diagnostics

Article Assessment of Renal via Computational Analysis of Label-free Raman Detection of Multiple Biomarkers

Marian Manciu 1,2,*, Mario Cardenas 1, Kevin E. Bennet 3, Avudaiappan Maran 4, Michael J. Yaszemski 4, Theresa A. Maldonado 5, Diana Magiricu 6 and Felicia S. Manciu 1,2,*

1 Department of Physics, University of Texas at El Paso, El Paso, TX 79968, USA; [email protected] 2 Border Biomedical Research Center, University of Texas at El Paso, El Paso, TX 79968, USA 3 Division of Engineering and Department of Neurologic Surgery, Mayo Clinic, Rochester, MN 55905, USA; [email protected] 4 Department of Orthopedic Surgery and Biomaterials and Histomorphometry Core Laboratory, Mayo Clinic, Rochester, MN 55905, USA; [email protected] (A.M.); [email protected] (M.J.Y.) 5 Department of Electrical and Computer Engineering, University of Texas at El Paso, El Paso, TX 79968, USA; [email protected] 6 Touro College of Osteopathic Medicine, New York, NY 10027, USA; [email protected] * Correspondence: [email protected] (M.M.); [email protected] (F.S.M.); Tel.: +1-915-747-7531 (M.M.); +1-915-747-8472 (F.S.M.)  Received: 15 January 2020; Accepted: 29 January 2020; Published: 31 January 2020 

Abstract: Accurate clinical evaluation of renal osteodystrophy (ROD) is currently accomplished using invasive in vivo transiliac bone biopsy, followed by in vitro histomorphometry. In this study, we demonstrate that an alternative method for ROD assessment is through a fast, label-free Raman recording of multiple biomarkers combined with computational analysis for predicting the minimally required number of spectra for sample classification at defined accuracies. Four clinically relevant biomarkers: the mineral-to-matrix ratio, the carbonate-to-matrix ratio, phenylalanine, and contents were experimentally determined and simultaneously considered as input to a linear discriminant analysis (LDA). Additionally, sample evaluation was performed with a linear support vector machine (LSVM) algorithm, with a 300 variable input. The computed probabilities based on a single spectrum were only marginally different (~80% from LDA and ~87% from LSVM), both providing an unacceptable classification power for a correct sample assignment. However, the Type I and Type II assignment errors confirm that a relatively small number of independent spectra (7 spectra for Type I and 5 spectra for Type II) is necessary for a p < 0.05 error probability. This low number of spectra supports the practicality of future in vivo Raman translation for a fast and accurate ROD detection in clinical settings.

Keywords: renal osteodystrophy; statistical analysis; Raman spectroscopy; label-free detection; multiple biomarkers; diagnostic devices; artificial intelligence

1. Introduction Bone is a dynamic tissue model. Consequently, a constant remodelling process, which is known as bone turnover, occurs throughout the life [1]. During this metabolic process, a variety of molecules are released into the circulatory system and have been identified as bone turnover markers (BTM) [1–3]. Renal osteodystrophy (ROD) is an exclusive diagnosis of bone abnormal mineralization and morphological changes in strict relationship with skeletal chronic -mineral and bone disorder (CKD-MBD) [4]. As part of bone quality, which is a commonly used terminology to describe

Diagnostics 2020, 10, 79; doi:10.3390/diagnostics10020079 www.mdpi.com/journal/diagnostics Diagnostics 2020, 10, 79 2 of 13 bone health, ROD manifests itself with abnormality in bone turnover rate [4–6]. Evaluation of bone quality is usually derived from both biological and clinical perspectives, and encompasses all presently known bone abnormalities in the following categories: bone turnover, mineralization, bone volume, linear growth, strength, as well as soft tissue and vascular calcifications [4,6–10]. As a descriptor of the bone turnover rate, BTM varies over a significant range. In low-rate turnover, cancellous bone volume and trabecular bone thickness are lower than those of normal-rate turnover, whereas in high-rate turnover an opposite trend is present, with increases in volume and thickness [6]. Concerning BTM ratios, high-rate turnover exhibits less minerals within the tissue, leading to reduced mineral-to-matrix ratios. Lower carbonate-to-phosphate ratios are also encountered in comparison with those for low-rate turnover [6]. Despite variances in bone turnover occurring in ROD, the overall bone quality is the primary and major indicator to determine if ROD is present. Since bone metabolism is complex, detrimental changes within the bone structure may develop during early onset of ROD, and become more acute with continuous degradation of the kidney function. As the kidney fails, there is a progressive disruption of mineral and waste homeostasis within the body. The main effect is the kidney’s influence on circulatory levels of phosphate and calcium. With the deterioration of the kidney’s ability to process these analytes, increased concentration of serum phosphate is observed. Excess serum phosphate binds with available calcium, and being a non-homeostatic event, the serum concentration of calcium decreases. In response, the parathyroid glands release parathyroid hormones (PTH) to increase serum calcium levels towards normal homeostasis levels. In CKD, the kidney cannot respond to PTH correctly, due to impairment of the kidney’s ability in converting 25-hydroxyvitamin D (also known as the pre-hormone ) to the hormonally active metabolite 1,25-dihydroxycholecalciferol (known as ). Calcitriol serves as the primary response to PTH, by increasing serum calcium levels through stimulating calcium uptake from the intestines. However, in kidney dysfunction, the synthesis of calcitriol is severely impacted, leading to a disruption of the calcium uptake from the gut. Consequently, the skeletal system being a large calcium reservoir is targeted, serving as the initiation of ROD. Thus, individuals with advanced CKD tend to exhibit more severe forms of ROD and extensive incidence of bone fractures [6–10]. It has been also reported that ROD can be a sign of metabolic aging [11,12]. Noninvasively, bone assessment is usually performed by dual energy X-ray absorptiometry (DEXA) or quantitative computerized tomography (QCT)-based methods [7]. While DEXA and QCT image the areal bone mass and volumetric bone mineral densities, respectively, they are still lacking the necessary resolution for detection of bone architecture disruption [13,14]. Thus, accurate clinical evaluations of bone remodelling and of ROD diagnosis are still accomplished using invasive transiliac bone biopsy followed by in vitro histomorphometry [7]. However, even if histomorphometry remains the gold standard technique, it lacks potentially in vivo translation. The main reason behind this failback is the compulsory sample staining in histomorphometric analysis. Furthermore, assessment of disease progression and its response to different treatments requires for additional invasive biopsies, since each histomorphometric investigation only provides data on a single point in time, preventing the time correlation of different histomorphometric patterns with that of fracture risks. This situation emphasizes the need for improvement in analytic techniques for minimally to non-invasive alternative analysis that could provide similar or better degrees of diagnostic information. Specifically, the need for techniques that could provide in-depth information regarding bone’s quality, progression of ROD by observing BTM, and risk evaluation of bone fractures. In comparison to the clinically implemented QCT and magnetic resonance imaging (MRI) procedures and related high cost (they can be performed mainly in well-equipped facilities affiliated to hospitals), besides histologic techniques, spectroscopic methods of investigation such as Raman and Fourier transform infrared (FT-IR) spectroscopies are more commonly used in research laboratories. Not only are they more available, but also they allow for a more detailed examination of bone quality parameters at once, without the requirement of histological sample staining. Whereas both spectroscopic techniques provide a comprehensive chemical analysis that is useful for understanding Diagnostics 2020, 10, 79 3 of 13 likelihood of fractures and is complementary to that from QCT and MRI, relating to potentially in vivo translation, Raman spectroscopy is superior due to its insensitivity to water absorption. However, despites their accessibility, there are only relatively few reports on such Raman studies [15–25], with a slightly larger number of FT-IR investigations [26–30]. In a recent Raman spectroscopic study, we demonstrated that the bone samples of patients with ROD exhibit an overall increase in phenylalanine and decreases in calcium content, in mineral to matrix ratio, and in carbonate to matrix ratio [25]. Since just a single Raman spectrum is clearly not sufficient to assess at statistically significant levels the differences between normal and ROD samples, we took advantage of confocal Raman microscopy. Thus, by accumulation of a large number of independent spectra (22,500 spectra for each Raman mapping), identification of the samples with an 300 excellent accuracy (less than 10− ) was achieved. All these significant biomarkers (i.e., phenylalanine, phosphate, carbonate, amide content, mineral-to-matrix ratio, and carbonate-to-matrix ratio) were simultaneously determined with this unprecedented accuracy. The power analysis showed that for each biomarker, a relatively low number of spectra (of the order of 20–50 spectra) was required to identify the ROD samples at the typically desired level of significance (p = 0.05). The current research, while being a logical continuation of our previous efforts, also seeks to advance this work by simultaneously considering all of these biomarkers in answering the question concerning the minimum number of spectra required to accurately classify an unknown sample. By utilizing artificial intelligence approaches and advanced statistical analysis of data, we attempt to prove the viability of in vivo Raman translation based on future development of an optical-fiber-based biosensor to allow data collection and signal multiplexing through a partially invasive needle biopsy procedure.

2. Materials and Methods

2.1. Sample Preparation The samples analyzed in this work were received from the Mayo Clinic, in Rochester, Minnesota, and consist of 7 iliac crest bone specimens (4 ROD and 3 normal) of adult female patients within ages of 67 8. The control (normal bone) group samples were acquired from postmenopausal ± healthy women. Confirmation of ROD was also validated by histomorphometric evaluations for the other group of samples. To protect patient confidentiality, the samples were blinded by keyed numerical identification prior to shipment for current analysis. They were also standardly embedded in polymethyl methacrylate (PMMA), to facilitate cutting of 5 µm thick sections with a Leica RM 2265 microtome (Leica Biosystems Inc., Illinois, USA). A standard protocol of sample preparation for histomorphometric analysis was used, without staining.

2.2. Raman Measurements and Equipment Confocal Raman microscopy was performed with an alpha 300RAS WITec confocal Raman system (WITec GmbH, Ulm, Germany), using a 532 nm excitation of a frequency-doubled neodymium-doped yttrium-aluminum-garnet (Nd:YAG) laser that was operated at a low power output of about 5 mW to avoid sample damage. The Raman signal was recorded with a 1024 127 pixel Peltier cooled × back-illuminated and VIS AR–coated Marconi 40–11 charge-coupled device (CCD) with a spectral resolution of 4 wavenumbers. To particularly measure just the trabecular bone and avoid PMMA interference, specific regions of interest were carefully selected using a 20 objective lens with a × 0.4 numerical aperture (Olympus, Tokyo, Japan). A low numerical aperture objective was used primarily to avoid the influence of polarization effects for phosphate and collagen amide I bands, besides to provide a greater working distance adequate for sample roughness. The WITec Control 1.60 software was employed for confocal mapping data acquisition and for controlling the piezoelectric stage during laser scanning. Arrays of 150 150 Raman spectra were recorded for all Raman images × using an integration time of 50 ms per spectrum. The Raman mapping images were acquired with 80 µm 80 µm scan sizes. × Diagnostics 2020, 10, 79 4 of 13

2.3. Computational Analysis

1 A general linear background subtraction in the region of 377 to 1720 cm− and a normalization to the laser line intensity were first applied to each spectrum; the latter was performed to account for potential fluctuation of the laser power between measurements of different samples. To increase Diagnostics 2020, 10, x FOR PEER REVIEW 4 of 13 the accuracy of current computational analysis, before calculating the integrated areas under the relevant2.3. Raman Computational features, Analysis an additional linear background subtraction was also performed in the 1 ν 3 characteristicA general frequency linear regions, background as follows: subtraction between in the region 395 and of 377 469 to cm 1720− forcm−1 the and a2 POnormalization4 band centered 1 1 3 1 at 430 cmto the− ; laser between line intensity 907 and were 990 first cm applied− for to the eachν spectrum;1PO4 band the latter centered was performed at 960 cm to −account; between for 1033 1 2 1 1 and 1135potential cm− forfluctuation the carbonate of the laserν1 powerCO3 − betweenband centered measurements at 1074 of different cm− ; betweensamples. To 1215 increase and 1332the cm− accuracy of current computational analysis, before1 calculating the integrated areas 1under the relevant for the amide III band centered at 1275 cm− ; between 1625 and 1725 cm− for the amide I band centeredRaman at 1660 features, cm 1 an; and additional between linear 970 background and 1040 subtraction cm 1 and was between also performed 1574 and in the 1543 characteristic cm 1 for the two − − −1 3 − −1 frequency regions, as follows: between 3951 and 469 cm for1 the 2PO4 band centered at 430 cm ; phenylalanine bands centered at 1005 cm− and 1609 cm− , respectively. The ratios corresponding to between 907 and 990 cm−1 for the 1PO43 band centered at 960 cm-1; between 1033 and 1135 cm−-1 for ν 3 the significantthe carbonate biomarkers, 1CO32− band namely centered the at mineral-to-matrix 1074 cm−1; between 1215 content and 1332 ( 1PO cm4−1 /foramide the amide I ratio) III band [15– 30], the 2 3 carbonate-to-matrixcentered at 1275 (ν cm1CO−1; 3between−/amide 1625 I ratio) and 1725 [15 –cm30−],1 for the the calcium amide I content band centered (ν2PO at4 1660/amide cm− III1; and ratio) [31], and thebetween phenylalanine 970 and 1040 content cm−1 and (phenylalanine between 1574 and/amide 1543 cm III−1 for ratio) the two were phenylalanine next calculated bands centered for each of the 7 boneat samples 1005 cm (i.e.,−1 and for 1609 each cm− of1, respectively. the 22,500 The7 ratios= 157,500 corresponding spectra). to A the linear significant discriminant biomarkers, analysis ×1 43 (LDA) usingnamely a logit the mineral classification,-to-matrix which content is a ( commonlyPO /amide employed I ratio) [15 approach–30], the in carbonate statistically-to-matrix supervised (1CO32−/amide I ratio) [15–30], the calcium content (2PO43/amide III ratio) [31], and the learning,phenylalanine was performed content considering (phenylalanine/amide simultaneously III ratio) allwere four next biomarkers. calculated for Alternatively,each of the 7 bone the whole informationsamples contained (i.e., for each in theof the Raman 22,500 × spectra 7 = 157,500 was spectra) also evaluated. A linear discriminant through dimensionalityanalysis (LDA) using reduction to the mosta logit relevant classification, 20 variables, which is a by commonly using principal employed component approach in analysisstatistically (PCA) supervised followed learning, by a linear supportwas vector performed machine considering (LSVM) simultaneously classification all withfour biomarkers a 10-fold. Alternatively, cross validation, the whole both inf implementedormation in MATLABcontained® version in the r2016a. Raman For spectra each was spectrum, also evaluated a score through was attributed dimensionality based onreduction the logit to the transformation. most relevant 20 variables, by using principal component analysis (PCA) followed by a linear support The reason of this prior dimensionality reduction was to decrease the computing time devoted to the vector machine (LSVM) classification with a 10-fold cross validation, both implemented in MATLAB® LSVM algorithm.version r2016a. For each spectrum, a score was attributed based on the logit transformation. The reason of this prior dimensionality reduction was to decrease the computing time devoted to the 3. ResultsLSVM and algorithm. Discussion Since reliable ROD detection cannot be based on a single ideal biomarker, to differentiate between 3. Results and Discussion the normal and the ROD samples, we took advantage of the inherent Raman capability of simultaneously providing informationSince reliable about ROD detection all significant cannot biomarkers. be based on a In single this idealway, biomarker, we could toalso differentiate account for any between the normal and the ROD samples, we took advantage of the inherent Raman capability of potentialsimultaneously changes, in aproviding label-free information and real-time about manner. all significant The integratedbiomarkers. RamanIn this way, spectra we could for each also sample, which wereaccount obtained for any potential from averagingchanges, in aover label-free 22,500 and real individual-time manner. Raman The integrated spectrarecorded Raman spectra per image, are presentedfor eachin sample, Figure which1. were obtained from averaging over 22,500 individual Raman spectra recorded per image, are presented in Figure 1.

Figure 1.FigureIntegrated 1. Integrated Raman Raman spectra spectra of 3 3 normal normal and and 4 renal 4 renal osteodystrophy osteodystrophy (ROD) bone (ROD) samples, bone each samples, each obtainedobtained byby averaging 22,500 22,500 Raman Raman spectra. spectra. The spectra The are spectra vertically are translated vertically and translated color labeled and color labeledfor for easier easier visualization. visualization.

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Diagnostics 2020, 10, x FOR PEER REVIEW 5 of 13 Although intensity differences in some of the Raman features can be observed in these spectra, 1 particularlyAlthough for thoseintensity corresponding differences in to some the of phenylalanine the Raman features peaks can at 1005be observed and 1609 in these cm− ,spectra, no other evidentparticularly information for those concerning corresponding additional to the phenylalanine biomarkers of peaks interests at 1005 can and be 1609 accurately cm-1, no extracted other withoutevident appropriate information computational concerning additional analysis. biomarkers Indeed, the of large interests amount can beof collected accurately Raman extracted data, 300 besideswithout facilitating appropriate an excellent computational statistics analysis. on the Indeed, results the (i.e., large an accuracy amount of lesscollected than 10Raman− for data, each biomarkerbesides facilitating [25]), also an allows excellent for astatistics direct visualizationon the results by(i.e., use an ofaccuracy pseudo-color of less t contrasthan 10-300 of for di eachfferent componentsbiomarker and[25]), their also distributions.allows for a direct Supporting visualization evidence by areuse theof pseudo Raman-color images contrast associated of different with the phenylalaninecomponents contentand their that distributions. are presented Supporting in Figure evidence2a–g. Generation are the Raman of these images images associated was performed with the by 1 applyingphenylalanine filters to content select certainthat are parts present of theed in spectra, Figure namely2 a–g. Generation the frequency of these region images from was 970 performed to 1040 cm − 1 1 forby the applying phenylalanine filters to peak select at certain 1005 cm parts− , of and the that spectra, from namely 1574 to the 1543 frequency cm− for region the phenylalanine from 970 to 1040 peak -1 1 -1 -1 at 1609cm for cm −the. Aphenylalanine brighter yellow peak pseudo-color at 1005 cm , inand these that imagesfrom 1574 corresponds to 1543 cm to for a higher the phen phenylalanineylalanine content,peak at as 1609the associated cm-1. A brighter color scale yellow bar reveals. pseudo-color An overall in these much images larger corresponds amount of phenylalanine to a higher (morephenylalanine dominant content, yellow regions)as the associated can be observedcolor scale for bar the reveals. ROD An samples overall (Figure much 2largerd–g) thanamount for of the normalphenylalanine bone samples (more (Figure dominant2a–c), yellow in agreement regions) withcan be our obser previouslyved for the quick ROD examination samples (Figure of the 2 spectra d–g) shownthan for in Figure the normal1. bone samples (Figure 2 a–c), in agreement with our previously quick examination of the spectra shown in Figure 1.

FigureFigure 2. 2.Representative Representative confocal confocal Raman Raman images images of phenylalanine content content in: in: (a (–ac)– cnormal) normal bone bone samplessamples and and (d– g(d)– RODg) ROD samples. samples. A bright A bright yellow yellow pseudo-color pseudo-color corresponds corresponds to a higher to a higher Raman Raman intensity. intensity. However, for in vivo data acquisition through an optical fiber-based biosensor, Raman spectral recordingHowever, versus for confocal in vivo Raman data acquisition mapping isthrough more suitable.an optical Consequently, fiber-based biosensor, the fundamental Raman spectral question aboutrecording the minimum versus confocal number Raman of spectra mapping necessary is more suitable. to obtain Consequently, a sample assessment the fundamental with aquestion sufficient (desired)about the accuracy minimum still number remains. of Wespectra already necessary demonstrated to obtain thata sample by considering assessment awith single a sufficient biomarker in(desired) the distinction accuracy between still remains. the samples We already at a typical demonstrated level of that significance by considering of p = a0.05, single about biomarker 18 spectra in weretheneeded distinction for thebetween mineral-to-matrix the samples at content,a typical 20level spectra of significance for the carbonate-to-matrix of p = 0.05, about 18 content,spectra were and 46 spectraneeded for for the the calcium mineral content-to-matrix [25]. content, The rationale 20 spectra implies for thatthe carbonate if we take-to into-matrix account content, in the and current 46 multivariatespectra for computationalthe calcium content analysis [25]. The all therationale biomarkers implies concurrently, that if we take a into smaller account number in the ofcurrent spectra willmultivariate be necessary, computational thus, emphasizing analysis all the the possibility biomarkers of concurrently, ROD detection a smaller in real-time number throughof spectra Raman will spectroscopy.be necessary It, is thus, known emphasizing that the larger the thepossibility number of of ROD employed detection variables, in real the-time more through likely is Raman to obtain a goodspectroscopy classification. It is kno power.wn that It should the larger also the be notednumber here of thatemployed by currently variables, using the onlymore four likely variables is to obtain a good classification power. It should also be noted here that by currently using only four classification (i.e., just four biomarkers), we reduce the potential impact of multicomparison correction variables classification (i.e., just four biomarkers), we reduce the potential impact of multicomparison analysis on the final p value [32]. correction analysis on the final p value [32]. Prior to finding this minimum number of spectra, a potential discrimination between the normal Prior to finding this minimum number of spectra, a potential discrimination between the normal and ROD bone samples is attempted in Figure3a,b through plotting of the carbonate-to-matrix and ROD bone samples2 is attempted in Figure 3a and 3b through plotting of the carbon3 ate-to-matrix component (ν1CO3 −/amide I ratio) versus the mineral-to-matrix component (ν1PO4 /amide I), and the component (1CO32-/amide I ratio) versus the mineral-to-matrix component (1PO43/amide I), and the

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3 phenylalaninephenylalanine content content (phenylalanine (phenylalanine/amide/amide III) versus III) versus that of calcium that of (ν calcium2PO4 /amide (2PO III),43/amide respectively, III), forrespectively, each of the for 22,500 each Raman of the 22,500spectra. Raman For consistency spectra. For andconsistency because and of dibecausefferences of differences in polarization in sensitivitiespolarization between sensitivities amide between I and amide amide I and III amide features, III features, the mineral the mineral and carbonate and carbonate contents contents were normalizedwere normalized to the amide to the Iamide band, I andband the, and calcium the calcium and phenylalanine and phenylalanine contents contents to the to amidethe amide III band. III Furthermore,band. Furthermore, to minimize to minimizethe calculation the calculation errors, we errors,consider we the consider ratio of areasthe ratio under of theareas corresponding under the peakscorresponding instead of the peaks ratio instead of their of intensitiesthe ratio of [ 15their–31 intensities]. While from [15–31 Figure]. While3a a from relatively Figure good 3a a relatively correlation cangood be implied correlation between can the be mineral-to-matrix implied between theand mineral the carbonate-to-matrix-to-matrix and the biomarkers carbonate- (bothto-matrix being indicatorsbiomarkers of bone (both turnover being indicators and remodeling of bone turnover activity), and unfortunately, remodeling onlyactivity), a very unfortunately, small differentiation only a betweenvery small the samplesdifferentiation can be between achieved. the Thesamples main can reason be achieved. behind The this main lack ofreason sample behind separation this lack is of the strongsample overlapping separation betweenis the strong majority overlapping of the between color-coded majority points of the representing color-coded independentpoints representing Raman independent Raman spectra. A better sample classification can be performed by examining the spectra. A better sample classification can be performed by examining the relationship between relationship between phenylalanine and calcium contents (see Figure 3b). The much larger amount phenylalanine and calcium contents (see Figure3b). The much larger amount of phenylalanine in of phenylalanine in comparison to that of calcium observed in this figure for the ROD samples comparison to that of calcium observed in this figure for the ROD samples (remark based on the (remark based on the location of these data points regarding an imaginary line of slope 1) location of these data points regarding an imaginary line of slope 1) corroborates with the clinical corroborates with the clinical reports for patients with kidney malfunction (identified as ROD reportspatients). for patients For example, with kidneysuch patients malfunction demonstrate (identified a substantially as ROD patients).lower level For of calcium example, in suchtheir patientsblood demonstratetest analyses a substantially[33–35]. lower level of calcium in their blood test analyses [33–35].

2 Figure 3. Representation of (a) the carbonate-to-matrix biomarker (ν1CO3 −/amide I) versus the Figure 3. Representation of (a) the3 carbonate-to-matrix biomarker (1CO32-/amide I) versus the mineral-to-matrix biomarker (ν1PO4 /amide I), and (b) the phenylalanine content (phenylalanine 3 mineral-to-matrix biomarker (1PO4 /amide3 I), and (b) the phenylalanine content (phenylalanine /amide III) versus that of calcium (ν2PO4 /amide III) for all the 22,500 independent Raman spectra /amide III) versus that of calcium (2PO43/amide III) for all the 22,500 independent Raman spectra measured per sample. A similar color labeling as in Figure1 was used for each of the 7 bone samples. measured per sample. A similar color labeling as in Figure 1 was used for each of the 7 bone samples.

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A more compact and easier easier visualization visualization of of the the results results presented presented in in both both Figure Figures 1 1and and Figure3a,b can3a,b be can obtained be obtained by plotting by plotting in Figure in 4Figurea,b the 4a,b combination the combination of these four of these biomarkers four biomarkers using statistical using 1-sigmastatistical ellipsoid 1-sigma representations,ellipsoid representations, with the biomarkerwith the biomarker averages averages over 22,500 over spectra 22,500 defined spectra bydefined solid circles.by solid For circles. consistency For consistency with Figure with3, the Figure carbonate-to-matrix 3, the carbonate versus-to-matrix mineral-to-matrix versus mineral is presented-to-matrix in is Figurepresented4a, andin Figure phenylalanine 4a, and phenylalanine versus calcium versus in Figure calcium4b. in Another Figure 4b. reason Another for using reason this for statistical using this representationstatistical representation is to inspect is for to potential inspect di forfferences potential between differences same types between of samples. same Indeed,types of a variation samples. fromIndeed, sample a variation to sample from issample observed to sample in the is relationships observed in the between relationships biomarkers, between even biomarkers, among normal even samplesamong normal or ROD samples samples or themselves. ROD samples We suggestthemselves. thatthis We anticipatedsuggest that variation this anticipated is based onvariation age or on is otherbased specific on age patientor on other conditions. specific However, patient besidesconditions. a much However, clear distinction besides a of much phenylalanine clear distinction to calcium of relationshipphenylalanine seen to calcium in Figure relationship4b than that seen observed in Figure previously 4b than in that Figure observed3b, no additionalpreviously informationin Figure 3b, no additional information regarding sample classification is attainable, even with this more compact regarding sample classification is attainable, even with this more compact statistical representation. statistical representation.

Figure 4. a Figure 4. Statistical representation using 1-sigma1-sigma ellipsoids of: (a) ( ) the carbonate carbonate-to-matrix-to-matrix biomarker versus the mineral-to-matrix biomarker, and (b) the phenylalanine content versus that of calcium. versus the mineral-to-matrix biomarker, and (b) the phenylalanine content versus that of calcium. The The solid circle defines the average over 22,500 spectra for each biomarker. For consistency, an identical solid circle defines the average over 22,500 spectra for each biomarker. For consistency, an identical color-code was again used. color-code was again used. Therefore, we present, in Figure5, the histograms associated with all of the above investigations Therefore, we present, in Figure, 5 the histograms associated with all of the above investigations (i.e., from both, Figures3 and4), and taking as variables all the four ratios concurrently. A linear (i.e., from both, Figure 3 and Figure 4), and taking as variables all the four ratios concurrently. A discriminant analysis with 10-fold cross validation of the training data was employed. For the linear discriminant analysis with 10-fold cross validation of the training data was employed. For the prediction classification, a logistic score transformation was used, with a score less than one for normal bone spectra and more than one for ROD spectra.

Diagnostics 2020, 10, 79 8 of 13 prediction classification, a logistic score transformation was used, with a score less than one for normal Diagnostics 2020, 10, x FOR PEER REVIEW 8 of 13 bone spectra and more than one for ROD spectra.

Figure 5. Combined histograms resulted from statistical investigations using all four biomarkers Figure 5. Combined histograms resulted from statistical investigations using all four biomarkers concurrently. Distribution of scores of more or less than 1 were assigned to each ROD and normal concurrently. Distribution of scores of more or less than 1 were assigned to each ROD and normal spectrum, respectively. spectrum, respectively. The strong overlapping seen in Figure5 between these histograms, not only agrees with the findingsThe previously strong overlapping discussed, seen but alsoin Figure confirms 5 between that a sample these classificationhistograms, not cannot only be agrees based justwith on the a singlefindings spectrum, previously since discussed, Type I and but Type also II confirms errors will that be a unacceptable sample classification large in this cannot case (seebe based solid just line on at 1).a single A summary spectrum, of the since results Type associated I and Type with II theerrors confusion will be matrix unacceptable and the usuallarge in parameters this case related(see solid to theline prediction at 1). A summary ability, which of the was results based associated on randomly with selectingthe confusion the spectra, matrix isand presented the usual in parameters Table1. related to the prediction ability, which was based on randomly selecting the spectra, is presented in Table 1. Table 1. Confusion matrix for single spectrum LDA classification (4 variables).

Condition Condition Prevalence Accuracy Table 1. Confusion matrix for single spectrum LDA classification (4 variables). Positive Negative 57.14% 80.5% FDR Condition Condition PrevalencePrecision Accuracy Prediction positive 70470 11205 (false discovery rate) 78.3% Positive Negative 57.14% 16.6%80.5% FDR Prediction PrecisionFOR NPV Prediction negative 7047019530 11205 56295 (false omission rate) (negative(false predictivediscovery value) rate) positive 78.3%21.7% 78.3% 16.6% FPR FNR Sensitivity Specificity (falseFOR positive rate) (false negativeNPV rate) Prediction 78.3% 83.7% 19530 56295 (false omission16.6% rate) (negative38.9% predictive value) negative 21.7% 78.3% The important question is whether focusing on onlyFPR four biomarkers (as measuredFNR variables) Sensitivity Specificity significantly affects the discrimination power of the(false method, positive since rate) the Raman(false spectra negative in the rate) frequency 78.3% 83.7% range of interest contain over 300 data points, thus,16.6% potentially over 300 independent38.9% variables. Consequently, we employed an alternative computational approach based on a linear support vector The important question is whether focusing on only four biomarkers (as measured variables) machine (LSVM) algorithm, which takes into account all of these independent variables in the significantly affects the discrimination power of the method, since the Raman spectra in the frequency classification of any unknown sample. The results associated with the confusion matrix from the LSVM range of interest contain over 300 data points, thus, potentially over 300 independent variables. are summarized in Table2. Even though the LSVM method involves about two orders of magnitude Consequently, we employed an alternative computational approach based on a linear support vector more independent variables than does the LDA, only a marginal improvement in sample classification machine (LSVM) algorithm, which takes into account all of these independent variables in the is accomplished based on a single spectrum. This observation, which arises from a comparison between classification of any unknown sample. The results associated with the confusion matrix from the the results presented in Tables1 and2, also demonstrates that the four previously chosen variables LSVM are summarized in Table 2. Even though the LSVM method involves about two orders of (biomarkers selected mainly from clinical reasons) contain most of the information (discrimination magnitude more independent variables than does the LDA, only a marginal improvement in sample power) necessary to differentiate between the normal and the ROD samples. classification is accomplished based on a single spectrum. This observation, which arises from a comparison between the results presented in Tables 1 and 2, also demonstrates that the four previously chosen variables (biomarkers selected mainly from clinical reasons) contain most of the information (discrimination power) necessary to differentiate between the normal and the ROD samples.

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Table 2. Confusion matrix for single spectrum LSVM classification (~300 variables). Table 2. Confusion matrix for single spectrum LSVM classification (~300 variables).

ConditionCondition ConditionCondition PrevalencePrevalence AccuracyAccuracy Positive Negative 57.1% 87.5% Positive Negative 57.1% 87.5% FDR Precision Prediction positive 70470 9112 (false discoveryFDR rate) Prediction Precision88.3% 70470 9112 (false discovery13.5% rate) positive 88.3% FOR 13.5%NPV Prediction negative 10530 58388 (false omission rate) (negative predictive value) FOR NPV Prediction 11.7% 88.3% 10530 58388 (false omissionFPR rate) (negative predictiveFNR value) negative Sensitivity Specificity 11.7%(false positive rate) (false88.3% negative rate) 88.3% 86.5% FPR 13.5% FNR15.6% Sensitivity Specificity (false positive rate) (false negative rate) 88.3% 86.5% To improve the accuracy of the classification, we next13.5% consider N measurements15.6% of independent spectraTo from improve different the accuracy locations of in the the classification, sample. For we N suchnext consider spectra (withN measurements N being an of odd independent integer), we assumespectra that from the different sample belongslocations to in ROD the sample. if n > N For/2spectra N such havespectra a score (with greater N being than an odd one. integer), On the otherwe hand,assume if n spectrathat the havesample a scorebelongs less to than ROD one, if n > the N/2 sample spectra is have assessed a score as greater normal. than Given one. a On probability the other p1 thathand, a normal if n spectra spectrum have hasa score a score less lessthan than one, 1,the and sample a probability is assessedp2 asthat normal. a ROD Given spectrum a probability has a score p1 largerthat thana normal 1 (see spectrum Table1), thehas Qa scoreI (N) probabilitiesless than 1, and for a Type probability I (rejection p2 that of aa trueROD null spectrum hypothesis, has a score or false positive),larger than and the1 (see QII Table(N) probabilities 1), the QI (N) for probabilities Type II error for (non-rejection Type I (rejection of a of false a true null null hypothesis, hypothesis, or falseor negative)false positive), can be calculatedand the QII as(N) follows: probabilities for Type II error (non-rejection of a false null hypothesis, or false negative) can be calculated as follows: k< N X2 ! N N k k Q (N) = 1 P (N) = (1 p ) − p (1) I 1 1 1 () = 1 −− () = k (1−− ) (1) k=0 N k< 2 ! X N N k k QII(N) = 1 P2(N) = (1 p2) − p2 (2) − k − () = 1 − () k=0 (1 − ) (2) The probabilities of Type 1 and Type II assignment errors, namely wrongfully assigned k = N, N 1, ...The, k probabilities< N/2 spectra of obtained Type 1 and from Type either II assignment a normal or errors, a ROD namely bone sample, wrongfully are plotted assigned in k Figure = N, 6 − as aN function-1,...k < N/2 of spectra the number obtained of independently from either a normal recorded or a spectra. ROD bone sample, are plotted in Figure 6 as a function of the number of independently recorded spectra.

FigureFigure 6. 6.Probability Probability of of Type Type II andand TypeType IIII errorserrors versusversus the number of of randomly randomly chosen chosen spectra spectra employedemployed in the in theclassification. classification. The The black black lines line in thes in inset the indicate inset indicate that a relatively that a relatively small set small of measured set of spectrameasured is su ffispectracient tois sufficient classify the to samplesclassify the with samples a typical withp a< typical0.05 error p < 0.05 probability. error probability.

Diagnostics 2020, 10, 79 10 of 13

While an examination of the large part of Figure6 reveals that the assignment error probability can be made as small as desired, the inset of this figure further indicates that for a defined precision, only a low number of sampling points is necessary. For example, the black lines in the inset show that to achieve a probability of less than 5%, 7 independent spectra are sufficient for Type I error and 5 spectra for Type II error. The corresponding confusion matrix and related probabilities for 11 independent spectra are summarized in Table3. A classification accuracy of ~99% is obtained. Since such a relatively small number of independent spectra can be in principle acquired through an optical-fiber-based biosensor (e.g., using depth profiles confocal Raman), the present work not only validate the feasibility of future in vivo Raman translation, but also emphasize the need of computational analysis for these essential predictions.

Table 3. Confusion matrix for 11 spectra classification.

Condition Condition Prevalence Accuracy Positive Negative 57.1% 98.8% FDR Precision Prediction positive 98.3% 0.5% (false discovery rate) 98.3% 0.5% FOR NPV Prediction negative 1.7% 99.5% (false omission rate) (negative predictive value) 0.0174% 98.3% FPR FNR Sensitivity Specificity (false positive rate) (false negative rate) 78.3% 99.5% 0.5% 2.3%

4. Conclusions Ideally, ROD should be reliably detected in real time and with noninvasive or minimally invasive methods, together with the fact that its detection cannot be based on a single biomarker. This research describes alternative techniques that could provide similar or better degrees of diagnosis. It is also a logical continuation of our previous efforts in demonstrating that Raman spectroscopy can be a viable approach [25]. One of the shortcoming of the Raman technique towards its potentially clinical translation is knowing the minimum number of independent spectra that will provide an accurate assessment of this complex diseases. Another drawback is the need for development of an optical-fiber probe biosensor. To overcome the first constraint, we took advantage of both, Raman providing simultaneously information about all the biomarkers of interests in a label-free manner, and computational analysis in answering the essential question of the minimal number of spectra necessary for sample classification with a desired accuracy. The resulting confusion matrix from a classification performed by standard LDA with 10-fold cross validation demonstrates that the probability of a correct sample assignment based on a single spectrum is about 80% (see Table1). For this classification, a logit transform score was used for each spectrum. Moreover, the current statistical analysis shows that a reasonably small number of randomly selected spectra suffices for assessment of any sample at any desired degree of accuracy; only 7 independent spectra are necessary for Type I error and 5 spectra for Type II error. This outcome is achievable because of simultaneous consideration of all the known physical differences between the normal and ROD samples. Furthermore, the classification of bone quality on just four variables (biomarkers) reduces the potential impact of multicomparison correction analysis on the final p value [32]. Finally, all the information contained in the spectra was used in an alternative statistical learning algorithm for sample classification. Prior implementation of this LSVM algorithm, a dimensionality reduction by PCA in 20 directions (of most variations) was employed. Although this later classification takes into consideration much more information (~300 independent variables), the results were only marginally superior to those obtained from the LDA approach. A correct sample assignment based on a single spectrum is about 87% in this case (see Table2). Diagnostics 2020, 10, 79 11 of 13

In conclusion, the current computational study validates that only a relatively low number of spectra is necessary for accurate ROD detection, supporting the feasibility of future in vivo Raman translation through development of a biosensor for signal recording and multiplexing. This work adds value to a potentially alternative method for fast ROD assessment and human health monitoring.

Author Contributions: M.M. and F.S.M. conceived of the study, its coordination, and draft of the manuscript. K.E.B., A.M., M.J.Y., and T.A.M. contributed to data analysis and helped to editing of the manuscript. M.M. and M.C. performed the statistical data analysis. F.S.M. and D.M. contributed to experimental Raman data acquisition. All authors contributed significant effort to manuscript preparation and gave their final approval for publication. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the NIH NIMHHD 2G12MD007592 award, The Grainger Foundation, a developmental grant support from the Mayo Clinic, and by a research agreement between the University of Texas at El Paso and the Mayo Clinic. Acknowledgments: The authors thank Mayo Clinic Biomaterials and Histomorphometry Core for tissue processing and sectioning. Conflicts of Interest: The authors declare no conflict of interest.

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