Water concentration and distribution in biotissues are important factors in many applications. THz-wave is a viable tool for water content measurement due to its highly sensitivity to water. In this study, the measuring errors of water concentration using THz-wave induced by transmittance and sample thickness were analyzed theoretically. The chosen basis for sample thickness and measuring THz frequency were presented theoretically. Measurements of the water two-dimensional mapping in different animal tissue samples were demonstrated experimentally, which clearly shows the spatial distribution of the tissues.
©2010 Optical Society of America
Terahertz-wave (THz-wave) lies between the infrared and microwave regions of the electromagnetic spectrum. It has the merits of nonionizing and low scattering, and can be used to excite large amplitude vibrational modes in various macromolecules and probe the weak interactions between them . The application of terahertz (THz) imaging in biotissues and medical imaging have been demonstrated extensively based on THz-TDS system [2–5], THz parametric sources , quantum cascade lasers , cw terahertz systems  and backward-wave oscillator  in recent years. At present, perhaps the most restrictive challenge facing THz imaging in biotissue applications is the high absorptivity of water and other polar liquids, which limits the sensing and imaging in water-rich samples and prohibits transmission-mode imaging through a thick tissue. Many research groups have attempted to use a certain degree of dehydrated tissue as a measure state, which requires specific sample preparation and can’t get enough information. However, on the other side, the presence of water may have its advantages. Experimental studies have verified THz image contrast and histology changes of biotissues both are closely consistent with the water content changes [10, 11].
Water content and distribution in sample are commonly used as a marker in food industry  and tissue diagnosis [13–15]. They are of great significance in determining the physical characteristics, technological processes, as well as microbiological stability. The evaporation method and chemical method are often used in food inspection, the processes of these methods are time consuming and water distribution can’t be detected simultaneously. In medical diagnosis, magnetic resonance imaging (MRI) usually provides useful information through measuring the three-dimensional water content distribution of signals originating from the water molecules’ protons. However, this technique also has many disadvantages, e.g. the use of a whole body imaging machine, high costs, system complexity, needs for special coils, acquisition time, and patient claustrophobia. THz-wave is uniquely sensitive to water, together with the advantages listed above, which makes it a viable tool for water content measurement.
In a previous work, a method for measuring the water contents and distribution in biological tissue samples was proposed . In this paper, we discussed the measurement errors of water content induced by the errors of transmittance and sample thickness. The chosen basis for sample thickness and measuring frequency were presented theoretically. Measurements of the water volume concentration and distribution in different tissue samples have been done based on the transmittance measurement using high-energy, tunable monochromatic THz-wave parametric source.
2. Theoretical calculation
THz wavelengths, corresponding to the range of 30μm to 3mm, is longer than that of optical or infrared, so THz radiation is less susceptible to scattering within freshly excised biological tissue  and in this paper it is assumed to be negligible. According to Lambert-Beer law, the transmission of a light through substance is18]. In water-rich tissues, is reasonable. So the water volume concentration can be expressed as
From Eq. (4), it is seen that the main sources of random error in νw are dominated by the experimental errors on T and d. Setting A=lnT, the standard deviation of νw, Δνws can be written as
Firstly, we consider the relation between the transmittance variation ΔT and the relative variation of water volume concentration , in other words, the calculated error due to the transmittance at a certain sample thickness. It can be deduced from Eq. (3) as
Because is always negative, plotting versus T gives a minimum relative error plot. Figure 1 shows the water concentration error as a function of the transmittance. When αnwd=0, the relative error in the concentration has its smallest value for a given T=36.8%. That means 1% error in T produces a 2.7% error in νw at the optimum transmittance. The minimum is not sharp and good results can be expected in a transmittance range from 0.2 to 0.6. Outside of these ranges, great error will be pronounced. Moreover, the small changes of αnwd will make little effect on the relative error when transmittance changes from 0.2 to 0.6. According to the literature, the absorption coefficients of the dehydrated stomach, kidney  and myoglobin are less than 20cm−1 below 2THz , therefore, the thickness of sample should be tens of micrometer magnitudes. Therefore, the principle of sample thickness choice should be depending on the absorption coefficients of the dehydrated tissues to make αnwd at a relatively small value. In addition, the thickness can’t be too thin compared with the penetration depth of the sample (the penetration depth of the sample is 1/α) because there must be sufficient bulk for interaction with the THz signal .
During the procedure of preparing sample and imaging measurement, the sample thickness will have some error, which in turn influences the transmission and the calculated water volume concentration. According to Eq. (1), the relative variation of transmittance produced by the thickness isFigure 2 shows the relative error of transmittance induced by sample thickness. The variation of transmittance is sensitive to the sample thickness variation. For a certain , decreases with the increasing of transmittance. Considering the discussed above, higher transmittance should be chosen during the experiment.
On the other hand, the absorption of other components αnwνnwd in tissue is neglected during this measurement. Here, the relative error ε between the true and measured transmittance value for water part should be estimated. It is defined asFigure 3 shows the calculated results of ε versus water volume concentration when the parameters αnwd are assumed to be 0.05, 0.1 and 0.2. It is therefore seen that the relative error ε for transmittance can be less than 5% for water volume concentration of 0.5-0.9 while the thickness of sample is micrometer magnitude. Moreover, when αnwd is smaller than 0.05, the relative error ε for transmittance is less than 5% even though the water volume concentration is very small.
For a certain transmittance, the uncertainty in νw is dominated by the experimental error in sample thickness d, so that Δνw can be expressed as
3. Experimental setup
The schematic diagram of the THz imaging system is shown in Fig. 4 . In this experiment, a coherent tunable monochromatic THz-wave source based on ring-cavity THz-wave parametric oscillators (TPO)  was used. This THz source has the merits of compact, good stability and higher signal to noise ratio owing to its higher energy output. The ring-cavity TPO was pumped using a multimode Q-switched Nd:YAG laser at 1.064μm. The output tunability of THz-wave is 0.9-2.5THz. The spectral resolution was about 30GHz at 1.5THz.The measurement unit includes several THz reflected mirrors, focusing aspherical lenses, a sample-mount XY stage, and a CCD camera. A wire-grid beam splitter separates the THz-wave into two beams, a signal beam for imaging and a reference beam. The signal beam is reflected and normally focused on the sample by using an aspherical lens, which can be adjusted in the axial directions to get a better resolution. The sample is mounted on a computer controlled x-y linear motor stages that move it through the focused beam in the horizontal plane. The THz beam transmitted through the sample is again collimated with another aspherical lens and then is reflected by mirrors onto a helium cooled 4.2-K Si bolometer. The signal-to-noise ratio of the present imaging setup was about 21dB.
For sample preparation, fresh tissue with uniform thickness was sliced at −20°C using a microtome (CM1900; Leica). It was sandwiched gently between two Tsurupica plates without any visible deforming of the tissue. Two spacers of chosen thickness to match the thickness of the sliced sample are used at both ends of plates to secure the tissue between two plates. An improved technique is to cover the tissue using oleic acid so that water content and the sample thickness can be preserved during the experiment. This is the technique employed in this study for decreasing sample dehydration to make accurate measurements. The whole imaging set-up was enclosed in a sealed box and purged with dry nitrogen to suppress the absorption induced by a water vapor. Measurements are made at a controlled room temperature.
4. Results and discussions
The imaging spatial resolution is a key parameter of the system. We have evaluated this parameter through detecting the THz focusing spot size at sample plane using the knife-edge method. A sharp metallic blade was placed in the focal plane, with its edge successively along the x and y directions, and moved perpendicularly to its orientation. Figure 5 shows the measurement result, which indicated the intensity distribution is approximately Gaussian. The x and y diameters of the Gaussian distribution, measured as the 10% and 90% distance between the peak and bottom, were found to be 360μm and 500μm, respectively. The measured beam profile showed an asymmetric elliptical distribution. This can be explained by the Si-prism coupling output. The asymmetric radiation might be improved by reshaping the pump beam and coupling system.
The imaging capability of the system was demonstrated on specimens of animal tissues. Firstly, we detected the transmittance spectra of the fresh pork and chicken with different thickness, as shown in Fig. 6 . Transmittances of the fresh pork lean, adipose and chicken are monotonic from 1.2 to 1.8THz. Figure 6(a) shows the transmittance for pork lean and adipose with 50μm thickness are 0.36 and 0.56 at 1.5THz, respectively. As analyzed above, this thickness is better for THz imaging in order to decrease the measurement error. The transmittance for chicken is 0.18 with 50μm thickness, whereas 0.45 with 40μm thickness at 1.5THz, as illustrated in Fig. 6(b). Therefore, 40μm thickness for chicken is chosen for THz imaging.
Figure 7 shows the CCD photographs and the water content distribution image of pork and chicken tissues. The THz frequency is 1.5THz. The scanning areas of pork and chicken samples are about 6×6mm2 and 7×7.5mm2, which correspond to 25×25 = 625 and 29×32=928 pixels, respectively. The measurement times were approximately 1min for pork tissue and 1.5min for chicken tissue. During the measurement, each pixel measurement was averaged with five THz pulses to reduce any noise from THz output fluctuations. Because biological tissue absorption is the dominant attenuation mechanism due to the high water content, scattering and Fabry–Perot effects are neglected in comparison. Low statistical errors in short measurement time have been accomplished. Figure 7(b) and (d) show two dimensional water level mapping with THz-wave allow clear identification of the histological structures of different tissues. Higher water contents were measured in the pork lean part, 70%, than in the adipose tissues, 15%. The two parts, lean and adipose tissues of pork, were clearly classified due to water content difference. Moreover, the changes of water content mapping correspond with the interface parts between tissues and structural difference in the visible image presented in Fig. 7(a) and (c).
Figure 8 shows the water volume concentrations for different samples were measured with THz tuning range of 1.2-1.8THz. The uniform section for each tissue was chosen for imaging. The average water volume concentrations for pork lean, pork adipose and chicken were nearly 70%, 65% and 15% at each THz frequency, respectively. The results presented here clearly indicate that water content mapping with THz-wave obtained with the method described above gives meaningful results in sample distinction.
The measuring errors of water concentration using THz-wave were analyzed theoretically. The chosen basis for sample thickness and measuring frequency were presented in theory. Measurements of the two-dimensional water mapping in different animal tissue samples were also experimentally verified with different THz frequency using tunable monochromatic THz-wave source, which clearly shows the spatial distribution of the tissues. This method can be complementary to MRI and dehydration method, but is rapid, easy to handle and more compact than MRI. With use of a new region of the electromagnetic spectrum that could improve the overall sensitivity to identifying different tissues. This method for obtaining the water concentration in biotissues will open new aspects in the research field of biology and medical pathological diagnosis.
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