2.1.

Imaging System

The THz pulsed imaging (TPI^™) system used in this study was the TPI Imaga 1000^™ (TeraView Limited, Cambridge, United Kingdom). Detailed information about the system can be found in our previous work.^{24, 25, 26} Briefly, the system uses photoconductive devices to generate and detect THz light: the optical excitation is achieved by an $800\text{-}\mathrm{nm}$ femtosecond pulsed laser. The system has a reflection geometry such that the THz pulses are collimated and focused using off-axis parabolic mirrors onto the top surface of a $z$ -cut $2\text{-}\mathrm{mm}$ -thick quartz window with an angle of incidence of $30\mathrm{deg}$ . The sample is placed on the quartz window, and the reflected THz pulse from the quartz/sample interface is detected coherently by a photoconductive receiver. In this system, the relaxation of the excited carriers produced broadband electromagnetic pulses typically with a full width at half maximum of $0.3\mathrm{ps}$ and results in a usable frequency range from about $0.1\text{to}3\mathrm{THz}$ with an average power of $\sim 1\mu \mathrm{W}$ . The THz beam path was purged with nitrogen gas to remove water vapor from the air, which would otherwise have attenuated the signal.²⁷ Figure 1 is a photograph of a tissue sample placed on the quartz window of our system.

Fig. 1

Photograph of a sample to be imaged placed on the quartz window.

2.2.

Sample Preparation

Three samples of white adipose tissue and two samples of porcine skeletal muscle were taken from the same piece of meat for investigation. The meat was from an abattoir and stored in a refrigerator, it was first measured within $24\mathrm{h}$ of collection. Adipose tissue was chosen because fatty tissue is known to have significantly different THz properties from other more fibrous/lean tissues; this means that it should be easier to see the contrast before and during the fixing process. The focus of this study was to see how fixing can affect THz image contrast—we are investigating intrasubject variation rather than subject-to-subject (or intersubject) variation. Thus, by taking all the samples from the same piece of meat, we were able to study the effects of the fixation process without added subject variation. The samples were therefore all treated and handled in the same way and exposed to the same environmental conditions. THz radiation can penetrate through several millimeters of some dehydrated tissues;^{25, 26, 27, 28} therefore, to avoid potential etaloning within the sample after the fixing, each sample was cut such that the thinnest dimension was no less than $1\mathrm{cm}$ in thickness. The fresh samples were imaged before the formalin-fixing process began. A standard protocol was followed for this process,^{29, 30} whereby nonbuffered 30% formalin was used. The volume of formalin applied to the sample was at least 20 times the initial sample volume. The sample was then left to soak in the fixative in a sealed container and refrigerated at a constant temperature $(4°\mathrm{C})$ . The penetration of formalin is related to the temperature of the solution,³¹ and thus, great care was taken to store all samples and formalin at the same temperature. Before placing the fixed tissue sample to be measured on the quartz window, the sample was washed under running water for $20\min$ to remove the excess formalin and then dried using blotting paper. During imaging, gentle pressure was applied to the sample to ensure it made good contact with the quartz.²⁰ This became more difficult as the fixing progressed because the sample became more rigid. In order to monitor the changes caused by the formalin, each sample was measured after being fixed for 24, 48, and $72\mathrm{h}$ . Only data points where the sample had made good contact with the quartz window were used in the following results.

3.1.

Frequency-Domain Analysis

The raw THz data obtained by our system are in the time domain. However, because the fundamental optical properties of interest, namely, the refractive index and absorption coefficient, are frequency dependent, we present the frequency domain analysis first.

By Fourier transforming the sample data and applying Fresnel equations to both sample and reference data, as detailed in Ref. 21, the refractive index and absorption coefficient were calculated. The reflection off the quartz/air interface was used as the reference data throughout this study. The calculated mean refractive index and mean absorption coefficient from the fresh and fixed sample measurements over time are plotted in Figs. 2 and 3 for the muscle and adipose tissue samples, respectively. Data for water and formalin are also plotted for comparison. In Fig. 4, we plot the mean refractive index and mean absorption coefficient from the adipose tissue and skeletal muscle samples for both when the samples were fresh and also after $72\mathrm{h}$ of formalin fixing. Following standard statistical methods, we calculate the 95% confidence intervals³² for the tissue samples by averaging over all samples of each tissue type (a total of $>500$ data points were used for each tissue type). The confidence intervals are plotted as error bars in Fig. 4 to illustrate that, both before and after fixing, there are statistically significant differences between the THz properties of the tissues (because the error bars do not overlap). The THz properties of water have also been plotted alongside those of the fresh muscle to highlight that, although the muscle tissue properties are close to those of water, they are significantly different over most of the frequency range investigated.

Fig. 2

(a) The mean refractive index and (b) absorption coefficient of skeletal muscle before and after formalin fixing for 24, 48, and $72\mathrm{h}$ . Bulk water and formalin optical properties are also plotted for reference.

Fig. 3

(a) The mean refractive index and (b) absorption coefficient of white adipose tissue before and after formalin fixing for 24, 48, and $72\mathrm{h}$ .

Fig. 4

The mean refractive index and absorption coefficient for fresh and fixed samples of fat and muscle. Error bars represent 95% confidence intervals. The water data were acquired in transmission, and the error bars are too small to be seen on this graph.

The refractive index of the skeletal muscle decreased as the fixation time increased and seemed to converge after $48\mathrm{h}$ . Comparing the fresh and fixed samples, the refractive index changed noticeably at the lower frequencies, falling from 2.6 (fresh) to 2.2 $\left(72\mathrm{h}\right)$ at $0.2\mathrm{THz}$ . From $\sim 0.8\mathrm{THz}$ and above, the curves of the fixed samples started to plateau toward a refractive index of 2 [Fig. 2a]. Because water was being removed from the tissue, it is logical that the absorption coefficient should also be reduced by the fixing process, as shown in Fig. 2. Before fixing, the absorption coefficient of the skeletal muscle tissue was $\sim 120{\mathrm{cm}}^{-1}$ at $0.2\mathrm{THz}$ ; it decreased rapidly to $60{\mathrm{cm}}^{-1}$ after only $24\mathrm{h}$ . During the first $24\mathrm{h}$ , the percentage of moisture being replaced was at its greatest, but as the fixing progressed there was less and less water left to be displaced and so the changes in optical properties decreased and tended toward zero as the fixing time increased. Other studies have also indicated that THz properties are dependent on the sample hydration. For instance, Stringer investigated ex vivo samples of human cortical bone and found that dehydrating the sample reduced both the absorption coefficient and the refractive index of the samples.³³

Similarly, above $0.6\mathrm{THz}$ , the refractive index and absorption coefficient of the white adipose tissue decreased as the fixation time increased. However, the changes in the adipose tissue refractive index were not as significant as for the muscle. We explain these observations by considering the molecular interactions of the formalin with both muscle and adipose tissue.

Formalin is a saturated solution of formaldehyde (HCHO), water, and methanol. Unlike most antibacterial and germicidal agents, which poison the bacteria and germ cells, formaldehyde kills cell tissue by dehydrating the tissue and bacteria cells and replacing the normal fluid in the cells with a gellike rigid compound.³⁴ Additionally, the structure of the protein in the “new” cell will resist further bacterial attacks. ^{35, 36} Tissue and bacterium cells are made of protoplasm and, as such, contain large amounts of moisture. Skeletal muscle cells contain several types of protein and have a high water content. The water content in the muscle tissue is about 75–80%,³⁷ and from Fig. 2, we see that the refractive index and absorption coefficient of the fresh muscle are close to those of water. Additionally, the refractive index and absorption coefficient of formalin are much lower than those of water or fresh tissue. The introduction of formaldehyde into the tissue dries out the protoplasm and destroys the cell. Because water is being removed from the tissue, it is logical that the absorption coefficient should be reduced by the fixing process. Similarly, the refractive index is also reduced and becomes closer to that of formalin. In contrast to the muscle tissue, white adipose tissue cells contain a single large fat droplet and the water content is about 10–30%,³⁷ which is far less than the muscle tissue. This means there is very little water for the formaldehyde to displace, and thus, we do not see such significant changes in the THz properties of the adipose tissue.

3.2.

Time-Domain Analysis

The amplitude and phase of a THz pulse reflected off a medium are dependent on the complex refractive index of the medium (as well as the incident pulse). As in optics, if a THz pulse is reflected by a medium of higher refractive index, then it incurs a phase change of $180\mathrm{deg}$ . Conversely, if a THz pulse is reflected by a medium of lower refractive index, then there is no phase change. Given that in Section 3.1 we have seen changes in the refractive index and absorption coefficients of the samples during the fixing process, we also expect to see changes in the reflected THz pulses.

To analyze the reflected time-domain pulses meaningfully, the system response was removed. This was done by deconvolving the sample pulse by the reference pulse and applying a bandpass (double Gaussian) filter to reduce the noise as detailed in our previous work.²⁵ The resulting waveforms for the three fresh adipose tissue samples and two fresh skeletal muscle samples and their corresponding means are illustrated in Fig. 5 . From Fig. 5, we see that there is some variation between samples from the same type of tissue but that this variation is slight. In Fig. 6, we illustrate the effects of the formalin fixing by plotting the mean deconvolved waveforms of each tissue type.

Fig. 5

The deconvolved waveforms for fresh samples of (a) adipose tissue and (b) skeletal muscle.

Fig. 6

The deconvolved mean waveforms for (a) adipose tissue and (b) skeletal muscle as the fixing time progressed.

As seen in Fig. 6a, when the fixing time increased, the waveform amplitude of the adipose tissue also increased. This was primarily because the refractive index of the adipose [Fig. 3a] was decreasing over the majority of the bandwidth (due to the fixing), and this meant there was a greater difference between the refractive index of the quartz (2.1) and that of the adipose (e.g., 1.5 at $1\mathrm{THz}$ when fixed compared to 1.6 when it was fresh). From Fresnel theory, this increased difference in refractive indices resulted in a greater reflected amplitude.

As the fixing time increased for the muscle, three main changes were apparent. A small peak started to appear preceeding the trough, and the width and magnitude of the trough decreased. These changes can also be explained by considering the effects of the formalin on the refractive index and absorption coefficient of the muscle. For the muscle, the formalin significantly reduced both the refractive index and the absorption coefficient. Before fixing, the refractive index of the fresh muscle was greater than that of quartz (2.1) over the whole of the frequency range measured. The fixing reduced the refractive index so much that the refractive index became lower than that of quartz at higher frequencies, and this was the cause for the small peak, which appeared and increased as the fixing time was increased. As the the refractive index and absorption coefficient were reduced they became closer to the optical properties of the quartz. This meant that the reflected waveform was not as intense. Additionally, because the absorption coefficient was reduced there was less broadening of the trough (as more of the higher frequency components were preserved), and thus, we observed a narrower reflection. Therefore, the formalin fixing can significantly affect the THz properties of samples such that they are apparent in both the frequency and time domain.

Figures 7a and 7b present the deconvolved THz waveforms for fresh and fixed tissue, respectively. In both figures, we can see clear differences between the adipose tissue and muscle waveforms; however, the differences are bolder for the fresh sample. When investigating a biological sample, we typically look at an image of the whole sample, and plot particular properties in the image. For instance, we may plot at each pixel the maximum or minimum reflected waveform amplitude, or the refractive index at $1\mathrm{THz}$ .

Fig. 7

The deconvolved waveforms for (a) fresh and (b) fixed white adipose tissue and skeletal muscle.

Figure 8b is the THz image corresponding to the area of interest in the photograph of the fixed tissue in Fig. 8a. To form the image, the maximum amplitude of the deconvolved waveform is plotted on a false-color scale. The more blue regions have higher maximum waveform amplitude, and the redder regions have lower maximum waveform amplitude. The dark blue areas in the image correspond to where there was no sample on the quartz window—these waveforms have the highest amplitude because the reflected pulses are identical to the reference pulses. We can also see contrast between the adipose tissue and the skeletal muscle: the region of this image corresponding to the adipose tissue is pale blue, but the rest of the image is more yellow/red. This is because the deconvolved waveforms from the adipose tissue have the same phase as the reference waveform, whereas the deconvolved waveforms from the muscle undergo a phase change due to the higher refractive index of the muscle relative to the quartz. Therefore, despite reducing the differences in both the time and frequency domain properties of the adipose and muscle, we were still able to distinguish the adipose tissue from the muscle in Fig. 8b.

Fig. 8

(a) Photograph of the fixed tissue. (b) THz image corresponding to the area of interest within the square in (a).