Open Access
Add to BibSonomy
Abstract
Sweat is one of the essential biofluids produced by the human body, and it contains various physiological biomarkers. These biomarkers can indicate human health conditions such as disease and illness. In particular, imbalances in the concentration of electrolytes can indicate the onset of disease. These same imbalances affect the dielectric properties of sweat. In this study, we used attenuated total reflection terahertz time domain spectroscopy to obtain the frequency-dependent dielectric properties of human sweat in a frequency range from 200 GHz to 2.5 THz. We have investigated the variation of dielectric properties of sweat collected from different regions of the human body, and we have observed that the real and imaginary part of dielectric permittivity decreases with the increase in frequency. A combination of left-hand Jonscher and Havriliak-Negami processes is used to model the results and reveal the presence of relaxation processes related to sodium and calcium ions concentrations. This information may help design novel biosensors to understand the human health condition and provide a hydration assessment.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Different organs of the human body produce various biological fluids such as blood, tears, urine, saliva and sweat. These biological fluids, also commonly known as biofluids contain a wide variety of biological markers such as glucose, chlorides, lipids, cortisol, dopamine, uric acid and others [1,2]. As such they carry crucial information on the physiological state of the human body. Therefore, an analysis of biomarkers can be helpful in screening, characterization, diagnosis and monitoring of various disease such as diabetes, cancer, arthritis, influenza and even the SARS corona virus. Moreover, characterization of biomarkers also helps guide clinical interventions such as the use of drugs and the prediction and treatment of adverse drug reactions.
Various photonics-based methods have been used to study biomarkers in biofluids using light of different frequency ranges. For example, carbon-nanotube based biosensors have been used to optically detect ovarian cancer in the near-infrared range [3] and label-free detection of stress-related biomarkers has been accomplished from different body fluids using optical absorption in the near-ultraviolet region [4]. Recently several attempts have been made to study biomarkers in the terahertz (THz) frequency region. For example, a THz metamaterial biosensor has been demonstrated for liver cancer biomarker testing [5]. Similarly, THz microfluidic sensors with graphene metasurfaces have been used for sensitive DNA detection [6]. Other examples of terahertz applications for biomarker detection includes terahertz plasmonic meta-devices for immunobiosensing [7], molecule-specific terahertz biosensors for steroid hormone detection [8] and blood plasma analysis to distinguish between malignant and benign thyroid nodules [9]. The majority of such biosensors rely upon the collection of blood samples, which requires an invasive procedure. In contrast to this, sweat is easily accessible from the skin surface of a human body. Sweat is very rich in various biomarkers and does not require an invasive process for collection. Moreover, it contains almost all the biomarkers as those present in blood and therefore sweat analysis could potentially replace a blood analysis in many cases. Therefore, the characterization of sweat in the terahertz frequency band has the potential to offer important insights into various biomarkers present in human sweat.
Sweat is a fluid secreted by eccrine sweat glands, which are distributed throughout the body. Normally, a typical adult produces around 500 mL to 700 mL of sweat per day under most climatic conditions [10]. Human sweat contains various biomarkers such as electrolytes (such as sodium, calcium, potassium, and chloride ions), metabolites (glucose, lactase) and other chemicals such as steroids, ethanol, ammonia, uric and ascorbic acid [11]. These biomarkers are a source of vital information on the state of the human body. Various optical spectroscopic methods such as Raman spectroscopy has been used to identify lactate, lactic acid, and urea in sweat for forensic investigation [12]. Similarly, Fourier-transform infrared spectroscopy (FTIR) has been used to measure sweat and it was shown that FTIR spectra can be used to identify biomarkers such as lactate [13,14]. Several dielectric studies of sweat in the microwave region have also been reported [15–17]. The measurement of the dielectric and optical properties of sweat coupled with the concentration of electrolytes such as Na+ and Cl-, provides information on the hydration status [18–20] of a person. The study of dielectric properties of sweat, especially in terahertz frequency band, is further of high interest due to recent research and development of terahertz wave applications making the THz frequency band more easily accessible [21–25]. Therefore, it is crucial to understand terahertz wave interactions of human skin and specific absorption ratios, which all requires a knowledge of the dielectric properties of skin and sweat in the terahertz frequency band [26–34].
In this study, we used a terahertz time-domain spectroscopy system in attenuated total reflection mode, to measure and calculate the frequency dependent dielectric properties of sweat samples in the frequency range from 0.2 THz to 2.5 THz. The dielectric properties of sweat collected from different regions of the human body are compared. Similarly, the dielectric properties of sweat obtained from different human subjects are also compared. A combination of left-hand Jonscher and Havriliak-Negami processes [35] are used to model the results and the model parameters are discussed.
2. Materials and methods
2.1 Terahertz time domain spectroscopy
Human sweat is predominantly water and the absorption of water in THz region is high (α = 200 $\textrm{c}{\textrm{m}^{ - 1}}$ at 1 THz) [36]. Therefore, the measurement of dielectric properties of such liquids using transmission mode terahertz time domain spectroscopy (THz-TDS) requires a special liquid transmission cell with the liquid thickness in the range of micrometers [37], as the signal transmitted through such sample decreases in proportion to exp(-αd), where α is the absorption coefficient and d is the sample thickness. However, such highly absorbing samples can also be measured either by reflection mode THz-TDS [21] or attenuated total reflection (ATR) THz-TDS [38,39]. In this study, we used THz-TDS in ATR mode, which makes it easy to measure the dielectric properties of highly absorbing liquids and does not require any specific cell to hold liquid. Instead, a sample under investigation without further preparation can be directly placed on a silicon prism (n = 3.41) [40].
The schematic of the time-domain spectroscopy system used in attenuated total reflection mode (ATR THz-TDS) is shown in Fig. 1. It consists of a femtosecond fiber laser (λ = 780 nm, average power = 20 mW, pulse width <100 fs, repetition rate = 50 MHz), two dipole-type photoconductive (PC) antennas for THz wave emission and detection, an optical delay stage to introduce the time delay between probe laser pulse and THz pulse, and a silicon prism providing a medium of total internal reflection for the terahertz waves. The pulse of the fs laser is divided into two beams using a 50:50 beam splitter. One optical beam in the optical paths is incident on the PC antenna to produce a pulse of THz wave, whereas the other is used to probe the detector antenna with a time delay governed by a linear stage. The emitted THz pulse is then guided by off-axis parabolic mirrors and incident on the silicon prism. The THz wave undergoes total internal reflection at the boundary between silicon and air, and finally is incident on another photoconductive antenna for detection purposes. The pulse of the THz wave is recorded by changing the relative timing between the probe pulse and the terahertz pulse at the detector antenna. The frequency resolution of the system is 24 GHz, and the maximum dynamic range is 65 dB. As the amplitude of the impinging THz electric field is recorded as a function of the relative delay time, a Fourier-transform of the result provides both, real and imaginary parts of dielectric permittivity of the sample in a frequency range of 200 GHz to 2.5 THz at sufficient signal to noise ratio [41].
Fig. 1. (a) Schematic of the terahertz-time domain spectrometer. (b) The triangular, high-resistivity float-zone silicon prism is used as a medium for total internal reflection of THz wave and placed at the “sample” position in (a). The sample under investigation is placed directly on the silicon prism.
2.2 Sample collection
In this study, we collected human sweat samples from five male subjects (age = 23.2 ± 0.8 years) from the skin surface of their chests, backs and foreheads immediately after jogging for 30 minutes. The protocol of sample collection was: 1) the target area is first rinsed with pure water and dried. Then a cotton swab was placed on the body surface before the start of jogging. 2) After jogging for 30 minutes, the swab was removed and squeezed using a syringe and transferred into individual Eppendorf tubes as shown in Fig. 2(a). Then the sweat samples were placed on the silicon prism immediately after collection for attenuated total reflection terahertz time-domain spectroscopy as shown in Fig. 2(b). Ethical approval (No. 20-48) for this study was obtained from Shizuoka University. Informed written consent was obtained from all the participants involved in this study.
Fig. 2. (a) Sweat samples and (b) sweat sample on the silicon prism for the measurement. The silicone well serves as a barrier and is used to prevent the spread of sweat on the prism face. (c) Sweat collection regions used in the study.
In this study, all the measurements were done at room temperature and ambient atmospheric pressure. Figure 3(a) shows the typical terahertz pulse measured using the ATR THz-TDS. The reference signal is measured without placing anything on the silicon prism, representing ambient air, whereas the sample signal is measured when the sample under investigation is placed on the prism. These two signals are transformed to frequency-domain intensity and phase spectra using fast Fourier transformation. Both, reference and sample spectra, are shown in Fig. 3(b). The complex dielectric permittivity $\tilde{\varepsilon } = \varepsilon ^{\prime} + i\varepsilon ^{\prime\prime}$ of the sample is calculated using the following equations [39].
Fig. 3. (a) Representative terahertz time-domain reference and sample signals and (b) their frequency domain intensity spectra. Real part (c) and imaginary part (d) of the dielectric permittivity of a sweat sample. At higher frequencies, the water vapor absorption lines are prominent in the intensity spectra as these measurements were done at room temperature and ambient atmospheric pressure. This introduces large errors due to low signal-to-noise ratios, so that the data evaluation is limited to a range from 0.2 THz to 2.5 THz, see (c) and (d).
3. Results and discussion
The real and imaginary part of the dielectric permittivity in the frequency region of 0.2 THz to 2.5 THz of sweat samples obtained from all five subjects for three different measurement regions (back, chest and forehead) are shown in Fig. 4. Both real and imaginary part of dielectric permittivity of sweat samples obtained from all measurement regions decrease with the increase in frequency. The same data set is presented in Fig. 7 in the Appendix II for easy comparison.
Fig. 4. Real and imaginary part of the dielectric permittivity of the sweat for three measurement sites: chest (a, b), back (c, d), and forehead (e, f) for 5 persons (subject 1 to subject 5). For further details, please refer Fig. 7 in the Appendix II.
Sweat can be considered as an aqueous solution of electrolytes, dominated by the ions $\textrm{N}{\textrm{a}^ + },{\textrm{K}^ + },\textrm{C}{\textrm{a}^{2 + }}$ and $\textrm{C}{\textrm{l}^ - }$. As such its terahertz spectra will be dominated by fluctuations in the spanned H-bonded network of bulk water. At room temperature (approximately 25 °C) the main dielectric relaxation peak for water is situated at 20 GHz [42] with an excess wing extending down to 1.5 THz [43,44]. The situation is similar in general for aqueous solutions of low molarity [45]. While it is customary to model the behavior of aqueous solutions in the frequency range 0.2 to 3 THz with two independent Debye processes [36], it has been noted that the excess wing scales with the main relaxation peak of water as a function of temperature [43,44]. This observation implies that the molecular mechanism responsible for the excess wing shares a common energy of activation with the main relaxation peak of water. Consequently, the low frequencies of our spectra are considered to be a tail of the main water relaxation peak, situated outside the frequency range of our study. It is necessary to add a further Debye process to continue modelling the data up to 2.5 GHz, above which one can observe the onset of the boson peak for water [42,46]. This general description is maintained for our results. The data was modelled using a combination of complex power law, often referred as a Jonscher process [35], and a Havriliak -Negami process for the higher frequencies [35,47].
Fig. 5. The imaginary component of the dielectric permittivity recorded from the back of the first subject. The fit (black solid line) to the data (open circle) is the sum of the Jonscher process (red dashed line) and the Havriliak-Negami process (blue dashed -dotted line).
The dielectric properties of sweat mainly depend upon the concentration of different electrolytes such as $\textrm{N}{\textrm{a}^ + },{\textrm{K}^ + },\textrm{C}{\textrm{a}^{2 + }}$ and $\textrm{C}{\textrm{l}^ - }$ as shown in Table 1 and Table 2. While the low frequency spectra are dominated by the tail of the bulk water peak, Funkner et al. demonstrated that the oscillation of the ion hydration shell, specifically from divalent ions, could be found in the frequency range 3 THz to 6 THz [49], with $\textrm{CaC}{\textrm{l}_2}$ peaking at approximately 4.5 THz. Measurements of molar concentrations of NaCl [50] point to an oscillation at 6.02 THz (201 $\textrm{c}{\textrm{m}^{ - 1}}$) whose origin is due to a rattling motion of Na+ within its immediate hydration shell as well as a peak at 5.39 THz related to a similar motion for the $\textrm{C}{\textrm{l}^ - }$ ion. The same study found peaks at lower frequencies as well, but at the concentration of ions in sweat (mmol/l), these peaks are dominated by the excess wing of water. The electrolyte concentration in sweat obtained from the different body parts are collected from the literature and shown in Table 1 [51]. Here, it is worthwhile to note that the electrolyte concentration of sweat collected from these parts shows considerable similarity. Therefore, while the dielectric strength of the Havriliak-Negami process would be proportional to the concentration of ions, it is more meaningful to study the relaxation times. The averages are presented in Fig. 6. The values of the dielectric strength are quite similar for each body position.
Fig. 6. (a) The averaged dielectric strength values of all persons and measurements ɛav derived from the fit-function to the data by Eq. (4) and (b) the averaged relaxation times (in wavenumbers with 100 cm−1 corresponding to 0.33 ps). The error bars correspond to the standard deviations.
Table 2. Concentration of various minerals in sweat collected from different body parts [52]
From the relaxation times it seems that the main contribution to the absorption on the chest and forehead comes from sweat containing mainly $\textrm{N}{\textrm{a}^ + }\; \textrm{and}\; \textrm{C}{\textrm{l}^ - }$ ions. Yet the relaxation time for the back suggests another ionic moiety. From vibrational densities of states calculations for aqueous solutions of divalent ions carried out by Funkner et al. [49], the relaxation time around 9 THz could be due to an excess of $\textrm{C}{\textrm{a}^{2 + }}$ in the sweat collected from the back. It has been noted in the past that during exercise as shown in Table 2, sweat on the back contains higher levels of $\textrm{C}{\textrm{a}^{2 + }}$ than on the forehead [52] lending some credence to the result above.
4. Conclusion
Human sweat is rich of various biomarkers and the study of such biomarkers may help to identify various health issues. In this study, we have reported the dielectric properties of sweat for the first time in the frequency range of 200 GHz to 2.5 THz. We observed that both, real and imaginary, parts of the permittivity of sweat samples from all measurement regions decrease with increasing frequency. Finally, combined left-hand Jonscher and Havriliak- Negami processes are used to model the results and the model parameters are discussed. While these fitting results suggest a dependence of the spectra on the type of ionic moieties involved in sweat, more work, including studies at higher frequencies than those used here, is required to consolidate these results. Even so, the dielectric properties reported in this article are useful to design terahertz biosensors in order to study the biomarkers. Moreover, THz properties of sweat also help to study the interaction of terahertz wave with human skin since the sweat gland are distributed throughout the human body.
Appendix I:
Table 3. The fitting parameters used in this study
Appendix II:
Funding
Japan Society for the Promotion of Science (21K04174); Hamamatsu Foundation for Science and Technology Promotion; Cooperative Research Project No. 2072 of the Research Center for Biomedical Engineering with the Research Institute of Electronics, Shizuoka University, and under the MOU between Shizuoka University and Karlsruhe Institute of Technology.
Acknowledgments
The authors thank Hikaru Sakata for his help during the initial stage of this study. The authors also like to thank Professor Emeritus of Shizuoka University Norihisa Hiromoto for his constructive comments.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. J. K. Aronson and R. E. Ferner, “Biomarkers: a general review,” Curr. Protoc. Pharma. 76, 9–23 (2017). [CrossRef]
2. K. Strimbu and J. A. Tavel, “What are biomarkers?” Curr. Opin. HIV AIDS 5(6), 463–466 (2010). [CrossRef]
3. R. M. Williams, C. Lee, T. V. Galassi, J. D. Harvey, R. Leicher, M. Sirenko, M.A. Dorso, J. Shah, N. Olvera, F. Dao, and D. A. Levine, “Noninvasive ovarian cancer biomarker detection via an optical nanosensor implant,” Sci. Adv. 4(4), 1090 (2018). [CrossRef]
4. A. J. Steckl and P. Ray, “Stress biomarkers in biological fluids and their point-of-use detection,” ACS Sens. 3(10), 2025–2044 (2018). [CrossRef]
5. Z. Geng, X. Zhang, Z. Fan, X. Lv, and H. Chen, “A route to terahertz metamaterial biosensor integrated with microfluidics for liver cancer biomarker testing in early stage,” Sci. Rep. 7(1), 1–11 (2017). [CrossRef]
6. R. Zhou, C. Wang, Y. Huang, K. Huang, Y. Wang, W. Xu, L. Xie, and Y. Ying, “Label-free terahertz microfluidic biosensor for sensitive DNA detection using graphene-metasurface hybrid structures,” Biosens. Bioelectron. 188, 113336 (2021). [CrossRef]
7. A. Ahmadivand, B. Gerislioglu, R. Ahuja, and Y. K. Mishra, “Terahertz plasmonics: The rise of toroidal metadevices towards immunobiosensings,” Mater. Today 32, 108–130 (2020). [CrossRef]
8. S. H. Lee, D. Lee, M. H. Choi, J. H. Son, and M. Seo, “Highly sensitive and selective detection of steroid hormones using terahertz molecule-specific sensors,” Anal. Chem. 91(10), 6844–6849 (2019). [CrossRef]
9. M. R. Konnikova, O. P. Cherkasova, M. M. Nazarov, D. A. Vrazhnov, Y. V. Kistenev, S. E. Titov, E. V. Kopeikina, S. P. Shevchenko, and A. P. Shkurinov, “Malignant and benign thyroid nodule differentiation through the analysis of blood plasma with terahertz spectroscopy,” Biomed. Opt. Express 12(2), 1020–1035 (2021). [CrossRef]
10. Y. Haixia and J. Sun, “Sweat detection theory and fluid driven methods: a review,” Nanotech. and Prec. Eng. 3(3), 126–140 (2020). [CrossRef]
11. W. He, C. Wang, H. Wang, M. Jian, W. Lu, X. Liang, X. Zhang, F. Yang, and Y. Zhang, “Integrated textile sensor patch for real-time and multiplex sweat analysis,” Sci. Adv. 5(11), 0649 (2019). [CrossRef]
12. V. Sikirzhytski A and Sikirzhytskaya I. K. Lednev, “Multidimensional Raman spectroscopic signature of sweat and its potential application to forensic body fluid identification,” Anal. Chim. Acta. 718(718), 78–83 (2012). [CrossRef]
13. A. Takamura, K. Watanabe, T. Akutsu, and T. Ozawa, “Soft and robust identification of body fluid using Fourier transform infrared spectroscopy and chemometric strategies for forensic analysis,” Sci. Rep. 8(1), 8459 (2018). [CrossRef]
14. P. Ray and A. J. Steckl, “Label-free optical detection of multiple biomarkers in sweat, plasma, urine, and saliva,” ACS Sens. 4(5), 1346–1357 (2019). [CrossRef]
15. A. R. Eldamak, S. Thorson, and E. C. Fear, “Study of dielectric properties of artificial sweat mixtures at microwave frequencies,” Biosensors 10(6), 62 (2020). [CrossRef]
16. A. N. Romanov, “Dielectric properties of human sweat fluid in the microwave range,” Biophysics 55(3), 473–476 (2010). [CrossRef]
17. A. Peyman, C. Gabriel, and E. H. Grant, “Complex permittivity of sodium chloride solutions at microwave frequencies,” Bioelectromagnetics 28(4), 264–274 (2007). [CrossRef]
18. M. Omari, K. Sel, A. Mueller, J. Edwards, and T. Kaya, “Detection of relative [Na+] and [K+] levels in sweat with optical measurements,” J. App. Phys. 115(20), 203107 (2014). [CrossRef]
19. A. R. Eldamak and E. C. Fear, “Conformal and disposable antenna-based sensor for non-invasive sweat monitoring,” Sensors 18(12), 4088 (2018). [CrossRef]
20. R. Carter, S. N. Cheuvront, D. W. Wray, M. A. Kolka, L. A. Stephenson, and M. N. Sawka, “The influence of hydration status on heart rate variability after exercise heat stress,” J. Therm. Biol. 30(7), 495–502 (2005). [CrossRef]
21. P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging–Modern techniques and applications,” Laser & Photon. Rev. 5(1), 124–166 (2011). [CrossRef]
22. S. S. Dhillon, M. S. Vitiello, E.H. Linfield, et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017). [CrossRef]
23. Y. H. Tao, A. J. Fitzgerald, and V. P. Wallace, “Non-contact, non-destructive testing in various industrial sectors with terahertz technology,” Sensors 20(3), 712 (2020). [CrossRef]
24. S. R. Tripathi, Y. Sugiyama, K. Murate, K. Imayama, and K. Kawase, “Terahertz wave three-dimensional computed tomography based on injection-seeded terahertz wave parametric emitter and detector,” Opt. Express 24(6), 6433–6440 (2016). [CrossRef]
25. A. Khalatpour, A. K. Paulsen, C. Deimert, Z. R. Wasilewski, and Q. Hu, “High-power portable terahertz laser systems,” Nat. Photonics 15(1), 16–20 (2021). [CrossRef]
26. Q. Sun, Y. He, K. Liu, S. Fan, E. P. Parrott, and E. P. MacPherson, “Recent advances in terahertz technology for biomedical applications,” Quant. Imaging Med. Surg. 7(3), 345–355 (2017). [CrossRef]
27. S. R. Tripathi, E. Miyata, P. B. Ishai, and K. Kawase, “Morphology of human sweat ducts observed by optical coherence tomography and their frequency of resonance in the terahertz frequency region,” Sci. Rep. 5(1), 9071 (2015). [CrossRef]
28. S. R. Tripathi, P. B. Ishai, and K. Kawase, “Frequency of the resonance of human sweat duct in normal mode of radiation,” Biomed. Opt. Express 9(3), 1301–1308 (2018). [CrossRef]
29. N. Betzalel, Y. Feldman, and P. B. Ishai, “The modeling of the absorbance of sub-THz radiation by human skin,” IEEE Trans. THz Sci. Technol. 7(5), 521–528 (2017). [CrossRef]
30. Y. Feldman, A. Puzenko, P. B. Ishai, A. Caduff, and A. J. Agranat, “Human skin as arrays of helical antennas in the millimeter and submillimeter wave range,” Phys. Rev. Lett. 100(12), 128102 (2008). [CrossRef]
31. S. Romanenko, R. Begley, A. R. Harvey, L. Hool, and V. P. Wallace, “The interaction between electromagnetic fields at megahertz, gigahertz and terahertz frequencies with cells, tissues and organisms: risks and potential,” J. R. Soc. Interface 14(137), 20170585 (2017). [CrossRef]
32. H. Lindley-Hatcher, A. I. Hernandez-Serrano, J. Wang, J. Cebrian, J. Hardwicke, and E. P. MacPherson, “Evaluation of in vivo THz sensing for assessing human skin hydration,” J. Phys. Photonics 3(1), 014001 (2021). [CrossRef]
33. S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y. T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Bio. 54(1), 149–160 (2009). [CrossRef]
34. K. I. Zaytsev, A. A. Gavdush, N. V. Chernomyrdin, and S. O. Yurchenko, “Highly accurate in vivo terahertz spectroscopy of healthy skin: Variation of refractive index and absorption coefficient along the human body,” IEEE Trans.THz Sci. Tech. 5(5), 817–827 (2015). [CrossRef]
35. F. Kremer and A. Schönhals, Broadband Dielectric Spectroscopy (Springer, 2002).
36. C. Ronne, L. Thrane, P. Astrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys. 107(14), 5319–5331 (1997). [CrossRef]
37. C. B. Reid, G. Reese, A. P. Gibson, and V. P. Wallace, “Terahertz time-domain spectroscopy of human blood,” IEEE J. Biomed. Health Inform. 17(4), 774–778 (2013). [CrossRef]
38. K. Hashimoto and S. R. Tripathi, “Non-destructive identification of drugs in plastic packaging using attenuated total reflection terahertz time domain spectroscopy,” Optics 3(2), 99–106 (2022). [CrossRef]
39. A. Nakanishi, Y. Kawada, T. Yasuda, K. Akiyama, and H. Takahashi, “Terahertz time domain attenuated total reflection spectroscopy with an integrated prism system,” Rev. Sci. Inst 83(3), 033103 (2012). [CrossRef]
40. J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, “Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon,” J. Opt. Soc. Am. B 21(7), 1379–1386 (2004). [CrossRef]
41. S. Takagi, S. Takahashi, K. Takeya, and S. R. Tripathi, “Influence of delay stage positioning error on signal-to-noise ratio, dynamic range, and bandwidth of terahertz time-domain spectroscopy,” Appl. Opt. 59(3), 841–845 (2020). [CrossRef]
42. W. J. Ellison, “Permittivity of pure water, at standard atmospheric pressure, over the frequency range 0-25THz and the temperature range 0-100°C,” J. Phys. Chem. Ref. Data 36(1), 1–18 (2007). [CrossRef]
43. P. Ben Ishai, S. R. Tripathi, K. Kawase, A. Puzenko, and Yu. Feldman, “What is the primary mover of water dynamics?” Phys. Chem. Chem. Phys. 17(23), 15428–15434 (2015). [CrossRef]
44. I. Popov, P. B. Ishai, A. Khamzin, and Y. Feldman, “The mechanism of the dielectric relaxation in water,” Phys. Chem. Chem. Phys. 18(20), 13941–13953 (2016). [CrossRef]
45. E. Levy, A. Puzenko, U. Kaatze, P. B. Ishai, and Y. Feldman, “Dielectric spectra broadening as the signature of dipole-matrix interaction. II. Water in ionic solutions,” J. Chem. Phys. 136(11), 114503 (2012). [CrossRef]
46. M.-C. Bellissent-Funel, A. Hassanali, M. Havenith, R. Hechman, P. Pohl, F. Sterpone, D. V. D. Spoel, Y. Xu, and A. E. Garcia, “Water determines the structure and dynamics of proteins,” Chem. Rev. 116(13), 7673–7697 (2016). [CrossRef]
47. S. Havriliak and S. Negami, “A complex plane analysis of α-dispersions in some polymer systems,” J. Pol. Sci. Part C: Pol. Sym. 14(1), 99–117 (1966). [CrossRef]
48. N. Axelrod, E. Axelrod, A. Gutina, A. Puzenko, P. B. Ishai, and Y. Feldman, “Dielectric spectroscopy data treatment: I. Frequency domain,” Meas. Sci. Technol. 15(4), 755–764 (2004). [CrossRef]
49. S. Funkner, G. Niehues, D. A. Schmidt, M. Heyden, G. Schwaab, K. M. Callahan, D. J. Tobias, and M. Havenith, “Watching the low-frequency motions in aqueous salt solutions: the terahertz vibrational signatures of hydrated ions,” J. Am. Chem. Soc. 134(2), 1030–1035 (2012). [CrossRef]
50. Z. R. Kann and J. L. Skinner, “Low-frequency dynamics of aqueous alkali chloride solutions as probed by terahertz spectroscopy,” J. Chem. Phys. 144(23), 234501 (2016). [CrossRef]
51. M. J. Patterson, S. D. R. Galloway, and M. A. Nimmo, “Variations in regional sweat composition in normal human males,” Exp. Physiol. 85(6), 869–875 (2000). [CrossRef]
52. L. B. Baker, J. R. Stofan, H. C. Lukaski, and C. A. Horswill, “Exercise-induced trace mineral element concentration in regional versus whole-body wash-down sweat,” Int. J. Sport Nutr. Exerc. Metab. 21(3), 233–239 (2011). [CrossRef]
