Fluorescence recovery after photobleaching: direct measurement of diffusion anisotropy


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.

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The Authors gratefully acknowledge the help of Ruth Seerattan for the help with sample preparation and of Elyar Asl Sabbaghian Hokm Abadi for useful discussions. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada, through the NSERC Discovery Programme [SF, WH], the Canadian Institutes of Health Research (CIHR) [WH], the Canada Research Chair Programme [WH], the Killam Foundation [WH], Dipartimento di Eccellenza 2018–2022, Politecnico di Torino, Project No. E11G18000350001 [AG, ART], the Biomedical Engineering Graduate Programme of the University of Calgary (Canada), through the BME GP Academic Award [KH] and the BME Research Scholarship Award [KH], the University of Calgary Eyes High Doctoral Programme [KH] and the Canadian Society for Biomechanics, through the CSB PhD Student Travel Grant [KH]. Part of this work was conducted during the visit of KH at the Department of Mathematical Sciences (DISMA) “G.L. Lagrange”, Politecnico di Torino, under the supervision of AG and with the support of the CSB PhD Student Travel Award.

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Correspondence to Salvatore Federico.

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Hashlamoun, K., Abusara, Z., Ramírez-Torres, A. et al. Fluorescence recovery after photobleaching: direct measurement of diffusion anisotropy. Biomech Model Mechanobiol (2020). https://doi.org/10.1007/s10237-020-01346-z

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  • FRAP
  • Anisotropic diffusion
  • Fibrous tissues
  • Ligaments
  • Direct measure