a^_oh and a^_dh, but from that of C^_oh and C^_dh. It is possible to obtain the regression equations needed for deriving C^_oh and C^_dh by performing MRA2. This subject will be examined in the near future.

6. Conclusion

A new method has been proposed for estimating the concentrations of melanin and hemoglobin, and oxygen saturation in human skin tissue. A multiple regression analysis based on the modified Lambert-Beer law was successfully used to determine the regression coefficients relating to the concentration of melanin and blood. Nonlinearity between the regression coefficients and the melanin and blood concentrations was compensated by using conversion vectors derived from Monte Carlo simulations. The potential of this method was verified by Monte Carlo simulation and phantom experiments using two-layered skin tissue models. The results of in vivo experiments presented expected variations in the melanin and blood concentrations and the oxygen saturation in human skin during cuff occlusion. At present, this method relies on typical values published in the literature for the scattering coefficient, anisotropy factor, refractive index, and thickness. It is thus necessary to evaluate how a change in these values affects the estimated results. It is also desirable to combine this method with other measurement techniques that provide some or all of the above four quantities, for example, optical coherence tomography.

Acknowledgment

Part of this work was supported by the research grant of CASIO Science Promotion Foundation, Japan.

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Notes

Address all correspondence to Dr. Yoshihisa Aizu, Muroran Institute of Technology, Department of Mechanical Systems Engineering, 27-1 Mizumoto-cho, Muroran 050-8585, Japan. Tel: 81 143 46 5348; Fax: 81 143 46 5360; E-mail: aizu@mmm.muroran-it.ac.jp

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Izumi Nishidate, Yoshihisa Aizu, and Hiromichi Mishina "Estimation of melanin and hemoglobin in skin tissue using multiple regression analysis aided by Monte Carlo simulation," Journal of Biomedical Optics 9(4), (1 July 2004). https://doi.org/10.1117/1.1756918

Published: 1 July 2004

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KEYWORDS

Skin

Absorbance

Tissues

Blood

Monte Carlo methods

Oxygen

Absorption

1.

Introduction

2.

Theory

2.1.

Multiple Regression Analysis

Eq. (1)

Eq. (2)

Eq. (3)

Eq. (4)

2.2.

Multiple Regression Model for Modified Lambert-Beer Law

Eq. (5)

Eq. (6)

Eq. (7)

Eq. (8)

Figure 1

Eq. (9)

Eq. (10)

Eq. (11)

Figure 2

Eq. (12)

Eq. (13)

2.3.

Compensation for the Nonlinearity

Eq. (14)

Eq. (15)

Eq. (16)

Eq. (17)

Eq. (18)

Eq. (19)

Eq. (20)

Eq. (21)

Eq. (22)

3.

Derivation of the Conversion Vectors

3.1.

Method

Table 1

Eq. (23)

Eq. (24)

3.2.

Numerical Investigation

Figure 3

Figure 4

Figure 5

4.

Experiments with Skin Tissue Phantom

4.1.

Skin Tissue Phantom

4.2.

Method

Figure 6

Figure 7

4.3.

Results and Discussion

Figure 8

Figure 9

5.

Experiments with Human Skin Tissue

5.1.

Method

5.2.

Results and Discussion

Figure 10

6.

Conclusion

Acknowledgment

REFERENCES

Notes

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