1.

Introduction

Despite recent advances in the ability to assess fracture risk,^1,2 definitive metrics do not yet exist to identify individuals in need of an intervention that lowers fracture risk. Complementary to established x-ray-based diagnostics of bone, Raman spectroscopy (RS) is an emerging technology that offers nondestructive^3–7 measures of the biochemical nature of tissue. As an indication of its potential to assess fracture risk, RS detected differences in carbonate concentration relative to phosphate between bone samples from nonfracture patients and bones from osteoporotic fracture cases.⁸ In addition to quantifying the amount of carbonate in calcified tissue,⁹ RS is sensitive to local changes in mineral accumulation through mineral to collagen peak ratios, as well as local changes in mineral maturation through measurements of crystallinity.¹⁰ These properties become less heterogeneous with aging,¹¹ change in response to tissue damage,¹² and correlate to mechanical strength of rodent bones,^13,14 as well as human cortical bone.¹⁰

While these attributes make RS a candidate for clinical diagnosis of bone quality and disease states, unresolved issues regarding instrument polarization and its impact on analysis hamper unambiguous derivation of quantities reflecting the biochemical properties of bone tissue, referred to henceforth as biomarkers. For example, probe-based instruments have been developed to acquire Raman spectra from bone through the overlying tissue.^15–17 However, most RS studies assessing bone use laser confocal microscopes¹⁸ in which the laser is polarized.^19,20 Since most fiber optic instruments do not preserve polarization, there is potential for significant discrepancy between the relevant biomarkers of fracture resistance as obtained from RS microscopes and those obtained from existing clinically relevant instruments.

Earlier studies in using Fourier transform infrared spectroscopy (FTIR) identified that vibrational spectroscopy markers for mineralization, crystallinity, carbonation, and collagen cross-linking all significantly associate with fragility fracture,²¹ and while the influence of polarization on FTIR was previously characterized,^22,23 the polarization state for this instrument was not reported. FTIR and RS are linked as vibrational spectroscopy methods, but fundamental differences give RS an apparent clinical advantage that has fueled cross-correlation and validation in RS.

Recent correlation studies linking RS to the fracture resistance of bone have reported different biomarker sensitivity of RS to the biomechanical properties of bone, possibly due to instrument polarization differences. In one RS study involving a commercial confocal system, differences in $\nu 1$ Phosphate/${\mathrm{CH}}_2$-wag between trabecular and cortical bone were related to differences in nanomechanical properties between the tissue types.²⁴In another study analyzing cortical bone from genetic mouse models involving matrix metalloproteinases (Mmp2-/- and Mmp9-/-) and using a similar commercial instrument, correlations among nanoindentation modulus, bending strength, and RS were reported for several mineral-to-collagen ratios, but not $\nu 1$ Phosphate/Amide I.²⁵ On the other hand, strength of bone from vehicle- and glucocorticoid-treated mice was correlated to various RS peaks when normalized to Amide I in a fiber optic system.²⁶ Despite differences in modes of biomechanical testing among these studies, the polarization state of the instrument likely influences which RS biomarkers are sensitive to experimental groups.

Even though bone is a birefringent material, only a few investigations have intentionally examined the effect of polarization on RS peaks of bone.^27–30 The vast majority of polarization RS studies of mineralized tissues utilized isolator and analyzer polarizers to “fully polarize” both the input light and collection arm of the Raman system (Table 1).To the best of our knowledge, the extent to which polarization may affect various peak ratios used to assess composition of bone is not well understood for RS instruments without these added optics. Addressing this is important because Raman scattering bands are inherently and differentially affected by polarization due to vibrational modes that give rise to the Raman effect.^31,32 Even though Legendre polynomials can be used to extract the distribution of collagen and mineral orientation by modulating polarization,³⁰ inherent polarization within the instrument can affect bands even in the absence of molecular organization (e.g., analyzing carbon tetrachloride).³³ Because sample volume, molecular organization, scattering anisotropy, and tissue turbidity influence the scattered light,³⁰ it is difficult to predict how polarization affects RS spectra of bone tissue (which is both turbid and organized), especially when the input laser light is unaltered (Table 1). In the context of RS instrumentation, we refer to changes in Raman peak intensities due to bone rotation (relative to light polarization) as a “polarization bias.”

Table 1

Previous polarized Raman studies used altered instrumentation to analyze mineralized tissues and collagen.

Rather than intentionally polarizing Raman collection, the present study compares RS biomarkers of human cortical bone with respect to inherent system polarization using commercial instrumentation. The hypothesis of this study was that the intensity of polarization-sensitive Raman bands would oscillate relative to input polarization. Thus, optimization of the relative phase of these Raman bands’ oscillations could yield biomarkers that are better suited for the study of either composition (phase matched and less polarization sensitive) or structure (phase mismatched and polarization sensitive). This study uses polarization theory to quantify the phase and amplitude for a number of Raman peaks of bone, and in doing so, identifies phase matching as the source of polarization insensitivity in known and newly characterized peak ratios of bone composition. Whereas other studies have observed the intensity change of specific peak ratios (Table 1), the present work establishes phase profiles for many of the prominent peaks arising from bone with and without added polarization optics.

2.

Methods

2.4.

Data Modeling and Statistics

Data modeling and statistics were performed on peak heights extracted from each processed spectrum [Fig. 1(a)]. Peak intensities were modeled to Malus’ Law^43,44 (intensity varies with polarization angle as a function of cosine squared) for phase and amplitude of oscillation [Fig. 1(b)]. The custom algorithm employed a least squares fit for amplitude nested inside a mean squared error driven optimization (Matlab implementation of Nelder-Mead simplex,⁴⁵ Mathworks, Natick, Massachusetts), outputting peak phase, amplitude, and mean intensity as illustrated in Fig. 1(b).The degree of orientation sensitivity across the three generated polarization regimes was quantified for each prominent peak as a function of oscillation amplitude normalized to mean peak intensity. For less sensitive peaks, individual sample oscillations could become noisy or undetectable, such that data fails the underlying assumptions of the Malus’ law model. Modeled data were excluded from quantitative analysis if the model fit was not significant ($p<0.05$) via analysis of variance (ANOVA) regression (all fits shown in figures and tables are significant). For each peak, the number of samples with statistically significant models and the observable percent change in intensity measurements of the same quantity were recorded.

Fig. 1

Diagram of representative labeled Raman spectrum of bone shows feature extraction. (a) $\nu 1$ Phosphate peak intensity is extracted from a wavenumber range and baselined. (b) Actual data from highly polarized osteon analysis shows ν1 Phosphate intensity for each analyzer rotation (output polarization angle). Data is then modeled to a sinusoidal fit to extract phase, amplitude, and mean intensity. Shown here for analyzer rotation, this method was also used in bone rotation experiments.

3.

Results

3.1.

Phase Differences in Raman Peaks of Bone Under Highly Polarized Light

Acquired under a highly polarized regime, RS biomarker peaks exhibited differential polarization behavior in both degree and relative phase of intensity oscillation. For the most part, relative phase varied insignificantly between osteonal and interstitial tissue types for any given peak. However, phase oscillation varied distinctly between different peaks representing the same bone compositional element (i.e., Amide I at ${1666\mathrm{cm}}^{-1}$ versus Amide III at $1247{\mathrm{cm}}^{-1}$, both biomarkers of collagen in Fig. 2).In reference to the ν1 Phosphate peak (${961\mathrm{cm}}^{-1}$), the strongest spectral signal for bone mineral, Proline (${854\mathrm{cm}}^{-1}$) was found to have the best phase match for the generation of a mineral to collagen ratio, a metric commonly used as an indicator of bone quality.

Fig. 2

Relative phase angle ($\text{mean}\pm \mathrm{SD}$) from highly polarized analysis of osteons, conducted with analyzer rotation, shows few differences between tissue type but strong compositional element differences in phase angle. The phase range of $\nu 1$ Phosphate was closest to the phase range of Proline and ${\mathrm{CH}}_2$-wag. In this regime, Amide I is the collagen peak with the greatest phase difference from $\nu 1$ Phosphate. ** Only $\nu 1$ Phosphate had a significant difference $p<0.05$ in phase between osteonal and interstitial tissue types by two-sided Student’s $t$-test.

Building upon our previous findings,¹⁸ the observed difference between osteonal and interstitial tissue composition (Fig. 3) was small (2% to 30% difference) relative to intensity change as a function of polarization angle (100% to 300% difference). However, under the traditional calculation of a mineral to collagen ratio using $\nu 1$ Phosphate (mineral) and Amide I (collagen) as biomarkers, different quantities would be observed at different polarization angles [e.g., 60 deg versus 140 deg in Fig. 3(a)]. As an alternative mineral to collagen ratio that still utilizes the signal strength of $\nu 1$ Phosphate, the phase-matched Proline peak can be used to represent collagen [Fig. 3(b)]. Also, as indicated by Kazanci et al.,²⁸ other RS mineral quantities can be substituted for $\nu 1$ Phosphate [Fig. 3(c) and 3(d)]. The distinct phase mismatch between $\nu 2$ Phosphate and Amide I [Fig. 3(c)] was reversed by using Amide III for collagen [Fig. 3(d)].

Fig. 3

Phase mismatch of peak intensity versus polarization angle [$\nu 1$ Phosphate and Amide I, (a)] leads to polarization bias of mineral to collagen ratio that can be eliminated by using Proline to represent collagen (b). Alternative biomarkers of mineral to collagen ratio can also be phase matched [$\nu 2$ Phosphate and Amide III, (d)] to eliminate Amide I polarization bias (c). This phase matching prevents spurious conclusions about osteonal and interstitial differences due to polarization angle.

3.2.

Susceptibility of Certain Raman Peaks to Polarization Bias

When defined as the model amplitude normalized to mean peak intensity, the peak sensitivity to polarization decreased from the highly polarized regime to the input polarized and unaltered polarized regimes (Fig. 4). Hydroxyproline (${870\mathrm{cm}}^{-1}$) and Amide I, the two most sensitive peaks in the highly polarized regime, remained polarization sensitive in the input polarized regime. Despite the fact that spectra were acquired from different bone samples, the oscillation sensitivity trends among most peaks remain consistent between the highly polarized and input polarized regimes. Comparing input polarized and unaltered polarization regimes (paired measurements of the same sample locations at the same rotation increments), polarization sensitivity dropped off markedly for some peaks like Carbonate and Hydroxyproline (Fig. 4). However, for other peaks like Amide I and $\nu 1$ Phosphate, degree of oscillation amplitude remains relatively unchanged. In the unaltered polarization regime, less sensitive peaks like Amide III fell into the noise floor, as evidenced by decrease in number of significant model fits by ANOVA regression (Table 2).

Fig. 4

Average model amplitude normalized to mean intensity shows a preservation of peak oscillation trends with decreasing polarization. Highly polarized data (green) shows greater sensitivity than input polarized data (red). Less sensitive peaks like Amide III continue to drop in sensitivity in the unaltered polarization regime (blue), whereas more sensitive peaks like Amide I show consistent sensitivity.

Table 2

Peak sensitivity ranking as a percent change in intensity during bone rotation shows that some peaks still oscillate with unaltered system polarization.

	Highly polarizeda		Input polarized		Unaltered polarization
Raman peakb	% Changec	Sig. modelsd	% Change	Sig. models	% Change	Sig. models
Amide III	125.2	9/10	11.2	4/6	2.2	1/6
Carbonate	116.5	10/10	13.5	5/6	2.8	1/6
${\nu }_4$ Phosphate	91.7	9/10	8.4	1/6	4.4	2/6
${\mathrm{CH}}_2$	26.0	10/10	4.1	2/6	4.6	1/6
Hydroxyproline	156.0	8/10	29.4	5/6	7.3	1/6
${\nu }_2$ Phosphate	77.9	8/10	N/Ae	0/6	7.4	2/6
${\nu }_1$ Phosphate	71.9	10/10	6.2	5/6	7.8	3/6
Proline	106.7	8/10	22.7	5/6	9.5	4/6
Amide I	149.1	10/10	21.2	6/6	14.4	5/6

^aDerived from separate samples.

^bRank is based on the degree of mean normalized intensity fluctuation for unaltered polarization.

^c% Change is defined as the range of observed intensities normalized to the mean intensity observed during specimen rotation (unaltered and input polarized) or during analyzer rotation (highly polarized) for significant (sig.) model fits. When more than one model fit is significant, the mean is given.

^dNumber of significant models. Significance of model fit is defined as p<0.05 of the ANOVA regression (goodness of fit).

^eN/A: No significant models.

An RS surface plot for a single osteon acquired with unaltered polarization [Fig. 5(a)] illustrates that $\nu 1$ Phosphate peak intensity fluctuations [Fig. 5(b)] were out of phase with Amide I intensity fluctuations [Fig. 5(c)] but matched to the fluctuations of Proline [Fig. 5(d)]. Although noise has a significant impact on model fit in the unaltered regime, the trends of polarization phase between mineral and collagen peaks (Fig. 5) remained consistent with trends observed when the analyzer was rotated with the bone sample stationary (Fig. 3). Phase mismatch trends of RS biomarkers from highly polarized data persisted in unaltered polarization.

Fig. 5

Surface plot of osteonal sample bone rotation under unaltered polarization setup indicates persistence of phase mismatch for mineral to collagen components. (a) Intensity colored surface plot shows spectral variance due to rotation angle. Cutaways show $\nu 1$ Phosphate peak intensity (b) is out of phase with Amide I (c) while in phase with Proline (d).

3.3.

Performance of Phase-Matched Ratios for Compositional Differences

RS maps demonstrate how phase mismatch in RS peak ratios confounds the consistent measurement of spatial heterogeneity, even in an unaltered polarization regime (Fig. 6). Expected differences in mineral to collagen ratio between an osteon and surrounding interstitial tissue is not maintained throughout bone rotation for polarization sensitive $\nu 1$ Phosphate/Amide I [Fig. 6(b)]; whereas, $\nu 2$ Phosphate/Amide III [Fig 6(c)] shows consistent overall intensity differences between the tissue types despite rotation. Yet, this latter image is noisier than the former image due to significantly lower SNR of the $\nu 2$ Phosphate and Amide III peaks, relative to $\nu 1$ Phosphate. Maps of $\nu 1$ Phosphate/Proline [Fig. 6(d)] illustrate a relatively consistent image of compositional heterogeneity throughout rotation, differentiating the osteonal tissue from the more mineralized interstitial tissue. This peak ratio map is independent of bone rotation because of the low phase difference between $\nu 1$ Phosphate and Proline (Table 3).

Fig. 6

Mineral to collagen biomarker heat maps of derived peak ratios validate differential rotational consistency. (a) Bright field images reference the rotation of the osteon in 45 deg increments from left to right. Color maps are set to universal scale within each quantity and frames are rotated so that same image should be apparent under a lack of polarization sensitivity. (b) $\nu 1$ Phosphate/Amide I shows greatest rotational dependence. (c) $\nu 2$ Phosphate/Amide III consistency is masked by noise due to lower peak intensities. (d) $\nu 1$ Phosphate/Proline shows rotational consistency with a lower noise floor. (e) $\nu 2$ Phosphate/ ${\text{CH}}_2$ shows strong rotational dependence.

Table 3

Paired phase difference between selected Raman peak ratios and overall variance of peak ratios were estimated for bone and tooth rotation using the unaltered polarization instrument.

		Bone samples		Dentin control
Peak ratio	Representation	Phase difference (deg)a	Coefficient of variationb	Phase difference (deg)	Coefficient of variation
$\nu 1$ Phosphate/Amide I	mineral:collagen	69.9	0.073	85.5	0.110
$\nu 2$ Phosphate/Amide III	mineral:collagen	N/Ac	0.0004	0.1	0.021
$\nu 1$ Phosphate/Proline	mineral:collagen	2.2	0.023	9.2	0.040
$\nu 1$ Phosphate/${\mathrm{CH}}_2$	mineral: protein	62.8	0.038	85.2	0.054
$\text{Carbonate}/\nu 1\text{Phosphate}$	carbonate substitution	0.1	0.020	3.1	0.009
$\text{Carbonate}/\nu 2\text{Phosphate}$	carbonate substitution	N/Ac	0.025	6.5	0.016
$\text{Carbonate}/\nu 4\text{Phosphate}$	carbonate substitution	31.6	0.022	9. 3	0.022

^aTo obtain phase difference, the difference in phase between paired peaks (same spectra for the same site of rotation) was averaged among the multiple sites of data collection in which model fit was significant for both peaks.

^bTo obtain coefficient of variation, the standard deviation per mean of the peak ratio for a given rotation was averaged across multiple sites of data collection.

^cN/A: No phase angle could be generated from significant models within the same sample. Significance of model fit is defined as p<0.05 of the ANOVA regression (goodness of fit).

Figure 7 shows how NA and subsequent differences in sample volume averaging affect the apparent sensitivity of mineral to matrix calculations to tissue type. The calculations compare ν1 Phosphate/Amide I sensitivity to the phase-matched $\nu 1$ Phosphate/Proline using a map at 20× magnification and a 50× map of a portion of the same area [Fig. 7(a)]. The polarization sensitive Amide I ratio produced a distinct intensity change at 50× magnification in the 45 deg map [Fig. 7(c)] that was less pronounced but arguably still apparent at 20× [Fig. 7(b)]. The mineral to matrix ratio with Proline [Fig. 7(d) and 7(e)] was relatively consistent throughout.

Fig. 7

Heat maps of derived peak ratios retain polarization sensitivity when rotated, even with reduction of objective numerical aperture (NA). Bright field images reference the scanned areas at 20x ($\mathrm{NA}=0.4$) and 50x ($\mathrm{NA}=0.75$). Color maps are set to universal scale within each quantity. (a) $\nu 1$ Phosphate/Amide I maps at 20x show mild intensity changes under rotation at the border between osteonal and interstitial tissue. (b) The effect on $\nu 1$ Phosphate/Amide I increases with increased NA in the 50x maps. (c) $\nu 1$ Phosphate/Proline shows no notable intensity changes with rotation at 20x. (d) $\nu 1$ Phosphate/Proline shows no notable intensity changes with rotation at 50x, but noise is increased.

4.

Discussion

Development of RS methods towards bone diagnostics requires a firm understanding of which RS measures are sensitive to bone tissue composition and which are sensitive to bone tissue organization. While the potential for highly polarized RS to discriminate bone organization is known (Table 1), the present study provides a thorough characterization of the contribution of polarization bias in a standard Raman microscope to RS measurements of bone. When the goal of RS analysis is to assess compositional differences in bone, polarization bias adds uncertainty to the measurements. The addition of polarization optics, even to reduce polarization bias, leads to increased data collection time. Therefore, this study characterized peak and peak ratio specificity without altering instrumentation and found that polarization bias exists in a standard microscope and needs to be addressed.

Consistent with findings from the highly polarized RS analysis of mouse bone by Raghavan et al.,³⁰ polarization bias can persist for a low NA objective ($\mathrm{NA}=0.4$) (Fig. 7) that effectively averages the signal over larger spatial volumes than a 50× objective with a NA of 0.75. Nonetheless, matching polarization-orientation phase, effectively matching the organizational component of RS peaks, allows for consistent measures of composition [Fig. 3(b) and 3(d), as well as Fig. 7(c) and 7(d)]. This study used spectral maps of spatial heterogeneity within bone (Fig. 6) to establish that peak ratio sensitivity identified by polarized RS studies (Table 1) remains in unaltered polarization regimes (i.e., standard confocal RS instruments). In effect, polarization phase can be exploited to distinguish compositional heterogeneity from organizational heterogeneity. Finally, throughput costs of added optics can be avoided by using less sensitive peaks and phase-optimized peak ratios.

Spectral fingerprints of disease may rely upon organization of collagen and mineral as much as the relative composition of these constituents. This is of particular importance because bone disorders and disease states including osteoporosis and osteogenesis imperfecta can involve deleterious changes in bone organization.³⁰ Moreover, the organization of the constituents of bone tissue influences the fracture resistance of bone.^46–50 The observations of phase difference (Fig. 2) from our modeling of spectral data as a function of analyzer rotation is consistent with findings from previous highly polarized studies,^19,28,37 as well as recent theoretical models of collagen orientation within osteons.⁵¹ The phase differences between RS biomarker peaks arise from the organization of mineral crystals and collagen fibrils, such that information encoded within polarization phase may provide new insight for future disease diagnosis or fracture risk assessments. However, clear associations of phase and bone’s fracture resistance remain to be established. Nonetheless, as RS matures toward clinical use, consistency in discriminating composition from organization may contribute to accurate assessment of fracture risk.

Alternatively, RS could prove especially effective in the diagnosis of bone diseases that are pathologically based upon bone composition, including diabetes, chronic kidney disease, and the discrimination of grades of osteogenesis imperfecta. Recent investigations employing spatial sampling regimens to average out polarization bias concur that alternative mineral to collagen ratios (Fig. 6) exhibit increased sensitivity to known osteonal and interstitial differences in composition.^18,52 Specifically, improvement in mineral to collagen ratio variance and microstructure delineation when utilizing Proline instead of Amide I as a collagen component can be explained by a decrease in underlying polarization phase difference between ν1 Phosphate (mineral constituent) and Proline (collagen constituent) (Table 3).

RS acquisition of bone spectra often spans a range of 300 to $1800{\mathrm{cm}}^{-1}$ to cover prominent peaks, though it is expanded in some studies to $3000{\mathrm{cm}}^{-1}$ to capture a CH peak. Collecting Proline, $\nu 1$ Phosphate, and Carbonate would require spanning only $300{\mathrm{cm}}^{-1}$, further reducing necessary instrumentation, data processing, and collection time. Despite the availability of commercial systems, RS instrumentation differs largely between research groups and studies, implying that polarization bias from orientation sensitive peaks may vary between studies.

Changes in Raman spectra as the bone or tooth rotates relative to the incident laser light reveal the persistence of a polarization-orientation bias for sensitive peaks like Amide I even within less sensitive unaltered RS setups. Polarization sensitivity trends (Fig. 4) are conserved among prominent peaks in both the highly polarized regime and in the input polarized regime, despite the fact that spectra were acquired from different bone samples. Phase trends seen in highly polarized acquisition of bone appear to persist in unaltered instrumentation as well (Fig. 5). Phase-matched peak ratios of mineral to collagen ratio demonstrate lower coefficients of variation and therefore greater consistency (Table 3). When determined from the same site of bone rotation and then averaged across the various sites, the phase difference between $\nu 1$ Phosphate and Proline was 2.2 deg for bone and 9 deg for more highly organized dentin (Table 3), suggesting that these trends in phase difference may be conserved between tissues and anatomical locations. Despite the low intensity of Proline, the high intensity of the $\nu 1$ Phosphate peak may make $\nu 1$ Phosphate/Proline a more practical compositional metric than $\nu 2$ Phosphate/Amide III, which also has a low paired phased difference (Table 3). In addition, the use of peak phase difference confirmed the compositional nature of carbonate substitution (Table 3). While results suggest optimal metrics for bone composition and caution against possible inconsistent use of other metrics, the polarization-orientation information of RS biomarkers may have greater implications for future clinical bone diagnostics.

Consistent use of less polarization sensitive peaks or phase-matched ratios may allow for clearer comparisons between instruments and studies. RS sensitivity to glucocorticoid-treatment in rheumatoid arthritis bone shows compositional difference despite normalization to Amide I when using a fiber optic (polarization insensitive) system.²⁶ These biomechanical correlations are likely separate and distinct from RS correlations to collagen tension changes seen in formal polarization analysis.³⁶ Given low instrument polarization and results from less polarization sensitive carbonate and Amide III bands, analysis of bone from osteoarthritic patients on different load bearing surfaces can be interpreted as a largely compositional effect.⁵³ Phase mismatch of $\nu 1$ Phosphate/${\mathrm{CH}}_2$ [see Figs. 2 and 6(e)] may have contributed to biomechanical correlation due to use of a commercial confocal system,²⁴ thereby indicating a predominantly organizational phenotype. Interpretation of results from these and future studies in light of instrument polarization may help to define consistent Raman signatures for compositional and organizational disease.

5.

Conclusions

Polarization-orientation information in bone biomarkers, as seen in highly polarized studies involving RS, persists in unaltered commercial systems with lower inherent sensitivity to polarization. Modeling this consistent bias shows that matched phase information between peaks yields biomarker ratios that are less sensitive to polarization-orientation, without the loss of throughput necessitated by additional optics. Bias in compositional measures can be minimized by phase matching; specifically, findings support using $\nu 1$ Phosphate/Proline for mineral to collagen and $\text{Carbonate}/\nu 1$ Phosphate for carbonate substitution. In the diagnosis of organizational phenotypes, polarization-orientation can be maximized by phase mismatch (i.e., $\nu 1$ Phosphate/Amide I) without necessarily including polarization optics. Optimizing polarization in the instrument and in biomarkers should help to increase discrimination and consistency in future studies of bone.