Skip to main content

Finite element modeling of drug distribution in the vitreous humor of the rabbit eye

Annals of Biomedical Engineering volume 25, pages 303–314 (1997)Cite this article

Abstract

Direct intravitreal injection of drug is a common method for treating diseases of the retina or vitreous. The stagnant nature of the vitreous humor and surrounding tissue barriers creates concentration gradients within the vitreous that must be accounted for when developing drug therapy. The objective of this research was to study drug distribution in the vitreous humor of the rabbit eye after an intravitreal injection, using a finite element model. Fluorescein and fluorescein glucuronide were selected as model compounds due to available experimental data. All required model parameters were known except for the permeability of these compounds through the retina, which was determined by fitting model predictions to experimental data. The location of the intravitreal injection in the experimental studies was not precisely known; therefore, several injection locations were considered, and best-fit retinal permeability was determined for each case. Retinal permeability of fluorescein and fluorescein glucuronide estimated by the model ranged from 1.94×10−5 to 3.5×10−5 cm s−1 and from 0 to 7.62×10−7 cm s−1, respectively, depending on the assumed site of the injection. These permeability values were compared with values previously calculated from other models, and the limitations of the models are discussed. Intravitreal injection position was found to be an important variable that must be controlled in both experimental and clinical settings.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

Abbreviations

C:

concentration of drug (g ml−1)

D:

diffusivity (cm2 s−1)

P:

pressure (g cm−1 s−2 or μPa)

t:

time (sec)

\(\vec U\) :

velocity vector (cm s−1)

μ:

viscosity (g s−1 cm−1)

ρ:

density (g cm−3)

∇:

grad (vector operator)

·:

dot product (vector operator)

n:

normal direction

t1,t2:

tangential directions

References

  1. Araie, M., and D. M. Maurice. The loss of fluorescein, fluorescein glucuronide and fluorescein isothiocyanate dextran from the vitreous by the anterior and retinal pathways.Exp. Eye Res. 52:27–39, 1991.

    PubMed  Article  CAS  Google Scholar 

  2. Davis, B. K. Diffusion in polymer gel implants.Proc. Natl. Acad. Sci U.S.A. 71:3120–3123.

  3. Forster, R. K., R. L. Abbott, and H. Gelender. Management of infectious endophthalmitis.Ophthalmology 87:313–319, 1980.

    PubMed  CAS  Google Scholar 

  4. Hosaka, A. Permeability of the blood-retinal barrier in myopia. An analysis employing vitreous fluorophotometry and computer simulation.Acta Ophthalmol. Suppl. 185:95–99, 1988.

    PubMed  CAS  Article  Google Scholar 

  5. Kinsey, V. E., and D. V. N. Reddy. Chemistry and dynamics of aqueous humor. In: The rabbit eye in research, edited by J. H. Prince. Springfield: C. C Thomas, 1964, pp. 218–319.

    Google Scholar 

  6. Koyano, S., M. Araie, and S. Eguchi. Movement of fluorescein and its glucuronide across retinal pigment epithelium-choroid.Invest. Ophthalmol. Vis. Sci. 34: 531–538, 1993.

    PubMed  CAS  Google Scholar 

  7. Larsen, J., H. Lund-Andersen, and B. Krogsaa. Transient transport across the blood-retina barrier.Bull. Math. Biol. 45:749–758, 1983.

    PubMed  CAS  Google Scholar 

  8. Lee, V. H. L., K. J. Pince, D. A. Frambach,et al. Drug delivery to the posterior segment. In: Retina, edited by T. E. Ogden and A. P. Schachat. St. Louis: C. V. Mosby, 1989, pp. 483–498.

    Google Scholar 

  9. Lund-Andersen, H., B. Krogsaa, M. la Cour, and J. Larsen. Quantitative vitreous fluorophotometry applying a mathematical model of the eye.Invest. Ophthalmol. Vis. Sci. 26:698–710, 1985.

    PubMed  CAS  Google Scholar 

  10. Lund-Andersen, H., B. Krogsaa, and J. Larsen. Calculation of the permeability of the blood-retinal barrier to fluorescein.Graef. Arch. Clin. Exp. Ophthalmol. 222: 173–176, 1985.

    Article  CAS  Google Scholar 

  11. McDonnell, J. H. Ocular embryology and anatomy. In: Retina: basic science, inherited retinal disease, and tumors, vol. 1, edited by T. E. Ogden, St. Louis: C. V. Mosby Company, 1989, pp. 1–12.

    Google Scholar 

  12. Ogura, Y., Y. Tsukahara, I. Saito, and T. Kondo. Estimation of the permeability of the blood-retinal barrier in normal individuals.Invest. Ophthalmol. Vis. Sci. 26:969–976, 1985.

    Google Scholar 

  13. Ohtori, A., and K. Tojo. In vivo/in vitro correlation of intravitreal delivery of drugs with the help of computer simulation.Biol. Pharm. Bull. 17:283–290, 1994.

    PubMed  CAS  Google Scholar 

  14. Palestine, A. G., and R. F. Brubaker. Pharmacokinetics of fluorescein in the vitreous.Invest. Ophthalmol. Vis. Sci. 21:542–549, 1981.

    PubMed  CAS  Google Scholar 

  15. Pflugfelder, S. C., E. Hernandez, S. J. Fliesler, J. Alvarez, M. E. Pflugfelder, and R. K. Forster: intravitreal vancomycin. Retinal toxicity, clearance, and interaction with gentamicin.Arch. Ophthalmol. 105:831–837. 1987.

    PubMed  CAS  Google Scholar 

  16. Stainer, G. A., G. A. Peyman, H. Meisels, and G. Fishman. Toxicity of selected antibiotics in vitreous replacement fluid.Ann. Ophthalmol. 9:615–618, 1977.

    PubMed  CAS  Google Scholar 

  17. Tabatabay, C. A., D. J. D'Amico, L. A. Hanninen, and K. R. Kenyon, Experimental drusen formation induced by intravitreal aminoglycoside injection.Arch. Ophthalmol. 105:826–830, 1987.

    PubMed  CAS  Google Scholar 

  18. Talamo, J. H., D. J. D'Amico, L. A. Hanninen, K. R. Kenyon, and E. T. Shanks. The influence of aphakia and vitrectomy on experimental retinal toxicity of aminoglycoside antiobiotics.Am. J. Ophthalmol. 100: 840–847, 1985.

    PubMed  CAS  Google Scholar 

  19. Tojo, K., and A. Ohtori. Pharmacokinetic model of intravitreal drug injection.Math. Biosci. 12359–12375, 1994.

  20. Yoshida, A., S. Ishiko, and M. Kojima. Outward permeability of the blood-barrier barrier.Graef. Arch. Clin. Exp. Ophthalmol. 230:78–83, 1992.

    Article  CAS  Google Scholar 

  21. Yoshida, A., M. Kojima, S. Ishiko,et al. Inward and outward permeability of the blood-retinal barrier. In: Ocular fluorophotometry and the future, edited by J. Cunha-Vaz and E. Leite. Amsterdam: Kugler & Ghedini Publishers, 1989, pp. 89–97.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College Street, M5S 3E5, Toronto, Ontario, Canada

    Stuart Friedrich, Yu-Ling Cheng & Bradley Saville

Authors
  1. Stuart Friedrich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu-Ling Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bradley Saville
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Friedrich, S., Cheng, YL. & Saville, B. Finite element modeling of drug distribution in the vitreous humor of the rabbit eye. Ann Biomed Eng 25, 303–314 (1997). https://doi.org/10.1007/BF02648045

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02648045

Keywords

  • Fluorescein
  • Fluorescein glucuronide
  • Intravitreal injection
  • Retinal permeability
  • Injection location