### 要約

As visible and infrared waves penetrate human skin, absorption and scattering in the skin layers occurs. The penetration depth of the waves depends on the wavelength and properties of each skin layer. Formulas are presented for generating the absorption and scattering properties as a function of wavelength for each layer of the skin. These properties can then be modeled to determine penetration depth of various wavelengths into human skin. By understanding penetration depth as a function of wavelength, the optimal wavelength can be selected for specific biosensor applications.

### Introduction

Knowledge of the behavior of light as it impinges upon and travels through the skin is crucial for optimizing optical biosensors because it allows for accurate simulation of penetration depth as a function of wavelength. This application note reviews the absorption and reduced scattering coefficients of human skin layers as a function of wavelength. Using these coefficients, penetration depth as a function of wavelength can be simulated and the optimal light source wavelength can be chosen for a given biosensor application.

### Simulating Light Transport Through the Skin

Skin
consists of three main layers from the surface: the blood-free epidermis layer (100µm
thick), vascularized dermis layer (1mm to 2mm thick), and subcutaneous adipose
tissue (from 1mm to 6mm thick, depending on the body site). Typically, the
optical properties of these layers are characterized by absorption μ_{a}
and scattering μ_{s} coefficients and the anisotropy factor *g*. The
absorption coefficient characterizes the average number of absorption events
per unit path length of photons travelling in the tissue. The main absorbers in
the visible spectral range are the blood, hemoglobin, β-carotene,
and bilirubin. In the IR spectral range, absorption properties of skin dermis
are dominated by absorption of water. The scattering coefficient characterizes the
average number of scattering events per unit path length of photons travelling
in the tissue, and the anisotropy factor *g*represents the average cosine
of the scattering angles.

In the following sections, we outline the biological characteristics of each layer and how they affect the propagation and absorption of light.

### Skin Structure and Optical Model

The
first and outermost section of human skin is the epidermis. The epidermis can
be subdivided into two sublayers: nonliving and living epidermis. Nonliving
epidermis or stratum corneum (about 20μm thick) is composed mainly of dead cells,
which are highly keratinized with high lipid and protein content. It also has a
relatively low water content^{1}. Light absorption in this tissue is
low and relatively uniform in the visible region.

The
living epidermis (100μm thick) propagates and absorbs light. The absorption
properties are mainly determined by a natural chromophore, melanin^{2}.
There are two types of melanin: a red/yellow pheomelanin and a brown/black
eumelanin, which is associated with skin pigmentation. The melanin absorption
level depends on how many melanosomes per unit volume are present. Typically,
the volume fraction of the epidermis occupied by melanosomes varies from 1%
(lightly pigmented specimens) to 40% (darkly pigmented specimens). The scattering
properties of melanin particles are dependent on particle size and can be
predicted by the Mie theory.

The
dermis is a 0.6mm to 3mm*
*thick structure composed
of dense, irregular connective tissue containing nerves and blood vessels. The
dermis can be divided into two layers based on the size of the blood vessels^{3}.
Smaller vessels lie closer to the skin surface in the papillary dermis while
larger blood vessels populate the deeper reticular dermis. Absorption in the
dermis is defined by the absorption of hemoglobin, water, and lipids. Since
oxyhemoglobin and deoxyhemoglobin have different absorption profiles, the
oxygen saturation must be known. For an adult, the
arterial oxygen saturation is generally above 95%^{4}. Typical venous
oxygen saturation is 60% to 70%^{5}.

The scattering properties of the dermal layers are mainly defined by the fibrous structure of the tissue. Light can scatter on interlaced collagen fibrils and bundles as well as single collagen fibrils. Since the dermal layer is relatively thick compared to the epidermis, the average scattering properties of the skin are dominated by dermal scattering.

The subcutaneous adipose tissue is formed by a collection of fat
cells containing stored fat (lipids). Its
thickness varies considerably throughout the body: from nonexistent in the
eyelids to up to 3cm thick in the abdomen. Absorption
of the human adipose tissue is defined by absorption of hemoglobin, lipids and
water. The main scatterers of adipose tissue are spherical droplets of lipids,
which are uniformly distributed within the fat cells. The diameters of the
adipocytes are in the range 15μm
to 250μm^{6} and their mean diameter
ranges from 50μm to 120μm^{7}. In the spaces
between the cells there are blood capillaries, nerves, and reticular fibrils
connecting each cell and providing metabolic activity to the fat tissue.

In this application note, we present a planar five-layer optical model of human skin (see Figure 1) based on the stratified skin layers outlined above. The layers included in the model are the stratum corneum, the living epidermis, the two layers of dermis (papillary and reticular), and the subcutaneous adipose tissue layer. Thickness of the layers as well as typical ranges of blood, water, lipids, and melanin contents, and refractive indices of the layers and mean vessel diameters are presented in Table 1.

Skin layers | Thickness (mm) | Refractive index | Volume fraction of (%) | Scattering coefficient at 577nm (bloodless) (cm-1) | Mean vessel diameter (µm) | |||

Melanosomes | Blood | Water | Lipids | |||||

Stratum Corneum | 0.01 | 1.55 | 0.00 | 0.00 | 35.00 | 20.00 | 300 | 0 |

Epidermis | 0.1 | 1.44 | 1-10 | 0.00 | 60.00 | 15.10 | 300 | 0 |

Papillary Dermis | 0.2 | 1.39 | 0.00 | 0.2-4 | 50.00 | 17.33 | 120 | 6 |

Reticular Dermis | 1.8 | 1.41 | 0.00 | 0.2-5 | 70.00 | 17.33 | 120 | 15 |

Subcutaneous Adipose Tissue | 3 | 1.44 | 0.00 | 5.00 | 5.00 | 75-95 | 130 | 75 |

### Absorption

In
the visible and NIR spectral ranges, the absorption coefficient of each layer
includes contributions from eumelanin,
pheomelanin, oxyhemoglobin, deoxyhemoglobin, bilirubin, ß-carotene, lipids, and
water. The spectral extinction coefficients for these pigments, denoted by ^{∈}eu(λ),^{∈}ph(λ),^{∈}ohb(λ),^{∈}dhb(λ),^{∈}bil(λ), and ^{∈}β(λ),
respectively, are given from the curves shown in Figure 2. The total absorption
coefficient for the ^{k}th layer is given by:

μa_{k}(a_{k,eu}(λ))ϑ_{k,mel}+(a_{k,ohb}(λ)+a_{k,dhb}(λ)+a_{k,bil}(λ))ϑ_{k,blood}

+ (a_{k,eu}(λ))ϑ_{k,water} + (a_{k,lip}(λ))ϑ_{k,lip}

+ (a_{base}(λ) + a_{k, β}(λ) )(1 - ϑ_{k,mel} - ϑ_{k,blood} - ϑ_{k,water} - ϑ _{k,lip})

where *k* = 1,…,5 is the layer number, ϑ_{k,mel},
ϑ_{k,blood}, ϑ_{k,water}, and ϑ_{k,lip}
are the volume fractions of melanin, blood, water, and
lipids in the *k*^{th }layer, and *a*_{k,eu}(λ), *a*_{k,ph}(λ), *a*_{k,ohb}(λ), *a*_{k,dhb}(λ), *a*_{k,bil}(λ),*a*_{k,water}(λ), *a*_{k,lip}(λ) and *a*_{k,β}(λ) are the absorption coefficients of eumelanin, pheomelanin, oxyhemoglobin,
deoxyhemoglobin, bilirubin, water, lipids, and β-carotene respectively. *a*_{base,β}(λ) is the wavelength dependent background
tissue absorption coefficient and is given by 7.84*e*8 × λ ^{-3.255} cm^{-1}.

The eumelanin and pheomelanin absorption coefficients are given by:

*a _{k.eu}*(λ) =

*∈*

_{eu}(λ)

*c*

_{k,eu}, and

*a*(λ) =

_{k,ph}*∈*

_{ph}(λ)c

_{k,ph}

where:

c_{k,eu} = eumelanin concentration (g/L) in the *k*^{th }layer

c_{k,ph} = pheomelanin concentration
(g/L) in the *k*^{th }layer

The oxyhemoglobin and deoxy hemoglobin absorption coefficients are given by:

*a _{k.ohb}*(λ) =

*c*γ , and

_{k,hb}**a*(λ) c

_{k,dhb}_{k,hb}* (1 - γ)

where:

66500 = molecular weight of hemoglobin (g/mol)

c_{k,hb} = hemoglobin
concentration of the blood (g/L) in the ^{k}th layer

γ = ratio of oxyhemoglobin to the total hemoglobin concentration.

The absorption coefficient of bilirubin is given by:

a_{k,bil}(λ) = c_{k,bil}

where:

585 = molecular weight of bilirubin (g/mol)

c_{k,bil} = bilirubin concentration (g/L) in the ^{k}th layer

The
β-carotene absorption coefficient *a _{k,β}*(λ) is given by:

*a _{k,β}*(λ) =

*c*

_{k,β}where:

537 = molecular weight of β-carotene (g/mol)

c_{k,β} = β-carotene concentration (g/L) in the ^{k}th layer

The absorption coefficient of water is given by:

*a*_{k,water}(λ) = *∈*_{water}(λ)*c*_{k,water3}

where:

*c*_{k,water} = water concentration (g/L) in the *k*th^{ }layer.

The lipid absorption coefficient is given by:

*a*_{k,lip}(λ) = *∈*_{water}(λ)*c*_{k,lip3}

where:

*c*_{k,lip} = lipid concentration (g/L) in the *k*th^{ }layer.

*a*_{k,lip}(λ) = *∈*_{water}(λ)*c*_{k,lip3}

### Scattering

The
total scattering coefficient for the ^{k}th layer can be defined as:

*μs(λ) = ϑ _{k,blood}C_{k}μs_{blood}(λ)+(1-ϑ_{k,blood})μsT_{k}(λ).*

where *C _{k}* is
a correction factor dependent on the mean vessel diameter and the blood scattering
coefficient as a function of wavelength and

*μsT*is the total scattering coefficient of the bloodless tissue layer.

_{k}The
following relations can be used for *C _{k}*

^{8}:

*C _{k}* =

where *d _{k,vessels}*is the blood vessels diameter (cm) in the

^{k}th

^{ }layer. In the case of collimated illumination of the vessels the coefficients

*a*and

*b*have values

*a*= 1.007 and

*b*= 1.228. In the case of diffuse illumination of the vessels the coefficients

*a*and

*b*have values

*a*= 1.482 and

*b*= 1.151.

The
total scattering coefficient of the bloodless tissue is given by^{9}:

*μsT _{k}(λ) = μs0_{k}*,

where *μs*0_{k} are the scattering coefficients at the
reference wavelength 577nm listed in Table 1. Note: *μs*T_{k}, falls monotonically with the increase
in the wavelength.

The
expression for the anisotropy of scattering may be constructed to include the
contribution from blood^{9}:

*g _{k}* (λ) = ,

where *g _{k}* (λ) is
the anisotropy factor of the bloodless tissue and

*gT _{k}* (λ) = 0.7645 + 0.2355 [1 - exp].

Finally,
the reduced scattering coefficients is defined as *μs' _{k}(λ) = μs_{k}(λ)(1 - g_{k}*(

*λ*)).

### H2Optical Model and Computer Simulations

To determine penetration depth as a function of wavelength, Zemax OpticStudio^{®}
software was utilized. The software uses a Monte Carlo (MC) method to trace optical
rays propagating in complex inhomogeneous, randomly scattering and absorbing
media. Basic MC modeling of
an individual photon packets trajectory consists of the sequence of the
elementary simulations: photon path length generation, scattering and
absorption events, reflection and/or refraction on the medium boundaries. The
specular reflection from the air-tissue surface is also considered in the
simulations. At the scattering site, a new photon packet direction is
determined according to the Henyey-Greenstein scattering phase function:

*f _{HG}(Θ)* =

where *Θ* is the polar scattering angle. The distribution over the azimuthal scattering angle was assumed as uniform. MC technique requires values of absorption and scattering coefficients and anisotropy factor of each skin layer, its thickness and refractive index. Additionally, the mean path defined as the inverse of the scattering coefficient is required.

### Results and Discussion

Using optical properties presented above, Henyey-Greenstein scattering phase function, and Zemax OpticStudio, we can simulate any biosensor configuration and determine the maximum penetration depth as a function of wavelength. For example, we have taken the following typical LED-PD biosensor configuration (Table 2 and Figure 3) and skin properties shown in Table 3, and simulated the maximum penetration depth as a function of wavelength.

Configuration property | Value | Unit |

Distance between LED and PD | 3.5 | mm |

PD size | 0.4 x 0.4 | mm x mm |

LED radiation pattern | Lambertian | - |

LED divergence angle FWHM | 60 | degrees |

LED size | 340 x 340 | µm x m |

LED/PD top to Stratum Corneum spacing | 0.5 | mm |

Skin layers | Volume fraction of (%) | Concentration of (g/L) | |||||||

Melanosomes | Blood | Water | Lipids | Beta carotene | Eumelanin | Pheomelanin | Bilirubin | Hemoglobin in blood | |

Stratum Corneum | 0.00 | 0.00 | 35.00 | 20.00 | 2.10E–04 | 0 | 0 | 0 | 0 |

Epidermis | 1-10 | 0.00 | 60.00 | 15.10 | 2.10E–04 | 80 | 12 | 0 | 0 |

Papillary Dermis | 0.00 | 0.2-4 | 50.00 | 17.33 | 7.00E–05 | 0 | 0 | 0.05 | 150 |

Reticular Dermis | 0.00 | 0.2-5 | 70.00 | 17.33 | 7.00E–05 | 0 | 0 | 0.05 | 150 |

Subcutaneous Adipose Tissue | 0.00 | 5.00 | 5.00 | 75-95 | 0 | 0 | 0 | 0.05 | 150 |

The absorption coefficients of the skin layers have been calculated in accordance with the presented optical model and are shown in Figure 4.

The scattering coefficient, anisotropy factor, and mean path of the skin layers have been calculated in accordance with the presented model, and the result presented in Figure 5, Figure 6, and Figure 7.

The penetration depth of light into a biological tissue is an important parameter used to determine the performance of a biosensor. Penetration depth is the distance into the skin that the light has traveled. Simulation of the optical penetration depth has been performed with the absorption and reduced scattering coefficient values presented above. Simulation results are shown in Figure 8.

### Conclusion

In this article, we have modeled human skin tissue with a five-layer structure where each layer represents its corresponding anatomical layer. To simulate light tissue interaction, the biological characteristics of each layer is moded with three wavelength-dependent numbers, absorption coefficient, scattering coefficient, and anisotropy factor. Then, we have used a commercial ray tracing software to calculate penetration depth of light into skin tissue for simulating the performance of optical biosensor architectures.