For skin, in vivo measurements of optical properties are possible only in the geometry of backscattering. The spatially resolved reflectance R(rsd) is defined as the power of the back – scattered light per unit of area detected by a receiver at the surface of the skin at a distance rsd from the source, rsd is the source-detector separation. R(rsd) depends on the optical properties of the sample, that is, the absorption coefficient цл, the scattering coefficient gs, and the anisotropy factor g, the refractive index n, and the numerical aperture NA of the receiving system [1,5,9-11,14-26].
When optical parameters of skin are under investigation, the small source-detector separations should be used, where the diffusion approximation is not valid due to its proximity to the tissue boundary. In that case, more sophisticated approximations of the RTE solution should be employed; in particular, a numerical solution of the inverse problem by the Monte Carlo (MC) method is prospective.
In the six-detecting-fiber system made of 0.4 mm-core diameter optical fiber that is described in ref. [23], source-detector distances were: rsd = 0.44, 0.78, 0.92, 1.22, 1.40, and 1.84 mm. In the course of their in vivo studies, temperature dependences of the absorption and the reduced scattering coefficients of human forearm skin have been determined.
Two precise optical systems, the fiber optic spectrometer yielding spatially resolved back – reflectance spectra and the single wavelength fiber-optic-CCD tissue imager, were used for in vivo measurements of anisotropy of scattering and absorption coefficients of human skin at different body locations [22]. The source-detector distances between 0.33 and 10.0 mm for 18 detecting 0.2 mm core diameter fibers linearly aligned with a central illuminating fiber provided a 2D mapping of reflected intensity by rotation of the detecting fiber system around the illuminating fiber. The MC code accounting for a two-layered tissue model (skin itself and a semi-infinite subcutaneous fat layer) with two groups of scatterers, one of randomly distributed scatterers and another of infinite dielectric cylinders (dermal collagen fibers) aligned along one of the principle Cartesian axes parallel to the skin surface, was designed to evaluate scattering and absorption coefficients distributions. In the skin layer, the scattering coefficient was recalculated before each interaction event according to the current direction of photon propagation as fjs = /Js0 [1 + fs(0.5 – jcosyj)], where д,0 is a base scattering coefficient, fs is the fraction of scatterers oriented in the preferential direction, and y is the angle between the current photon direction and the cylinder axis.
Optical coherence tomography (OCT) is a newly developed modality that allows one to evaluate the scattering and absorption properties of tissue in vivo within the limits of an
OCT penetration depth of 1-3 mm [1,24]. In its simplest form, this method assumes that backscattered light from a tissue decreases in the intensity according to Ib = I0exp[-2(/ta + g)z], where 2z is the round-trip distance of light backscattered at depth z. For most tissues in the NIR, ga << /Js; thus, fis can be estimated roughly as fis = 1/2z{ln[Ib(z)/I0]}.
Direct measurement of the scattering phase function p(9) is important for the choice of an adequate model for the tissue being examined. The scattering phase function or g-factor is usually determined from in vitro goniophotometric measurements [10 , 11]. For human dermis and epidermis in the wavelength range from 300 to 1300 nm, g-factor is well – described by the empirical formula [10]: ge ~ gd ~ 0.62 + l x 0.29 x 10-3, where the wavelength l is given in nanometers.
The values of absorption and scattering coefficients and scattering anisotropy factor for the human skin measured in vitro, ex vivo, or in vivo are presented in Table 3.1.
The direct measurement of the penetration depth of a tissue at some specific wavelength is important for providing of laser phototherapy strategy. For example, at attenuation of a wide laser beam of intensity I0 in a thick tissue at depths z >ld = 1/^eff may be described instead of Eq. (3.1) by the following equation [1]:
I(z) – ZA^-mf), (3.7)
where bs accounts for additional irradiation of upper layers of a tissue due to multiple back – scattering (photon recycling effect) and geff = [3^a(^s’ + /ta)]1/2 photon diffusion due to multiple scattering. Respectively, the depth of light penetration into a tissue is
le = ld[ln bs + 1]. (3.8)
Typically, for tissues bs =1-5 for beam diameter of 1-20 mm. Thus, when wide laser beams are used for irradiation of highly scattering tissues with low absorption, CW light energy is accumulated in the tissue due to high multiplicity of chaotic long-path photon migrations. A highly scattering medium works as a random cavity providing the capacity of light energy. The light power density within the superficial tissue layers may substantially (up to threefold for the human skin [10]) exceed the incident power density and cause the overheating at laser photothermolysis or the overdosage during photodynamic therapy. On the other hand, photon recycling effect can be used for more effective irradiation of undersurface lesions at relatively small incident power densities.
Figure 3.8 illustrates results of the reconstruction of the spectral dependences of the absorption (a) and reduced scattering coefficients (b) of the human skin [16]. The reconstruction was done on the basis of in vitro measurements of skin samples transmittance and reflectance. Using received data for ga(X) and g'(A), calculations of the skin penetration depth (le – ld) was performed (c). The maximal penetration depth of 3.5 mm was found at the wavelength 1090 nm. At some other wavelengths, such as 600, 633, 660, 700, 750, 800, 850, and 900 nm, the penetration depth was correspondingly equal to 1.5, 1.7, 1.8, 2.0, 2.2, 2.3, 2.4, and 2.5 mm.
It is important to note that the penetration depth shown in Fig. 3.8 is defined as depth at which an initially collimated large diameter beam is attenuated e = 2.7 times. The attenuation profile of light in the skin is approximately an exponential function and photons with low density can be found at depths much deeper than defined by Fig. 3.8. Smaller diameter
|
Tissue к (nm) |
Pa (Cm ‘) |
ps (cm1) |
p/ (cm1) |
g |
Remarks |
|
In vitro measurements Stratum corneum 193 |
6000 |
Frozen sections [9] |
|||
|
250 |
1150 |
2600 |
260 |
0.9 |
Data from graphs of ref. [10]; fi) is |
|
308 |
600 |
2400 |
240 |
0.9 |
calculated |
|
337 |
330 |
2300 |
230 |
0.9 |
|
|
351 |
300 |
2200 |
220 |
0.9 |
|
|
400 |
230 |
2000 |
200 |
0.9 |
|
|
Epidermis 250 |
1000 |
2000 |
616 |
0.69 |
Data from graphs of ref. [10]; fi) and g |
|
308 |
300 |
1400 |
407 |
0.71 |
are calculated |
|
337 |
120 |
1200 |
338 |
0.72 |
|
|
351 |
100 |
1100 |
306 |
0.72 |
|
|
415 |
66 |
800 |
206 |
0.74 |
|
|
488 |
50 |
600 |
143 |
0.76 |
|
|
514 |
44 |
600 |
139 |
0.77 |
|
|
585 |
36 |
470 |
99 |
0.79 |
|
|
633 |
35 |
450 |
88 |
0.80 |
|
|
800 |
40 |
420 |
62 |
0.85 |
|
|
Dermis 250 |
35 |
833 |
257 |
0.69 |
Data from graphs of ref. [10]; values |
|
308 |
12 |
583 |
170 |
0.71 |
are transformed in accordance with data |
|
337 |
8.2 |
500 |
141 |
0.72 |
for = 633 nm [11] (bloodless tissue, |
|
351 |
7 |
458 |
127 |
0.72 |
hydration—85%), fi) and gare calculated |
|
415 |
4.7 |
320 |
82 |
0.74 |
|
|
488 |
3.5 |
250 |
60 |
0.76 |
|
|
514 |
3 |
250 |
58 |
0.77 |
|
|
585 |
3 |
196 |
41 |
0.79 |
|
|
633 |
2.7 |
187.5 |
37 |
0.80 |
|
|
800 |
2.3 |
175 |
30 |
0.85 |
|
(Continued) |
|
3: Physics Behind Light-Based Systems, Altshuler & Tuchin |
|
Hispanic male skin |
500 |
5.1 |
– |
37.6 |
|
(n = 3), external |
810 |
0.93 |
– |
11.4 |
|
pressure 0.1 kg/ cm2 |
||||
|
Hispanic male skin |
500 |
6.2 |
– |
40.4 |
|
(n = 3), external |
810 |
0.87 |
– |
10.2 |
|
pressure 1 kg/cm2 |
||||
|
Caucasian skin |
400 |
3.76 (0.35) |
– |
71.79 (9.42) |
|
(n =21) |
500 |
1.19 (0.16) |
– |
32.46 (4.21) |
|
600 |
0.69 (0.13) |
– |
21.78 (2.98) |
|
|
700 |
0.48 (0.11) |
– |
16.69 (2.27) |
|
|
800 |
0.43 (0.11) |
– |
14.02 (1.89) |
|
|
900 |
0.33 (0.02) |
– |
15.66 (2.06) |
|
|
1000 |
0.27 (0.03) |
– |
16.83 (2.77) |
|
|
1100 |
0.16 (0.04) |
– |
17.11 (2.69) |
|
|
1200 |
0.54 (0.04) |
– |
16.71 (2.89) |
|
|
1300 |
0.41 (0.07) |
– |
14.69 (2.59) |
|
|
1400 |
1.64 (0.31) |
– |
14.28 (3.69) |
|
|
1500 |
1.69 (0.35) |
– |
14.41 (3.75) |
|
|
1600 |
1.19 (0.22) |
– |
14.16 (3.41) |
|
|
1700 |
1.55 (0.28) |
– |
14.71 (3.51) |
|
|
1800 |
1.44 (0.22) |
– |
13.36 (2.91) |
|
|
1900 |
2.14 (0.28) |
– |
12.15 (3.05) |
|
|
2000 |
1.74 (0.29) |
– |
12.01 (2.91) |
IS, IAD; sample thickness: 0.35, 0.62, 0.48 mm [15]
IS, IAD; sample thickness: 0.28, 0.48, 0.33 mm [15]
IS, IAD; tissue slabs, 1-6 mm; postmortem; <24 hr after death; stored at 20°C in saline; measurements at room temperature; in the spectral range 400- 2000 nm: /</ = 1.1 x 1012?C4 + 73.77г0 22, [7J = nm [16]
Subcutaneous fat
Caucasian dermis
(n =12)
Negroid dermis (л =5)
Subdermis (primarily globular fat cells) (n = 12)
0.8 IS, IMC, slabs [17]
0. 8
0. 8
0. 8
0. 8
0. 8
0. 8
0. 8
0. 8
0. 8
0. 8
0. 8
0. 8
0.9 A single integrating sphere “comparison”
0.9 method, IMC; samples from abdominal
0.9 and breast tissue obtained from plastic
surgery or post-mortem examinations, g = 0.9 is supposed value in calculations [18] 0.9 0.9 0.9
0.9
0.9
0.9
(Continued)
|
12/07; M, age = 33 |
1000 |
0.82 (0.02) |
– |
14.35 (0.81) |
|
yr; posterior thigh, |
1460 |
19.01 (1.28) |
– |
13.30 (0.91) |
|
right side; mild |
1600 |
5.81 (0.33) |
– |
10.14 (0.49) |
|
chronic dermatitis; |
2200 |
11.13 (1.21) |
– |
9.00 (0.33) |
|
SC = 2-5 цт; E = 5-10 цт; D = 300 цт 13/08; F, age = |
1000 |
0.97 (0.08) |
13.70 (0.35) |
|
|
52 yr; axillary, |
1460 |
21.39 (1.25) |
– |
12.54 (0.72) |
|
right side; mild |
1600 |
6.17 (0.30) |
– |
9.94 (0.78) |
|
perivascular |
2200 |
12.53 (0.84) |
– |
9.45 (0.84) |
|
chronic inflammation; SC = 5-7 цт; E = 25 цт; D = 100 цт 14/09; M, age = 37 |
1000 |
0.82 (0.02) |
15.00 (0.49) |
|
|
yr; back of thigh, |
1460 |
23.31 (0.71) |
– |
12.32 (0.51) |
|
upper left; mild |
1600 |
6.68 (0.11) |
– |
10.01 (0.37) |
|
chronic dermatitis; |
2200 |
15.19 (1.37) |
– |
8.54 (0.52) |
|
SC = 3 цт; E = 13 цт; D = 300 цт 15/10; M, age = |
1000 |
1.04 (0.02) |
12.26 (0.44) |
|
|
70 yr; scalp; mild |
1460 |
15.95 (0.99) |
– |
10.75 (1.20) |
|
chronic dermatitis |
1600 |
5.09 (0.23) |
– |
8.83 (0.92) |
|
w/solar elastosis; |
2200 |
12.65 (0.52) |
– |
8.83 (1.94) |
|
SC = 4-15 цт; E = 8-10 цт; D = 200 цт |
|
19/13*; F, age = |
1000 |
1.55 (0.02) |
– |
11.96 (0.65) |
|
53 yr; scalp/facial |
1460 |
16.13 (1.38) |
– |
11.52 (0.64) |
|
tissue; mild chronic |
1600 |
5.38 (0.31) |
– |
8.65 (0.54) |
|
inflammation; SC = 4 цт; E = 10 ціп; D = 200 цт |
2200 |
13.84 (1.02) |
9.67 (0.65) |
|
|
20/13; F, age = |
1000 |
1.53 (0.02) |
– |
12.89 (0.77) |
|
53 yr; scalp/facial |
1460 |
16.82 (1.13) |
– |
12.01 (0.81) |
|
tissue; mild solar |
1600 |
5.57 (0.19) |
– |
9.47 (0.60) |
|
damage; SC = 4 цт; E = 10 цт; D = 200 цт |
2200 |
13.46 (0.58) |
10.41 (0.71) |
|
|
21/14; F, age = |
1000 |
0.88 (0.03) |
– |
14.96 (1.28) |
|
52 yr; abdomen; |
1460 |
18.21 (2.51) |
– |
14.20 (0.71) |
|
mild chronic |
1600 |
5.74 (0.68) |
– |
10.58 (0.44) |
|
inflammation; SC = 4-5 цт; E = 10 цт; D = 200 цт |
2200 |
11.33 (0.76) |
10.40 (0.47) |
|
|
22/14; F, age = |
1000 |
0.94 (0.02) |
– |
15.26 (0.63) |
|
52 yr; abdomen; |
1460 |
18.46 (1.64) |
– |
15.10 (1.01) |
|
mild chronic |
1600 |
5.76 (0.31) |
– |
11.05 (0.39) |
|
inflammation; SC = 4-5 цт; E = 10 цт; D = 200 цт |
2200 |
13.72 (0.52) |
13.72 (0.42) |
|
Skin (0-1 mm) |
633 |
0.67 |
– |
16.2 |
|
Skin (1-2 mm) |
633 |
0.026 |
– |
12.0 |
|
Skin (>2 mm) Forearm: |
633 |
0.96 |
– |
5.3 |
|
Epidermis |
633 |
8A |
– |
17.5 |
|
Dermis |
633 |
0.15 |
– |
17.5 |
|
Epidermis and |
750 |
0.375 |
– |
15 |
|
dermis Subcutaneous fat |
750 |
0.03 |
– |
10 |
|
Arm |
633 |
0.17 (0.01) |
– |
9.08 (0.05) |
|
660 |
0.128 (0.005) |
– |
8.68 (0.05) |
|
|
700 |
0.090 (0.002) |
– |
8.14 (0.05) |
|
|
Foot sole |
633 |
0.072 (0.002) |
– |
11.17 (0.09) |
|
660 |
0.053 (0.003) |
– |
10.45 (0.09) |
|
|
700 |
0.037 (0.001) |
– |
9.52 (0.08) |
|
|
Forehead |
633 |
0.090 (0.009) |
– |
16.72 (0.09) |
|
660 |
0.052 (0.003) |
– |
16.16 (0.08) |
|
|
Abdominal skin: |
700 |
0.0240 (0.002) |
15.38 (0.06) |
|
|
Chosen direction |
810 |
0.014 |
– |
20 |
|
perpendicular direction (along collagen fibers) Forearm (light skin, n = |
810 7): |
0.07 |
10 |
|
|
Skin |
590 |
2.372 (0.282) |
– |
9.191 (0.931) |
|
temperature—22°C |
750 |
0.966 (0.110) |
– |
7.340 (0.901) |
|
950 |
0.981 (0.073) |
– |
6.067 (0.847) |
|
|
Skin |
590 |
2.869 (0.289) |
– |
9.613 (0.894) |
|
temperature—38°C |
750 |
1.157 (0.106) |
– |
7.649 (0.971) |
|
950 |
1.135 (0.123) |
– |
6.234 (0.928) |
Ref. [21]
0.9Л SRR; (л) from literature [21]
0.9Л
SRR; diffusion approximation [22]
SRR, 9 detecting 600-|j, m fibers; mean separation 1.7 mm; Mie phase function [5]
SRR; CCD detector, rsd<10 mm; diffusion approximation [22]
SRR; MC-generated grid [23]
(Continued)
CO
CO
|
Tissue |
к (nm) |
Pa (cm ‘) |
Ps W |
P/ (cm"1) |
g |
Remarks |
|
Dermis of a lower |
1300 |
– |
47 |
– |
– |
OCT [24] |
|
arm Stratum corneum of finger Volar side of lower |
1300 |
12 |
||||
|
arm: |
1300 |
– |
15-20 |
– |
– |
OCT [25] |
|
Epidermis Upper dermis |
1300 |
– |
80-100 |
– |
– |
|
|
Palm of hand: Stratum corneum |
1300 |
– |
10-15 |
– |
– |
|
|
Epidermis: |
1300 |
– |
60-70 |
– |
– |
|
|
Gl andular layer |
1300 |
– |
40-50 |
– |
– |
|
|
Basal layer Upper dermis Volar side of lower arm (epidermis and |
1300 |
50-80 |
OCT [26]; depth up to 350 |j, m; skin treated with a detergent solution (2% of |
|||
|
dermis) |
1300 |
– |
140 |
– |
– |
anionic tensides in water) |
|
Normal Treated |
1300 |
– |
80 |
– |
– |
|
|
Forearm (5 subjects, 14 measurements) |
800 |
0.23 (0.04) |
6.8 (0.8) |
Time-domain technique, ц’ (cm4) ~ 11 5.1×10 3Я, X = 760-900 nm [14] |
|
Basic Technology and Targets for Light-Based Systems |
|
(a) (b) |
|
Figure 3.8 Results of in vitro measurements of optical properties of the human skin samples (N = 21) using integrating sphere (IS) technique for measurements and inverse adding-doubling method (IAD) for the reconstruction of the optical properties [16]. Tissue slabs of 1-6 mm in thickness taken post-mortem (<24 hours after death) and stored at 20°C in saline were investigated. Measurements were taken at room temperature. (a) The spectral dependence of absorption coefficient fJa, the vertical lines show the standard deviation values. (b) The spectral dependence of reduced scattering coefficient д/ , and its approximation by the power law; the symbols correspond to the averaged experimental data and the vertical lines show the standard deviation values; the bold and dashed lines show the contribution of the Mie and Rayleigh scattering, respectively; the solid line shows the combination of the Mie and Rayleigh scattering. (c) The optical penetration depth of light le ~ ld into skin over the wavelength ranges from 400 to 2000 nm. |
beams always have low penetration depth than large diameter beams. The penetration depth can be increased by focusing beam into the skin. Mechanical skin deformation by compression or vacuum allows for increase of penetration depth due to scattering coefficient reduction by skin deformation and absorption coefficient decrease by blood displacement to the neighboring tissue regions. Another method of penetration depth increase is optical clearing that is based on tissue impregnation by a biocompatible solution and causes matching of refractive indices of scatterers and tissue ground material which may dramatically decrease tissue scattering coefficient [1].
The quantity usually measured in dosimetry is the irradiance F(r), which is defined as the power per receiving area of a flat detector. For such definition, light entering differently from perpendicular incidence contributes with reduced impact, and light from below does not contribute at all. Light-induced tissue heating or any photobiological effect in tissue or cells depends on light absorption. For isotropic media, absorption is not sensitive to the angle of irradiation; thus, an adequate light dosimetric quantity should be the total radiant energy fluence rate U{r) or the space irradiance, defined as the light power hitting a sphere divided by sphere’s cross-section [27]. For an isotropic space distribution of light intensity, the space irradiance is four times the irradiance measured for the same point within tissue (r).
The mean refractive index n of a tissue is defined by the refractive indices of its scattering centers material ns and ground (surrounding) matter n0 [Eq. (3.6)]. The refractive index variation in tissues, quantified by the ratio m = ns/n0, determines light scattering efficiency. Measuring refractive indices in tissues and their constituent components is an important focus of interest in tissue optics because index of refraction determines light reflection and refraction at the interfaces between air and tissue, detecting fiber and tissue, and tissue layers; it also strongly influences light propagation and distribution within tissues, defines speed of light in tissue, and governs how the photons migrate.
Indeed, the optical properties of tissues, including refractive indices, are known to depend on water content. The refractive indices of water over a broad wavelength ranging from 200 nm to 200 pm have been reported in ref. [28]. Specifically, nw = l.396 for 1 = 200 nm, l.335 for 1 = 500 nm, 1.142 for 1 = 2,800 nm, 1.400 for 1 = 3,500 nm, 1.218 for 1 = 10,000 nm, and 2.130 for 1 = 200 pm.
To model tissue by a mixture of water and a bioorganic compound of a tissue is more adequate. For instance, the refractive index of human skin can be approximated by a 70/30 mixture of water and protein [19]. Assuming that protein has a constant refractive index value of 1.5 over the entire wavelength range, the authors of ref. [19] have suggested the following expression for estimation of skin index of refraction:
nskin(1)=0.7(1.58 – 8.45 x 10-41 + 1.10 x 10-612 – 7.19 x 101013
+ 2.32 x 10-1314 – 2.98 x10-1715) + 0.3 x 1.5, (3.9)
where the wavelength 1 is in nanometers.
A more precise semiempirical dispersion formula for a whole human skin, derived from in vitro experimental data for normal and immersed (optically cleared) skin, has a view [29]:
nskin(1)=1.30 90 – 4.34 60 x 102Г2 + 1.6065 x 1091 4 – 1.2811 x 101416. (3.10)
For skin optics, this is of great importance to know the dispersion properties of melanin, which is contained in skin and hair. Melanin granules are the major back-reflecting particles in OCT and small-scale spatially resolved spectroscopy of skin. The wavelength dependence of the refractive index of melanin particles in the range from 350 to 800 nm was reconstructed on the basis of spectroscopic and electronic microscopy studies of water suspensions of natural melanin [29,30]:
nM(1)=1.6840 – 1.87 23 x 10412 + 1.0964 x 101014 – 8.6484 x 10141Л (3.11)