2.1.

VRR Spectra Measured from Healthy Tissue, Normal Control, and Grades I through IV Glioma Tissues

Figure 1 shows a set of typical RR spectra measured from healthy tissues, control tissues, and gliomas of six different grades from human brain tissues ex vivo. The RR spectrum from healthy brain tissue in Fig. 1(a) shows eight major peaks at 1005, 1157, 1521, 1438, 1667, 2850, 2885, and $2932{\mathrm{cm}}^{-1}$. The relatively sharp and enhanced peaks of 1157 and $1521{\mathrm{cm}}^{-1}$ should be carotenoids (low-density lipoprotein) and lipoprotein (high-density lipoprotein). Rich fatty acid RR peaks at 1438, 2850, and $2885{\mathrm{cm}}^{-1}$ are stronger than protein bands at 1005, 1667, and $2932{\mathrm{cm}}^{-1}$ in intensity. In a comparative study,⁴⁸ Verdiyan et al. collected Raman spectra from the myelin sheath of sciatic nerve fiber tissue using 532 nm laser excitation and a 50-s exposure time and observed peak intensities at 1160, 1520, 2850, 2885, and $2935{\mathrm{cm}}^{-1}$, respectively.

Fig. 1

Typical baseline-subtracted VRR spectra from (a) healthy human brain tissue, (b) normal control tissue, and human brain glioma tumors of (c) grade I, (d) grade II, (e) grade II-III, (f) grade III, (g) grade III-IV, and (h) grade IV, respectively. Insets are the raw spectra.

The normal control spectrum is collected from the cancer margin of grade IV glioma, which is also called the negative margin of the cancer or the cancer–normal tissue interface [Fig. 1(b)]. Compared with healthy tissue [Fig. 1(a)], the relative peak intensity of $2885{\mathrm{cm}}^{-1}$ is significantly reduced and the peak at $2931{\mathrm{cm}}^{-1}$ is higher than that at $2885{\mathrm{cm}}^{-1}$. These differences can be explained by the hypothesis that the composition and conformation of lipids (saturated and unsaturated fatty acids) and proteins (full amino acids contribution) in cells and tissues changed from those in normal tissue to those found in cancer margins.^35,46,47,49

In this study, it is important to understand the classification of glioma. Traditionally, gliomas are classified into grades I to IV according to the morphology, the degree of malignancy, and the location of tumor cells. Low-grade gliomas refer to the first and second level of gliomas. With the development of molecular biology¹⁴ and the rise of molecular pathology (genetic code), the molecular grading of glioma has become increasingly important. Figures 1(c) and 1(d) show RR spectra of grade I and grade II glioma examined by histopathology, which are also called chronic neoplastic diseases. A grade I glioma tumor is considered to be at the benign level. The data show that its RR spectral profile is close to that of the control tissue [Fig. 1(b)], but some features are different. For example, the strength of the saturated fatty acid bond (1441 and $1452{\mathrm{cm}}^{-1}$) is weaker, and the RR molecular fingerprints of amide I ($1640{\mathrm{cm}}^{-1}$), amide II ($1550{\mathrm{cm}}^{-1}$), amide III ($1306{\mathrm{cm}}^{-1}$), tryptophan and mitochondrion (1587 and $754{\mathrm{cm}}^{-1}$), and the RR peak at $1358{\mathrm{cm}}^{-1}$ (higher than $1378{\mathrm{cm}}^{-1}$), which reflects ${\mathrm{HbO}}_2$ saturation status and oxygen delivery at the cellular level, all show a tendency of either growing or weakening, respectively. Figures 1(d)–1(h) demonstrate grades II to IV gliomas. The RR molecular fingerprints that occurred in grade I glioma tissue all distinctly increased, decreased, or shifted in higher grades of glioma tissues. In addition, the intense sharp peak at 1127 and $2938{\mathrm{cm}}^{-1}$ suggested contributions from lactate.⁵⁰ A shift of the center of characteristic peaks and a change in peak intensities were found in glioma tumors of grades III and IV. For example, the intense peak at 1358 (low grades) shifting to $1378{\mathrm{cm}}^{-1}$ (high grades) was observed. The changes in the RR spectral peaks at 1358 (deoxy-Hb) and $1378{\mathrm{cm}}^{-1}$ (oxy-Hb) show deoxy-hemoglobin dominating at low-grade levels and oxy-hemoglobin dominating at high levels. This RR spectral peak shift may be used to monitor hypoxia and necrosis status in high-grade glioma tissues in vivo.^51,52 RR spectral vibrational modes of fingerprints are shown in Supplemental Table S1.

2.2.

Identification of Glioma Grades by Carotenoids

The resonance-enhanced intrinsic molecular fingerprints with intense RR modes at $1157{\mathrm{cm}}^{-1}$ ($({\nu }_s(\mathrm{C}─\mathrm{C}))$, $1521{\mathrm{cm}}^{-1}$ ($({\nu }_s(\mathrm{C}═\mathrm{C}))$, and $1008{\mathrm{cm}}^{-1}$ ($(\rho (\mathrm{C}─{\mathrm{H}}_3),\nu (\mathrm{C}─\mathrm{C}))$ and major overtone peaks at 2320 and $2667{\mathrm{cm}}^{-1}$ should mainly arise from carotenoids. Carotenoids play an important role in the antioxidant defense system in the healthy brain [Fig. 1(a)]^53–61 and have been considered as a cancer biomarker.^62,63 Johnson et al. have also reported the important role of carotenoids and, particularly, the presence of lutein and zeaxanthin in normal brain tissue.^64–66 They studied the roles of lutein and zeaxanthin for health and brain functions. Classifying vibrational Raman modes is shown in Supplemental Table S1. Previous studies have shown that the concentration of carotenoids in blood plasma is inversely related to the risk of developing cancer according to epidemiological and experimental investigations. Carotenoids are specifically distributed in different lymphocyte subtypes. They are in the immune system to perform their own specific functions, although the relative concentration of carotenoids in blood plasma (of the order of ${10}^{-6}\mathrm{M}$) is relatively low compared to other components in lymphocytes (white blood cells).^53,54 The enhancement in these two Raman bands occurs in our VRR measurements because carotenoids have an absorption band at $\sim 480\mathrm{nm}$, which leads to a preresonance enhancement with 532 nm excitation. A clear decrease in the intensities of the 1157 and $1521{\mathrm{cm}}^{-1}$ peaks was observed with the increase of the glioma tissue grades. This indicates a progression of the mutation process in the gliomas. When compared to grade I, these two RR peaks reduced significantly in grades II to IV.^25,34 This reduction may be associated with a direct decrease of the original peaks at these wavenumbers or a shift in the chemical vibrational bands. Such changes reveal a decreased concentration of carotenoids, which may be caused by the structural changes in the microenvironment of the tumors. Carotenoids are natural fat-soluble pigments and reduce with the reduction of fat. For example, the peak $1521{\mathrm{cm}}^{-1}$ drastically decreases with the decreasing concentration of saturated fatty acid lipids reflected by the peaks at 1442 and $2854{\mathrm{cm}}^{-1}$. These observations indicate that a fast activation and deactivation of Raman vibrational modes at 1521 and $1157{\mathrm{cm}}^{-1}$ exists in glioma tissues. Although carotenoid Raman signals seem to be not very different among different grades of glioma tumors, therefore, they not very helpful for distinguishing among glioma grades, a dramatic decrease in carotenoid signal in gliomas versus normal and control brain tissue is quite remarkable. RR modes of 1157 and $1521{\mathrm{cm}}^{-1}$ could be a significant marker to diagnose glioma and other CNS cancers.^48,53,54

2.3.

Identification of Glioma Grades by Tryptophan

The peak at $1588{\mathrm{cm}}^{-1}$ observed in the RR spectra is considered to be the main vibrational mode ($W_{8\mathrm{b}}$) of the fingerprint of tryptophan.^67–70 It was enhanced due to resonance, especially in the malignant gliomas of high grades (III and IV). In addition to tryptophan, we consider that the Raman mode of $1588{\mathrm{cm}}^{-1}$ may be contributed by mitochondria, hemeproteins, and DNA bases ( Supplemental Table S1).^71–73 Based on our previous experimental data using VRR method and autofluorescence method (to be published) on human glioma tumors^{23,26,42,43,74} and the experimental and theoretical studies reported in the literature,^{47,67–70,75} we propose tryptophan as the main contributor to the Raman mode of $1588{\mathrm{cm}}^{-1}$. One possible form of the tryptophan contribution to $1588{\mathrm{cm}}^{-1}$ mode may be tryptophan radicals because of the microenvironment in the malignant tumor tissues.^76–79 The intensity ratio of 1588 to $1440{\mathrm{cm}}^{-1}$ (protein to lipids) was used to analyze the concentration changes of tryptophan in glioma tissue of different grades, and the difference is shown in Fig. 2(a). For calculations and comparisons of peak intensities, the spectral peak intensities were normalized to the intensity of the $1004{\mathrm{cm}}^{-1}$ peak, which is an intense peak insensitive to conformational changes of proteins and is therefore usually used for normalization of the Raman spectra of proteins. This peak at $1004{\mathrm{cm}}^{-1}$ is assigned to the breathing mode of phenylalanine that has a relatively stable intensity and position in different environments. The data show an increasing trend in both the concentration of tryptophan and the ratio of 1588 to $1440{\mathrm{cm}}^{-1}$ in glioma tissue with increasing tumor grade. However, the ratio decreased in grade IV glioma tumor, which may be due to the metabolism of high-grade tumors, with the changes of cell apoptosis and tissue necrosis where the concentration of tryptophan is also reduced. Studies in the literature have shown that the heterocyclic amino acid tryptophan in human brain gliomas is an essential factor and plays a critical role in the metabolic process.^80–83 The $1588\text{-}{\mathrm{cm}}^{-1}$ peak reveals that tryptophan in glioma tissues accumulates during tumor progression.

Fig. 2

Typical experimental VRR spectral data plots: the ratios of (a) $I_{1588{\mathrm{cm}}^{-1}}/I_{1440{\mathrm{cm}}^{-1}}$ and (b) $I_{2934{\mathrm{cm}}^{-1}}/I_{2885{\mathrm{cm}}^{-1}}$ from normal human brain tissues and glioma tissues with increasing malignancy. G0-N, normal human brain tissues; GI, grade I; GII, grade II; GIII, grade III; and GIV, grade IV.

Tryptophan is one of the 10 essential amino acids that the body uses to synthesize proteins. It is highly hydrophobic and has an indole ring attached to a methylene group. In addition to its participation in the synthesis of proteins, tryptophan is also used to generate biologically active products, such as the biosynthesis of the aminergic neurotransmitter serotonin (5-hydroxytryptamine, 5-HT). Tryptophan metabolism involves the kynurenine pathway.^{67–70,84–86} The catabolism of $>95\%$ of tryptophan in the brain metabolic process takes place through the kynurenine pathway. Previous studies have found that the degradation of tryptophan and the tryptophan metabolite, kynurenine (Kyn), can inhibit the antitumor immune response. As reported in the literature, tryptophan-2,3-plusoxidase is an enzyme that can convert tryptophan into Kyn in glioma and other cancers and acts directly on glioma cells and promotes tumorigenesis.^85,87

One possible explanation for the enhancement of the spectral peak of tryptophan (heterocyclic amino acids) in human brain glioma tissues is two-photon absorption.⁸⁸ We will further study the enhancement of $1588{\mathrm{cm}}^{-1}$ mode in the future. If the enhancement in the Raman signal from tryptophan is due to the use of 532 nm, the same process should also occur for phenylalanine and tyrosine, which are both aromatic amino acids. However, compared to those two, tryptophan is much more active. Its maximum molar absorptive ($L_a$ to $L_b$) band is centered at 278 nm with a bandwidth of 60 nm. Both fluorescence quantum yield and differential Raman cross section of phenylalanine and tyrosine are much smaller than tryptophan. Often, almost no signal can be detected from these molecules because of the efficient quenching by neighboring tryptophan.^89–91 Alternatively, an $L_a$ resonant Raman band of tryptophan (W2) at $\sim 1580{\mathrm{cm}}^{-1}$ gave the highest intensity when the indole ring was not hydrogen-bonded in hydrophobic environments; therefore, resonant Raman structural markers of tryptophan may arise from the side chains in proteins.^89,90

2.4.

Identification of Glioma Grades by the Intensity Ratio of Proteins to Lipid Metabolites

The Raman modes 2934 and $2885{\mathrm{cm}}^{-1}$ are both symmetric stretches that correspond to methyl ($─{\mathrm{CH}}_3$) and methylene ($─{\mathrm{CH}}_2─$), respectively. The $2934{\mathrm{cm}}^{-1}$ mode arises from proteins, whereas the $2885{\mathrm{cm}}^{-1}$ mode is from lipids and fatty acids of lipids, which contribute significant RR signal in the healthy brain tissues [Fig. 1(a)]. In this study, an increase in the intensity ratio was observed between these two Raman modes $I_{2934{\mathrm{cm}}^{-1}}/I_{2885{\mathrm{cm}}^{-1}}$ in glioma tissues of different grades. This ratio represents the ratio between proteins and lipids. It is greater in gliomas than in normal brain tissues and gradually increases in gliomas with increasing grades, as shown in Fig. 2(b). According to the Raman modes, it is shown in Fig. 2(b) that the relative concentration of lipid is $\sim 15\%$ more than that of the protein in healthy brain tissues. However, in grade IV gliomas, the relative concentration of lipids is 18% less than that of the protein. This result may be attributed to the changes in the biochemical compositions of macromolecules including lipids and proteins during tumor development and progression. The decrease in the lipid concentration in the malignant gliomas has been reported in previous studies on glioblastoma multiforme (GBM) in the human brain using Raman spectroscopy in vitro and ex vivo.^{20–22,27,81,82}

2.5.

Identification of Glioma Grades by Protein Secondary Structure Conformation Changes

Another major finding of this study is that brain glioma tumors of various grades presented distinct rearrangements of protein secondary structures reflected by observed characteristic RR spectra changes (Fig. 1 and Supplemental Table S1). From a qualitative point of view, these changes could be described as a redistribution of RR spectral peak intensities from low grades of glioma to high grades of glioma; the RR spectral central positions of the peaks shifted. These shifts were confirmed by the differences in the spectral peak positions and the protein secondary spectral structure changes that were observed in proteins vibration modes in different grades of gliomas. Among various peptide vibration modes of amide I, amide II and amide III, for the shifts of peak central positions and changes of peak intensities, the amide I band was the most pronounced.^92,93 The RR spectrum of amide I has a peak at $1667{\mathrm{cm}}^{-1}$ for the $\alpha$-helix form in normal brain tissues. This Raman frequency of the peak decreased and transitioned to $1640{\mathrm{cm}}^{-1}$ corresponding to a $\beta$-sheet conformation with an increased intensity in grade IV glioma tissues. This shift in amide I may indicate conformational changes of the peptide backbone of proteins. Similar to amide I, amide III protein secondary structural conformation changes were also observed in normal brain tissues and glioma tissues of different grades. An amide III band of $1270{\mathrm{cm}}^{-1}$ associated with the $\alpha$-helix form in normal brain tissues appeared on the sideband and was not strong, but in grade IV gliomas, the amide III band showed a transition with the new peak centered at $1225{\mathrm{cm}}^{-1}$, corresponding to a $\beta$-sheet form with a sharp and enhanced $\beta$-sheet conformation. Other studies have reported that a tryptophan W104 mutation is one of the reasons that the lipophilic protein structure changes from an $\alpha$-helix to $\beta$-sheet structure.^94–96 The changes in protein conformation require further research to understand the mechanism and contribution to glioma grading.

2.6.

Identification of Brain Cancer Margins Using Peak Ratio and SVM

Brain tumors are classified as grades I to IV according to the WHO grading system. In this study, a noncancerous tissue from the perifocal area of a tumor was taken as the normal control, whereas the normal tissues were from surgeries for traumatic brain injury or posttraumatic death for noncancer patients.

We present an application of the above statistical approach as a new optical molecular histopathology method to evaluate the negative margins of human brain glioma tissue. The specimens included seven normal and six grade IV glioma human brain tissues along with fifteen negative margins of glioma cancerous tissues.

The RR spectra of all the above-mentioned types of human brain tissue samples were smoothed at first to reduce noise. Then the baselines of the spectra were removed using a polynomial fitting with an asymmetric Huber loss function.⁹⁷ Typical preprocessed RR spectra are shown in Figs. 1(a), 1(b), and 1(h). The peak intensity ratios of $I_{2932{\mathrm{cm}}^{-1}}/I_{2885{\mathrm{cm}}^{-1}}$ and $I_{1588{\mathrm{cm}}^{-1}}/I_{1442{\mathrm{cm}}^{-1}}$ were calculated and scatter-plotted in Fig. 3. The three types of tissue samples are clustered with some overlap. Both ratios for the negative margins of glioma cancer tissues are greater than normal tissues and lower than glioma tissues.

Fig. 3

(a) Scatter plot of peak intensity ratio $2932/2885{\mathrm{cm}}^{-1}$ versus $1588/1442{\mathrm{cm}}^{-1}$, for normal tissue (circle), negative margin (triangle), and grade IV glioma (plus). SVM classifiers (boundary lines) were trained to separate each tissue type from the other two types. In total, three SVM classifiers were trained: (b) an ROC curve was generated to classify normal tissues and negative margins of glioma (not including grade IV glioma). The AUC of the ROC curve was 0.905.

The peak ratios of normal tissues versus the negative margins of glioma and the negative margins of glioma versus glioma were compared using Student’s $t$-test. For the ratio $1588/1442{\mathrm{cm}}^{-1}$, the $p$-values were 0.0196 and $3.9694\times {10}^{-8}$ for normal versus negative margins of glioma and the negative margins of glioma versus glioma, respectively. Therefore, the RR spectra for these tissue types are statistically significantly different at a 0.05 significance level. Similarly for the ratio $2932/2885{\mathrm{cm}}^{-1}$, the RR spectra were also statistically significantly different for normal tissue versus the negative margin of glioma and the negative margin of glioma versus glioma, with $p$-values of $2.6785\times {10}^{-4}$ and $1.1215\times {10}^{-5}$, respectively.

A linear support vector machine (SVM) was used to classify the spectra for the three types of samples, as shown in Fig. 3. The total accuracy was 92.9% with two normal tissue samples falling in the region for the negative margins of glioma tissue. If only normal tissues and the negative margins of glioma tissues were compared (normal, negative and negative margins, positive), the sensitivity, specificity, and accuracy were 100%, 71.4%, and 90.9%, respectively. The receiver operating characteristic (ROC) curve is plotted as a true positive rate versus false positive rate (or $1-\text{specificity}$) as shown in Fig. 3(b), and the area under curve (AUC) was 0.905. Leave-one-out cross validation (LOOCV) was also used to further evaluate the classification and also achieved a sensitivity, specificity, and accuracy of 100%, 71.4%, and 90.9%, respectively.

This result demonstrated that the proposed ratio criterion is so sensitive that it can even detect the difference between the negative margin brain tissues and pure normal brain tissues. Ideally, the method can not only classify the tissue samples into the categories using the well-established cancer grading system but also identify the tissue type that is between normal and cancer of a particular grade.

2.7.

Classification of Brain Glioma Grades by Statistical Analysis of SVM and PCA Methods

To further analyze the predicative effectiveness and robustness using the pathway signatures emerging from the Raman spectra, the statistical analyses of the VRR data collected from the brain tissues were conducted with principal component analysis (PCA) and SVM and compared with the histopathology and immunohistochemistry analysis (the “gold standard”). This analysis only used earlier data up to the year of 2017, which included 241 spectra from 95 samples in total, specifically containing 27, 7, 75, 44, and 88 spectra collected from 20, 2, 24, 14, and 35 samples for normal tissue (including negative controls), grades I to IV glioma tissues, respectively. All the sample types were confirmed by H&E-based histopathology reports. Different tissue samples (e.g., cancerous and negative control tissues) may be from one patient, and such samples are considered as different cases separately. The analyses here allowed us to evaluate the performance of the classification of normal brain tissue and glioma tissues, as shown in Fig. 4. The detailed explanation of the methods can be found in Sec. 4. When the first two principal components (PCs), PC1 and PC2, were used for classification, the scatter plot of the PC scores of normal and all grades of glioma tissue samples are shown in Fig. 4(a) along with the ROC curve shown in Fig. 4(b). When resubstitution validation was performed, the sensitivity, specificity, and accuracy for the SVM classifier shown in Fig. 4(a) were 96.3%, 81.5%, and 94.6%, respectively. The AUC of ROC was 0.968. If LOOCV was used, the sensitivity, specificity, and accuracy were 96.3%, 74.1%, and 93.8%, respectively. When PC2 and PC6 were used, the scatter plot of the PC scores of normal and all glioma tissue samples are shown in Fig. 4(c) along with the ROC curve in Fig. 4(d). The sensitivity, specificity, and accuracy for the SVM classifier with resubstitution validation as shown in Fig. 4(c) were 99.5%, 92.6%, and 98.8%, respectively. The AUC of ROC was 0.994. LOOCV sensitivity, specificity, and accuracy were equal to those with resubstitution validation. If PC1, PC2, and PC6 were used, the sensitivity, specificity, and accuracy for both resubstitution validation and LOOCV were 100%, 96.3% and 99.6%, respectively, with an AUC of ROC of $\sim 1.0$.

Fig. 4

(a) A scatter plot of scores of PC2 versus PC1 of normal and all glioma tissue samples along with a linear SVM classifier. (b) The ROC curve corresponding to the SVM classifier in (a). (c) A scatter plot of scores of PC6 versus PC2 of normal and all glioma tissue samples along with a linear SVM classifier. (d) The ROC curve corresponding to the SVM classifier in (c).

In Fig. 5, the separation lines were calculated based on PC1 and PC2 using the SVM algorithm to classify the spectra collected from normal and glioma tissues into three categories, including normal tissue, glioma grades I and II, and glioma grades III and IV. The results yielded a total diagnostic accuracy of 71.4% when compared to the pathology reports as the “gold standard.” Here grades “II and III” glioma tissues were included in grade III, and grades “III and IV” glioma tissues were included in grade IV. The PC scores for PC1 and PC2 were used for classification. The entire two-dimensional space is divided into three regions for the three groups of brain tissue, respectively. The accuracy for each group is calculated based on the percentage of the tissue samples correctly falling into the corresponding region. The accuracies for the three classes were calculated as 81.5%, 52.4%, and 81.1%, respectively. The results are relatively effective for glioma diagnosis based on Raman spectra and the classification of brain glioma tissues of low versus high grades. The results also show that approximately half of the low-grade tissue samples fall in the high-grade region, which may be due to mixed features in the low-grade tissue samples. If all three PC scores of PC1, PC2, and PC6 were used, the accuracies were 96.3%, 53.7%, and 84.1% for the three groups, respectively, with a total accuracy of 75.1%.

Fig. 5

A scatter plot of the scores of PC2 versus PC1 of normal versus grades I and II glioma samples versus grades III and IV glioma samples along with the linear SVM classifiers. The entire two-dimensional space is divided into three regions as labeled.

4.1.

Materials and Experiments

There are more than 125 histologically different types of brain and CNS tumors that are usually categorized as a primary brain tumor of a high grade (rapidly growing) or low grade (slow growing) and metastatic or secondary brain tumor (the cancer began in another part of the body and spread to the brain).

In this report, we studied primary glioma brain tumors. VRR spectra were measured from normal human brain tissues and glioma tissues including glioblastoma and astrocytoma ex vivo. The label-free RR spectral data reported in this paper were measured from the year of 2011 to 2018. The measurements were performed using a confocal micro-Raman spectrometer with an excitation wavelength of 532 nm over a spectral scan region of 500 to $3500{\mathrm{cm}}^{-1}$. Five hundred and ten RR spectra were collected from one hundred and twenty-one subjects, including healthy brain tissue, normal control tissues (the negative margin of brain cancer tissues), and glioma tumors at low grades (I and II) and high grades (grade III including grade II-III, and grade IV including grade III-IV). For glioma tumor specimens, $\sim 3$ to 5 spectra were collected from each sample; for normal tissue specimens, less spectra were collected since the spectra from normal samples seem to be more consistent. The types and levels of all of the samples were examined according to the WHO standard (the gold standard) by regular histopathological analysis methods.

4.2.

Sample Preparation

The tissue specimens were provided by the Air Force Medical Center in Beijing, China. Glioma grading was performed according to the standard WHO classification system.

There were no human participants in this study. All the samples used in this study were deidentified. Therefore, this study did not involve any personal or other identifying information, and this report does not include any identifying information. The experiments were approved by the committee of the Air Force Medical Center in Beijing, China. All irregularly shaped specimens were uncut and stored at $-80°\mathrm{C}$ in snap freezing. Specimens were not chemically treated prior to the spectroscopic studies. Most specimens were measured within 36-h postsurgery. Before experiments, specimens were thawed to ambient temperature. Then they were put on a quartz plate for Raman spectroscopic measurements.

4.3.

RR Spectral Measurement

During a measurement, RR spectra were collected from multiple points in a region of interest from the center to both edges on one side of the sample with a step size of 1 to 2 mm. The spectra were measured and investigated for the spectral changes around the margin.²⁶

The main instrument used to acquire the RR spectral data was HORIBA Jobin Yvon (JY HR-800, France) confocal micro-Raman spectrometer. The instrument was equipped with a single-channel modular Raman system and a confocal microscope using a $50\times$ objective lens. This Raman system is similar to those described in our previous publications.²³ It uses a 532-nm single-mode solid-state Coherent Verdi-2 Nd:YAG laser (Coherent Company, Santa Clara, California) for excitation. The maximum output power of the laser was 50 mW. In the experiments, the laser beam was focused onto the surface of the sample with a spot size of $\sim 2\mu \mathrm{m}$ in diameter and its power was kept at 1.0 mW. The typical acquisition time was 30 s for each spot. Other signal acquisition times such as 1, 5, and 15 s were also tested in order to compare the signal-to-noise ratio and sensitivity among different Raman systems in our laboratory and to evaluate the robustness of the VRR technique (results not included in this report). All spectra were collected at the room temperature with a spectral resolution of $2{\mathrm{cm}}^{-1}$ in the range of interest, i.e., from 400 to $4000{\mathrm{cm}}^{-1}$. For inspection and confirmation of the VRR database, we also studied 26 tumors, including 6 pieces of grade II glioma samples, 7 pieces of grade II-III glioma samples and 13 pieces of grade III-IV glioma specimens, using a WITec 300R confocal micro-Raman system¹⁰⁰ and an in-house developed micro-Raman system equipped with a liquid-nitrogen cooled CCD (Pylon:100B, Princeton Instruments) with a spectral resolution of $\sim 1.0{\mathrm{cm}}^{-1}$.¹⁰¹ The three RR systems have spectral resolutions in the range of 0.4 to $2{\mathrm{cm}}^{-1}$. The RR spectral peak positions of biomarkers maintained high consistency within the system resolution, suggesting that calibrations of the three Raman systems prior to the experiments were accurate, and the possibility of peak shifts caused by measurement errors or environmental factors can be neglected.

4.4.

PCA-SVM

Before the use of the statistical model, the spectral data were preprocessed with baseline removal. The baseline of each raw Raman spectrum was fitted with a polynomial using an asymmetric Huber function as the cost function.¹⁰² The difference between the raw spectrum and the baseline was calculated. Each baseline-subtracted Raman spectrum was then normalized using its Euclidean norm and was used for subsequent analysis.

The normalized baseline-subtracted Raman spectra were analyzed using PCA.¹⁰³ PCA finds the uncorrelated components that explain the most variance in the signal. PCA has been widely used in various applications, such as spectroscopy,¹⁰⁴ face recognition,¹⁰⁵ and optical imaging.¹⁰⁶ Mathematically, PCA solves an eigenvalue equation and finds a set of orthonormal eigenvectors corresponding to eigenvalues that are the variances. The Raman spectral data are contained in a matrix $X_{M\times N}$, where $M$ is the number of wavenumbers and $N$ is the number of spectra or samples (assuming $M>N$). PCA considers the spectrum $x_i$ to be a linear combination of eigenspectra $\{w_j\}$ with coefficients $\{h_{ji}\}$, i.e.,

The PC scores of different spectra (samples) were considered characteristic features of the spectra (samples) and used for classification after standardization. The scores were standardized for each spectrum using the following formula: (score − score mean)/score standard deviation. An SVM^108–110 with a linear kernel was then used for classification using the standardized features. In general, SVM attempts to find a hyper plane (a boundary line in two dimension) to separate two classes with the largest distance from the nearest class members (data points), which are called support vectors. Once the SVM classifier is trained, it is tested for classification using all of the data points, which is called resubstitution validation. Various combinations of features were tested for classification. Because the contributions due to higher-order PCs significantly decrease according to eigenvalues, only a limited number of PCs need to be evaluated and compared. A more careful optimal feature selection method can be used and is presented elsewhere.¹¹⁰ The classification performance of the SVM classifier was evaluated using statistical measures, including sensitivity, specificity, and accuracy,¹¹¹ along with the ROC curve.¹¹² To plot the ROC curve for the SVM classifier, the positive class (cancer) posterior probability (a data point classified into positive class) for each data point was calculated using the sigmoid function to map the SVM scores, which are the distances from the data points to the SVM separation line.¹¹³ Then the posterior probabilities were used to calculate the true positive rate (i.e., sensitivity) and false positive rate (i.e., $1-\text{specificity}$) by varying the threshold and generating the ROC curve. The area under the ROC curve^112,114 was calculated to show the performance of the classifier. To reduce bias in classification, LOOCV¹¹⁵ was used to re-evaluate the classification performance. To perform LOOCV, each time one individual data point, i.e., a set of features corresponding to a spectrum, was removed from the dataset. The rest of the dataset was used to train an SVM classifier. The removed data point was then classified using the classifier for testing. This process was repeated for all data points. In the end, sensitivity, specificity, and accuracy were calculated based on the results of all tests as an overall evaluation of the classification performance. All of the computations for PCA-SVM were performed in MATLAB.