Fluorescence recovery after photobleaching (FRAP) is a widely used technique for studying diffusion in biological tissues. Most of the existing approaches for the analysis of FRAP experiments assume isotropic diffusion, while only a few account for anisotropic diffusion. In fibrous tissues, such as articular cartilage, tendons and ligaments, diffusion, the main mechanism for molecular transport, is anisotropic and depends on the fibre alignment. In this work, we solve the general diffusion equation governing a FRAP test, assuming an anisotropic diffusivity tensor and using a general initial condition for the case of an elliptical (thereby including the case of a circular) bleaching profile. We introduce a closed-form solution in the spatial coordinates, which can be applied directly to FRAP tests to extract the diffusivity tensor. We validate the approach by measuring the diffusivity tensor of \(3~\mathrm {kDa}\) FITC-Dextran in porcine medial collateral ligaments. The measured diffusion anisotropy was \(1.42 \pm 0.015\) (SE), which is in agreement with that reported in the literature. The limitations of the approach, such as the size of the bleached region and the intensity of the bleaching, are studied using COMSOL simulations.

光漂白后的荧光恢复 (FRAP) 是一种广泛使用的技术，用于研究生物组织中的扩散。大多数现有的 FRAP 实验分析方法都假设各向同性扩散，而只有少数方法考虑了各向异性扩散。在纤维组织中，如关节软骨、肌腱和韧带，扩散是分子运输的主要机制，是各向异性的，取决于纤维排列。在这项工作中，我们解决了控制 FRAP 测试的一般扩散方程，假设各向异性扩散张量并使用椭圆（因此包括圆形）漂白剖面的情况的一般初始条件。我们在空间坐标中引入了一个封闭形式的解，它可以直接应用于 FRAP 测试以提取扩散张量。\(3~\mathrm {kDa}\) FITC-葡聚糖在猪内侧副韧带中。测量的扩散各向异性为\(1.42 \pm 0.015\) (SE)，这与文献中报道的一致。使用 COMSOL 模拟研究了该方法的局限性，例如漂白区域的大小和漂白强度。