# THz Sensing of Human Skin: A Review of Skin Modeling Approaches

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Terahertz Radiation and Systems

^{12}Hz), corresponding to wavelengths ranging from 30 μm to 3 mm. The rapid development of THz technology in the last three decades has promoted numerous applications in communication, security, biosensing, aerospace etc. Among them, biomedicine has long been considered a promising application area [1]. One important reason is the non-ionizing and non-invasive nature of THz radiation, making it a safe modality for biomedical in vivo imaging. Another key factor comes from the high absorption of water, which despite limiting the depth of penetration, provides high sensitivity to the water content in living tissues. Given these characteristics, THz in vivo studies have been mainly focused on skin, as THz waves can penetrate through the superficial layer, and the measured THz response is sensitive to its water concentration and tissue structure.

#### 1.2. Biomedical Applications of THz Imaging

#### 1.3. Variables Affecting In Vivo THz Measurements of Skin

#### 1.4. Aim of this Review

## 2. New Advances of THz Measurement and Modeling of Skin

#### 2.1. Dielectric Model

#### 2.1.1. Double Debye Model

#### 2.1.2. Effective Medium Theory

#### 2.2. Structural Models for THz Waves

#### 2.2.1. Single Layer Model

_{q}(θ

_{q}), $\tilde{n}$

_{a}(θ

_{a}), $\tilde{n}$

_{s}(θ

_{s}), are the complex refractive indices (incident angles) of quartz, air and skin, respectively. In this case, the analytical solution of the complex refractive index of skin can be expressed as:

#### 2.2.2. Two-Layer Model

_{qs}, r

_{se}are the reflection coefficients of the quartz-SC and SC-epidermis interfaces calculated by Equations (10) and (11). β is given by Equation (12). Note that $\tilde{n}$

_{q}, $\tilde{n}$

_{s}, $\tilde{n}$

_{e}and θ

_{q}, θ

_{s}, θ

_{e}are the complex refractive index and incident angle in quartz, SC and epidermis respectively and d

_{s}is the thickness of the SC. The incident angle in each layer θ is related to the complex refractive indices of each layer by Snell’s law given in Equation (13). Divided by the reflection from the quartz-air interface shown in Equation (14), the complex reflection ratio is obtained as illustrated by Equation (15) as a function of water content (${p}_{i})$ in each layer and SC thickness(d

_{s}) which is then fitted to the measured data in the frequency domain.

#### 2.2.3. Model with Depth-Dependent Water Concentration

- Stratified media model:

_{1}) and epidermis (d

_{2}), and the hydration level at the SC surface (H

_{0}), SC-epidermis boundary (H

_{1}) and epidermis-dermis boundary (H

_{2}). There is no direct equation to describe the light-skin interaction which has a linear depth-dependent water concentration. Instead, it is separated into multiple discrete layers to approximate the continuous water changes as shown by the red curve in Figure 6. With the number of slabs increasing, the accuracy increases as well as the computational complexity. However, considering that the wavelength is of the order of hundreds of micrometers, a slab thickness of 1 μm is sufficient to represent the water variation that can be sensed by the THz waves. A larger slab thickness can be used if the water-variation slope is flat, such as that in the epidermis. Given that the penetration depth is usually less than 100 μm, only a few tens of layers are needed in total, thus the computation time is usually considerably short. The permittivity of each layer (${\epsilon}_{m}$) is determined by water concentration (${p}_{i}$) with the Bruggeman EMT, which can be expressed as Equation (16).

_{m}) and the reflection coefficient Γ

_{m}in layer m by Equations (17) and (18), where the longitudinal propagation constant (k

_{m}) and characteristic impedance (ζ

_{m}) are related to the permittivity $({\epsilon}_{m})$ and permeability $({\mu}_{m})$ of each layer by Equations (19) and (20). Details can be found in reference [51]. The thickness and depth at the corresponding layer are given by t

_{m}and z

_{m}respectively. Therefore, the water gradient inside the skin, eventually represented by H

_{0}, H

_{1}, H

_{2}and d

_{1}, d

_{2}, determines the reflection coefficient at the skin surface. In addition, this work employed a non-contact measurement and Rayleigh scattering due to the roughness of the skin surface is calibrated. By fitting to the measured reflection, the water gradient can be calculated. To better illustrate the process of calculating the refection coefficient, Figure 7 shows the flowchart of the procedure.

^{2}to 3.5 N/cm

^{2}in a reflection geometry with pressure sensors to give real-time feedback. A quartz window was employed to flatten the skin. The reflected THz signal and skin optical properties changed under different pressures. Instead of using a constant value for the refractive index of dehydrated skin in the EMT model, they treated the refractive index of dehydrated skin as another fitting parameter. After fitting the data measured under different pressures with the stratified media model, the water profiles and the refractive index of dehydrated skin are extracted as shown by Figure 8. It is found that increasing the applied pressure leads to an increase in the hydration level of the SC surface as shown by Figure 8a. It also shows that the SC thickness decreased slightly with increased pressures, which is shown by the red curve in Figure 8b. As a result of the increased hydration level, the increase in the contact pressure also leads to an increase in the refractive index of dehydrated skin, as shown in Figure 8b. This can be explained by the fact that, at low contact pressures, there is the inevitable subtle air gap between the quartz window and skin due to the texture of skin.

_{S0}($\mathrm{g}/\mathrm{c}{\mathrm{m}}^{3}$) and W

_{B0}($\mathrm{g}/\mathrm{c}{\mathrm{m}}^{3}$) are the initial water concentrations at the surface and bottom of the SC respectively. L

_{0}is the initial SC thickness. They can be found by fitting to the measured data when skin is first put onto the quartz window. At the occluded state, the water flux on the surface of the skin decreases to zero while the water concentration at the SC-epidermis boundary (z = 0) remains unchanged. This leads to the second boundary conditions in Equation (24). With the convection velocity (u) equal to the swelling velocity of the SC, the third boundary condition can be given by Equation (25). The finite difference method [59] was employed to calculate the numerical solution of Equations (21)–(25). Details of the fitting and procedure diagram can be found in reference [27].

^{3}to 0.55 g/cm

^{3}and SC swells by approximately 7.6 μm. However, the hydration and thickness of the SC increase most dramatically at the onset of occlusion compared to later stages of occlusion due to the decreasing water concentration gradient in the SC. This work estimates the water diffusivity in occluded skin for the first time. However, various assumptions were made to enable the model to be solved, such as the zero water flux at the skin surface, equaling the convection velocity to the swelling velocity, the constant water profile at the steady state, and the exponential diffusivity function, etc.

- Fresnel equation-based model:

_{0}, H

_{1}, and H

_{2}). Whether the fitting parameters can be found unambiguously depends on the number of parameters to be found, the sensitivity of the system, the noise of the measured data and the algorithm designed for the optimization. Therefore, there is a trade-off between the model accuracy and the result accuracy. A comprehensive and accurate model may not be able to be accurately solved, while adding more assumptions and simplifications may reduce the credibility of the results.

#### 2.2.4. Model with Anisotropic Stratum Corneum

#### 2.3. Comparison of Different Models

## 3. Future Perspective

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Liebe, H.J.; Hufford, G.A.; Manabe, T. A model for the complex permittivity of water at frequencies below 1 THz. Int. J. Infrared Millim. Waves
**1991**, 12, 659–675. [Google Scholar] [CrossRef] - Cal, K.; Stefanowska, J.; Zakowiecki, D. Current tools for skin imaging and analysis. Int. J. Dermatol.
**2009**, 48, 1283–1289. [Google Scholar] [CrossRef] [PubMed] - Rallan, D.; Harland, C.C. Skin imaging: Is it clinically useful? Clin. Exp. Dermatol.
**2004**, 29, 453–459. [Google Scholar] [CrossRef] [PubMed] - Boyd, A.; Cain, O.; Chauhan, A.; Webb, G.J. Medical liver biopsy: Background, indications, procedure and histopathology. Front. Gastroenterol.
**2020**, 11, 40–47. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bergh, B.A.I.V.D.; Swartzendruber, D.C.; Hoogstraate, J.J.; Schrijvers, A.H.G.J.; Boddé, H.E.; Junginger, H.E.; Bouwstra, J.A.; Der Geest, A.B.-V. Development of an optimal protocol for the ultrastructural examination of skin by transmission electron microscopy. J. Microsc.
**1997**, 187, 125–133. [Google Scholar] [CrossRef] [PubMed] - White, N.S.; Errington, R.J. Fluorescence techniques for drug delivery research: Theory and practice. Adv. Drug Deliv. Rev.
**2005**, 57, 17–42. [Google Scholar] [CrossRef] - Kilpatrick-Liverman, L.; Kazmi, P.; Wolff, E.; Polefka, T.G. The use of near-infrared spectroscopy in skin care applications. Ski. Res. Technol.
**2006**, 12, 162–169. [Google Scholar] [CrossRef] - Caspers, P.; Lucassen, G.; Puppels, G. Combined In Vivo Confocal Raman Spectroscopy and Confocal Microscopy of Human Skin. Biophys. J.
**2003**, 85, 572–580. [Google Scholar] [CrossRef] [Green Version] - Eberhardt, K.; Stiebing, C.; Matthäus, C.; Schmitt, M.; Popp, J. Advantages and limitations of Raman spectroscopy for molecular diagnostics: An update. Expert Rev. Mol. Diagn.
**2015**, 15, 773–787. [Google Scholar] [CrossRef] [PubMed] - Welzel, J.; Lankenau, E.; Birngruber, R.; Engelhardt, R. Optical coherence tomography of the human skin. J. Am. Acad. Dermatol.
**1997**, 37, 958–963. [Google Scholar] [CrossRef] - Schwartz, M.; Levine, A.; Markowitz, O. Optical coherence tomography in dermatology. Cutis
**2017**, 100, 163–166. [Google Scholar] - Goldman, L.W. Principles of CT: Radiation Dose and Image Quality. J. Nucl. Med. Technol.
**2007**, 35, 213–225. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Huang, S.-Y.; Boone, J.M.; Yang, K.; Kwan, A.L.C.; Packard, N.J. The effect of skin thickness determined using breast CT on mammographic dosimetry. Med. Phys.
**2008**, 35, 1199–1206. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Mirrashed, F.; Sharp, J.C. In vivo morphological characterisation of skin by MRI micro-imaging methods. Ski. Res. Technol.
**2004**, 10, 149–160. [Google Scholar] [CrossRef] - Mirbeik-Sabzevari, A.; Tavassolian, N. Ultrawideband, Stable Normal and Cancer Skin Tissue Phantoms for Millimeter-Wave Skin Cancer Imaging. IEEE Trans. Biomed. Eng.
**2018**, 66, 176–186. [Google Scholar] [CrossRef] [PubMed] - Fear, E.C. Microwave Imaging of the Breast. Technol. Cancer Res. Treat.
**2005**, 4, 69–82. [Google Scholar] [CrossRef] [Green Version] - Owda, A.Y.; Salmon, N.; Casson, A.J.; Owda, M. The Reflectance of Human Skin in the Millimeter-Wave Band. Sensors
**2020**, 20, 1480. [Google Scholar] [CrossRef] [Green Version] - Owda, A.Y.; Salmon, N.; Harmer, S.W.; Shylo, S.; Bowring, N.J.; Rezgui, N.D.; Shah, M. Millimeter-wave emissivity as a metric for the non-contact diagnosis of human skin conditions. Bioelectromagnetics
**2017**, 38, 559–569. [Google Scholar] [CrossRef] [PubMed] - Nakagawa, N.; Matsumoto, M.; Sakai, S. In vivo measurement of the water content in the dermis by confocal Raman spectroscopy. Ski. Res. Technol.
**2010**, 16, 137–141. [Google Scholar] [CrossRef] - Chen, X.; Parrott, E.P.J.; Ung, B.S.-Y.; Pickwell-MacPherson, E. A Robust Baseline and Reference Modification and Acquisition Algorithm for Accurate THz Imaging. IEEE Trans. Terahertz Sci. Technol.
**2017**, 7, 493–501. [Google Scholar] [CrossRef] - Rakić, A.D.; Taimre, T.; Bertling, K.; Lim, Y.L.; Dean, P.; Valavanis, A.; Indjin, D. Sensing and imaging using laser feedback interferometry with quantum cascade lasers. Appl. Phys. Rev.
**2019**, 6, 021320. [Google Scholar] [CrossRef] [Green Version] - Rakić, A.D.; Lim, Y.L.; Taimre, T.; Agnew, G.; Qi, X.; Bertling, K.; Han, S.; Wilson, S.J.; Kundu, I.; Grier, A.; et al. Optical feedback effects on terahertz quantum cascade lasers: Modelling and applications. In Infrared, Millimeter-Wave, and Terahertz Technologies IV; International Society for Optics and Photonics: Beijing, China, 2016; p. 1003016. [Google Scholar]
- Rakic, A.D.; Taimre, T.; Bertling, K.; Lim, Y.L.; Wilson, S.J.; Nikolić, M.; Valavanis, A.; Indjin, D.; Linfield, E.H.; Davies, A.G.; et al. THz QCL self-mixing interferometry for biomedical applications. In Terahertz Emitters, Receivers, and Applications V; International Society for Optics and Photonics: San Diego, CA, USA, 2014; p. 91990M. [Google Scholar]
- Shi, L.; Shumyatsky, P.; Rodríguez-Contreras, A.; Alfano, R. Terahertz spectroscopy of brain tissue from a mouse model of Alzheimer’s disease. J. Biomed. Opt.
**2016**, 21, 015014. [Google Scholar] [CrossRef] [Green Version] - Hou, D.; Li, X.; Cai, J.; Ma, Y.; Kang, X.; Huang, P.; Zhang, G. Terahertz spectroscopic investigation of human gastric normal and tumor tissues. Phys. Med. Biol.
**2014**, 59, 5423–5440. [Google Scholar] [CrossRef] - Wang, J.; Lindley-Hatcher, H.; Liu, K.; Pickwell-MacPherson, E. Evaluation of transdermal drug delivery using terahertz pulsed imaging. Biomed. Opt. Express
**2020**, 11, 4484–4490. [Google Scholar] [CrossRef] [PubMed] - Sun, Q.; Stantchev, R.I.; Wang, J.; Parrott, E.P.J.; Cottenden, A.; Chiu, T.-W.; Ahuja, A.T.; Pickwell-MacPherson, E. In vivo estimation of water diffusivity in occluded human skin using terahertz reflection spectroscopy. J. Biophotonics
**2018**, 12, e201800145. [Google Scholar] [CrossRef] [PubMed] - Lindley-Hatcher, H.; Hernandez-Serrano, A.I.; Wang, J.; Cebrian, J.; Hardwicke, J.; Pickwell-MacPherson, E. Evaluation of in vivo THz sensing for assessing human skin hydration. J. Phys. Photonics
**2021**, 3, 014001. [Google Scholar] [CrossRef] - Pickwell, E.; Cole, B.E.; Fitzgerald, A.J.; Pepper, M.; Wallace, V.P. In vivo study of human skin using pulsed terahertz radiation. Phys. Med. Biol.
**2004**, 49, 1595. [Google Scholar] [CrossRef] - Fitzgerald, A.J.; Wallace, V.P.; Jimenez-Linan, M.; Bobrow, L.; Pye, R.J.; Purushotham, A.D.; Arnone, D.D. Terahertz Pulsed Imaging of Human Breast Tumors. Radiology
**2006**, 239, 533–540. [Google Scholar] [CrossRef] - Ji, Y.B.; Oh, S.J.; Kang, S.-G.; Heo, J.; Kim, S.-H.; Choi, Y.; Song, S.; Son, H.Y.; Kim, S.H.; Lee, J.H.; et al. Terahertz reflectometry imaging for low and high grade gliomas. Sci. Rep.
**2016**, 6, 36040. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wallace, V.P.; Fitzgerald, A.J.; Shankar, S.; Flanagan, N.; Pye, R.; Cluff, J.; Arnone, D.D. Terahertz pulsed imaging of basal cell carcinoma ex vivo and in vivo. Br. J. Dermatol.
**2004**, 151, 424–432. [Google Scholar] [CrossRef] - Cole, B.E.; Woodward, R.M.; Crawley, D.A.; Wallace, V.P.; Arnone, D.D.; Pepper, M. Terahertz imaging and spectroscopy of human skin in vivo. In Commercial and Biomedical Applications of Ultrashort Pulse Lasers; Laser Plasma Generation and Diagnostics; International Society for Optics and Photonics: San Jose, CA, USA, 2001; pp. 1–10. [Google Scholar]
- Fan, S.; Ung, B.S.Y.; Parrott, E.P.J.; Wallace, V.P.; Pickwell-MacPherson, E. In vivo terahertz reflection imaging of human scars during and after the healing process. J. Biophotonics
**2016**, 10, 1143–1151. [Google Scholar] [CrossRef] [PubMed] - Wang, J.; Sun, Q.; Stantchev, R.I.; Chiu, T.-W.; Ahuja, A.T.; Pickwell-MacPherson, E. In vivo terahertz imaging to evaluate scar treatment strategies: Silicone gel sheeting. Biomed. Opt. Express
**2019**, 10, 3584–3590. [Google Scholar] [CrossRef] [PubMed] - Kim, K.W.; Kim, K.-S.; Kim, H.; Lee, S.H.; Park, J.-H.; Han, J.-H.; Seok, S.-H.; Park, J.; Choi, Y.; Kim, Y.I.; et al. Terahertz dynamic imaging of skin drug absorption. Opt. Express
**2012**, 9, 9476–9484. [Google Scholar] [CrossRef] - Kim, K.W.; Kim, H.; Park, J.; Han, J.K.; Son, J.-H. Terahertz Tomographic Imaging of Transdermal Drug Delivery. IEEE Trans. Terahertz Sci. Technol.
**2011**, 2, 99–106. [Google Scholar] [CrossRef] - Wang, J.; Stantchev, R.I.; Sun, Q.; Chiu, T.-W.; Ahuja, A.T.; MacPherson, E.P. THz in vivo measurements: The effects of pressure on skin reflectivity. Biomed. Opt. Express
**2018**, 9, 6467–6476. [Google Scholar] [CrossRef] [Green Version] - Sun, Q.; Parrott, E.P.; He, Y.; Pickwell-MacPherson, E. In vivo THz imaging of human skin: Accounting for occlusion effects. J. Biophotonics
**2017**, 11, e201700111. [Google Scholar] [CrossRef] - Lindley-Hatcher, H.; I Hernandez-Serrano, A.; Sun, Q.; Wang, J.; Cebrian, J.; Blasco, L.; Pickwell-MacPherson, E. A Robust Protocol for In Vivo THz Skin Measurements. J. Infrared Millim. Terahertz Waves
**2019**, 40, 980–989. [Google Scholar] [CrossRef] [Green Version] - Pickwell, E.; Cole, B.E.; Fitzgerald, A.J.; Wallace, V.P.; Pepper, M. Simulation of terahertz pulse propagation in biological systems. Appl. Phys. Lett.
**2004**, 84, 2190–2192. [Google Scholar] [CrossRef] - Zaytsev, K.I.; Dolganova, I.N.; Chernomyrdin, N.V.; Katyba, G.M.; Gavdush, A.A.; Cherkasova, O.P.; Komandin, G.; Shchedrina, M.A.; Khodan, A.N.; Ponomarev, D.S.; et al. The progress and perspectives of terahertz technology for diagnosis of neoplasms: A review. J. Opt.
**2019**, 22, 013001. [Google Scholar] [CrossRef] - Truong, B.C.Q.; Tuan, H.D.; Fitzgerald, A.J.; Wallace, V.P.; Nguyen, H.T. High correlation of double Debye model parameters in skin cancer detection. In Proceedings of the 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago, IL, USA, 26–30 August 2014; Volume 2014, pp. 718–721. [Google Scholar]
- Yada, H.; Nagai, M.; Tanaka, K. Origin of the fast relaxation component of water and heavy water revealed by terahertz time-domain attenuated total reflection spectroscopy. Chem. Phys. Lett.
**2008**, 464, 166–170. [Google Scholar] [CrossRef] - Stantchev, R.I.; Yu, X.; Blu, T.; Pickwell-MacPherson, E. Real-time terahertz imaging with a single-pixel detector. Nat. Commun.
**2020**, 11, 2535. [Google Scholar] [CrossRef] - Gente, R.; Born, N.; Voß, N.; Sannemann, W.; Léon, J.; Koch, M.; Castro-Camus, E. Determination of Leaf Water Content from Terahertz Time-Domain Spectroscopic Data. J. Infrared Millim. Terahertz Waves
**2013**, 34, 316–323. [Google Scholar] [CrossRef] - He, Y.; Liu, K.; Au, C.; Sun, Q.; Parrott, E.P.J.; Pickwell-MacPherson, E. Determination of terahertz permittivity of dehydrated biological samples. Phys. Med. Biol.
**2017**, 62, 8882–8893. [Google Scholar] [CrossRef] - Scheller, M.; Jansen, C.; Koch, M. Applications of Effective Medium Theories in the Terahertz Regime. In Recent Opt. Photonic Technol; IntechOpen: London, UK, 2010; pp. 231–250. [Google Scholar] [CrossRef] [Green Version]
- Hernandez-Cardoso, G.G.; Rojas-Landeros, S.C.; Alfaro-Gomez, M.; Hernandez-Serrano, A.I.; Salas-Gutierrez, I.; Lemus-Bedolla, E.; Castillo-Guzman, A.R.; Lopez-Lemus, H.L.; Castro-Camus, E. Terahertz imaging for early screening of diabetic foot syndrome: A proof of concept. Sci. Rep.
**2017**, 7, srep42124. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hernandez-Cardoso, G.G.; Singh, A.K.; Castro-Camus, E. Empirical comparison between effective medium theory models for the dielectric response of biological tissue at terahertz frequencies. Appl. Opt.
**2020**, 59, D6–D11. [Google Scholar] [CrossRef] - Bennett, D.B.; Li, W.; Taylor, Z.D.; Grundfest, W.S.; Brown, E.R. Stratified Media Model for Terahertz Reflectometry of the Skin. IEEE Sens. J.
**2010**, 11, 1253–1262. [Google Scholar] [CrossRef] - Chen, X.; Sun, Q.; Wang, J.; Pickwell-MacPherson, E. Skin Surface Feature Influence on Terahertz in vivo Measurements. In Proceedings of the 2020 45th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), Institute of Electrical and Electronics Engineers (IEEE), Paris, France, 1–6 September 2020; pp. 1–2. [Google Scholar]
- Chen, X.; Sun, Q.; Wang, J.; Lindley-Hatcher, H.; Pickwell-MacPherson, E. Exploiting Complementary Terahertz Ellipsometry Configurations to Probe the Hydration and Cellular Structure of Skin In Vivo. Adv. Photonics Res.
**2021**, 2, 2000024. [Google Scholar] [CrossRef] - Nibali, V.C.; Havenith, M. New Insights into the Role of Water in Biological Function: Studying Solvated Biomolecules Using Terahertz Absorption Spectroscopy in Conjunction with Molecular Dynamics Simulations. J. Am. Chem. Soc.
**2014**, 136, 12800–12807. [Google Scholar] [CrossRef] [PubMed] - Menon, G.K.; Cleary, G.W.; Lane, M.E. The structure and function of the stratum corneum. Int. J. Pharm.
**2012**, 435, 3–9. [Google Scholar] [CrossRef] - Tippavajhala, V.K.; Magrini, T.D.; Matsuo, D.C.; Silva, M.G.P.; Favero, P.P.; De Paula, L.R.; Martin, A.A. In Vivo Determination of Moisturizers Efficacy on Human Skin Hydration by Confocal Raman Spectroscopy. AAPS PharmSciTech
**2018**, 19, 3177–3186. [Google Scholar] [CrossRef] - Dąbrowska, A.K.; Adlhart, C.; Spano, F.; Rotaru, G.-M.; Derler, S.; Zhai, L.; Spencer, N.D.; Rossi, R.M. In vivo confirmation of hydration-induced changes in human-skin thickness, roughness and interaction with the environment. Biointerphases
**2016**, 11, 031015. [Google Scholar] [CrossRef] [Green Version] - Egawa, M.; Hirao, T.; Takahashi, M. In vivo Estimation of Stratum Corneum Thickness from Water Concentration Profiles Obtained with Raman Spectroscopy. Acta Derm. Venereol.
**2007**, 87, 4–8. [Google Scholar] [CrossRef] [Green Version] - Smith, G.D. Numerical Solution of Partial Differential Equations: Finite Difference Methods; Oxford University Press: Oxford, UK, 1985. [Google Scholar]
- Hale, D.K. The physical properties of composite materials. J. Mater. Sci.
**1976**, 11, 2105–2141. [Google Scholar] [CrossRef] - Rawlings, A.V. Ethnic skin types: Are there differences in skin structure and function? Int. J. Cosmet. Sci.
**2006**, 28, 79–93. [Google Scholar] [CrossRef] [PubMed] - Farage, M.A.; Miller, K.W.; Elsner, P.; Maibach, H.I. Structural Characteristics of the Aging Skin: A Review. Cutan. Ocul. Toxicol.
**2007**, 26, 343–357. [Google Scholar] [CrossRef] - Baumann, L. Skin ageing and its treatment. J. Pathol.
**2007**, 211, 241–251. [Google Scholar] [CrossRef] [PubMed] - Firooz, A.; Sadr, B.; Babakoohi, S.; Sarraf-Yazdy, M.; Fanian, F.; Kazerouni-Timsar, A.; Nassiri-Kashani, M.; Naghizadeh, M.M.; Dowlati, Y. Variation of Biophysical Parameters of the Skin with Age, Gender, and Body Region. Sci. World J.
**2012**, 2012, 1–5. [Google Scholar] [CrossRef] [Green Version] - Ehlers, C.; Ivens, U.I.; Møller, M.L.; Senderovitz, T.; Serup, J. Females have lower skin surface pH than men: A study on the influence of gender, forearm site variation, right/left difference and time of the day on the skin surface pH. Ski. Res. Technol.
**2001**, 7, 90–94. [Google Scholar] [CrossRef] - Wilhelm, K.P.; Cua, A.B.; Maibach, H.I. Skin Aging: Effect on Transepidermal Water Loss, Stratum Corneum Hydration, Skin Surface pH, and Casual Sebum Content. Arch. Dermatol.
**1991**, 127, 1806–1809. [Google Scholar] [CrossRef] - Barker, X.R.; Pickwell-MacPherson, E. In vivo THz Measurements of Human Skin: Investigating the Dependence on Ethnicity and Arm Dominance. In Proceedings of the 2019 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), Institute of Electrical and Electronics Engineers (IEEE), Paris, France, 1–6 September 2019; pp. 1–2. [Google Scholar]
- Peralta, X.G.; Lipscomb, D.; Wilmink, G.J.; Echchgadda, I. Terahertz spectroscopy of human skin tissue models with different melanin content. Biomed. Opt. Express
**2019**, 10, 2942–2955. [Google Scholar] [CrossRef] [PubMed] - Clegg, J.; Robinson, M.P. A genetic algorithm used to fit Debye functions to the dielectric properties of tissues. In Proceedings of the IEEE Congress on Evolutionary Computation, Barcelona, Spain, 18–23 July 2010; pp. 1–8. [Google Scholar] [CrossRef]
- Clegg, J.; Robinson, M.P. A genetic algorithm for optimizing multi-pole Debye models of tissue dielectric properties. Phys. Med. Biol.
**2012**, 57, 6227–6243. [Google Scholar] [CrossRef] [PubMed] - Ding, X.; Yang, F.; Yu, X.; Li, M.; Gao, B.; Fang, Y.; Huang, X. Optimization of Data Fitting Algorithm for Tissue Dielectric Properties in THz-band using Genetic Algorithm. In Proceedings of the 2019 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), Institute of Electrical and Electronics Engineers (IEEE), Paris, France, 1–6 September 2019; pp. 1–2. [Google Scholar]
- Truong, B.C.Q.; Tuan, H.D.; Kha, H.H.; Nguyen, H.T. Global optimization for human skin investigation in terahertz. In Proceedings of the 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society, IEEE, San Diego, CA, USA, 28 August–1 September 2012; Volume 2012, pp. 5474–5477. [Google Scholar]
- Truong, B.C.Q.; Tuan, H.D.; Kha, H.H.; Nguyen, H.T. Debye Parameter Extraction for Characterizing Interaction of Terahertz Radiation with Human Skin Tissue. IEEE Trans. Biomed. Eng.
**2013**, 60, 1528–1537. [Google Scholar] [CrossRef] [PubMed] - Yang, K.; Chopra, N.; Abbasi, Q.H.; Qaraqe, K.A.; Alomainy, A. Collagen Analysis at Terahertz Band Using Double-Debye Parameter Extraction and Particle Swarm Optimisation. IEEE Access
**2017**, 5, 27850–27856. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Typical THz pulsed laser imaging system in reflection geometry. The THz optical system is assembled on a x-y 2D stage to enable raster scanning the sample. (

**b**) Examples of the THz pulses reflected from the quartz-volar forearm and quartz-air interfaces, respectively.

**Figure 2.**Comparison of measured and simulated impulse functions of the (

**a**) (volar) forearm and (

**b**) the palm. Reprinted with permission from ref. [29]. Copyright 2004 Physics in Medicine and Biology.

**Figure 3.**(

**a**) Real part and (

**b**) imaginary part of porcine skin permittivity. Reprinted with permission from ref. [47] Copyright 2017 Physics in Medicine and Biology.

**Figure 4.**(

**a**) Refractive index and (

**b**) extinction coefficient of dehydrated skin obtained from work done by He et al. [47], Hernandez-Cardoso et al. [49] and Bennett et al. [51] and compared to that of water. Reprinted with permission from ref. [47]. Copyright 2017 Scientific Reports. Reprinted with permission from ref. [51]. Copyright 2011 IEEE Sensors Journal.

**Figure 5.**(

**a**) Diagram of the THz interaction with a two-layer skin model consisting of SC and epidermis; (

**b**) Water content in the SC and (

**c**) refractive index in the SC and epidermis, before and after the application of silicone gel sheeting, respectively [35].

**Figure 6.**Schematic diagram showing the water profile in skin and the derivation of the reflection of a plane wave by a slab of stratified permittivity and permeability. The blue curve is the modeled water profile defined by H

_{0}, H

_{1}, H

_{2}and d

_{1}, d

_{2}. The red curve is the approximated water profile used to estimate the permittivity in each layer.

**Figure 8.**(

**a**) Water profile in skin under different applied pressures; (

**b**) Refractive index of dehydrated skin and SC thickness under different pressures. The error bars in (

**b**) are the standard deviation of three measurements [38].

**Figure 9.**(

**a**) Water dynamics of skin in a steady state; (

**b**) Water dynamics of skin under occlusion; (

**c**) The water concentration profile at different occlusion times; (

**d**) The convection velocity as a function of the occlusion time; (

**e**) A colormap of the water concentration as a function of depth (z) in skin and occlusion time. The black curve shows the change in the thickness of the SC with occlusion time. The white dashed curves are the contour lines of the water concentration at 0.5, 0.6 and 0.7 g/cm

^{3}. Reprinted with permission from ref. [27] Copyright 2019 Journal of Biophotonics.

**Figure 10.**Schematic diagram of the multiple layer structure and the derivation of the reflection coefficient based on the Fresnel equations. n

_{m}(m > 0) is the refractive index of the mth layer calculated using an EMT. d

_{m}is the thickness of the mth layer. r

_{m}is the reflection coefficient from medium m to m + 1. R

_{0}is the reflection of light incident from medium 0 to the N-layer structure.

**Figure 11.**(

**a**) Defined water concentration gradient; (

**b**) Reflection coefficients calculated based on the stratified media model and Fresnel theory, respectively.

**Figure 12.**(

**a**) Illustration of the double prism system and the two alternative THz optical paths; The double-prism system is assembled in (

**b**) a THz transmission-form ellipsometer; (

**c**) The “bricks and mortar” biological structure in the SC; (

**d**) layered model (

**left**) and the anisotropic skin model (

**right**) [53].

**Figure 13.**(

**a**) The amplitude and (

**b**) phase of the reflection ratios calculated for the four experimental geometries, indicated by s-θ

_{i}

_{1}, p-θ

_{i}

_{1}, s-θ

_{i}

_{2}, and p-θ

_{i}

_{2}. The symbols are the results from the layered model and the solid curves are the results from the anisotropic model [53].

**Figure 14.**(

**a**) The refractive index and (

**b**) extinction coefficient of the SC in the extraordinary and ordinary directions and epidermis at 0.6 THz during 30 min of occlusion [53].

**Figure 15.**Refractive index and extinction coefficient spectra of the SC in the extraordinary and ordinary directions and epidermis during 30 min of occlusion [53].

**Figure 16.**(

**a**) Dispersion and (

**b**) n birefringence of one subject. The symbols are the raw data and the solid curves are the moving average of every 5 data [53].

Model | Merits | Limitations |
---|---|---|

Double Debye model | Physical properties obtained Very little prior knowledge needed | Accuracy for dry tissues is questionable |

Effective medium theory | Direct extraction of the water content Very few fitting parameters | Requires a prior knowledge on the biological background EMT assumptions may not be satisfied |

Single-layer model | Simple characterization | Oversimplified Cannot distinguish different tissues No comparability between different setups |

Double-layer model | Differentiate SC and epidermis Good accuracy | Dielectric models needed |

Stratified media model/Fresnel Theory | Clear water concentration distribution Good consistency with Raman spectroscopy | Pre-defined water profile needed More difficult convergence |

Anisotropic SC model | Birefringence induced by SC cellular structure considered No dielectric model used Both hydration and structural information obtained | Needs multiple uncorrelated measurements for a convergent fit |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, J.; Lindley-Hatcher, H.; Chen, X.; Pickwell-MacPherson, E.
THz Sensing of Human Skin: A Review of Skin Modeling Approaches. *Sensors* **2021**, *21*, 3624.
https://doi.org/10.3390/s21113624

**AMA Style**

Wang J, Lindley-Hatcher H, Chen X, Pickwell-MacPherson E.
THz Sensing of Human Skin: A Review of Skin Modeling Approaches. *Sensors*. 2021; 21(11):3624.
https://doi.org/10.3390/s21113624

**Chicago/Turabian Style**

Wang, Jiarui, Hannah Lindley-Hatcher, Xuequan Chen, and Emma Pickwell-MacPherson.
2021. "THz Sensing of Human Skin: A Review of Skin Modeling Approaches" *Sensors* 21, no. 11: 3624.
https://doi.org/10.3390/s21113624