Advertisement

Pharmaceutical Research

, Volume 31, Issue 9, pp 2297–2311 | Cite as

Prediction of Passive Drug Permeability Across the Blood-Retinal Barrier

  • Aapo Tervonen
  • Iina Vainio
  • Soile Nymark
  • Jari Hyttinen
Research Paper

ABSTRACT

Purpose

The purpose of this study is to develop a computational model of the physical barrier function of the outer blood-retinal barrier (BRB), which is vital for normal retinal function. To our best knowledge no comprehensive models of BRB has been reported.

Methods

The model construction is based on the three-layered structure of the BRB: retinal pigment epithelium (RPE), Bruch’s membrane and choriocapillaris endothelium. Their permeabilities were calculated based on the physical theories and experimental material and permeability studies in the literature, which were used to describe diffusional hindrance in specific environments.

Results

Our compartmental BRB model predicts permeabilities with magnitudes similar to the experimental values in the literature. However, due to the small number and varying experimental conditions there is a large variability in the available experimental data, rendering validation of the model difficult. The model suggests that the paracellular pathway of the RPE largely defines the total BRB permeability.

Conclusions

Our model is the first BRB model of its level and combines the present knowledge of the BRB barrier function. Furthermore, the model forms a platform for the future model development to be used for the design of new drugs and drug administration systems.

KEY WORDS

blood-retinal barrier permeability structure-based model compartmental model lipophilicity 

ABBREVIATIONS AND NOTATION

Å

Angstrom (1 Å = 1 × 10−10 m)

AMD

Age-related macular degeneration

BRB

Outer blood-retinal barrier

BrM

Bruch’s membrane

CE

Choriocapillaris endothelium

Da

Dalton (1 Da = 1.66 × 10−27 kg)

D0

free diffusion coefficient (m2 s−1)

Deff,m

Effective diffusion coefficient within the matrix m (m2 s−1)

Dlat

Lateral diffusion coefficient within the membrane (m2 s−1)

DICL

Effective diffusion coefficient within ICL (m2 s−1)

dICL

ICL thickness (m)

DOCL

Effective diffusion coefficient within OCL (m2 s−1)

dOCL

OCL thickness (m)

Dm

Diffusion coefficient within the matrix m (m2 s−1)

dlat,i

Diffusion distance of ith part of the lateral diffusion pathway (m s−1)

dRPE

RPE cell flat-to-flat diameter (m)

dTJp

TJ pore separation (m)

f

Adjusted fiber volume fraction

Fm

Hydrodynamic interactions in matrix m

hfen

Fenestration height (m)

hLS

Lateral space height (m)

Hpp)

Pore hindrance factor

hpore

Pore height (m)

hRPE

RPE cell height (m)

Hss)

Slit hindrance factor

hslit

Slit height (m)

hTJ

TJ region height (m)

hTJs

TJ strand height (m)

hTJss

TJ strand separation (m)

ICL

Inner collagenous layer

Kmem

Membrane distribution coefficient

kB

Boltzmann’s constant (1.38 × 10−23 J K−1)

KD

Octanol-water distribution coefficient

lcb

Cell boundary length per unit area (m m−2)

Ms

Solute’s molecular mass (Da)

m

Membrane size selectivity (Da−1)

nTJs

TJ strand number

OCL

Outer collagenous layer

PBRB

BRB permeability coefficient (m s−1)

PBrM

BrM permeability coefficient (m s−1)

Pcyt

Cytoplasm permeability coefficient (m s−1)

PCE

CE permeability coefficient (m s−1)

PICL

ICL permeability coefficient (m s−1)

Plat

Lateral diffusion transcellular permeability coefficient (m s−1)

POCL

OCL permeability coefficient (m s−1)

Plat,i

Permeability coefficient of ith part of the lateral diffusion pathway (m s−1)

PLS

Lateral space permeability coefficient (m s−1)

Pmem

Membrane permeability coefficient (m s−1)

P0mem

Membrane permeability coefficient of a theoretical infinitely small molecule (m s−1)

Ppara

Paracellular permeability coefficient (m s−1)

Ppore

Pore permeability coefficient (m s−1)

PRPE

RPE permeability coefficient (m s−1)

Pslit

Slit permeability coefficient (m s−1)

PTJ

TJ permeability coefficient (m s−1)

PTJl

TJ leak pathway permeability coefficient (m s−1)

PTJp

TJ pore pathway permeability coefficient (m s−1)

PTJs

TJ strand permeability coefficient (m s−1)

PTJss

Permeability coefficient of the space between TJ strands (m s−1)

Ptr

Transverse transcellular permeability coefficient (m s−1)

Ptrans

Transcellular permeability coefficient (m s−1)

RPE

Retinal pigment epithelium

rCF

Collagen fibril radius (m)

rdia

Diaphragm pore radius (m)

rf

Fiber radius (m)

rPG

Proteoglycan radius (m)

rpore

Pore radius (m)

r*RPE

Average RPE cell radius (m)

rs

Solute molecule’s radius (m)

rTJp

TJ pore radius (m)

Sm

Steric interactions in matrix m

T

Absolute temperature (K)

TJ

Tight junctions

τRPE

RPE lateral space tortuosity

WLS

Lateral space half-width (m)

Wslit

Slit half-width (m)

αleak

TJ leak parameter

εlat,i

Hindrance factor of ith part of the lateral diffusion pathway (m s−1)

εLS

Relative surface area of the lateral space

εpore

Relative surface area of the pores

εslit

Relative surface area of the slit

εTJp

Relative surface area of the TJ pores

φCF,ICL

Collagen volume fraction in ICL

φCF,OCL

Collagen volume fraction in OCL

Φm

Partition coefficient between the matrix m and solvent

φf

Fiber volume fraction

φPG,ICL

Proteoglycan volume fraction in ICL

φPG,OCL

Proteoglycan volume fraction in OCL

εdia

Relative surface area of the diaphragm pores

η

Dynamic viscosity (Pa s)

Notes

ACKNOWLEDGMENTS AND DISCLOSURES

The study was financially supported by the Academy of Finland (grant numbers 252225 and 260375) and TEKES—the Finnish Funding Agency for Technology and Innovation (grant number 718/31/2011).

REFERENCES

  1. 1.
    Strauss O. The retinal pigment epithelium in visual function. Physiol Rev. 2005;85(3):845–81.PubMedCrossRefGoogle Scholar
  2. 2.
    Bhutto I, Lutty G. Understanding age-related macular degeneration (AMD): relationships between the photoreceptor/retinal pigment epithelium/Bruch’s membrane/choriocapillaris complex. Mol Aspects Med. 2012;33(4):295–317.PubMedCrossRefPubMedCentralGoogle Scholar
  3. 3.
    Del Amo EM, Urtti A. Current and future ophthalmic drug delivery systems. A shift to the posterior segment. Drug Discov Today. 2008;13(3–4):135–43.PubMedGoogle Scholar
  4. 4.
    Booij JC, Baas DC, Beisekeeva J, Gorgels TGMF, Bergen AAB. The dynamic nature of Bruch’s membrane. Prog Retin Eye Res. 2010;29(1):1–18.PubMedCrossRefGoogle Scholar
  5. 5.
    Pitkänen L, Ranta V-P, Moilanen H, Urtti A. Permeability of retinal pigment epithelium: effects of permeant molecular weight and lipophilicity. Investig Ophthalmol Vis Sci. 2005;46(2):641–6.CrossRefGoogle Scholar
  6. 6.
    Mac Gabhann F, Demetriades AM, Deering T, Packer JD, Shah SM, Duh E, et al. Protein transport to choroid and retina following periocular injection: theoretical and experimental study. Ann Biomed Eng. 2007;35(4):615–30.PubMedCrossRefGoogle Scholar
  7. 7.
    Amrite AC, Edelhauser HF, Kompella UB. Modeling of corneal and retinal pharmacokinetics after periocular drug administration. Investig Ophthalmol Vis Sci. 2008;49(1):320–32.CrossRefGoogle Scholar
  8. 8.
    Ranta V-P, Mannermaa E, Lummepuro K, Subrizi A, Laukkanen A, Antopolsky M, et al. Barrier analysis of periocular drug delivery to the posterior segment. J Control Release. 2010;148(1):42–8.PubMedCrossRefGoogle Scholar
  9. 9.
    Balachandran RK, Barocas VH. Computer modeling of drug delivery to the posterior eye: effect of active transport and loss to choroidal blood flow. Pharm Res. 2008;25(11):2685–96.PubMedCrossRefGoogle Scholar
  10. 10.
    Haghjou N, Abdekhodaie MJ, Cheng Y-L. Retina-choroid-sclera permeability for ophthalmic drugs in the vitreous to blood direction: quantitative assessment. Pharm Res. 2013;30(1):41–59.PubMedCrossRefGoogle Scholar
  11. 11.
    Edwards A, Prausnitz MR. Fiber matrix model of sclera and corneal stroma for drug delivery to the eye. AIChE J. 1998;44(1):214–25.CrossRefGoogle Scholar
  12. 12.
    Edwards A, Prausnitz MR. Predicted permeability of the cornea to topical drugs. Pharm Res. 2001;18(11):1497–508.CrossRefGoogle Scholar
  13. 13.
    Mitragotri S. Modeling skin permeability to hydrophilic and hydrophobic solutes based on four permeation pathways. J Control Release. 2003;86(1):69–92.PubMedCrossRefGoogle Scholar
  14. 14.
    Anderson JM, Van Itallie CM. Physiology and function of the tight junction. Cold Spring Harb Perspect Biol. 2009;1(2):1–16.CrossRefGoogle Scholar
  15. 15.
    Guo P, Weinstein AM, Weinbaum S. A dual-pathway ultrastructural model for the tight junction of rat proximal tubule epithelium. Am J Physiol Ren Physiol. 2003;285(2):F241–57.Google Scholar
  16. 16.
    Goldbaum MH, Madden K. A new perspective on Bruch’s membrane and the retinal pigment epithelium. Br J Ophthalmol. 1982;66(1):17–25.PubMedCrossRefPubMedCentralGoogle Scholar
  17. 17.
    Bearer EL, Orci L. Endothelial fenestral diaphragms: a quick-freeze, deep-etch study. J Cell Biol. 1985;100(2):418–28.PubMedCrossRefGoogle Scholar
  18. 18.
    Ho NFH, Raub TJ, Burton PS, Barsuhn CL, Audus KL, Borchardt RT. Quantitative approaches to delineate passive transport mechanisms in cell culture monolayers. In: Amidon GL, Lee PI, Topp EM, editors. Transport processes in pharmaceutical systems. New York: Marcel Dekker, Inc; 2000. p. 219–316.Google Scholar
  19. 19.
    Johansson L, Löfroth J-E. Diffusion and interaction in gels and solutions. 4. Hard sphere Brownian dynamics simulations. J Chem Phys. 1993;98(9):7471–9.CrossRefGoogle Scholar
  20. 20.
    Dechadilok P, Deen WM. Hindrance factors for diffusion and convection in pores. Ind Eng Chem Res. 2006;45(21):6953–9.CrossRefGoogle Scholar
  21. 21.
    Lieb WR, Stein WD. Non-Stokesian nature of transverse diffusion within human red cell membranes. J Membr Biol. 1986;92(2):111–9.PubMedCrossRefGoogle Scholar
  22. 22.
    Verkman AS. Solute and macromolecule diffusion in cellular aqueous compartments. Trends Biochem Sci. 2002;27(1):27–33.PubMedCrossRefGoogle Scholar
  23. 23.
    Mitragotri S. A theoretical analysis of permeation of small hydrophobic solutes across the stratum corneum based on Scaled Particle Theory. J Pharm Sci. 2002;91(3):744–52.PubMedCrossRefGoogle Scholar
  24. 24.
    Johnson EM, Berk DA, Jain RK, Deen WM. Diffusion and partitioning of proteins in charged agarose gels. Biophys J. 1995;68(4):1561–8. Elsevier.PubMedCrossRefPubMedCentralGoogle Scholar
  25. 25.
    Ogston AG. The spaces in a uniform random suspension of fibres. Trans Faraday Soc. 1958;54(1):1754–7.CrossRefGoogle Scholar
  26. 26.
    Phillips RJ. A hydrodynamic model for hindered diffusion of proteins and micelles in hydrogels. Biophys J. 2000;79(6):3350–3.PubMedCrossRefPubMedCentralGoogle Scholar
  27. 27.
    Clague DS, Phillips RJ. Hindered diffusion of spherical macromolecules through dilute fibrous media. Phys Fluids. 1996;8(7):1720–31.CrossRefGoogle Scholar
  28. 28.
    Amsden B. Solute diffusion within hydrogels. Mechanisms and Models. Macromolecules. 1998;31(23):8382–95.CrossRefGoogle Scholar
  29. 29.
    Avdeef A. Leakiness and size exclusion of paracellular channels in cultured epithelial cell monolayers-interlaboratory comparison. Pharm Res. 2010;27(3):480–9.PubMedCrossRefGoogle Scholar
  30. 30.
    Sutherland WLXXV. A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin. Philos Mag. 1905;9(54):781–5.CrossRefGoogle Scholar
  31. 31.
    Garron LK. The ultrastructure of the retinal pigment epithelium with observations on the choriocapillaris and Bruch’s membrane. Trans Am Ophthalmol Soc. 1963;61:545–88.PubMedPubMedCentralGoogle Scholar
  32. 32.
    Prünte C, Kain HL. Enzymatic digestion increases permeability of the outer blood-retinal barrier for high-molecular-weight substances. Graefes Arch Clin Exp Ophthalmol. 1995;233(2):101–11.PubMedCrossRefGoogle Scholar
  33. 33.
    Rajasekaran SA, Hu J, Gopal J, Gallemore R, Ryazantsev S, Bok D, et al. Na, K-ATPase inhibition alters tight junction structure and permeability in human retinal pigment epithelial cells. Am J Physiol Cell Physiol. 2003;284(6):C1497–507.PubMedCrossRefGoogle Scholar
  34. 34.
    O’Leary TJ. Lateral diffusion of lipids in complex biological membranes. Proc Natl Acad Sci U S A. 1987;84(2):429–33.PubMedCrossRefPubMedCentralGoogle Scholar
  35. 35.
    Ogston AG, Preston BN, Wells JD. On the transport of compact particles through solutions of chain-polymers. Proc R Soc A Math Phys Eng Sci. 1973;333(1594):297–316.CrossRefGoogle Scholar
  36. 36.
    Watson CJ, Rowland M, Warhurst G. Functional modeling of tight junctions in intestinal cell monolayers using polyethylene glycol oligomers. Am J Physiol Cell Physiol. 2001;281(2):C388–97.PubMedGoogle Scholar
  37. 37.
    Hirsch M, Prenant G, Renard G. Three-dimensional supramolecular organization of the extracellular matrix in human and rabbit corneal stroma, as revealed by ultrarapid-freezing and deep-etching methods. Exp Eye Res. 2001;72(2):123–35.PubMedCrossRefGoogle Scholar
  38. 38.
    Melamed S, Ben-Sira I, Ben-Shaul Y. Ultrastructure of fenestrations in endothelial choriocapillaries of the rabbit—a freeze-fracturing study. Br J Ophthalmol. 1980;64(7):537–43.PubMedCrossRefPubMedCentralGoogle Scholar
  39. 39.
    Federman JL. The fenestrations of the choriocapillaris in the presence of choroidal melanoma. Trans Am Ophthalmol Soc. 1982;80:498–516.PubMedPubMedCentralGoogle Scholar
  40. 40.
    Kadam RS, Cheruvu NPS, Edelhauser HF, Kompella UB. Sclera-choroid-RPE transport of eight β-blockers in human, bovine, porcine, rabbit, and rat models. Investig Ophthalmol Vis Sci. 2011;52(8):5387–99.CrossRefGoogle Scholar
  41. 41.
    Steuer H, Jaworski A, Elger B, Kaussmann M, Keldenich J, Schneider H, et al. Functional characterization and comparison of the outer blood-retina barrier and the blood–brain barrier. Investig Ophthalmol Vis Sci. 2005;46(3):1047–53.CrossRefGoogle Scholar
  42. 42.
    Cheruvu NPS, Kompella UB. Bovine and porcine transscleral solute transport: influence of lipophilicity and the Choroid-Bruch’s layer. Investig Ophthalmol Vis Sci. 2006;47(10):4513–22.CrossRefGoogle Scholar
  43. 43.
    Pescina S, Santi P, Ferrari G, Padula C, Cavallini P, Govoni P, et al. Ex vivo models to evaluate the role of ocular melanin in trans-scleral drug delivery. Eur J Pharm Sci. 2012;46(5):475–83.PubMedCrossRefGoogle Scholar
  44. 44.
    Hussain A, Rowe L, Marshall J. Age-related alterations in the diffusional transport of amino acids across the human Bruch’s-choroid complex. J Opt Soc Am A. 2002;19(1):166.CrossRefGoogle Scholar
  45. 45.
    Peng S, Rahner C, Rizzolo LJ. Apical and basal regulation of the permeability of the retinal pigment epithelium. Investig Ophthalmol Vis Sci. 2003;44(2):808–17.CrossRefGoogle Scholar
  46. 46.
    Warnke PH, Alamein M, Skabo S, Stephens S, Bourke R, Heiner P, et al. Primordium of an artificial Bruch’s membrane made of nanofibers for engineering of retinal pigment epithelium cell monolayers. Acta Biomater. 2013. doi: 10.1016/j.actbio.2013.07.029.PubMedGoogle Scholar
  47. 47.
    Johnson EM, Deen WM. Electrostatic effects on the equilibrium partitioning of spherical colloids in random fibrous media. J Colloid Interface Sci. 1996;178(2):749–56.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Aapo Tervonen
    • 1
    • 2
  • Iina Vainio
    • 1
    • 2
  • Soile Nymark
    • 1
    • 2
  • Jari Hyttinen
    • 1
    • 2
  1. 1.BioMediTechTampere University of TechnologyTampereFinland
  2. 2.Department of Electronics and Communications EngineeringTampere University of TechnologyTampereFinland

Personalised recommendations