INSTITUTE OF PHYSICS PUBLISHING
`
`J. Phys. D: Appl. Phys. 38 (2005) 2543–2555
`
`JOURNAL OF PHYSICS D: APPLIED PHYSICS
`
`doi:10.1088/0022-3727/38/15/004
`
`Optical properties of human skin,
`subcutaneous and mucous tissues in the
`wavelength range from 400 to 2000 nm
`
`A N Bashkatov1, E A Genina, V I Kochubey and V V Tuchin
`
`Institute of Optics and Biophotonics, Saratov State University, 83, Astrakhanskaya Str.,
`Saratov, 410012, Russia
`
`E-mail: bash@optics.sgu.ru
`
`Received 11 January 2005, in final form 7 April 2005
`Published 22 July 2005
`Online at stacks.iop.org/JPhysD/38/2543
`
`Abstract
`The optical properties of human skin, subcutaneous adipose tissue and
`human mucosa were measured in the wavelength range 400–2000 nm. The
`measurements were carried out using a commercially available
`spectrophotometer with an integrating sphere. The inverse adding–doubling
`method was used to determine the absorption and reduced scattering
`coefficients from the measurements.
`
`1. Introduction
`
`The development of optical methods in modern medicine
`in the areas of diagnostics, therapy and surgery has stimulated
`the investigation of optical properties of various biological
`tissues, since the efficacy of laser treatment depends on the
`photon propagation and fluence rate distribution within
`irradiated tissues.
`Examples of diagnostic use are the
`monitoring of blood oxygenation and tissue metabolism [1,2],
`laser Doppler flowmetry [3], pulse oximetry [4], detection
`of cancer by fluorescence [5, 6] and spectrophotometric
`methods [7, 8] and various techniques recently suggested
`for optical
`imaging [9–11].
`Therapeutic uses include
`applications in laser surgery [12],
`laser angioplasty and
`ablation [13–16] and in photodynamic therapy [17–25]. For
`these applications, knowledge of tissue optical properties is
`of great importance for interpretation and quantification of
`diagnostic data, and for prediction of light distribution and
`absorbed dose for therapeutic use. The knowledge of tissue
`optical properties is also necessary for the development of
`novel optical technologies of photodynamic and photothermal
`therapy, optical tomography, optical biopsy, etc. Numerous
`investigations related to determination of
`tissue optical
`properties are available. However, the optical properties of
`many tissues have not been studied in a wide wavelength range.
`Review of
`the literature [5, 6, 17, 19, 21–36] shows
`that skin and mucous are the most important tissues for
`photodynamic therapy of cancer and other diseases. Many
`authors have studied optical properties of these tissues.
`
`1 Author to whom any correspondence should be addressed.
`
`Recently the skin optical properties have been measured with
`the integrating sphere technique in the visible and near-
`infrared (NIR) spectral ranges by Prahl [37], Chan et al
`[38], Simpson et al
`[39], Du et al
`[40] and Troy and
`Thennadil [41], but the presented data are characteristically
`different, especially in the IR spectral range. Knowledge
`of the optical properties of subcutaneous adipose tissue is
`also important, since optical properties of this tissue layer
`determine light distribution in the irradiated skin in the
`course of photodynamic treatment.
`In addition, analysis
`of adipose tissue absorption and scattering properties in a
`wide wavelength range is essential for developing novel
`optical technologies for treatment of obesity and cellulite,
`as, evidently, the optical technologies promise less danger to
`the patient than the widely used surgical and pharmaceutical
`treatments.
`Investigation of the mucous optical properties is necessary
`for light dosimetry in photodynamic therapy of bladder, colon,
`oesophagus, stomach, etc. The treatment of purulent maxillary
`sinusitis is an important problem in modern rhinology,
`despite the wide application of surgical and pharmaceutical
`methods [42,43]. One of the new methods of treatment of this
`disease is photodynamic therapy of the mucous membrane of
`the maxillary sinus [42]. The optical properties of mucous
`tissues were shown by M¨uller and Roggan [44] for the
`wavelength 1064 nm. However, in a wide wavelength range
`the optical properties of mucous tissues have not been studied.
`The goal of this paper is to measure the absorption and
`reduced scattering coefficients of human skin, subcutaneous
`adipose tissue and mucous in the wavelength range from 400
`to 2000 nm.
`
`0022-3727/05/152543+13$30.00 © 2005 IOP Publishing Ltd Printed in the UK
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`A N Bashkatov et al
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`2. Physical properties and structure of the
`investigated tissues
`
`The skin presents a complex heterogeneous medium, where the
`blood and pigment content are spatially distributed variably
`in depth [45–48]. The skin consists of three main visible
`layers from the surface: epidermis (100 µm thick, the blood-
`free layer), dermis (1–4 mm thick, vascularized layer) and
`subcutaneous fat (from 1 to 6 mm thick, in dependence from
`the body site). Typically, the optical properties of the layers
`are characterized by the absorption and scattering coefficient,
`which equals the average number of absorption and scattering
`events per unit path length of photon travel in the tissue and
`the anisotropy factor, which represents the average cosine of
`the scattering angles.
`The randomly inhomogeneous distribution of blood
`and various chromophores and pigments in skin produces
`variations of the average optical properties of the skin layers.
`Nonetheless, it is possible to define the regions in the skin,
`where the gradient of skin cells structure, chromophores
`or blood amounts, changing with a depth, which roughly
`equals zero [45]. This allows subdivision of these layers
`into sublayers, where the physiological nature, physical
`and optical properties of their cells and pigments content
`are concerned.
`The epidermis can be subdivided into
`two sublayers: non-living and living epidermis. Non-living
`epidermis or stratum corneum (about 20 µm thick) consists
`of only dead squamous cells, which are highly keratinized
`with a high lipid and protein content, and has a relatively
`low water content
`[45, 46, 48]. Living epidermis (100 µm
`thick) contains most of the skin pigmentation, mainly melanin,
`which is produced in the melanocytes [49]. Large melanin
`particles such as melanosomes (>300 nm in diameter) exhibit
`mainly forward scattering. Whereas, melanin dust, whose
`particles are small (<30 nm in diameter) has the isotropy in the
`scattering profile and optical properties of the melanin particles
`(30–300 nm in diameter) may be predicted by the Mie theory.
`The dermis is a vascularized layer and the main absorbers
`in the visible spectral range are the blood haemoglobin,
`carotene and bilirubin.
`In the IR spectral range absorption
`properties of skin dermis are determined by the absorption of
`water. Following the distribution of blood vessels, [47] skin
`dermis can be subdivided into four layers: the papillary dermis
`(150 µm thick), the upper blood net plexus (100 µm thick), the
`reticular dermis (1–4 mm thick) and the deep blood net plexus
`(100 µm thick).
`The scattering properties of the dermal layers are defined
`mainly by the fibrous structure of the tissue, where collagen
`fibrils are packed in collagen bundles and have lamellae
`structure.
`The light scatters on both single fibrils and
`scattering centres, which are formed by the interlacement of
`the collagen fibrils and bundles. To sum up, the average
`scattering properties of the skin are defined by the scattering
`properties of the reticular dermis because of the relatively
`big thickness of the layer (up to 4 mm [48]) and comparable
`scattering coefficients of the epidermis and the reticular dermis.
`Absorption of haemoglobin and water of the skin dermis
`and lipids of the skin epidermis define absorption properties
`of the whole skin.
`It should be noted that absorption of
`haemoglobin is defined by the haemoglobin oxygen saturation,
`
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`since absorption coefficients of haemoglobin are different
`for oxy and deoxy forms. For an adult the arterial oxygen
`saturation is generally above 95% [4]. Typical venous oxygen
`saturation is 60–70% [1]. Thus, absorption properties of blood
`have been defined by absorption of both oxy and deoxy forms
`of haemoglobin.
`The subcutaneous adipose tissue is formed by aggregation
`of fat cells (adipocytes) containing stored fat (lipids) in the form
`of a number of small droplets for lean or normal humans and
`a few or even a single big drop in each cell for obese humans;
`the lipids are mostly represented by triglycerides [50, 51].
`Content of the lipids in a single adipocyte is about 95% of
`its volume. The diameters of the adipocytes are in the range
`15–250 µm [52] and their mean diameter ranges from 50 [50]
`to 120 µm [51]. In the spaces between the cells there are blood
`capillaries (arterial and venous plexus), nerves and reticular
`fibrils connecting each cell and providing metabolic activity to
`the fat tissue [50, 51]. Absorption of the human adipose tissue
`is defined by absorption of haemoglobin, lipids and water. The
`main scatterers of adipose tissue are spherical droplets of lipids,
`which are uniformly distributed within adipocytes.
`The mucous membrane plays a leading role in the
`physiology of the nose and paranasal sinuses [43, 53].
`It is
`covered with a pseudostratified epithelium, which consists of
`ciliated, columbar as well as short and long inserted epithelial
`cells. The membrane called basic divides epithelial and proper
`layers of the mucous tissue and consists of reticular fibrils,
`which are located in the interstitial homogeneous media. The
`membrane does not have a constant thickness. In the case of
`hyperplasia of the mucous membrane, the membrane thickens
`considerably [54].
`The proper layer of the mucous membrane is similar in
`structure to connective tissue, consisting of collagen and elastin
`fibrils. The interstitial fluid of the mucous membrane contains
`proteins and polysaccharides and is similar in composition
`to the interstitial fluid of most of the connective tissues.
`The proper layer of the mucous membrane consists of three
`sublayers. A subepithelial (or lymphoid) layer contains a
`great amount of leukocytes.
`In the intermediate sublayer
`of the proper layer, tubuloalveolar glands are contained.
`In
`the deep sublayer of the proper layer, venous plexuses are
`arranged, which consist of a surface network of smaller
`vessels and a deeper network of larger vessels. Normally,
`the total thickness of the mucous membrane varies from 0.1
`to 0.5 mm [43, 53]. In the presence of pathology (maxillary
`sinusitis, rhinitis or other rhinological disease), the thickness
`of the mucous membrane increases considerably and can reach
`2–3 mm [43].
`It should be noted that the proper layer of
`the mucous membrane is the main layer protecting against
`micro-organisms causing infectious diseases [53]. The optical
`properties of the mucous membranes are determined mainly
`by the optical properties of the proper layer since this layer is
`much thicker than the epithelial layer.
`
`3. Materials and methods
`
`in vitro with skin
`Measurements have been carried out
`samples obtained from post-mortem examinations and fresh
`human subcutaneous adipose tissue samples taken from the
`peritoneum area of patients during planned surgery. Optical
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`Optical properties of human tissues
`
`calculations [68]. Loss of light through the sides of the
`sample and the sample holder may erroneously increase the
`calculated value of the absorption coefficient. These losses
`depend on the physical size and geometry of the sample, i.e.
`the losses existing in the case when the sizes of a sample do
`not significantly exceed the diameter of the incident beam.
`The size of the exit and the entrance ports of the integrating
`sphere are also important for errorless measurements of the
`total transmittance and diffuse reflectance [68]. The tissue
`sample should completely cover the port in the integrating
`sphere, and the distance from the edge of the irradiating
`beam on the sample to the edge of the port should be much
`larger than the lateral light propagation distance, which is
`determined by 1/(µa + µ
`). If this is not satisfied, then light
`will be lost from the sides of the sample and the loss will be
`attributed to absorption, and so the absorption coefficient will
`be overestimated. These requirements have been met in our
`experiments, since maximal size of the sphere port does not
`exceed 20 mm, whereas the minimal size of the tissue samples
`is 20 mm. In addition, using the absorption and the reduced
`scattering coefficients of the investigated tissues presented
`below, in the next section, we calculated the lateral light
`propagation distance. For the skin, the maximal lateral light
`propagation distance is equal to 0.7 mm for the wavelength
`1929 nm. For the subcutaneous adipose tissue the maximal
`value of the lateral light propagation distance is equal to
`1.25 mm for the wavelength 1620 nm. For the mucous tissue,
`the value is equal to 2.2 mm for the wavelength 1284 nm.
`Taking into account the diameter of the incident beam (3 mm),
`the minimal size of a tissue sample has to be larger than 7.5 mm,
`which was satisfied for each tissue sample under study.
`It
`is seen that the lateral light propagation distance is smaller
`than the distance from the edge of the irradiating beam on the
`sample to the sample port edge. In addition, Pickering et al
`[68] reported that the area of tissue sample has to be smaller
`than the area of the inner surface of the integrating sphere.
`This requirement has also been met in our experiments, since
`the area of the inner surface of integrating sphere used in the
`measurements was 314.16 cm2, whereas the area of any tissue
`sample did not exceed 5.0 cm2. Figure 1 shows geometry
`and parameters of the measurements in the transmittance and
`reflectance modes, respectively.
`Calculation of tissue optical properties was performed
`for each wavelength point. The algorithm consists of the
`following steps: (a) estimation of a set of optical properties;
`(b) calculation of the reflectance and transmittance with
`the adding–doubling iterative method;
`(c) comparison of
`the calculated with the measured values of the reflectance and
`the transmittance; (d) iteration of the above steps until a match
`(within the specified acceptance margin) is reached. With
`this iterative process the set of optical properties that yields
`the closest match to the measured values of reflectance and
`transmittance are taken as the optical properties of the tissue.
`For estimation of the mean size of scatterers of the
`investigated tissues, the spectroturbidimetric method described
`in [69] has been used. This method is based on approximation
`of the scattering coefficient µs of turbid media by a power law
`µs = aλ
`−w, where parameter a is defined by the concentration
`of particles in the media. The wavelength exponent w is
`independent of the particle concentration and characterizes the
`
`(cid:1)s
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`properties of the mucous membrane of the maxillary sinuses
`were measured for samples, which were obtained from patients
`with chronic maxillary sinusitis during planned surgery. All
`tissue samples were kept in saline at room temperature of
`about 20˚C until spectroscopic measurements were carried out.
`The skin tissue samples were measured one day after autopsy.
`The adipose tissue samples were measured during 3–4 h after
`biopsy, and the mucous tissue samples were measured during
`2–3 h after biopsy. All the tissue samples were cut into pieces
`each with an area of about 20 × 20 mm2. For mechanical
`support, the tissue samples were sandwiched between two
`glass slides. Since compression of tissue causes an increase
`in the tissue absorption and scattering coefficients [38], in
`the measurements of the tissue the samples were sandwiched
`without (or with minimal) compression. In order to provide
`optical contact between the sample and the glass slides and to
`prevent the sample compression, the distance between the glass
`slides was regulated by a special plastic bush, whose thickness
`varied according to the samples thickness. The thickness of
`each tissue sample was measured with a micrometer in several
`points over the sample surface and averaged. Precision of the
`single measurement was ±50 µm.
`The total transmittance and diffuse reflectance measure-
`ments have been performed in the 400–2000 nm wavelength
`range using the commercially available CARY-2415 (‘Varian’,
`Australia) spectrophotometer with an integrating sphere. The
`inner diameter of the sphere is 100 mm, the size of the entrance
`port is 20 × 20 mm and the diameter of the exit port is 16 mm.
`As a light source, a halogen lamp with filtering of the radia-
`tion in the studied spectral range has been used in the mea-
`surements. The diameter of incident light beam on the tissue
`−1.
`sample is 3 mm. The scan rate is 2 nm s
`For processing the experimental data and determination of
`the optical properties of the tissue, the inverse adding–doubling
`(IAD) method developed by Prahl et al [55] has been used.
`The method is widely used in tissue optics for processing
`the experimental data of spectrophotometry with integrating
`spheres [41, 56–60]. This method allows one to determine
`the absorption (µa) and the reduced scattering coefficients
`= µs(1 − g)) of a tissue from the measured values of
`(µ
`the total transmittance and the diffuse reflectance. Here µs
`is the scattering coefficient and g is the anisotropy factor of
`scattering. In these calculations the anisotropy factor has been
`fixed at 0.9, since this value is typical for many tissues in the
`visible and NIR spectral ranges [17]. The main advantage of
`the IAD method, when compared with many other methods
`of solution of the radiative transfer equation, is related to
`its validation for the arbitrary ratio of the absorption and
`scattering coefficients [55]. The property of the IAD method
`becomes very important in the case of determination of the
`optical properties of tissues within strong absorption bands,
`when the values of the absorption and scattering coefficients
`become comparable. Other methods, such as the diffusion
`approximation [61–63] or the Kubelka–Munk method [64–66],
`require, for their applicability, a fulfilment of the condition
`µa/µs (cid:2) 1.
`The inverse Monte Carlo technique [67]
`can also be used for the arbitrary ratio of µa and µs, but
`requires very extensive calculations. The main limitation
`of the IAD method is that there may be a possible loss of
`scattering radiation through the lateral sides of a sample, at
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`λ is the wavelength, d the diameter of the particles and N the
`number of scattering particles in the unit of volume.
`In the case of spectrophotometric measurements with
`integrating sphere technique, measured parameter is the
`reduced scattering coefficient and wavelength dependence of
`the reduced scattering coefficient can be approximated in
`accordance with a power law [69–72]
`
`(λ) = aλ−w.
`
`(cid:1)s
`
`µ
`
`(2)
`
`On the other hand, the reduced scattering coefficient can
`be calculated for monodisperse system of spherical particles
`(x, m) = N (π d 2/4)Q
`(cid:1)
`with the formula µ
`(x, m), where
`(x, m) = Q(x, m)(1 − g).
`(cid:1)
`Q
`In this case equation (1) can be rewritten in the form
`(cid:1)
`w(x, m) = ∂ ln Q
`(x, m)
`∂ ln x
`
`.
`
`(3)
`
`(cid:1)s
`
`In this study, calculation of the scattering efficiency
`factor Q(x, m) and anisotropy factor g has been performed in
`accordance with the Mie scattering model, using the algorithm
`presented by Bohren and Huffman [73].
`The mean diameter of the scattering particles has been
`obtained by minimization of the target function
`F (x) = (w(x, m) − wexp)2
`(4)
`with the boundary condition 0.7 (cid:1) g (cid:1) 0.95. Here w(x, m) is
`the wavelength exponent calculated with equation (3) and wexp
`is the experimentally measured wavelength exponent value
`from equation (2). When parameter x was estimated then the
`mean diameter of the scattering particles was calculated from
`the relation d = xλ/(π nI). In this calculation the refractive
`indices ns and nI for corresponding wavelengths have been
`obtained from literature.
`the Levenberg–
`function,
`To minimize the target
`Marquardt nonlinear least-squares-fitting algorithm, described
`in detail by Press et al [74], has been used. Iteration procedure
`is repeated until the experimental and the calculated data are
`matched. As a termination condition of the iteration process,
`we have used the expression |w(x, m) − wexp|/wexp (cid:1) 0.01.
`
`4. Results and discussion
`
`4.1. Skin optical properties
`
`skin samples obtained from post-mortem
`Twenty-one
`examinations were used for the in vitro measurements.
`Figures 2(a) and (b) and 3(a) and (b) show the measured
`optical properties of the human skin samples calculated by
`the IAD method on the basis of measured values of the
`total transmittance and the diffuse reflectance. Figure 2(a)
`presents the wavelength dependence of the skin absorption
`coefficient. The vertical lines correspond to the values of
`standard deviation (SD), which is determined by SD =
`(cid:1)(cid:2)
`=1( ¯µa − µai )2/n(n − 1), where n = 21 is the number of
`the measured tissue samples, µai is the absorption coefficient
`of each sample and ¯µa is the mean value of the absorption
`(cid:2)
`coefficient for each wavelength, which is calculated as
`=1 µai /n.
`In the visible spectral range of the spectrum,
`
`N i
`
`N i
`
`A N Bashkatov et al
`
`(a)
`
`(b)
`
`Figure 1. The geometry of the measurements in (a) transmittance
`mode (b) reflectance mode. 1—the incident beam (diameter 3 mm);
`2—the glass slides; 3—the tissue sample; 4—the entrance port
`(square 20 × 20 mm); 5—the transmitted (or diffuse reflected)
`radiation; 6—the integrating sphere (inner diameter is 100 mm);
`7—the exit port (diameter 16 mm). LPD—the maximal value of
`lateral light propagation distance (0.7 mm for skin, 1.25 mm for
`subcutaneous adipose tissue and 2.2 mm for mucous tissue under
`study).
`
`mean size of the particles and defines the spectral behaviour of
`the scattering coefficient [69]. Both the parameter a and the
`wavelength exponent w are defined by the ratio of refractive
`indices of the scatterers and environment medium [69].
`In experiments, w is expressed in terms of the scattering
`coefficients measured in a small enough spectral interval
`(about 200 nm) by the relationship w = −∂ ln µs/∂ ln λ. The
`substitution in the relationship of a theoretical expression
`for µs obtained for some disperse system models results
`in equations for determination of either the particle size or
`the particle refractive index [69].
`In the first case,
`the
`particle refractive index has to be determined beforehand
`in independent experiments or has to be obtained from the
`literature. As a first approximation, w can be calibrated by the
`formula
`w(x, m) = ∂ ln Q(x, m)
`∂ ln x
`with the scattering efficiency factor Q(x, m) calculated
`for monodisperse system of homogeneous spherical (or
`cylindrical) isotropic particles. Note that
`the scattering
`coefficient µs
`can be connected with the scattering
`efficiency factor Q(x, m) by the relationship µs(x, m) =
`N (π d 2/4)Q(x, m). Here m = ns/nI is the relative refractive
`index of the scattering particles, i.e. the ratio of the refractive
`indices of the scatterers (ns) and the ground materials
`(i.e. interstitial fluid) (nI) and x is the dimensionless relative
`size of scatterers, which is determined as x = π dnI/λ, where
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`(a)
`
`4.5
`
`410 nm
`
`Optical properties of human tissues
`
`540 nm
`
`575 nm
`
`1710 nm
`1925 nm
`1780 nm
`
`1430 nm
`
`1200 nm
`970 nm
`
`500
`
`750
`
`1500
`1250
`1000
`Wavelength, nm
`
`1750
`
`2000
`
`3.0
`
`1.5
`
`0.0
`
`Absorption coefficient, 1/cm
`
`(b)
`
`25
`
`20
`
`15
`
`10
`
`5
`
`0
`
`Absorption coefficient, 1/cm
`
`500
`
`750
`
`1500
`1250
`1000
`Wavelength, nm
`
`1750
`
`2000
`
`Figure 2. The wavelength dependence of the absorption coefficient µa of human skin in vitro. (a) The vertical lines show the SD values;
`(b) the solid line corresponds to the averaged experimental data and the vertical lines show the SD values. The symbols correspond to the
`experimental data presented in [37–41]. The squares correspond to the data of [37], the open circles correspond to the data of [38], the up
`triangles correspond to the data of [39], the open up triangles correspond to the data of [40] and the diamonds correspond to the data of [41].
`
`the absorption bands of oxyhaemoglobin with maximums at
`410, 540 and 575 nm are observed [75]. Absorption of water
`in this spectral range is negligible [76]. In the NIR spectral
`range, the main chromophores are the water of skin dermis and
`the lipids of epidermis. In this spectral range the absorption
`bands of water with maximums at 970 nm [77], 1430 and
`1925 nm [78, 79] and lipids with maximums at 1710 and
`1780 nm [80] are well seen. At the same time, low-intensity
`lipid absorption band with the maximum at 930 nm [77]
`are not observed. Absorption band with the maximum at
`1200 nm is the combination of the absorption bands of water
`(with the maximum at 1197 nm [78, 79]) and lipids (with
`the maximum at 1212 nm [81]).
`Increasing the SD in the
`range of the absorption bands is connected to the differences
`
`in the blood and water content in respect of different skin
`samples. Figure 2(b) shows skin absorption coefficient values
`obtained in this paper (solid line) and those presented by other
`authors [37–41] (symbols). Comparison of the data obtained in
`this study and those presented by Simpson et al [39] shows an
`agreement between them. Simpson et al [39] reported that in
`the spectral range 620–1000 nm, skin absorption coefficient
`is 0.13 ± 0.12 cm
`−1.
`In this spectral range, we obtained
`µa ≈ 0.37 ± 0.12 cm
`−1. Our data are also close to the
`data of Du et al [40] (µa ≈ 0.5 ± 0.1 cm
`−1) in the spectral
`range 900–1100 nm. On the other hand, in this spectral range,
`Chan et al [38] obtained µa ≈ 2.1 ± 0.5 cm
`−1. Prahl [37], in
`the spectral range 620–800 nm obtained, µa ≈ 1.8±0.4 cm
`−1.
`Figure 2(b) shows that Chan et al [38] (in the spectral range
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`500
`
`750
`
`1500
`1250
`1000
`Wavelength, nm
`
`1750
`
`2000
`
`µ's (Mie + Rayleigh) = 1.1*1012 λ -4 + 73.7 λ -0.22
`
`µ's (Mie) = 73.7 λ -0.22
`
`µ's(Rayleigh) = 1.1*1012 λ -4
`
`(a)
`
`120
`
`100
`
`80
`
`60
`
`40
`
`20
`
`0
`
`Reduced scattering coefficient, 1/cm
`
`(b)
`
`90
`
`75
`
`60
`
`45
`
`30
`
`15
`
`Reduced scattering coefficient, 1/cm
`
`A N Bashkatov et al
`
`0
`250
`
`500
`
`750
`
`1500
`1250
`1000
`Wavelength, nm
`
`1750
`
`2000
`
`2250
`
`(cid:1)s
`
`Figure 3. (a) The spectral dependence of reduced scattering coefficient µ
`of human skin in vitro. The solid line corresponds to the
`averaged experimental data and the vertical lines show the SD values. The symbols correspond to the experimental data presented
`in [37–41]. The squares correspond to the data of [37], the open circles correspond to the data of [38], the up triangles correspond to the data
`of [39], the open up triangles correspond to the data of [40] and the diamonds correspond to the data of [41]; (b) the spectral dependence of
`reduced scattering coefficient µ
`of human skin in vitro and its approximation by power law. The symbols correspond to the averaged
`experimental data and the vertical lines show the SD values. The bold and dashed lines show the contribution of the Mie and Rayleigh
`scattering in the total reduced scattering spectrum, respectively. The solid line shows the combination of the Mie and Rayleigh scattering.
`
`(cid:1)s
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`400–600 nm) and Prahl [37] (in the spectral range 450–600 nm)
`demonstrated the absorption coefficient values, which are
`larger (up to 2–4 folds) than those presented in this paper.
`In the spectral range 1200–2000 nm, we obtained absorption
`coefficient values, which are significantly smaller than those
`obtained by Chan et al
`[38], Du et al
`[40] and Troy and
`Thennadil [41], especially in the range of the water absorption
`band with the maximum at 1450 nm. It is possible that such
`big discrepancies are related to differences in the water content
`in respect of different skin samples. At the same time, we have
`not completely excluded the lateral light loss in the sample that
`may lead to the overestimation of the absorption coefficient.
`
`Figure 3 presents spectral dependence of the scattering
`properties (shown as reduced scattering coefficient) of
`human skin tissue.
`The dependence was obtained by
`averaging the scattering spectra measured for the 21 skin
`samples. The vertical lines show SD values of the reduced
`scattering coefficients of the skin tissue obtained during
`the measurements.
`Figure 3(a) shows that
`the reduced
`scattering coefficients decreased with an increase in the
`wavelength, which, in general, corresponds to the common
`nature of spectral behaviour of the scattering characteristics
`of tissues [17, 70–72]. However,
`in the spectral range
`400–800 nm the reduced scattering coefficient decreased
`abruptly with an increase in the wavelength,
`in contrast
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`2548
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`Petitioner Apple Inc. – Ex. 1034, p. 2548
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`Optical properties of human tissues
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`0.7
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`0.6
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`0.5
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`0.4
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`0.3
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`0.2
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`0.1
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`Rayleigh fraction of total reduced scattering
`
`500
`
`750
`
`1500
`1250
`1000
`Wavelength, nm
`
`1750
`
`2000
`
`Figure 4. Fraction of total reduced scattering attributed to Rayleigh
`scattering. The fraction was calculated with data presented in
`figure 3(b) as described in section 4.1.
`
`scattering coefficient in the IR spectral range. However, in
`the spectral range 400–600 nm, the wavelength dependence of
`the reduced scattering coefficient could not be described by the
`power law with w = 0.22. In this spectral range the reduced
`scattering coefficient decreased sharply and the effect of the
`decrease in the reduced scattering coefficient can be explained
`by the contribution of small, so-called Rayleigh scatterers, i.e.
`the collagen and elastin fibrils [89,90]. The Rayleigh scattering
`(Rayleigh) = bλ
`−4, where the factor
`can be represented as µ
`b varies only with the magnitude of the Rayleigh scattering.
`The measured reduced scattering coefficient spectrum, which
`is a combination of the Mie and Rayleigh scattering spectra,
`has been fitted by:
`(measured) = µ
`(Mie) + µ
`= 73.7λ
`−0.22 + bλ
`−4
`(5)
`and the factor b has been estimated from the fitting as 1.1 ×
`1012. From figure 3(b) it is seen that the combination of
`the wavelength dependences of the Rayleigh and the Mie
`scattering describes the measured wavelength dependence of
`the reduced scattering coefficient very well.
`The fraction fRayleigh of the total reduced scattering that is
`due to Rayleigh scattering by collagen fibrils can be calculated
`as fRayleigh = (1.1 × 1012λ
`−4)/(1.1 × 1012λ
`−4 + 73.7λ
`−0.22).
`The result of the calculations is presented in figure 4. From the
`figure it is seen that in the visible spectral range the Rayleigh
`scattering is dominant, but with the increase of the wavelength
`the contribution of the Rayleigh scattering is decreased sharply
`and in the NIR the contribution is insignificant. For the
`wavelength of 633 nm, Saidi et al
`[89] and Graaff et al
`[90] have reported fRayleigh = 0.1 for skin dermis. For this
`wavelength we have obtained fRayleigh = 0.2, but for the
`whole skin. The larger value indicates that for the whole
`skin, in the visible spectral range, the contribution of small
`scatterers of skin epidermis such as melanin dust and structural
`cell component is significant. It should be noted that the full
`description of skin scattering implies taking into account light
`scattering by medium-size scatterers, the so-called Rayleigh–
`Gans scatterers, such as melanocytes, which are about 300 nm
`in size. Accounting the contribution of the Rayleigh and
`
`(Rayleigh)
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`(cid:1)s
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`(cid:1)s
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`(cid:1)s
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`µ
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`(cid:1)s
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`to its spectral behaviour in the spectral range from 800 to
`2000 nm, where the reduced scattering coefficient decreased
`very smoothly as wavelength increased. A comparison of the
`obtained data (solid line) with the data presented by Chan et al
`[38], Simpson et al
`[39] and Troy and Thennadil [41]
`(symbols) shows a good agreement between them. At the same
`time, Prahl [37] and Du et al [40] reported values of the reduced
`scattering coefficient, which are larger than those presented
`in this paper. The discrepancies are a result of the natural
`dissipation of tissue properties and the tissue preparation and
`storage methods.
`In the spectral range 600–1500 nm, for many tissues, the
`reduced scattering coefficient decreases with the wavelength
`(λ) = aλ
`−w [69–72]. The
`in accordance with a power law µ
`wavelength exponent w characterizes the mean size of the
`tissue scatterers and defines spectral behaviour of the reduced
`scattering coefficient. Figure 3(b) shows approximation of the
`wavelength dependence of the reduced scattering coefficient
`
`(λ) = 73.7λ−0.22, where λ is wavelength,
`by the power law µ
`in nanometres.
`In the figure it is seen that in the spectral
`range from 600 t