The annulus fibrosus (AF) of the intervertebral disc (IVD) exhibits a fiber-organized structure which is responsible for anisotropic and inhomogeneous mechanical and transport properties. by and and the positive which depends on the choice of the frequencies and (or [averaged over the entire frequency space of the ring [i.e., an arch of circumference with = constant in the (+ is equal to the averaged value of two diffusion coefficients in the principal directions (within the focal plane with surface normal Xanthone (Genicide) supplier in the in the three principal planes, one can determine the three diffusion coefficients in the principal directions. Note that for an isotropic case where = = = is a constant (independent of over a range of in order to reduce the noise and to improve the accuracy.46 For an anisotropic case, it is possible to obtain the value of or individually by choosing special frequency couples along the axes of the Fourier space, namely (is a function of the frequency couples. Xanthone (Genicide) supplier The diffusion coefficient was obtained by averaging over Ring 3 and Ring 4 by Equation (7), similar to the isotropic case proposed in the literature.46 MLB Protocol For each FRAP test four different layers of AF samples were sequentially bleached. The distance between the bottom glass slide (see Figure 7) and the focal plane of the microscope objective, where fluorescence recovery was observed, was 7 m and the diameter of the bleach spot was 28.75 m. The other bleach spots were produced in layers at 17, 27 and 32 m from the bottom of the sample and their diameters were 43.12, 50.31 and 71.88 m, respectively. The bleached spots were produced from top to bottom. Measurements of fluorescence intensity within the sample indicated that, after bleaching the four sample layers, the final shape of the bleached region is a cylinder of approximately 28 m diameter and 47 m height. Numerical simulations demonstrated that in these conditions the highest relative error (in the case using 2D SFA is estimated to be approximately 18% (see Appendix for details). Figure 7 Schematic of the computational domain: (a) the three-dimensional sample is confined between two glass slides (top and bottom) with a cylinder representing bleached volume, obtained by multi-layer bleaching; (b) Cross-sectional view of the sample and the … Determination Diffusion Tensor Components Let and stand for the averaged diffusion coefficients measured in the IVD principal planes with surface normal along the axial, circumferential and radial directions Xanthone (Genicide) supplier of the disc, respectively; and for the principal components of the diffusion tensor in the axial, circumferential, and radial directions, respectively. Applying Equation (8) to the three principal IVD planes, it follows that: Xanthone (Genicide) supplier and is inhomogeneous within AF. In both posterior and anterior regions, the diffusion coefficient within the radial plane was significantly higher than that within the circumferential or axial plane. In both anterior and posterior regions, axial and circumferential diffusion coefficients were not significantly different. The principal components of the diffusion tensor (in the anterior region and in the posterior region. In comparison, the mean values of the circumferential and axial diffusion coefficients were similar: along the for the anterior region and for the posterior region; along the and for the anterior and posterior regions respectively, see Figure 4. Figure 4 Anisotropic Xanthone (Genicide) supplier diffusion coefficients of fluorescein in axial, circumferential, and radial directions of AF. DISCUSSION The main objective of this study was to investigate the anisotropic diffusion of solute in AF using the FRAP technique. The results showed that the diffusion coefficients of the fluorescein dye in AF are different along its principal directions (axial, circumferential, and radial). In particular, the results showed that the diffusion coefficient in the radial direction is about 66-75% the value of axial or circumferential direction for specimens harvested from anterior and posterior regions respectively, see Figure 4. This study represents the first measurement of anisotropic diffusion of a relatively small solute in AF using a video-FRAP technique. A new FRAP testing protocol (i.e., multilayer bleaching) was developed for bulk samples to achieve an approximately 2D diffusion condition (see Appendix). Numerical simulations showed that it was possible to combine multilayer beaching and the 2D SFA algorithm for determining anisotropic diffusion coefficients in AF (less than 18% error, Appendix). To further validate our method, our results were compared with the anisotropic diffusion coefficients of glucose in axial and radial directions MYO9B of bovine coccygeal AF, measured by a direct diffusion experiment (manuscript in preparation). It was found that our results were consistent with those from the direct diffusion experiment in which the value of diffusion coefficient of glucose in the radial direction was about 66% of the value in the axial.