Brillouin micro-spectroscopy of subchondral, trabecular bone and articular cartilage of the human femoral head

: Brillouin micro-spectroscopy is applied for investigating the mechanical properties of bone and cartilage tissues of a human femoral head. Distinctive mechanical properties of the cartilage surface, subchondral and trabecular bone are reported, with marked heterogeneities at both micrometric and millimetric length scales. A ubiquitous soft component is reported for the first time, characterized by a longitudinal modulus of about 4.3 GPa, possibly related to the amorphous phase of the bone. This phase is mixed, at micrometric scales, with a harder component, ascribed to mineralized collagen fibrils, characterized by a longitudinal modulus ranging between 16 and 25 GPa.


Introduction
Bone is a lively tissue, whose structure is remodeled by function, age, gender differences, etc., depending on both mechanical stimuli and by mineral, metabolic and hormonal homeostasis. Understanding biomechanical properties of this tissue at different spatial scales is crucial, not only to figure out how bones and joints can resist to stresses but also to detect early changes in their functionality which can lead to pathologic conditions. Bone is a hierarchically-organized tissue [1], with a mineralized extracellular matrix (ECM) that contains about 25% organic matrix, 5% water, and 70% inorganic mineral compound. The organic matrix is composed of bundles of mineralized collagen fibers assembled together with non-collagenous proteins (NCPs), such as osteocalcin, osteopontin, bone-sialoprotein, glycosaminoglycans, and proteoglycans. At micrometric level of organization, mammalian adult bones are principally composed by lamellar bone [2,3]. Each lamella (3-7 microns), is made by two different materials: a predominant ordered phase, composed by arrays of mineralized collagen fibrils organized in precisely oriented patterns, and a disordered phase, composed by a mineralized ECM with poorly oriented collagen fibers and a great amount of NCPs, proteoglycans, and water. The disordered phase is made by a lacuno-canalicular network, with mechano-sensing and mineralization functions [4] performed by bone cells (osteoblasts, osteoclasts, and osteocytes) which can survive and communicate one with the others within this disordered structure. Depending on the spatial position and the timing of bone formation and remodeling, several lamellae can adopt a number of complex structural motifs [5,6]. The inner structure of long bones, such as the femur, is composed by different sub-structures: a compact bone body, a small portion of spongy tissue (trabecular or cancellous bone) and bone marrow. The ends of long bones ( Fig. 1(a)) are usually covered by cartilage, a highly specialized connective tissue. It is composed by specialized cells (chondrocytes), which produce an abundant extracellular matrix, very rich in proteoglycans,  [16]. Briefly, the sample was fixed in a solution of 4% paraformaldehyde (PFA; Sigma-Aldrich) for 24 hours, washed in running tap water and distilled water and stored at room temperature in a solution of 70% ethanol, which does not destroy the sample due to prior PFA fixation. Before measurement, the sample was extracted from ethanol and dried in air.

Measurements and data elaboration
The micro-Brillouin spectroscopic set-up here employed, characterized by 2μm spot size, and the sample installation are described in Refs [17,18]. 172 spectra were collected at random in the articular non-calcified cartilage surface (Fig. 1(c)), 196 spectra in the subchondral bone, down to 3 mm from the edge of the section, and 218 spectra in the trabecular bone ( Fig. 1(b)). Each spectrum was recorded for about 150 s. Typical spectra are reported in Fig. 1(d). Each spectrum shows two main peaks, one at low frequency (green box) and the other at high frequency (magenta box). Relevant for the elastic characterization of the sample is the frequency shift ν of these peaks. In fact, in back-scattering experiments, the longitudinal elastic modulus M of the tissue can be obtained from ν through the relationship , where λ is the wavelength of the laser, ρ is the mass density and n the refractive index of the sample. In the following we assume ρ = 2 gr/cm 3 and n = 1.55 [19] and a constant ratio ρ / n 2 through the whole sample, which has been found as a reasonable approximation in different tissues [20]. Finally, to get the values of ν, the choice of any particular spectral function for fitting the line-shape of Brillouin peaks in Fig. 1(d) would be quite unjustified due to the mixing of homogeneous and heterogeneous mechanisms of broadening. For this reason, we adopt a model-independent estimate of the average frequency shift of each peak through calculation of the first spectral moment [21], i.e.
where the index i spans spectral channels in the range 4-13 GHz and 13-32 GHz for the low-frequency (ν L ) and high-frequency (ν H ) modes, respectively.

Results and discussion
On the basis of what is already known about the morphology of the bone, the low-frequency peak in Fig. 1(d) can be tentatively attributed to the soft component of the tissue, related to a disordered phase of thin-poorly oriented collagen fibers, proteoglycans, and water. On the other hand, the high-frequency peak, with a peculiar frequency distribution, can be related to wide bundles of mineralized fibers characterized by different degrees of mineralization, ranging from the absence of mineralization in collagen fibers on the articular surface up to the high mineralized structures presents in the bone tissue. From 586 random measurements performed within different areas in the sample, we obtained the distribution of values for the frequency shift of the low and high-frequency peaks that are reported in Fig. 2, left panel.

Articular cartilage
The articular cartilage surface is characterized by a distribution of low-frequency Brillouin peaks ( Fig. 2(a)

Subchondral bone
Subchondral bone spectra are characterized by a low-frequency mode, which covers values from 7.9 to 8.9 GHz (Fig. 2(b)), very similar to that of the articular cartilage. On the other hand, the high-frequency mode shows values comprised from 21 up to 25 GHz and centered at about 23 GHz (Fig. 2(e)), corresponding to an elastic modulus of about 31.2 GPa. This is the largest value for the longitudinal modulus found in our sample, suggesting that this part of the bone is characterized by the highest rate of ordered mineralized fibers, giving to the tissue its characteristic stiffness and mechanical resistance.

Trabecular bone
Trabecular bone is the most heterogeneous region of the sample. The low-frequency mode, which covers a range from 7.8 GHz to 8.4 GHz (Fig. 2(c)), shows an overall softer behavior with respect to the other two regions. Moreover, the high-frequency mode ( Fig. 2(f)) shows a bi-modal distribution in frequency with a first maximum at about 17.5 GHz (M = 18 GPa), close to that of the articular surface, and the second maximum at about 20 GHz (M = 23.6 GPa), which is intermediate between the articular surface and the subchondral bone. This mechanical heterogeneity is possibly due to the co-existence of regions characterized by different degrees of mineralization. In particular, softer regions are probably characterized by ordered collagen fibers not fully mineralized, while stiffer regions are made by ordered bundles of mineralized collagen fibers, but with a lower content on hydroxy-apatite crystals with respect to the subchondral bone. Moreover, it is interesting to notice that the frequency shifts of low and high-frequency modes show some degree of correlation: the stiffness of the mineralized tissue tends to increase together with that of the softest component (Fig. 2).

Comparison with elastic moduli measured by other techniques
Thought Brillouin scattering gives the longitudinal modulus rather than the Young modulus, it is interesting to notice that our results are consistent with those already obtained by both nano-indentation and scanning acoustic microscopy (SAM), namely an elastic modulus of trabecular lamellae in the TB zone considerably lower than that of the subchondral bone (SB). In particular, Turner et al. [10]  With respect to previous mechanical studies of femoral bones, we stress that our micro-Brillouin investigation has provided a piece of new important information: both the subchondral bone plate and the trabecular bone core present an additional soft component, characterized by a longitudinal modulus of about 4.3 GPa, highlighting the bio-composite mechanical nature of the analyzed bone tissue. This is an anomalous feature with respect to previous mechanical investigations, which can be tentatively attributed to the presence of submicrometric soft heterogeneities in the sample (see Fig. 8, inset VII of Ref [4].). In fact, these heterogeneities can elude both SAM and nanoindentation measurements, averaged out by the long wavelength of ultrasounds and the 1-5 μm resolution of indenters [10], but can be revealed by the ~200 nm wavelength of Brillouin micro-spectroscopy.

Conclusions
Brillouin microspectroscopy has been applied for the first time to the study of the mechanical properties of the human femoral head. Measurements performed at random on cartilage surface, subchondral and trabecular bone have given evidence of marked mechanical heterogeneity. In all the investigated regions, bimodal spectra have been revealed, a clear signature of the coexistence of soft (4.3 GPa) and hard (16 and 25 GPa) regions within the few micrometers of the scattering volume. The soft component, never evidenced before, can be attributed to the propagation of acoustic phonons through the amorphous fraction of the bone. The hard region can be identified with mineralized collagen fibrils. The quite large distribution of elastic moduli in mineralized regions is usually attributed to mechanical anisotropies induced by different orientations of collagen fibrils. Measurements in progress in our labs on samples obtained by different donors, with and without fixation, confirm the generality of the coexistence of soft and hard regions. Their characteristic frequencies and relative intensities have the potential of giving precious mechanical information at the micrometric scale on the pathological condition of bones.

Funding
Ricerca Corrente funding of the Italian Ministry of Health to the Rizzoli.