2.1.

Steatosis Induction

Male C57BL/6 mice of 16 weeks of age and weighting $25\pm 5\mathrm{g}$ were obtained from the Animal Care Facilities at the Experimental Medicine Unit from the Hospital General de México and maintained under controlled conditions. Both food and water were allowed ad libitum. All procedures were approved by the Institutional Ethics Review Board at the Hospital General de México.

In order to develop different degrees of steatosis, mice were randomly assigned to be fed either a methionine–choline deficient (MCD) or a methionine–choline control (MCC) diet (MP Biomedicals, California, USA) during 2 (MCD2w) or 8 weeks (MCD8w). To avoid confounding factors due to the complexity of the degree of NAFLD, only animals developing simple steatosis were included in this study.

2.2.

Sample Collection

After appropriate time of treatment, 2 weeks for MCD2w and 8 weeks for MCD8w, animals were anesthetized with xylazine–ketamine. Liver samples from the right lobe were obtained and preserved in sterile cold PBS for immediate DRS assessment as described below. The left lobe was divided to either be embedded in Tissue-tek OCT (Sakura Finetek, USA) and stored at $-20°\mathrm{C}$ until assayed; or be fixed in 3.7% formaldehyde-PBS solution to be embedded in paraffin.

2.3.

Hepatic Fat Content Assessment

Histological evaluation of the degree of fatty liver disease was performed in Hematoxylin-Eosin stained sections according to the nonalcoholic fatty liver disease activity score (NAS).¹⁸ Liver fat contents were assessed in frozen sections stained with oil red O (Abcam, California, USA) and quantified by a morphometric analysis using Image J software (NIH, USA).

2.4.

Diffuse Reflectance Instrumentation and Measurements

The diffuse reflectance instrumentation used in this study has been reported elsewhere.⁹ Briefly, the light source employed was a light emitting diode (LED-P3WW120-120/41 115 by SiLED Int), which operates in the range of 400 to 800 nm. The spectrometer employed was a QE65000 (Ocean Optics Corp.), which operates in the region from 400 to 1100 nm with an entrance slit of $10\mu \mathrm{m}$. The fiber-optic bundle (QR400-UV-VIS, Ocean Optics Corp.) is composed of two branches, one with a single fiber-optic to collect the diffusely reflected light and deliver it to the spectrometer, and the other with a circular array of six fibers that are employed for irradiation. All fibers have a diameter of $400\mu \mathrm{m}$. The operation of both spectrometer and light source is performed by means of a programmed LabVIEW interface. A schematic of the instrumentation is shown in Fig. 1.

Fig. 1.

(a) DRS setup: the spectrum of the excitation light source as well as the geometry of the probe is shown and (b) system showing the measurement of the diffuse reflectance standard.

Ex vivo DR spectra were acquired from a total of 22 samples of liver tissue gathered from the same number of subjects: nine for MCC group, six for MCD2w group, and seven for MCD8w group. Measurements were carried out in a darkened room putting the probe tip manually establishing surface contact with the liver surface at different points without puncturing the Glisson’s capsule at a spatial density of 22 points per square centimeter. This procedure was always conducted by the same operator to ensure that a nearly constant pressure was applied. Prior to spectral measurements of liver samples and after 15 min warm-up time, the dark spectrum was obtained by blocking the light input to the spectrometer. During data processing, the dark spectrum was subtracted from each measured spectrum using appropriate software. Also, reference LED-source reflectance spectrum was measured using a reflectance standard (Spectralon WS-1, Ocean Optics Corp.) with a reflectivity above 95% for the 250- to 1500-nm range, positioning the probe in close contact with the surface of the standard and perpendicular to it. For all measurements, the radiant flux power of the light source was configured at 0.7 mW (measured at the tip of the probe). The integration time of the spectrometer was set to 100 ms. All spectra were limited to the 400- to 800-nm range. The spectrometer setting was such that its spectral resolution is equal to 0.77 nm, which yields 522 measuring points in each spectrum.

Diffuse reflectance measurements of each sample were converted to relative reflectance values using

2.5.

Statistical Analysis

A total of 428 DR spectra were acquired: 153 spectra for MCC group, 143 for MCD2w group, and 132 for MCD8w group. For every group, the mean of all the measured spectra as well as its standard deviation were calculated. Areas under the curve (AUC) of all spectra in the interval from 400 to 800 nm were computed in relative units. Then, one-way ANOVA followed by Tukey post hoc tests were carried out to determine statistical differences between the means of the AUC of each group with a 0.05 significance level.

As a second step, a multivariate statistical analysis of principal components (PCA) was performed over the whole spectral data set. This analysis reduces the number of variables with minimum loss of information.¹⁹ Principal components (PCs) that accounted for most of the variance ($>99\%$) and that correspond to the eigenvalues before the cut-off point or “elbow” of the Scree plot²⁰ were taken for the construction of a linear discriminant analysis (LDA) classification model. A linear model was chosen due to the limited number of available observations and its better stability to variations in the statistical data.²¹ A supervised classification scheme was developed using the LDA model, where the independent variables were the five most significant PCs that accounted for over 99% of the variance of the whole set of observations, and taking into account the membership to the groups—MCC, MCD2w, and MCD8w—as the classes in this classification framework. Afterward, the classification and cross-validation procedures were carried out following a leave-one-out scheme for each one of the observations, i.e., for each measured spectrum that was reduced to its five PCs, to prove the belonging of each observation to its corresponding class. To be specific, all data were used as training data and cross validation was performed excluding data “one at a time” to judge which group it should be assigned to and then verifying whether the classification was correct or not. Such framework allows the validation of the classification scheme through the determination of the confusion matrix, which was constructed to contrast the predicted versus the actual class membership; the calculation of the classification rate errors as the value in percent of misclassifications relative to the number of observations.

Also, a canonical score plot of LDA was performed to define the axes that provide and visualize maximum separation among the groups. Given the fact that the canonical variables are uncorrelated linear functions of the original set of variables, in our case, there were three groups or classes; therefore, there will be two canonical variables. Probability estimates obtained from the above classification model were then used as scores to obtain receiver operating characteristic (ROC) curves fixing in every case one state as positive (i.e., belonging to its class) and the other two as negative. The ROC curve plots the proportion of true positives (sensitivity) against the proportion of false positives ($1-\text{specificity}$) for every possible value of the threshold (in our case, the posterior probability obtained from the classification model).²² The AUC was obtained for every ROC curve and they were used for comparison of the discriminative power of different tests. Optimal values of sensitivity and specificity for each ROC curve were found using the criterion of the Youden index, which is calculated as the cut-point where the maximum of $(\text{sensitivity}+\text{specificity})-1\text{occurs}$.²³ In this way, the effectiveness of using the classification results as predictors was evaluated, the Youden index is optimal in the sense that it is the cut-point that optimizes the predictors differentiating ability when equal weight is given to sensitivity and specificity. The whole statistical analysis was conducted using MATLAB R2016a (Mathworks, Natick, Massachusetts, USA).

3.1.

Hepatic Steatosis

Mice receiving MCC diet for 2 or 8 weeks did not exhibit any hepatic architectural alteration as it can be observed in the first row of Fig. 2(a), where typical images of Hematoxylin-Eosin stained liver sections are displayed on the left side; on the right side, characteristic images of liver sections stained with oil red are shown. Thus liver samples from mice fed with MCC diet for 2 or 8 weeks were considered as one single control group (MCC). For the MCD groups, simple steatosis was confirmed by NAS (values 1 or 2). According to the time of treatment, significantly increased liver fat was observed in mice fed MCD diet [see the second and third rows of Fig. 2(a)]. The obtained percent values of liver fat content are displayed in a bar plot in Fig. 2(b), where the error bars stand for the positive half of the standard deviation. An ANOVA statistical test was performed with the null hypothesis that the means of all groups are equal at the 0.05 significance level. The null hypothesis could be rejected by ANOVA test. However, it was still necessary to determine which one of the fat-content mean-values is different from the rest. For that reason, a Tukey multiple comparison test was applied. It was found that it is not possible to differentiate the mean fat content between the MCD2w and MCD8w groups [indicated by a line over the bars in Fig. 2(b)] while the mean fat content of the MCC group differentiates, with 0.05 significance level, from both simple steatosis groups: MCD2w and MCD8w. However, the mean size of fat droplets was significantly different among MCD2w and MCD8w ($\mathrm{MCD}2\mathrm{w}=17.3\pm 8.5$; MCD8w $33.0\pm 7.9\mu \mathrm{m}$, $p<0.05$).

Fig. 2

(a) Images of tinctured liver samples and (b) liver fat content expressed in percent values. $\text{Mean value}\pm \text{standard deviation}$. $p<0.05$, ANOVA. Line over bars indicates groups, which were not significantly different (Tukey multiple comparison test).

3.2.

Diffuse Reflectance Spectra

Average diffuse reflectance measurements were obtained for every group. The calculated $\text{mean}\pm \text{dispersion}$ bars spectra for each group are plotted in Fig. 3(a). Although the dispersion bars for MCD groups partially overlap, there is evidence that reflectance spectra from different groups have intensity differences in the range from 500 to 800 nm, which become more significant as the fat content increases. Interestingly, around 560 nm, a large decrease in reflectance is observed. Also, the AUC from 400 to 800 nm seems to point to a difference between groups with simple steatosis and the control (AUC: $\mathrm{MCC}=0.20\pm 0.06$, $\mathrm{MCD}2\mathrm{w}=0.29\pm 0.07$, and $\mathrm{MCD}8\mathrm{w}=0.35\pm 0.05$; $p<0.05$) as seen from Fig. 3(b); these differences increase when the AUC is calculated from 630 to 800 nm (AUC for $\mathrm{MCC}=0.26\pm 0.06$, $\mathrm{MCD}2\mathrm{w}=0.41\pm 0.09$, and $\mathrm{MCD}8\mathrm{w}=0.50\pm 0.09$; $p<0.05$). The ANOVA and Tukey tests yielded that at 0.05 significance level it is possible to reject the hypothesis that the population means are equal and determined that the difference between the means of all groups is significant, thus pointing to the fact that indeed the DR spectra have distinctive differences for all groups. However, a more detailed statistical analysis will follow below to delve into these observations. Visually, the percentage of liver fat content in Fig. 2(b) and the areas of DR curves in Fig. 3(b) appear to be correlated, in fact averaging those variables for each animal a Spearman correlation coefficient of 0.836 was found.

Fig. 3

(a) $\text{Mean}\mathrm{DRS}\pm \text{standard deviation}$ from MCC, MCD2w, and MCD8w groups and (b) bar plot of the $\mathrm{AUC}\pm \text{standard deviation}$ of the DRS from 400 to 800 nm shown in (a). Bars not sharing a letter are significantly different (Tukey test, $p<0.05$).

3.3.

PCA and LDA

The first five PC values, accounting for 99.97% of the variance, were estimated and selected for a supervised discriminant analysis classification. Even though equality test of group covariance matrices failed at 0.05 significance level (natural log of the determinants of each group’s covariance matrix being $-19.94$, $-18.35$, and $-15.72$, respectively), the linear variant of the discriminant analysis was enforced because the number of observations was near the recommended lower valid number of observations for its quadratic analog, which may cause an incremented variance with variations on input data. The canonical score plot of the LDA is shown in Fig. 4(a), where the center of each group is marked with “×.” The coefficients of the equations of the straight lines shown in Fig. 4(a) for the boundaries between classes were readily available from the linear discriminant classifier model. Discrimination of the healthy group from the groups suffering from fatty liver is observed. Table 1 shows the confusion matrix (actual classification of groups based on the exposure time to MCD diet versus predicted classification groups obtained from DRS measurements plus statistical analysis) for the LDA. The diagonal values (highlighted in bold font) reflect the percentage of correct group classification, where all controls were correctly assigned to control group, whereas 78.32% and 87.88% were assigned to the simple steatosis groups MCD2w and MCD8w, respectively. Values in the total line reflect the sum in percentage of all measurements assigned by the classification model to every predicted group, relative to all measurements.

Fig. 4

(a) Canonical score plot for the LDA performed with the five first PCA values of diffuse reflectance spectra. The straight lines show the boundaries between classes obtained from the LDA model. (b) ROC curves describing the capacity of correctly assigning any of the measurements to its group. The AUC is referred for each curve.

Table 1

Confusion matrix for the linear discriminant model.

Cross-validation error rates of 0.00%, 22.38%, and 12.88% were close enough to the classification error rates at 0.00%, 21.68%, and 12.12% for the respective MCC, MCD2w, and MCD8w groups to validate the used classification model. The corresponding overall cross-validation classification error at 11.45% is calculated using the cross-validation error rate values obtained for each group corrected by the different in group membership of each group, this difference is accounted multiplying each error rate value for the prior probability for each group (number of observations in the group divided by the total number of observations) and it was in good agreement with the 10.98% classification error, which was calculated in a similar way $(21.68\%*0.33411)+(12.12\%*0.30841)=10.9814\%$. Figure 4(b) shows the obtained ROC curves; the high specificity and sensitivity are observed for control (MCC) versus simple steatosis (MCD2w and MCD8w). For each ROC curve, the AUC was obtained and the optimal threshold points in the form of (sensitivity, $1-\text{specificity}$) were found according to the criterion of the Youden index as follows: (0.99, 0.00), (0.93, 0.11), and (0.90, 0.05) for MCM, MCD2w, and MCD8w groups, respectively; which gives an average value of (0.94, 0.05).