2.1.

Tissue Samples

Human adult liver contains 74.5% of water, while the remaining 25.5% represents a combination of lipids, proteins, carbohydrates, and minerals.²³ The liver is divided into roughly hexagonal units, designated as hepatic lobules. They are composed of liver parenchymal cells (hepatocytes), arranged into plates, lined by a vascular network of sinusoids that empty into a central vein, and a portal triad at the lobule’s corners. Figure 1 presents a typical human liver histology section:

Fig. 1

Human liver histology section, showing hepatocyte plates and a portal triad (lower left) (HE, $100\times$).

All the liver tissue samples used in this study were collected from three adult patients undergoing partial liver resection at the Portuguese Oncology Institute of Porto, Portugal. After collection of the specimens from patients, only healthy fragments were made available for our studies, since the rest was used for clinical diagnosis and analysis at the Portuguese Oncology Institute of Porto. These patients, two men and a woman with ages between 41 and 61, have signed a written consent previous to surgical procedures allowing for subsequent use of surgical specimens for diagnostic and research purposes. Such agreement has been approved by the Ethics Committe of the Portuguese Oncology Institute of Porto, Portugal.

The samples to be used in the RI measurements had approximated rectangular shape ($\sim 4\times 3{\mathrm{cm}}^2$) and $\sim 1\mathrm{cm}$ thickness. These samples were flattened on one side to adhere perfectly to a prism surface during measurements with the total internal reflection method. The samples to be used in the spectral $T_{\mathrm{c}}$ measurements were prepared with a 0.5-mm thickness, and an approximate circular form ($\varphi \cong 1\mathrm{cm}$). To prepare the liver samples with these conditions, a cryostat from Leica^™, model CM 1850 UV was used.

2.2.

RI Measurements

To measure the RI of liver at discrete wavelengths, we have used the total internal reflection method,^24–28 with a setup as represented in Fig. 2.

Fig. 2

Setup used on internal reflection measurements.

In Fig. 2, the detector is connected to an electrical multimeter to measure the electrical potential at different angular positions. Using this method, angular reflectance measurements at the prism/tissue interface were performed with lasers at wavelengths of 401.4, 532.5, 668.1, 782.1, 820.8, and 850.7 nm. Measurements were made with all lasers from three liver samples with 1 deg resolution. All the lasers are diode lasers from Edmund Optics^™, with the exception of the 668.1-nm laser, which was acquired from Melles Griot^™. The dispersion prism represented in Fig. 2 is an equilateral prism made of SCHOTT N-SF11 glass, and it was also supplied by Edmund Optics^™. This type of glass has an RI with a wavelength dependence described by the Sellmeyer equation ²⁹

Since the angle of the reflected beam could only be measured outside the prism at the prism/air interface, we have used the Snell–Descartes equation [Eq. (2)] to convert between this angle ($\alpha$) and the reflected angle at the prism/tissue interface ($\theta$)³⁰

Fig. 3

Wavelength dependence for the RI of the prism used in the RI measurements.

As a result of each set of measurements with a particular laser, we obtained a reflectance curve for the tissue/prism interface. Such a reflectance curve was calculated according to

By calculating the first derivative of the reflectance curve, we were able to identify a strong peak that corresponds to the critical angle (${\theta }_c$) at the prism/tissue interface. The first derivative of the reflectance curve is calculated according to

After determining ${\theta }_{\mathrm{c}}$ from the curve calculated with Eq. (4), the RI of the tissue ($n_{\mathrm{t}}$) is calculated with

Since the lasers we used do not cover the entire wavelength range from 400 to 1000 nm, some literature data were used to extrapolate from 850 to 1000 nm.³¹ All the calculations and the procedure used in this extrapolation are presented in Sec. 3.

2.3.

$T_{\mathrm{c}}$ Measurements During Treatments with Glycerol Solutions

According to our previous studies with different tissues and OCAs,^11,16 the free water content in a biological tissue can be determined, based only on temporal [$T_{\mathrm{c}}(t)$] measurements made during treatments with solutions containing different OCA concentrations.

To obtain the free water content in human liver, we have performed similar measurements using the setup represented in Fig. 4.

Fig. 4

[$T_{\mathrm{c}}(t)$] measuring setup.

The chamber that is represented in Fig. 4 was constructed in black hard-plastic and contains a transparent glass at the bottom to allow the passage of the collimated light beam. The light beam, with 1 mm in diameter, crosses the tissue sample at the center of the chamber and exits at the top to be delivered to the spectrometer. The four black rectangles that are placed above and below the tissue represent two rings that are used to fix the sample at the center of the chamber. This setup was used to measure the $T_{\mathrm{c}}$ spectra for natural tissue and during treatment, after filling the chamber with the treating solution. Optical fiber cables are used between the lamp and the chamber and between the chamber and the spectrometer and some appertures are placed on both sides to guarantee beam diameter equal to 1 mm all the way.

Using this setup, we have measured the [$T_{\mathrm{c}}(t)$] spectrum from 10 liver samples in natural state and from several samples during treatment with aqueous solutions having the following glycerol concentrations: 20%, 25%, 30%, 35%, 40%, 45%, 50%, 55%, and 60%. For the treatments with each glycerol concentration, three studies were made, meaning that 27 liver samples were used in the studies during treatments with glycerol solutions. All samples to use in these measurements were prepared with 0.5-mm thickness. The average natural $T_{\mathrm{c}}$ spectrum and average time dependencies obtained during treatments are presented in Sec. 3.

2.4.

Calculation Procedure

Considering the [$T_{\mathrm{c}}(t)$] spectra measured during each particular treatment, we have selected the spectral range between 600 and 800 nm and calculated the mean time dependence for individual wavelengths within this range. This range is selected due to the almost linear $T_{\mathrm{c}}$ increase that the natural liver presents (see mean natural liver $T_{\mathrm{c}}$ spectrum at the beginning of Sec. 3). According to similar spectra observed for other tissues, muscle³² and colorectal mucosa tissues,¹¹ tissue scattering in this range should be significantly greater than absorption.

The OCA diffusion into the interstitial space of the tissue is approximated by a free diffusion model. Since $T_{\mathrm{c}}$ measurements made during treatment are sensitive to the OCA diffusion, these measurements can be fitted with an equation that describes the free diffusion approximation, at least within the time range where this approximation is valid^5,11,32

When the fitting of experimental data is made, the diffusion time, $\tau$ for a particular wavelength and treatment is identified. The various values of $\tau$ obtained for the individual wavelengths are averaged to determine the mean diffusion time for that particular treatment.

Since this entire procedure is to be made for each treatment with a particular glycerol concentration, we have used a software application that we have developed for this purpose,³³ which authomatizes the calculation procedure. This application uses MATLAB’s CFTOOL to estimate the $\tau$ values while fitting the discrete time dependence data with a curve described by Eq. (6). After determining all the mean $\tau$ values for all treatments, the application generates a graph with the $\tau$ values represented as a function of the glycerol concentration in the treating solution, along with a smooth spline to fit the discrete data. From this graph, we can identify the maximal $\tau$ value that is observed at an optimal solution that contains the same water as the free water content in the liver. Section 3 contains graphs relative to the essential steps of this calculation.

Considering the RI values of liver tissue obtained for discrete wavelengths between 400 and 850 nm, we had to calculate the RI dispersion for this tissue. We also wanted to extrapolate the dispersion to 1000 nm. To do this extrapolation, we considered the discrete RI values for human liver collected by another group.³¹ To obtain the correct dispersion, we have used CFTOOL in MATLAB. We fitted the discrete RI data with curves described by the usual equations for biological tissues, as described in the literature:^34,35 Cauchy [Eq. (7)], Cornu [Eq. (8)], and Conrady [Eq. (9)] equations to verify which one provides the best fit

After determining the RI dispersion for human liver, we calculated the dispersion curves for the dry matter and scatterers. Since we have performed our entire measurements having a temperature range between 19°C and 21°C, we collected the water dispersion between 400 and 1000 nm for 20°C from the literature.³⁶ Considering the total water content of 74.5% in human adult liver,²³ we subtracted the water contribution from liver dispersion to obtain the dispersion for dry matter. Considering the estimated free water content in liver, we subtracted its contribution from the liver dispersion to obtain the dispersion curve for scatterers. In these calculations, we used corrected versions of the Gladstone and Dale equation ²⁰

All the results from the sequential calculation steps are presented in Sec. 3.

3.1.

RI Dispersion for Human Liver

To obtain the RI dispersion of human liver, we performed measurements with various lasers, using the total internal reflection method. As explained in Sec. 2.2, the liver samples to use in these measurements were prepared to have a flat surface, so they could be placed at the prism surface (see Fig. 2), without creating any air bubbles inbetween. For each of the lasers used, three angular reflectance curves at the prism/tissue interface were calculated from measurements with Eqs. (2) and (3). These curves are presented in Fig. 5 for the 668.1-nm laser.

Fig. 5

Reflectance curves for 668.1-nm laser.

Calculating the first derivative for each curve in Fig. 5, we obtained the curves presented in Fig. 6, where we can see a significant peak for each curve.

Fig. 6

First derivative curves of the reflectance measurements represented in Fig. 5.

By identifying the angles for the peaks in the curves of Fig. 6, we could calculate the RI of the tissue for each set of measurements with the 668.1-nm laser. A mean value and correspondent standard deviation (SD) value were calculated for this wavelength. Such procedure was repeated for all the other lasers and the mean RI and SD values for all laser wavelengths are presented in Table 1.

Table 1

Experimental RI data of healthy human liver at different wavelengths.

The data in Table 1 and the reported RI values for wavelengths of 964 and 1551 nm³¹ were used to calculate the equation that better describes the RI dispersion for human liver. In this calculation, the RI values for 820.8 and 850.7 in Table 1 were neglected, since they are not well in line with the smooth RI decrease with wavelength. The experimental data in Table 1 and the calculated dispersion curve for human liver are presented in Fig. 7.

Fig. 7

Wavelength dependence of the RI of human liver between 400 and 1000 nm.

The dispersion curve represented in Fig. 7 is described by

The numerical values in Eq. (12) were obtained during the fitting of the experimental data with an $R$-square value of 0.999. As can be seen in Fig. 7, the experimental RI values for 820.8 and 850.7 nm are a little higher than the calculated fitting curve. As in the case of colon mucosa tissues that we have previously studied,^37,38 the increase in the RI at these wavelengths is evidence of lipid content in liver. Such evidence of lipids in human liver is not surprising since liver is reported to accumulate lipids.^23,39,40 Since in this wavelength range (784 to 870 nm) we have made measurements with only two lasers, it is not possible to make perfect characterization of the wavelength dependence created by lipids. Instead, we have represented the curve described by Eq. (12) in Fig. 7 for the entire wavelength range but with dashed lines between 784 and 870 nm. The curve described by Eq. (12) for the entire range between 400 and 1000 nm will be used later to calculate the RI dispersion curves for dry matter and scatterers in liver tissue.

3.2.

Determination of the Free Water Content in Human Liver

To proceed with the calculations of the dispersion curves of dry matter and scatterers in human liver, we need first to estimate the free water content in this tissue.

To obtain that value, we have performed spectral $T_{\mathrm{c}}$ measurements from liver samples under treatment with glycerol solutions. We will also use these measurements to calculate the diffusion coefficients of glycerol and water in liver that characterize the dehydration and RI matching mechanisms for these treatments. As indicated in Sec. 2.3, all samples used in these treatments had 0.5-mm thickness and three treatments were made for each glycerol concentration in solution. The measurements performed in the three treatments with each glycerol concentration were averaged to create a mean spectral time dependence for each case. Figure 8 presents the average $T_{\mathrm{c}}$ spectrum of natural liver—average of 10 samples.

Fig. 8

$T_{\mathrm{c}}$ spectrum of natural human liver between 250 and 1000 nm.

Figure 8 shows that only between 300 and 500 nm experimental spectra is not too dispersive. This range contains the hemoglobin absorption bands, meaning that tissue transparency is approximately the same for all samples used due to the presence of blood. All samples were prepared with 0.5-mm thickness, but the data in Fig. 8 show that the samples considered were more or less transparent at shorter and longer wavelengths.

Considering now the OC treatments, Fig. 9 presents the mean time dependencies for the treatments with 20%-, 40%-, and 60%-glycerol solutions.

Fig. 9

Mean $T_{\mathrm{c}}$ time dependencies for wavelengths between 600 and 800 nm for treatments with: (a) 20%-glycerol, (b) 40%-glycerol, and (c) 60%-glycerol.

Similar behavior to the one presented in graphs of Fig. 9 was already observed in our previous studies with different tissues.^11,32 As described in Sec. 2.4, we identified for each treatment the range of validity for Eq. (6). For the treatment with 20%-glycerol, this range terminates at 10 min. For the treatment with 40%-glycerol, the range terminates at the end of the treatment, and for the treatment with 60%-glycerol, it terminates at 9 min. This means that the $T_{\mathrm{c}}$ data after 10 min in the treatment with 20%-glycerol [Fig. 9(a)] and after 9 min in the treatment with 60%-glycerol [Fig. 9(c)] were neglected for further data processing and calculations.

Similar graphs were generated by our software application³³ for the treatments with other concentrations of glycerol. For each particular treatment, and after trimming the $T_{\mathrm{c}}$ time dependencies to the range of validity of Eq. (6), the $T_{\mathrm{c}}$ data were displaced to have $T_{\mathrm{c}}=0$ at $t=0$. The following step consisted of normalizing the trimmed time dependence data to its highest value. After these adjustements, we used CFTOOL in MATLAB^® to fit the adjusted time dependence with a curve described by Eq. (6). With this fitting, we obtained the $\tau$ value for that particular time dependence that corresponds to an individual wavelength and an individual treatment. Averaging between all $\tau$ values for a single treatment, we obtained the mean and SD for $\tau$. This entire procedure was made for all treatments, and the calculated data are presented in Table 2.

Table 2

Mean diffusion time of glycerol solutions in human liver.

Representing the data in Table 2 as a function of glycerol concentration in the treating solutions used in the study, we can adjust a spline to see the dependence. This graph is represented in Fig. 10.

Fig. 10

Mean diffusion time as a function of glycerol concentration in solution.

For any particular treatment, the estimated $\tau$ value represents a combination of two fluxes: water flowing into (low glycerol concentrations) or out (high glycerol concentrations) and glycerol flowing only into the tissue. By calculating the fitting spline in Fig. 10, we see that it shows a maximum for a glycerol concentration of 40.0% in the treating solution. This slowest $\tau$ value indicates that due to the existence of an equilibrium between the water in the treating solution and the free water in the tissue, only glycerol flows in, without any water flowing in or out. This means that the free water content in human liver is 60.0%. The slowest $\tau$ value in Fig. 10 (211.2 s) is the true diffusion time for glycerol in liver and it can be used to calculate the characteristic diffusion coefficient through ^5,11,16,32

Similarly, the fastest $\tau$ value in Fig. 10 (57.2 s) represents the diffusion time for water, and it can be used in Eq. (13) to calculate the diffusion coefficient of water during the dehydration mechanism. To perform these calculations, we need thickness measurements ($d$) made during the treatments with 40%- and 60%-glycerol. For an individual thickness set of measurements during a particular treatment, we have adopted the following procedure. The liver sample was placed in between two microscope glasses. Such a setup was introduced inside a precision micrometer to measure the global thickness of the glasses with the sample inside. The treating solution (40%-glycerol or 60%-glycerol) was injected inside the two glasses to initiate the treatment, and measurements were taken at each 15 s until 2 min of treatment and at each min after that. We obtained the sample thickness during treatment by subtracting the glasses thickness from the measurements performed. Three sets of measurements were made from three liver samples under treatment with 40%-glycerol and other three from liver samples under treatment with 60%-glycerol. Figure 11 presents the mean values for each treatment and the corresponding SD bars (in blue). The lines in Fig. 11 represent smooth splines that were created to interpolate each set of measured data.

Fig. 11

Mean thickness time dependencies of liver samples under treatment with 40%-glycerol and 60%-glycerol.

Considering the data in Fig. 11, we retrieved the sample thickness of 0.41 mm from the spline that corresponds to the treatment with 40%-glycerol at 211.2 s and calculated the diffusion coefficient for glycerol in human liver as $8.2\times {10}^{-7}{\mathrm{cm}}^2/\mathrm{s}$. Similarly, the mean sample thickness when treated with 60%-glycerol is 0.43 mm, as retrieved from the spline in Fig. 11 for that treatment at 57.2 s. Using this value in Eq. (13), the diffusion coefficient for water in liver was calculated as $3.2\times {10}^{-6}{\mathrm{cm}}^2/\mathrm{s}$. These diffusion coefficients are the values that characterize the OC mechanisms of tissue dehydration and RI matching for liver treatments with glycerol.

3.3.

Calculation of the Dispersion Curves for Scatterers and Dry Matter in Liver

Considering the total water content in liver that has been reported²³ and the experimental data presented in previous sections, it is now possible to calculate the RI dispersion curves for the dry matter and scatterers.

To calculate the dispersion for the dry matter, we considered the liver dispersion curve in Fig. 7 and described by Eq. (12). We have also considered the total water content of 74.5% that is reported in the literature.²³ Using these data in Eq. (10), we calculated the RI dispersion for dry matter. Using the same procedure, but now considering the estimated free water content of 60% in Eq. (11), we have calculated the dispersion curve for scatterers in human liver. Figure 12 contains both the calculated curves.

Fig. 12

Wavelength dependence of the RI of liver scatterers and dry matter.

Figure 12 has two vertical axis to allow representing both curves toguether. As indicated by the ovals and arrows, the dispersion for scatterers is reported to the left vertical axis, whereas the dispersion of dry matter is reported to the right vertical axis. Although both curves show decreasing behavior with wavelength, the curve for dry matter presents higher values as it was expected due to the the fact that dry matter has no water. Since the dry matter in human liver contains lipids, proteins, carbohydrates, and minerals, the brown curve in Fig. 12 is a result of such particular combination. As an example, if similar studies are to be made in other liver samples that have excess of lipids (e.g., in steatotic liver), the calculated dispersion for dry matter might be compared to that depicted in Fig. 12 to identify that pathological condition. Liver accumulation of other materials that produce changes in RI can also be detected. The same dispersion may be useful for calculations in extreme OC treatments where bound water may convert into free water and new scatterers with smaller hydration are present.

The curve for scatterers in Fig. 12 is very important for OC treatment planning. If short-time treatments are to be planed, this curve will remain unchanged during treatment, due to the fact that only free water participates in the dehydration mechanism. Such curve can be used in calculations to quantify and characterize the RI matching mechanism that occurs due to the exchange of free water by OCA. Such calculations are described in the literature,⁵ and in one case that we have studied recently for skeletal muscle under treatment with glucose and ethylene glycol.¹⁹

3.4.

Possible Applications of Received Data

During short-term immersion agent treatments, the RI matching mechanism occurs due to the exchange of free water in tissue fluids and the OCA in the treating solution. Bound water remains tightly connected with the other tissue components, a combination designated as tissue scatterers. Due to this water descrimination in biological tissues and its importance in OC treatments, the total water content of 74.5% for human liver previously reported in the literature is not sufficient to characterize OC treatments. In particular, the estimated 60.0%-content for the free water and 14.5% for the bound water in human liver will allow one to perform prediction, quantification, and characterization of the RI matching mechanism at OC.

The knowledge of free/bound water content is also necessary for many other clinical applications, including tissue cryoprotection^41,42 and cancer diagnostics.^11,37,38,43 The OCAs are also mostly cryogenic agents and often used for cryoprotection of living tissues. Their strong osmotic properties and low-temperature freezing abilities are needed to prevent formation of ice crystals in order to keep tissue undamaged at low temperatures.^41,42 Besides free and bound water contents, all these clinical technologies will be beneficial due to knowledge of the RI of scatterers and dry matter in tissues, including human liver, if optical monitoring is applied. The RI data for major tissue components may also be useful for different diagnostic purposes or to characterize long-term OC treatments when part of the bound water is converted into free water.

The calculated diffusion coefficients for glycerol and water in human liver are also important for cryoprotection applications or for OC treatment planning. Similar methods can be applied in studies with other OCAs, such as ethylene glycol, glucose, etc. to obtain similar data.