1.

Introduction

The behavior of light in biological tissues is governed by intrinsic fundamental and wavelength-dependent properties (optical properties), including absorption coefficient (${\mu }_a$), scattering coefficient (${\mu }_s$), extinction coefficient (${\mu }_t={\mu }_s+{\mu }_a$), scattering anisotropy factor ($g$), reduced scattering coefficient (${\mu }_s^{\prime }$), and refractive index ($n$).^1–3 The key factors determining the optical properties of biological tissues are chemical composition, concentration, size, distribution, and alignment of the tissue matrix’s biomolecules.³ Since these vary between biological tissues and within the same tissue due to biological or pathological processes, this variation often leads to differences in optical properties between healthy and pathological tissues. Thus, the optical properties of biological tissues have been adopted as biomarkers for the non-invasive screening of tissue pathologies in multiple organs, including muscles, brain, skin, heart, and breast.¹

In musculoskeletal research, particularly relating to osteoarthritis, there is growing research interest in applying diffuse optical technologies for the diagnostic assessment of musculoskeletal tissues, particularly with a focus on early detection and characterization of degenerative diseases, such as osteoarthritis.^4–9 One of the primary tissues of focus in musculoskeletal research is articular cartilage, the highly specialized connective tissue covering the ends of bones in articulating joints. Articular cartilage enables joint lubrication and transmission of load to the underlying bone, thus allowing smooth joint motion. The function of articular cartilage is inherently related to the structure and composition of its extracellular matrix. Articular cartilage comprises a biphasic matrix and chondrocytes—the sole cellular component of the tissue embedded within the matrix. Articular cartilage solid matrix mainly comprises of collagen fibers, proteoglycan macromolecules, and water.¹⁰ The size and orientation of collagen fibers in articular cartilage is a function of tissue depth, varying from the articular surface to the subchondral bone, resulting in three distinct zones, namely: superficial zone, middle zone, and deep zone.¹¹ The collagen fibers are oriented parallel to the articular surface in superficial zone, exhibit a skewed orientation in middle zone, and have a perpendicular orientation in deep zone.¹⁰ Furthermore, there is a mineralized layer of calcified cartilage at the interface between cartilage matrix and subchondral bone.¹² The unique alignment of collagen fibers and the high osmotic pressure created by proteoglycans equip cartilage matrix with unique biomechanical properties to withstand various mechanical stresses.

In the past two decades, various studies have reported the ${\mu }_a$ and ${\mu }_s^{\prime }$ of articular cartilage and assessed their potential for characterizing the tissue.^13–22 However, little attention is given to how articular cartilage zonal architecture affects light propagation through the tissue matrix. In particular, the scattering properties of articular cartilage zones and their impact on the overall optical properties and response of the bulk tissue are not well understood. Few studies in the literature have investigated ${\mu }_s$ and $g$ values of articular cartilage bulk tissue and zones.^13,23,24 Beek et al.¹³ reported $g$ of bulk rabbit cartilage tissue at 632.8 nm using a double-integrating sphere and the inverse adding doubling method.²⁵ Shyu et al.²³ reported the effective $g$ of bulk porcine articular cartilage estimated by optical coherence tomography. Jambor et al.²⁴ utilized goniometric setup to estimate the ${\mu }_s$ and $g$ of articular cartilage superficial, middle, and deep zones at 445 and 890 nm and showed how enzymatic degradation such as depletion of proteoglycan and disruption of the collagen mesh will affects these parameters.

The present study aims to provide the spectral values of ${\mu }_s$ and $g$ of healthy articular cartilage zones from different anatomical origins within the bovine knee. We hypothesized the unique compositional and structural properties of articular cartilage zones affects the scattering properties of the tissue and this influence is represented in the scattering properties of articular cartilage zones. We carried out a series of optical spectroscopic and imaging measurements to validate this hypothesis.

2.

Materials and Methods

2.2.

microCT Imaging

To estimate the thickness and surface diameter of the articular cartilage samples, set A was subjected to microCT imaging immediately after extraction. The samples were imaged with a microCT scanner (XT H 225, Nikon Metrology, Leuven, Belgium). The images were acquired with $40\times 40\times 40\mu {\mathrm{m}}^3$ isotropic voxel size, but the voxel size was increased to $50\times 50\times 50\mu {\mathrm{m}}^3$ when reconstructions were calculated. The tube voltage was set to 80 kVp with a 1.0 mm aluminum filter.

After image acquisition and reconstruction, the thickness and surface diameter of the articular cartilage part of the osteochondral samples were estimated via processing the microCT images. In summary, the 3D osteochondral microCT images were segmented to obtain the volume of the articular cartilage segment. Considering that the microCT image histogram has three peaks, it can be readily segmented into three classes using histogram thresholding. The classes are bone, soft tissue (articular cartilage and moisture), and background (including air and the sample holder). Distinguishing moisture from articular cartilage is not possible using their intensity values alone. Therefore, the segmentation was done using morphological operators and surface normal vectors to geometrically isolate the articular cartilage tissue from the moisture.²⁶ Figure 1 depicts the processing of the microCT images of the osteochondral samples. After microCT imaging, the articular cartilage portion of the osteochondral samples was mechanically detached from sunchondral bone using a scalpel, and then samples were stored in PBS at −20.

Fig. 1

(a) The schematics and image of the integrating sphere setup used for estimation of ${\mu }_a$ and ${\mu }_s^{\prime }$ of articular cartilage bulk tissue. (b) The schematic and image of the collimated transmittance setup used for estimation of ${\mu }_t$ of articular cartilage zones. (c) The distribution of the physical properties (thickness (mm), surface diameter (mm), and volume (${\mathrm{mm}}^3$) of the articular cartilage bulk samples, estimated from the microCT images. (c) (right) The top surface of an articular cartilage sample after segmentation and the X-Z cross-section of the sample, which is segmented to articular cartilage (cyan), bone (yellow), and background medium (black). The error of the articular cartilage volume segmentation from the microCT images was $\sim <18\%$.

3.

Results

The values of ${\mu }_a$ of bulk articular cartilage suggest that the tissue possesses low light absorption strength with apparent water absorption peaks at 950 and 1150 nm [Fig. 2(a)]. On average, the decrease of values of bulk articular cartilage ${\mu }_s^{\prime }$ shows the presence of Rayleigh scatterers in the tissue and their contribution to ${\mu }_s^{\prime }$ [Fig. 2(b)]. The similarity of bulk articular cartilage ${\mu }_a$ and ${\mu }_s^{\prime }$ over different anatomical locations suggest anatomical variation has minimal impact on the bulk optical properties [Figs. 2(a) and 2(b)]. The values of ${\mu }_t$ of articular cartilage zones are predominantly influenced by the tissue’s ${\mu }_s$, with minimal impact of ${\mu }_a$, including the water absorption peaks at 950 and 1150 nm (Fig. 3). Mean values of ${\mu }_s$ and ${\mu }_t$ exhibited higher values in deep zone than middle zone and superficial zones over the anatomical sites of medial femur and patella, and lateral and medial tibia. In addition, similar to ${\mu }_s^{\prime }$, the decrease of ${\mu }_s$ of articular cartilage zones suggests the presence of Rayleigh scattering and its contribution to ${\mu }_s$ [Fig. 3(b)].

Fig. 2

Absorption coefficient (a) (${\mu }_a$, ${\mathrm{mm}}^{-1}$) and reduced scattering coefficient (b) (${\mu }_s^{\prime }$, ${\mathrm{mm}}^{-1}$) of bulk articular cartilage tissue. FL and FM are the lateral and medial femur sites, PL and PM are the lateral and medial patella sites, and TL and TM are the lateral and medial tibia sites. The values represent mean ± standard deviation.

Fig. 3

The extinction coefficient (a) (${\mu }_t$, ${\mathrm{mm}}^{-1}$) and scattering coefficient (b) (${\mu }_s$, ${\mathrm{mm}}^{-1}$) of articular cartilage zones of different anatomical locations. ${\mu }_t$ was experimentally obtained from collimated transmittance measurements while ${\mu }_s$ was obtained by fitting the Mie–Rayleigh formula to the experimental ${\mu }_t$. SZ, MZ, and DZ are the superficial, middle, and deep zones of articular cartilage, respectively. FL and FM are the lateral and medial femur sites, PL and PM are the lateral and medial patella sites, and TL and TM are the lateral and medial tibia sites. The values represent mean ± standard deviation.

When the Mie–Rayleigh parameters of ${\mu }_s$ of cartilage zones are considered [Fig. 4(a)], on average and across all anatomical locations, the scatterer density parameter ($\alpha$) increases consistently with tissue depth. That is, $\alpha$ is highest in deep zone and also higher in middle zone than in superficial zone (Table 2). The scatterer size parameter ($b$) shows a similar trend to $\alpha$ when averaged across all anatomical locations. However, the contribution of Rayleigh scatterer to ${\mu }_s$ ($c$) is highest in middle zone with a mean value of 10.65% across all anatomical locations (Table 2). When the Mie–Rayleigh parameters of bulk articular cartilage ${\mu }_s^{\prime }$ are considered [Fig. 4(b)], on average, the scatterer density parameter (${\alpha }^{*}$) is higher in the lateral groups (lateral femur, tibia, and patella) than in the medial groups (medial femur, tibia, and patella). The scatterer size parameter ($b^{*}$) shows a similar trend in the lateral and medial groups. However, when the contribution of Rayleigh scatterer to ${\mu }_s^{\prime }$ ($c^{*}$) is considered, the medial groups possess larger values of $c^{*}$ than the lateral groups (Table 2).

Fig. 4

(a) The Mie–Rayleigh parameters obtained from fitting the ${\mu }_s$ of articular cartilage zones to Mie–Rayleigh formula over different anatomical location. (b) The Mie–Rayleigh parameters obtained from fitting the ${\mu }_s^{\prime }$ of bulk articular cartilage tissue to Mie–Rayleigh formula over different anatomical location. SZ, MZ, and DZ are the superficial, middle, and deep zones of articular cartilage, respectively. FL and FM are the lateral and medial femur sites, PL and PM are the lateral and medial patella sites, and TL and TM are the lateral and medial tibia sites. $\alpha$ and ${\alpha }^{*}$ are the scatterer-density parameter of ${\mu }_s$ and ${\mu }_s^{\prime }$; $b$ and $b^{*}$ are the scatterer-size parameter of ${\mu }_s$ and ${\mu }_s^{\prime }$; and $c$ and $c^{*}$ are the normalized contribution of Rayleigh scatterers to ${\mu }_s$ and ${\mu }_s^{\prime }$, respectively.

Table 2

The mean values of the scatterer-density parameter (α and α*), the scatterer-diameter parameter (b and b*) and normalized contribution of Rayleigh scatterers (c and c*) to the scattering coefficients of articular cartilage zones and bulk tissue across different anatomical location. μs and μs′ are the single and reduced scattering coefficients. SZ, MZ, and DZ are the superficial, middle, and deep zones of articular cartilage, respectively. FL and FM are the lateral and medial femur sites; PL and PM are the lateral and medial patella sites; and TL and TM are the lateral and medial tibia sites. The Mie–Rayleigh parameters were obtained by fitting Eqs. (2) and (3) to μs and μs′ values, respectively. The mean R2 and RMSE scores of Mie–Rayleigh fit for μs are 96.84% and 1.1576. The mean R2 and RMSE scores of Mie–Rayleigh fit for μs′ are 98.83% and 0.0909.

The results of the statistical analysis indicate a nonuniform statistically significant difference between the Mie–Rayleigh parameters of ${\mu }_s$ of the articular cartilage zones and anatomical sites (Table 3). In particular, $\alpha$ is significantly different between superficial and deep zones ($p\text{-}\text{value}=0.001$) and between middle and deep zones ($p\text{-}\text{value}=0.015$). However, $b$ and $c$ are not statistically significant across the different zones (Table 3).

Table 3

The p-value of posthoc method of group statistical test for assessing the statistically significant difference of Mie–Rayleigh parameters of μs over different articular cartilage zones and anatomical locations. μs is the single scattering coefficient of articular cartilage tissue. α is the scatterer-density parameter, b is the scatterer-size parameter, and c is the contribution of the Rayleigh scatterers to μs of articular cartilage zones. SZ, MZ, and DZ are the superficial, middle, and deep zones of articular cartilage, respectively. FL and FM are the lateral and medial femur sites, PL and PM are the lateral and medial patella sites, and TL and TM are the lateral and medial tibia sites. The italicized values highlight the statistical significance difference.

In addition, the statistical analysis suggests significant difference of Mie–Rayleigh parameters of articular cartilage ${\mu }_s$ (from all zones) when considered over anatomical locations. $\alpha$, $b$, and $c$ are significantly different between lateral femur and medial patella, between lateral femur and tibia, between medial femur and patella, between medial femur and lateral tibia, between lateral and medial patella, and between lateral patella and tibia, all with $p$-values $<0.001$ (Table 3). No statistically significant difference were observed for the Mie–Rayleigh scattering parameters of ${\mu }_s^{\prime }$ over different anatomical locations. Furthermore, similar statistical analysis was carried out for the Mie-collagen parameters of ${\mu }_s$ and ${\mu }_s^{\prime }$. The results are presented in the Supplementary Material.

As observed in Fig. 5(c), deep zone forms a significant part of articular cartilage ($\sim 80\%$) with collagen angular alignment of $\ge 60\mathrm{deg}$. Whereas superficial (collagen angular alignment of $\le 30\mathrm{deg}$) and middle zone ($30\mathrm{deg}\le$ collagen angular alignment of $\le 60\mathrm{deg}$) contribute roughly to 20% of articular cartilage tissue depth across different anatomical locations. The values of $g$ ($g_{\mathrm{HG}}$ and $g_{m\mathrm{HG}}$) for the different zones [Figs. 5(a) and 5(b)] suggest that light in the visible and NIR bands follows a forward-direction propagation in articular cartilage zones with higher $g_{\mathrm{HG}}$ and $g_{m\mathrm{HG}}$ in the spectral band of 800 to 1400 nm than the short visible band (400 to 800 nm). In addition, across all anatomical locations, $g_{\mathrm{HG}}$ shows a monotonically increasing trend as function of tissue depth. That is $g_{\mathrm{HG}}$ is highest in deep zone; middle zone exhibits the lowest $g_{\mathrm{HG}}$ values across the anatomical sites lateral femur, and medial femur, patella, and tibia, whereas superficial zone possess the lowest $g_{\mathrm{HG}}$ values across the lateral patella and tibia. When the contribution of Rayleigh scatterers are considered, superficial zone has the lowest $g_{m\mathrm{HG}}$ values over the anatomical locations of lateral patella, medial patella, and lateral tibia. Whereas middle zone exhibits lowest $g_{m\mathrm{HG}}$ values over the anatomical locations lateral femur, medial femur, and medial tibia.

Fig. 5

The Henyey–Greenstein scattering anisotropy factor ($g_{\mathrm{HG}}$) of articular cartilage zones (SZ, MZ, and DZ) for different anatomical origins (a). The modified Henyey-Greenstein scattering anisotropy factor ($g_{m\mathrm{HG}}$) of articular cartilage zones (SZ, MZ, and DZ), accounted for the impact of the Rayleigh scatterers on $g_{\mathrm{HG}}$ (b). The depth-wise alignment of collagen fiber of articular cartilage of different anatomical origins (c); the orange shaded areas depicts the percentage of the articular cartilage zones of the total thickness according to the alignment of collagen fibers. SZ, MZ, and DZ are the superficial, middle, and deep zones of articular cartilage defined as the regions where the collagen fibers have alignment of 0 deg to 30 deg, 30 deg to 60 deg, and 60 deg to 90 deg, respectively. FL and FM are the lateral and medial femur sites, PL and PM are the lateral and medial patella sites, and TL and TM are the lateral and medial tibia sites. $g_{\mathrm{HG}}$ and $g_{m\mathrm{HG}}$ are unitless parameters. The values were plotted as mean ± standard deviation.

4.

Discussion

This study addresses the gap in knowledge on the scattering properties of articular cartilage depth-wise zones by determining its values of ${\mu }_s$ and $g$ in the different zones, in addition to the depth-wise Mie–Rayleigh parameters. The present findings enhance understanding on the scattering properties of healthy bulk articular cartilage and its depthwise zones. In addition, the depth-wise angular distribution of articular cartilage collagen fibers were provided to investigate the impact of collagen orientation on articular cartilage $g$. In this study, we hypothesized that normal variation in articular cartilage zones will influence its scattering properties. Our results indicate that $\alpha$, the Mie-Rayleigh parameter representing scatterer density in articular cartilage, exhibits statistically significant variations throughout the zones of articular cartilage. Furthermore, $g_{\mathrm{HG}}$ and $g_{m\mathrm{HG}}$ of articular cartilage zones show that they vary across the tissue depth.

In our view, various factors affect the values of articular cartilage $g$, including the depth-wise normalized fraction of the Rayleigh scatterers contribution to the scattering coefficients, the intensity of light scattered by the Rayleigh and Mie scatterers as a function of wavelength, and the heterogeneity of the tissue’s structure. When the contribution of Rayleigh scatterers to ${\mu }_s^{\prime }$ of bulk articular cartilage tissue is considered, on average, $\sim 5.14\%$ of ${\mu }_s^{\prime }$ can be attributed to these scatterers. Hence, the impact of Rayleigh scatterers on bulk articular cartilage $g$ is expected to be weak ($g_{\mathrm{HG}}\approx g_{m\mathrm{HG}}$). When the contribution of Rayleigh scatterers to ${\mu }_s$ of the different cartilage zones is considered, their impact on $g$ becomes more apparent. On average, these scatterers contribute to 10.19%, 10.65%, and 3.87% of ${\mu }_s$ of articular cartilage superficial, middle, and deep zones, respectively. Therefore, as observed in Fig. 5, the broadband values of articular cartilage $g$ at superficial and middle zones are lower than those at deep zone. When $g$ is considered in the different zones and anatomical locations (Fig. 5), our findings suggest that $c$ (the contribution of the Rayleigh scatterers) acts as a scaling factor on the magnitude of $g$ ($g_{m\mathrm{HG}}\propto c{g}_{\mathrm{HG}}$), which is supported by Eq. (5).

To understand how articular cartilage $g$ changes as a function of wavelength in the spectral band of 400 to 1400 nm, we investigated this behavior in the different tissue zones, separately from the bulk tissue. This is because collagen orientation within each zone is relatively homogeneous, except in middle zone, but the angular distribution of collagen fibers in the bulk tissue exhibits a wide range of variation, as high as 70 deg [Fig. 5(c)]. Therefore, it is plausible that the spectral behavior of $g$ within articular cartilage zones stems from the ratio between the intensity of light scattered by the Rayleigh and Mie scatterers, whereas in the bulk tissue, the heterogeneity of angular distribution of collagen fibers acts as a confounding factor. As stated earlier, the behavior of $g$ is primarily dependent upon the scattering phase function. The scattering phase function describes the intensity of the scattered light, which is affected by the Rayleigh and Mie scatterers. The intensity of light scattered by the Rayleigh and Mie scatterers varies in proportion to ${\lambda }^{-4}$ and ${\lambda }^{-b}$, respectively. On average, the parameter $b$ was estimated as 1.4068, 1.3508, and 1.2925 for articular cartilage superficial, middle, and deep zones, respectively (Table 2). The 4% to 8% difference in $b$ suggests similarities across the zones, which in turn leads to similar trends of ${\mu }_s$ and $g$ (both $g_{\mathrm{HG}}$ and $g_{m\mathrm{HG}}$) in superficial, middle, and deep zones (Figs. 3 and 5).

When the impact of the zonal structure of articular cartilage on $g$ is considered, the importance of the angular distribution of collagen fibers across the tissue depth becomes apparent. 80% of bovine articular cartilage matrix consists of deep zone with collagen fibers oriented between 60 deg and 80 deg [Fig. 5(c)]. Whereas superficial zone (fiber orientation of 0°-30°) and middle zone (fiber orientation of 30 deg to 60 deg) together comprise roughly the first 20% of bovine cartilage matrix. Hence, we speculate that in the short visible spectral band (400 to 700 nm), the structural and scattering features of superficial and middle zones, including collagen orientation and contribution of Rayleigh scatterers to the scattering coefficients, will affect the $g$ values of articular cartilage bulk tissue. This is because of the higher intensity of Rayleigh scattering in this spectral band and the higher contribution of Rayleigh scatterers to ${\mu }_s$ of cartilage superficial and middle zones. In addition, the change of collagen fiber orientation from parallel to the articular surface in superficial zone to a skewed orientation in middle zone is likely to alter the light propagation behavior and cause the values of $g$ to be dependent on the alignment of collagen fibers. This speculation can also be supported by the scattering mean free path ($=1/{\mu }_s$). Due to large values of ${\mu }_s$ in the short visible band, the scattering mean free path decreases while the number of scattering events in superficial and middle zones increases. Hence, the impact of structural and scattering properties of superficial and middle zones on light scattering is higher in this spectral band.

In the far visible and NIR bands (700 to 1400 nm), the values of $g$ for bulk cartilage is affected by the structural and scattering properties of deep zone predominantly. As the photon wavelength shifts from the short visible to the NIR region, the magnitude of ${\mu }_s$ declines and the size of the scattering mean free path increases. Given that articular cartilage is mostly comprised of deep zone with collagen fibers oriented perpendicular to the surface, most of the scattering events occur in a forward direction in deep zone. Hence, bulk articular cartilage is expected to have $g$ values like those of superficial and middle zones in the short visible region and $g$ values close to those of deep zone in the far visible and NIR regions.

Detailed knowledge of the light propagation characteristics in articular cartilage is critical for a better understanding of the origin of the optical response of the tissue. Light penetration depth, depth-origin, and path length of photons propagating the articular cartilage matrix are the key parameters that can shed light on the contribution of the different zones of the articular cartilage on its optical response. This study provides critical input for developing Monte Carlo models of light propagation in articular cartilage to estimate photon penetration depth, depth origin, and path length and subsequently the wavelength-dependent optical response of the tissue.

In this study, certain reasonable assumptions were made. Light propagation in biological tissues are complex. That is, due to complex architecture of their matrix, light propagation becomes anisotropic and tissue scattering coefficients and phase function become dependent on the light’s incident direction. Skin, muscle, and dentin are example of such tissues that exhibit anisotropic light propagation.^33,34 We speculate that articular cartilage, due to its zonal architecture, is an example of such biological tissues too. However, we assumed an isotropic light propagation model to investigate the light interaction in articular cartilage and estimate its optical properties. The underlying reason is due to numerous unknowns associated with the anisotropic model of light propagation in articular cartilage that makes its usage not feasible.

In general, the reported ${\mu }_s$ values are from different layers of articular cartilage, whereas the ${\mu }_s^{\prime }$ values are obtained from the bulk of articular cartilage tissue, hence ${\mu }_s^{\prime }$ is a lump-sum representation of the ${\mu }_s^{\prime }$ of articular cartilage layers. However, the low thickness of the tissue’s superficial and middle zones (less than a few hundred micrometers) makes it impossible to extract sufficiently thick sections from superficial and middle zones to estimate their ${\mu }_s^{\prime }$. Therefore, our approach was to estimate the ${\mu }_s^{\prime }$ of bulk articular cartilage and ${\mu }_s$ of articular cartilage zones and investigate the relationship between the scattering properties of the bulk tissue and its zones through [Eq. (4)]. In this context, we assumed ${\mu }_{s,\text{bulk tissue}}^{\prime }/{\mu }_{s,\text{cartilage zone}}$ represents a normalized contribution of individual cartilage zones to the scattering properties of bulk tissue.

As the broadband values of $n$ and scattering phase function of bulk articular cartilage tissue are not known and the estimation of ${\mu }_a$ and ${\mu }_s^{\prime }$ depends on these parameters, we used fixed values of $n$ and $g$ (applying to the Henyey–Greenstein scattering phase function used in this study) to estimate its broadband ${\mu }_a$ and ${\mu }_s^{\prime }$ values. Bergmann et al.²² reported that the variation of $n$ in the range of 1.3 to 1.5 could result in a relative change of less than 5% for ${\mu }_s^{\prime }$ and $<13\%$ for ${\mu }_a$ of biological tissues. More so, in our previous study,²⁹ we showed that using fixed value of $g$ ($0.8\le g\le 0.99$) will not result in statistically significant change in the estimation of articular cartilage ${\mu }_a$ and ${\mu }_s^{\prime }$. Thus, we expect that using fixed value of $g$ for estimation of bulk articular cartilage ${\mu }_s^{\prime }$ has minimal impact on the reported values of $g$ for different zones of articular cartilage.

Furthermore, the choice of scattering phase function used in the estimation of ${\mu }_s^{\prime }$ plays a crucial role in determining the spectral values of $g$, which is inherently dependent upon the scattering phase function, and defined as the first Legendre moment of the scattering phase function.¹ In this study, the Henyey–Greenstein phase function was used to estimate the ${\mu }_s^{\prime }$ of bulk articular cartilage. As we utilized the relationship between ${\mu }_s^{\prime }$ and ${\mu }_s$ [Eq. (4)] to estimate articular cartilage $g$, we expect that the estimated values of $g$ will also be dependent upon the Henyey-Greenstein scattering phase function. The Henyey–Greenstein phase function is biased toward the forward scattering of light by Mie scatterers.^1,3 Therefore, the impact of the Rayleigh scatterers on the isotropic scattering of light and subsequently $g$ might not be properly captured by the Henyey–Greenstein scattering phase function. To minimize the impact of this bias, Eqs. (2) and (5) were utilized to estimate the volume fraction of the Rayleigh scatterers and to account for their impact on articular cartilage $g$. We estimated the volume fraction of the Rayleigh scatterers in each zone of articular cartilage from different anatomical origins and showed how the depth-wise normalized contribution of the Rayleigh scatterers to ${\mu }_s$ of articular cartilage will impact the corresponding $g$ values [Table 2 and Fig. 5(b)]. We also provided the spectral values of $g$ based on the Henyey–Greenstein phase function ($g_{\mathrm{HG}}$) and when the contribution of Rayleigh scatterers is accounted for ($g_{m\mathrm{HG}}$). We then enumerated the similarities and differences between $g_{\mathrm{HG}}$ and $g_{m\mathrm{HG}}$ across cartilage zones and various anatomical locations.

Although it is often theoretically expected to observe decreasing broadband values of $g$ with increasing wavelength, our results show an increasing trend in the broadband values of $g$ for articular cartilage. We performed Monte Carlo simulations, for which we considered the actual experimental setup, showing that for our apparatus and ${\mu }_t\le 50{\mathrm{mm}}^{-1}$ and a $g\le 0.99$, there was no significant contribution from multi-scattered light using the Henyey–Greenstein phase function. Hence, the measurement geometry and the resulting values for ${\mu }_t$ should be precise. Therefore, the increasing trend of $g$ observed in this study could be potentially due to the alignment of collagen fibers, a special diameter distributions of the involved collagen fibers, and further scattering structures, such as the chondrocytes. Formulating the impact of these structures in articular cartilage ${\mu }_s$ and its broadband $g$ requires an independent investigation, which is out of the scope of the present study.

5.

Conclusion

This study reports the broadband ${\mu }_s$ and $g$ of articular cartilage zonal structure in the spectral band of 400 to 1400 nm. To achieve this, we carried out integrating sphere measurements on bulk tissue of articular cartilage and collimated transmittance measurements on thin layers of articular cartilage that represent its zonal structure. Our findings suggest that the depth-wise distribution of the volume fraction of Rayleigh scatterers, the intensity of the light scattered by the Rayleigh and Mie scatterers, and the orientation of collagen fibers across the articular cartilage matrix are the key parameters that affect the broadband values of $g$ of articular cartilage zones and bulk tissue.