1.

Introduction

Vibrational spectroscopy has been used to monitor the response of bone to external stress. One common spectroscopic response to external stress is a wavenumber shift in one or more of the spectral bands. For example, in high-pressure studies of calcium hydroxyapatite and other inorganic minerals similar to bone mineral,^{1, 2, 3, 4} the vibrational bands associated with the phosphate groups were shown to exhibit strain-dependent shifts. Subsequent high-pressure x-ray diffraction and Raman spectroscopic studies by Comodi found that the phosphate $v_1$ band shift in fluorapatite was mainly due to a change in the cation/anion spacing of phosphate.^{5, 6} Similar effects in bone have been seen in our laboratory, including high-pressure Raman studies⁷ and ongoing nuclear magnetic resonance spectroscopy (NMR) experiments.⁸

In studies on bone, the mineral component has been examined in microdamaged,⁹ fractured,¹⁰ and nanoindented¹¹ regions. Researchers have observed a shift in the $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ symmetric stretch, the most intense band in the bone spectrum. In microdamaged and fractured regions, an additional mineral factor was present, whose $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ band corresponded to a higher wavenumber (963 and $965{\mathrm{cm}}^{-1}$ , respectively) than the carbonated hydroxyapatite typically found in bone $(\sim 959{\mathrm{cm}}^{-1})$ . In the nanoindentation study, a $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ band shift occurred in the middle of the indent where compression had occurred. A shift was not observed in the control region outside the indent, indicating that the shift was an effect of damage, and not a cause of it.

Pezzotti and Sakakura have taken advantage of this phenomenon and monitored a shift in the $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ band during fracture propagation of bovine cortical bone.^{12, 13, 14} Quantitative stress fields were calculated and Raman stress maps were generated, allowing toughening mechanisms such as microcracking to be visualized. In subsequent studies, the $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ band shift was monitored in murine bone during physiological loading and observed to change.¹⁵ On nanoindented teeth, Raman images were generated mapping this wavenumber shift.¹⁶ The results of these studies suggest bone mineral plays a dynamic role in the response to external stress.

Because the mineral band position is sensitive to stress, we wanted to monitor the mineral response in a bone model where understanding stress distributions would be important, such as in a fracture model. Nalla, Kinney, and Ritchie introduced into the biomechanics literature the double-notch specimen, a model in which the early stages of fracture can be examined.¹⁷ The specimens are rectangular beams of bone that have similar rounded notches milled equidistant from each end. In four-point bend tests, maximum strains occur at the roots of the notches, and eventually the bone fractures at one of the notches. Because both notches experience the same bending moment, when one notch breaks, the other remains “frozen” in the state directly preceding fracture.

The objective of this preliminary study was to determine stress distributions in the double-notch specimen using Raman imaging. We acquire spectra around the roots of unbroken and fractured notches and monitor stress via spectral shifts in the $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ band. The resulting Raman images map the stress distribution.

2.

Materials and Methods

2.1.

Specimen Preparation

Fresh-frozen equine third metacarpals (Mc-3) from three female thoroughbreds were used. One horse died of a fracture of the left forelimb fetlock, and the cause of death of the other two horses was unknown. Specimens were milled to approximate dimensions of $2\mathrm{mm}$ $\left(\text{width}\right)\times 2\mathrm{mm}$ $\left(\text{thickness}\right)\times 21\mathrm{mm}$ (length). The geometry of the specimens is shown in Fig. 1 . Specimen length corresponded to the long axis of the bone. Rounded notches (depth $\sim 0.6\text{to}0.7\mathrm{mm}$ ) were created using a $0.75\text{-}\mathrm{mm}$ dental cutting disk (SummaDisk, Shofu Corporation) mounted on a CNC machine. The depths of both notches were made as similar as possible to ensure comparable stress-strain fields at the notch tips. Symmetric four-point bending tests (inner loading span $S\sim 5\mathrm{mm}$ ) were conducted on the double-notch specimens. The specimens were loaded at $0.01\mathrm{mm}∕\mathrm{s}$ using an EnduraTec ELF 3200 testing machine (BOSE Corporation, ElectroForce Systems Group, Eden Prairie, Minnesota). The bone was in tension on the side where the notches were located. The specimens remained hydrated throughout the preparation and testing procedures. Specimens were stored at $-80°\mathrm{C}$ until Raman images were acquired.

Fig. 1

Double-notch specimens. (a) Specimen geometry. (b) At four-point bending, the bone fractured at one of the notches. The dashed lines indicate the three regions where Raman images were acquired: 1. control, 2. non-fractured, and 3. fractured regions, respectively.

3.

Results

A representative Raman spectrum of bone is shown in Fig. 2 . The most intense band in the bone spectrum is phosphate $v_1$ , which is indicative of carbonated hydroxyapatite, and its position is sensitive to the mineral environment. The inset of the figure shows the non-Gaussian shape of the $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ band, with the CG labeled.

Fig. 2

Representative Raman spectrum of bone. The phosphate $v_1$ peak is centered at $\sim 959{\mathrm{cm}}^{-1}$ . The non-Gaussian shape of this band is shown in the inset, and its center of gravity is $956.9{\mathrm{cm}}^{-1}$ .

In this preliminary study, three bone specimens were imaged. Raman images taken on beam 1 from an undamaged region and at the base of the unbroken and fractured notch are shown in Fig. 3 . It is important to note that all of these Raman images are maps of the stress calculated using Eq. 3. All the images for this beam are on the same color scale, and the $x$ and $y$ axes are in microns, where the $y$ axis corresponds to the length of the laser line. The average stress value in the control region [Fig. 3a] was $0.004\mathrm{MPa}$ . The Raman image of the unbroken notch is shown in Fig. 3b, along with a superimposed outline of the notch edge $(x\sim 30\text{to}360\mu \mathrm{m})$ to visualize where certain features of the notch appear. In the corresponding microscope image, the central black box denotes the imaged region and the tickmarks in the box represent every $100\mu \mathrm{m}$ . The Raman image of the unbroken notch had higher stress, with the highest stress being concentrated at the corners of the notch. At each of the unbroken notches, an average stress value was calculated from a $50\times 50\text{-}\mu \mathrm{m}$ area above each corner, indicated by the dashed lines in Figs. 3b, 4b, 5b . The averages from all specimens and regions are compiled in Table 1 . At the left and right corners of beam 1, the average stress values were 140.1 and $127.0\mathrm{MPa}$ . The stress propagated $\sim 100\mu \mathrm{m}$ away from the notch edge. For the fractured notch [Fig. 3c], the edge of the notch and beginning of the fracture are located in the lower left-hand corner of the image. The outline from $x\sim 100\text{to}250\mu \mathrm{m}$ indicates the edge of the notch. The outline from $0\text{to}100\mu \mathrm{m}$ designates the edge of the fracture; the bone fractured at $\sim 100\mu \mathrm{m}$ in the image and propagated off to the left. At the failed notches, average stress values were calculated from a $25\times 25\text{-}\mu \mathrm{m}$ area near the edges of the fracture [these ROIs are shown in Figs. 3c, 4c, 5c]. For beam 1, regions of higher stress $\left(137.1\mathrm{MPa}\right)$ were only observed near the edge of the fracture and propagated $\sim 50\mu \mathrm{m}$ away (from $y\sim 40\text{to}90\mu \mathrm{m}$ ).

Fig. 3

Raman images of stress for specimen 1. The $x$ and $y$ axes are in microns, and the color bar range for all $\text{images}=(-184\text{to}276\mathrm{MPa})$ . (a) The average stress value in the control region was $0.004\mathrm{MPa}$ . $[\text{area}=0.027{\mathrm{mm}}^2]$ . (b) Higher stresses were concentrated at the corners of the unbroken notch, represented by the dashed boxes. The average stress values in those regions were 140.1 and $127.0\mathrm{MPa}$ . The outline at the bottom of the image was the edge of the notch. $[\text{area}=0.075{\mathrm{mm}}^2]$ . (c) Higher stresses were observed at the edge of the fracture ( $137.1\mathrm{MPa}$ in the dashed region). The outline from $x\sim 0\text{to}100\mu \mathrm{m}$ was the edge of the fracture, and from $x\sim 100\text{to}250\mu \mathrm{m}$ was the edge of the notch. The subtle vertical lines visible every $50\mu \mathrm{m}$ were because the scanning mirror dictated images be taken in $50\text{-}\mu \mathrm{m}$ sections, whereas the horizontal striations were due to imperfect flat-field correction $[\text{area}=0.098{\mathrm{mm}}^2]$ . (Color online only.)

Fig. 4

Raman images of stress for specimen 2. The x and y axes are in microns, and the color bar range for all $\text{images}=(-92\text{to}276\mathrm{MPa})$ . (a) The average stress value in the control region was $-0.01\mathrm{MPa}$ $[\text{area}=0.021{\mathrm{mm}}^2]$ . (b) Higher stresses were concentrated at the corners of the unbroken notch with the average stress values being 81.0 and $162.2\mathrm{MPa}$ . The corners of the notch were just below the Raman image, near $x\sim 200\mu \mathrm{m}$ and $x\sim 600\mu \mathrm{m}$ $[\text{area}=0.088{\mathrm{mm}}^2]$ . (c) Higher stresses were observed at both the left $\left(234.3\mathrm{MPa}\right)$ and right $\left(197.8\mathrm{MPa}\right)$ edges of the fracture. The fracture was located from $x\sim 100\text{to}400\mu \mathrm{m}$ in the image. A region of higher stress was also located in the lower right-hand corner of the image, above the right corner of the notch. For the images in (b) and (c), the white spaces resulted from removal of data. For all images, imperfect flat-field correction led to striations in the horizontal direction $[\text{area}=0.099{\mathrm{mm}}^2]$ . (Color online only.)

Fig. 5

Raman images of stress for specimen 3. The $x$ and $y$ axes are in microns, and the color bar range for all $\text{images}=(-184\text{to}184\mathrm{MPa})$ . (a) The average stress value in the control region was $-0.01\mathrm{MPa}$ $[\text{area}=0.025{\mathrm{mm}}^2]$ . (b) Rather than being concentrated at the corners of the unbroken notch, stress propagated across the notch $[\text{area}=0.083{\mathrm{mm}}^2]$ . (c) The bone fractured in the middle of the notch. The stresses near the left and right fracture edge were 13.2 and $43.2\mathrm{MPa}$ , respectively. Horizontal striations were due to imperfect flat-field correction $[\text{area}=0.116{\mathrm{mm}}^2]$ . (Color online only.)

Table 1

Average stress values and standard deviations for all regions. The units are MPa, and the control, strain, and failed regions are denoted by C, S, and F, respectively.

For beam 2 (Fig. 4), the average value in the control region was $-0.01\mathrm{MPa}$ . For the nonfractured notch of beam 2, a stress pattern similar to the nonfractured notch of beam 1 was observed. The corners of the unbroken notch were right below $x\sim 200$ and $\sim 600\mu \mathrm{m}$ in the image. Average stresses of $81.0\mathrm{MPa}$ (left) and 162.2 (right) were seen at the very edge of these corners. Above the left corner, a stress of $\sim 90\mathrm{MPa}$ extended $\sim 100\mu \mathrm{m}$ away from the edge of the notch. At the right corner, a similar pattern was observed, except a larger magnitude stress extended into the tissue. For the fractured notch of beam 2, the fracture was located from $x\sim 100\text{to}400\mu \mathrm{m}$ and extended along the entire $y$ axis. The regions of greatest stress were located near the left $\left(234.3\mathrm{MPa}\right)$ and right $\left(197.8\mathrm{MPa}\right)$ edges of the fracture. Also, a region of higher stress was located from $x\sim 850\text{to}900\mu \mathrm{m}$ , near the bottom of the image. It can be seen in Fig. 4 that the hardware change of replacing the scanning mirror with the motorized stage had a beneficial effect on image quality; images taken with the motorized stage (i.e., Fig. 4) are “seamless,” whereas images taken with the scanning mirror (i.e., Figs. 3 and 5) usually show a “seam” every $50\mu \mathrm{m}$ , the increment at which the specimens were manually translated.

For beam 3 (Fig. 5), the stress pattern was different from those of the previous two specimens. The average stress value in the control region was $-0.01\mathrm{MPa}$ . Unlike beams 1 and 2, the stressed regions at the unbroken notch were not really focused at the corners, but instead propagated across the notch $(x=0\text{to}500\mu \mathrm{m})$ in the center of the image $(y\sim 40\text{to}110\mu \mathrm{m})$ . In this large region, the average stress value was $57.2\mathrm{MPa}$ . However, at the left and right notch corners, the average stress was 15.1 and $26.6\mathrm{MPa}$ , respectively. For the fractured notch, the fracture was in the middle of the image. In the designated region on the left side of the fracture, the average stress value was $13.2\mathrm{MPa}$ . On the right side, the average value was $43.2\mathrm{MPa}$ . Other regions of higher stress existed across the center of the image, but this was not different from the unbroken notch.

Repeated measures of ANOVA were used to test for any differences in stress values among regions (control, strain, fail). A repeated measures design was used because the three regions were imaged in each specimen. In each region, the average stress values were calculated over the two ROIs indicated on the stress maps, and these measurements were treated as an independent replicate. For the control regions, the two average stress values were calculated by splitting the image in half at $x=100\mu \mathrm{m}$ and averaging over the first $100\mu \mathrm{m}$ for the first subregion and the last $100\mu \mathrm{m}$ for the second subregion. Treating the region as the repeated factor, a significant difference in stress values was found $(\mathrm{p}=0.0166)$ . Using the Tukey-Kramer post-hoc analysis, we found that the stress values in the control region were significantly smaller than those in the strain $(\mathrm{p}=0.0425)$ and fail regions $(\mathrm{p}=0.0169)$ . Stress values did not differ significantly between the strain and fail regions $(\mathrm{p}=0.4256)$ .

Because the stress patterns were different for specimen 3, a one-way ANOVA was used to detect differences among specimens, which was the between-subjects factor. A significant difference was detected $(\mathrm{p}<0.0001)$ , and the Tukey-Kramer post-hoc analysis found that specimen 3 had significantly lower stress values than specimens 1 $(\mathrm{p}=0.0003)$ and 2 $(\mathrm{p}<0.0001)$ .

4.

Discussion

It can be seen in Fig. 2 that the shape of the $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ band is non-Gaussian because of unresolved shoulder bands that correspond to other phosphate environments. Thus, the CG of the $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ band is a useful way to gather information about different mineral environments present via changes in intensity or position of these shoulder bands. Any changes in shoulder bands are overlooked if only the peak center is examined.

Shifts in the $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ CG were converted into stress values using a conversion factor of $2.5{\mathrm{cm}}^{-1}∕\mathrm{GPa}$ . This term represents the expected wavenumber shift of the $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ band, and allows for the calculation of unknown stress fields in the mineral phase. It was determined by loading bovine cortical bone under four-point bending, the same type of loading used for the double-notch specimens. This value is similar to the $2.47{\mathrm{cm}}^{-1}∕\mathrm{GPa}$ calculated for hydroxyapatite.¹⁹ The observed spectral shift was mainly due to a change in the spacing between the cations and anions of phosphate (a reversible effect), and a permanent change like distortion (changing bond lengths relative to one another) was far less likely. For example, Comodi found very little change in the P-O bond lengths of phosphate, even when applying $4.72\mathrm{GPa}$ .⁵ This pressure is far greater than that needed to fracture equine third metacarpals in four-point bending (bending $\text{strength}=227\pm 27\mathrm{MPa}$ ).²⁰ Hence, it is very likely that the $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ band shift is entirely due to changes that occur in spacing between the ions of phosphate.

The region near the unbroken notch corresponded to bone in a state directly preceding fracture. The most commonly observed pattern was a higher stress concentrated above the corners of the notch. This existence of residual stress suggested that the tissue remained in a loaded state. The residual stress formed a “U” or “V” pattern, with the greatest stress being located near the notch corners, and the vertex or least stressed region being located close to the center of the notch. This pattern is consistent with the stress profile generated from a finite element model of the double-notch four-point bending specimen (Fig. 6 ). The ${\mathrm{S}}_{11}$ stress component is plotted, which is the direction along the length of the beam. The model shows the stress is most concentrated near both corners of the notch, with predicted stresses of approximately $230\mathrm{MPa}$ . For beams 1 and 2 [Fig. 3b and 4b], the stress in these V-shaped regions was $\sim 134\mathrm{MPa}$ (average of the two ROIs) for beam 1 and $\sim 122\mathrm{MPa}$ (average of the two ROIs) for beam 2, which were significantly different from the control regions. The average values we calculate are less than the bending strength $(227\pm 27\mathrm{MPa})$ but greater than the yield stress $(110\pm 27\mathrm{MPa})$ for equine third metacarpals.²⁰ Some likely reasons that the average values are lower than the bending strength and predicted stresses of the model are because: 1. the $dv∕dP$ coefficient was not calculated for the equine bone samples, but estimated from the $dv∕dP$ coefficient for bovine bone: and 2. The mineral is deposited in and around the matrix and its distribution is not homogeneous. This distribution probably contributes to the stripe-like morphology seen in the images, where points of high stress and low stress exist side by side. This is similar to the effect that Pezzotti has observed.^{12, 14} If the individual data points (rather than the averages) in these ROIs are examined, it can be seen that numerous individual points do experience stresses of over $200\mathrm{MPa}$ .

Fig. 6

Stress profile generated from a finite element model of the double-notch four-point bending specimen. The models were linear elastic and had homogeneous properties such as modulus. The ${\mathrm{S}}_{11}$ stress component is plotted, and the model shows that the stress is most concentrated near both corners of the notch, with predicted stresses of approximately $210\text{to}240\mathrm{MPa}$ . The units of the color scale are MPa. (Color online only.)

In examination of images of unbroken notches, care must be exercised in interpretation. For beam 1, the notch was located along the bottom edge of the Raman image from about $30\text{to}360\mu \mathrm{m}$ . In this region, $<20\mu \mathrm{m}$ of the laser line was focused in the notch and not on bone. However, a bone signal was still detected even though the boundary of the notch appeared to be a sharp edge in the corresponding microscope image. The peak response of the video camera was lower than $700\mathrm{nm}$ , which minimized scattering effects in the microscope image. The near-infrared (NIR) excitation light used to generate the Raman images penetrated farther into the tissue, and the scattering response of the signal was emphasized. The nonsharp boundary in the Raman image was mainly because NIR light is multiply scattered in bone.²¹ Thus, the boundary of the notch seen with visible light (microscope image) is sharper and more distinct than the boundary seen with near-infrared light (Raman image). The excitation (and Raman-generated) light propagates through the depth of the specimen, and Raman light is remitted not only from the surface of the bone, but also deeper along the notch edge. Hence, even though part of the laser beam was focused in the notch and not directly over bone, bone spectra could still be collected with our objective, albeit at a lower absolute signal and lower signal-to-noise ratio. Even in regions where the entire length of the laser line was focused on bone, Raman light that originated from deeper layers was collected. However, this out-of-focus light had a lower intensity and lower signal-to-noise ratio than the in-focus light at the surface of the bone. To exclude this effect, the system would need to be confocal, but this would result in reduced signal.

The stress pattern near the unbroken notches was different from the pattern near the fractured notches, even though both regions nominally experienced the same loading (because of the nearly symmetrical notches). When compared to the unbroken notch, the tissue at the corners of the fractured notch did not have as high of a residual stress. In these corner regions, the tissue appears to have elastically recovered after the notch fractured, resulting in a smaller residual stress in the mineral component. However, mineral stress can still be seen near the edges of the fracture where the tissue did not elastically recover. The reason is that we have made permanent changes to the matrix in this region and have broken or distorted collagen cross-links. Because the mineral is deposited in and around the matrix, the response of the mineral and matrix are coupled. In regions near the fracture, there are permanent changes to the matrix, but not necessarily permanent changes to the mineral. However, an increased stress in the mineral is observed because of the coupling with the permanently stressed matrix. If all the collagen was removed, the mineral might return to almost its original state. The average stresses near the beam 1 and 2 fracture edges were about 137 and $216\mathrm{MPa}$ (average of the two ROIs). Again, this was significantly higher than in control regions.

To determine the effects of protease inhibitor on bone spectra, protease inhibitor was added to the buffer used for all regions of beam 2, but not in the buffer used for beam 1. The protease inhibitor exhibited a band at $951{\mathrm{cm}}^{-1}$ that overlapped with the $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ band in bone. When the laser was focused on the bone surface, the $951\text{-}{\mathrm{cm}}^{-1}$ band comprised approximately 1% of the total area of the $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ band, and it was determined that the protease inhibitor did not interfere with CG calculations. However, in regions where the buffer was pooled (i.e., within the fracture), the spectrum of the protease inhibitor contributed approximately 20% or more to the total area. This contribution could not be effectively removed by subtraction. Multivariate techniques were not used to remove the contribution because of the continuous, overlapping distribution of protease inhibitor and bone. For these reasons, the data in the fractured region were not used and the regions were left as white space. The other small white spaces in Figs. 4b and 4c resulted from removal of data contaminated with a noise spike that overlapped with the $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ band, or a fluorescent background that could not be properly removed by baselining.

Beam 3 displayed different stress patterns for both notches, and was significantly different from beams 1 and 2. The stress observed at both notches was less than that of beams 1 and 2. This lower-magnitude stress was spread out across the length of the notch and not really concentrated at the corners [Fig. 5b]. For the fractured notch, stress was present away from the edge of the fracture and across the middle of the image, suggesting the tissue did not relax during or after fracture, and the stress did not recover elastically. Another difference was that beam 3 fractured from the center of the notch, whereas the other specimens fractured at the corner of the notch where the greatest tension would be expected.

Differences among the specimens were analyzed to determine the reason for the discrepancy in residual stress patterns. Specimens 1, 2, and 3 were all excised from the dorsal-medial region of the Mc-3 bone of female thoroughbreds, from either the distal or proximal end of the bone. A mixture of left and right bones was used; however, previous studies have shown that no differences existed in collagen orientation²² and bone mineral content (BMC)²³ for left and right bones. The most likely reason for the discrepancy in specimen stress response was the age of the specimens. Beam 3 came from a horse that was $6\text{years}$ old, whereas beams 1 and 2 came from horses that were 2 and $4\text{years}$ younger, respectively.

The average strength of equine Mc-3 bone peaks sometime between the age of $4\text{to}7\text{years}$ ; El Shorafa, Feaster, and Ott found that peak strength was attained within this range,²⁴ and Lawrence showed that both BMC and bone breaking strength, defined as the maximum stress the material can withstand, peaked near $6\text{years}$ of age.²³ From the force-displacement curves, the maximum breaking force for the $6\text{-}\text{year}$ -old bone (beam 3) was 54.9 N, whereas for the 2- and $4\text{-}\text{year}$ -old specimens it was 63.8 N and 66.5 N, respectively. In our study, the $6\text{-}\text{year}$ -old bone (specimen 3) was less strong than the younger bones. The study by Lawrence also found that in maturing horses, the strength of bone was due mainly to the increasing BMC. The Raman mineral-to-matrix band ratio (intensity values of phosphate $v_1$ at $\sim 959{\mathrm{cm}}^{-1}$ /proline at $\sim 853{\mathrm{cm}}^{-1}$ ), a measure of the amount of mineral in bone, for the three specimens was calculated in the failed notch ROIs designated in Figs. 3c, 4c, 5c. The average mineral-to-matrix ratio for specimens 1, 2, and 3 were $13.9\pm 1.1$ , $13.8\pm 1.1$ , and $11.8\pm 1.6$ . The mineral-to-matrix ratio was lower in the beam that had the smallest breaking force. The lower mineral content, perhaps from recent remodeling, may have contributed to the lower strength of that beam. Another reason for the different stress patterns at both notches could be because the bone structure caused the stress distribution to be different than the two previous specimens. However, because of the small number of specimens, these conclusions are only preliminary.

It can be seen in Fig. 5c that signal was collected from within the fractured region. Unlike beam 2, no protease inhibitor was used for beam 3. The reason bone signal was collected was because the fracture process was irregular, and the break was not perpendicular to the surface. Regions of bone were present below the plane of best focus (i.e., plane of bone surface), as illustrated in Fig. 7 . Because the Raman microprobe was not confocal, signal from these deeper layers was collected, albeit at a lower intensity.

Fig. 7

Irregular fracture process. When bone fractured, the break was not perpendicular to the surface; regions of bone were present below the surface of the bone, as shown for specimen 3. The white outline corresponded to the uppermost surface of bone at the left edge of the fracture. The regions of bone below the surface contributed to the signal that was collected from within the fractured region.

In conclusion, residual stress in the loaded bone tissue was measured by analyzing band shifts in $\mathrm{P}{\mathrm{O}}_4^{-3}$ $v_1$ . These mineral band shifts were a consequence of changes in spacing between phosphate cations and anions, which is a reversible effect. A band shift in the mineral component still could be measured after four-point bending, implying that the tissue near the unbroken notch and the edge of the fracture were left in a loaded state. Residual stresses in the strain and fail regions were significantly different than in control regions (0.0425 and 0.0169, respectively). In beams 1 and 2, the location and pattern of the residual stresses was in agreement with that of the predicted stresses from a linear finite element analysis of the fracture specimen, where the highest stresses at the unbroken notch were concentrated at the corners. The calculated average stress magnitudes were lower than predicted, mainly because the $dv∕dP$ value used in the study was an estimate for equine bone, and the mineral distribution was not uniform. The exact stress distributions probably depend on specimen age, BMC, and local load distribution. Careful interpretation of Raman images was required because both multiple light scattering in bone and irregularity of the fracture site caused signal to be collected from below the uppermost surface of the bone (i.e., the best plane of focus).

Future work includes examining the stress response of the matrix. In fractured regions, collagen cross-links rupture, but the fate of cross-links just before bone breaks (i.e., region near unbroken notch) is not known, even though the breaking of cross-links is thought to be one of the last processes to occur before bone failure. Also, polarization measurements would be useful, because some mineral and matrix spectral bands are strongly polarized, and the orientation of different bone components could be determined.^{25, 26}