Anisotropic Diffusive Transport in Annulus Fibrosus: Experimental Determination of the Diffusion Tensor by FRAP Technique

Abstract

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. Due to its particular morphology, nutrient transport within AF is regulated by complex transport kinetics. This work investigates the diffusive transport of a small solute in the posterior and anterior regions of AF since diffusion is the major transport mechanism for low molecular weight nutrients (e.g., oxygen and glucose) in IVD. Diffusion coefficient (D) of fluorescein (332 Da) in bovine coccygeal AF was measured in the three major (axial, circumferential, and radial) directions of the IVD by means of fluorescence recovery after photobleaching (FRAP) technique. It was found that the diffusion coefficient was anisotropic and inhomogeneous. In both anterior and posterior regions, the diffusion coefficient in the radial direction was found to be the lowest. Circumferential and axial diffusion coefficients were not significantly different in both posterior and anterior regions and their values were about 130% and 150% the value of the radial diffusion coefficient, respectively. The values of diffusion coefficients in the anterior region were in general higher than those of corresponding diffusion coefficients in the posterior region. This study represents the first quantitative analysis of anisotropic diffusion transport in AF by means of FRAP technique and provides additional knowledge on understanding the pathways of nutritional supply into IVD.

Strain Dependent Oxygen Diffusivity in Bovine Annulus Fibrosus

“…Previous studies have shown that transport in IVD tissues is anisotropic (i.e., direction-dependent) [20,28,[38][39][40]. For instance, our earlier studies have shown that, for bovine AF tissue, diffusivity in the axial direction is approximately 1.5 times that in the radial direction [20,38].…”

“…Previous studies have shown that transport in IVD tissues is anisotropic (i.e., direction-dependent) [20,28,[38][39][40]. For instance, our earlier studies have shown that, for bovine AF tissue, diffusivity in the axial direction is approximately 1.5 times that in the radial direction [20,38]. Therefore, further investigation into the effects of compression on oxygen diffusivity in other directions (e.g., radial and circumferential) of AF, similar to our previous study on strain-dependent glucose diffusivity in bovine AF [20], is needed to better understand the anisotropy of oxygen transport in IVD.…”

Anisotropic Solute Diffusion Tensor in Porcine TMJ Discs Measured by FRAP with Spatial Fourier Analysis

“…Given that $\stackrel{true~}{C}(u,v,t)={\int }_{-\infty }^{\infty }{\int }_{-\infty }^{\infty }C(x,y,t)e^{-i2\pi (\mathit{ux}+\mathit{vy})}\mathit{dxdy}$ is the Fourier transform of C ( x , y , t ) , with an arbitrary initial condition and a boundary condition that C ( x , y , t ) is a constant as ( x, y ) → ±∞, Equation (2) can be solved by using 2D SFA in the frequency domain: 3, 30, 35, 37, 38 $$\stackrel{true~}{C}(u,v,t)=\stackrel{true~}{C}(u,v,0)e^{-4{\pi }^2(u^2+v^2)D(u,v)t}$$ where $\stackrel{true~}{C}(u,v,0)$ is the initial solute concentration and D ( u , v ) represents the diffusion coefficient in Fourier space (with frequencies u and v ) and is defined as: $$D(u,v)=\frac{u^2{D}_{\mathrm{italicxx}}+2\mathit{uv}{D}_{\mathrm{italicxy}}+v^2{D}_{\mathrm{italicyy}}}{u^2+v^2}$$ The function D ( u , v ) can be determined by curve fitting the light intensity of a time series of fluorescence recovery images (in the Fourier space) to Equation (3).…”

“…1 Another approach for FRAP analysis is based on the spatial Fourier analysis of the recovery images and has the advantage of potential detection of anisotropic diffusion. 3, 14, 26, 30, 35, 38, 39 Tsay and Jacobson, using SFA of FRAP images, developed a method for the determination of a two-dimensional (2D) diffusion tensor along the fixed coordinate system. 38 Most recently, Travascio et al reported a method for calculating an anisotropic diffusion tensor based on two independent analyses of FRAP images: the Fourier transform (FT) and the Karhunen-Loeve transform (KLT).…”

Ybridization of laser-induced spectrofluorescence analysis (lifs), matrix-assisted laser desorption / ionization mass spectrometry (maldi), fluorescence recovery after photobleaching (frap) anf fluorescence loss in photobleaching (flip) microtechnics

“…FRAP (Fluorescence Recovery After Photobleaching) is a method for the diffusion kinetics (and also, correctly, reaction-diffusion kinetics) measurements in living cells using fluorescence microscopy (Zlatanov, 1987;Lopez, 1988;Swaisgood, 1989; Anders, 1990;Nagy, 1990; Bryers, 1998;Salomé, 1998;Tinland, 1998;Higgs, 2000;Reits, 2001;Carrero, 2003;Cha 2004;Joubert, 2004;Fukano, 2004;James, 2004;Sprague, 2005;Lele, 2006;Abbaci, 2007;Febo-Ayala, 2007;Travascio, 2007;Dushek, 2008;Kang, 2008;McNally, 2008;Tolentino, 2008;Lambert, 2009;Travascio, 2009; Hagman, 2010;Mueller, 2010;Mai, 2011;Wachsmuth, 2014;Yapp, 2016) which allows to estimate quantitatively the two dimensional lateral diffusion in molecularly thin film containing fluorescent-labeled probes, or for single cell examination (i.e. the study of lateral mobility of cellular molecules).…”