Optical properties of biological tissues: a review

The optical properties of a tissue affect both diagnostic and therapeutic applications of light. The ability of light to penetrate a tissue, interrogate the tissue components, then escape the tissue for detection is key to diagnostic applications. The ability of light to penetrate a tissue and deposit energy via the optical absorption properties of the tissue is key to therapeutic applications. Hence, specifying the optical properties of a tissue is the first step toward properly designing devices, interpreting diagnostic measurements or planning therapeutic protocols. The second step is to use the optical properties in a light transport model to predict the light distribution and energy deposition. This review will resist the temptation to describe light transport, and will focus on the expected optical properties of various tissue types, and how to routinely formulate the optical properties of a tissue at any given wavelength.

In the past, reviews have tabulated the optical properties (absorption, scattering, anisotropy, reduced scattering, refractive index) of various tissues measured at some (or many) wavelengths and such tabulations have been useful (Cheong 1995, Kim and Wilson 2011, Sandell and Zhu 2011, Bashkatov et al 2011). But if one needed to know the optical properties of a particular tissue in vivo, would one be confident in using a tabulated value? Firstly, the tabulated values may not be accurate due to measurement artifacts. Secondly, the living tissue of a particular person is subject to variations in blood content, water content, collagen content and fiber development. The variations are significant from person to person, site to site on one person or even time to time on one site. The tabulated values may not include the wavelength of interest. Perhaps it is more useful to understand the expected standard behavior of optical properties, and to anticipate the variation in tissue constitution that yields the tissue optical properties at any desired wavelength.

This review summarizes the tissue optical absorption coefficient, µ_a, in terms of the average hemoglobin (HGb) concentration (C_HGb) in the tissue or alternatively as whole blood volume fraction (B), the arterio-venous oxygen saturation (S) of HGb in the blood, the average water content (W) and the average fat content (F). These parameters scale standard absorption spectra. If there are other minor absorbers in the tissue (melanin, bilirubin, betacarotene, etc), they can be added to the tissue absorption.

The review summarizes the optical reduced scattering coefficient, $\mu _s^\prime$, by the parameters (a, b), or alternatively (a', f_Rayleigh, b_Mie) (explained later). These parameters specify standard scattering behavior versus wavelength. Hence, data on at least three wavelengths is sufficient to allow prediction of scattering at all wavelengths in the UV, visible, near-IR range. The $\mu _s^\prime$ and µ_a properties describe diffusion of light in a tissue and reflection of multiply scattered light from a tissue. These optical properties govern the reflectance from a tissue seen by a camera or the lateral diffusion of light within a tissue collected by an optical fiber probe.

The review also reviews reports of the tissue scattering coefficient, µ_s, and the angular function of single scattering, p(θ), that in turn allows calculation of the anisotropy, g, that characterizes the effectiveness of scattering. The real refractive index (n') of tissues is discussed, which pertains to interferometric measurements and some microscopy applications. These three parameters (µ_s, g, n') influence how light penetrates to a focus and returns to a microscope.

Section 1 offers an introduction to the basics of tissue optical properties. Section 2 considers the reduced scattering coefficient of tissues. Section 3 discusses the scattering coefficient and the anisotropy of scattering. Section 4 describes the refractive index. Section 5 summarizes the absorption properties of blood, water, melanin, fat and yellow pigments. Section 6 presents a bookkeeping scheme for predicting the optical properties at any wavelength based on the components of the tissue.

The optical properties of a tissue are described in terms of the absorption coefficient, µ_a (cm⁻¹), the scattering coefficient µ_s (cm⁻¹), the scattering function p(θ,ψ) (sr⁻¹) where θ is the deflection angle of scatter and ψ is the azimuthal angle of scatter, and the real refractive index of the tissue, n'. An introduction to these properties is presented elsewhere (Cheong 1995, Jacques and Pogue 2008, Welch and van Gemert 2011).

The p(θ,ψ) is appropriate when discussing only a single or few scattering events, such as during transmission microscopy of thin tissue sections or during confocal reflectance microscopy, which includes optical coherence tomography. In thicker tissues where multiple scattering occurs and the orientations of scattering structures in the tissue are randomly oriented, the ψ dependence of scattering is averaged and hence ignored, and the multiple scattering averages the θ such that an average parameter, g = 〈cos θ〉, called the anisotropy of scatter, characterizes tissue scattering in terms of the relative forward versus backward direction of scatter. Figure 1 summarizes these properties and their inter-relationships.

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Optical scattering can be described either as scattering by particles that have a refractive index different from the surrounding medium, or as scattering by a medium with a continuous but fluctuating refractive index. The particle description can be approximated by Mie theory, which describes the scattering from ideal spheres within a medium (Prahl and Jacques 2012). A mixture of spheres of different sizes can mimic the optical scattering behavior of a tissue. Continuum scattering theory describes tissue scattering in terms of the autocorrelation function for the spatial distribution of the fluctuating refractive index in a tissue (Schmitt and Kumar 1996, Xu and Alfano 2005, Rogers et al 2009, Yi and Backman 2012). The Wiener–Khinchin theorem relates an autocorrelation function to its corresponding power spectrum, and continuum scattering theory relates the spatial autocorrelation of refractive index fluctuations to the wavelength dependence of scatter. Both descriptions are adjusted to match experimental data and hence both are descriptors for the scattering behavior of tissues.

The terms Rayleigh scattering and Mie scattering are commonly used in the field of biomedical optics, with Rayleigh scattering referring to scattering by small particles or mass density fluctuations much smaller than the wavelength of light, and Mie scattering referring to scattering by particles comparable to or larger than the wavelength of light. But this common use of these terms is not actually correct. Mie scattering is the generic name for scattering by a sphere of any size, both small and large, and the common term Rayleigh scattering refers to the Rayleigh limit of Mie scattering due to particles much smaller than the wavelength of light. Nevertheless, the common usage of Rayleigh and Mie is followed in this review because it is familiar to many in our field.

A review of tissue $\mu _s^\prime$ properties as a function of wavelength is presented, which is not exhaustive but sufficient to characterize the behavior of seven groups of tissues: skin, brain, breast, bone, other soft tissues, other fibrous tissues and fatty tissues. The data of $\mu _s^\prime$(λ) were fit with two equations:

$$\begin{equation} \mu _s^\prime = a\left( {\frac{\lambda }{{500\;({\rm nm)}}}} \right)^{ - b} \end{equation} \tag{ 1 }$$

and alternatively

$$\begin{equation} \mu _s^\prime (\lambda ) = a'\left( {f_{{\rm Ray}} \left( {\frac{\lambda }{{500\;({\rm nm)}}}} \right)^{ - 4} + \left( {1 - f_{{\rm Ray}} } \right)\left( {\frac{\lambda }{{500\;({\rm nm)}}}} \right)^{ - b_{{\rm Mie}} } } \right). \end{equation} \tag{ 2 }$$

In equation (1), the wavelength λ is normalized by a reference wavelength, 500 nm, to yield a dimensionless value, which is then raised to a power b, called the 'scattering power'. This term characterizes the wavelength dependence of $\mu _s^\prime$. The factor a is the value $\mu _s^\prime$(λ = 500 nm), which scales the wavelength-dependent term.

In equation (2), the wavelength dependence of scattering is described in terms of the separate contributions of Rayleigh and Mie scattering at the reference wavelength. The scaling factor a' equals $\mu _s^\prime$(λ = 500 nm). The Rayleigh scattering is a'f_Ray(λ/500 nm)⁻⁴, and the Mie scattering is a'(1 – f_Ray)(λ/500 nm)$^{ - b_{{\rm Mie}} }$, where 1 – f_Ray indicates the fraction of Mie scattering.

Table 1 summarizes the parameters of equations (1) and (2) obtained by analysis of the literature data for $\mu _s^\prime$(λ). Figure 2 displays the data for each of the seven tissue types. Also shown are the fits to the data using the mean parameters for equations (1) and (2) listed in table 1 for each data set.

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Table 2 summarizes the mean values of the parameters for equations (1) and (2) as applied to each of the seven tissue types in table 1.

So which is better, equation (1) or equation (2)? The equations are equally good for routine prediction of tissue scattering for use in predicting behavior of light diffusion within the 400–1300 nm wavelength range. But outside this range in either the ultraviolet or the longer infrared, the two equations diverge. More data is needed, especially at longer wavelengths, to resolve which equation is better.

The bigger issue is the variability of the a and a' values, which scale the wavelength-dependent terms in equations (1) and (2). In particular, the category 'other soft tissues' show significant variability in a and a'. Figure 3 ranks the data according to the value of a in equation (1), showing that skin and other fibrous tissues have higher values of a ($\mu _s^\prime$_500 nm) than other tissues. Breast tissues are seen at both low and high scattering, perhaps dependent on the relative fibrous versus fatty character of the particular breast.

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If one is interested in using the scattering properties to characterize the sub-µm structure of a cell, then the details of equations (1) and (2) become important. In general, cellular tissues will present a simple λ^−b behavior, and equation (1) is sufficient. Cellular tissues with a high density of mitochondria (Beauvoit et al 1995) or lysosomes (Wilson et al 2007) will present Rayleigh scattering due to the high density of lipid membranes, which causes an elevation of b in equation (1) and an elevation of f_Ray in equation (2). Collagenous tissues, such as skin and some fibrous tissues, present much more Rayleigh scattering putatively due to the 70 nm periodic density along collagen fibrils and the sub-100 nm inter-fibril spacings (Saidi et al 1995, Jacques 1996), which also elevates b and f_Ray.

Figure 4(a) plots b_Mie versus b, and shows some tissues tracking as b_Mie = b, while other tissues, especially the skin and fibrous tissues, show a lower b_Mie than b. When the data allow specification of both a short wavelength rise and a long wavelength stability in $\mu _s^\prime$, then f_Ray can account for the Rayleigh scattering and b_Mie can account for the slower fall in $\mu _s^\prime$ versus longer wavelengths. Figure 4(b) shows the ratio b_Mie/b versus f_Ray, illustrating the drop in b_Mie relative to b as f_Ray grows.

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More data, especially at longer wavelengths, is needed to clarify if Mie scattering is indeed relatively wavelength independent (b_Mie ≤ 1). If so, then equation (2) is a better descriptor than equation (1), and the short wavelength rise in $\mu _s^\prime$ specifies an f_Ray that becomes a useful parameter for quantifying the scattering due to organelles and collagen fibrils. If not, then the entire spectrum is consistent with equation (1) and the simple a(λ/λ_reference)^−b behavior implies the corresponding autocorrelation of refractive index fluctuations (i.e. mass fluctuations) follows a simple form. Whether one form or the other is more useful remains to be seen. This question is an area of study that hopes to use changes in the structure of cells and tissues in the ∼50–600 nm range as a contrast parameter while imaging cells or tissues macroscopically. Such surveillance may prove useful in imaging the margins of cancers, for example.

The measurement of µ_s can be a difficult task. The measurement of µ_s is usually made by a collimated transmission measurement (T_c) through tissue of thickness L to specify µ_s = –ln(T_c)/L. But such measurements must be made through a thin tissue sample, on the scale of one mean free path (mfp = 1/µ_s), which is typically 100 µm or less, or else multiple scattering becomes an issue. But preparing such thin tissues is not easy, and they are subject to desiccation. Also, the heterogeneity of tissues becomes apparent in such thin samples. Another issue is the solid angle of collection at the detector, which if too large will collect photons despite their being slightly deflected, thereby underestimating µ_s.

Similarly, the measurement of g can be difficult. Direct measurement of p(θ) using goniometry involves measurement of the angular scattering of light by a thin tissue sample, which then allows calculation of g (see below). The concerns about local heterogeneity in a thin sample pertain to goniometry. Also, the measurements in the backward direction are often low, and must be well above any noise floor of measurement since the backward signal is critical to the net value of g. When measuring a thin tissue slab, the angle and intensity of exit from the tissue can be modified by refraction at the tissue/air or tissue/glass/air interface. Using a hemispherical lens coupled to the tissue allows exiting photons to encounter a glass/air interface perpendicularly, which mitigates refraction. Measurements of scattering around θ = 90 can be experimentally complicated.

One approach toward measuring g is to use the values of $\mu _s^\prime$ from diffuse light measurements and µ_s from collimated transmission measurements to deduce g: g = 1 – $\mu _s^\prime$/µ_s. While the $\mu _s^\prime$ value is usually robust, the µ_s value may not be so reliable, as discussed above. An artifactual decrease in µ_s causes an artifactual decrease in g.

A recent approach (Gareau 2006, Samatham et al 2008, Jacques et al 2008) has been to measure the attenuation of backscattered reflectance collected by a confocal microscope as the focus is scanned down into a tissue. A high g value allows light to penetrate to the focus despite multiple scattering, and to return from the focus and still reach the pinhole of collection. However, a high g value reduces the amount of light backscattered at the focus which decreases the collected reflectance. The measurement of reflectance, R(z_f) = ρ exp(–µz_f), depends on two parameters, (1) the attenuation (µ (cm⁻¹)) versus depth of focus and (2) the absolute value of reflected signal within the focus (ρ, a mirror defines ρ = 1). Together, µ and ρ specify the two unknown values µ_s and g.

Figure 5(a) shows the measurements at 488 nm wavelength of Samatham (2012) on freshly excised mouse tissues, illustrating how µ and ρ specify µ_s and g. Figure 5(b) plots µ_s versus g as well as iso-$\mu _s^\prime$ contours. The data show that µ_s and g increase coordinately, while µ_s(1 – g) remains somewhat constant in the range of 30–50 cm⁻¹.

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Mourant et al (2002) reported on the scattering properties of cultured cells in suspension. Figure 6 shows the scattering function p(θ) (sr⁻¹) for light polarized perpendicular to the scattering plane (p(θ)_per) and for light polarized parallel to the scattering plane (p(θ)_par). The scattering plane is defined as the plane containing the laser source, cell sample and the detector. The forward scattering is denoted by θ = 0°, and direct backscatter is denoted by θ = 180°. The cells show a very forward-directed scatter, with anisotropies of g = 0.925, 0.950 and 0.930 for the perpendicular, parallel and total scattering functions (arccos(0.925) = 22.3°, arccos(0.950) = 18.2° and arccos(0.930) = 21.6°).

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Xu et al (2008) reported on the angular and wavelength dependence of the scattering function p(θ, λ). Figure 7 shows the p(θ) for their cells (SiHa cells in phosphate buffered saline suspensions) at 633 nm wavelength. Their report is especially interesting because they demonstrated that the first 10° of angular deflection are dominated by the cell as a whole and by the nucleus, consistent with Mie scattering from large spheres. At wider angles >10°, the scattering was due to the small-scale refractive index fluctuations of the organelles, aggregates and membranes of the cell, and this broad scattering was modeled by a continuum model.

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Jacques et al (1987) and Hall et al (2012) studied the goniometry of light transmission through tissues of varying sample thickness. The scattered light could be described by an equivalent Henyey–Greenstein function with an apparent g. As the tissue thinned, this apparent g value extrapolated toward the expected g value for a single-scattering Henyey–Greenstein function. These reports cited values of g greater than 0.90 for visible wavelengths (see figure 8). This method offers an approach toward direct measurement of p(θ) by goniometry using thicker samples.

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Figure 8 plots literature data on anisotropy versus wavelength. There is a lot of variation in the data, but in general the values of g are rather high. There appears to be a trend toward increasing g as the wavelength increases. This observation, if true, is surprising. If the small sub-wavelength structures within a cell are scattering light, then as the wavelength increases the ratio of structure size to wavelength should decrease, and the scattering should become more Rayleigh-like, i.e. lower g. Why does g increase with increasing λ? This contradiction between experiment and expectation is an opportunity to better understand the nature of light scattering in tissues. Perhaps the Mie scattering from the nuclei dominates in certain experiments, which keeps g high. Perhaps there is some mesoscopic scale of structure in tissue, ≫10 µm, that generates constructive interference so that more light is forward-scattered and hence g increases. The efficiency of the smallest scatterers decreases as λ increase, and perhaps their contribution to the apparent g simply diminishes, yielding a higher g at longer wavelengths. Because of the importance of g in microscopy and interferometry, more studies on anisotropy should be a priority.

The complex refractive index, n = n' + jn'', includes the real refractive index, n', which describes energy storage and hence affects the speed of light in a medium. The imaginary refractive index, n'', describes energy dissipation and specifies the absorption coefficient, µ_a = 4πn''/λ. To a first approximation, the value of n' scales as the water content (W) of a tissue.

$$\begin{equation} n^{\prime} = n^{\prime}_{\rm dry} - ( n^{\prime}_{\rm dry} - n^{\prime}_{\rm water})W, \end{equation} \tag{ 3 }$$

where $n^{\prime} _{{\rm dry}}$ is the refractive index of the tissue's dry mass and $n^{\prime} _{{\rm water}}$ is the refractive index of water. Jacques and Prahl (1987) estimated that $n^{\prime} _{{\rm water}}$ = 1.33 and $n^{\prime} _{{\rm dry}}$ = 1.50, based on an old Bausch and Lomb graphic that had plotted n' versus water content for various biological materials and food products. A more recent report by Biswas and Luu (2011) on a range of biological tissues used magnetic resonance imaging (MRI) to indicate that ρ_dry = 1.53 g cm⁻³ and $n^{\prime} _{{\rm dry}}$ = 1.514. Figure 9 summarizes their data illustrating this relationship.

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A light-absorbing medium will absorb a fraction of incident light per incremental pathlength of travel within the medium. The absorption coefficient µ_a (cm⁻¹) is defined as

$$\begin{equation} \mu _a = - \frac{1}{T}\frac{{\partial T}}{{\partial L}}, \end{equation} \tag{ 4 }$$

where T (dimensionless) is the transmitted or surviving fraction of the incident light after an incremental pathlength ∂L (cm). This fractional change ∂T/T per ∂L yields an exponential decrease in the intensity of the light as a function of increasing pathlength L:

$$\begin{equation} T = {\rm e}^{ - \mu _a L} = 10^{ - \varepsilon CL} = {\rm e}^{ - 4\pi n''L/\lambda } . \end{equation} \tag{ 5 }$$

Equation (5) also cites two alternative expressions using alternative descriptors for absorption. The first spectrometers measured the transmission through a nonscattering medium containing a chromophore as T = 10^−εCL, where C is the concentration ((mol L⁻¹) or (M)) and ε is the extinction coefficient (cm⁻¹ M⁻¹) for the chromophore. Historically, ε has been recorded in the literature using this base 10 nomenclature. Optical wave theory describes transmission of intensity as T = exp(–4πn''L/λ), where n'' is the imaginary refractive index of the medium, hence µ_a = 4πn''/λ. You can find the absorption of a chromophore recorded in these three different ways, ε, µ_a and n'', but they are equivalent descriptors.

The absorption coefficient µ_a of a tissue is the sum of contributions from all absorbing chromophores within the tissue:

$$\begin{equation} \mu _a = \ln (10)\sum\limits_i {C_i \varepsilon _i } . \end{equation} \tag{ 6 }$$

For example, consider HGb. The HGb mass concentration within blood, C_m.HGb (g L⁻¹), varies for men (138 to 172 g L⁻¹), women (121 to 151 g L⁻¹), children (110 to 160 g L⁻¹) and pregnant women (110 to 120 g L⁻¹) (Tresca 2012). But the blood volume fraction (B) in a tissue also varies. The molecular weight of HGb is MW = 64 458 g mol⁻¹ (van Beekvelt et al 2001). If B = 0.01 and C_m.HGb = 150 g L⁻¹, then the apparent average HGb molar concentration in the tissue is C_HGb = BC_m.HGb/MW = (0.01)(150 g L⁻¹)/(64 458 g mol⁻¹) = 2.33 × 10⁻⁵ M. The extinction coefficient of HGb varies with its oxygen saturation and with wavelength. At the isobestic point at ∼806 nm, both oxyHGb and deoxyHGB have the same absorption, and the value of ε is ∼818 cm⁻¹ M⁻¹. At 806 nm, the contribution of blood (B = 0.01) to the tissue absorption is µ_a = ln(10)C_HGbε = (2.302)(2.33 × 10⁻⁵ M)(818) = 0.0438 cm⁻¹.

Sometimes one wishes to describe the absorption properties of a material that does not have a well defined concentration, and an alternative concentration must be used, for example, C (mg mL⁻¹), and an alternative extinction coefficient must be used, ε (cm⁻¹ (mg mL⁻¹)⁻¹). The product εC still has units of cm⁻¹, and εCL is dimensionless. So, while the literature usually uses C (M), ε (cm⁻¹ M⁻¹) and L (cm), alternative units for C, ε and L may be used, as long as εCL is dimensionless.

Studies on tissue optical properties will usually cite values of a tissue's average absorption coefficient µ_a, since the molecular composition of the tissue is not well specified. It is convenient to modify equation (6) so that the equation uses the volume fraction of a tissue component (f_v.i (L L⁻¹) or (dimensionless)) and the absorption coefficient of that pure component (µ_a.i (cm⁻¹)). Using this approach, equation (6) can be rewritten as

$$\begin{equation} \mu _a = \sum\limits_i {f_{v.i} \mu _{a.i} } . \end{equation} \tag{ 7 }$$

For example, sometimes it is helpful to describe the apparent blood volume fraction B in a tissue rather than citing an average C_HGb in the tissue. Citing B conveys a more anatomical sense of the density of vasculature. If one adopts the convention followed by Prahl (2012a) of assigning whole blood the HGb mass concentration C_m.HGb = 150 g L⁻¹, then in equation (7) the f_v.blood would equal B. The µ_a.blood would equal ε_bloodln(10)C_m.HGb/MW = ε_bloodln(10) (150 g L⁻¹)/(64 458 g mol⁻¹) = 0.0536ε_blood, where ε_blood varies with wavelength. At the isobestic point ε_blood = 818 cm⁻¹, as above, and the value of µ_a.blood becomes 4.38 cm⁻¹. If a tissue has an average volume fraction (f_v.blood = B = 0.01) of blood, then the blood contribution to µ_a equals (0.01)(4.38 cm⁻¹) = 0.0438 cm⁻¹.

Another example is water content. The imaginary refractive index of water at 970 nm is n'' = 3.47 × 10⁻⁶. The absorption coefficient of water at λ = 970 nm is µ_a.water = 4πn''/λ = 0.45 cm⁻¹. If a tissue has a volume fraction of water f_v.water = 0.65, then the contribution of water to the total tissue absorption at 970 nm is µ_a = f_v.waterµ_a.water = (0.65)(0.45 cm⁻¹) = 0.29 cm⁻¹.

There are a variety of chromophores, both natural and exogenously supplied, which can contribute to µ_a in equation (6) or (7). Usually, blood and water will dominate the absorption. Sometimes, melanin, fat, bilirubin, beta-carotene or an additive such as indocyanine green must be considered. Other chromophores offer quite minor contributions. If one is interested in spectroscopic detection, then the minor contributions are important. If one is interested in understanding light penetration into a tissue for some therapeutic protocol, then the minor contributions usually do not significantly perturb the light transport.

5.1. Blood

The absorption coefficient of whole blood is shown in figure 10, using data compiled by Prahl (2012a), citing data from Gratzer and Kollias (1999), Moaveni (1970), Schmitt (1986) Takatani and Graham (1987). Figure 10(a) shows fully oxygenated blood, and figure 10(b) shows fully deoxygenated blood. Reliable data beyond 1000 nm wavelength is difficult to find in the literature. In figure 10, dashed red lines extrapolate data beyond 1000 nm, either using a Gaussian or an exponential, indicating where water absorption might begin to dominate over HGb absorption.

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5.2. Water

The water absorption spectrum is plotted in figure 11(a), based on the work of Hale and Querry (1973), Zolotarev et al (1969) and Segelstein (1981), as cited on the website by Prahl (2012b). Figure 11(b) shows the difference between free water and bound water reported by Chung et al (2012), in which the absorption of bound water slightly sharpens the absorption peak at about 970 nm, i.e., absorption of bound water decreases above and below 970 nm relative to free water.

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If interested in water absorption during exposure to high energy laser pulses, the report of Cummings and Walsh (1993) discusses how the mid-infrared water absorption near 3 µm wavelength broadens and the peak absorption decreases as the pulsed laser energy deposition (J cm⁻³) in the water increases.

5.3. Melanin

The absorption coefficient of the interior of a typical cutaneous melanosome, µ_a.melanosome (cm⁻¹), is shown in figure 12 (open black symbols), based on the work of Jacques and McAuliffe (1991). In that report, the threshold radiant exposure, H (J cm⁻³), of a ruby laser (690 nm wavelength) for causing explosive vaporization of melanosomes within cadaver skin was tested as a function of initial tissue temperature. A colder initial temperature required a higher laser pulse energy to pop the melanosomes. The results predicted the threshold temperature for explosive vaporization to be 112 °C. This value was used to interpret the literature of reported values of threshold H for exploding cutaneous melanosomes using a variety of lasers at various wavelengths. The analysis yielded the µ_a for the interior of cutaneous melanosomes. The resulting spectrum was consistent with optical fiber spectra for the ventral versus sun-exposed dorsal forearm skin of subjects; the difference in optical density attributed to cutaneous melanin (red circles, scaled to match laser results). The figure also shows the optical fiber probe measurements of Zonios et al (2008), again scaled to match laser results. The data of Sarna and Swartz (1988) specified the extinction coefficient ε (cm⁻¹ M⁻¹) of monomers for eumelanin and pheomelanin. In figure 11, these data are scaled by an intra-melanosome concentration of 461 mM for eumelanin monomers and 564 mM for pheomelanin monomers, in order to match the µ_a.melanosome spectra at 500 nm. The fits use a power curve,

$$\begin{equation} \mu _{a{\rm .melanosome}} = \left( {519\;{\rm cm}^{ - 1} } \right)\left( {\frac{\lambda }{{500\;{\rm nm}}}} \right)^{ - m} , \end{equation} \tag{ 8 }$$

where the value 519 cm⁻¹ at 500 nm was specified by the laser experiments. The value of the power factor m cited by different reports varies as shown in the figure, and an approximate value for m is 3. More work on the absorption spectrum of in vivo melanin is needed.

To calculate the µ_a contribution for melanin in a tissue, one estimates the equivalent volume fraction (f_v.melanosome) of cutaneous-like melanosomes within a tissue, f_v.melanin, which is then multiplied by this µ_a.melanosome to yield the contribution to the total µ_a of a tissue:

$$\begin{equation} \mu _a \,{\rm due\ to\ melanin} = f_{v{\rm .melanosome}} \mu _{a{\rm .melanosome}} . \end{equation} \tag{ 9 }$$

Using f_v.melanosome as a concentration of melanin may seem odd, but melanin is an extended polymer that does not have a unique molecular weight. Also, histology can document the number density of melanosomes in a tissue, so using f_v.melanosome is perhaps a more familiar metric to some people, such as pathologists. However, melanosomes do not all have the same melanin content. The µ_a.melanosome of figure 12 is for a typical cutaneous melanosome, predominantly eumelanin, used as a convention. The figure shows the difference between eumelanin (black) and pheomelanin (red).

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Alternatively, one can cite the apparent concentration of monomers (C_eumelanin and C_pheomelanin (M)) in a tissue and use the extinction coefficients of Sarna and Swartz (1988),

$$\begin{equation} \begin{array}{@{}l} \varepsilon _{{\rm eumelanin}} = \left( {2.37 \times 10^4 \,{\rm cm}^{ - 1} \,{\rm M}^{ - 1} } \right){\rm e}^{ - 0.0056\lambda } , \\ \varepsilon _{{\rm pheomelanin}} = \left( {1.01 \times 10^5 \,{\rm cm}^{ - 1} \,{\rm M}^{ - 1} } \right){\rm e}^{ - 0.0087\lambda } , \\ \end{array} \end{equation} \tag{ 10 }$$

such that the absorption due to melanin is

$$\begin{equation} \mu _a \,{\rm due\ to\ melanin} = \left( {\varepsilon _{{\rm eumelanin}} C_{{\rm eumelanin}} + \varepsilon _{{\rm pheomelanin}} C_{{\rm pheomelanin}} } \right)\ln (10). \end{equation} \tag{ 11 }$$

5.4. Adipose tissue and fat

The absorption coefficient spectra of several fatty tissues are shown in figure 13. The work of van Veen et al (2004) involved careful purification and dehydration of porcine fat before measurement, and perhaps is the best spectra available at this point. Other measurements are on tissues of unknown fat and water content. An attempt to correct for the fat and water content has been made, and the spectra are in general agreement that the dominant absorption peak is at 930 nm.

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5.5. Yellow pigments

The yellow pigments, bilirubin and β-carotene, are sometimes present to a small degree in the absorption spectra of tissues. Bilirubin absorption in the skin is routinely used to detect hyperbilirubinemia in neonates. β-carotene can also give a yellow hue to tissues. Figure 14 cites the extinction coefficient for bilirubin and β-carotene. Dr Angelo Lamola provided the spectrum of bilirubin associated with albumin in human serum (bilirubin/HSA) (Lamola 2011). A report of bilirubin in chloroform is also shown (Du et al 1998), illustrating the solvent effect on absorption. The β-carotene spectrum in a solvent, hexane, is shown (Du et al 1998) and the in vivo value is expected to differ slightly.

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The optical properties of tissues should be regarded as variable from tissue to tissue, person to person and even time to time. Methods for measuring optical properties continue to improve and it is feasible to make rapid assessment of a particular tissue, much like taking a temperature with a thermometer.

For the reader who wishes to estimate optical properties to guide device or protocol design, a generic tissue can be constructed that is specified by the absorbing chromophores in the tissue and by the balance of Rayleigh and Mie scattering in the tissue.

Figure 15 shows the absorption coefficient µ_a increasing as water, blood, bilirubin, fat and melanin are sequentially added. This figure does not describe a real tissue, but simply illustrates the spectral consequence of the various absorbing chromophores. Any tissue can be characterized by

• S     HGb oxygen saturation of mixed arterio-venous vasculature
• B     average blood volume fraction (f_v.blood)
• W       water content (f_v.water)
• Bili   bilirubin concentration (C (M))
• βC    β-carotene concentration (C (M))
• F     fat content (f_v.fat)
• M   melanosome volume fraction (f_v.melanosome), or alternatively the molar concentration of melanin monomers (C (M)).

The total absorption coefficient is calculated

$$\begin{eqnarray} &&\fl \mu _a = BS\mu _{a{\rm .oxy}} + B(1 - S)\mu _{a{\rm .deoxy}} + W\mu _{a{\rm .water}} + F\mu _{a{\rm .fat}} \nonumber\\ &&+ M\mu _{a{\rm .melanosome}} + 2.3C_{{\rm bili}} \varepsilon _{{\rm bili}} + 2.3C_{{\rm \beta C}} \varepsilon _{{\rm \beta C}} . \end{eqnarray} \tag{ 12 }$$

Figure 16 shows a more realistic tissue, in which the blood content is fixed at B = 0.002, S = 0.75, and there is a baseline volume fraction of fibrous material, f_v.fibrous = 0.30. The tissue fat content and water content offset each other, with F = [0 by 0.1 to 0.7] as W = [0.7 by −0.1 to 0.1] such that fat + water = 0.70. The fat signature is evident at water contents below 30, but is less obvious at higher water contents.

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Figure 17 shows the generic reduced scattering coefficient of tissues, based on equation (2). The contribution of Mie scattering (a_Mie) is shown as blue lines. The contribution of Rayleigh scattering (a_Rayleigh) is added to the highest Mie scattering, and the combination is shown as red lines (a_Rayleigh + a_Mie). As the Rayleigh component of scattering increases, the short wavelength scattering increases significantly.

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Equations (1), (2) and (6), (7) can mimic the optical properties of a generic tissue at any wavelength, but one must specify the tissue parameters in these equations. The literature is limited in its reporting of in vivo optical properties. The task now is to better understand the constitution of tissues in terms of tissue chromophores and tissue parameters that govern absorption to enable use of the generic model. Table 3 lists a brief survey of the in vivo optical parameters that affect absorption (C_HGb, B, S, W, M, F).

The data in table 3 lists average tissue parameters that affect scattering (a, b, a', f_Ray, b_Mie). Many of these data were measured on excised tissues. The optical scattering properties of excised tissues are relatively stable for a short time (hours) if one avoids overhydration by soaking in saline or dessication by exposure to ambient air, and the data of table 2 are representative of in vivo optical scattering properties. But there is one distinct exception. The optical scattering of white matter of the brain drastically decreases upon excision, on the order of minutes.

Certainly, more work on in vivo tissue measurements is needed, reporting both tissue optical properties and tissue parameters as in tables 1–3.

The use of a generic tissue can adequately mimic any real tissue, and has the advantage of generating smoothly predictable spectra for absorption and scattering. The generic equations, equations (1) or (2) for scattering and equations (6) or (7) for absorption allow calculation of the expected optical properties versus wavelength of tissues with varying chromophore content and ultrastructural character. The average tissue parameters (C_HGb or B, S, W, M, F, and a, b or a', f_Ray, b_mie) can specify the wavelength dependence of tissue optical properties and guide design of devices, diagnostics and treatment protocols. However, the variation from subject to subject, site to site and time to time argues for real-time optical property measurements on patients when working with individuals.