Terahertz meta-biosensor for bovine serum albumin sensing based on electromagnetic-induced transparency-like effect

Introduction

Protein sensing is intimately linked to human health and plays an important role in the early detection of cancer markers (1) and in the diagnosis of various diseases. Bovine serum albumin (BSA), with a molecular weight of 66.5 kDa, is one of the most common and extensively utilized proteins in this field (2). Its structural similarity to human serum albumin has made it a widely used model protein (3). BSA is also pivotal in many biomedical applications, such as Bradford assays (4) to quantify protein concentrations in solutions. Additionally, BSA serves as an affordable and versatile blocking agent in bio-specific binding assays (5), preventing non-specific binding and ensuring accurate measurement of protein interactions. It is also used in enzymatic reactions to inhibit enzyme adsorption to surfaces (6). Given these versatile uses, the development of reliable methods for the detection and quantification of BSA is of great significance.

Electromagnetically induced transparency (EIT) is a quantum phenomenon observed in atomic systems, which produces a narrow transparency window through the destructive interference (7-9) between the atomic configurations and the incident electromagnetic field. However, the stringent requirements for experiments in atomic systems, including the necessity for extremely low operating temperatures and the stabilization of the pumping laser, impede its practical deployment (10). Metamaterials (MMs) are artificial structures composed of sub-wavelength building blocks called meta-atoms and can exhibit extraordinary characteristics unavailable in natural materials (11-13). MMs have attracted considerable interest within optical systems due to their capacity to readily mimic EIT-like behavior across a broad spectrum from microwave to ultraviolet frequencies, by simply tailoring the geometry and dimensions of meta-atoms (14,15). Typically, the EIT-like effect within an MM can be achieved through two coupling modes: the bright-dark mode and the bright-bright mode coupling (16-18). The bright mode is directly excited by the incident electromagnetic field, while the dark mode remains unexcited by it. In the first scheme, the transparency window is generated by the destructive interference between the bright and dark modes via near-field interaction. In the second, the EIT-like effect is accomplished by disrupting the overall symmetry of the structure through the frequency mismatch of two bright modes. Recent studies have focused on toroidal resonance excitations for creating transparency windows (19) and sharp dispersion at microwave frequencies due to their unique properties, such as low radiation loss and high sensitivity to minute biological changes. Toroidal excitation-induced EIT-like effects (20-22) in the terahertz (THz) regime offer narrower linewidths and higher-Q transparency windows than dipole-coupled systems and are therefore promising for sensitive chemical and biomolecular detection.

Terahertz waves occupy the electromagnetic spectrum at frequencies between 0.1 to 10 THz and wavelengths from 0.03 to 3 mm, and are recognized for their very low radiation energy (23). This characteristic makes THz waves highly compatible with biological tissues, as they pose no ionization risk, rendering them particularly suitable for biosensing applications (24-27). Moreover, THz waves exhibit exceptional properties, including strong penetrative capabilities and distinctive spectral fingerprints for various materials. These waves enable non-invasive, non-contact, label-free, and non-destructive detection of biomolecules, garnering considerable interest in biomedicine and clinical practice. Consequently, the exploration of EIT-like MM biosensing operating in the THz frequency range has emerged as a prominent research area. In 2019, Yan et al. demonstrated a THz biosensor based on EIT-like asymmetrical double-split ring resonators (28) to detect oral cancer cells (HSC3) with a maximum experimental sensitivity of 900 kHz/cell/mL. In the following year, Zhang et al. introduced a polarization-insensitive THz MM biosensor (29) that distinguished malignant glioma cells from wild-type counterparts by their water-content difference, with a sensitivity of 248.75 kHz/cell/mL. They also designed an EIT-like MMs sensor for lung cancer cells (A549) (30). This sensor’s amplitude changes were directly linked to cell concentrations and could detect with as few as 1.3 cells/mm². In 2023, Wang et al. engineered a polarization-insensitive THz MM for the detection of four cell types, including normal lung (BEAS-2B), lung cancer (NCI-H520), normal brain (HA), and astrocytoma (U-118MG) cells (31), which required significantly fewer cells and time than clinical assays. In 2024, Liang et al. combined gold nanoparticles with graphene to push the limit of detection (LOD) for aspartic acid down to 10.48 fg/mL (32). In 2025, Cong et al. developed a high-sensitivity flexible metasurface for terahertz-based breast cancer differentiation and the sensitivity reached 448 GHz/RIU (refractive index unit) (33). Wang et al. utilized a graphene-composite MM to achieve trace detection of midkine, reaching an LOD of 125 pg/mL. When combined with the signal-enhancing effect of gold nanoparticles, the LOD was further lowered to 10 pg/mL (34).

Overall, THz EIT-like MMs can be effectively applied in biosensing (35). However, most of the current research uses single-band EIT-like MMs, which can only detect a single resonance peak frequency shift. Studies on multi-band THz EIT-like MMs (36) are still primarily at the theoretical analysis and simulation verification stage. Additionally, existing research has mostly focused on cellular-level testing, with fewer studies on the detection of smaller analytes such as protein molecules. Therefore, there is an urgent need to design a multi-band THz EIT-like MM to verify its feasibility for BSA detection. This manuscript introduces a biosensor based on multi-band EIT-like MMs that exhibits high sensitivity within the range of 0.7 to 1.3 THz and has been successfully implemented for the detection of BSA, achieving a low LOD. The ability to detect BSA is a critical hallmark in biological and medical sciences.

In this study, a multi-band THz EIT-like MM biosensor based on quartz and gold is proposed. The meta-atoms consist of a C-shaped resonator, a toroidal resonator (37) and a D-shaped split resonator. The proposed MMs are named CTD (C-toroidal-D)-shaped MMs. Two transparency windows are generated by the coupling with adjacent structures. Both transparent peaks of the EIT-like MMs are sensitive to the refractive index of the samples on the MMs, reaching 222.6 and 257.8 GHz/RIU, respectively. Furthermore, the newly designed EIT-like MMs are used for the detection of BSA solution, with sensitivities of 14.43 and 18.98 GHz/(mg/mL) and LODs of 26.33 and 20.02 µg/mL for the two transparency peaks, respectively. These results indicate that this sensor holds promising prospects and significant potential for advancement in the field of biosensing.

Methods

Structural design

Figure 1A shows the schematic picture of the proposed CTD-shaped meta-biosensor and the specific structure of the meta-atom is shown in Figure 1B. The unit cell of the MM consists of three parts: the left ‘C’ shaped split ring resonator, the middle toroidal resonator with symmetric gaps on each arm, and the right ‘D’ shaped split ring resonator. The periodicity in x and y directions is given by Px=150 µm and Py=70 µm, respectively. The line width for all the patterns is designed as w=4 µm and the patterns are separated by d=10 µm from each other. The length of the left ‘C’ shaped resonator is L₂=26 µm and the size of the capacitive gap is g₂=21 µm. The length of the mid toroidal resonator is L₁=36 µm and the capacitive gaps are designed as g₁=4 µm. The right ‘D’ shaped resonator has an outer radius of r₁=17.5 µm and inner radius of r₂=13.5 µm. The size of the capacitive gap is designed as g₃=6 µm. The height in the y direction is Ly=35 µm. The specific parameters are listed in Table 1. The electromagnetic fields of the adjacent resonator couple with each other, leading to EIT-like effect. The substrate is 500 µm quartz with a permittivity of 3.75 and the metal layer is gold with a thickness of 200 nm.

Figure 1 Structural design. (A) Schematic picture of the biosensor. (B) Structure of the meta-atom.

The transmission spectra are modeled using CST Microwave Studio 2020 with finite element analysis. The geometry is constructed with parameters listed in Table 1. Electric (E) and magnetic (H) fields are set parallel to the incidence plane, with E parallel to the capacitive gap, and the wave vector (k) is set perpendicular to the MMs’ surface. Periodic boundaries are applied in the x and y axes, and open (add space) boundaries in the z-axis. An adaptive mesh is used to refine the simulation accuracy, and a frequency domain solver is used to calculate the S parameters of the proposed MMs. The frequency step is set as 500 MHz and the mesh convergence criteria is set as the default value of 10⁻³. During the simulation, the permittivity of quartz is set as 3.75 and the conductivity of the gold layer is set to 4.561×10⁷ S/m. The transmittance [T(ω)] of the MM can be calculated with the S₂₁ parameter (38), as expressed by Eq. [1]:

T(ω)=|S21|2[1]

Modes analysis

To gain a deeper understanding of the mechanism of the transparency window in the transmission spectra, we have conducted simulation studies on the individual resonators as well as on the combined structure after assembly. The transmission spectra and electric field profiles of the three individual resonators and combined structure are shown in Figure 2. As shown in Figure 2A,2B, the left C-shaped resonator has a resonant dip at 0.915 THz and the field is strongly confined to the split gap at the resonant frequency. Figure 2C shows the transmission of the mid toroidal resonator, which shows a resonance dip at 1.031 THz. The electric field profile of the mid toroidal resonator is shown in Figure 2D and the field is confined to the symmetric capacitive gaps. The transmission plot and electric field distribution of the right D-shaped resonator are shown in Figure 2E,2F. A resonance dip at 1.150 THz is observed and the field is confined to the split gap.

Figure 2 Working modes analysis of the CTD-shaped metamaterials. (A) Transmission spectrum of the left C-shaped resonator. (B) Electric field distribution at the resonance peak (0.9149 THz) of the left C-shaped resonator. (C) Transmission spectrum of the mid toroidal resonator. (D) Electric field distribution at 1.0309 THz of the mid toroidal resonator. (E) Transmission spectrum of the right D-shaped resonator. (F) Electric field distribution at 1.1498 THz of the right D-shaped resonator. (G) Transmission spectrum of the EIT-like MMs with the transparent window 1 marked by the red line. (H) Electric field distribution at the transparent window 1 (0.9729 THz). (I) Transmission spectrum of the EIT-like MMs with the transparent window 2 marked by the red line. (J) Electric field distribution at the transparent window 2 (1.1179 THz). CTD, C-toroidal-D; EIT, electromagnetically induced transparency; MM, metamaterial.

The transmission spectrum of the combined CTD-shaped MMs is shown in Figure 2G,2I. Three resonance dips (named D1, D2 and D3) and two resonance peaks (named as P1 and P2) are observed. The resonant frequency of the three resonance dips are 0.909, 1.037 and 1.176 THz, respectively, which correspond to the resonance dips of the three separate resonators mentioned above. Thus, the three resonators are excited by the incidence THz waves simultaneously in the CTD-shaped MMs and operating in the bright mode. By the interference from the adjacent resonator, two transparency windows appear, which correspond to the resonance peaks in the transmission line. The resonance frequency of the first transparency window is 0.973 THz and the electric field profile is shown in Figure 2H. The left resonator and mid resonator are excited strongly at 0.973 THz. Thus, the strong bright-bright mode near-field coupling between the left and mid resonators leads to the first transparency window at 0.973 THz. The second transparency window appears at 1.118 THz and the electric field profile is shown in Figure 2J. The middle and right resonators are excited, which leads to the appearance of the second transparency window. Hence, the multiband EIT-like windows at 0.973 and 1.118 THz are generated by the strong bright-bright near-field coupling between adjacent resonators (39,40).

Structure optimization

To acquire optimal performance of the CTD-shaped MMs, we scanned each structural parameter to obtain a set of transmission spectra. Then the variation of Q factor and resonance intensity with the variation of the pattern parameters is studied. Q factor (37) is defined as Eq. [2]:

Q=f0FWHM[2]

where f0 is the resonance frequency, FWHM is the full width at half maximum of the resonance peak or valley. Q factor represents the sharpness of the resonance peak. Higher Q factor leads to generally better sensing performance.

The resonance intensity ΔAmn is defined as Eq. [3] (41):

ΔAmn=Apeak_m−Adip_n[3]

where Apeak_m and Adip_n are the transmittance of the adjacent resonance peak and dip. The subscripts m and n are the number of the peak and dip respectively. ΔAmn represent the amplitude difference between the peak and dip, which is significant for practical applications.

Ly is the pattern length for all three resonators in y direction, which affects the performance of the MMs significantly. As shown in Figure 3A, the transmission spectrum varies with changes of Ly. Figure 3B shows the transmittance as a function of Ly and frequency. With the increase of Ly, the resonance frequency of all the dips and peaks decreases and the amplitude of all the dips and peaks decreases. To evaluate the variation of the spectrum accurately, we draw the variation of Q factors and ΔAmn as a function of Ly, as shown in Figure 3C,3D. With the increase of Ly, Q factor of D1, D2 decreases slightly and Q factor of P1, P2 increases slightly. The Q factor of D3 decreases from 74.8 to 33.8 dramatically when Ly is less than 35 µm and the variation becomes gentle when Ly is larger than 35 µm. Meanwhile, ΔA11, ΔA12, ΔA22 decrease slightly with the increase of Ly. ΔA23 increases from 0.536 to 0.653 when Ly increases from 30 to 35 µm and then decreases slightly when Ly is larger than 35 µm. Finally, Ly is optimized as 35 µm to acquire a larger ΔA23 and satisfactory Q factors for all dips and peaks at the same time. The influence from the other structure parameters is discussed in Figures S1-S4. The Q factor and ΔAmn are summarized in Tables 2,3 with the optimal parameters shown in Table 1. Q factors of the two transparency peaks are 11.2 and 10.7 respectively and resonance intensity between the peak and dip exceeds 0.65. The proposed CTD-shaped MM shows a great potential for biosensing.

Figure 3 Performance of CTD-shaped MM with different Ly. (A) Transmission spectrum with different Ly. (B) Dependence between ΔA and Ly. (C) Contour map of transmission spectrum and Ly. (D) Dependence between Q factor and Ly. CTD, C-toroidal-D; MM, metamaterial.

Sensing performance analysis

The sensing performance of the CTD-shaped meta-biosensor with the optimized parameters is simulated (30). Analyte layers with different thicknesses are added onto the MMs. The relative permeability (μr) is set to 1, as most biomolecules are non-magnetic. The complex relative permittivity is varied to simulate the dielectric properties of different analytes. The complex relative permittivity can be expressed as εr=ε′r+iε″, in which ε′r is the real part and ε″r is the imaginary part of permittivity. The refractive index (n) is related to the real part of the permittivity (ε′r) by equation n=μrε′r=ε′r. The dielectric dissipation factor (tanδ) can be expressed as tanδ=ε″ε′r, which is related to the real part and imaginary part simultaneously. Thus, the sensing performance of CTD-shaped MM under different dielectric properties can be characterized by varying n and tanδ of analytes.

Sensing performance affected by thickness

The resonance frequency and resonance intensity vary significantly with different analyte thicknesses (t_a), with n=1.3 and tanδ=0.02, as shown in Figure 4A. The variation of resonance frequency is defined as Δf=f0−ft, where f₀ is the resonance frequency for t_a =0 and f_t is the resonance frequency for other thicknesses. The relationship between Δf and t_a is shown in Figure 4B. The results show that the resonance frequency decreases with increasing thickness, along with a slowdown in increment rate. The variation reaches saturation when t_a exceeds 10 µm, which corresponds to the confinement length of the electric field. Furthermore, the relation between Δf and the thickness of analytes can be fitted by the exponential function: Δf=αe−βta+c, in which α, β and c are the fitting parameters. Fitting parameters of the three dips and two peaks are shown in Figure 4B. R² for all the fittings is larger than 0.99. Meanwhile, we study the relationship between Δf and t_a with different refractive index (n) and the results show that α is linear to refractive index, as shown in Figure S5A. Δf is affected by the thickness and refractive index of the analytes simultaneously, which corresponding to the amount and dielectric properties of the analytes, respectively. Similarly, the relationship between resonance intensity and analytes thickness is shown in Figure 4C. The results show that ΔA decreases with increasing thickness, along with a slowdown rate. Meanwhile, the results are fitted with the same exponential decay function as described hereinbefore and the fitting parameter α is linear to refractive index (as shown in Figure S5B), which indicates that ΔA will also be affected by the amount and dielectric properties of the analytes simultaneously in measurement process.

Figure 4 Sensing performance. (A) Transmission spectrum with different analytes’ thickness. (B) Relationship between frequency shift and analytes’ thickness. (C) Relationship between resonance intensity and analytes’ thickness. (D) Transmission spectrum with different analytes’ refractive index. (E) Relationship between frequency shift and analytes’ refractive index. (F) Relationship between resonance intensity and analytes’ refractive index. (G) Transmission spectrum with different dielectric dissipation factor. (H) Relationship between frequency shift and dielectric dissipation factor. (I) Relationship between resonance intensity and dielectric dissipation factor.

Sensing performance affected by refractive index

To evaluate the sensing performance of the MMs with the variation of the analyte’s refractive index, n varies from 1.0 to 2.0 with the condition that tanδ is 0.02 and thickness is 20 µm. As shown in Figure 4D, a significant frequency shift is obtained in the transmission spectra with the variation of the refractive index. The relation between Δf and n is illustrated in Figure 4E and fitted with a linear function. R² for all fits is greater than 0.99 and the good linearity is critical for biosensing. The slope of the fitting line is the sensitivity (defined as S=ΔfΔn) of the CTD-shaped MMs. The sensitivities of the three dips are calculated to be 204.3, 228.3, and 256.5 GHz/RIU and the sensitivities of two peaks are calculated to be 222.6 and 257.8 GHz/RIU, respectively, which shows the great potential of the proposed CTD-shaped MMs for biosensing. The resonance intensity varies slightly with the variation of refractive index. The relationship between ΔA and refractive index is plotted in Figure 4F. ΔA11, ΔA12, ΔA22 exhibit good linearity with refractive index. While the linearity between ΔA23 and n is poor. ΔA could be used as a supplementary method for biosensing.

Sensing performance affected by dielectric dissipation factor

To evaluate the sensing performance of the MMs with variations in the analytes’ dielectric dissipation factor, tanδ is varied from 0 to 0.1 with the condition that n is 1.3 and thickness is 20 µm. The transmission spectrum with different tanδ is illustrated in Figure 4G, which shows that the frequency shift Δf changes slightly while the resonant intensity varies significantly. As shown in Figure 4H, Δf changes by less than 16 GHz when tanδ varies from 0 to 0.1 and shows no significant correlation with tanδ. As shown in Figure 4I, ΔA exhibits a linear dependence on tanδ. Compared with thickness and refractive index, the dielectric dissipation factor is the most influential parameter affecting the transmission of the CTD-shaped MMs.

Results

The proposed patterns are fabricated on a 4-inch 500 µm-thick quartz substrate by projection step photolithography, as shown in Figure 5A. A layer of 10 nm Cr layer is deposited on the substrate by magnetron sputtering to enhance the adhesion between the Au layer and quartz. Then the MMs are cut into 1.5×1.5 cm² square chips with laser cutting technology for subsequent measurements. Figure 5B shows the optical image of the fabricated MMs and the processed pattern matches the design. Then the transmission spectrum is measured with the commercial THz time-domain system (Advantest AS7400TS). As shown in Figure 5C, the resonance frequencies show good consistency with the simulation results. The slight discrepancies between them are primarily due to the manufacturing errors. The resonance intensity is weaker compared with the simulated results, which means the THz waves absorption from the substrate is greater than that in the simulation process.

Figure 5 Fabrication and measuring process. (A) Fabrication process. (B) Optical microscopy image of the fabricated metamaterials. Inset: enlarged view of the unit cell. (C) Simulated (black curve) and measured (red curve) transmittance spectra. (D) Measuring process for the samples.

Then the fabricated THz CTD-shaped EIT-like MMs are used for the measurement of BSA solution with different concentrations. The measuring process is illustrated in Figure 5D. Firstly, 100 µL of solution is dropped on the surface of MMs with pipette and then dried in an oven at 50 ℃ for approximately 20 min. Then the transmission spectrum of the MMs with BSA film is measured with the THz time-domain system. Each concentration is tested with 4 different MMs to reduce the accidental error, and the mean value for the 4 tests is used as the final results. To minimize the impact of air humidity on the test results, nitrogen was passed through the testing system, maintaining air humidity below 5% during the testing process.

The measured results of BSA solutions with concentration from 0 to 6 mg/mL are shown in Figure 6. As shown in Figure 6A, it is observed that, as the BSA concentration increases, there is a consistent shift of the transmission spectrum’s transparency peaks towards lower frequencies, aligning with the predictions of the simulation. The resonance intensity also decreases with the increase of the BSA concentration. When the BSA concentration exceeds 6 mg/mL, the resonance intensity is too weak to determine the transparency peak exactly. This could be due to the fact that when the concentration exceeds 6 mg/mL, the excessive BSA molecules lead to greater absorption of the terahertz waves. The frequencies of the two transparency peaks shifted by 94.46 and 119.44 GHz, respectively, with the BSA concentration changing from 0 to 6 mg/mL. The relationship between transparency peak shifts and BSA concentration is fitted with a linear function, as shown in Figure 6B. Sensitivities for measuring BSA solution of P1 and P2 are 14.43 and 18.98 GHz/(mg/mL), respectively. LOD can be calculated from the resolution (42) with Eq. [4]:

LOD=ResolutionS[4]

Figure 6 Measuring results of BSA solutions with different concentration. (A) Transmittance spectrum with dashed lines marking the position of P1 and P2. (B) Resonance peak shift. (C) Resonance intensity for different BSA concentration. BSA, bovine serum albumin.

With the high-frequency-resolution option enabled, the system spectral resolution is 380 MHz (43). The LOD for the fabricated CTD-shaped THz EIT-like MM biosensor is calculated to be 26.33 and 20.02 µg/mL for the two transparency peaks respectively. Table 4 displays findings from other research employing MMs for BSA detection in the THz range.

Discussion

Compared to other studies, the sensitivity achieved in this study is higher and the LOD is lower, indicating the sensor’s efficient application in biosensing. With the increase in the spectral resolution of the THz time-domain system, a lower LOD will be acquired. Meanwhile, results of three dips can also be used for the measurement of BSA solutions, as shown in Figure S6. However, the resonance intensities have a large test error and show a weak linear relationship with BSA concentration, as shown in Figure 6C. It is hard to use the resonance intensity for the quantitative calculation, but it can still be used as a supplementary parameter for qualitative analysis.

The thickness of the analyte is the primary factor influencing the EIT-like phenomenon discussed in this paper. In the absence of an analyte layer, there is an increased concentration of electromagnetic-field intensity at the grooves and at the boundary between the device and the air. When a layer of analyte coats the MM structure, the enhanced resonant electric field is further compressed within a reduced spatial area along the direction of wave incidence, causing a larger proportion of the field to be trapped within the grooves. Simultaneously, the presence of the analyte layer alters the resonance frequencies. As the thickness of the analyte builds up, an increasing fraction of the resonant field is distributed within the analyte layer, which has a higher refractive index than air, leading to a red shift of the resonance frequencies. In this experiment, varying concentrations of BSA solutions contain different amounts of solute, leading to a variation in the mass of BSA per given volume of solution. Thus, the variation in solution concentrations translates to disparities in analyte thickness, which in turn causes a shift in the frequency of the transparency peak.

Conclusions

In this study, we propose a CTD-shaped EIT-like MM with two transparency windows in the THz region through coupling between adjacent resonators. Using simulation, the sensitivity is calculated to be 222.6 and 257.8 GHz/RIU for P1 and P2. The resonance intensity also shows a linear relationship with the refractive index. Then the MM is fabricated for BSA solution sensing. The sensitivity reaches 14.43 and 18.98 GHz/(mg/mL) and the LOD is as low as 26.33 and 20.02 µg/mL, respectively for P1 and P2 over the 0–6 mg/mL concentration range. Meanwhile, the resonance intensity can be used as a supplementary parameter for qualitative analysis. In terms of sensitivity, our device outperforms THz sensors based on the quasi-bound states in the continuum effect by 17% higher, and the theoretical LOD is even lower. The designed CTD-shaped EIT-like MM biosensor shows great potential for biological detection with good linearity and has the ability for detecting trace number of substances. It shows considerable promise for disease diagnosis, cancer marker identification, and biological specimen examination.

Acknowledgments

None.

Footnote

Data Sharing Statement: Available at https://qims.amegroups.com/article/view/10.21037/qims-2024-2574/dss

Funding: This study was supported by the Academic Promotion Program of Shandong First Medical University (grant number 2019QL009), Science, Technology funding from Jinan (grant number 2020GXRC018), Natural Science Foundation of Shandong Province (grant number ZR2022QA034), and Talent Introduction Project of Shandong First Medical University (grant number YS23-0000041).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-2024-2574/coif). The authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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