DOI 10.1007/s10812-014-0013-8
Journal of Applied Spectroscopy, Vol. 81, No. 5, November, 2014 (Russian Original Vol. 81, No. 5, September–October, 2014)
METHOD FOR ESTIMATING BILIRUBIN ISOMERIZATION EFFICIENCY IN PHOTOTHERAPY TO TREAT NEONATAL JAUNDICE S. A. Lisenko* and M. M. Kugeiko
UDC 535.36;547.937:616.36-0085-0.53.31
We propose a method for quantitative assessment of the efficacy of phototherapy to treat neonatal jaundice using the diffuse reflectance spectrum for the newborn’s skin, based on the analytical dependence of the measured spectrum on the structural and morphological parameters of the skin, affecting the optical conditions in the medium, and an algorithm for rapid calculation of the bilirubin photoisomerization rate in the skin tissues as a function of the structural and morphological parameters of the skin and the wavelength of the exciting radiation. From the results of a numerical simulation of the process of radiation transport in the skin, we assess the stability of our method to variations in the scattering properties of the skin and the concentrations of its optically active chromophores (melanin, oxyhemoglobin, deoxyhemoglobin). We show that in order to achieve the maximum efficacy of phototherapy, we should use light from the range 484–496 nm. In this case, the intensity of the exciting radiation should be selected individually for each newborn according to the bilirubin photoisomerization rate characteristic for it. Keywords: neonatal jaundice, bilirubin, lumirubin, phototherapy, photoisomerization, skin, optical parameters, diffuse reflection. Introduction. Hyperbilirubinemia (jaundice) develops in newborns as a result of accumulation of excess ZZbilirubin molecules, a toxic pigment formed from hemoglobin as a result of breakdown of erythrocytes, in the blood (and consequently in the skin tissues). The most widely used method for treating hyperbilirubinemia is phototherapy. When the skin of a newborn is exposed to optical radiation, isomerization of the ZZ-bilirubin molecules found in the skin occurs, with formation of low-toxicity photoisomers: ZE-bilirubin, EZ-bilirubin (configurational photoisomers), and lumirubin (LR, structural photoisomer) [1]. EZ-bilirubin, by absorbing a photon of radiation, then is also transformed to LR. LR molecules are considerably more hydrophilic than ZZ-bilirubin molecules and its configurational isomers, and so LR dissolves well in water and is easily excreted from the body. ZZ-bilirubin molecules from the blood replace the isomerized bilirubin in the subcutaneous tissue and also undergo isomerization. Treatment is accompanied by periodic blood draws from the patient, and is continued until the blood bilirubin level is reduced to a value safe for the patient. Currently in medical practice there is no standardized method for phototherapy to treat neonatal jaundice. Phototherapy systems are diverse, as are the radiation sources used in them (fluorescent lamps, halogen lamps, light-emitting diodes, etc.). In a number of cases, modern phototherapy is characterized by low efficiency (slow reduction of the blood bilirubin level), and is associated with harmful side effects of overdosing [2]. A large number of theoretical and experimental papers have been published that are devoted to selecting the light source that will provide the highest rate of decrease in the ZZbilirubin content in skin tissue and blood of newborns with the lowest possible exposure dose. The results of most of the studies show that a promising approach is to use radiation from the region 475–515 nm for phototherapy to treat neonatal jaundice [3–6]. Papers have also been published [7, 8] comparing the effect of emission from blue light (with maximum at λ = 450 nm) and cyan light (λ = 490 nm) fluorescent lamps on the skin of newborns and model biological media containing bilirubin, but no statistically significant differences were observed in the rate of transformation of ZZ-bilirubin to the watersoluble photoisomer LR. In the literature, it is also noted that the most effective use of therapeutic light is achieved for laser
_____________________ *
To whom correspondence should be addressed.
Belorussian State University, 4 Nezavisimost' Ave., Minsk, 220030, Belarus; e-mail:
[email protected]. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 81, No. 5, pp. 761–769, September–October, 2014. Original article submitted April 7, 2014. 834
0021-9037/14/8105-0834 ©2014 Springer Science+Business Media New York
and light-emitting diode sources, since all the light they emit ensures isomerization of bilirubin, while part of the emission spectrum of fluorescent and halogen lamps lies below the bilirubin absorption range [5, 9]. The whole-body illumination needed for effective phototherapy to treat jaundice depends on the type of radiation source and can differ several-fold for newborns with about the same blood bilirubin level [6, 10, 11]. According to [11], a statistical correlation with a small correlation coefficient (0.27) is seen between the whole-body illumination of the newborn and the relative change in the bilirubin content in the newborn's blood over 24 hours of phototherapy. The reason for this is probably the variation in optical properties of the skin in the experimental group of newborns, since for the same exposure dose, the rate of transformation of ZZ-bilirubin to LR in the skin of newborns can differ considerably depending on the skin scattering coefficient and the concentrations of its optically active chromophores (melanin, oxyhemoglobin, deoxyhemoglobin), affecting the optical conditions in the medium. In order to select single phototherapy doses and to determine the optimal time between procedures for a course of treatment, it is important to be able to assess the efficacy of an individual phototherapeutic treatment. A common method for solving this problem involves a periodic blood draw from the newborn and measurement of the total serum bilirubin concentration by direct photometry or by biochemical analysis [2]. The method takes a long time and is painful for the newborn. Also it does not allow us to assess the efficacy of phototherapy in its initial stage, since the water-soluble bilirubin photoisomer (LR) is formed extremely slowly and the total blood content of normal and isomerized bilirubin remains practically unchanged over the first few hours of phototherapy [12]. In [13], it is suggested to evaluate the efficacy of phototherapy to treat neonatal jaundice using the transcutaneous bilirubin index of the skin, measured in a certain time sequence as the logarithm of the intensity ratio for light reflected by skin at λ = 460 nm and 550 nm. This method assumes that the bilirubin concentrations are equal in the skin tissue and blood of the newborn before beginning phototherapy, and that there is a dynamic equilibrium between these concentrations during phototherapy (i.e., the decrease in the bilirubin concentration in the skin as a result of the photoisomerization process is compensated by its increase as a result of influx of bilirubin molecules from blood vessels permeating the skin tissue). The method allows us to estimate only the difference between the bilirubin content in the skin and blood of the patient, depending on a number of physiological factors and not directly connected with the bilirubin photoisomerization rate. The method also is applicable only in the initial stage of phototherapy (as long as the blood bilirubin concentration remains unchanged) and does not allow us to predict the efficacy of phototreatment using a specific therapeutic system before beginning treatment, or to select the spectral and energy parameters for an individual phototreatment. This paper focuses on solution of the problems of continuous monitoring of the efficacy of phototherapy to treat neonatal jaundice, selection of the spectral and energy phototreatment parameters that are optimal for a specific patient, quantitative comparison of the efficacy of treatment of neonatal jaundice in each specific case, using different phototherapeutic systems. The problems posed are solved based on measurements of the diffuse reflectance spectrum for reflection of light from the skin of the newborn and our own algorithm for processing the measurement information, allowing us in real time to determine the rate of transformation of ZZ-bilirubin to the nontoxic and water-soluble photoisomer LR as a function of the wavelength of the exciting radiation. Model for Photoisomerization of Bilirubin. Let us consider a model for skin with two homogeneous and planeparallel layers: the epidermis and the dermis [14–16]. Obviously in such a medium, the radiation field is horizontally homogeneous, i.e., the radiation density E(z, λ) depends only on the one vertical coordinate z, measured from the surface of the medium. Let us assume that all the bilirubin is found in the dermis, where the blood vessels are concentrated, and is uniformly distributed over its depth. The rate of conversion of one bilirubin isomer (A) to another (B) at depth z of irradiated tissue is proportional to the radiation density E(z, λ) at that depth, the concentration of the original isomer CA in the dermis, the absorption coefficient for absorption of light by the original isomer εA(λ), and the photoisomerization quantum yield ϕAB(λ) at the wavelength λ of the exciting radiation. The penetration depth of light into skin varies from fractions of a millimeter to several millimeters, depending on λ [17]. Accordingly, when assessing the efficacy of phototherapy, it is reasonable to consider the photoisomerization rate averaged over the entire thickness of the dermis: ∂CB λ ln 10 = CA ∂t Ld N μ hc
z2
∫
z1
λ2
dz ∫ E ( z , λ )ε A (λ )ϕ AB (λ )d λ ,
(1)
λ1
where λ1 and λ2 are the limits of the spectrum for the exciting radiation; CA and CB are the molar concentrations of isomers A and B, μM; εA is the molar absorption coefficient for isomer A, cm–1/μM; h = 6.63·10–34 J·s is Planck's constant; 835
c = 3·1010 cm/s is the speed of light; Nμ = 6.02·1023 mol–1 is Avogadro’s number; Le and Ld are the geometric thicknesses of the epidermis and dermis; z1 = L3, z2 = Le + Ld. The duration of a phototherapy session directly depends on the rate of LR formation in the skin tissue of the patient, since it is specifically this photoproduct of bilirubin that is most rapidly excreted from the body. However, the quantum yield of LR formation is low (ϕLR ≈ 0.001) and the isomerization process ZZ → LR occurs very slowly [18, 19]. At the same time, the photoconversion ZZ ↔ ZE is characterized by high quantum yield and is reversible (ϕZE ≈ 0.1 and ϕZZ ≈ 0.2 for the processes ZZ → ZE and ZE → ZZ) [20], so a stable equilibrium is rapidly established between the amounts of ZZ-bilirubin and ZE-bilirubin molecules in the illumination area, where the ZZ ↔ ZE isomerization rate is the same in both directions, i.e., ∂CZZ/∂t = ∂CZE/∂t. The ratio between the concentrations of ZZ-bilirubin and ZE-bilirubin when they are in photoequilibrium according to (1) is specified by the expression: z2
λ2
z2
z1
λ1
z1
C ZZ ∫ dz ∫ E ( z , λ )ε ZZ (λ )ϕ ZE (λ )d λ = C ZE
∫
λ2
dz ∫ E ( z , λ )ε ZE (λ )ϕ ZZ (λ )d λ ,
(2)
λ1
where εZZ and εZE are the molar absorption coefficients for ZZ-bilirubin and ZE-bilirubin. From (1) and (2), we obtain a formula for the rate of LR formation at any instant of time t during phototherapy: z2
M LR
CTB λ = Ld N μ hc
∫
z1 z2
1+
∫
z1
λ2
dz ∫ E ( z , λ )ε ZZ (λ )ϕ LR (λ )d λ λ1
λ2
z2
λ1
z1
dz ∫ E ( z , λ )ε ZZ (λ )ϕ ZE (λ )d λ
∫
λ2
,
(3)
dz ∫ E ( z , λ )ε ZE (λ )ϕ ZZ (λ )d λ λ1
where MLR = ∂CLR/∂t; CTB = CZZ + CZE is the total bilirubin concentration in tissue (the concentration of LR is negligibly small, and LR rapidly leaves the tissue via the blood vessels). When using a narrow spectral region [λ1, λ2], all the integrals with respect to λ in formula (3) should be replaced by the values of the functions under the integral sign at the central point λ = (λ1 + λ2)/2. In this case, formula (3) gives the dependence of MLR on the wavelength of the exciting radiation. The dependences of εZZ, εZE, ϕZZ, ϕZE, and ϕLR on λ used in our calculations are taken from [4, 19]. Noninvasive Determination of the Bilirubin Photoisomerization Rate. As follows from expression (3), in order to estimate the LR formation rate during phototherapy, we need to know the tissue concentration of total bilirubin and the distribution of radiation density over the tissue depth in the spectral range of the therapeutic light. The tissue concentration of bilirubin can be determined by noninvasive methods by measuring the spectral or the spectral and spatial characteristics of the diffuse reflection by the tissue [14–16, 21, 22]. The measurements can be made based on both fiber-optic technology [14–16] and contactless measurement systems [21, 22]. Analytical solutions of the corresponding forward and inverse problems, proposed in [14, 16, 21, 22], allow us to process the measurement data in real time and with high accuracy. Taking into account the similarity of the absorption spectra for ZZ-bilirubin and ZE-bilirubin [19], the total bilirubin concentration, determined based on the methods indicated above, will correspond to the total concentration of bilirubin photoisomers in tissue (CTB). The possibility for noninvasive determination of the radiation density in the tissue E(z, λ) was demonstrated for the first time in [17, 23], where it was proposed to use measurements of the spectral diffuse reflection coefficient for the tissue, R(λ), representing the ratio of the diffuse radiation flux reflected by the medium to the directional radiation flux incident on it. The basis for this is the dependence of the penetration depth of light into the tissue on λ. The probing radiation with different λ values penetrates into different layers of the tissue, and therefore contains information about these layers. Speed and accuracy of recovery of E(z, λ) from the R(λ) spectrum is achieved as a result of using a semi-analytical method for solving the radiation transport equation in an optically dense multilayer tissue [23], allowing us to calculate in a fraction of a second E(z, λ) and R(λ) in the spectral regions of strong (λ < 0.6 μm) and weak (λ = 0.6–1.0 μm) absorption of light by the tissue. The greatest practical interest is in the possibility of determining CTB, E(z, λ), and MLR based on relatively inexpensive and commercially available devices: fiber-optic spectrophotometers [24, 25]. In such devices, a deuterium halogen lamp is used as the radiation source while a diffraction grating CCD spectrometer is used as the detector. Radiation from the source is delivered to the tissue and the radiation backscattered by the tissue is delivered to the detector using a miniature fiber-optic sensor in which the fibers are arranged in a natural configuration: six illuminating fibers surrounding a single read fiber.
836
As shown in [16], such measurements allow us to reliably determine the total bilirubin concentration in the skin tissue when all the skin parameters affecting the radiation flux backscattered by the skin are a priori uncertain. Let us consider the possibility of determining the LR formation rate in the skin tissues of a newborn using data from optical probing of the skin with a fiber-optic spectrometer. An analytical model for the reflectance spectrum of the skin, measured with a baseline separation between the radiation source and the radiation detector, was proposed in [16]. By reflectance we mean the ratio r = P/P0, where P0 is the power of the collimated light incident on the medium; P is the power of diffuse radiation leaving the area on the surface of the medium outside the region hit by the incident light. The model parameters are nsk, the refractive index of skin; Bsca, the scattering transport coefficient for connective tissue at λ0 = 400 nm; ρMie, the fraction of Mie scattering in the total scattering by the tissue at λ0 = 400 nm; x is a parameter describing the spectral dependence of the Mie scattering transport coefficient; Le is the thickness of the epidermis; fm is the volume concentration of melanin in the epidermis; fbl is the volume concentration of capillaries in the dermis; dv is the average diameter of capillaries; CtHb is the molar concentration of total hemoglobin in the blood; S is the blood oxygenation level. We also take into account the presence of ZZ-bilirubin and ZE-bilirubin in the tissue and blood vessels of the dermis. We assume that the ratio of the total bilirubin concentrations in the blood and in surrounding tissue, QTB, is equal to five [26]. In the general case, this ratio depends on the bilirubin photoisomerization rate and the diffusion rate of bilirubin through blood vessel walls, but considering how small the effect of blood bilirubin is on the light field in the skin compared with bilirubin in the tissues of the dermis [27], we can use a fixed value for the parameter QTB. For specified parameters of the medium modeling skin tissue, the optical characteristics of the medium, taking into account the above comments, are calculated using the formulas [14–16, 22]: g(λ) = 0.7645 + 0.2355[1 – exp (–(λ – 500)/729.1)] ,
(4)
β′(λ) = Bsca[ρMie(λ0/λ)x + (1 – ρMie)(λ0/λ)4] ,
(5)
ke(λ) = fmkm(λ) + (1 – fm)kt(λ) ,
(6)
kd(λ) = fblα(λ)kbl(λ) + (1 – fbl)[kt(λ) + CZZεZZ(λ) + CZEεZE(λ)] ,
(7)
kbl(λ) = CtHb[SεHb(λ) + (1 – S)εHbO2(λ)] + QTB[CZZεZZ(λ) + CZEεZE(λ)] ,
(8)
1 − exp (− d v k bl (λ ))
α (λ ) =
,
d v k bl (λ )
(9)
where β′ and g are the scattering transport coefficient and the scattering anisotropy factor for the epidermis and dermis; ke and kd are the absorption coefficients for the epidermis and the dermis; kt is the absorption coefficient for connective (bloodless) tissue [28]; kbl is the absorption coefficient for blood; ε HbO 2 and εHb are the molar absorption coefficients for oxyhemoglobin and deoxyhemoglobin [29]; α is a correction factor taking into account the effect of localized absorption of light by the blood vessels [30]. The relationship between the reflectance spectrum of skin and its optical and structural characteristics within the model used is described by the expression [16]: 3
− ln r = 3
∑
a1, m (β′) + m
m =1
+∑
m =1
3
a6, m δ dm 3
+
∑
3
∑
3
a2, m k em +
m =1
a7, m ( k e Le ) + m
m =1
3
3
a3, m k dm +
∑
a8, m ( k d δ d ) + k e Le ∑ a9, m ( k e β′)
m =1 3 m =1
∑
m =1
m =1
a4, m g m +
m =1
3
m
+ Le ∑ a10, m ( k e β′) + δ d ∑ a11, m ( k d β′) + m
3
∑
m
Le δd
3
∑
∑
a5, m ( nsk − 1)
m
m =1 m
(10)
m =1
a12, m ( k d δ d )
m
,
m =1
where the ai,m are coefficients depending on the geometric parameters of the fiber-optic sensor; δd = [3kd(kd + β′)]–1/2 is the penetration depth of light into the dermis (in the diffusional approximation). 837
Fig. 1. Results of the numerical experiment determining the bilirubin photoisomerization rate in skin from its diffuse reflectance spectrum: a) normalized diffuse reflectance spectra of skin, calculated by the Monte Carlo method (points) and selected using analytical expressions (4)–(10) (lines); b) spectral dependences of the LR formation rate in skin, recovered from its diffuse reflectance spectra: 1) gestational age = 30 weeks, fm = 2%, fbl = 0.2%; 2) gestational age = 30 weeks, fm = 10%, fbl = 2%; 3) gestational age = 40 weeks, fm = 2%, fbl = 0.2%; 4) gestational age = 40 weeks, fm = 10%, fbl = 2%.
Therefore the reflectance spectrum of skin can be calculated analytically as a function of λ and the above-indicated model parameters. This allows us to do real-time processing of the detected signals and to determine all the optical and structural parameters of the skin that affect the radiation density in the medium, E(z, λ). In order to rapidly calculate the function E(z, λ), we can use the semi-analytical method in [23]. The accuracy of this calculation is comparable with the accuracy of the Monte Carlo method, but the calculation times for the methods differ by several orders of magnitude (on personal computers with average technical specifications by today’s standards, the calculation of the radiation density distribution over the depth of the skin by the method in [23] takes milliseconds). Knowing the total bilirubin concentration in tissues of the dermis, the radiation density distribution over the depth of the dermis, and the illumination of the skin of the patient E(0, λ), using formula (3) we can calculate the rate of transformation of ZZ-bilirubin to the nontoxic and water-soluble isomer LR that is provided by the specific phototherapy system. Measurements and analysis of the diffuse reflectance spectrum of the skin at several points on the patient’s body before beginning phototherapy allow us to also determine the dependence of the rate of LR formation in skin tissue on E(0, λ) and to thus select the spectral and energy parameters of the phototreatment that will provide the best therapeutic effect for the lowest possible exposure dose. Analysis of the Effectiveness of the Method. The effectiveness of the proposed method for determining the bilirubin isomerization rate in skin tissue was assessed based on the results of numerical solutions of the radiation transport equation in the medium modeling skin. We considered a two-layer model for the skin, the optical characteristics of which are described by formulas (4)–(9). The thickness of the epidermis and the total hemoglobin concentration in blood were assumed to be fixed: Le = 60 μm, CtHb = 2.3 mM. The light scattering parameters of the layers Bsca, ρMie, and x were specified according to the experimental data for skin of newborns with gestational age of 20 weeks or more [31]: Bsca = 2.35–9.96 mm–1, ρMie = 1, x = 1.6–3.0. The total bilirubin concentration in blood QTNCTB varied in the range 20–500 μM; the ratio between the concentrations of bilirubin isomers in blood and surrounding tissue was CZE/CZZ = 0–1. For variations of the other model parameters, we selected ranges typical for moderately pigmented skin of newborns [28, 32]: fm = 1–16%, fbl = 0.2–3%, S = 20–98%, dv = 5–30 μm, nsk = 1.4–1.5. The reflectance spectrum of the medium rMC(λ) was calculated by the Monte Carlo method [33] as the ratio of the total "weight" of the photons leaving the circular receiving area on the surface of the medium to the total "weight" of all the photons entering the medium within the illuminating area. The diameter of the illuminating and receiving areas is 0.8 mm, the distance between their centers is 0.83 mm. The coefficients ai,m in expression (10), corresponding to such an experimental geometry, are given in Table 1. The radiation density at depth z in the medium was calculated by summing the "weight" of all the photons traveling through level z in all directions.
838
TABLE 1. Coefficients in Formula (10) for Calculating Skin Reflectivity (i, m)
ai,m
(i, m)
ai,m
(i, m)
ai,m
(1, 1)
0.0847
(5, 1)
–8.1287
(9, 1)
–1.1419
(1, 2)
0.0413
(5, 2)
21.329
(9, 2)
0.2703
(1, 3)
–0.0038
(5, 3)
–16.079
(9, 3)
–0.0223
(2, 1)
–0.0154
(6, 1)
0.3936
(10, 1)
–2.0241
(2, 2)
0.0011
(6, 2)
–0.0282
(10, 2)
0.5741
(2, 3)
0.0000
(6, 3)
0.0010
(10, 3)
–0.0730
(3, 1)
1.4851
(7, 1)
6.5092
(11, 1)
2.9094
(3, 2)
–0.4444
(7, 2)
–2.7701
(11, 2)
–4.8814
(3, 3)
0.0606
(7, 3)
1.6099
(11, 3)
1.6287
(4, 1)
–2.1242
(8, 1)
16.925
(12, 1)
–9.2751
(4, 2)
15.478
(8, 2)
–55.178
(12, 2)
23.034
(4, 3)
–11.822
(8, 3)
90.164
(12, 3)
–27.204
The model parameters x = (Bsca, ρMie, x, CZE, CZZ, fm, fbl, S, dv, nsk) were recovered from normalized diffuse reflectance spectra of skin ωMC(λ) = rMC(λ)/rMC(λref), where λ = 4560–750 nm, λref = 750 nm, by looking for the minimum deviation of ωMC(λ) from the analogous analytical spectra ω(λ) = r(λ)/r(λref), calculated from formulas (4)–(10). The spectrum ωMC(λ) does not depend on the numerical apertures of the fibers, and in practice is determined by comparing the relative spectral dependences of the diffuse reflectance signals from skin and a white diffuse reflector [16]. In this case, we do not need to know the reflectance spectrum of the reference reflector. Figure 1 shows examples of determination of the bilirubin isomerization rate in skin tissue MLR from the diffuse reflectance spectrum of the skin. The spectra ωMC(λ) correspond to the same bilirubin isomer content in the tissue (CTB = 40 μM, CZE/CZZ = 0.5) and different contents of other chromophores in the skin (hemoglobin and melanin). In order to estimate the effect of the gestational age of the newborn, ωMC(λ) is calculated for two values of the skin light scattering parameters, corresponding to a gestational age of 30 weeks (Bsca = 4.22 mm–1, ρMie = 1, x = 2.1) and 40 weeks (Bsca = 8.04 mm–1, ρMie = 1, x = 1.7) [31]. Other model parameters, corresponding to the spectra presented, are the following: S = 75%, dv = 18 μm, nsk = 1.45. Minimization of the residual between the numerical ωMC(λ) and analytical ω(λ) diffuse reflectance spectra of skin was done by the Levenberg–Marquardt method [34]. The original ωMC(λ) spectra and the ω(λ) spectra, calculated from formulas (4)–(10) for the recovered model parameters x*, are presented in Fig. 1a. The radiation density distributions over depth in the skin and the wavelength of the light were calculated according to the values of x* found by the method in [23]. Illumination of the skin was assumed to be independent of λ and equal to 1 mW/cm2. The spectral dependences MLR(λ), calculated from formula (3) for the true values (corresponding to the ωMC(λ) spectrum) and the recovered values of CTB and E(z, λ), are compared in Fig. 1b . We see that the proposed method allows us to obtain rather accurate estimates of MLR(λ) in the spectral region of light absorption by bilirubin isomers (450–530 nm). The results presented in Fig. 1b demonstrate the significant dependence of the efficacy of phototherapy on the gestational age and skin pigmentation of the newborn. The screening effect of melanin and hemoglobin is apparent in the broadening of the MLR(λ) spectrum and the decrease in the bilirubin isomerization rate. Gestational age does not have a significant effect on the shape of the MLR(λ) spectrum, but affects the absolute values of MLR(λ). The reason for such an effect is the increase in the collagen fiber density in connective tissue with age in the newborn [31], leading to an increase in the fraction of the light flux backscattered by the skin compared with the flux absorbed within the skin. Note that all MLR(λ) spectra presented have a maximum near λ = 490 ± 6 nm, and its position depends slightly on the structural and morphological parameters of the skin. Accordingly, in order to achieve maximum efficacy of phototherapy to treat neonatal jaundice, we can recommend using light from this narrow spectral range. In this case, the intensity of the
839
Fig. 2. Bilirubin photoisomerization rates in skin tissues at λ = 490 nm, calculated based on the Monte-Carlo method (x-axis) for 550 realizations of the model parameters and recovered from the corresponding realizations of the skin diffuse reflectance spectra (y-axis). therapeutic radiation should be selected individually for each newborn, according to the bilirubin photoisomerization rate MLR characteristic for the baby. Similar numerical experiments on recovery of MLR from the ωMC(λ) spectra were run for 550 realizations of the * model parameters. Fig. 2 compares the true MLR and the recovered M LR values of the LR formation rate in the medium 2 modeling skin, for illumination of the medium equal to 1 mW/cm and wavelength of the therapeutic radiation 490 nm. The * * mean-square deviation of M LR from the regression line M LR = MLR is 0.9 μM/h; the correlation coefficient between MLR * and M LR is 0.988. Experimental Results. We were interested in testing our method experimentally. To do this, we used the diffuse reflectance spectra (diffuse reflection coefficient vs. wavelength) for the skin of newborns that were obtained in [35] based on an integrating-sphere spectrophotometer. Despite the drawbacks of such measurements (the large weight and external dimensions of the integrating sphere, the impossibility of separating the contributions of diffuse and surface reflections to the detected signals, the need for absolute calibration), they can also be used to assess the efficiency of bilirubin photoisomerization in tissue. In this case, the collection aperture for photons backscattered by the medium corresponds to the entire area of the medium covered by the entrance port of the integrating sphere. We proposed an analytical model for the diffuse reflection coefficient of skin corresponding to such an experimental geometry in [22]. This model allows us to calculate the diffuse reflection coefficient of skin as a function of the thickness of the epidermis and the optical parameters (absorption coefficient and scattering transport coefficient) of the epidermis and dermis. The spectral dependences of the optical parameters of the skin are described by formulas (5)–(9). Minimization of the residual between the experimental and analytical diffuse reflectance spectra of the skin allows us to estimate its structural and morphological parameters within the model used. The experimental and analytical diffuse reflectance spectra are compared in Fig. 3a. We see that the model used describes the experimental data rather well. The total bilirubin concentrations in the tissues of the dermis, obtained from the experimental diffuse reflectance spectra for the heels of healthy newborns and those with hyperbilirubinemia are 5.8 and 50.2 μM. The ratio of these concentrations (0.11) approximately matches the ratio of the serum bilirubin concentrations (0.12) for the tested newborns [35]. The dependences of the rate of LR production in the tissues of the dermis on the wavelength of the exciting radiation, calculated according to the recovered skin parameters for the newborns, are presented in Fig. 3b. We see that the functions MLR(λ) obtained from experimental data match their modeling results rather well (Fig. 1b). The maximum of the "experimental" MLR(λ) functions is about at the left-hand limit of the spectral interval which, according to our calculations, is optimal for phototherapy to treat jaundice (484–496 nm). The values obtained for MLR allow us to estimate the illumination of the skin of newborns needed for effective phototherapy. A clinical effect from phototherapy is achieved for a rate of decrease in the bilirubin level by 34 μM over a period of Δt = 4–6 hours [2]. Let the change in the ZZ-bilirubin concentration in the skin tissues, due to its production in blood, during this time period be ΔCZZ. The value of ΔCZZ can be determined based on noninvasive measurements of the total
840
Fig. 3. Results of recovery of the spectral dependences of the bilirubin photoisomerization rate in tissue from experimental diffuse reflectance spectra (diffuse reflection coefficient vs. wavelength) for skin of a healthy patient (1) and skin of a patient with hyperbilirubinemia (2): a) experimental (solid curves) and calculated (dashed curves) diffuse reflectance spectra; b) recovered dependences of the lumirubin production rate in tissue on the wavelength of the exciting radiation.
bilirubin concentration in the skin of the patient before phototherapy begins [14–16, 22]. Then the illumination of the skin of the patient during phototherapy should satisfy the obvious condition: Е ≥ [(34 μM + ΔСZZ)/MLRΔt] · 1 mW/cm2 .
(11)
As an example, let us consider the situation corresponding to spectrum 2 in Fig. 3b. Let us use light with λ = 484 nm for irradiation of the skin of the newborn (the phototherapy is the most effective for this case). The corresponding value of MLR(λ) is 11.25 μM/L. If in the 5 hours before beginning phototherapy the ZZ-bilirubin concentration in the tissue increased, for example by 15 μM, the illumination of the skin of the patient according to condition (11) should be at least 0.87 mW/cm2. Conclusions. The results presented are evidence for the feasibility of noninvasive monitoring of the bilirubin photoisomerization efficiency during phototherapy to treat neonatal jaundice. To do this, we need to temporarily turn off the phototherapy radiation source, take the diffuse reflection spectrum of the skin of the newborn based on a fiber-optic spectrophotometer, and determine from the spectrum the instantaneous rate of transformation of the ZZ-bilirubin to the LR form that is easily excreted from the body. Based on these data and also on the results of noninvasive measurements of the rate of rise in the total bilirubin concentration in the skin tissue CTB in the newborn, made before beginning phototherapy (for example, by the method in [16]), by controlling the whole-body illumination of the newborn we can achieve the required rate of LR formation during phototherapy. We should point out that noninvasive measurements of CTB, made after certain time intervals during phototherapy, do not provide adequate information about the rate of decrease in the ZZ-bilirubin concentration in the tissue and the blood, since the concentration CTB can change both as a result of the process of bilirubin photoisomerization in tissue and as a result of influx of bilirubin from blood vessels into the surrounding tissue [12]. It is not possible to separate the effect of these factors on the measured values of CTB. The proposed method allows us to determine the rate of decrease in ZZ-bilirubin in the tissue due directly to its photoisomerization process. And measurements of this rate can be made even before the beginning of phototherapy, which allows us to select the optimal illumination of the skin for a specific patient, taking into account its structural and morphological features. According to our calculations, the highest rate of photoconversion of ZZ-bilirubin to LR is achieved when using light with λ = 484–496 nm to irradiate the skin. In our opinion, the phototherapy duration should be selected based on the total bilirubin concentration in the tissue and its photoisomerization rate. However, to do this, we need to conduct clinical studies establishing the correlation between the rate of rise in bilirubin concentration in the skin of newborns before beginning phototherapy and its isomerization rate during phototherapy, as the blood bilirubin content changes in the blood of the newborns during treatment. 841
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