A promising technique for enhancing the

A promising technique for enhancing the corneal permeability to ophthalmic drugs involves the use of ultrasound. In medical procedures performed in Russia with the aid of ultrasound systems operating at frequencies between 500 and 900 kHz, and intensities on the order of 0.2 W/cm2, a substantial (up to 10-fold) increase in drug delivered through the cornea was reported (Nuritdinov 1981; Panova et al. 1995; Tsok 1979). Zderic et al. (2004a, 2004b) reported increases in corneal permeability with the aid of ultrasound, in both in vitro and in vivo experiments. In these experiments, an ultrasound transducer operating at 880 kHz, with intensities between 0.19 and 0.56 W/cm2, was employed. Ultrasound application in vitro at frequencies of 400 kHz to 1 MHz, intensities of 0.3–1.0 W/cm2, and exposure duration of 5 min resulted in an increase in corneal permeability of 32%–47% for tobramycin, 46%–126% for sodium fluorescein and 32%–109% for dexamethasone sodium phosphate (Nabili et al. 2013). In an in vivo study, ultrasound application at frequencies of 400 and 600 kHz caused 2.8- and 2.4-fold increases, respectively, in drug concentration in aqueous humor samples as compared with sham treated samples (Nabili et al. 2014).
The mechanisms underlying the enhancement of drug delivery with the aid of ultrasound are not well understood, and the level of enhancement for a given set of exposure parameters is difficult to quantify. One possible mechanism is acoustic streaming arising from the ultrasound SAR405 absorbed by the fluid. Another proposed mechanism is an alteration of the corneal structure caused by cavitation. In experiments with rabbit eyes, Zderic et al. (2004b) observed a strong increase in drug transport with measured increase in cavitation activity. In the eyes with large increases in permeability (relative to the no-ultrasound case), damage was observed in the first and second epithelial cell layers. The damage appeared to be transient, with pitting disappearing within approximately 90 min.
Toward the goal of quantifying the relationship between corneal porosity and drug transport, mathematical models can be useful. Edwards and Prausnitz (2001) used a brick-like model of the cornea to predict the permeability of the human eye to different compounds. Cooper and Kasting (1987) modeled the cornea as a laminated membrane, with the epithelium being a lipophilic layer with aqueous pores. They proposed a diffusion coefficient with an exponential dependence on molecular weight. In the work described here, the cornea is modeled as a three-layer porous medium. Our assumptions are threefold: (i) the physical effects of ultrasound can be adequately captured using a model of the epithelium with porosity and thickness that are intensity dependent; (ii) the porosity model can be accurately calibrated via diffusion-cell experiments with rabbit cornea, before and after sonication; and (iii) once the dependence of the porosity on intensity is known, the amount of drug transported for a given set of experimental conditions can be estimated from knowledge of the molecular diffusivity of the drug alone. The model in its present form is confined to cases in which the epithelium is the layer that limits transport through the cornea, and the dominant mechanism is transport between cells (paracellular route), as opposed to transport through cells (transcellular route). As reported in previous studies (Edwards and Prausnitz 2001; Gaudana et al. 2010; Shih and Lee 1990), an important example is the transport of hydrophilic (low-distribution) compounds. The extension of the model to other cases is addressed in the Discussion. The changes in epithelial porosity and epithelial thickness arising from ultrasound exposure are determined using a mathematical inverse method in conjunction with a numerical solution to a diffusion equation. The diffusion-equation solver was used in an iterative fashion—adjusting the porosity and epithelium thickness at each iteration—to yield values that produced the best agreement between computational and experimental measures of dye concentration as a function of time. The computational model calibrated in this manner can then be used to determine the rate of transport of other drugs through the cornea, provided the molecular diffusivity is supplied.