1. Introduction

Blood is a critical body fluid and THz wave interaction with blood has recently been addressed in several studies [1–4]. To date, blood has always been studied ex- vivo [1–4], and it is essential to develop a THz system to investigate blood in vivo for future non-invasive imaging and sensing applications. Because fresh tissues have high absorption to THz waves and the skin penetration depth of THz waves in fresh tissue is less than 0.2 mm (absorption coefficient α: ~70 cm⁻¹ at 300 GHz V.S. to ~170 cm⁻¹ at 1 THz [5–10]), it is thus more desirable to investigate blood in vivo by using lower sub-THz waves with a frequency near 300 GHz for higher penetration capability. In this study, the THz signal transmitted through the vessel rather than the signal reflected from the skin surface was received, due to the fact that most reflected signals were dominated by the response on the very surface of the tissue (within skin depth) rather than from more deeply buried vessels. Transmission imaging is also easier for quantitative analysis. We chose mouse ears as our living tissue samples for their thinness (< 0.3 mm) and visible vessel locations, which make verification and further numerical studies easier. However, the vessel diameters in the mice ears are mostly less than 0.22 mm, smaller than the wavelength of lower sub-THz waves (1 mm wavelength at 300 GHz). Therefore, to image vessels with a sub-wavelength diameter, a near-field imaging technique must be applied.

Near-field sub-THz and THz imaging systems have been in use for over a decade for various applications ranging from semiconductor inspection to biomedical imaging [5,6,11–17]. However, none of the previously demonstrated near-field systems were ever applied in vivo for THz transmission imaging. As long as the living object is not moved, direct near-field illumination or detection with a sub-wavelength aperture should be one of the most reasonable approaches. With this approach, one can choose to shrink the source- or the detector-aperture to a sub-wavelength size and place it very close to or in contact with the object to be imaged [15–17]. Several previous reports applied this approach with THz time-domain spectroscopic (THz-TDS) systems because the optical generation or detection spot served as the sub-wavelength aperture, and the image resolution was thus much improved [15–17].

In this paper, we demonstrate a sub-THz in vivo near-field system for vessel imaging by adopting wave-guided illumination and near-field scanning detection with a sub-wavelength aperture. The frequency of continuous-wave (CW) generation from the Gunn-oscillator-based source was 340 GHz. This frequency was chosen for higher penetration and higher signal-to-noise-ratio (SNR) of the THz transmission images. In addition, from previous reports, no characteristic frequency for THz power absorption or transmission was found in either tissues or blood in the frequency region less than 1 THz [1–10]. This frequency is much higher than that applied in a previously reported THz in vivo transmission imaging system (~120 GHz) [7], and thus much improved image resolution can be achieved for vessel imaging. The THz power was detected by a waveguide-based detector with a sub-wavelength-sized aperture. Our samples were the ears of living nude mice with thickness of around 0.27 mm and blood vessels with a diameter of less than 0.21 mm buried inside. The distance between the tissue surface and the detector aperture was kept near to or less than 0.2 mm, which is shorter than 1/4 of the wavelength and was comparable to the vessel diameter. Applying this transmission imaging setup, nearby blood vessels could be clearly resolved in our THz images, with a lateral resolution of around 0.5 mm. The characteristic of the near-field measured power transmittance, variance of different dielectric parameters of the tissues and blood vessels, is also discussed with the help of finite-difference time-domain (FDTD) numerical simulation [18] in this work. The numerically simulated curves were found to have good correspondence to the measured results. The capability of the system for in vivo long-term monitoring was also demonstrated. The proposed THz system has potential applicability to non-invasive blood examination and monitoring in the future.

2. System setup

Our CW THz wave was generated from a Gunn oscillator module (80-106 GHz; J. E. Carlstrom, combined with two doublers WR5.1 x2 and WR2.8 x2; Virginia Diodes Inc.), which was done with mechanical adjustment of a coaxial cavity to control the resonant frequencies [19]. The generated frequency range was from 320 to 420 GHz, and the operating frequency was set at 340 GHz (wavelength λ = 0.88 mm) for the highest radiating power. The radiated THz wave was collected by two 2-inch parabolic mirrors and coupled into an air-core glass pipe waveguide with 30-cm length, 9-mm inner diameter, and 2-mm glass cladding thickness [20,21]. The glass-pipe waveguide was measured to have a low guiding loss (0.001 mm⁻¹) and low wave divergence (equivalent NA of 0.0279, ~88.4° normal to the cladding) at 340 GHz. The guided mode in the pipe waveguide was dominantly the HE₁₁ (Gaussian-like) mode with a 3.5-mm beam waist [20,21]. The power density on the surface of the mouse ear was about 5 W/m² (the safe value according to the IEEE standard is up to 100W/m² [22]). The transmitted THz power was detected by a Schottky diode detector (Virginia Diodes, Inc.; response time < 5 μs) operated at room temperature and mounted with a 1-cm-long WR-2.8 rectangular metallic waveguide with an aperture size of 0.7 mm (0.8λ) x 0.35 mm (0.4λ). The single guiding mode in this most common commercial waveguide is the TE₁₀ mode [23], of which the electric field has a polarization direction perpendicular to the longer side of the waveguide aperture and has a cosine field distribution along the longer side and a uniform field distribution along the shorter side of the waveguide. The detector was mounted to a computer-controlled 3-axis stage. During imaging, the detector was mostly scanned at 0.1-mm scanning steps. With this scanning rate, one 8-mm x 8-mm image could be obtained within 8 minutes, and one 4-mm x 2-mm image could be obtained within 1 minute. Configuration of the in vivo THz near-field transmission imaging system is shown in Fig. 1. Without positioning any test object between the end of the pipe waveguide and the detector aperture, the radiated HE₁₁ mode size expects no variation within a detection distance d_f = 2D²∕λ ~18 cm [24] away from the pipe-waveguide end, where D is the inner diameter of the pipe. A directly scanned image of the power pattern of the wave-guided mode, with a detection distance d of ~0.5 mm from the pipe-waveguide end to the WR-2.8 aperture, is shown in Fig. 2(a). To increase the SNR of the system, a lock-in amplifier (SR830, Stanford Research Systems) was applied. With a 230-Hz chopping frequency and a 10-ms time constant of the lock-in amplifier, the SNR at the center of the image was 1000. The cross-section through the central part of the measured pattern is shown in Fig. 2(b) as a blue solid curve. Comparison with a Gaussian fit (red dashed line) showed that the measured power cross-section was close to a Gaussian profile having a 3.5-mm beam waist.

 

Fig. 1 Configuration of the in vivo THz near-field transmission imaging system.

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Fig. 2 (a) The measured HE₁₁ mode power pattern by the metallic WR-2.8 rectangular waveguide with a detection distance d of ~0.5 mm from the pipe-waveguide end. (b) Cross-section through the central part of the pattern shown in (a). The red dashed line is a Gaussian curve having a 3.5-mm beam waist.

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For transmission vessel imaging, hairless nude mice were selected (BALB/c-nude males aged from 7 weeks old). Before we scanned the mouse ear, each mouse was anesthetized with avertin (2.5 g 2-2-2 tribromoethanol and 5 ml 2-methyl-2-butanol added in 200 ml DI water). The avertin was injected intraperitoneally at a dose of with 0.4 ml/20 g body weight. The anesthetization time lasted around 50 minutes, and during this time more than three THz images of the mouse ear could be obtained. All animal experiments were approved by the Institutional Animal Care and Use Committee (IACUC) of National Taiwan University, Taipei, Taiwan. During the experiments, mouse ears were stabilized at the end of the glass pipe waveguide, sandwiched between the glass-pipe waveguide and a hollowed 0.1-mm-thick plastic slide with a hollowed window size of 0.8 mm x 0.6 mm. The thickness of the mouse ears was measured by a micrometer (Mituyoto Digimatic) with a resolution of 0.001 mm and was found to be between 0.22 to 0.27 mm from the edge to the center of the ear. Because the thickness of the whole ear was not uniform, the surface of the skin was not perfectly flat but slightly curved when it was sandwiched between the waveguide end and the plastic slide. The WR-2.8 power detector was placed 0.1 mm behind the plastic slide, and the distance between the detector and skin surface was controlled by an actuator with 0.01-mm resolution, as shown in the schematic diagram in Fig. 3. From Fig. 3, the distance between the detector and the skin surface was equal to or less than 0.2 mm, with −0.05-mm variation at most. This distance was shorter than 1/4 of the wavelength and was comparable to the vessel diameter (< 0.21 mm). The diameters of the vessels and the intervals (distance) between the vessels were measured with a USB camera (UPMOST UPG621) during each experiment (an example is shown in Fig. 4(a)), and the images obtained with a visible-light microscope (Leica DM500) were used to check the vessel distributions in detail (Fig. 4(b)). The image resolution of the Leica DM500 microscope was better than 0.001 mm, and the resolution of the UPMOST camera was around 0.005 mm (1600 pixels/ 8.7 mm).

 

Fig. 3 Schematic diagram showing the distance relation between the detector metallic waveguide and the skin surface.

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Fig. 4 (a) Photograph of the ear of a nude mouse taken by the USB camera. The blue line indicates the interval (distance) between two neighboring vessels. (b) Photomicrograph taken by a Leica DM500 visible- light microscope. The blue line indicates the average diameter of the vessel.

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When the polarization direction was parallel to the extension direction of the vessel, as shown in Fig. 5(a), the cross-section of the power transmittance through the vessel was scanned by the longer side of the waveguide. When the polarization direction was perpendicular to the extension direction, as shown in Fig. 5(b), the cross-section of the power transmittance through the vessel was scanned by the shorter side of the waveguide (0.35-mm width). When the cross-section was scanned by the longer side of the rectangular waveguide aperture (0.7-mm width), the wider aperture width would decrease the imaging resolution. Therefore, in our experimental setup, the vessel extension direction was set quasi-perpendicular to the polarization direction of the THz wave, as in case (b), which was, however, determined by the radiation source and the waveguide.

 

Fig. 5 (a) Schematic diagram of the two polarization directions of the transmitting field with profile scanning by (a) the longer side and (b) the shorter side of the waveguide. The arrows show the polarization direction of the electric field. The red pipe represents the blood vessel.

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3. Result and discussion

3.1 THz imaging in vivo

Figures 6(a)-(h) show two example sets of in vivo THz near-field transmission images of mouse ears. The vessels positioned near the center of the pipe waveguide having higher power radiation were chosen for investigation. The imaging areas of Fig. 6(a) and 6(e) were around 6 mm² and 8 mm² respectively, and the corresponding image acquisition time were around 45 seconds and 1 minute. Figure 6(a) and 6(e) are the ear photographs taken by the USB camera, and Fig. 6(b) and 6(f) are the corresponding in vivo THz near field images showing the power transmittance having the definition of P_ear/P_{without_ear}, where P_{without_ear} is the received power without the mouse ear placed at the waveguide end, and P_ear is the received power with the mouse ear placed at the waveguide end. From Fig. 6(b) and 6(f), the SNR of the system after the mouse ears was within 10 and 50. From the near-field images one can easily find that vessels had much lower THz transmission than the surrounding tissues so that the locations of the transmission dips are overlapped with or are very close to the central locations of the thick vessels (> 0.17 mm) shown in Fig. 6(a) and 6(e). Here, we focus our analysis on the in vivo THz near-field images of two quasi-parallel vessels. Figure 6(c) and 6(g) show the normalized near-field images after normalization to the transmittance peak average between two parallel vessels. The normalized dip values in the vessel areas were less than 0.7, showing the much stronger THz absorption in blood than in tissues. Figure 6(d) and 6(h) show the normalized transmission cross-section through the nearby vessels marked in Fig. 6(c) and 6(g). The observed transition width from the transmittance peak to the dip, which also equals the full-width half-minimum (FWHM) of the transmittance dip cross-section, represents the upper bounds of the lateral resolution of our system. Our measured FWHM widths of the vessel transmission dip were around 0.5 mm, as exampled by Fig. 6(d) and 6(h). This 0.5-mm lateral resolution is a bit wider than the diffraction limit of λ/2 (0.44 mm) [24] and is already high enough to clearly resolve neighboring vessels, as illustrated in Fig. 6. In reference to the diffraction theory [24], as the gap between the vessel edge and the detector aperture decreases, or as the effective wavelength decreases, the transition width can be shorter. Thus, for example, the image resolution can be further improved by positioning the detector even closer to the skin surface. In comparing our in vivo results with those of other existing THz near-field systems demonstrating ex vivo imaging [5,6,25–27], the highest ex vivo image resolution reached was around 0.3 mm with a shallow penetration depth of 0.02 mm [5,6]. Of the previously reported in vivo THz imaging systems, none showed a lateral image resolution of better than 1 mm [7, 26–28].

 

Fig. 6 Two examples of the in vivo transmission near-field images of mouse ears. (a) and (e): Optical images taken by the USB camera. (b) and (f): Original THz near-field images showing measured transmittance. (c) and (g): Normalized transmission images with the measured transmittance normalized to the transmittance peak located between two vessel transmission dips. (d) and (h): Normalized transmission cross-section through the locations marked with arrows in (c) and (g). The scale of the distance in the optical images (a), (d), and the transmittance scale bar of the THz images (b), (c), (e), and (f) are all provided.

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The normalized values of the transmission dips shown in Fig. 6(d) and 6(h) are related to the vessel diameter and the relative dielectric properties of the blood and tissues. By closely examining the absolute values of the near-field images, one might possibly monitor the THz dielectric properties, especially the relative changes of the absorption constants, not just qualitatively but also quantitatively. Here, we focus on numerically investigating the transmittance curve variance with different dielectric properties while the vessel diameter was monitored and measured with the help of high-resolution optical microscopy. According to previous reports [29,30], mouse ear tissue is comprised of epidermis, the outermost portion of the skin composed mainly of keratinocytes; dermis, which is largely composed of fibroblasts and connective tissues; fatty tissue; and cartilage, which forms the structural support for the ear. The absorption coefficient of human fibrous tissue near 340 GHz was reported to be around 80 cm⁻¹ [6,10], and that of fatty tissue near 340 GHz was around 30 cm⁻¹ [6,10]. The absorption coefficients of human cartilage with different water contents were observed to range from 20 to 80 cm⁻¹ at 340 GHz [9]. The refractive index of human fibrous tissue near 340 GHz was found to be around 2.2 [10], that of fatty tissue near 340 GHz to be around 1.55 [10], and that of human cartilage with different water contents to be around 2.5 at 340 GHz [9]. In the ex vivo blood of humans and rats with anticoagulant added, the absorption coefficients at 340 GHz range between 105 and 135 cm⁻¹ [1–4], and the refractive index ranges between 2.3 and 2.7 [1–4]. Because blood has a higher water content than the surrounding tissue, the effective refractive index of the total surrounding tissue is not likely to be higher than the refractive index of blood. On the basis of these reports, we assumed in our experiments that the effective refractive index of the surrounding tissue was equivalent to or lower than that of blood. We further assumed the absorption coefficient of blood at 340 GHz to be between 105 and 135 cm⁻¹, and the effective absorption coefficient of the surrounding tissues to be between 20 and 80 cm⁻¹.

3.2 Simulation

We performed a numerical investigation by adopting a simple FDTD method using Rsoft FullWAVE software (Synopsys, Inc.). The simulated wavelength equaled 0.88mm (340 GHz), and the calculating grid size was 0.005 mm x 0.005 mm. As shown in Fig. 5, we placed the simulated blood vessel with the extension direction perpendicular to the polarization direction. Figure 7 schematically illustrates the vessel distributions, extension directions, and the polarization direction of the THz wave set in the numerical simulation. The simulated ear thickness was 0.27 mm. The vessel was wrapped at the very center of the tissue, which means that the distances from the center of the cylindrical vessel to the two sides of the skin surface were equal. Because the power distribution is uniform in the y direction, as shown in Fig. 7, the transmittance cross-section was simulated only in the x-z plane. The detecting plane was set 0.2 mm behind the tissue bottom surface. The simulation range in the x direction equaled 4 mm, with two parallel vessels set in the layout. The vessel diameter and vessel interval (the distance from vessel center to vessel center) adopted were based on the measured values in the optical images as shown in Fig. 6(a) and 6(e). The refractive indices and the absorption coefficients were set referring to the values discussed above [1–9]. Because we had only power transmittance information as a function of position in our real experiment and these dielectric parameters could not be obtained exactly, in our simulation, we were primarily concerned with the normalized transmittance curves across the vessels in our detection plane. Similarly, in our simulation we were also concerned with the relative dielectric property differences between blood and its surrounding tissues.

 

Fig. 7 Schematic illustration of the vessel distributions, extension directions, and polarization direction of the THz wave set in the numerical simulation.

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3.3 Comparisons between the simulated and measured curves

Figure 8(a) and 8(b) show the comparison between the measured (red curves) and simulated (black curves) cross-sections of the normalized transmittance. In Fig. 8(a) and 8(b) the measured experimental curves are those for the images shown in Fig. 6(d) and 6(h). The vessel diameter and vessel interval in the simulation were set according to the measured values shown in Fig. 6(a) and 6(e). We first set the refractive indices of both the blood (n_blood) and of the tissue (n_tissue) as 2.4, which is within the reported region. The absorption coefficient of blood (α_blood) was first set as 120 cm⁻¹, which is in the middle of the reported range, and we observed that while the absorption coefficient of tissue was set as 40 cm⁻¹ (α_tissue), which is 80 cm⁻¹ lower than the value of blood, the normalized simulated (red) curve matched better with the normalized measured (black) curve. It is important to note the observable discrepancies between the numerical simulation and the experimental data. This discrepancy should be attributed to the over-simplified model shown in Fig. 7, which neglects the extremely complicated situations in real ear tissues, including the non-circular vessel shape, non-straight vessel extension direction, and the non-uniform tissue parameters, that could not be exactly simulated. However our simplified model is able to provide the best fit to the experimental data so as to retrieve the effective value quantitatively.

 

Fig. 8 Comparison between the measured and simulated cross-sections normalized to the tissue transmittance. The red curves are the normalized transmittance from the images shown in Fig. 6(c) and 6(g). The black curves are the FDTD simulated normalized transmittance cross-sections with n_tissue, n_blood, α_tissue, and α_blood equal to 2.4, 2.4, 40 cm⁻¹, and 120 cm⁻¹, respectively. The vessel diameter and the vessel interval (distance from vessel center to vessel center) adopted were based on the measured values in the optical images shown in Fig. 6(a) and 6(e). (a): The same case as in Fig. 6(c). (b): The same case as in Fig. 6(g).

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Results of our investigation to determine whether the range of dielectric parameters fit our data to the same degree are summarized in Fig. 9. As we decreased n_tissue (n_tissue is lower than n_blood), the normalized dip value increased (the difference between the peak and dip values decreased) because with lower n_tissue, the effective diameter of the vessel to the wavelength becomes shorter, and more constructive interference would occur behind the vessels. In this situation, to fit the measured curve, the difference between α_blood and α_tissue needs to be further increased. In Fig. 9 we show 4 simulated curves that all fit our image well. By fixing the blood parameters n_blood and α_blood equivalent to 2.4 and 120 cm⁻¹, blue, green, and red curves show three almost overlapping fittings having n_tissue and α_tissue equivalent to 2.4 and 40 cm⁻¹, 2.3 and 30 cm⁻¹, and 2.2 and 20 cm⁻¹, respectively. By setting the absorption coefficient difference between the blood and tissue to the upper bound of 115 cm⁻¹, where α_blood was set as 135 cm⁻¹ and α_tissue was set as 20 cm⁻¹, we found that to match the measured curve, n_blood could be set at most only 0.3 higher than n_tissue . The corresponding fitting with n_blood set as 2.5 and n_tissue set as 2.2 is shown as the pink curve in Fig. 9. This result indicates a small difference in the refractive index (at most 0.3, when the absorption coefficient difference was as astonishingly high as 115 cm⁻¹) and a large difference in the absorption coefficient (at least 80 cm⁻¹ when the refractive index difference was zero) between blood and the surrounding tissues. This result revealed that the fatty tissue and the cartilage, having much lower sub-THz absorption coefficients than blood, should occupy a large volume fraction in the mouse ear. By changing different fitting parameters, we also found that our system is sensitive to the differences in the refractive index and absorption coefficient rather than to their absolute values.

 

Fig. 9 Comparison between the respectively measured and simulated cross-sections normalized to the tissue transmittance. Pink curve: n_tissue, n_blood, α_tissue, α_blood equal to 2.2, 2.5, 20 cm⁻¹, 135 cm⁻¹; red curve: n_tissue, n_blood, α_tissue, α_blood equal to 2.2, 2.4, 20 cm⁻¹, 120 cm⁻¹ ; green curve: n_tissue, n_blood, α_tissue, α_blood equal to 2.3, 2.4, 30 cm⁻¹, 120 cm⁻¹ ; blue curve: n_tissue, n_blood, α_tissue, α_blood equal to 2.4, 2.4, 40 cm⁻¹, 120 cm⁻¹, respectively.

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From our simulations we concluded the following points. 1) It is not possible to deduce the absolute value of n_blood, n_tissue, α_blood, and α_tissue directly via the normalized transmittance curve. 2) Our numerical simulation indicates that the near-field transmission images measure the refractive index and absorption constant differences between blood and surrounding tissues. Within the previously reported value ranges, the same results will be obtained if the differences in the refractive index and absorption constant between blood and the surrounding tissues are fixed. 3) One of the four parameters can be estimated if the other three parameters are known. For example, it is possible to evaluate the effective n_tissue and α_tissue individually by using the THz TDS system before the near-field imaging experiments. The two parameters n_tissue and α_tissue of living tissue samples are rather stable in an environment with stable humidity and temperature and are less sensitive to short-term physiological parameter changes in blood. The other two parameters of blood, n_blood and α_blood, might tend to vary with short-term physiological parameter changes in blood, such as those due to metabolism or to intravenous injection of a drug. However, according to our previous research [4], n_blood showed no significant correlation with the concentration of biochemical contents in blood. Even though further studies are necessary to clarify whether n_blood varies significantly with short-term physiological parameter changes in blood, if one assumes that n_blood does not vary significantly with short-term metabolism or the injection of a drug, then the variation in transmittance dip can quantitatively reflect the α_blood absolute value and its temporal variation with the studied physiological parameter changes in blood.

The monitoring of short-term transmission change in blood is one of the potential future applications of our near-field imaging system; therefore, we numerically studied the relation between the dip variation and $\Delta$α_blood so that the system’s sensitivity to changes in the absorption coefficient can be estimated. In Fig. 10, we have two sets of stabilized parameters: the first set has n_blood, n_tissue, and α_tissue equal to one extreme of our fitting parameter, i.e., 2.5, 2.2, and 20 cm⁻¹, respectively, and the second set has n_blood, n_tissue, and α_tissue equal to the other extreme, 2.4, 2.4, and 40 cm⁻¹, respectively. The values of α_blood were set as 105 cm⁻¹, 120 cm⁻¹, and 135 cm⁻¹. As the three curves in Fig. 10(a) show with n_blood, n_tissue, and α_tissue equal to 2.5, 2.2, and 20 cm⁻¹, respectively, the dip value transmitted through the 0.17-mm-thick vessel decreases from 0.709 to 0.665 when α_blood increases from 105 cm⁻¹ to 120 cm⁻¹, and decreases from 0.665 to 0.626 when α_blood increases from 120 cm⁻¹ to 135 cm⁻¹. On average, for a 0.17-mm-thick vessel, the decrease in 1% normalized dip value corresponds to about a 3.5 cm⁻¹ increase in α_blood. As the three curves in Fig. 10(b) show, with n_blood, n_tissue, and α_tissue equal to 2.4, 2.4, and 40 cm⁻¹, respectively, the dip value transmitted through the 0.17-mm-thick vessel decreases from 0.687 to 0.636 when α_blood increases from 105 cm⁻¹ to 120 cm⁻¹, and decreases from 0.636 to 0.592 when α_blood increases from 120 cm⁻¹ to 135 cm⁻¹. On average, for a 0.17-mm-thick vessel, the decrease in 1% normalized dip value corresponds to about a 3.1 cm⁻¹ increase in α_blood. We observe that the different parameter sets cause different but very closely aligned slopes of $\Delta$α_blood/dip-variance in the two extremes. Without detailed knowledge of the dielectric properties of the surrounding tissues and the refractive index of blood, we can conclude that the $\Delta$α_blood/dip-variance is 330 ± 20 cm⁻¹ for a 0.17-mm-thick vessel. For a thicker vessel (e.g., 0.2 mm), the slope decreases a bit. For example, the $\Delta$α_blood/dip-variance is 300 ± 10 cm⁻¹ for a 0.2-mm-thick vessel. In real-world measurement, changes in the resolution of α_blood depend on the system’s long-term stability. The smaller transmittance difference the system can distinguish, the higher absorption resolution the system can achieve. With the same system stability, to achieve higher resolution of α_blood, thicker vessels should be chosen for analysis.

 

Fig. 10 Comparison between simulated cross-sections normalized to the tissue transmittance with different absorption coefficients of blood. (a) n_blood, n_tissue, and α_tissue equal to 2.5, 2.2, and 20cm⁻¹. (b) n_blood, n_tissue, and α_tissue equal to 2.4, 2.4, and 40cm⁻¹, respectively.

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3.4 Polarization dependency

Normalized transmittance through the vessel varies with relative angle between the polarization of THz radiation and the extension direction of the vessel. Figure 11 shows the simulated normalized transmittance curve through the vessel having the relative angles (θ) of 0 degree and 90 degrees and having other simulation conditions the same as Fig. 8(b). As can be seen, the dip values through the near-0.2-mm-thick vessels increase around 0.1, and the simulated FWHMs of the transmittance dip cross-section also decrease 0.13 mm, as θ decreases from 90 degrees to 0 degree. If our system alignment cannot make perfect 90 degrees between the polarization and the vessel extension direction, this non-perpendicular θ condition will require our simulation to increase the absorption difference between the blood and the tissue so as to fit the measured curve. While the non-perpendicular θ is applied in our simulation, the absorption difference between the blood and the tissue needs to be higher to fit the measured curve. In our real-world measurements, θ can be easily controlled to be within 90 $\pm$15 degrees. The transmitted power could be approximately represented as the linear combination of sin²(θ) x (Power _{90 degree}) + cos²(θ) x (Power _{0 degree}). The maximum 15-degree misalignment would cause a less-than-0.005 variation in normalized dip for a 0.2-mm-thick vessel, and the 0.005 variation corresponds to a less-than-2-cm⁻¹ absorption coefficient difference according to the discussion in Fig. 10.

 

Fig. 11 Normalized transmittance with different relative angles between the polarization of THz radiation and the extension direction of the vessel. Red line: relative angles equivalent to 0 degree; black line: relative angles equivalent to 90 degrees.

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3.5 Long-term monitoring

One important application of this in vivo THz transmittance image system is the performance of long-term monitoring to observe physiological variations in vivo. First, we tested system stability by imaging a micro-tube with a 0.2-mm outer diameter and 0.167-mm inner diameter, made of a polymer composed of tetrafluoroethylene, hexafluoropropylene and vinylidene fluoride (INCOM Inc.). The micro-tube was placed with its extension direction parallel to the longer side of the detector aperture. The detector was placed 0.2 mm behind the micro-tube edge for near-field scanning. Figure 12(a) shows the optical image of the micro-tube, and two near-field transmittance images (P_tube/P_{without_tube}) with a 30-minute acquisition interval between are shown in Fig. 12(b) and 12(c). Figure 12(d) shows the two cross-sections through the locations marked by the black arrows in Fig. 12(b) and 12(c). As can be seen, the two cross-sections almost overlap. The variation in dip value after normalization over 30 minutes was less than 0.5%. According to the discussion for Fig. 10, system sensitivity to the change in the absorption constant in blood for a 0.17-mm-thick vessel is better than 2 cm⁻¹.

 

Fig. 12 Micro-tube for testing of system stability. (a) Image of the micro-tube taken by the USB camera. (b) THz image showing measured transmittance. (c) THz transmittance image obtained 30 minutes after (b). (d) Cross-section through the location marked by the arrows in (b) (black curve) and (c) (red curve). The scale of the distance in the optical images (a)-(c), and the transmittance scale bar of the THz images in (b) and (c) are both provided.

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Then, we performed simple long-term monitoring on two nude mice. One received a subcutaneous injection of insulin (0.5 U/ml insulin-saline solution, at 1 U/kg (0.05 ml/20 g body weight) at the beginning of anesthetization, and the other received no injection during anesthetization. Two THz transmittance images (P_ear/P_{without_ear}) were obtained for each mouse, one at the beginning of the anesthetization and the other 30 minutes later. The 30-minute interval was wide enough to observe the physiological effect of insulin, which usually starts 20 minutes after injection [31]. Figure 13(a) and 13(d) show the optical images of the ears of the mice with and without insulin injection, and Fig. 13(b)-(c) and Fig. 13(e)-(f) show the corresponding P_ear/P_{without_ear} normalized to the average transmittance peak located between the transmittance dips through the vessels. Figure 14(a) plots the two cross-sections through the locations marked by the black arrows in Fig. 13(b) and 13(c), and Fig. 14(b) plots the two cross-sections through the locations marked by the black arrows in Fig. 13(e) and 13(f). Compared to the mouse without insulin injection in Fig. 14(b), the transmittance dip values of the mouse with insulin injection in Fig. 14(a) showed a more apparent decrease (~5%, corresponding to around a 15 cm⁻¹ increase in absorption coefficient for a 0.19-mm-thick vessel) after 30 minutes. However, the relation between the physiological variation of blood in mouse and the change in the transmittance dip require further detailed investigation and are not addressed in this work.

 

Fig. 13 Two examples of mouse ear images. (a)-(c): Ear photograph and normalized THz transmittance images of the mouse with insulin injection. (d)-(f): Ear photograph and normalized THz transmittance images of the mouse without insulin injection. The image acquisition interval between (b) and (c) and the interval between (e) and (f) were both 30 minutes.

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Fig. 14 (a) Cross-section through the locations marked by the arrows in Fig. 13(b) (black curve) and 13(c) (red curve). (b) Cross-section through the locations marked by the arrows in Fig. 13(e) (black curve) and 13(f) (red curve).

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4. Conclusion

A THz near-field transmission imaging system was successfully demonstrated to image the vessels inside the ears of nude mice in vivo. Wave-guided illumination and near-field scanning detection with a sub-wavelength aperture were applied. An operating frequency of 340 GHz was chosen to achieve a higher penetration depth in tissues with a reasonable SNR. Nearby blood vessels could be clearly resolved in our THz images with a lateral resolution of around 0.5 mm. The near-field pattern of the power transmittance through the vessel was also numerically simulated and showed good correspondence to the measured results. Our numerical study indicated a small difference in the refractive index of 0.3 at most and a large difference in the absorption coefficient of at least 80 cm⁻¹ between blood and the surrounding tissues, whereas the sensitivity our system to a change in the absorption coefficient in blood can be better than 2 cm⁻¹. The potential application of the system for quantitative monitoring of the change in the absorption coefficient in blood was discussed, and its ability for long-term monitoring in vivo was also demonstrated.