Each of the five sections was imaged twenty-six times using identical protocol for different analyzer angles. Since the results from these individual sections were highly consistent, the following analysis was based on one section. (For the amide I component at the 0° analyzer angle, the maximum standard error out of all five sections is 1.1% at the 18.75μm depth, 2.9% at the 81.25μm depth, and 2.0% at the 300μm depth respectively.) shows four 2D maps of IR absorption of the specimen with no analyzer in the instrument. shows the infrared spectra at three spatial locations (one in each histological zone) for 0° and 90° analyzer angles, along with the unpolarized spectra. (Since nearly identical tissues from this source of animals have been studied extensively in our lab for more than 14 years, the thicknesses of the total non-calcified tissue and the tissue's histological zones are approximately known [12
].) At the 18.75μm location from the articular surface (in the superficial zone), we observed that the amide I peak at 90° was higher than the same at 0°, and the other two peaks (amide II and amide III) were higher at 0°. At the 81.25μm location (in the transitional zone), there was no big variation for all the peaks for different analyzer angles, indicating the randomness of the fibrils in this zone. At 300μm location (in the radial zone), all major amide peaks behaved exactly the opposite to those in the superficial zone, indicating the perpendicularity of the radial zone fibrils in comparison with the superficial zone fibrils. The spectra acquired for these three zones without the analyzer in the light path are also shown in .
Fig 3 FTIRI spectra at three single pixel locations under different analyzer angles: (a) at 18.75 μm (superficial zone), (b) at 81.25 μm (transitional zone), (c) at 300 μm (radial zone). The solid lines are the spectra obtained without (more ...)
The absorption profile for amide I, amide II, amide III and sugar across the tissue depth in the first quadrant of the analyzer rotation are shown in . (Note that although for each tissue section, there were twenty-six depth profiles for different analyzer angles; only a few profiles are presented in for simplicity.) Since the tissue section was not rotated or moved during the entire experiment, it was straightforward to locate the boundary of the tissue from different imaging experiments and to compare the depth profiles. The figure shows clearly that the infrared absorptions of amide I, amide II, amide III and sugar are all depth-dependent; the first three being anisotropic while the sugar being nearly isotropic. The profiles of these components at 180° analyzer angle (not shown) are identical to that at 0° analyzer angle.
Fig 4 The profiles of different FTIR images through the tissue depth for different analyzer angles: (a) amide I, (b) amide II, (c) amide III and (d) sugar. The solid black lines are the profiles for the unpolarized light, the red lines are for the 0° (more ...)
We combined all absorption profiles for each component into a new type of 2D map (), where each row was one absorption profile as a function of the tissue depth at a fixed angle (), and each column was a plot of absorbance versus the analyzer angle for the sample (). We term this 2D image as “the absorbance anisotropy map” and the 1D column-plot as “the absorbance anisotropy cross-section” (which is depth-dependent). These types of anisotropy maps and cross-sections have the ability to summarize the massive amount of anisotropic information from all twenty-six images by graphically illustrating any periodic modulation of the infrared absorption in the specimen.
Fig 5 FTIRI absorbance anisotropy maps: (a) amide I, (b) amide II, (c) amide III and (d) sugar. These maps enable the visualization and summary of the distributions of IR anisotropy at every tissue depth over the angle space of 0° - 180°. At (more ...)
Fig 6 FTIRI anisotropy cross-sections of amide I (a), amide II (b), amide III (c) and sugar (d) at one depth in the superficial zone (31.25μm) and one depth in the radial zone (300μm). The left margins with the solid circles represent the radial (more ...)
These absorbance anisotropy maps were closely examined for each of the four components of interest, profile by profile () along the tissue depth at a 6.25-μm increment. The following are the summarized features. (1) From the surface of the tissue (set as 0μm) until about 81.25 - 87.5μm, the absorbance anisotropies of amide I, amide II and amide III are sinusoidal. The typical profile at the 31.25μm depth is shown in the right vertical scale in . The anisotropy of such profiles gets weaker and weaker as one moves towards the 81.25 - 87.5μm depth, and reaches a minimum at the 81.25 - 87.5μm depth. (2) Going deep into the tissue from the 81.25 - 87.5μm depth, the absorbance anisotropies of amide I, amide II and amide III gradually become sinusoidal again and get stronger when one moves deep into the radial zone of the tissue. The typical profile at the 300μm depth is shown in the left vertical scale in . A distinct difference between the characteristics in the surface to the deep tissues is that the sinusoidal features of the deep zone tissue are inverse to those of the surface zone tissue. (3) The sugar shows no periodic variations for different analyzer angles ().
A close examination of these anisotropic cross-sections at different tissue depth () revealed that the infrared absorbance in articular cartilage exhibited quite complex variations for different histological zones. Since these variations seemed sinusoidal, we used the following equation to model the anisotropy of the tissue absorbance:
This equation resembles Malus's Law of polarized light. Absorbance(r, θ)
emphasizes that the tissue absorbance is a depth dependent and angle dependent variable, A(r)
are two depth-dependent scaling parameters, and θ0(r)
is the parameter that accounts for the angular offset
which is also depth dependent (with reference to the center of our angular space at 90°). Using this simple equation, we have fitted the three components (amide I, amide II and amide III) in both the radial and the superficial zones, shown as the solid lines in . A parameter of interest in the curve fitting is θ0(r)
, which is a variable that depends upon the tissue depth. At the 300μm location (the radial zone) θ0
was −8° for amide I and −2° for amide II bonds; and at the 31.25μm (the superficial zone), θ0
was −4° for amide I and +4° for amide II bonds.
Following the FTIRI experiments, several cartilage sections were imaged sequentially using a PLM system, where each section had two quantitative images: the angle map and the retardation map. The retardation image illustrates the fibril organization within each pixel based on birefringence (the value 0 means the fibers are random and the value high means a higher order of organization), whereas the angle image represents the averaged orientation of the collagen fibers in the pixel (there is an approximate 90° difference between the collagen fibril orientations in the superficial zone and radial zone of mature/healthy cartilage). This procedure has been used extensively in our lab to study healthy and lesioned cartilage [12
]. shows the angle and retardation images from one PLM experiment, which has features consistent with several of our previous μ
MRI/PLM correlation studies [12
]. The vertical lines in the profiles of represent the approximate divisions of three histological zones, based on our published PLM criteria using similar tissues from this source of animals [12
Fig 7 The angle and retardation maps (a) of a specimen from one PLM experiment. A small section of the rectangular box was analyzed and plotted as the cross-sectional profiles (b). The two vertical lines indicate the approximate division of the histological (more ...)
To facilitate the comparison between the physical/morphological features of the tissue and the chemical distributions in cartilage, the complex information in the depth-dependent anisotropy profiles () needs to be further analyzed. To that end, we explored the statistical variation of the anisotropy profiles () by taking the standard deviation of the amide I anisotropic profile at each pixel depth – a big/small standard deviation means a large/small sinusoidal variation in its anisotropic profile at that particular tissue depth. compares the PLM retardation profile () and the standard deviation of the amide I anisotropy based on the same tissue section - many common features of these two profiles have a surprisingly good agreement. The anisotropy profiles of the standard deviation of amide II and amide III (not shown) contain several features that are common to that of amide I, while the profile of sugar lacks these features.
Fig 8 The comparison of the retardation profile of the tissue (open circles) and the standard deviation of the amide I component anisotropy (solid dots) at every pixel location. Each value of the standard deviation measures the absorption variation of the amide (more ...)