1. Introduction

In the last three decades, terahertz radiation has met a wide set of applications. The field is growing rapidly thanks to a very active scientific community [1–4]. In particular, many review articles have remarked the importance and impact of terahertz technology for biological and medical applications [5–14]. Most of these research aims to determine the water content of a sample, using the results to draw further conclusions regarding its biological state. The water content is measured by calculating the dielectric function of the sample and using effective medium theory to quantify the volume of water within a sample. For instance, excised cancerous tissue exhibits clear contrast to healthy one because of its higher water content and higher values of the dielectric function [15,16]. In-vivo applications of skin measurements have also shown how changes on the dielectric function can be used to study different conditions, such as diabetic foot [17], burn severity [18,19] or scar treatment [20]. In the biological field, measuring the state of hydration of plant leaves through the dielectric function has also led to understanding important biological behaviour such as responses to light or drought stress [21–25].

Biological systems are in general heterogeneous in nature. In the THz band, they can be studied as a mixture of different materials modeled with effective medium theory. In these models, the dielectric function is calculated using the volumetric fractions and the individual dielectric properties of the sample components [26,27]. For example, the Landau-Lifschitz-Looyenga model, which is commonly used for THz analysis, assumes a non-linear superposition of the dielectric functions of the components that gives the dielectric function of the mixed hydrated tissue. With this model, a biological sample is most commonly assumed as a composition of water, dehydrated material and air. In materials such as skin, which have higher density in the dehydrated part, the air contribution can be sometimes neglected. In most of such studies, the temperature dependent dielectric function of water is obtained from a well established Double-Debye model [28], while the dielectric function of dried tissue is experimentally characterized, usually at room temperature, neglecting any influences of the temperature. As THz technology targets and gets closer to clinical applications, it is important to analyze all the variables that may give possible measurement deviations, temperature being one of them. As mentioned earlier, dehydrated samples are usually characterized at room temperature, however, many living organisms, including humans, regulate their own temperature. This means that individuals may present different body temperatures and even change their own temperature during a diagnostic test procedure. Therefore, it is important to know how the non-water component of a tissue may change its dielectric function for different temperatures. Here, we investigate the possible temperature dependence of the dielectric function for various dehydrated biological samples of different nature and discuss the implication of the results for the biological applications of THz technology. Our main objective is to provide evidence that there is a non-negligible dependence of the dielectric function of the non-water part of the tissue, but by no means to provide quantitative rule that is generally applicable to tissues, since each particular dehydrated tissue will have to be characterized in future studies accordingly.

2. Materials and methods

2.1 Biological samples

We considered the analysis of three biological samples from different organism classifications in our study as shown in Fig. 1(a). The first sample was porcine skin tissue, which is an accepted model of human skin [29,30]. The second sample was an oak leaf (Quercus robur) and the last one was a mushroom sample (Agaricus bisporus). Tissue samples were put first into a Formaldehyde-solution for 24 hours to avoid cellular decomposition and retain their original structure [31,32]. After this, the samples were dehydrated using ethanol baths ranging from 20 to 60 min, depending on their thickness. The main dehydration process included successively increasing ethanol concentrations in the order: 70%, 80%, 90%, 95%, and 100%. After the 100% concentration bath, we dried the samples in the oven at 40°C for at least 24 h to ensure no ethanol is left for THz measurements and to reassure the dehydration status.

 

Fig. 1. (a) Biological samples from different organism classifications after dehydration process. The samples are (from left to right) oak leaf (Quercus robur), brown mushroom (Agaricus bisporus) and porcine skin tissue. (b) Design of the heat chamber (height × width × depth = 10.5 × 12.5 × 3.0 cm with 1.0 cm wall thickness). $V_0$ indicates the voltage supply, R are the resistors, H is the sample holder, M indicates linear movement for sample (red) and reference (green) focus P of the THz beam. (c) Schematically representation of the terahertz time-domain transmission set-up used for the measurement series.

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2.2 Temperature controlled chamber

During the spectroscopic measurements, the samples were placed in a self-designed and constructed temperature-controlled chamber to study the possible temperature dependence of their dielectric properties as shown in Fig. 1(b). The chamber was designed to regulate temperatures between room temperature ($\sim$20°C) and 40°C. For this purpose, two resistors (R) were attached to the aluminum housing forming the main heating system. The resistors temperatures were regulated proportionally to an applied electrical voltage ($V_0$). An Arduino ONE micro-controller monitored the temperature in the chamber and controlled the current flowing through the resistors. The temperature data was continuously acquired with a thermistor (T) placed near the sample. The resistors were turned on or off by switching a relay after comparing the measured to the target temperature. To ensure that the sample itself holds the target temperature, the target temperature was kept constant for a few minutes to guarantee thermal equilibrium of the chamber and the sample. To keep the heat inside the chamber and to allow the penetration of both THz radiation and nitrogen into the cavity, each side was covered by a window made of thin plastic foil.

2.3 THz time-domain measurements

We used the previously described cavity in combination with a standard transmission terahertz time-domain spectrometer as shown in Fig. 1(c). Terahertz radiation was created and detected by overlapping femtosecond laser pulses together with an external electrical DC signal on two photoconductive antennae with 2 THz bandwidth. The heat chamber was mounted on a translation stage allowing us to acquire sample and reference signals by linearly moving the unit (M) to reference ($P_{Ref}$) and sample ($P_{Sam}$) positions as shown in Fig. 1(b). By choosing to place the reference measurement ($P_{Ref}$) inside the cavity, the influences from the plastic foil and the current environmental conditions could be compensated for. The measurements were made under nitrogen atmosphere to improve the signal-to-noise ratio (SNR) and avoid the spectral features of water vapour.

The complex refractive index $\tilde {n}(\omega )$ and the dielectric function $\epsilon (\omega )$ were related through $\epsilon (\omega )=\tilde {n}^2$, where $\tilde {n}(\omega )=n(\omega )+i\kappa (\omega )$, with $n(\omega )$ the refractive index and $\kappa (\omega )$ the extinction coefficient. These were calculated using the Fourier transforms of the measured electric field waveforms for reference and sample ($\tilde {T}(\omega )=\tilde {E}_{\mathrm{sam}}(\omega )/\tilde {E}_{\mathrm{ref}}(\omega )$) and the theoretical Fresnel transmission ($\tilde {T}=t_{12}(\omega )t_{21}(\omega )e^{i\frac {d\omega }{c}(\tilde {n}(\omega )-1)}$). From this,

For each biological specimen type, the dielectric function was analyzed under temperature conditions of 20°C, 22.5°C, 27.5°C, 32.5°C, and 36.5°C. Five samples for each kind of tissue where used and measured independently, the error bars shown in the plots represent the standard deviation of the five measurements. We limited our analysis to the frequency interval of 0.2 THz to 1 THz, where the signal-to-noise ratio of our set-up is highest.

3. Results and discussion

The real and imaginary parts of the dielectric functions of dehydrated samples of porcine skin, oak leaf and mushroom are shown in Fig. 2.(a)-(c), respectively, for a temperature interval from 20°C to 36.5°C as we show, together with additional parameters, in Dataset 1, (Ref. [33]) Dataset 2, (Ref. [34]) and Dataset 3, (Ref. [35]). Notice that all spectra show a soft and continuous shape, without prominent features. When we compare the actual values for porcine skin, oak leaf and mushroom samples, we see large differences among them, which we believe, may be mostly attributed to their different densities with values of 998$\pm$20 kg/m$^3$, 544$\pm$70 kg/m$^3$, and 359$\pm$60 kg/m$^3$, respectively. These density values were measured directly from our samples. As a point of comparison, the dielectric function of water from the Double-Debye model is shown in Fig. 2(d), depicting a much more pronounced dependence with temperature. The dielectric function at 500 GHz for the temperature intervals, as well as a linear fit are shown in Fig. 3. The slope of the linear fit gives the rate of change of the dielectric function with respect to temperature. The slope values for each fit are shown in Table 1.

 

Fig. 2. Real and imaginary parts of the dielectric function of dehydrated (a) porcine skin, (b) oak leaf, (c) brown mushroom and (d) water for different temperatures in a frequency range of 0.2 THz to 1 THz.

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Fig. 3. Changes of the real part (left column) and the imaginary part (right column) of the dielectric function at 500 GHz for dehydrated (a) porcine skin, (b) oak leaf, (c) brown mushroom and (d) water.

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Table 1. Change of real and imaginary parts of the dielectric function with respect to temperature for the bio-samples and water. The values are the slopes of the linear fits presented in Fig. 3. The last column shows the densities of the biological tissues calculated for each tissue type, determined by measuring the volume and mass for each sample.

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Until now, most THz analyses of biological samples had assumed that the dielectric function of dry tissue would have little or no temperature dependence. This assumption implies that any temperature dependence would be attributed only to the dielectric function of water. From the results shown in Fig. 3(a)-(d), it can be seen that the change in dielectric function for the dehydrated tissues is less than that of water at 500 GHz, yet not entirely negligible. Furthermore, while changes of the imaginary part of the dielectric function of water are higher at lower frequencies, the changes in the tissue samples appear to be less frequency-dependent.

The results confirm that temperature changes on the dielectric function of dehydrated samples should be taken into account in order to improve the accuracy of the results. While we do not think that qualitative behaviour inferred from previous studies or their general conclusions would be significantly different, the accuracy of the quantitative part of some of them might need to be re-discussed. The experiment was performed with animal, vegetative and fungal tissues, covering a variety of tissue types of potential interest for future THz biological and biomedical applications.

4. Conclusions

We characterized the dielectric function of dehydrated samples of pig skin, plant leaves and mushroom under different temperatures. Our results confirm that changes on the dielectric function of dehydrated biological samples are smaller than that of water but not always negligible, an example is porcine skin, which shows a significant effect. This implies that biological and biomedical samples might need to take this into account in order to be trustfully modeled through effective medium theory.