1.

Introduction

Liver ischemia–reperfusion involves a complex series of processes that may culminate in hepatocellular injury. Liver ischemia–reperfusion is a common consequence of liver surgery, particularly after hepatectomy and liver transplantation, complicated by microcirculatory liver failure, followed by necrosis and cell death.¹ Occlusion of hepatic inflow (Pringle maneuver) by portal vein clamping was initially devised to reduce intraoperative blood loss during emergency liver resection.² The important side effect of partial liver resection is the ischemia in the remnant liver following temporary vascular occlusion.³ The liver contains many more chromophores [oxygenated hemoglobin (HbO), deoxygenated hemoglobin (HbR), cytochrome c oxidase (CcO), lipid, water, etc.] than other organs. Since liver function depends greatly upon the oxygen supply, it is clinically important to monitor the oxygenation state of the liver in patients after liver surgery. In the present study, we demonstrate the characterization of the light scattering and absorption properties of in vivo liver tissue based on diffuse reflectance spectroscopy (DRS). DRS is a promising method of detecting the macroscopic information of tissue samples, such as the scattering property, the total hemoglobin concentration, and the tissue oxygen saturation of hemoglobin (${\mathrm{StO}}_2$).^4,5 Near-infrared (NIR) spectroscopy has been reported to be useful in detecting the oxygenation state of the graft liver after transplantation, and the ${\mathrm{StO}}_2$ value can be an indicator of the patient’s prognosis.^6,7 The recent development of DRS has made it possible to determine the absorption coefficient ${\mu }_{\mathrm{a}}$ and the reduced scattering coefficient ${{\mu }_{\mathrm{s}}}^{\prime }$ of a tissue independently. The absorption coefficient ${\mu }_{\mathrm{a}}$ is defined as the probability of photon absorption per unit infinitesimal path length, and the reduced scattering coefficient ${{\mu }_{\mathrm{s}}}^{\prime }$ is defined as the probability of photon scattering per unit infinitesimal path length.⁸ DRS is an optical measurement technique that records changes in the spectral distribution of light after its interaction with the tissue. Changes in the diffuse reflectance spectra are primarily a result of the combination of absorption and scattering of light for each wavelength of light produced by a broadband light source. Light absorption is primarily related to chromophore contents of tissue, whereas light scattering is influenced primarily by cellular and subcellular structures of tissue. The total light absorption is the sum of the absorption due to endogenous chromophores.⁹ HbO and HbR are the primary absorbers in biological tissues in the visible wavelength region,¹⁰ whereas the dominant absorbers in the NIR wavelength region are lipids, water, and collagen.¹¹ The severity of liver ischemia–reperfusion injury can be reliably assessed by measuring changes in HbO, HbR, and the redox state of heme aa3 in CcO.⁹ By illuminating tissue with a selected spectral band of light and subsequent analysis of the characteristic scattering and absorption patterns, it is possible to obtain an “optical fingerprint” of the tissue. Such an optical fingerprint represents specific quantitative biochemical and morphological information from the examined tissue and may depend on the metabolic rate, vascularity, intravascular oxygenation, and alterations in tissue morphology.¹² DRS has been used for tissue surface analysis during endoscopical procedures and analysis of tissue abnormalities in solid organs.¹³ Light scattering and absorption properties of in vivo tissues can be evaluated by several noninvasive methods, such as time-resolved measurements,¹⁴ a frequency-domain method,¹⁵ optical coherence methods,¹⁶ a pulsed photothermal radiometry method,¹⁷ and spatially resolved measurements.^18–21 DRS based on the spatially resolved measurements with continuous-wave light can be simply achieved with a white light source, inexpensive optical components, and a spectrometer. The primary notable changes within a light spectrum after interaction with tissue are a result of either the absorption or scattering of light. Using various mathematical models, the spectral characteristics of the absorption coefficient ${\mu }_{\mathrm{a}}(\lambda )$ and the reduced scattering coefficient ${{\mu }_{\mathrm{s}}}^{\prime }(\lambda )$ can be extracted from the measured reflectance spectrum.²² DRS using a fiber optic probe is a promising technique for monitoring tissue oxygenation, demonstrating promising results in the discrimination of malignant lesions from normal tissue^23–26 and assessment of tissue viability.²⁷ In addition, DRS has been demonstrated to identify irreversible cell damage during radiofrequency ablation,²⁸ severe steatosis, and hepatitis, thereby preventing overly extensive resections in these high-risk patients.^29–32 Furthermore, DRS could potentially be used intraoperatively for the assessment of bowel viability in real time.³³ Various source-collector geometries have been used to estimate the reduced scattering coefficient ${{\mu }_{\mathrm{s}}}^{\prime }$ and the absorption coefficients ${\mu }_{\mathrm{a}}$ in DRS with a fiber-optic probe.^{18,26,33–36} Moreover, a single-reflectance fiber probe will be easy to use for practical uses, especially in clinical situations. Nevertheless, to our knowledge, information regarding measurement of ischemia–reperfusion injury using a DRS system is very limited.

In the present study, we use a simple DRS system previously developed by Nishidate et al.³⁷ to estimate the reduced scattering coefficient spectrum ${{\mu }_{\mathrm{s}}}^{\prime }(\lambda )$ and the absorption coefficient spectrum ${\mu }_{\mathrm{a}}(\lambda )$ of in vivo biological tissue. In order to confirm the validity of the method for evaluating changes in the optical properties of in vivo liver tissue, we performed in vivo experiments using exposed rat liver before and during ischemia–reperfusion induced by the occlusion of the hepatic portal as well as postmortem.

2.

Principle

2.1.

Reflectance Fiber Probe System

Figure 1 shows a schematic diagram of the single-reflectance fiber probe system with the two source-collection geometries used in the present study. The system consists of a reflectance fiber probe, bifurcated fiber, a light source, and two spectrometers under the control of a personal computer. The bifurcated fiber has two optical fibers of the same diameter of $400\mu \mathrm{m}$ placed side by side in the common end. The reflectance fiber probe has one $600\text{-}\mu \mathrm{m}$-diameter fiber in the center surrounded by six $600\text{-}\mu \mathrm{m}$-diameter fibers. One end of the center fiber of the reflectance probe is connected to the common end of the bifurcated fiber through a fiber connector. A halogen lamp light (HL-2000, Ocean Optics Inc., Dunedin, Florida), which covers the visible to NIR wavelength range, is used to illuminate the sample via one lead of the bifurcated fiber and the central fiber of the reflectance probe. Diffusely reflected light from the sample is collected by both the central fiber and the six surrounding fibers. The center-to-center distances between the surrounding fibers and the central fiber are $700\mu \mathrm{m}$. The light collected by the central fiber is delivered to a multichannel spectrometer (USB4000, Ocean Optics Inc.) via another lead of the bifurcated fiber, whereas the light collected by the six surrounding fibers is delivered to a different multichannel spectrometer (USB4000, Ocean Optics Inc.). A solution of Intralipid 10%³⁸ was prepared in order to calibrate the spectral responses of both spectrometers as a reference solution. Diffuse reflectance spectra $R_{\mathrm{c}}(\lambda )$ and $R_{\mathrm{s}}(\lambda )$ ranging from 500 to 800 nm were calculated from the spectral intensities of light collected by the central fiber and the six surrounding fibers, respectively, based on the reflected intensity spectra from the reference solution.

Fig. 1

Single-fiber probe system for measuring the diffuse reflectance spectra with two source-collection geometries setup.

2.2.

Determination of Empirical Formulas for Estimating ${{\mu }_{\mathrm{s}}}^{\prime }$ and ${\mu }_{\mathrm{a}}$

In order to estimate ${{\mu }_{\mathrm{s}}}^{\prime }$ and ${\mu }_{\mathrm{a}}$ from the measurements of $R_{\mathrm{c}}$ and $R_{\mathrm{s}}$, we consider the following equation based on the results of the Monte Carlo simulation:

Eq. (1)

$$\left[\begin{array}{l}{{\mu }_{\mathrm{s}}}^{\prime }\\ {\mu }_{\mathrm{a}}\end{array}\right]=\left[\begin{array}{cc}{\alpha }_{\mathrm{c}}& {\alpha }_{\mathrm{s}}\\ {\beta }_{\mathrm{c}}& {\beta }_{\mathrm{s}}\end{array}\right]\left[\begin{array}{c}{A}_{\mathrm{c}}\\ A_{\mathrm{s}}\end{array}\right],$$

where $A_{\mathrm{c}}=-{\log }_{10}{R}_{\mathrm{c}}$ and $A_{\mathrm{s}}=-{\log }_{10}{R}_{\mathrm{s}}$ are the apparent absorbances for the recording by the center fiber and the surrounding fibers, respectively. In order to improve the accuracy of Eq. (1), we used the higher order terms of $A_{\mathrm{c}}$ and $A_{\mathrm{s}}$ in Eq. (1) as follows:

Eq. (2)

$$\left[\begin{array}{l}{{\mu }_{\mathrm{s}}}^{\prime }\\ {\mu }_{\mathrm{a}}\end{array}\right]=\left[\begin{array}{cccccc}{\alpha }_0& {\alpha }_1& {\alpha }_2& {\alpha }_3& {\alpha }_4& {\alpha }_5\\ {\beta }_0& {\beta }_1& {\beta }_2& {\beta }_3& {\beta }_4& {\beta }_5\end{array}\right][{\begin{array}{cccccc}1& {A_{\mathrm{c}}}^2& {A_{\mathrm{s}}}^2& A_{\mathrm{c}}{A}_{\mathrm{s}}& A_{\mathrm{c}}& A_{\mathrm{s}}\end{array}]}^t,$$

where coefficients ${\alpha }_i$ and ${\beta }_i$ ($i=0,1,2,3,4,5$) in Eq. (2) can be determined statistically by multiple regression analysis of the results of the Monte Carlo simulations, and ${[]}^t$ represents the transposition of a vector. The details of the Monte Carlo simulation model were published previously.³⁷ In the Monte Carlo simulations, $R_{\mathrm{c}}$ and $R_{\mathrm{s}}$ were calculated for the ranges of ${\mu }_{\mathrm{a}}=0.1$ to $80{\mathrm{cm}}^{-1}$ and ${{\mu }_{\mathrm{s}}}^{\prime }=5.0$. The values of ${{\mu }_{\mathrm{s}}}^{\prime }(\lambda )$ and ${\mu }_{\mathrm{a}}(\lambda )$ can be estimated by applying Eq. (2) to each wavelength point of $A_{\mathrm{c}}(\lambda )$ and $A_{\mathrm{s}}(\lambda )$. Figures 2(a) and 2(b) show the results obtained from the Monte Carlo simulations for $R_{\mathrm{c}}$ and $R_{\mathrm{s}}$, respectively. The value of $R_{\mathrm{c}}$ increases monotonically as ${{\mu }_{\mathrm{s}}}^{\prime }$ increases, whereas $R_{\mathrm{s}}$ reaches a plateau for larger values of ${\mu }_{\mathrm{s}}^{\prime }$. Both $R_{\mathrm{c}}$ and $R_{\mathrm{s}}$ decrease exponentially as ${\mu }_{\mathrm{a}}$ increases, but the effect is more pronounced for $R_{\mathrm{s}}$. Figure 3 shows the estimated and given values of the reduced scattering coefficient ${{\mu }_{\mathrm{s}}}^{\prime }$ [Fig. 3(a)] and the absorption coefficient ${\mu }_{\mathrm{a}}$ obtained from the preliminary numerical investigations [Fig. 3(b)]. In both Figs. 3(a) and 3(b), the estimated values will agree with the given values for the given ranges of ${{\mu }_{\mathrm{s}}}^{\prime }$ and ${\mu }_{\mathrm{a}}$. The coefficient of determination $r^2$ for ${\mu }_{\mathrm{a}}$ and ${{\mu }_{\mathrm{s}}}^{\prime }$ was 0.996 and 0.994, respectively, which indicates a good regression.

Fig. 2

Results obtained from the Monte Carlo simulations for (a) $R_{\mathrm{c}}$ collected by the center fiber and (b) $R_{\mathrm{s}}$ collected by the surrounding six fibers.

Fig. 3

Estimated and given values obtained from the numerical investigations for (a) the reduced scattering coefficient ${{\mu }_{\mathrm{s}}}^{\prime }$ and (b) the absorption coefficient ${\mu }_{\mathrm{a}}$.

2.3.

Evaluation of Tissue Oxygen Saturation and Redox State of Heme aa3 in Cytochrome c Oxidase from ${\mu }_{\mathrm{a}}(\lambda )$

The absorption coefficient spectrum is given by the sum of absorption due to oxygenated and deoxygenated hemoglobin. Using the absorption coefficient spectrum ${\mu }_{\mathrm{a}}(\lambda )$ as a response variable and the extinction coefficient spectra of ${\epsilon }_{\mathrm{HbO}}(\lambda )$ and ${\epsilon }_{\mathrm{Hb}}(\lambda )$³⁹ as predictor variables, the multiple regression model can be expressed as:

Eq. (3)

$${\mu }_{\mathrm{a}}({\lambda }_k)=a_{\mathrm{HbO}}\times {\epsilon }_{\mathrm{HbO}}({\lambda }_k)+a_{\mathrm{Hb}}\times {\epsilon }_{\mathrm{Hb}}({\lambda }_k)+a_0+e({\lambda }_k),$$

where $a_{\mathrm{HbO}}$, $a_{\mathrm{Hb}}$, and $a_0$ are the regression coefficients, $e({\lambda }_k)$ is an error component, and ${\lambda }_k$ indicates discrete values in the wavelength range treated in the analysis. By executing the multiple regression analysis for one sample of the absorption coefficient spectrum consisting of $p$ discrete wavelengths, one set of the three regression coefficients is obtained. In this case, the regression coefficient $a_0$ is a constant component or an intercept and is expressed as:

$$a_0={\overline{\mu }}_a-{\overline{\epsilon }}_{\mathrm{HbO}}·a_{\mathrm{HbO}}-{\overline{\epsilon }}_{\mathrm{HbR}}·a_{\mathrm{HbR}},$$

where ${\overline{\mu }}_{\mathrm{a}}$, ${\overline{\epsilon }}_{\mathrm{HbO}}$, and ${\overline{\epsilon }}_{\mathrm{HbR}}$ are the averages of ${\mu }_{\mathrm{a}}({\lambda }_k)$, ${\epsilon }_{\mathrm{HbO}}({\lambda }_k)$, and ${\epsilon }_{\mathrm{HbR}}({\lambda }_k)$ over the wavelength range, or $k=1$ to $p$. In the present study, we used the spectral data in the range from 500 to 600 nm at intervals of 10 nm for the multiple regression analysis because the spectral features of oxygenated and deoxygenated hemoglobin notably appear in this wavelength range. The regression coefficients $a_{\mathrm{HbO}}$ and $a_{\mathrm{Hb}}$ describe the degree of contributions of ${\epsilon }_{\mathrm{HbO}}(\lambda )$ and ${\epsilon }_{\mathrm{Hb}}(\lambda )$, respectively, to the absorption coefficient spectrum ${\mu }_{\mathrm{a}}(\lambda )$ and, consequently, are closely related to the concentrations of $C_{\mathrm{HbO}}$ and $C_{\mathrm{Hb}}$, respectively. The oxygen saturation of hemoglobin, ${\mathrm{StO}}_2$, is defined as the percentage of concentration of oxygenated hemoglobin in the concentration of total hemoglobin. In this study, the oxygen saturation is estimated from the regression coefficients $a_{\mathrm{HbO}}$ and $a_{\mathrm{Hb}}$ as follows:

Eq. (5)

$${\mathrm{StO}}_2[\%]=\frac{a_{\mathrm{HbO}}}{a_{\mathrm{HbO}}+a_{\mathrm{Hb}}}\times 100.$$

We also used the estimated absorption coefficient spectrum ${\mu }_{\mathrm{a}}(\lambda )$ to evaluate the redox state of heme aa3 in CcO. There is an isosbestic point of heme aa3 around 620 nm, where the absorption of light by the reduced heme aa3 and oxidized heme aa3 take the same value, while the absorption spectrum of the reduced heme aa3 is maximized at 605 nm.⁴⁰ The ratio of absorption at 605 nm and that at 620 nm can be used to evaluate the redox state of heme aa3, which indicates the state of mitochondrial energy metabolism. Therefore, in the present study, we evaluate the redox state of heme aa3 based on the ratio of the estimated absorption coefficient at 605 nm and that at 620 nm as ${\mu }_{\mathrm{a}}(605)/{\mu }_{\mathrm{a}}(620)$.

In order to justify the use of ${\mu }_{\mathrm{a}}(605)/{\mu }_{\mathrm{a}}(620)$ to represent the redox state of heme aa3 in CcO of liver tissue, we performed the preliminary experiments with an in vitro excised liver sample. A normal saline was infused into the excised liver via the portal vein to remove blood from the liver tissue. The oxidation of heme aa3 in CcO was induced by continuous infusion of a saline saturated with 95% ${\mathrm{O}}_2–5\%$ ${\mathrm{CO}}_2$ into the liver via the portal vein and subsequent submersion of the liver sample into the saline saturated with 95% ${\mathrm{O}}_2–5\%$ ${\mathrm{CO}}_2$. The reduction of heme aa3 in CcO was induced by submersing the liver sample into the mixture of normal saline and a sodium dithionite (${\mathrm{Na}}_2{\mathrm{S}}_2{\mathrm{O}}_4$). Figure 4 shows the estimated absorption coefficient spectra ${\mu }_{\mathrm{a}}(\lambda )$ normalized at 620 nm obtained from the excised liver sample submerged into the saline saturated with 95% ${\mathrm{O}}_2–5\%$ ${\mathrm{CO}}_2$ and the mixture of saline and ${\mathrm{Na}}_2{\mathrm{S}}_2{\mathrm{O}}_4$. The normalized absorption at 605 nm under the hyperoxic condition is higher than that treated with ${\mathrm{Na}}_2{\mathrm{S}}_2{\mathrm{O}}_4$, which corresponds to the absorption change due to the reduction of heme aa3 in CcO reported in literature.⁴⁰

Fig. 4

Estimated absorption coefficient spectra normalized at 620 nm obtained from the excised rat liver sample submerged into the saline saturated with 95% ${\mathrm{O}}_2–5\%$ ${\mathrm{CO}}_2$ (red square) and the mixture of saline and ${\mathrm{Na}}_2{\mathrm{S}}_2{\mathrm{O}}_4$ (blue circle).

3.

Experiments

3.2.

Animal Experiments

Six male Wister rats weighing from 150 to 300 g were maintained at 27°C with a $12\text{-}/12\text{-}\mathrm{h}$ dark/light cycle and allowed food and water ad libitum. Experiments performed in the present study were approved by the Animal Research Committee of Tokyo University of Agriculture and Technology. Rats were anesthetized by intraperitoneal injection of a mixture of $\alpha$-chloralose ($50\mathrm{mg}/\mathrm{kg}$) and urethane ($600\mathrm{mg}/\mathrm{kg}$). A rat model with ischemia–reperfusion to 90% of the liver (Fig. 5) was used.⁴¹ After laparotomy was performed by a transversal injection, the ligaments around the liver lobes were dissected in order to mobilize the left lobe. At the same time, the hepatoduodenal ligament was taped in preparation for further clamping. Before induction of ischemia, the diffuse reflectance spectra of liver tissue were recorded as baseline values. Hepatic ischemia was induced by clamping the hepatic portal (the hepatic artery, the portal vein, and the bile duct) for 30 min, followed by declamping. Anoxia was induced by nitrogen breathing at 60 min after the onset of reperfusion (t = 100 min). The caudate lobe of the liver was kept as a passage for the portal blood. The reflectance fiber probe was placed on the surface of the liver lobe. Measurements of $R_{\mathrm{c}}(\lambda )$ and $R_{\mathrm{s}}(\lambda )$ were obtained simultaneously in the wavelength range from 500 to 800 nm at 30-s intervals for 160 min: oxygen breathing for 5 min, normal air breathing for 5 min, ischemia for 30 min, reperfusion for 60 min, and nitrogen breathing for 60 min. In order to identify the respiration arrest or euthanasia, the respiration of the rat was confirmed by observing the periodic movement of the lateral region of the abdomen during the experiments. The estimations of ${{\mu }_{\mathrm{s}}}^{\prime }(\lambda )$ and ${\mu }_{\mathrm{a}}(\lambda )$ were performed based on the process described above. Data are presented as $\text{mean}\pm \mathrm{SD}$. An unpaired $t$-test was performed in order to compare the average values over the samples between the normal (air breathing) and the other periods (oxygen breathing, ischemia, reperfusion, and nitrogen breathing) and $P<0.05$ was considered significant.

Fig. 5

Graphical illustration of the surgical operation on the rat liver and the protocol in the present study. (a) Schematic drawing representing the ischemic model of the rat liver by blood inflow occlusion on the pedicles of the left lobe, the median lobe, and the right lobe, with no occlusion of the caudate lobe, which is kept as a passage for the portal blood. (b) The dorsal surface of the liver lobe is used for the measurement sites for the diffuse reflectance spectra of the liver.

4.

Results

4.1.

Validation of the Method Using Optical Phantoms

Figure 6 shows the estimated and given values for (a) the reduced scattering coefficient ${{\mu }_{\mathrm{s}}}^{\prime }$ and (b) the absorption coefficient ${\mu }_{\mathrm{a}}$, obtained from the phantom experiments. Reasonable results were obtained for both ${{\mu }_{\mathrm{s}}}^{\prime }$ and ${\mu }_{\mathrm{a}}$. Correlation coefficients between the estimated and given values are $R=0.97$ ($P<0.0001$) and $R=0.98$ ($P<0.0001$) for ${{\mu }_{\mathrm{s}}}^{\prime }$ and ${\mu }_{\mathrm{a}}$, respectively. The average root mean square error for ${{\mu }_{\mathrm{s}}}^{\prime }$ is $9.2\pm 8.0\%$ and that for ${\mu }_{\mathrm{a}}$ is $34.9\pm 45.6\%$. The empirical model yields, in principle, good results for both ${{\mu }_{\mathrm{s}}}^{\prime }$ and ${\mu }_{\mathrm{a}}$, as shown in Figs. 3(a) and 3(b). In Fig. 6(b), however, the estimated error for ${\mu }_{\mathrm{a}}$ increases as the given value increases, which could be attributed to the fact that the current simulation model does not accurately represent the actual experimental conditions, e.g., the distance between the central and surrounding fibers is not accurately taken into consideration.

Fig. 6

Estimated and given values obtained from the phantom experiments for (a) the reduced scattering coefficient ${{\mu }_{\mathrm{s}}}^{\prime }$ and (b) the absorption coefficient ${\mu }_{\mathrm{a}}$.

4.2.

Animal Experiments

Figure 7 shows the time courses of ${\mu }_{\mathrm{a}}$ averaged over the six samples at specific wavelengths during the period of preischemia (oxygen breathing and air breathing), ischemia, reperfusion, and nitrogen breathing. The error bars in Fig. 7 represent the standard deviation over the six samples. The average values of ${\mu }_{\mathrm{a}}$ over the six samples at each wavelength are averaged over each period and are summarized in Table 1. The baseline absorption coefficients at 530 and 570 nm are noticeably higher than at the other wavelengths, which coincides with the absorption spectrum of hemoglobin.³⁹ The decrease in ${\mu }_{\mathrm{a}}$ following the induction of ischemia and increase in ${\mu }_{\mathrm{a}}$ after the restoration of blood circulation can be observed at 500, 530, 570, and 584 nm. These changes in ${\mu }_{\mathrm{a}}$ are indicative of a decrease in total hemoglobin concentration because these wavelengths correspond to the isosbestic wavelengths of hemoglobin in the visible wavelength region. The occlusion of total blood inflow to the liver (except for the caudate lobe) resulted in a drop in ${\mu }_{\mathrm{a}}$ from the baseline ($P<0.05$) for 500, 530, 570, and 584 nm, and ${\mu }_{\mathrm{a}}$ values were gradually recovered 60 min after the onset of reperfusion. In vivo liver tissues examined in the present study exhibited an absorption coefficient that was strongly related to the hemoglobin absorption spectra. The maximum baseline of ${\mu }_{\mathrm{a}}$ was $36.02\pm 10.77{\mathrm{cm}}^{-1}$ at 570 nm and was $3.15\pm 1.10{\mathrm{cm}}^{-1}$ at 800 nm. We found a significant difference in ${\mu }_{\mathrm{a}}$ between the normal and ischemic liver tissues ($P<0.05$) for a wavelength range from 500 to 700 nm, between the normal and reperfused liver tissues ($P<0.05$) for a wavelength range from 500 to 800 nm, and between the normal and anoxic liver tissues ($P<0.05$) for a wavelength range from 500 to 800 nm, as shown in Table 1. In the NIR wavelength region, the changes in ${\mu }_{\mathrm{a}}$ remain, but the ${\mu }_{\mathrm{a}}$ value increases during the ischemic phase as compared to the baseline value. The decrease in ${\mu }_{\mathrm{a}}$ during ischemia and gradual increase in ${\mu }_{\mathrm{a}}$ following reperfusion in the visible wavelength region indicate that ${\mu }_{\mathrm{a}}$ at the isosbestic wavelengths can be used as a parameter to evaluate the change in total hemoglobin concentration under the hepatic ischemia–reperfusion injury. The period between the onset of nitrogen breathing and respiratory arrest averaged over all six samples was $87\pm 77\mathrm{s}$.

Table 1

Absorption coefficient μa of in vivo rat liver tissue at specific wavelengths averaged over the period of oxygen breathing, air breathing, ischemia, reperfusion, and nitrogen breathing. Values are presented as mean±standard deviation (SD) for each period. An unpaired t-test revealed the significant differences between air breathing and the other conditions.

μa(λ) (cm−1)	O2 breathing	Air breathing	Ischemia	Reperfusion	N2 breathing
500 nm	$17.77\pm 0.20$*	$18.48\pm 0.32$	$13.48\pm 0.95$*	$19.51\pm 1.03$*	$27.08\pm 2.04$*
530 nm	$30.89\pm 0.48$	$31.41\pm 0.99$	$19.81\pm 1.71$*	$33.15\pm 1.98$*	$47.85\pm 4.17$*
570 nm	$34.31\pm 0.61$	$35.07\pm 1.07$	$21.55\pm 2.20$*	$37.85\pm 2.63$*	$59.18\pm 5.75$*
584 nm	$20.40\pm 0.26$*	$21.93\pm 0.49$	$16.47\pm 1.67$*	$25.21\pm 2.47$*	$44.32\pm 4.42$*
605 nm	$6.03\pm 0.08$*	$7.23\pm 0.13$	$8.66\pm 0.56$*	$8.88\pm 1.05$*	$14.99\pm 1.09$*
620 nm	$4.60\pm 0.07$*	$5.40\pm 0.10$	$6.14\pm 0.31$*	$6.36\pm 0.60$*	$8.86\pm 0.48$*
700 nm	$2.90\pm 0.07$*	$3.31\pm 0.09$	$3.70\pm 0.16$*	$3.77\pm 0.31$*	$3.98\pm 0.11$*
800 nm	$2.82\pm 0.08$*	$3.00\pm 0.10$	$3.02\pm 0.17$	$3.24\pm 0.24$*	$2.62\pm 0.09$*

Note: *P<0.05

Fig. 7

Time courses of the absorption coefficient ${\mu }_{\mathrm{a}}$ averaged over six samples during ischemia–reperfusion experiments at (a) 500 nm, (b) 530 nm, (c) 570 nm, (d) 584 nm, (e) 605 nm, (f) 620 nm, (g) 700 nm, and (h) 800 nm. The error bars represent the standard deviation over six samples ($n=6$). In each figure, i, ii, iii, iv, and v indicate ${\mathrm{O}}_2$-breathing, air-breathing, ischemia under air-breathing, reperfusion under air-breathing, and ${\mathrm{N}}_2$-breathing, respectively.

Figure 8 shows the time courses of ${{\mu }_{\mathrm{s}}}^{\prime }$ averaged over the six samples at specific wavelengths during the period of preischemia (oxygen breathing and air breathing), ischemia, reperfusion, and nitrogen breathing. The error bars in Fig. 8 represent the standard deviation over the six samples. The average values of ${{\mu }_{\mathrm{s}}}^{\prime }$ over the six samples at each wavelength are averaged over each period and are summarized in Table 2. Time courses of ${{\mu }_{\mathrm{s}}}^{\prime }$ are well correlated with those of ${\mu }_{\mathrm{a}}$ in the wavelength range from 500 to 584 nm, which is probably due to scattering by red blood cells. The average values of ${{\mu }_{\mathrm{s}}}^{\prime }$ at 700 and 800 nm over the ischemia period were significantly ($P<0.05$) higher than that over the air breathing period. On the other hand, the average values of ${{\mu }_{\mathrm{s}}}^{\prime }$ at 500, 530, 570, and 585 nm over the ischemia period decreased significantly ($P<0.05$) as compared to the average values of ${{\mu }_{\mathrm{s}}}^{\prime }$ over the air breathing period, although the maximum value was recorded after the onset of nitrogen breathing.

Table 2

Absorption coefficient μs′ of in vivo rat liver tissue at specific wavelengths averaged over the period of oxygen breathing, air breathing, ischemia, reperfusion, and nitrogen breathing. Values are presented as mean±SD for each period. An unpaired t-test revealed the significant differences between air breathing and the other conditions.

μs′(λ) (cm−1)	O2 breathing	Air breathing	Ischemia	Reperfusion	N2 breathing
500 nm	$28.32\pm 0.31$*	$30.76\pm 0.31$	$27.87\pm 1.60$*	$33.68\pm 1.53$*	$38.27\pm 1.63$*
530 nm	$40.53\pm 0.41$*	$43.13\pm 0.90$	$33.46\pm 2.21$*	$46.42\pm 2.33$*	$52.21\pm 2.67$*
570 nm	$43.64\pm 0.55$*	$46.13\pm 0.81$	$34.14\pm 2.61$*	$50.07\pm 2.94$*	$60.72\pm 3.26$*
584 nm	$29.64\pm 0.28$*	$32.62\pm 0.36$	$28.89\pm 2.13$*	$37.30\pm 3.07$*	$48.44\pm 3.00$*
605 nm	$14.75\pm 0.22$*	$16.96\pm 0.35$	$20.30\pm 1.12$*	$20.23\pm 1.65$*	$22.93\pm 1.53$*
620 nm	$12.90\pm 0.23$*	$14.60\pm 0.35$	$17.06\pm 0.90$*	$17.07\pm 1.16$*	$16.90\pm 1.34$*
700 nm	$10.25\pm 0.23$*	$11.23\pm 0.33$	$12.92\pm 0.65$*	$12.75\pm 0.81$*	$10.73\pm 1.22$
800 nm	$9.38\pm 0.25$*	$9.83\pm 0.33$	$10.60\pm 0.58$*	$9.98\pm 0.72$	$6.77\pm 1.29$*

Note: *P<0.05.

Fig. 8

Time courses of the absorption coefficient ${{\mu }_{\mathrm{s}}}^{\prime }$ averaged over six samples during ischemia–reperfusion experiments at (a) 500 nm, (b) 530 nm, (c) 570 nm, (d) 584 nm, (e) 605 nm, (f) 620 nm, (g) 700 nm, and (h) 800 nm. The error bars represent the standard deviation over six samples ($n=6$). In each figure, i, ii, iii, iv, and v indicate ${\mathrm{O}}_2$-breathing, air-breathing, ischemia under air-breathing, reperfusion under air-breathing, and ${\mathrm{N}}_2$-breathing, respectively.

Figure 9 shows the time courses of ${\mathrm{StO}}_2$ averaged over six samples during the period of preischemia (oxygen breathing and air breathing), ischemia, reperfusion, and nitrogen breathing. The average values of ${\mathrm{StO}}_2$ over each period are summarized in Table 3. A sharp decrease in ${\mathrm{StO}}_2$ following induction of ischemia is clearly observed. Sixty minutes after the onset of reperfusion, the value of ${\mathrm{StO}}_2$ recovered gradually but remained lower than the baseline ${\mathrm{StO}}_2$. The ${\mathrm{StO}}_2$ was $59.56\pm 1.58\%$ during oxygen breathing, $45.14\pm 3.86\%$ during normal air breathing before ischemia, $3.60\pm 3.53\%$ after 30 min of ischemia, $33.35\pm 7.27\%$ 60 min after reflow of blood to the liver, and $4.91\pm 3.40\%$ 60 min after death. The downslope was linear over the entire 30-min period of ischemia. Hence, after 30 min of ischemia, the value of ${\mathrm{StO}}_2$ decreased significantly from the baseline and increased gradually ($P<0.05$) after 60 min of reperfusion compared to the ischemic value. Figure 10 shows the time courses of ${\mu }_{\mathrm{a}}(605)/{\mu }_{\mathrm{a}}(620)$ averaged over six samples during the period of preischemia (oxygen breathing and air breathing), ischemia, reperfusion, and nitrogen breathing. The average values of ${\mu }_{\mathrm{a}}(605)/{\mu }_{\mathrm{a}}(620)$ over each period are summarized in Table 4. The value of ${\mu }_{\mathrm{a}}(605)/{\mu }_{\mathrm{a}}(620)$ increased significantly after the onset of ischemia and reverted to the preischemic level after 30 min of reperfusion. The value of ${\mu }_{\mathrm{a}}(605)/{\mu }_{\mathrm{a}}(620)$ increased dramatically under hypoxia and reached the maximum level 10 min after the onset of nitrogen breathing.

Table 3

Tissue oxygen saturation StO2 of in vivo rat liver tissue at specific wavelengths averaged over the period of oxygen breathing, air breathing, ischemia, reperfusion, and nitrogen breathing. Values are presented as mean±SD for each period. An unpaired t-test revealed the significant differences between air breathing and the other conditions.

	O2 breathing	Air breathing	Ischemia	Reperfusion	N2 breathing
${\mathrm{StO}}_2$ (%)	$59.56\pm 1.58$*	$45.14\pm 3.86$	$3.60\pm 3.53$*	$33.35\pm 7.27$*	$4.91\pm 3.40$*

Note: *P<0.05.

Table 4

Ratio μa(605)/μa(620) of in vivo rat liver tissue at specific wavelengths averaged over the period of oxygen breathing, air breathing, ischemia, reperfusion, and nitrogen breathing. Values are presented as mean±SD for each period. An unpaired t-test revealed the significant differences between air breathing and the other conditions.

	O2 breathing	Air breathing	Ischemia	Reperfusion	N2 breathing
${\mu }_{\mathrm{a}}(605)/{\mu }_{\mathrm{a}}(620)$	$1.32\pm 0.01$*	$1.35\pm 0.01$	$1.42\pm 0.02$*	$1.39\pm 0.03$*	$1.66\pm 0.04$*

Note: *P<0.05.

Fig. 9

Time course of the tissue oxygen saturation ${\mathrm{StO}}_2$ averaged over six samples during ischemia–reperfusion experiments. The error bars represent the standard deviation over six samples ($n=6$). In each figure, i, ii, iii, iv, and v represent ${\mathrm{O}}_2$-breathing, air-breathing, ischemia under air-breathing, reperfusion under air-breathing, and ${\mathrm{N}}_2$-breathing, respectively.

Fig. 10

Time course of the ratio of ${\mu }_{\mathrm{a}}(605)$ and ${\mu }_{\mathrm{a}}(620)$, averaged over six samples during ischemia–reperfusion experiments. The error bars represent the standard deviation over six samples ($n=6$). In each figure, i, ii, iii, iv, and v represent ${\mathrm{O}}_2$-breathing, air-breathing, ischemia under air-breathing, reperfusion under air-breathing, and ${\mathrm{N}}_2$-breathing, respectively.

5.

Discussion

The experimental results revealed that ${\mu }_{\mathrm{a}}$ decreased sharply after the onset of ischemia at the isosbestic wavelengths of hemoglobin in the visible wavelength region, which indicates the decrease in hemoglobin concentration in liver tissue due to the occlusion of the hepatic portal. The value of ${\mu }_{\mathrm{a}}$ for in vivo liver tissue is primarily affected by the absorption properties of hemoglobin and CcO.⁴² Since the hemoglobin absorbs light strongly in the wavelength range of 500 to 600 nm, the decrease in ${\mu }_{\mathrm{a}}$ at 500, 530, 570, and 585 nm [Figs. 7(a)–7(d)] after the onset of ischemia is primarily reflected by the lower blood content of ischemic liver as compared to normal liver. The remarkable increase in ${\mu }_{\mathrm{a}}$ at 500, 530, 570, and 585 nm is probably due to the increase in blood volume in the liver after death, which is consistent with the observations of increased liver weight in postmortem animals without immediate bleeding.^43–45 The change in ${\mathrm{StO}}_2$ during ischemia and reperfusion was also reasonable, as shown in Fig. 9. The value of ${\mathrm{StO}}_2$ decreased rapidly to $1.83\pm 1.39\%$ after the onset of ischemia, whereas in the case of reperfusion, the value of ${\mathrm{StO}}_2$ recovered up to $46.24\pm 12.29\%$, which is as high as that before ischemia ($46.05\pm 11.72\%$) under the normal condition with air breathing. The results showed that the current DRS system could effectively monitor the decrease in ${\mathrm{StO}}_2$ resulting from the occlusion of blood inflow to the liver, which reflects the dysfunction of microcirculation in the liver induced by ischemia.⁴⁶ Hepatic ischemia–reperfusion injury reduces total hepatic blood flow and causes severe microcirculatory dysfunction, which results in venous stagnation, adversely affecting hepatic tissue oxygenation.⁴⁷ The decrease in HbO immediately after occlusion of the hepatic portal vein resulted in a decrease in the ${\mathrm{StO}}_2$ level. At the end of the reperfusion period, HbO levels recovered, which helps to increase ${\mathrm{StO}}_2$ following reperfusion.⁴⁷ We also observed significant increases in ${\mu }_{\mathrm{a}}(605)/{\mu }_{\mathrm{a}}(620)$ during ischemia and after the onset of nitrogen breathing (Fig. 10), representing a reduction in heme aa3, which is a sign of mitochondrial energy failure. This is supported by the change in absorption spectrum of in vitro blood-free liver induced by the application of ${\mathrm{Na}}_2{\mathrm{S}}_2{\mathrm{O}}_4$, as shown in Fig. 4. On the other hand, it has been reported that noninvasive optical evaluation of CcO redox state in vivo can suffer from optical cross talk from hemoglobin absorption signals.^48,49 Hence, the measurements of heme aa₃ in CcO based on the value of ${\mu }_{\mathrm{a}}(605)/{\mu }_{\mathrm{a}}(620)$ could be varied with the changes in the concentrations of oxygenated and deoxygenated hemoglobin. However, the possibility of relative measurements of the redox state of heme aa₃ in CcO of in vivo rat liver could still prove valuable. Studies on the multiple regression analysis for the estimated ${\mu }_{\mathrm{a}}(\lambda )$ with the extinction coefficient spectra of oxygenated hemoglobin, deoxygenated hemoglobin, oxidized heme aa₃, and reduced heme aa₃ would strengthen the method in the future. We will investigate the multiple regression analysis for ${\mu }_{\mathrm{a}}(\lambda )$ involving those four chromophores further in future work.

It has been reported that ischemia–reperfusion may cause postischemic microvascular reperfusion failure,⁵⁰ which is characterized by a reduction in sinusoidal red blood cell velocity,⁵¹ ultimately affecting ${\mu }_{\mathrm{a}}$ and ${{\mu }_{\mathrm{s}}}^{\prime }$. The value of ${{\mu }_{\mathrm{s}}}^{\prime }$ for in vivo liver tissue is affected by light scattering by cellular structures in tissues and red blood cells in microcirculation. The changes in light scattering at 500, 530, 570, and 584 nm [Figs. 8(a)–8(d)] reflect that scattering is strongly affected by red blood cells and is well synchronized with the absorption changes of corresponding wavelengths [Figs. 7(a)–7(d)]. By contrast, the light scattering in the NIR wavelength region [Figs. 8(g) and 8(h)] is primarily affected by changes in tissue morphology. The changes in ${{\mu }_{\mathrm{s}}}^{\prime }$ in the NIR region during the experiments were quite different from those at the isosbestic wavelengths of hemoglobin in the visible wavelength region. The spectrum of the reduced scattering coefficient ${{\mu }_{\mathrm{s}}}^{\prime }(\lambda )$ of biological tissues can be treated as a combination of ${{\mu }_{\mathrm{s}}}^{\prime }(\lambda )$ for cellular and subcellular structures of different sizes.⁵² Generally, the sizes of the cellular and subcellular structures in biological tissues are distributed as follows: membranes, $<0.01\mu \mathrm{m}$;⁵³ ribosomes, $<0.01\mu \mathrm{m}$;⁵⁴ vesicles, 0.1 to $0.5\mu \mathrm{m}$;⁵³ lysosomes, 0.1 to $0.5\mu \mathrm{m}$;⁵⁵ mitochondria, 1 to $2\mu \mathrm{m}$;⁵² nuclei, 5 to $10\mu \mathrm{m}$;⁵² and cells, 5 to $75\mu \mathrm{m}$.⁵² Figure 11 shows the spectra of the reduced scattering coefficient ${{\mu }_{\mathrm{s}}}^{\prime }(\lambda )$ calculated by the Mie theory for spheres of various sizes. In the Mie-theory based calculation, the refractive indices of a sphere and the surrounding medium were set to be 1.46 and 1.35, respectively, at a volume concentration of 2%. The slope of ${{\mu }_{\mathrm{s}}}^{\prime }(\lambda )$ decreases as the diameter of the sphere $d$ increases. The entire spectrum of ${{\mu }_{\mathrm{s}}}^{\prime }(\lambda )$ increases as the diameter of the sphere $d$ increases in the range of $d=0.01$ to $0.2\mu \mathrm{m}$, but decreases as the diameter of the sphere $d$ increases in the range of $d=0.6$ to $10.0\mu \mathrm{m}$.

Fig. 11

Reduced scattering coefficient ${{\mu }_{\mathrm{s}}}^{\prime }(\lambda )$ calculated by the Mie theory for spheres of various sizes.

Anoxia has been reported to induce postmortem hepatocyte vacuolation and liver weight increase.^43,44 Pronounced hepatocyte vacuolation can occur as soon as 30 s after the suspension of organ perfusion in vitro or up to 3 to 4 min after death under an anoxic condition.^43,44 The hepatocyte vacuoles are single or multiple and round or oval, and are often well demarcated, with variable displacement of hepatocyte nuclei. Some vacuoles are clear, but most have pale or eosinophilic contents with a homogeneous, granular, and/or fibrillary appearance. A mixed clear/eosinophilic stained appearance has been frequently observed within a single vacuole or vacuoles in the same hepatocyte. Intracytoplasmic vacuoles increased in size and number, and hepatocyte vacuolation and sinusoidal congestion extended from more centrilobular to periportal regions as the postmortem interval increased.⁴⁵ Several studies demonstrated that hepatocyte vacuoles for rats were 2 to $15\mu \mathrm{m}$ in diameter within 15 min after death^43,44 or up to $25\mu \mathrm{m}$ in diameter 25 min after death.⁴⁵ As shown in Fig. 11, the volume increase in structures larger than $0.6\mu \mathrm{m}$ contributes to the decrease in ${{\mu }_{\mathrm{s}}}^{\prime }$ in the NIR wavelength region. Therefore, the decrease in ${{\mu }_{\mathrm{s}}}^{\prime }(\lambda )$ in the NIR wavelength region after the onset of nitrogen breathing or pulmonary arrest obtained by the proposed method indicates hepatocyte vacuolation. This implies that the irreversible morphological changes due to the loss of hepatic viability can be evaluated using the reduced scattering coefficients estimated by the current DRS system. The causes of the temporary increase of ${{\mu }_{\mathrm{s}}}^{\prime }$ in the NIR region during ischemia remain unclear. One possible explanation for such a reversible scattering change is the volume changes in structures smaller than 0.$2\mu \mathrm{m}$ (membranes, ribosomes, small vesicles, and mitochondrial matrix granules), as shown in Fig. 11. The severity of hepatocyte damage has been reported to depend on the length of warm ischemia.^56,57 Short periods of ischemia result in reversible cell injury, in which liver oxygen consumption reverts to normal levels when oxygen is resupplied during reperfusion. Reperfusion after more prolonged periods of ischemia (2 to 3 h) results in irreversible cell damage. The time limit for hepatocytes survival was estimated to be 1.5 h of warm ischemia.^56,57 It has also been reported that as an ischemia–reperfusion injury, necrosis and apoptosis occur 3 to 6 h after ischemia–reperfusion.⁵⁸ The scattering changes in the NIR wavelength region during reperfusion for at least 6 h after more prolonged periods of ischemia should be investigated in the future. Liver transplantation would be one useful clinical application of this technology because an adequate blood supply and tissue oxygenation of the graft is essential to its initial function.^59,60 The results for ${\mu }_{\mathrm{a}}(\lambda )$, ${{\mu }_{\mathrm{s}}}^{\prime }(\lambda )$, ${\mathrm{StO}}_2$, and ${\mu }_{\mathrm{a}}(605)/{\mu }_{\mathrm{a}}(620)$ indicate that the method applied in the present study is reliable and has potential application in the intraoperative assessment of graft tissue viability.

6.

Conclusions

We investigated a method for evaluating the reduced scattering coefficient, the absorption coefficient, the tissue oxygen saturation, and the reduction of heme aa3 of in vivo liver tissue using a single-reflectance fiber probe with two source-collector geometries. The time courses of ${\mu }_{\mathrm{a}}$ at 500, 530, 570, and 584 nm indicated the hemodynamic change in the liver tissue as well as ${\mathrm{StO}}_2$. A significant increase in ${\mu }_{\mathrm{a}}(605)/{\mu }_{\mathrm{a}}(620)$ during ischemia and after euthanasia induced by nitrogen breathing was observed, indicating a reduction in heme aa3, which is a sign of mitochondrial energy failure. The time courses of ${{\mu }_{\mathrm{s}}}^{\prime }$ at 500, 530, 570, and 584 nm were well correlated with those of ${\mu }_{\mathrm{a}}$, which also reflects the scattering by red blood cells. On the other hand, at 700 and 800 nm, a temporary increase in ${{\mu }_{\mathrm{s}}}^{\prime }$ and an irreversible decrease in ${{\mu }_{\mathrm{s}}}^{\prime }$ were observed during ischemia–reperfusion and after euthanasia induced by nitrogen breathing, respectively. The change in ${{\mu }_{\mathrm{s}}}^{\prime }$ in the NIR wavelength region during ischemia is indicative of the morphological changes in the cellular and subcellular structures induced by ischemia, whereas that after euthanasia implies hepatocyte vacuolation. The results of the present study indicate the potential application of the current DRS system in evaluating the pathophysiological conditions of in vivo liver tissue. The advantages of the proposed method are its simplicity and portability, because the only devices required are a white light source, fiber optics, and two spectrometers. Since the proposed method can be used to simultaneously evaluate changes in hemodynamics, mitochondrial energy level, and tissue morphology, this method will be useful for studying tissue viability of in vivo liver tissue. We intend to further extend the proposed method in order to investigate pathophysiological conditions of liver tissue, such as those resulting from liver transplantation.