Measurement and Modeling of Diffusion Kinetics of a Lipophilic Molecule Across Rabbit Cornea

Imaging-Based Drug Penetration Profiling in an Excised Sheep Cornea Model

Formulations designed to address ocular conditions and diseases are predominantly administered topically. While in vitro test systems have been developed to assess corneal permeation under extended contact conditions, methods focusing on determining the penetration depth and kinetics of a substance within the cornea itself rather than through it, are scarce. This study introduces a method for time-dependent penetration depth analysis (10 and 60 min) by means of a semiquantitative imaging method in comparison with a quantitative corneal depth-cut technique, employing fluorescein sodium at concentrations of 0.2 and 0.4 mg/mL as a small molecule model substance and sheep cornea as a human surrogate. Excised tissues exhibited sustained viability in modified artificial aqueous humor and maintained thickness (746 ± 43 µm) and integrity (electrical resistance 488 ± 218 Ω∙cm2) under the experimental conditions. Both methods effectively demonstrated the expected concentration- and time-dependent depth of penetration of fluorescein sodium, displaying a significantly strong correlation. The traceability of the kinetic processes was validated with polysorbate 80, which acted as a penetration enhancer. Furthermore, the imaging-based method enabled detecting the retention of larger structures, such as hyaluronic acid and nanoemulsions from the commercial eyedrop formulation NEOVIS® TOTAL multi, inside the lacrimal layer.

Computational Model of In Vivo Corneal Pharmacokinetics and Pharmacodynamics of Topically Administered Ophthalmic Drug Products

INTRODUCTION

Although the eye is directly accessible on the surface of the human body, drug delivery can be extremely challenging due to the presence of multiple protective barriers in eye tissues. Researchers have developed complex formulation strategies to overcome these barriers to ophthalmic drug delivery. Current development strategies rely heavily on in vitro experiments and animal testing to predict human pharmacokinetics (PK) and pharmacodynamics (PD).

OBJECTIVE

The primary objective of the study was to develop a high-fidelity PK/PD model of the anterior eye for topical application of ophthalmic drug products.

METHODS

Here, we present a physiologically-based in silico approach to predicting PK and PD in rabbits after topical administration of ophthalmic products. A first-principles based approach was used to describe timolol dissolution, transport, and distribution, including consideration of ionized transport, following topical instillation of a timolol suspension.

RESULTS

Using literature transport and response parameters, the computational model described well the concentration-time and response-time profiles in rabbit. Comparison of validated rabbit model results and extrapolated human model results demonstrate observable differences in the distribution of timolol at multiple time points.

CONCLUSION

This modeling framework provides a tool for model-based prediction of PK in eye tissues and PD after topical ophthalmic drug administration to the eyes.

How can machine learning and multiscale modeling benefit ocular drug development?

The eyes possess sophisticated physiological structures, diverse disease targets, limited drug delivery space, distinctive barriers, and complicated biomechanical processes, requiring a more in-depth understanding of the interactions between drug delivery systems and biological systems for ocular formulation development. However, the tiny size of the eyes makes sampling difficult and invasive studies costly and ethically constrained. Developing ocular formulations following conventional trial-and-error formulation and manufacturing process screening procedures is inefficient. Along with the popularity of computational pharmaceutics, non-invasive in silico modeling & simulation offer new opportunities for the paradigm shift of ocular formulation development. The current work first systematically reviews the theoretical underpinnings, advanced applications, and unique advantages of data-driven machine learning and multiscale simulation approaches represented by molecular simulation, mathematical modeling, and pharmacokinetic (PK)/pharmacodynamic (PD) modeling for ocular drug development. Following this, a new computer-driven framework for rational pharmaceutical formulation design is proposed, inspired by the potential of in silico explorations in understanding drug delivery details and facilitating drug formulation design. Lastly, to promote the paradigm shift, integrated in silico methodologies were highlighted, and discussions on data challenges, model practicality, personalized modeling, regulatory science, interdisciplinary collaboration, and talent training were conducted in detail with a view to achieving more efficient objective-oriented pharmaceutical formulation design.

Quantitative systems pharmacology of the eye: Tools and data for ocular QSP

Good eyesight belongs to the most-valued attributes of health, and diseases of the eye are a significant healthcare burden. Case numbers are expected to further increase in the next decades due to an aging society. The development of drugs in ophthalmology, however, is difficult due to limited accessibility of the eye, in terms of drug administration and in terms of sampling of tissues for drug pharmacokinetics (PKs) and pharmacodynamics (PDs). Ocular quantitative systems pharmacology models provide the opportunity to describe the distribution of drugs in the eye as well as the resulting drug-response in specific segments of the eye. In particular, ocular physiologically-based PK (PBPK) models are necessary to describe drug concentration levels in different regions of the eye. Further, ocular effect models using molecular data from specific cellular systems are needed to develop dose-response correlations. We here describe the current status of PK/PBPK as well as PD models for the eyes and discuss cellular systems, data repositories, as well as animal models in ophthalmology. The application of the various concepts is highlighted for the development of new treatments for postoperative fibrosis after glaucoma surgery.

Computational modeling of corneal and scleral collagen photocrosslinking

Scleral photocrosslinking is increasingly investigated for treatment of myopia and glaucoma. In this study a computational model was developed to predict crosslinking efficiency of visible/near infrared photosensitizers in the sclera. Photocrosslinking was validated against riboflavin corneal crosslinking experimental studies and subsequently modeled for the sensitizer, methylene blue, administered by retrobulbar injection to the posterior sclera and irradiated with a transpupillary light beam. Optimal ranges were determined for treatment parameters including light intensity, methylene blue concentration, injection volume, and inspired oxygen concentration. Additionally, sensitivity of crosslinking to various parameters was quantified. The most sensitive parameters (in order of greatest to least sensitive) were tissue parameters (including scleral thickness and choroidal melanin concentration), treatment parameters (including treatment duration and inspired oxygen concentration), and sensitizer parameters (including triplet quantum yield).

Biopolymer-based nanoparticles with tunable mucoadhesivity efficiently deliver therapeutics across the corneal barrier

To overcome the natural barriers of the ocular system that limit the topical delivery of therapeutically active molecules to the posterior eye, nanoscale drug carriers can be used to improve transcorneal drug transport. So far, using mucoadhesive drug carriers has been put forward as the most promising strategy to optimize drug transport. However, if the mucoadhesivity of a drug carrier is too high, this might limit the diffusive entry of molecules/drug carriers into the vitreous. In this study, we show how modulating the net charge of biopolymer-based drug carrier particles alters not only their mucoadhesivity but also other important properties, e.g., their stability, drug loading capacity and drug release profiles. Compared to simple aqueous solutions of free drug molecules as used in current treatments, nanoparticulate drug carriers with intermediate mucoadhesivity show improved drug transport across the corneal barrier. Therefore, our study shows that mucoadhesion of drug carrier particles is a feature that needs to be considered with great care - not only for ocular delivery attempts but for all drug delivery approaches dealing with mucosal barriers.

Multi-region finite element modelling of drug release from hydrogel based ophthalmic lenses

Understanding the way in which drug is released from drug carrying hydrogel based ophthalmic lenses aids in the development of efficient ophthalmic drug delivery. Various solute-polymer interactions affect solute diffusion within hydrogels as well as hydrogel-bulk partitioning. Additionally, surface modifications or coatings may add to resistance of mass transfer across the hydrogel interface. It is necessary to consider both interfacial resistances as well as the appropriate driving force when characterizing interface flux. Such a driving force is induced by a difference in concentration which deviates from equilibrium conditions. We present a Galerkin finite element approach for solute transport in hydrogels which accounts for diffusion within the gel, storage effects due to polymer-solute interaction, as well as partitioning and mass transfer resistance effects at the interface. The approach is formulated using a rotational symmetric model to account for realistic geometry. We show that although the resulting global system is not symmetric in the case of partitioning, it is similar to a symmetric negative semidefinite system. Thus, it has non-positive real eigenvalues and is coercive, ensuring the validity of the finite element formulation as well as the numerical stability of the implicit backward Euler time integration method employed. Two models demonstrating this approach are presented and verified with release experimental data. The first is the release of moxifloxacin from intraocular lenses (IOLs) plasma grafted with different polyacrylates. The second accounts for both loading as well as the release of diclofenac from disc shaped IOL material loaded for varied time periods and temperature.

Corneal epithelial permeability to fluorescein in humans by a multi-drop method

Purpose

The permeability of the corneal epithelium to fluorescein P_dc is an indicator of the health of the ocular surface. It can be measured in a clinical setting by determining the accumulation of fluorescein in the stroma following administration of the dye on the ocular surface. Here we demonstrate a new multi-drop method for the measurement of P_dc by a spot fluorometer.

Methods

Twenty-nine healthy participants were recruited for this study. First, a probe-drop of fluorescein (0.35%, 2 μL) was instilled on the conjunctiva. The clearance of the dye from the tears was immediately measured using the fluorometer. Following this, two loading drops (2%; 6 μL each) were administered 10 min apart. Fifteen minutes later, the ocular surface was washed and fluorescence from the stroma F_s was measured. Permeability was calculated using P_dc = (Q x F_s)/ (2 x AUC), where Q is the stromal thickness and AUC is the area under the fluorescence vs. time curve for the loading drops.

Results

After the probe drop, the tear fluorescence followed an exponential decay (elimination rate constant; k_d = 0.41 ± 0.28 per min; 49 eyes of 29 subjects), but the increase in F_s was negligible. However, after the loading drops, the measured F_s was ~ 20-fold higher than the autofluorescence and could be recorded at a high signal to noise ratio (SNR > 40). The intra-subject variability of k_d was insignificant. Since fluorescein undergoes concentration quenching at > 0.5%, the value of AUC for the loading drops was estimated by scaling the AUC of the probe drop. The calculated P_dc was 0.54 ± 0.54 nm/sec (n = 49). A Monte Carlo simulation of the model for the multi-drop protocol confirmed the robustness of the estimated P_dc.

Conclusions

The new multi-drop method can be used in place of the single-drop approach. It can overcome a lack of sensitivity in fluorometers of high axial resolution. The P_dc estimated by the multi-drop method is ~ 11-fold higher than previously reported but closer to the value reported for other drugs with equivalent octanol/water partition coefficient.

Computational modeling of drug transport across the in vitro cornea

A novel quasi-3D (Q3D) modeling approach was developed to model networks of one dimensional structures like tubes and vessels common in human anatomy such as vascular and lymphatic systems, neural networks, and respiratory airways. Instead of a branching network of the same tissue type, this approach was extended to model an interconnected stack of different corneal tissue layers with membrane junction conditions assigned between the tissues. The multi-laminate structure of the cornea presents a unique barrier design and opportunity for investigation using Q3D modeling. A Q3D model of an in vitro rabbit cornea was created to simulate the drug transport across the cornea, accounting for transcellular and paracellular pathways of passive and convective drug transport as well as physicochemistry of lipophilic partitioning and protein binding. Lipophilic Rhodamine B and hydrophilic fluorescein were used as drug analogs. The model predictions for both hydrophilic and lipophilic tracers were able to match the experimental measurements along with the sharp discontinuities at the epithelium-stroma and stroma-endothelium interfaces. This new modeling approach was successfully applied towards pharmacokinetic modeling for use in topical ophthalmic drug design.

Mechanistic modeling of ophthalmic drug delivery to the anterior chamber by eye drops and contact lenses

Ophthalmic drug for the anterior chamber diseases are delivered into tears by either eye drops or by extended release devices placed in the eyes. The instilled drug exits the eye through various routes including tear drainage into the nose through the canaliculi and transport across various ocular membranes. Understanding the mechanisms relevant to each route can be useful in predicting the dependency of ocular bioavailability on various formulation parameters, such as drug concentration, salinity, viscosity, etc. Mathematical modeling has been developed for each of the routes and validated by comparison with experiments. The individual models can be combined into a system model to predict the fraction of the instilled drug that reaches the target. This review summarizes the individual models for the transport of drugs across the cornea and conjunctiva and the canaliculi tear drainage. It also summarizes the combined tear dynamics model that can predict the ocular bioavailability of drugs instilled as eye drops. The predictions from the individual models and the combined model are in good agreement with experimental data. Both experiments and models predict that the corneal bioavailability for drugs delivered through eye drops is less than 5% due to the small area of the cornea in comparison to the conjunctiva, and the rapid clearance of the instilled solution by tear drainage. A contact lens is a natural choice for delivering drugs to the cornea due to the placement of the contact in the immediate vicinity of the cornea. The drug released by the contact towards the cornea surface is trapped in the post lens tear film for extended duration of at least 30min allowing transport of a large portion into the cornea. The model predictions backed by in vivo animal and clinical data show that the bioavailability increases to about 50% with contact lenses. This realization has encouraged considerable research towards delivering ocular drugs by contact lenses. Commercial contacts are, however, not ideal for drug delivery due to the short release durations which may necessitate wearing multiple lenses each day, reducing the viability of this approach. Recent research has focused on designing contacts that retain all critical properties while increasing the release durations to a few hours or a few days. Beagle dog studies with contact lenses containing vitamin E nanobarriers to attenuate drug transport have shown promising results. Human studies using contacts for drug delivery have also been conducted for allergy therapy but drug eluting contacts are not available in the market for any therapy.

Characterization of sensitivity and specificity in leaky droplet-based assays

This paper uses numerical methods to characterize the crosstalk of small fluorescent molecules and molecular probes among aqueous droplets immersed in a continuous phase of hydrocarbons or fluorocarbons in microfluidic systems. Droplet-based biochemical assays rely on the reagents to remain isolated in individual droplets. It has been observed, however, that small and hydrophobic fluorescent molecules can diffuse across the droplet boundary into other drops. The contents among droplets become mixed and homogenized over time. Such cross-contamination can have detrimental effects on the accuracy of droplet-based assays, especially those using fluorescent molecules and the corresponding number of fluorescent droplets for a quantitative readout. This work examines the competing dynamics of the generation of fluorescent molecules in "positive" drops (in response to the presence of molecules or cells of interest), against its leakage into "negative" drops, where such molecules or cells of interest are absent. In ideal droplet assays, the signal-to-noise ratio (SNR)--defined as the fluorescence signal from a positive drop to that from a negative drop--would increase and saturate with time. In a leaky droplet assay, the SNR tends to decay with time. Under certain conditions, however, the SNR from a leaky droplet assay could increase and reach a maximum value before it starts to diminish. This maximum value can be estimated from a dimensionless number relating the rate of leakage relative to the rate of generation of fluorescence signal in the drops. Beyond the time when the SNR peaks, the SNR value, as well as the accuracy of the leaky droplet assay continues to degrade. In the absence of immediate experimental remedies to completely eliminate the crosstalk of molecules among drops, performing detection at the optimal time point becomes critical to minimize errors in leaky droplet assays.

Penetration of fluorescein across the rabbit cornea from the endothelial surface

PURPOSE

To model the kinetics of penetration of fluorescein across the cornea from the endothelial surface.

METHODS

Rabbit corneas mounted in vitro were exposed to fluorescein at their endothelial surface. Trans-corneal fluorescence were acquired periodically for 6 h using a custom-built confocal microfluorometer. The profiles were then employed to fit a kinetic model for calculation of permeability and diffusion coefficients across the cellular layers and stroma, respectively.

RESULTS

At the endothelium-stroma and stroma-epithelium interfaces, the fluorescence profile exhibited sudden jumps. In each case, the fluorescence was higher at the stroma, indicating reduced partitioning of the dye into the lipid-rich cellular layers. The stroma did not swell significantly until 180 min of perfusion. The fluorescence profiles reached a pseudo-steady state at ~6 h. A transport model, which included convective and diffusive fluxes into the stroma, showed a good fit to the trans-corneal profiles at different time points. The estimated permeability coefficients for the cellular layers were close to the values reported previously, but the diffusion coefficient of fluorescein in the stroma was found to be smaller than the values obtained previously using Ussing chambers.

CONCLUSIONS

The penetration of fluorescein could be modeled accurately by a combination of diffusion and convection.