Ind. Eng. Chem. Res. 1998, 37, 2903-2907
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Measurement and Prediction of Transient Transport across Sclera for Drug Delivery to the Eye Mark R. Prausnitz,*,† Aure´ lie Edwards,‡ Jeremy S. Noonan,† David E. Rudnick,†,§ Henry F. Edelhauser,§ and Dayle H. Geroski§ School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100, Department of Chemical Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, and Department of Ophthalmology, Emory University School of Medicine, Atlanta Georgia, 30322
Drug delivery to the eye for treatment of a number of important diseases involves non-steadystate transport across the sclera. Although the literature contains steady-state measurements of permeability, the transient transport properties of sclera have not been determined experimentally or described theoretically. In this study, carboxyfluorescein flux across human sclera is shown experimentally to approach a quasi-steady state with a lag time of 0.37 h. Because drug-sclera contact times in the body are often shorter than this, the use of steadystate permeability models will overpredict the amount of drug delivered to the eye. A theoretical model is also developed to describe the observed transient flux by accounting for both diffusion and solute binding within the sclera. Introduction Targeted administration of drugs to the eye is a significant challenge in drug delivery which often involves transient transport across the sclera (Figure 1). Conventional eye drops typically act transiently, delivering only a small fraction of their dose to the eye before being washed away by tear fluid (Robinson and Lee, 1988; Lang, 1995; Tasman, 1995). That which does enter the eye does so either by diffusing across the cornea (the clear part of the eye) or across the conjunctiva and sclera (the white of the eye). Although delivery through the cornea is often desirable, transport across the sclera is sometimes preferred, since it provides a more direct path to the ciliary body, the target organ for some antiglaucoma agents (Schoenwald et al., 1997). Glaucoma afflicts more than 15 million Americans and is the leading cause of blindness in the United States (Tasman, 1995). Topical eye drops are not capable of delivering drugs to tissues in the back of the eye, such as the retina, due to long diffusional path lengths and counterdirectional convection within the eye (Lang, 1995; Tasman, 1995; Schoenwald et al., 1997). As a result, drug administration targeted to the back of the eye usually requires either direct injection into the eyeball or peribulbar injection into the space surrounding the eye. For a drug to reach the retina following peribulbar injection, it must transiently diffuse across the sclera before being diluted and washed away by interstitial fluid and blood. Treatment of the retina is important to a number of diseases, including diabetic retinopathy, which is the primary cause of blindness among working-age Americans, and macular degeneration, an increasingly important cause of blindness especially among the older population (Tasman, 1995). * To whom correspondence is addressed: Tel.: (404) 8945135. Fax: (404) 894-2866. E-mail: mark.prausnitz@ che.gatech.edu. † Georgia Institute of Technology. ‡ Pennsylvania State University. § Emory University School of Medicine.
Figure 1. Cross-sectional anatomy of the eye. Drugs administered with eye drops enter the eye either across the cornea (route 1) or across the conjunctiva and sclera (route 2). Drugs injected into the peribulbar space can enter the eye directly across the sclera (route 3).
Drug delivery either by eye drops or peribulbar injection is governed in part by transient diffusion across the sclera which typically occurs over a time scale of minutes unless controlled release formulations, such as gels, are used (Robinson and Lee, 1988; Lang, 1995). Despite its importance to drug delivery, there is no published information on sclera’s transient transport properties (e.g., diffusional lag times). Experimental data exist only for sclera permeability determined at steady state (Maurice and Polgar, 1977; Edelhauser and Maren, 1988; Olsen et al., 1995; Prausnitz and Noonan, 1998). To facilitate a better understanding of drug delivery and eye physiology, experimental studies and predictive models of non-steady-state trans-scleral diffusion are needed. In this study, we present the first experimental measurements of transient transport across the sclera and provide a theoretical model which describes the observed non-steady-state transport behavior. In a previous study (Edwards and Prausnitz, 1998), we developed a fiber matrix model which predicts the permeability of sclera to water and solutes; all parameters corresponded to the geometrical and physicochem-
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2904 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998
ical characteristics of the eye and solutes and required no adjustable parameters. Here, we provide a complimentary model to predict the sclera’s transient transport properties and find quantitative agreement with experiments. Experimental Methods Experimental Apparatus. Transient flux of a model drug, carboxyfluorescein, was measured across human sclera using a flow-through permeation chamber coupled with a spectrofluorimeter. Human sclera was obtained from cadavers (Georgia Eye Bank, Atlanta, GA) and stored in moist containers for up to 6 days at 4 °C until use (Olsen et al., 1995). Circular disks (1520-mm diameter) of full-thickness sclera were cut from the superior temporal quadrant of the globe. Adherent tissue associated with the retina, choroid, episclera, or Tenon’s capsule was gently removed with a cotton swab (VWR, Suwanee, GA). Following a procedure described previously (Olsen et al., 1995), sclera was mounted in a vertically oriented permeation chamber (Rudnick et al., 1998) which was maintained at 37 °C with a water jacket and a constanttemperature water bath (model 1162; VWR). The area of sclera available for transport was 0.79 cm2. The donor compartment of the permeation chamber (above, facing the episcleral surface) was filled with BSS Plus solution (Alcon Laboratories, Ft. Worth, TX) for 5-10 min before initiating an experiment and then replaced at the beginning of an experiment with 250 µL of 10-4 M carboxyfluorescein (Sigma Chemical, St. Louis, MO) in phosphate-buffered saline (Sigma Chemical). Due to limitations of the apparatus, the donor solution could not be mixed during the experiment. The receiver compartment (below, facing the uveal surface) was a flow-through chamber which was mixed with a magnetic stirrer (VWR), held to 0.91 mL, and was fed with 2.4 mL/h of BSS Plus solution from a reservoir at the same height as the permeation chamber to prevent the development of a trans-scleral pressure. The contents of the receiver compartment were fed to a flow-through quartz cell (model 59FL; NSG, Farmingdale, NY) housed in a spectrofluorimeter (model QM1; Photon Technology International, South Brunswick, NJ) which was followed in series by a peristaltic pump (model 72-500-000; Manostat, New York, NY) emptying into a waste container. All components of the flowthrough apparatus were connected with 0.77-mm i.d. tubing. The spectrofluorimeter was set for excitation at 492 nm and emission at 517 nm and made fluorescence intensity measurements once per minute. Analysis of Experimental Data. Using a calibration curve, measured fluorescence intensity data were converted into carboxyfluorescein concentration data, which were in turn converted into trans-scleral fluxes. Scleral permeability was determined by dividing flux by the concentration difference between the donor and receiver solutions. To correct for transient effects introduced by the apparatus, three corrections were made. First, the lag time for transport from the permeation chamber receiver compartment to the spectrofluorimeter cell was estimated in two ways, both of which yielded a lag of 0.2 h, and was subtracted from all time measurements. The lag time was (1) calculated using the geometry of the apparatus, assuming plug flow in the tubing, and (2) determined experimentally by measuring the time
it took for the spectrofluorimeter to respond to the direct injection of carboxyfluorescein into the receiver compartment. The agreement between the calculation and measurement suggests that binding of carboxyfluorescein to the apparatus was not significant, which is important for the analysis below. Second, assuming perfect mixing in the receiver compartment, a transient mass balance on the permeation chamber receiver compartment was used to calculate fluxes across the sclera from the measured concentration in the spectrofluorimeter using the following equation (Pliquett et al., 1995):
V
∂C ) JS - QC ∂t
(1)
where V is the volume of the receiver compartment, C is the concentration in the receiver compartment, S is the sclera area, J is the trans-scleral flux at the uveal surface, Q is the flow rate out of the receiver compartment, and t is time. Finally, because a small, finite dose of carboxyfluorescein was used in the donor compartment, the donor concentration of carboxyfluorescein decreased over time during long experiments. Therefore, a mass balance on the donor compartment was used to determine the actual carboxyfluorescein concentration in the donor compartment when scleral permeabilities were calculated. We assumed that the flux out of the donor compartment equals the flux into the receiver compartment, which is only strictly correct at steady state. Mathematical Model One-Dimensional Diffusion without Binding. To model diffusion across the sclera using a one-dimensional approximation, the transient concentration profile in the sclera is given by
∂2C ∂C ) D∇2C ) D 2 ∂t ∂x
(2)
where C is solute concentration and ∇ is the gradient operator. Equation 2 is based on external concentrations, so that D is defined as the product of the solute diffusivity and partition coefficient in sclera. Assuming the donor and receiver compartments were well mixed and given that a finite dose of carboxyfluorescein is added to the donor compartment at t ) 0 and never replenished, the concentrations Co and C1 in the donor and receiver compartments, respectively, obey the following equations:
C0 ) 10-4 M
at x ) 0 and t ) 0
∂V0C0 ) -J0S ∂t
at x ) 0 and t > 0
C1 ) 0
at x ) L and t ) 0
∂V1C1 ) J1S - QC1 ∂t
at x ) L and t > 0
(3)
where L is the thickness of the sclera, S is the membrane cross-sectional area, Vo and V1 are the volumes of the donor and receiver compartments, respectively, J0 and J1 are the solute fluxes at x ) 0 and x ) L,
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respectively, and Q is the volumetric flow rate leaving the receiver chamber. The diffusivity D is given by kL, where k is the permeability of sclera to the solute, and L is the sclera thickness (0.53 mm; Olsen et al., 1998). Because no independent measurements of sclera permeability to carboxyfluorescein exist in the literature and we do not want to “fit” our predictions to our experimental data, we estimated sclera permeability based on literature values for benzolamide and penicillin G, each of which have molar volumes very close to that of carboxyfluorescein and similarly carry a negative charge at physiological pH (Edwards and Prausnitz, 1998). Under experimental conditions similar to ours, the permeability of sclera to benzolamide has been measured as 1.5-2.0 × 10-5 cm/s (Edelhauser and Maren, 1988) and penicillin G as 0.9-1.0 × 10-5 cm/s (adjusted for human scleral thickness; Maurice and Polgar, 1977). We thus estimated the permeability of sclera to carboxyfluorescein as 1 × 10-5 cm/s. A one-dimensional approach is appropriate given the geometry of the experimental apparatus, in which a portion of the scleral surface (10-mm diameter) is exposed to the donor solution, while the outer annulus is sandwiched in the chamber. Because the thickness of the sclera (0.6 mm) is much less than the width of the exposed tissue, the diffusing solute will reach the uveal surface of sclera much more rapidly than its side edges. To verify this, simulations (as described below) conducted over the time scale of the experiments using a two-dimensional model yielded almost identical results for the trans-scleral flux as the one-dimensional approach outlined above. One-Dimensional Diffusion with Binding. As described below, carboxyfluorescein is expected to bind to proteins in the sclera. This was not included in the above analysis, but can be accounted for in the following manner. Given that the adsorption site concentration is much greater than the carboxyfluorescein concentration (Thomas et al., 1990), the solute concentration in the bulk phase, C, and that in the adsorbed phase, CA, can be described by
∂C ∂2C ) D 2 - k1(C - KCA) ∂t ∂x ∂CA ) k1(C - KCA) ∂t
(4)
where k1 is the adsorption rate constant and K is the ratio of free-to-bound solute at equilibrium; the product k1K corresponds to the desorption constant, k-1. The initial and boundary conditions for C are the same as above (eq 3); those for CA are
CA ) 0 ∂CA )0 ∂x
at t ) 0, ∀ x (5) at x ) 0 and x ) L, ∀ t
Equations in (4) together with the initial and boundary conditions were solved using a finite-difference method (explicit Euler scheme programmed in Fortran), and the fluxes J0 ) -D ∂C/∂x|0 and J1 ) -D ∂C/∂x|L were calculated for each time iteration. The accuracy of our numerical results was checked against the analytical solution in the limiting case where there is no adsorp-
tion and the concentrations at the boundaries are fixed (Carslaw and Jaeger, 1959). This comparison showed very good agreement. Determining the Ratio of Free-to-Bound Carboxyfluorescein. Fluorescein and its derivatives, including carboxyfluorescein, are known to bind to proteins in the eye, the blood, and other tissues (Barsotti et al., 1990). Although binding to the sclera has not been reported, there is evidence for carboxyfluorescein binding in the corneal stroma (Araie and Maurice, 1987), which is structurally and chemically similar to sclera. To estimate the fraction of carboxyfluorescein bound within the sclera at equilibrium, we used the equilibrium constant for the dissociation reaction of pyranine and albumin, Kd ) 3.1 × 10-4 M (Thomas et al., 1990), defined as follows:
Kd )
[P][F] [PF]
(6)
where [P] indicates the concentration of protein (albumin), [F] is the concentration of the free fluorophore (pyranine), and [PF] is the concentration of the fluorophore which is bound to protein. Pyranine is a fluorescein derivative with a structure related to that of carboxyfluorescein. Albumin serves as a model for proteins found in the sclera. Since there are 3.3 binding sites per albumin molecule (Thomas et al., 1990), the dissociation equilibrium constant can be changed from a per-albumin molecule basis to a per-binding site basis, Kd* ) 1.0 × 10-3 M. Sites for carboxyfluorescein binding in the sclera include collagen and noncollagenous proteins. The noncollagenous proteins make up 2.4 vol % of the sclera and have a specific gravity of 1.35 (Edwards and Prausnitz, 1998). Thus, the concentration of noncollagenous protein is 3.2 × 10-2 g of protein/cm3 of sclera. Scleral collagen is found in the form of cylindrical fibrils with an average diameter of 133 nm (Edwards and Prausnitz, 1998). Assuming that only collagen found at the outer surface of fibrils is accessible for binding, we can use the 1.5-nm diameter of the basic collagen unit, tropocollagen (Darnell et al., 1986), to define the thickness of the outer accessible shell. This yields a volume fraction of 4.5% of each fibril available for binding. Since the sclera contains 18.4 vol % collagen with a specific gravity of 1.37 (Edwards and Prausnitz, 1998), the scleral concentration of accessible collagen is 1.1 × 10-2 g/cm3. Thus, the total accessible protein concentration is 4.3 × 10-2 g/cm3. To identify the number of binding sites available on scleral proteins, we assumed the same density of sites found in albumin (Mr ) 68 kDa), which is 4.9 × 10-2 mol of binding sites/kg of protein (Thomas et al., 1990). This yields a binding site concentration in the sclera of 2.1 × 10-3 M. Finally, the equilibrium ratio of free-tobound carboxyfluorescein (K) is equal to the ratio of the dissociation equilibrium constant (Kd*) to the scleral binding site density. This ratio has a value of 0.48 based on the above analysis. Results and Discussion Experimental Measurements of Transient Flux. Although steady-state measurements of sclera permeability have been reported for a number of different compounds, the literature does not provide any measurements of the sclera’s transient transport properties.
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Figure 2. Measured and predicted flux of carboxyfluorescein across human sclera in vitro: (b) experimental data and model predictions for (s - - -) no adsorption; (- - - -) k1 ) 0.1 h-1; (- -) k1 ) 1 h-1; (s) k1 ) 20 h-1. Good agreement between predicted and measured behavior is seen when adsoprtion of carboxyfluorescein to scleral proteins is accounted for with a rate constant of 20 h-1. Representative standard deviation bars are shown.
In Figure 2, the transient flux of carboxyfluorescein is shown across human sclera in vitro. There is an initial lag period during which the flux sharply increases and reaches a quasi-steady state after approximately 1 h. This lag time is due to the effects of both diffusion and binding within the sclera, as described by the theoretical model. In the quasi-steady-state region (>∼1 h), the flux slowly decreases. This is because the donor source of solute is finite and becomes depleted over time, thereby reducing the concentration gradient across the sclera. The application of a small finite dose of drug which is consumed over time simulates the way in which an eye drop or peribulbar injection would be administered. On the basis of data from the five experiments used to generate Figure 2 and when the changing donor concentration is accounted for, the apparent quasisteady-state permeability was determined to be 1.1 × 10-5 ( 0.2 × 10-5 cm/s, which is in excellent agreement with reported values for other compounds of similar size and charge (Maurice and Polgar, 1977; Edelhauser and Maren, 1988). To characterize the initial lag time, the time to reach 50% of the maximum flux was determined to be τ50 ) 0.37 ( 0.13 h. This value cannot be compared to literature values, because there have been no previous reports of lag times for transport across sclera. Note that the flux measured is that which exits the uveal surface of the sclera. This is of most interest for drug delivery and other scenarios where solutes transport across the sclera to locations within the eye. Theoretical Model Predictions. Model predictions are shown in Figure 2 along with experimental data. The theoretical model which accounts only for diffusion and does not include solute binding shows qualitative agreement with the data, in that flux rapidly increases and then attains a steadily decreasing quasi-steady state. However, for this prediction, the initial lag time is much shorter, the peak flux is much greater, and the “steady state” decreases much more steeply than that observed experimentally. This simple model does not quantitatively describe the observed transport phenomena. Previous experiments suggest that carboxyfluorescein may bind to proteins within the sclera, as described above. Modeling solute binding to scleral proteins
requires two additional parameters: the adsorption rate constant, k1, and the equilibrium ratio of free-to-bound solute, K (see above). We were able to estimate a value for K based on literature data, but not for k1, lacking information on the kinetics of binding. Using the model which accounts for both diffusion and binding, we found good quantitative agreement with the data. The effects of changes in k1 on the flux are illustrated in Figure 2, where the adsorption rate constant was varied. As expected, for greater k1, changes in flux occur more slowly, as solute binds faster to the membrane and thus diffuses out of the sclera less rapidly. It therefore takes longer for the flux to reach a quasi-steady state and start slowly to decrease. The results shown in Figure 2 indicate that the adsorption rate constant which best describes the experimentally determined kinetic data is approximately 20 h-1. For this condition, the lag time (defined as the time to reach 50% of the maximum flux), τ50 ) 0.41 h, which is in good agreement with the experimental value (i.e., 0.37 h). Relevance of Findings. This study was motivated by the need to measure and theoretically describe the transient transport behavior of sclera. Understanding scleral permeability is important for drug delivery to the eye, most notably for eye drops used in glaucoma therapy and for peribulbar injection of compounds directed against retinal diseases. Until now, predictions of the amount of drug delivered to the eye were made based only on steady-state transport measurements available in the literature. The experiments presented here (e.g., Figure 2) suggest that predictions of trans-scleral transport based on steady-state measurements significantly overpredict the amount of drug delivered, because the lag time for transport across the sclera is similar to or longer than the drug-sclera contact time during conventional drug administration. In this study, the scleral lag time was shown to be more than 20 min for carboxyfluorescein, a model compound which is similar in size (and thus diffusivity) to most conventional drugs. This is significantly longer than the few minutes which eye drops remain on the eye’s surface before being washed away by tear fluid (Robinson and Lee, 1988l Tasman, 1995). This lag time is also similar to the residence time at the scleral surface for drug introduced by peribulbar injection. As a result, flux across the sclera does not achieve steady state for most drug delivery applications, and thus, the use of a steady-state model is inappropriate to describe most drug delivery scenarios. Carboxyfluorescein serves as a model solute. Because other compounds will bind within the sclera to different extents and at different rates, the lag time of other compounds will probably not be the same as the lag time observed here. Moreover, compounds of larger size, including both therapeutic and endogenous macromolecules, will diffuse much more slowly. For example, the permeability of albumin measured at steady state across sclera is approximately 500 times less than that for carboxyfluorescein (Edwards and Prausnitz, 1998), which indicates that albumin’s lag time will be 2-3 orders of magnitude longer, neglecting differences in binding. The importance of binding to transient transport across sclera can be exploited for drug delivery applications. Because binding will be a function of the solute and its chemical environment within the sclera, drugs and formulation enhancers can be modified to control lag times. For fast-acting formulations, minimal drug
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binding to scleral proteins would be best. In contrast, when sustained release of a drug is needed, binding could be increased to form a drug depot within the sclera. This could provide an alternative to the conventional approach to sustained release, usually involving encapsulation of drug within gels or polymeric devices. In a previous paper (Edwards and Prausnitz, 1998), we developed a model which required no fitted parameters and predicted sclera permeability for a broad range of molecules, which was validated with steady-state transport data from almost 20 compounds including small drugs and macromolecules. Here, we present a complimentary model which predicts transient transport behavior and was validated with experimental data on carboxyfluorescein flux. This model requires information on the kinetics of binding, which may not be available in the literature for many compounds. Because no other transient experimental data are presently available, we cannot validate the transient model more broadly. However, given the good agreement seen for transient transport of carboxyfluorescein in this work and for the permeability of many compounds determined at steady state in the previous work, these two studies can provide a complete model for transport across the sclera which should be broadly applicable. Conclusion Despite the importance of non-steady-state transport to ophthalmic drug delivery, the transient transport properties of sclera have not previously been measured experimentally or described theoretically. Here, we provide such measurements for a model solute and show that the lag time can be significantly longer than the drug-sclera contact time following administration of peribulbar injection or eye drops (which can be as short as minutes). Using a theoretical approach for which independently determined values were available for all parameters except the adsorption rate constant, we developed a model which provides quantitative agreement with experimental data. This model shows the importance of accounting for solute binding within the sclera to accurately predict transient behavior. Acknowledgment This work was supported by a NSF Career Young Investigator Award BES-9624832 (M.R.P., J.S.N.), NSF Grant BES-9707512 (A.E.), NIH Grant P30 EY06360 (D.E.R., D.H.G., H.F.E.), and the Emory/Georgia Tech
Biomedical Technology Center (M.R.P., H.F.E., D.H.G., D.E.R.). H.F.E. is a Research to Prevent Blindness Senior Investigator. Literature Cited Araie, M.; Maurice, D. The rate of diffusion of fluorophores through the corneal epithelium and stroma. Exp. Eye Res. 1987, 44, 73. Barsotti, M. F.; Bartels, S. P.; Kamm, R. D.; Freddo, T. F. Background-protein effects on fluorophotometric data. Invest. Ophthalmol. Vis. Sci. 1990, 31, 2046. Carslaw, H. S.; Jaeger, J. C. Conduction of Heat in Solids, 2nd ed.; Oxford University Press: London, 1959. Darnell, J.; Lodish, H.; Baltimore, D. Molecular Cell Biology; Scientific American Books: New York, 1986. Edelhauser, H. F.; Maren, T. H. Permeability of human cornea and sclera to sulfonamide carbonic anhydrase inhibitors. Arch. Ophthalmol. 1988, 106, 1110. Edwards, A.; Prausnitz, M. R. A fiber matrix model of sclera and corneal stroma for drug delivery to the eye. AIChE J. 1998, 44, 214. Lang, J. C. Ocular drug delivery conventional ocular formalations. Adv. Drug Deliv. Rev. 1995, 16, 39. Maurice, D. M.; Polgar, J. Diffusion across the sclera. Exp. Eye Res. 1977, 25, 577. Olsen, T. W.; Edelhauser, H. F.; Lim, J. I.; Geroski, D. H. Human scleral permeability: effects of age, cryotherapy, transscleral diode laser, and surgical thinning. Invest. Ophthalmol. Vis. Sci. 1995, 36, 1893. Olsen, T. W.; Aaberg, S. Y.; Geroski, D. H.; Edelhauser, H. F. Human sclera: thickness and surface area. Am. J. Ophthalmol. 1998, 125, 237. Pliquett, U.; Prausnitz, M. R.; Chizmadzhev, Y. A.; Weaver, J. C. Measurement of rapid release kinetics for drug delivery. Pharm. Res. 1995, 12, 549. Prausnitz, M. R.; Noonan, J. S. Permeability of the cornea, sclera and conjunctiva: A meta-analysis of the literature for drug delivery to the eye. 1998, submitted for publication. Robinson, J. R., Lee, V. H., Eds.; Controlled Drug Delivery: Fundamentals and Applications; Marcel Dekker: New York, 1988. Rudnick, D. E.; Noonan, J. S.; Geroski, D. H.; Prausnitz, M. R.; Edelhauser, H. F. The effect of intraocular pressure on scleral permeability. Invest. Ophthalmol. Vis. Sci. 1998 (in press). Schoenwald, R. D.; Deshpande, G. S.; Rethwisch, D. G.; Barfknecht, C. F. Penetration into the anterior chamber via the conjunctival/scleral pathway. J. Ocul. Pharmacol. Ther. 1997, 13, 41. Tasman, W. Duane’s Foundations of Clinical Ophthalmology; Lippincott-Raven: Philadelphia, PA, 1995. Thomas, J. V.; Brimijoin, M. R.; Neault, T. R.; Brubaker, R. F. The fluorescent indicator pyranine is suitable for measuring stromal and corneal pH in vivo. Exp. Eye Res. 1990, 50, 241.
Received for review February 18, 1998 Revised manuscript received April 7, 1998 Accepted April 9, 1998 IE9800952
