2.1.

Specimens and Reagents

The specimens used for in-vitro transcutaneous Raman measurements through skin and overlying tissue were tibiae from mice sacrificed between the ages of 12 and $20\text{weeks}$ in the course of other unrelated studies. These mice were sacrificed according to study designs and protocols approved by the University of Michigan Committee on Use and Care of Animals. Both tibiae from healthy female animals from four randomly selected mice strains were used.

The depilatory agent was Sally Hansen Hair Removal Lotion (Sally Hansen Corporation, Uniondale, New York). The optical clearing agent was American Chemical Society reagent grade glycerol (Sigma-Aldrich Corporation, Milwaukee, Wisconsin).

2.2.

Instrumentation

A schematic of the Raman instrument is shown in Fig. 1 . A $400\text{-}\mathrm{mW}$ , $785\text{-}\mathrm{nm}$ external cavity diode laser (Invictus, Kaiser Optical Systems, Incorporated, Ann Arbor, Michigan) was used for excitation. The laser beam was passed through a $200\text{-}\mu \mathrm{m}$ core NIR optical fiber (PCN200 4-FF-HT-GN, Multimode Fiber Optics, Hackettstown, New Jersey). The light was collimated with a fiber optic collimator (F230FC-B, Thorlabs Incorporated, Newton, New Jersey) and directed through a $5\text{-}\mathrm{deg}$ fan angle Powell lens/collimating optics assembly (C10, StockerYale Montreal, Quebec, Canada) and a $75\text{-}\mathrm{mm}$ focal length NIR coated achromat (AC254-075-B, Thorlabs Incorporated, Newton, New Jersey) to obtain a $3\times 0.75\text{-}\mathrm{mm}$ line illumination. A nonconfocal fiber optic probe (PhAT probe, Kaiser Optical Systems, Incorporated) was employed to collect backscattered Raman shifted light and present it to the spectrograph. The probe contained a circular bundle of fifty $100\text{-}\mu \mathrm{m}$ core collection fibers. At the probe head, a $75\text{-}\mathrm{mm}$ focal length lens was employed to obtain a $3\text{-}\mathrm{nm}$ -diam circular field of view. A dichroic mirror (Chroma Technology Corporation, Rockingham, Vermont) reflected the $785\text{-}\mathrm{nm}$ light to the sample and transmitted the Raman signal to the collection fibers. A NIR-optimized imaging spectrograph (HoloSpec f/1.8i, Kaiser Optical Systems) fitted with a $50\text{-}\mu \mathrm{m}$ slit was used to provide a $6\text{to}8{\mathrm{cm}}^{-1}$ spectral resolution. The detector was a thermoelectrically cooled, deep-depletion $1024\times 256\text{pixel}$ charged-coupled device (CCD) camera (DU420-BR-DD, Andor Technology, Belfast, Northern Ireland) operated at $-75°\mathrm{C}$ with no binning.

Fig. 1

Schematic of experimental apparatus.

2.3.

Spectroscopic Measurements

Transcutaneous Raman spectroscopic measurements were made on intact, sacrificed animals. Prior to measurement, the depilatory lotion was used on the tibiae to facilitate hair removal with a tissue paper wipe from the region of interest. Excess depilatory was rinsed off with distilled water after hair removal was complete. After transcutaneous measurements, the entire tibia was excised, and overlying tissue was removed with a scalpel. The Raman spectrum of the exposed bone was then measured in the same region.

Transcutaneous Raman spectra were acquired with the illumination line and the collection disk focused onto the skin at the medial side of the tibia mid-diaphysis just below the tibial proximal tuberosity. The laser line was positioned so that the long axis of the line was parallel to the bone and centered over the bone. The power of the laser light at the specimen was $35\mathrm{mW}$ . The acquisition time was $300\mathrm{s}$ for transcutaneous measurements and $120\mathrm{s}$ for exposed bone measurements. For optical clearing experiments, glycerol was applied topically with a cotton swab. The glycerol was left to diffuse into the skin for approximately three minutes before spectra were acquired.

For six of the tibiae, seven sequential replicate spectra were acquired prior to optical clearing. After application of glycerol and a three minute wait, seven replicate spectra were acquired in the same location. For one of the tibiae, only five measurements were taken before optical clearing, and five afterward. After the sequence of transcutaneous measurements was completed, soft tissue was removed, and 20 consecutive Raman spectra of the exposed bone were acquired.

2.4.

Data Analysis

Data reduction was performed in Matlab 6.1 (The Mathworks Incorporated, Natick, Massachusetts) using vendor-supplied scripts and locally written scripts that had been described previously. Statistical analyses were performed in SAS, version 9.1 (SAS Institute Incorporated, Cary, North Carolina).

A single CCD frame contained 256 Raman spectra. Initial preprocessing included CCD calibration against a neon discharge lamp, with a check against a Teflon® Raman spectrum. White light correction and dark current subtraction were used to account for the spectral response of the detector. The image was then corrected for curvature caused by the large gathering angle of the spectrograph.

The spectrum from each of the 50 collection fibers of the probe was imaged onto slightly more than five rows of the CCD. To avoid cross talk, spectra from only the central three rows of each fiber image were used. These three spectra were averaged to generate one spectrum for each collection fiber. Finally, the $905\text{to}1500{\mathrm{cm}}^{-1}$ region of interest (ROI) was selected. This region contains the mineral phosphate P–O and carbonate C–O stretches, and matrix bands including collagen amide III and $\mathrm{C}{\mathrm{H}}_2$ wag.^{2, 8, 38}

The amount of noise in the transcutaneous measurements was quantified using spectral averages, that is, without background correction and without separation into bone and overlying tissue components. The three spectra from each of the 50 collection fibers were averaged, and the power spectrum of each averaged spectrum was computed. For this purpose, the dispersion axis was not converted to wavenumber, but was left in wavelength (nm) so that the noise contribution from each pixel would be equally weighted. The root-mean-square (rms) value was calculated for the high transform frequency region between 0.02 and $0.07\text{cycles}∕\mathrm{nm}$ . Data from one tibia were excluded, because the probe was improperly aligned during the measurements. For each of the remaining six tibiae, the mean rms values were computed for each of the seven sequential acquisitions.

For each tibia, a paired t-test was used to assess the difference in rms noise magnitudes between spectra of each tibia acquired with and without optical clearing. The effect of optical clearing on the noise rms values was examined for all six tibiae using a repeated measures analysis of variance (ANOVA). Using a mixed-effects model,³⁹ optical clearing was treated as a fixed factor with two levels (glycerol-treated and controls). The repeated measure was the series of measurements made on each mouse. The series had seven (or five) levels and was treated as a random effect. A significance level of 0.05 was used for all statistical calculations.

Recovery of a bone factor for each transcutaneous measurement followed previously described procedures.⁴⁰ An iterative background removal with a fifth-order polynomial was used to subtract the background fluorescence.^{41, 42} The resulting spectra were normalized, the covariance matrix was calculated, and band target entropy minimization (BTEM)^{40, 43, 44} was used to recover the spectral factors. A $3\text{-}{\mathrm{cm}}^{-1}$ interval around the phosphate band (ca. $959{\mathrm{cm}}^{-1}$ ) was chosen for band targeting. Between 3 and 23 eigenvectors from the dataset were included for the calculation of Raman spectral factors. Eigenvectors containing predominantly random noise were used to improve the signal-to-noise ratio of the recovered bone spectra. An eigenvector weight distribution test for selecting the appropriate number of eigenvectors was used, as described elsewhere.⁴⁰ A stopping point was reached when additional eigenvectors added only noise.

Once the bone spectral factors were calculated, the cross-correlation coefficient between the bone factor and the exposed bone measurement was calculated using the “xcorr” function of the Matlab signal processing toolbox. To exclude the intense P–O stretch, while including enough of the spectrum for computation, the interval used was $988\text{to}1500{\mathrm{cm}}^{-1}$ . The mean cross-correlation coefficient was computed for the average of the spectra from each of the six tibiae. For each tibia, a paired t-test, as described before, was used to examine the difference in the cross-correlation coefficients between transcutaneous spectra measured with and without optical clearing. The effect of optical clearing on the correlation between transcutaneous and exposed bone measurements was tested for all six tibiae using a repeated measures ANOVA. Optical clearing was treated as a fixed factor with two levels (glycerol-treated and controls), and the repeated measure was the series of measurements on each mouse, which had seven (or five) levels and was treated as a random effect.

3.1.

Noise Level Determined by Power Spectra

Transcutaneous Raman spectra taken through approximately $1\mathrm{mm}$ of tissue on a mouse tibia are shown in Fig. 2a . CCD white light correction, dark current subtraction, and correction of spectrograph-induced curvature was applied, but no further processing was done. The measurements made after glycerol application have visibly less intense and more reproducible background fluorescence than those from the control spectra, which were acquired prior to optical clearing. The power spectra for these Raman spectra are shown in Fig. 2b. In the high transform frequency region $(>0.02\text{cycles}∕\mathrm{nm})$ , where mostly noise is represented, the measurements made after optical clearing have both lower noise power and reduced measurement-to-measurement variability.

Fig. 2

Raman spectra of a murine tibia (distal diaphysis). The bone tissue is approximately $1\mathrm{mm}$ below the skin. The gray traces are raw spectra obtained without optical clearing, and the black traces are spectra obtained after glycerol application. (a) transcutaneous Raman spectra and (b) power spectra.

We attribute the spectroscopic effects of optical clearing to reduced specimen fluorescence in the acquired spectra. With $785\text{-}\mathrm{nm}$ excitation, the most important source of fluorescence is melanin, which is located in the melanocytes. In mice, as in humans and other mammals, the melanocytes lie just below the stratum corneum.⁴⁵ Decreasing the scattering at and just below the skin surface decreases the amount of fluorescence that is generated and the amount reaching the collection fibers, thereby decreasing its contribution to the total collected signal. Some photobleaching may also be occurring during the first few minutes of laser illumination. The background decreases rapidly between the first and second spectrum acquisition, but slowly thereafter [Fig. 2a].

Bar graphs of noise levels and measurement variability for each tibia are shown in Fig. 3a . The measurements taken after optical clearing had a significantly lower noise level $(\mathrm{p}<0.05)$ in four out of the six tibiae. In addition, the variability in a set of spectra, indicated by the error bars, was lower for spectra acquired after the application of glycerol, although the differences were not statistically significant in tibiae 2 and 6. The mean noise levels for the six tibiae are presented in Fig. 3b. The spectra acquired after optical clearing have significantly less noise $(\mathrm{p}=0.0037)$ .

Fig. 3

rms intensity for power spectra in high transform frequency region ( $\text{mean}+\text{standard}$ deviation). (a) Results for measurements made on six different tibiae. (b) Results across tibiae from all mice.

Recovery of the bone spectrum depends on separation of the bone component from that of the overlying tissue, which includes skin, tendon, blood vessels, and even some adipose tissue. Optical clearing can actually degrade the recovered bone spectrum if the fiber optic probe is not aligned to maximize the contribution from bone and minimize the contribution from overlying tissue. This effect is illustrated in Fig. 4 . The illumination line must be positioned directly over the bone, and the collection fibers must be centered on this line, as shown in Fig. 4a. The field of view of the collection fibers is then as illustrated in Fig. 4b.

Fig. 4

Effect of not centering the illumination line in the center of the collection fibers. (a) Correct alignment of illumination line and collection disk with respect to the bone. (b) Field of view of the collection fibers for proper alignment. (c) Field of view of the collection fibers for improper alignment. (d) Resulting noise levels in measurements made with improper alignment (compare to Fig. 3). (e) Mean transcutaneous spectra, after baselining and normalizing, for a measurement before and after glycerol application.

However, if the collection fibers are not positioned directly over the bone and centered on the illumination line, spectra from soft tissue are oversampled. We demonstrated these effects by misaligning the probe. The field of view of the collection fibers was shifted toward the medial side of the tibia while the illumination line centered over the bone. The improper collection fiber alignment is shown in Fig. 4c. The rms noise for the control and optical clearing cases are shown in Fig. 4d. Significantly more noise was observed in the measurement made after glycerol application $(\mathrm{p}<0.00001)$ . This seemingly contradictory result is caused by the reduction of light scattering by the skin, allowing oversampling of Raman scatter from the soft tissue directly below. As expected, the overall intensity of the bone component of the recovered spectrum is decreased. The effect is seen most clearly in the phosphate $v_1$ band at $959{\mathrm{cm}}^{-1}$ [Fig. 4e]. The absolute intensity of the phosphate $v_1$ band recovered with the misaligned probe is not as great as that obtained when the probe is properly aligned. Because the signal-to-noise ratio is reduced and the contribution from skin and tendon collagen is increased by probe misalignment, the accuracy of the recovered bone factor is also lowered.

3.2.

Cross-Correlation Coefficients

The cross-correlation coefficients between bone factors recovered from transcutaneous and exposed bone spectra further illustrate the effects of optical clearing. Because in the mouse tibia the bone lies only about $1\mathrm{mm}$ below the skin, a strong phosphate $v_1$ band is actually visible in the spectrum, after removal of fluorescence background (Fig. 5 ). The Raman spectrum of type-1 collagen in skin and tendon is similar to that of type-1 collagen in bone. As a consequence, the collagen bands are much more intense than the similar bands in exposed bone, as comparison to the exposed bone spectrum shows. Collagen bands near the $1070\text{-}{\mathrm{cm}}^{-1}$ region effectively mask the carbonate $v_1$ band at $1070{\mathrm{cm}}^{-1}$ . By reducing the skin collagen contribution, optical clearing with glycerol improves the accuracy of the recovered bone factor, as shown in Fig. 5b. The difference is clearest in the less intense bands.

Fig. 5

(a) Typical mean transcutaneous spectrum (gray) and typical mean exposed bone spectrum (black). (b) Recovered bone factor without an optical clearing agent (gray), recovered bone factor after glycerol application (black), and exposed bone measurement (dotted).

To quantify the difference between the recovered bone factors and the exposed bone measurements, cross-correlation coefficients were calculated in the low signal-to-noise portion of the recovered spectra, i.e., excluding the phosphate $v_1$ band (Fig. 6 ). The spectra acquired after optical clearing had a significantly higher correlation with the exposed bone spectra $(\mathrm{p}<0.07)$ in four of the six tibiae. The mean cross-correlation coefficients are shown in Fig. 6b. The measurements made after optical clearing have a significantly higher correlation with the exposed bone spectra $(\mathrm{p}=0.025)$ than those of controls, without optical clearing.

Fig. 6

Cross-correlation coefficient between the exposed bone measurement and the recovered bone factor ( $\text{mean}+\text{standard}$ deviation). (a) Results for measurements made on six different tibiae. (b) Results across tibiae from all mice.