purpose. Drug delivery via the sclera is a promising approach to retinal disorder treatments that require access to the posterior segment of the eye. To complement existing studies of transverse diffusion across the sclera, this study examined lateral diffusion within the sclera parallel to the scleral surface.

methods. Using sulforhodamine as a model hydrophilic drug, rates of diffusion were measured in strips of human cadaveric sclera for up to 1 week. Data were analyzed with a mathematical model based on theoretical expressions for one-dimensional diffusion.

results. Measurable amounts of sulforhodamine were detected at distances of 5 and 10 mm from the sulforhodamine donor reservoir at 4 hours and 3 days, respectively. The effective lateral diffusivity of sulforhodamine was determined to be 3.82 × 10^{−6} cm^{2}/s, which is similar in magnitude to the transverse diffusivity. The theoretical model agreed with experimental values with an average error of 39%.

conclusions. This study shows that the lateral diffusion of sulforhodamine in human sclera is slow and localizes to the site of administration.

^{ 1 }

^{ 2 }However, none of these approaches provides fully satisfactory ocular delivery to the posterior part of the eye.

^{ 1 }

^{ 3 }Although intraocular injection and implants can provide delivery targeted to the posterior segment, they can lead to complications such as retinal detachment, hemorrhage, endophthalmitis, and cataract, especially when repeated injections are required.

^{ 3 }

^{ 4 }

^{ 2 }The sclera’s large surface area, which averages 17 cm

^{2}on the human eye,

^{ 5 }is approximately 20 times larger than the cornea. Moreover, sclera is much more permeable, especially to large and hydrophilic drugs.

^{ 6 }

^{ 7 }Conventional subconjunctival and peribulbar injections provide access to the transscleral route. Novel delivery systems, involving implants, gels, and patches applied to the scleral surface, and intrascleral injections are being developed to enable extended-release and better-targeted drug delivery via the sclera.

^{ 2 }

^{ 8 }

^{ 9 }

^{ 10 }

^{ 11 }

^{ 12 }However, little attention has been given to diffusion within the sclera in the lateral direction parallel to the scleral surface, which could affect drug distribution caused by lateral spread of the released drug—for example, from an extraocular implant or intrascleral injection. The nonisotropic architecture of collagen lamellae and other features of scleral microanatomy

^{ 13 }suggest that lateral diffusion may behave differently from transscleral diffusion.

^{−5}M sulforhodamine in physiological saline (Balanced Salt Solution [BSS]; Alcon Laboratories, Fort Worth, TX). A scleral strip was suspended vertically in the glass vial such that the lower 3 mm of the tissue dipped into the donor solution (Fig. 1) . The vial was then capped and sealed with parafilm to maintain scleral hydration and placed in a 37°C water bath, although some tissue dehydration probably still occurred. After a designated experimental period (4, 24, 48, 72, or 168 hours), the scleral strip was removed from the vial, rinsed with BSS, placed in a sample block containing freezing agent (OCT; Sakura Finetechnical, Tokyo, Japan), and snap frozen with liquid nitrogen.

*V*

_{cuvette}= 1.8 mL) to determine its sulforhodamine concentration by calibrated spectrofluorimetry (Photon Technology International, Lawrenceville, NJ) at an excitation wavelength of 565 nm and emission spectra collected at 580 to 620 nm. The sulforhodamine concentration within the tissue,

*C*

_{tissue}, was calculated using the following equation:

*C*

_{cuvette}is the sulforhodamine concentration in the cuvette, determined by spectrofluorimetry, and

*V*

_{tissue}is the volume of each tissue sample, which is equal to the measured cross-sectional area multiplied by the total thickness of 14 tissue pieces analyzed per section (i.e., 700 μm). In this way, drug concentration within the tissue was determined as a function of distance along the sclera at each time point.

^{ 14 }scleral discs 10 to 15 mm in diameter were excised from human globes and mounted in two-compartment perfusion chambers. A 300-μL depot of 9.0 × 10

^{−5}M sulforhodamine donor solution was added to the episcleral surface while BSS was perfused across the choroidal side. Every 1 hour, a fraction containing 2 mL of the perfusate was collected over a 24-hour period and its fluorescence concentration was measured by spectrofluorimetry. From these measurements, the effective transverse diffusivity (

*D*

_{trans}) was calculated as

*d*is scleral thickness (0.6 mm),

^{ 7 }

*A*is the scleral surface area exposed to donor solution (0.37 cm

^{2}), Δ

*t*is sampling time (1 hour) and

*C*

_{donor}is the sulforhodamine concentration in the donor solution, which was initially at 9.0 × 10

^{−5}M and decreased over time. This effect was accounted for by correcting

*C*

_{donor}in the calculation by using equation 2 . The transscleral permeability coefficient can be obtained by dividing the transverse diffusivity by scleral thickness.

^{ 15 }

^{−5}M sulforhodamine donor solution for 24 hours. After the tissue was removed and rinsed with the saline solution, it was sectioned into 50-μm-thick pieces on a cryostat. All tissue pieces were collected and incubated in 20 mL of BSS. The sulforhodamine concentration in the solution was measured over time by spectrofluorimetry until it reached a constant value (after ∼1 hour). Assuming 100% sulforhodamine extraction efficiency, the sclera-to-saline distribution coefficient (

*K*

_{D}) was obtained as

*C*

_{sclera}is the concentration in the sclera determined by extraction, and

*C*

_{bath}is the original concentration of the donor solution (9.0 × 10

^{−5}M).

^{ 8 }

^{ 16 }

*C*

_{free}is the free sulforhodamine concentration in the sclera,

*C*

_{bound}is the bound sulforhodamine concentration in the sclera,

*k*

_{1}is the binding rate constant,

*D*

_{lat}is the effective lateral diffusivity of free sulforhodamine in the sclera,

*x*is the lateral position in the sclera, and

*K*

_{eq}is the ratio of free-to-bound sulforhodamine at equilibrium in the sclera,

*C*

_{free}is equal to

*C*

_{bath}. Thus,

*C*

_{free}=

*K*

_{eq}

*C*

_{bound}), Equations 4 and 5can be rewritten as

*z*is the length of the scleral strip above the donor solution. Solving equation 10subject to the conditions in equation 11yields the final expression for sulforhodamine concentration in the sclera as a function of time and position

^{ 16 }:

*erf*is the error function.

*C*

_{exp}is the experimentally measured concentration,

*C*

_{theor}is the theoretically predicted concentration, and

*n*is the number of measurements.

*P*< 0.0001). Over time, the sulforhodamine concentration at each position increased with time (ANOVA,

*P*< 0.0001).

*K*

_{D}) experimentally to be 13.6, which indicates a strong binding between sulforhodamine molecules and the sclera tissue. The free-to-bound sulforhodamine ratio (

*K*

_{eq}) was then calculated with equation 8to be 0.08. This left sulforhodamine diffusivity (

*D*

_{lat}) as the only unknown variable. The diffusion model was then fitted to the experimental data, as shown in Figure 4 , which yielded an effective sulforhodamine diffusivity of

*D*

_{lat}= 3.82 × 10

^{−6}cm

^{2}/s.

*D*

_{trans}= 1.28 ± 0.22 × 10

^{−6}cm

^{2}/s, which corresponds to a permeability of 2.15 ± 0.37 × 10

^{−5}cm/s. These values compare well with previously reported experimental data for scleral permeability of other molecules of similar molecular weight

^{ 17 }and to a predicted diffusivity of 2.5 × 10

^{−6}cm

^{2}/s for sulforhodamine generated using an independent theoretical model described previously (calculation not shown).

^{ 15 }

*D*

_{lat}= 3.82 × 10

^{−6}cm

^{2}/s) and transverse (

*D*

_{trans}= 1.28 × 10

^{−6}cm

^{2}/s) diffusivity values generated in this study indicates that diffusing in the lateral direction occurs approximately three times faster than in the transverse direction. Although a rigorous analysis of statistical significance is difficult due to the way that lateral diffusivity was determined, this threefold difference may be insignificant due to experimental variability. If there is a significant difference, then the larger diffusivity of lateral diffusion might be explained by the lateral orientation of collagen fibers in the sclera. Diffusion parallel to these fibers might encounter less hindrance than diffusion across the fibers, which might be more torturous. However, the importance of the collagen fibers is not clear, since diffusion in the sclera is expected to be governed by the extracellular glycosaminoglycan matrix,

^{ 15 }which is randomly oriented

^{ 13 }and thus should not favor diffusion in any particular direction.

^{2}× (3.82 × 10

^{−6}cm

^{2}/s)

^{−1}= 2.6 × 10

^{5}s = 3.0 days. Based on a similar calculation, it should take at least 6 weeks for sulforhodamine to diffuse from a localized source throughout all the sclera in a human eye (using a characteristic distance of 3.75 cm, which is half the circumference of the human eye

^{ 13 }).

^{ 8 }lateral diffusion of proteins and other macromolecules is expected to be one or more orders of magnitude slower than that of sulforhodamine.

^{−6}cm

^{2}/s. This calculation enabled the prediction that a point source of sulforhodamine would require 6 weeks to diffuse throughout all the sclera in a human eye. Comparison of experimental measurements of lateral diffusion within the sclera to transverse diffusion across the sclera indicated similar effective diffusivities, although lateral diffusion was approximately three times faster. A theoretical model for one-dimensional diffusion in the sclera was developed and shown to match experimental data with an MAPE of 39%. This model can be used to predict rates of lateral diffusion in the sclera for various drug delivery scenarios. Altogether, this study shows that lateral diffusion in the sclera is a slow process that localizes drug distribution on the millimeter scale for hours to days. Lateral diffusion over larger surface areas could occur over longer times—for example, during extended release drug delivery from an implant.

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**