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Fluorescence recovery after photobleaching: direct measurement of diffusion anisotropy

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Abstract

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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References

  • Axelrod D, Koppel D, Schlessinger J, Elson E, Webb WW (1976) Mobility measurement by analysis of fluorescence photobleaching recovery kinetics. Biophys J 16(9):1055–1069

    Article  Google Scholar 

  • Brezis H (2010) Functional analysis. Sobolev spaces and partial differential equations. Springer, New York

    Book  Google Scholar 

  • Brinkman H (1949) A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl Sci Res 1(1):27–34

    Article  Google Scholar 

  • Burton-Wurster N, Lust G (1990) Fibronectin and proteoglycan synthesis in long term cultures of cartilage explants in Ham’s F12 supplemented with insulin and calcium: effects of the addition of TGF-\(\beta\). Arch Biochem Biophys 283(1):27–33

    Article  Google Scholar 

  • Curnier A, He Q-C, Zysset P (1995) Conewise linear elastic materials. J Elast 37:1–38

    Article  MathSciNet  Google Scholar 

  • DiDomenico CD, Lintz M, Bonassar LJ (2018) Molecular transport in articular cartilage—what have we learned from the past 50 years? Nat Rev Rheumatol 14(7):393–403

    Article  Google Scholar 

  • Greene GW, Zappone B, Zhao B, Söderman O, Topgaard D, Rata G, Israelachvili JN (2008) Changes in pore morphology and fluid transport in compressed articular cartilage and the implications for joint lubrication. Biomaterials 29(33):4455–4462

    Article  Google Scholar 

  • Jönsson P, Jonsson MP, Tegenfeldt JO, Höök F (2008) A method improving the accuracy of fluorescence recovery after photobleaching analysis. Biophys J 95(11):5334–5348

    Article  Google Scholar 

  • Kang M, Day CA, DiBenedetto E, Kenworthy AK (2010) A quantitative approach to analyze binding diffusion kinetics by confocal frap. Biophys J 99(9):2737–2747

    Article  Google Scholar 

  • Kang M, Day CA, Kenworthy AK, DiBenedetto E (2012) Simplified equation to extract diffusion coefficients from confocal frap data. Traffic 13(12):1589–1600

    Article  Google Scholar 

  • Le Bihan D, Mangin J-F, Poupon C, Clark CA, Pappata S, Molko N, Chabriat H (2001) Diffusion tensor imaging: concepts and applications. J Magn Reson Imaging 13(4):534–546

    Article  Google Scholar 

  • Leddy HA, Guilak F (2003) Site-specific molecular diffusion in articular cartilage measured using fluorescence recovery after photobleaching. Ann Biomed Eng 31(7):753–760

    Article  Google Scholar 

  • Leddy HA, Haider MA, Guilak F (2006) Diffusional anisotropy in collagenous tissues: fluorescence imaging of continuous point photobleaching. Biophys J 91(1):311–316

    Article  Google Scholar 

  • Lee JI, Sato M, Ushida K, Mochida J (2011) Measurement of diffusion in articular cartilage using fluorescence correlation spectroscopy. BMC Biotechnol 11(1):19

    Article  Google Scholar 

  • Lori N, Akbudak E, Shimony J, Cull T, Snyder A, Guillory R, Conturo T (2002) Diffusion tensor fiber tracking of human brain connectivity: aquisition methods, reliability analysis and biological results. NMR Biomed 15(7–8):494–515

    Article  Google Scholar 

  • Maroudas A (1968) Physicochemical properties of cartilage in the light of ion exchange theory. Biophys J 8(5):575–595

    Article  Google Scholar 

  • Mazza D, Braeckmans K, Cella F, Testa I, Vercauteren D, Demeester J, De Smedt SS, Diaspro A (2008) A new FRAP/FRAPa method for three-dimensional diffusion measurements based on multiphoton excitation microscopy. Biophys J 95(7):3457–3469

    Article  Google Scholar 

  • Qian H, Sheetz MP, Elson EL (1991) Single particle tracking. Analysis of diffusion and flow in two-dimensional systems. Biophys J 60(40):910–921

    Article  Google Scholar 

  • Shi C, Cisewski SE, Bell PD, Yao H (2014) Measurement of three-dimensional anisotropic diffusion by multiphoton fluorescence recovery after photobleaching. Ann Biomed Eng 42(3):555

    Article  Google Scholar 

  • Shi C, Kuo J, Bell PD, Yao H (2010) Anisotropic solute diffusion tensor in porcine TMJ discs measured by frap with spatial fourier analysis. Ann Biomed Eng 38(11):3398–3408

    Article  Google Scholar 

  • Sprague BL, Pego RL, Stavreva DA, McNally JG (2004) Analysis of binding reactions by fluorescence recovery after photobleaching. Biophys J 86(6):3473–3495

    Article  Google Scholar 

  • Verkman AS (2002) Solute and macromolecule diffusion in cellular aqueous compartments. Trends Biochem Sci 27(1):27–33

    Article  Google Scholar 

  • Xia Y, Farquhar T, Burton-Wurster N, Ray E, Jelinski LW (1994) Diffusion and relaxation mapping of cartilage-bone plugs and excised disks using microscopic magnetic resonance imaging. Magn Reson Med 31(3):273–282

    Article  Google Scholar 

  • Xia Y, Farquhar T, Burton-Wurster N, Vernier-Singer M, Lust G, Jelinski L (1995) Self-diffusion monitors degraded cartilage. Arch Biochem Biophys 323(2):323–328

    Article  Google Scholar 

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Acknowledgements

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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Author notes

  1. Ziad Abusara

    Present address: Advanced Imaging and Histopathology Core, Qatar Biomedical Research Institute, Hamad Bin Khalifa University, Qatar Foundation, P.O. Box 34110, Doha, Qatar

Authors and Affiliations

  1. Department of Mechanical and Manufacturing Engineering, The University of Calgary, Calgary, Canada

    Kotaybah Hashlamoun, Walter Herzog & Salvatore Federico

  2. Human Performance Laboratory, The University of Calgary, Calgary, Canada

    Kotaybah Hashlamoun, Ziad Abusara, Walter Herzog & Salvatore Federico

  3. Graduate Programme in Biomedical Engineering, The University of Calgary, Calgary, Canada

    Kotaybah Hashlamoun

  4. Department of Mathematical Sciences “G.L. Lagrange”, ‘Dipartimento di Eccellenza 2018-2022’, Politecnico di Torino, Torino, Italy

    Ariel Ramírez-Torres & Alfio Grillo

Authors
  1. Kotaybah Hashlamoun
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  2. Ziad Abusara
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  3. Ariel Ramírez-Torres
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  4. Alfio Grillo
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  5. Walter Herzog
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  6. Salvatore Federico
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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 19, 2397–2412 (2020). https://doi.org/10.1007/s10237-020-01346-z

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  • DOI: https://doi.org/10.1007/s10237-020-01346-z

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