The sources of absorption in skin are mainly chromophores dissolved in blood or de-posited in tissue, most importantly haemoglobin and melanin. Melanin is the most important factor behind the colour of the skin. It is a deposited in the otherwise weakly absorbingepidermis. The absorption spectrum of melanin is measured and a formula for modelling the absorption spectrum is proposed in (Jacques & McAuliffe 1991):
(46) µa,m= fm·1.7·1012·λ−3.48 [1/cm],
where fmis the relative amount of melanin, the melanin fraction, and, λ¸ is the wave-length in nanometers. The concentration of melanosomes does not have a direct rela-tionship with absorption, since the size, structure and molar absorption efficiency of melanin may vary. Therefore the melanin fraction is often used instead of the melanin concentration. The absorbtion of melanin, estimated by Equation (46), is shown in Figure 8.
Like theepidermis, the dermisitself does not absorb much light either, but it contains blood, and the haemoglobin contained in the red blood cells is a strong absorber. It is the iron complex of the haemoglobin molecule, which causes the red colour of blood, by strongly absorbing blue and green. The specific property of haemoglobin is that it can carry oxygen atoms with it. When oxygen atoms are bound with the iron complex of haemoglobin, its absorption spectrum changes. The absorption spectrum of oxy-haemoglobin and deoxyoxy-haemoglobin is determined, for example, in (Horecker 1942) and tabulated by (Prahl 1999). They are shown in Figure 8.
The nominal amount of heamoglobin in blood, hematocrit, is 150 grams/liter. The concentration of haemoglobin in blood, is obtained by dividing the hematocrit with the molar mass of hemoglobin as follows:
(47) cHb,blood= 150 g/l
64500 g/mol=2.326 mol/l
400 500 600 700 800 900 1000
0.010.050.505.00
Wavelength / nm
Absorbtion coefficient / AU
Melanin Oxyhaemoglobin Deoxyhaemoglobin Water
Figure 8. The absorption spectra of the most important skin chromophores: melanin, µmel(λ), oxyhaemoglobin,µHbo(λ), deoxyhaemoglobin,µHbd(λ), and water, µw(λ). Notice the logarithmic y–axis. (Jacques & McAuliffe 1991; Horecker 1942; Prahl 1999)
Thedermiscontains blood in arteries, veins and capillaries, but not normally outside the blood vessels. Therefore, the blood is not evenly distributed over the whole der-mis. However, the microcirculation network formed by capillaries is dense, and the reflectance, even from thepapillary plexus, is an average over a skin area, because it is based on the light beam, which is made diffuse by the strong scattering in the stra-tum corneum. The blood vessel network in the cutaneous plexusis coarser, but the reflectance is even more averaged due to additional scattering in the dermis. Due to averaging, the blood is often assumed to be evenly distributed inside the whole layer.
The average concentration of haemoglobin in skin is the haemoglobin concentration in blood multiplied by the amount of blood in skin, the blood fraction, fb:
(48) cHb,skin= fbcHb,blood
The typical value for fbin normal skin was 0.05 in (Reuss 2005). We have found lower fbvalues in our studies, for example in (Publication III), where fb∈[0.0016,0.0045].
The oxygen saturation level of blood, SO2, is defined as the percentage of the oxy-genated blood of the total blood concentration:
(49) SO2= cHbo
cHbo+cHbd
Typical values of oxygen saturation in arteries,Sa,O2∈[90%,99%]and in veins,Sv,O2>
60%.
The absorption spectrum of water is available, for example, in the MiePlot program, measured by Segelstein (Segelstein 1981). The absorption spectrum of water is also shown in Figure 8.
The absorbtion of the skin without blood, the skin baseline, can be simulated, using the following formula (Saidi 1992):
(50) µa,d(λ) =7.84·108·λ−3.255
The absorption coefficient representing the different layers of skin can be calculated using the known molar extinction coefficients,ε(λ)and the concentrations, as follows:
(51) µi(λ) =
N
∑
j=1
εi,j(λ)ci,j,
whereµi(λ)is the absorption coefficient of layeri,εi,j(λ)is the molar extinction coef-ficient of chromophore j in layeri, andci,j is the concentration of the chromophore j in layeri.
For example, the absorption coefficient of thepapillary plexuscan be estimated using following equation:
(52) µa,p(λ) =µa,d(λ) +εHbo(λ)cHbfb,pSO2+εHbd(λ)cHbfb,p(1−SO2) +εw(λ)cw,p, whereµa,p(λ)is the total absorption coefficient of thepapillary plexus,cHbis the total concentration of heamoglobin in blood, fb,pis the blood fraction, andcw,pis the water concentration in thepapillary plexus.
3.4 Scattering
The human skin is a strong scatterer. Thestratum corneum in the epidermisalready makes the light beam diffuse, the collagen and the elastine fibres in thedermisscatter light and so do the cytoplasm membranes.
The size of the cells, mitochondrias and collagen fibers are usually larger than 1000 nm, and therefore larger than the wavelength in the diagnostic–therapeutic window. When the scattering particle is close to the wavelength of light, the scattering can be modelled best with Mie scattering (Mie 1908; Tuchin 2007; Igarashiet al.2007; Jacques 1996).
The strength of the Mie scattering is roughly proportional to λ−1.5, where λ is the wavelength of radiation.
The cell nucleus and membranes also scatter light, but they are much smaller than the wavelength. The scattering introduced by these small particles is often described using the Rayleigh scattering formula, which is more strongly wavelength dependent, being proportional toλ−4.
400 500 600 700 800 900 1000
020406080100
Wavelength [nm]
Scattering coefficient [1/cm]
Mie Rayleigh Mie+Rayleigh
Figure 9. The dependency of scattering on the wavelength: Mie, Rayleigh and both combined, according to Equation (53).
The optical models of skin do not usually work at the individual cell level, because it would be much too complicated to model mathematically and slow to simulate. In-stead, the skin layers are assumed to be homogeneous, and the scattering sources are distributed evenly in each layer. The scattering of human skin is often modelled as a combination of Mie and Rayleigh scattering, as follows: (Jacques 1996)
(53) µs(λ) =µs,Mie(λ) +µs,Rayleigh(λ) =2·105·λ−1.5+2·1012·λ−4.0, where the wavelength,λ, is in nanometers.
The Mie and Rayleigh scattering, as well as the combined scattering, are plotted in Figure 9.