Quantization of collagen organization in the stroma with a new order coefficient

Abstract

Many optical and biomechanical properties of the cornea, specifically the transparency of the stroma and its stiffness, can be traced to the degree of order and direction of the constituent collagen fibers. To measure the degree of order inside the cornea, a new metric, the order coefficient, was introduced to quantify the organization of the collagen fibers from images of the stroma produced with a custom-developed second harmonic generation microscope. The order coefficient method gave a quantitative assessment of the differences in stromal collagen arrangement across the cornea depths and between untreated stroma and cross-linked stroma.

Keywords: (100.2960) Image analysis; (170.3880) Medical and biological imaging; (170.6900) Three-dimensional microscopy; (170.6935) Tissue characterization; (180.4315) Nonlinear microscopy.

Fig. 1

Sketch of two-photon microscope setup. The pulsed source was a MaiTai Ti-Sapphire femtosecond laser. The beam position and angle were controlled by a pair of scanning galvanometer mirrors (SGM), and the beam passed through a pair of lenses (L) before entering the focusing objective (F. Obj.) in order to overfill the entrance pupil of the objective. SHG was collected in the forward direction by a collection objective (C.Obj.) and was separated from the excitation wavelength by a pair of dichroic filters (F). SHG signal was single photon counted with a photomultiplier tube (PMT), and a National Instruments PCI card (NI-PCI). The SGM were also controlled with the same PCI card. A beam block (BB) was employed to absorb excess excitation light filtered from the SHG signal.

Fig. 2

Image Processing Procedure. The edges of the collagen fibers in the raw images (a) were sharpened (b) and a Hanning window (c) was applied to the image to produce a windowed image (d), which concentrates analysis on the central fibers. The windowed image was Fourier transformed in two dimensions (e) and the resulting transformed image was translated to a polar representation (f), where anti-biasing windows were applied (points within 90° ± 2.8° and 270° ± 2.8° on the polar plot were excluded). The polar plot was then divided into 10° windows (g) (30° shown in (g) for easier visibility to the reader) and the points in each window were used to calculate the order coefficient (h). The white bars in (a), (b), and (d) represent a distance of 60 μm.

Fig. 3

Order coefficient vs depth for four z-stacks in the paraformaldehyde treated cornea.

Fig. 4

Anterior-to-posterior and posterior-to-anterior order coefficient averages of untreated eyes (n = 3). Averages were taken over 100 μm depth slices (number of images averaged per point n = 150) and the same samples were used for the anterior-posterior and posterior-anterior image stacks. Error bars here represent the variance of the average order coefficient value at each point.

Fig. 5

Images of collagen from the anterior ((a) and (b)), intermediate (c), and posterior (d) of a de-epithelialized eye. The anterior images were collected at 10 μm and 140 μm below that anterior stromal surface, the intermediate 740 μm, and the posterior 1015 μm. White bars represent 50 μm. All images presented here are from an anterior to posterior z-scan and the contrast was artificially increased for the images presented here to increase fiber visibility for the reader.

Fig. 6

SHG images of stromal collagen fibers ((a), (c), and (e)) with different treatments and corresponding Fourier transforms ((b), (d), and (f)). The untreated ((a) and (b)) and riboflavin only ((c) and (d)) treatments showed more fibers with crimps and the Fourier transform was spread across more windows than the UVX case ((e) and (f)). The order coefficient values of the individual images were; 0.357 for the untreated, 0.369 for the riboflavin only, and 0.791 for the UVX cornea. Images have been rotated by 90° and contrast has been enhanced so the reader can more clearly see the collagen fibers. All three images were taken 108 μm below the anterior surface of the stroma. The white bars represent a distance of 50 μm.

Fig. 7

Average order coefficient vs. depth. Order coefficient values are averaged over 20 μm sections across all eyes of the same treatment type, untreated (n = 8), riboflavin only (n = 8), and UVX (n = 8) eyes. Error bars represent the variance in order coefficient over the 20 μm sections.

Fig. 8

Distribution of the order coefficient across the anterior, intermediate, and posterior section of the stroma across all eyes of the same treatment type, for de-epithelized (n = 8), riboflavin only (n = 8), and UVX (n = 8) eyes. The total number of images used in each graph is listed in Table 1. Fits of the normal distribution are displayed (red line) and the mean value and variance are displayed in Fig. 9. The mean value for each range ((a), (b), and (c), first 100 μm; (d), (e), and (f), 100-400 μm range; (g), (h), and (i), 400-700 μm range) and treatment ((a), (d), and (g), untreated; (b), (e), and (h), Riboflavin only; (c), (f), and (i), UVX) is marked with a dashed black line.

Fig. 9

Order coefficient averages of corneal treatments. The number of images used to compute each average in the separate depths regions and treatments (averages computed across all samples in each treatment, untreated n = 8, riboflavin only n = 8, UVX n = 8) is listed in Table 1. Black bars represent the variance.

Fig. 10

Ideal examples of order and disorder with Fourier transforms.