Numerical investigation of topical drug transport in the anterior human eye
Introduction
Drug delivery to the eye can be broadly classified according to the target locations, namely anterior and posterior segments (Fig. 1). Accessibility of the exposed corneal surface renders it a convenient site for the administration of ophthalmic medications, and topical drug application has been the most natural choice for the treatment of eye diseases, especially anterior segment eye diseases such as glaucoma [1], cataract [1] and iritis [2]. Currently, more than 90% of the marketed ophthalmic medications are applied topically in the form of eye drops or ointment [3]. Posterior eye diseases usually require high vitreal drug concentrations, and it is more difficult for topically applied drugs to reach the vitreous body. Therefore, drug delivery to the posterior eye is usually implemented clinically by other means such as transscleral delivery [4], intravitreal injection/implant [5], and vitreous substitution [6].
Currently, the efficacy of topically applied drugs in the treatment of anterior eye diseases is mainly limited by the difficulties in delivering enough doses to the target tissues, including loss on the ocular surface due to tear dilution and turnover [7], and physiological barriers [8] such as the corneal and sclera epithelial layers. It has been shown that less than 5% of the drug dose penetrates the cornea and reaches the aqueous humor (AH) in the anterior chamber [9]. After penetrating into the AH, a smaller portion of the drug can actually reach its target tissue. On the other hand, many of these ophthalmic drugs have a narrow therapeutic window and high drug doses required to overcome the poor drug availability may result in severe toxicity in eye tissues [10]. Therefore, appropriate drug usage is important and understanding of the transport process of topically applied drugs becomes crucial. To date, a direct and non-invasive measurement of spatio-temporal distribution of drug concentration in the eye is still practically impossible, and numerical models can be useful tools in understanding the ocular drug delivery process and predicting local drug concentration in the anterior eye.
After penetrating the cornea, transport of the topically applied drug is closely related to the AH flow in the anterior chamber. Fig. 1 illustrates anatomical structures of the human eye. There are two chambers in the anterior segment of the eye, the anterior chamber (between the cornea and the iris) and posterior chamber (behind the iris and anterior to the lens). Both of these two chambers are filled with the AH, a transparent and gelatinous fluid. The AH enters the eye in the posterior chamber by secretion and ultrafiltration at the ciliary body, and flows into the anterior chamber through the pupil between the lens and iris. Most (70–90%) of the AH leaves via the trabecular meshwork (TM) while the remaining exits through the uveoscleral outflow [11]. In addition to secretion and outflow, there are various mechanisms that may be responsible for causing the AH flow, such as temperature nonuniformity, phakodenesis (vibration of the lens as the head or eye moves) and rapid eye movement during sleep. Heys and Barocas [12] and Canning et al. [13] adopted a Boussinesq model in the study of AH natural convection and explained several features observed in traumatized eyes, such as hyphemas, keratic precipitates, hypopyons, and Krukenberg’s spindles. Kumar et al. [14] numerically studied AH fluid dynamics in a rabbit eye, and investigated effects of parameters such as the pupil size, eye orientation, and temperature difference across the eye. They concluded that the pupil size has little influence on the intra-ocular pressure (IOP), whose increase is believed to be the cause of glaucoma. Fitt and Gonzalez [15] conducted thorough investigation of various physical mechanisms responsible for causing AH flow, and concluded that natural convection induced by temperature difference between the corneal surface (which, under normal conditions, is exposed to the ambient environment) and interior tissues of the eye, is the dominant one.
Besides providing nutrients, the AH flow also has influences on heat and mass transport across the eye. In the early study of heat transfer in the eye [16], [17], [18], [19], the AH was assumed to be stagnant. A 2D eye model developed by Ooi and Ng [20], [21] and a 3D eye model developed by Karampatzakis and Samaras [22] considered the coupling of the AH flow and heat transfer in the eye. Their results suggested that AH natural convection has non-negligible influences on the temperature distribution in the anterior eye. Most of the research work on heat transfer in the eye has been focused on the consequences of thermal disturbances such as the extreme ambient temperature (from −10 °C to 60 °C) [23], laser-thermokeratoplasty [24], eye tumor [25], and laser surgery [26]. Excellent agreement between experimental and numerical results reported in these studies highlights the versatility of numerical modeling in the study of heat transfer in the eye.
On the numerical modeling of ocular drug delivery, posterior-segment drug delivery has aroused lots of interests [27], [28], [29], [30]. In contrast, transport of topically applied drugs in the anterior eye has received far less attention. Avtar and Tandon [31] proposed a zero-dimensional model of drug transport in the anterior segment in which the AH was assumed to be stationary, and predicted the temporal evolution of the total concentration of topically applied drugs in the anterior chamber. In a one-dimensional model by Ferreira et al. [32], drug transport from a therapeutical contact lens to the anterior chamber was studied, but the AH was also assumed to be stationary. Wyatt et al. [33], [34] proposed ‘a schematic and simplified’ parabolic profile for the convective AH flow in the study anterior segment kinetics with focally applied mydriatics, and the convective AH flow was believed to play a substantial role in pharmacokinetics of the anterior segment. Recently, Lin and Yuan [35] numerically studied the transport of ethacrynic acid (ECA), an ophthalmic drug for the treatment of primary open-angle glaucoma (POAG), from the precorneal region to trabecular meshwork, but their model only incorporated secretion-drainage flow of the AH, and neglected AH natural convection. Since AH velocities generated by natural convection are at least the same order of magnitude as those caused by AH secretion-drainage and increase rapidly with increasing temperature difference across the eye [12], it is necessary to explore how temperature difference, hence AH natural convection, affects transport of topically applied drugs in the anterior eye. Wyatt [36] proposed a simplified numerical model to study drug transport in the anterior segment, but only a fixed temperature difference of 1 K between the cornea and the iris was assumed and a highly simplified analytical formulation of Canning et al. [13] was used to predict a maximal convectional speed of AH.
In this paper, full-scale 2D and 3D finite element numerical models of the human eye are developed, which incorporate essential components of the eye (cornea, sclera, anterior chamber, posterior chamber, lens, vitreous, iris, trabecular meshwork and ciliary body), and consider necessary physical processes, including heat transfer from the cornea to the posterior segments of the eye, AH secretion-drainage and natural convection flow in the anterior and posterior chambers, and diffusive and convective transport of topically applied drugs to various target tissues in the anterior eye. Effects of temperature difference across the eye, hence natural convection of the AH flow, on the transport of topically applied drugs, as well as influences of eye orientation and means of drug administration (eye drops or ointment), are investigated in detail.
Section snippets
Eye geometry
An axisymmetric 2D eye model (Fig. 1(a)) and a 3D eye model (Fig. 1(b)) are developed based on the anterior segment geometry data in [35] and posterior segment geometry data in [20], including the cornea, sclera, anterior chamber, posterior chamber, lens, vitreous, iris, TM and ciliary body (CB). Geometric dimensions of the eye models are listed in Table 1. When the eye is up-facing, the gravitational force is parallel to the eye’s optical axis, and the axisymmetric 2D model can be used. When
Temperature distribution in the entire eye
Fig. 4(a) and (b) show the temperature distribution and isothermal lines in the up-facing eye and horizontally-facing eye (side view), respectively, in which the ambient is at the room temperature of 298 K. It can be seen in Fig. 4(a) and (b) that temperature increases gradually from the cornea to the interior eye, and effects of the eye orientation are perceptible only in the anterior eye, where the isotherms bend towards the exterior on the upper half of the eye and towards the interior on the
Validation
In order to validate our computational model and numerical results, we first compared our results of the AH velocity in the x = 0 plane (side view) of the horizontally-facing eye with that in [23], and excellent qualitative agreement can be seen in Fig. 10, although the geometric models are slightly different. In addition, the AH velocity we obtained has the same order of magnitude (10−4 m/s) as given by [23].
The temperature results are compared with the experimental data from [16] in Fig. 11. In
Effects of means of drug administration
In Fig. 14, we plot the time-dependent changes of drug concentration in the TM with three different methods of drug administration, with the eye facing upward. In the first drug administration method, drug concentration on the precorneal surface is maintained at C0 = 75 μM, which is an ideal condition. The other two methods correspond to the application of eye drops and eye ointment on the precorneal surface with the initial concentrations of drug being C0 = 75 μM. As is shown in Fig. 14, drug
Effects of ambient temperature
Fig. 15 shows the AH velocity field and temperature distribution when the ambient temperature is 306 K, 310 K, 312 K, and 314 K, in an up-facing eye, where the arrows indicate both the direction and magnitude of the local AH velocity, and the colors represent the magnitude of temperature. The effects of ambient temperature on the peak drug concentration are more clearly demonstrated in Fig. 16. When the ambient temperature is lower than the body temperature, increase of the ambient temperature
Conclusions
In this paper, coupled numerical models of heat transfer, AH flow and drug transport are developed to investigate delivery of topically applied drugs in the anterior human eye. Our numerical models are validated by comparison with experimentally measured data and simulation results in the literature. Effects of the ambient temperature and eye orientations are studied. The following are the major conclusions of the present study.
- (1)
Heat transfer in the eye has a significant influence on the AH
Acknowledgements
This work was supported by Natural Science Foundation of China (No. 51175196), Natural Science Foundation of Hubei Province (No. 2011CDB294), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.
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