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1 DEVICES AND MECHANISMS FOR OPHTHALMIC DRUG DELIVERY By CHHAVI GUPTA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010
2 2010 Chhavi Gupta
3 To my family and friends
4 ACKNOWLEDGMENTS My first and foremost gratitude goes to my research advisor Dr. Anuj Chauhan, without whose continual support it would have been impossible to do this research work. He has been a huge inspiration and a great mentor who has helped me in all phases of my graduate life. I have learnt from him not just on technical front but also on personal front and would c ontinually do that in the coming years. Also, I would like to thank Dr. SP Srinivas from Indiana University with whom I conducted work on understanding mechanism of transport of hydrophobic molecules across co rnea. I would also like to acknowledge my dissertation defense committee members Dr. Yilder Tseng, Dr. Tanmay Lele and Dr. Malisa Sarntinoranont for their extremely useful comments and discussions about my work. I extend my thanks to Dr. Oscar D. Crisalle and Dr. Spyros Svoronos for providing me an opportunity to be a teaching assistant in their respective courses. I have had an extremely friendly and understanding atmosphere in my lab and all that is attributed to my advisor and my research group members. I would like to thank Dr. Yash Kapoor who has been a great friend and helped me to get through some tough times in initial stages of my research. D r. Brett Howell has been an awesome group member and I have learnt a lot from him in sense of discipline, dedication and commitment towards the wor k. Also, I would like to thank Dr. Heng Zhu and Dr. Jinah Kim for teaching me lab techniques and for all the intellectual discussions I had with them. Also, I am extremely thankful to Chen Chun Peng and Hyun jung Jung for being extremely caring and underst anding lab members. Lokendra Bengani has been an excellent friend and has been a great support in last stages of my research.
5 Also, I would like to extend a special mention to Rahul Kekre, a graduate student in University of Florida, for all the entertaini ng discussions I had with him during my day break. Also I would like to extend my thanks to some amazing undergraduate students Dane Cohen and Andrew Daechsel whom I had a chance to interact with during my graduate stay. They have an exceptional learning a cumen and performed work with great devotion and commitment. Also, I would like to acknowledge James Hinnat and Dennis Vince for providing technical support in my research. Also I would extend my thanks to staff members specially Shirley Kelly, Deborah S andoval and Sean Poole for all their help in making my stay at University of Florida smooth and comforting. Lastly, but definitely not the least, I extend my sincere thanks to my mother and father, Mrs. Kumud Gupta and Mr. Sumod Kumar Gupta, for all their sacrifices in providing me best possible education. Words are not enough to express my devotion and gratitude towards them and I hope I get same blessings, love and care from them for the rest of my life. Also, I have a great respect and gratitude towards my friends from my undergraduate college, who have been a constant motivation and have been there with me during my tough times.
6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 9 LIST OF FIGURES ................................ ................................ ................................ ........ 10 ABSTRACT ................................ ................................ ................................ ................... 12 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ ..... 15 2 TRANSCORNEAL PENETRATION OF RHODAMINE B ACROSS RABBIT CORNEA ................................ ................................ ................................ ................ 26 2.1 Introduction ................................ ................................ ................................ .... 26 2.2 Materials and Methods ................................ ................................ ................... 26 2.3 Results ................................ ................................ ................................ ........... 27 2.3.1 Transcorneal P enetration of Topical Rhodamine B ............................. 27 2.3.2 Model for Representing the RhB Penetration Kinetics ......................... 28 2.3.3 Transport across the Cellular Layers ................................ ................... 29 2.3.4 Transport across the Stroma ................................ ............................... 31 2.3.6 Parameter Estimation ................................ ................................ .......... 33 2.3.7 Initial Guess for Parameter Estimation ................................ ................ 33 2.4 Parameter Sensitivity Analysis ................................ ................................ ....... 36 2.4.1 Contour Plots and Correlation Coeffecients ................................ ......... 36 2.4.2 Single Parameter Sensitivity Analysis ................................ ................. 38 2.5 Prediction of In Vivo Pharmacokinetics ................................ .......................... 39 2.6 Discussion ................................ ................................ ................................ ...... 41 2.6.1 Modeling Interphase and Intraphase Transport ................................ ... 41 2.6.2 Model Validation ................................ ................................ .................. 42 2.6.3 Asym ptotic Behavior ................................ ................................ ............ 45 2.7 Conclusions ................................ ................................ ................................ .... 47 3 TRANSCORNEAL PENETRATION OF FLUORESCEIN ACROSS RABBIT CORNEA ................................ ................................ ................................ ................ 59 3.1 Introduction ................................ ................................ ................................ .... 59 3.2 Materials and Methods ................................ ................................ ................... 59 3.3 Results and Discussion ................................ ................................ .................. 60 3.3.1 Fluorescence Profiles ................................ ................................ .......... 60 3.3.2 Swelling of Cornea ................................ ................................ .............. 62 3.3.3 Mathematical Model for Fl Transport in Cornea ................................ ... 63 188.8.131.52 Transport in stroma ................................ ................................ 63
7 184.108.40.206 Transport in endothelium ................................ ........................ 64 220.127.116.11 Transport in epithelium ................................ ........................... 66 18.104.22.168 Parameter estimation ................................ .............................. 67 3.4 Sensitivity Analysis ................................ ................................ ......................... 69 3.4.1 Contour Plots and Correlation Coefficients ................................ .......... 69 3.4.2 Sensitivity Index ................................ ................................ ................... 70 3.5 Discussion ................................ ................................ ................................ ...... 71 3.6 Conclusion ................................ ................................ ................................ ..... 72 4 DRUG TRANPORT IN HEMA CONJUNCTIVAL INSERTS CONTAINING PRECIPITATED DRUG PARTICLES ................................ ................................ ..... 79 4.1 Introduction ................................ ................................ ................................ .... 79 4.2 Materials and Methods ................................ ................................ ................... 79 4.2.1 Fabrication of Inserts ................................ ................................ ........... 79 4.2.3 Drug Release ................................ ................................ ....................... 81 4.3 Results and Discussion ................................ ................................ .................. 81 4.3.1 Estimation of Diffusivity in the p HEMA Inserts ................................ .... 81 4.3.2 Measurement of Diffusivity in the p HEMA inserts ............................... 82 4.3.3 Design I I nsert ................................ ................................ ..................... 86 22.214.171.124 Effect of length on drug release ................................ .............. 86 126.96.36.199 Effect of drug loading ................................ .............................. 87 188.8.131.52 Effect of crosslinking ................................ ............................... 88 4. 3.3.4 Effect of convection ................................ ................................ 88 184.108.40.206 SEM imaging of inserts ................................ ........................... 89 220.127.116.11 Model ................................ ................................ ...................... 89 4.3.4 Design II Insert ................................ ................................ .................... 96 18.104.22.168 Effect of length ................................ ................................ ........ 96 22.214.171.124 Effect of drug loading ................................ .............................. 96 126.96.36.199 Effect of convection ................................ ................................ 96 188.8.131.52 Mechanisms ................................ ................................ ........... 97 184.108.40.206 Effect of crosslinking in shell ................................ ................... 98 4.3.5 Bioavailability of Conjunctival Inserts ................................ ................... 99 4.4 Conclusion ................................ ................................ ................................ ... 101 5 DRUG DELIVERY BY PUNCTAL PLUGS ................................ ........................... 120 5.1 Introduction ................................ ................................ ................................ .. 120 5.2 Materials and Methods ................................ ................................ ................. 120 5.2.1 Punctal Plug Fabrication ................................ ................................ .... 120 5.2.2 Drug Release ................................ ................................ ..................... 121 5.3 Results ................................ ................................ ................................ ......... 121 5.3.1 Mechanisms of Release ................................ ................................ .... 123 5.3. 2 Effect of Convection ................................ ................................ .......... 124 5.4 Model for the Zero Order Release ................................ ................................ 124 5.5 Pharmacokinetics of Cyclosporine A Delivery via Restasis and Punctal Plugs ................................ ................................ ................................ ............ 126
8 5.5.1 Pharmacokinetics of Cyclosporine A Delivery via Restasis ............ 127 220.127.116.11 Aqueous phase mass balance ................................ .............. 128 18.104.22.168 Oil phase mass balance ................................ ....................... 129 22.214.171.124 Drug balance ................................ ................................ ........ 129 126.96.36.199 Geometric relationship ................................ .......................... 130 188.8.131.52 Bioavailability ................................ ................................ ........ 130 5.5.2 Pharmacokinetics of Cyclosporine A Delivery via Punctal Plugs ....... 1 31 5.6 Conclusion ................................ ................................ ................................ ... 132 6 CONCLUSION ................................ ................................ ................................ ..... 138 LIST OF REFERENCES ................................ ................................ ............................. 140 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 147
9 LIST OF TABLES Table page 2 1 Description of the model parameters ................................ ................................ .. 55 2 2 The optimal values of the model parameters obtained by minimizing the total error between the model prediction and experimen tal data for RhB concentration in cornea at various times ................................ ............................ 56 2 3 Coefficient of correlation between all the model parameters obtain ed by fixing all parameters except the two chosen parameters ................................ ............. 57 2 4 Characteristic time scales for the principal mechanisms include d in the model. ................................ ................................ ................................ ................. 58 3 1 Values of parameter in the model and their sensitivity to the model ................... 78 3 1 Correlation coefficients are calculated for limiting contours encompassing the 78 4 1 Values of parameters used to estimate theoretical diffusivity inside HEMA ..... 119 4 2 Values of parameters used in fitting the model to experimental results for release of drug from design I insert ................................ ................................ .. 119 5 1 Physiological parameters used for the pharmacokinetic model ........................ 137
10 LIST OF FIGURES Figure page 1 1 Cornea as a Oil:Water:Oil multi laminate ................................ ........................... 24 1 2 Schematic and Image of the drug loaded punctal plug (not to scale). ................ 25 2 1 Trans corneal penetration of RhB after topical administration across rabbit cornea mounted in vitro ; Y axis represents fluorescence in arbitrary units (AU) ................................ ................................ ................................ .................... 48 2 2 Transport across the cellular layers ................................ ................................ .... 49 2 3 Partition equilibrium of a lipophilic topical drug ................................ ................... 50 2 4 Comparison of model predictions (solid lines) and experimental measurements (circles) for transient fluorescence profiles in corne a at t = 6, 30, 60, and 140 min. ................................ ................................ ........................... 51 2 5 Contour plots of error, i.e., square of the difference between the model predictions and experimental values for Rhodamine B concentration in cornea (eq 13) ................................ ................................ ................................ .... 52 2 6 Contour plots of error, i.e., square of the difference b etween the model predictions and experimental values for Rhodamine B concentration in cornea (eq 13). ................................ ................................ ................................ ... 53 2 7 Comparison of ex perime ntal data by Guss et al., and model prediction for spatially averaged transient epithelium concentration of RhB in rabbit cornea ... 54 3 1 Transient concentration profiles of Fluorescein in rabbit cornea, when endothelium side was exposed to a fixed concentration of the dye. ................... 73 3 2 Plot of concentration of fluorescein at stroma endothelium interface vs concentration in endothelium(cytoplasm in endothelium) with time as parameter. ................................ ................................ ................................ .......... 74 3 3 Transient swelling of corneal layers specifically, (A)Stroma and (B) Epithelium. ................................ ................................ ................................ .......... 75 3 4 Comparison of model predictions and experimental profiles of fluorescein concentration in stroma for short times (t < 3 hours) ................................ .......... 76 3 5 Contour plots are plotted by picking two parameters and fixing all other parameters ................................ ................................ ................................ ......... 77
11 4 1 Schemati c representation of Design I (A) and Design II (B) inserts (not to scale). ................................ ................................ ................................ ............... 105 4 2 Estimation of diffusivity of cyclosporine A in p HEMA insert ............................. 106 4 3 Effect of length on release profiles from design I conjunctival inserts (drug loading =20%). ................................ ................................ ................................ 107 4 4 Effect of drug loading ................................ ................................ ........................ 108 4 5 X SEM images of Inserts loaded with cyclosporine A ................................ ....... 110 4 6 Scaled drug Release profiles from Design I inserts with various drug loadings 111 4 7 Model for drug release from a cylindrical rod (conjunctival insert) that contains drug at concentrations C p which is above the solubility limit, and so a f raction of the drug precipitates as particles ................................ .................. 112 4 8 Comparison of model predictions and experimental measurements of drug release without convection and with convection from Design I inserts. ........... 113 4 9 Effect of length on release profile of design II insert (dru g loading 20%) on Cumulative release, and % release. ................................ ................................ 114 4 10 Release profiles from 7.5 mm long design II conjunctival inserts ..................... 115 4 11 Image of a soaked design II insert with a sony T 700 digital camera and an enlarged image of the crack taken at higher reso lution by an optical microscope. ................................ ................................ ................................ ...... 117 4 12 Dependence of % change in weight of gels due to swelling in water on HEMA % in HEMA:EGDMA gels. ................................ ................................ ................. 118 5 1 X SEM images of punctal plugs with 20% drug loading. ................................ .. 134 5 2 Effect of crosslinking on cumulative drug release profiles from the punctal plugs with 20% drug loading (131 g) ................................ .............................. 134 5 3 Effect of increased drug loading on cumulative drug release profiles from the punctal plugs with 100X crosslinking. ................................ ............................... 135 5 4 Effect of increased convection on cumulative drug release profiles from the punctal plugs with crosslinking of 100X and drug loading of (A) 20% (131 g) and (B) 40% (225 g ) ................................ ................................ ................. 135 5 5 Drug release profile of plugs totally covered with silicon (only ends are exposed, sides are covered) ................................ ................................ ............. 136
12 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DEVICES AND MECHANISMS FOR OPHTHALMIC DRUG DELIVERY By Chhavi Gupta August 2010 Chair: Anuj Chauhan Major: Chemical Engineering Currently millions of people in the United States suffer from eye ailments such as glaucoma, infections, cataract, macular degeneration dry eyes etc. and the number is likely to increase due to the continuous increase in the mean age in the c ountry. Most current ophthalmic drugs are delivered through eye drops, which are relatively inefficient due to rapid clearance from the ocular surface. Improvements in ophthalmic drug delivery require a th o rough understanding of various transport mechani sms in the eyes so that optimal delivery vehicles and devices could be developed. This thesis focuses on understanding and modeling various transport processes in the eyes to predict the effectiveness of var ious drug delivery approaches. The thesis also f ocuses on development of novel devices for drug delivery, and modeling release from the devices i n vitro and predicting the release behavior in vivo. Ophthalmic drugs that are instilled via eye drops get cleared through tear drainage from eyes to the nose, and through transport across various ocular epithelia. We focused on understanding each of these pathways individually, and then combining these int o a comprehensive model that can be used to predict the bioavailability of drugs delivered through eye drops or through any other device. While permeability
13 values are reported in literature for transport of drugs across cornea and conjunctiva, these are based on assumptions of pseudo steady state which are likely not accurate. To understand the detailed transport mechanisms in the eyes, we exposed an excised rabbit cornea to fluor e scent drug analogs and measured the time and position dependent fluorescen ce through a confocal microscope. The profiles were than fitted to mechanistic mul t iscale diffusion binding models to obtain various transport parameters. These studies were conducted for a hydrophobic molecule Rhodamine B and a hydrophilic molecule fluo rescein. In future, similar studies will be conducted to obtain the detailed models for various ophthalmic drugs. Based on our models and previous existing tear drainage models, we demonstrate that the bioavailability increases when drugs are delivered t hrough extended release devices rather than through eye drops. We thus also focused on developing some extended release devices for ocular applications particularly for treatment of dry eyes. We developed conjunctival inserts and puncta plugs that can del iver dry eye drug cyclosporine A for about 3 months at therapeutic doses. These devices will likely increase bioavailability and also improve patient compliance. These devices were prepared by thermal polymerization in presence of drug at high loadings t o create inserts and plugs containing particles of drug dispersed in the matrix. The drug release rates were measured to explore the effect of length, drug loading, crosslinking, and mixing in the release medium. Mathematical models were developed and simu lated to understand the mechanism of transport of drug molecules inside these polymeric devices. A model combining tear drainage and tear balance is u sed to predict that our plugs can deliver similar amount of drug as Restasis eye drops, the only approved medication for dry eyes.
14 The results from this thesis will hopefully lead to a better understanding of various transport mechanisms in eyes, and to development of better drug delivery vehicles. While the main focus of this work is in ophthalmology, the m echanisms for transport across epithelia and also from drug delivery devices may find applications in other areas of biomedical engineering.
15 CHAPTER 1 INTRODUCTION More than 100 million people in the United States suffer from mild or severe eye ailments. Eye drops are the most common treatment for most of the ocular disease [1,2] But, it has been well established that drug delivered through eye drops have very less bioavailability (<5%). When a drug is delivered through eye drops, it leaves the body through two routes. One route is that it gets absorbed across the outer most membrane of the eye named as cornea and other route is getting eliminated along with the tears through the tear drainage. M ost of the ocular drugs have to traverse through cornea to reach the target tissues Therefore bioavailability of drugs delivered through eye drops or any other ocular device would be determined by the amount absorbed across the cornea relative to the amou nt eliminated through tear drainage. Therefore, there is a need to understand the transport of drugs or eye drops in front surface of the eye and based on this develop better ophthalmic treatments In this research we have mainly focused on developing drug delivery device s for dry eye treatment which is a medical condition in which there is a lack of moisture or tear film on the corneal surface D evices such as conjunctival inserts and punctal plugs have been proposed which could solve the problem of low bi oavailability and improve patient compliance. Eye drops have low bioavailability because m ore than 90% of the drug instilled is lost from the ocular surface by tear drainage towards the nose and only a small fraction gets absorbed across the cornea, scler a, and/or conjunctiva. The rate of tear drainage is determined by the blink action, which pumps the tears from the ocular surface into the nasolacrimal duct. Consequently, the topically applied drug is absorbed across the nasal mucosa into systemic circula tion. This fraction of the applied drug along with the
16 drug absorbed across the conjunctival epithelium may provoke systemic side/adverse effects. Thus, topical administration, besides having the potential for systemic toxicity, results in a rapid decay o f the drug concentration on the ocular surface [1 5] Since half life of the drug on the ocular surface is only 4 6 mi n [1,2] [3,4] and because of potential for systemic toxicity, there is a need for rational design of topical drugs such that kinetics of their penetration into the intraocular structures of the eye is maximized. As indicated above, most topical drugs access the intraoc ular structures by penetration across the cornea. Trans scleral penetration is known to play a role only for a few drugs [1,2,4,5] The cornea is a transp arent structure with a central matrix of connective tissue called the stroma bounded by cellular layers. The anterior cellular layer is the epithelium. This layer is stratified into ~5 6 layers and is ~40 m thick in humans. The superficial epithelium form s the main barrier to the penetration of topically applied hydrophilic drugs as exhibits multi stranded tight junctions  Accordingly, lipophilic drugs penetrate the epithelium readily presumably by dissolving in the l ipid bilayers of the plasma membrane and subsequent movement by the transcellular route. For further transport towards the anterior chamber, however, the ability to partition into the stroma would be an important consideration for lipophilic drugs. In fact the stroma being hydrophilic with > 80% water, offers no more resistance than an equivalent thickness of wa ter layer for most topical drugs  Thus, although the drugs may diffuse readily in the stroma, poor partiti oning of lipophilic drugs would be a determinant for transport across the cornea. Finally, the posterior layer of the cornea is a monolayer of leaky endothelium, and thus does not offer much resistance to the paracellular movement of solutes. This multi la minate structure (i.e., oil:water:oil layers) of the
17 cornea, shown by the schematic in Figure 1 1 strongly suggests the importance of lipophilicity of the drug for its trans corneal penetration. Pharmacokinetics of topical drugs has been frequently d escri bed by compartmental models [8 9,10 11] which assume that drug concentration becomes uniform throughout the cornea instantaneously after topical administration. Hence, the compartmental models disregard the heterogeneity (i.e., multi laminate structure) of the cornea and diffusive nature of transport in each of its layers as described above. This over simplification h as led to a poor understanding of the dynamics of trans corneal drug transport and consequently to empirical approaches for design of dosage regimen. Several attempts have been made to model the transport across the cornea that takes into consideration of the multi laminate structure [12 14] In the absence of measurements of trans corneal concentration profiles, the distributed parameter models developed to date are based on general considerations, and accordingly, assumptions used in such models have never been tested for robustness of the mo dels. In essence, it is difficult to determine which transport step among those involved in the drug penetration forms a key determinant of the bioavailability and rate of penetration. The overall trans corneal penetration of drug could be broken down in to elementary steps consisting of drug cell binding/partition dynamics, interfacial resistance to transport, and/or transport dynamics inside the cells. Since measurement of concentration vs depth profiles of real drug molecules is not easily achieved, in this study we have employed a fluorescent dye Rhodamine B (RhB) as a lipophilic drug analog  and hydrophilic fluorescein as hydrophilic drug analaog, and determined their concentration profile s across the cornea b y a custom built confocal fluorescence
18 microscope. The transient concentration profiles have been used subsequently to develop a phenomenological non compartmental pharmacokinetic model. Thus, for the first time, the model reported herein exemplifies a mic roscopic approach to correlate the physico chemical properties of drug analogs to their transport properties across the cornea. As discussed above, this thesis also focuses on developing drug delivery devices for dry eye treatments. Currently about one in seven Americans suffer from dry eyes, which is an ocular condition characterized by a dryness sensation in the eye accompanied by a foreign body sensation, discomfort, tearing, burning, and blurred vision. Furthermore, many of the contact lens wearers suff er from mild or severe dry eyes [ [16 20] The dryness in the eyes is potentially caused by tear imbalance that could lead to a loss of proper lubrication, leading to discomfort The dry eye symptoms can ultimately lead to inflammation of ocular surface and epithelial cell damage, which in turn reduces the production of tears or mucus leading to a further decrease both the quality and quantity of tears. Dry eyes symptoms are commonly alleviated by in stillation of artificial tears  which results in an increase in tear volume. The tear volume slowly returns to its steady state value within a fe w minutes  due to tear drainage through the canaliculi, and fluid loss through other means such as evaporation or transport across the ocular epithelia. Therefore only a temporary relief is achieved through the use of eye drops or artificial tear formulations. The residence time and thus the efficacy of the artificial tears could be increased by a ddition of viscosity enhancers [23 25] ; howeve r a high viscosity leads to increased shear on the ocular surface, which causes discomfort.
19 In 1935, it was first proposed that the tear volume could also be increased through occlusion of the tear drainage route by inserting a puncta l plug into the canaliculi  which connects eyes to the nose. Currently, occlusion of puncta through punctal plugs is the most common non medical treatment of dry eyes  I nsertion of puncta plugs has been reported to improve disorders related to inflammation of conjunctival and corneal epithelial cells  and also impr ove vision for dry eye patients  Also, insertion of punctal plugs has been reported to improve tear film stability a nd tear osmolarity  Another potential treatment of dry eyes is administration of cyclosporine A, which is an immuno sup pressant that is often used for pre vention of transplant rejection [31,32] and has shown promising result s in the treatment of dry eyes [33, 34] When applied on the ocular surface, cyclosporine A is believed to inhibit T cell activation [35,36] that are responsible for production of inflammatory substances. These inflammatory substances apart from performing tissue damage also lead to activation of more T cells which in turn produc e more inflammatory substances  Due to low solubility of cyclosporine A in water, its delivery through aqueous eye drops will lead to very low bioavailability and potential side effects due to systemic uptake of the drug. To increase bioavailability and residence time on the ocular surface, other delivery methods such as ointments have also been used, but they may cau se discomfort due to increased shear on the corneal epithelium [38,39] Optimmune [Schering Plough], 0.2% USP ophthalmic ointment has be en approved for veterinary use  but is not being used for human beings because of its poor acceptability by patients  Effect of several permeation enhancers on transcorneal permeation of c yclosporine A has been
20 studied  but in spite of showing promising results their low corneal tolerance limit their usage. Also PLGA implants loaded with cyclosporine A have been developed to deliver the drug through subconjunctival route  but these are invasive leading to reduced patient acceptability. Currently, cyclosporine A is delivered through 2 drops per day of oil in drop vol ume of 28 l) of drug to the eye  While delivery of cyclosporine A through Restasis is therapeutically effective, it still suffers from issues of low bioavailability and low residence time due to rapid clearance of th e eye drops from the ocular surface perhaps leading to limited efficacy. Also, cyclosporine A levels delivered by Restasis are not sufficient to prevent rejection after corneal allograft, therefore a in situ gelling microemulsion fo rmulation has been pro posed in  which claims to have higher concentrations and higher duration of cyclosporine A in cornea as compared to Restasis Since both punctal plugs and cyclosporine A improve dry eye symptoms, albeit due to differ ent reasons, it was speculated and then shown in a clinical study that a combination therapy including punctal plug and instillation of cyclosporine A could ha ve additive therapeutic effect  In the study by Rob erts et al., dry eye patients were randomized to 1 of 3 treatments: cyclosporine A 0.05% ophthalmic emulsion (RESTASIS) twice daily, lower lid punctal plugs (PARASOL), or a plugs cyclosporine A combination. Results showed that the combination therapy pro duced the greatest improvement. While the combination therapy was useful, it still suffers from issues related to rapid clearance of cyclosporine A and difficulties in eye drop instillation particularly for elderly subjects. Here we propose a novel appro ach of providing the
21 combination therapy by designing punctal plugs which also release cyclosporine A for extended periods of time. Plug Design : A punctal plug is inserted into the canaliculi to block drainage of tears from the ocular surface to the nose. According to anatomical studies, each canaliculus has a vertical part that is about 2 mm long and a horizontal part that is about 10 mm long  The diameter of the vertical and the horizontal parts are about 0.3 mm and 0.5 mm, respectively. The joint between these two parts is called the ampulla and its diameter can be up to 2 to 3 mm. The commercial punctal plugs range in length from 1.1 to about 2 mm and in diameter from 0.4 to 1.1 mm. The punctal plugs are insert ed into the vertical portion of the canaliculi. Typical drug eluding puncta plug designs described in patent literature consist of cylindrical cores coated with an impermeable shell to minimize the drug lo ss into the canaliculus tissue [48 50] In such devices, the drug essentially diffuses out from the circular cross section in contact with the tears. The punctal plug design proposed here and shown in Figure 1 2 is novel as on ly a fraction of the plug length is covered with an impermeable shell. The diameter of the shell is 0.94 mm to ensure a snug fit into the canaliculus and diameter of the core is 0.51 mm. Since only a fraction of the total plug length is covered with the s hell, the drug will diffuse out from the circular cross section and also the exposed curved surface. The drug molecules released from the curved surface will diffuse axially through the tear filled canaliculus into the tears in about 15 30 minutes due to the short axial distance of about 1 mm that molecules travel to reach the ocular tear volume. The uptake of the canalicular tissue during this time may not be significant but if this is an issue, the device can be further modified by including an impermeab le sleeve that covers the
22 entire device. The advantage of the design proposed here compared to prior designs proposed in literature is that the release from the curved surface presents another variable that can be optimized to obtain suitable release rates Additionally, if the release occurs only from the circular cross section in contact with the tears, the release rates may depend strongly on the degree of mixing in the tear fluid in the canthus region, and could also be significantly impacted by protei n binding to the cross section. To our knowledge, there are no prior publications on release of ophthalmic drugs from puncta l plugs. Also the design desc ribed above and shown in Figure 1 1 is novel and significantly different from those in patent literature for drug eluding puncta plugs. Also, we propose to deliver cyclosporine A through conjunctival inserts which can be placed in the inferior conjunctival sac of the eyes. Several resear chers have explored ophthalmic drug delivery through inserts [51 56] and some commercially available inserts such as Ocusert and Lacrisert have been used to treat glaucoma and dry eyes, respectively. Lacrisert, the conjunctival insert prescribed for treating dry eyes, is a 3.5 mm long and 1.27 mm diameter insert made of hydroxypropyl cellulose  The insert dissolves over a period of a day after insertion leading to increased tear viscosity and lubrication. The inserts proposed here were chosen to be geometrically similar to lacrisert and thus have a length ranging from 4 mm to 10 mm and a diameter ranging from 1.02 to 1.47 mm. Also, according to a few authors the cylindrical shaped inserts are best for retention in the conjunctival sac [58 60] More over, the inserts proposed here are prepared from HEMA and EGDMA, which are both commonly used in ocular applications such as contact lenses.
23 In addition to t he goal of development of punctal plugs and conjunctival inserts this research also aims to focus on the mechanisms of drug transport in the cylindrical inserts and plugs particularly for situations in which the drug loadings are so high that the drug is dispersed in the gel as particles. The drug transport in such systems involves a combination of particle dissolution, diffusion in the gel, and diffusion in the surrounding fluid. Also, drug transport in the gel is impacted by drug binding on the polymer. This research focuses on developing a comprehensive model that accounts for each of these issu es. Furthermore, the pharmacokinetic models proposed here are novel and are very helpful in preliminary evaluation of the efficacy of the devices at treating dry eyes. Also, chapter 5 in thesis deals with evaluating bioavailability of Restasis eye drops to compare the effectiveness of our devices with commercially existing solutions for dry eyes.
24 Figure 1 1. Cornea as a Oil:Water:Oil multi laminate. This is a well accepted pharmacokinetic view of the cornea. However, mos t pharmacokinetic models to date assume either the whole cornea as a single compartment or three well stirred compartments. The innovation of the model in this study assumes the three layers of the cornea to be uniform and their transport across each layer to occur by diffusion.
25 Figure 1 2 Schematic and Image of the drug loaded punctal plug (not to scale). 0.94mm HEMA core + Drug + EGDMA crosslinking Silicon Shell 0.51 mm
26 CHAPTER 2 TRANSCORNEAL PENETRATION OF RHODAMINE B ACROSS RABBIT CORNEA 2.1 Introduction This chapter focuses on understanding transport of Rhodamine B, a lipophilic drug analog, across rabbit cornea. Cornea consists of three layers namely eptihelium, stroma and endothelium. A comprehensive model is developed to explain the transient concentra tion profiles in all the three layers when tear side of cornea is exposed to a fixed concentration of Rhodamine B dye. 2.2 M aterials and Methods RhB (Cat # R6626; MW: 479; CAS Number 81 88 9) and all other reagents for Ringers solution were obtained from Sigma Chemical Company (St. Louis, MO). Eyes were obtained from freshly killed albino (New Zealand White) rabbits of either sex. All procedures for animal handling were in accordance with the guidelines set by the Association for Research in Vision and Op hthalmology (ARVO) and approved by Laboratory Animal Care Committee in the laboratory of (late) Prof. David Maurice, Ophthalmology at Stanford University (SP. Srinivas). The corneas were isolated and mounted as previously described [61,62] They were maintained at 34 C by circulating water through the jacket and perfused with HCO 3 Ringers (containing reduced glutathione, glucose, adenosine, 40 mM HEPES, and 40 mM NaHCO 3 ) at the anterior and po sterior surfaces  The trans corneal profiles of RhB were obtained using a custom built confocal scanning microfluorometer, as described previously [61, 62] About 30 minutes after mounting the cornea, the epithelial surface was exposed to RhB dissolved (1 g/mL) in the Ringers. Depth scanning was performed through a stepper motor mechanically
27 coupled to the fine focus knob of the microscope. Depth resolution was ~ 8 m at a sensitivity of 10 6 gm/mL of fluorescein (SNR > 20) using a 40x water immersion objective of 0.75 NA (Zeiss Inc) [ 62,64] Scanning was performed at ~ 600 m/min over 800 m depth. Scatter and fluorescence scans were measured to obtain corneal thickness and trans corneal concentration profile of RhB, respectively. More than 6 experiments were performed and data from one typical experiment is considered in this study for analysis. The experimental data alone were presented in an abstract form by Srinivas and Maurice previously at the Association of Research in Vision and Ophthalmology  2.3 R esults 2.3.1 Transcorneal Penetration of Topical Rhodamine B The implications of the multi layer oil:water:oil structure of cornea, as well as the shortcomings of the compartmental models, are illustrated by our experimental observations of the penetration of RhB, as shown in Figure 2 1 It is clearly evident that R hB distributes across the cornea with distinct fluorescence discontinuities at the cellular boundaries between the epithelium and stroma as well as between stroma endothelium. Furthermore, in the epithelium and stroma, the concentration is non uniform. Als o noteworthy is that the RhB fluorescence is elevated in the lipophilic cellular layers (epithelium and endothelium) relative to its level in the hydrophilic stroma. The concentration discontinuities and the increased levels in the cellular layers are indi cative of the preferential partitioning of RhB into the lipophilic structures across the cornea. The time and position dependent fluorescence gradients, apparent in the epithelium and stroma, indicate diffusional resistance for RhB transport. These
28 observ ations, in turn, suggest that the epithelium and stroma are not well stirred and cannot be construed as homogenous compartments let alone the entire cornea. Therefore, penetration of RhB cannot be described by conventional compartmental models. In additio n to the above general observations on the penetration characteristics of RhB, the fluorescence profiles in Figure 2 1 also suggests the following: (a) The fluorescence at the epithelial surface reaches a high value within 6 minutes, and then increases at a decreasing rate, (b) The fluorescence gradient in the epithelial layer shows a sharper gradient at ~ 140 min compared to earlier times. (c) A peak in the epithelial fluorescence profile begins to evolve for t > 30 min, and is quite distinct at 140 min at the epithelium stroma interface. (d) The gradient of fluorescence in the stroma reaches a near constant value at 30 min. (e). The fluorescence peak in the endothelium appears after 30 min, and the peak concentration increases slowly. Key observations that should be included in modeling include: (a) accumulation of RhB in the epithelium and endothelium, (b) negligible accumulation in the stroma, and (c) appearance of the peak at the epithelium stroma interface. 2.3.2 Model for Representing the RhB Pene tration Kinetics In this section, we develop a general mathematical model for trans corneal penetration of a lipophilic solute. Its parameters will be estimated subsequently from the unsteady state trans corneal profiles of RhB shown in Figure 2 1 In accordance with the physio chemical properties of RhB, we assume that RhB is not metabolized during transport across the cornea.
29 2.3.3 Transport a cross the Cellular Layers The first step in the transcorneal penetration of a topically administered lip ophilic solute is its partitioning into the lipid bilayers of the plasma membrane (referred to as the epithelial or lipid bilayer) of the superficial corneal epithelium that is in contact with the tears. Depending on the octanol water partition coefficient a fraction of the solute in the epithelial bilayer will partition into the hydrophilic cytoplasm. Once in the cytoplasm, the solute could also partition into putative intracellular lipophilic domains, such as the lipid membranes of the intracellular orga nelles (e.g., endoplasmic reticulum) ( Figure 2 2 ). We model these steps as follows: The rate of transport from the epithelial bilayer to intracellular domains is expressed as the product of a rate constant (k 1 ) and the net driving force for transport where C 1 is the average concentration of the solute in the epithelial bilayer, is the average concentration in the intracellular lipophilic domains, and K 1 is the ratio of and C 1 at equilibriu m. More precisely, is the concentration in the lipid bilayers based on total cell volume, i.e., it is the product of the actual concentration in the bilayers and the volume fraction of the bilayers in the epithelial cells. Similarly, C 1 b is the product of the concentration in the internal hydrophobic regions and the volume fraction of such regions in the cell. The parameter k 1 is the permeability of cytoplasm that separates the epithelial bilayer from intracellular lipophilic domains
30 Based on the above model for accumulation in the intracellular domains, transient mass balance of the solute in the corneal epithelium and its association with the intracellular lipophilic domains can be written as ( 2 1) In the above and subsequent equations, the y coordinate refers to the depth across the cornea; y = 0 is at the tear epithelium interface and t refers to time ( Figure 2 3 ). The parameter D 1 is the effective diffusion coefficien t in the lipid bilayer. For ease of reference, we have compiled all the parameters of the model in Table 2 1. The second term on the right side of the mass balance can also be interpreted as a first order reversible binding of the solute. Since the expres sion for the rate limiting binding is mathematically identical to that for diffusion limited rates of transport into the internal hydrophobic domains, we combine the two rate mechanisms together. Since the posterior surface of the cornea is a cellular laye r, we assume that the model for transport across the endothelium is mathematically similar to the epithelium. Thus, the trans endothelial solute transport is described: ( 2 2)
31 In the above formulation, we us e subscript 3 to refer endothelium. Thus, the parameters D 3 K 3 k 3 C 3, and C 3 b have same definitions to the corresponding variables for the epithelium (Table 2 1). 2.3.4 Transport across the Stroma The corneal stroma is composed of ~ 300 lamellae of collagen fibrils bound with glycosaminoglycans (GAGs)  In general, a solute could bind to collagen and GAGs We assume that binding unbinding reactions occur at a faster time scale compared to that of diffusion. Th is assumption is consistent with the experimental data on diffusion of small molecules in artificial collagen networks, which suggests that the binding unbinding events are rapid and transport of small solutes is governed by diffusion alone  Therefore, the bound and the unbound forms are always at equilibrium so that we need to address the mass balance for the total solute only. Accordingly, the following describes solute transport across the stroma: ( 2 3) where D 2 and C 2 are effective diffusivity and total concentration of the solute in the stroma, respectively (Table 2 1). 2.3.5 Boundary Conditions At the tear epithelium interface, the solute concentration in epithelium is at equilibrium with concentration in tear fluid. This can be written as: ( 2 4)
32 where is the partition coefficient between the epithelium and the tears and C 0 is the drug concentration in tears (Table 2 1 and Figure 2 3 ). At the epithelium stroma interface, we expect concentration equilibrium and flux continuity. We model condition of concentration equilibrium as ( 2 5) where k perm is the permeability of epitheli um stroma interface, and is the equilibrium partition coefficient between the stroma and the epithelium (Table 2 1 and Figure 2 3 ). Inclusion of the permeability at the epithelium stroma interface in Equation 2 5 is consistent with the observed increasing concentration gradient with time in the epithelium and the development of concentration peak at the epithelium stroma interface. In Equation 2 5, 1/k perm represents mass transfer resistance at the interface. When k perm is large, Equation 2 5 correctly reduces to the concentration equilibrium requirement. As discussed later, we have evaluated the model with and without the k perm parameter. For flux continuity, we impose the following boundary condition at the interface: ( 2 6) We now specify similar boundary conditions for the interface between the stroma and endothelium, but we assume that the interface concentrations to be in equilibrium so that
33 ( 2 7) Finally, at the endothelium aqueous humor interface, the diffusing drug is swept away rapidly from the interface, and thus a reasonable representation of this is to set the concentration to zero (i.e., sink conditions) ( 2 8) The initial conditions correspond to zero concentration across the entire cornea and the known initial concentration of the solute in the tears. 2.3.6 Parameter Estimation We have employed unsteady state concentration profiles of RhB in Figure 2 1 to estimate the 11 parameters (Table 2 1) in the above model. We first note that the model has no non linear terms so that the concentration at any point across the cornea would be proportional to the solute concentration in tears. Secondly, at the low concentration used, fluorescence of RhB is linearly proportional to concentration so that measured fluorescence value represents concentration of diffusing RhB. Therefore, we use the fluorescence and the solute concentration across the cornea interchangeably in the following estimation procedures. 2.3.7 Initial Guess for Parameter Estimation For the case of constant concentration in the tears (C 0 ), the concentration at the tear epithe lium interface (y = 0) can be given by
34 ( 2 9) Since C 0 was constant in our measurements, a plot of experimental C t (y = 0) vs. t can be fitted to Equation 2 9 for estimating K 1 and k 1 At t ~ 0 or at small times, at the epithelium stroma interface, the ratio of the total concentration at the stroma to the epithelium is the partition coefficient 21 The diffusivity of the solute in stroma (D 2 ) is assumed to be that in free solut ion, and the diffusivity in epithelium (D 1 ), is approximated by multiplying D 2 with the ratio of average slopes of concentration profiles in the stroma and epithelium. The value of D 3 is expected to be equal to D 1, recognizing that both consist of similar biological cell layer(s). Also, the values of k 3 and K 3 are expected to be equal to k 1 and K 1 respectively. With these initial constraints i mposed on the parameters of Equation 2 1to 2 9, we developed a MATLAB program that estimated model parameters by m inimizing the sum of the residual errors (denoted by E) between the calculated and measured fluorescence (i.e., concentration) values. The measured fluorescence at a given depth y arises from the excitation of all fluorophores at the neighborhood, and is o btained by convoluting the concentration profiles with the instrument response function (IRF) given by ( 2 10) where (2.36 ) represents full width of the Gaussian. This was measured to be ~ 10 m for the 40x objective (Zeiss, 0.75 NA; Water immersion) and a defined excitation and emission slit widths employed during the measurements [61,62,64] Further, since the
35 measured flu orescence arises from RhB present both in the cellular bilayers as well as intracellular lipophilic domains, we write ( 2 11) where and represent concentrations in the cellular bilayers and intracellular lipophilic domains. Note and represent the bound RhB in the epithelium and endothelium, respectively. To compare the model prediction (C Model ) with measured fluorescence values, we performed convolution of C total with IRF as ( 2 12) We define the following objective function for estimating the model parameters ( 2 13) where C Exp is the measured concentration at a given position and time t, N i is the total number of data points in the i th layer, with i = 1 to 3 (representing the three corneal layers), and C Model is RhB concentration predicted by the model. The nu mber of points in each layer N i is the product of the total number of data points at each time step and the total number of time instants at which data were recorded. The error function (E) was minimized using the fminsearch program of the MATLAB, to obtai n optimal parameter values. The values of the parameters thus estimated are given in Table 2 2 and the model predicted fluorescence profiles are compared with the experimental data in Figure 2 4 We also examined cases with and without inclusion of the k p erm parameter
36 ( Equation 2 5). The parameters given in Table 2 2 are only provided for the case with k perm since the profiles without this term did not match the data well, and in particular the model without k perm cannot capture the characteristics (b) an d (c) of the transient concentration profiles listed above. 2.4 Parameter Sensitivity Analysis 2.4.1 Contour Plots and Correlation C oeffecients In order to check for the robustness of the model, we examined the identifiability of parameters by constructing sensitivity contour plots and also by calculating parameter correlation coefficients  The sensitivity contour plots consisted of contour lines of E (i.e., iso E lines; calculated using Equation 2 13) for variation s in parameters taken one pair at a time, keeping all other parameters at their estimated values. Thus, for any parameter pair to be uncorrelated and be true/robust estimates (i.e., based on global minimum of E), we expect that the E contours would show a single minima that would converge towards small circles or small line segments. Contours that manifest as long lines should imply that the optimal values of the parameters are not unique, i.e., different sets of parameters could yield the same minimum erro r, and thus the parameters are not identifiable. Specifically, long horizontal lines imply that the parameters on the x axis are not identifiable and similarly, long vertical lines imply that the y axis parameter is not identifiable. Long slanted lines i mply that the parameters on the x and the y axes are correlated. In order to examine the kinetic model, contour plots for 55 possible pairs of parameters pairs ( 11 C 2 combinations) were constructed around the minima using MATLAB defined by the parameter est imates in Table 2 2 (Col. 3). Each of the parameters was varied + 50% around the estimate. Illustrative cases of E contour plots
37 are shown in Figs. 2 5 and 2 6 For D 2 and K 1 parameter pairs, the error contours are shown in Figure 2 5 A and 2 5 C, respectively. The error minima conve rges along small, vertical line segments which eventually converge to a point. These observations confirm, as expected, negligible correlation between and D 2 as well as between and K 1 Similarly, the limiting contours for k 1 D 2 and D 1 k perm pairs presented in Figure 2 5 B and Figure 2 5 D, respectively, repre sent small horizontal lines segments converging to a point. Again, these plots indicate a negligible correlation between k 1 and D 2 as well as D 1 and k perm In contrast to these representative plots representative of robust parameter estimates, we also foun d that certain estimates that appear to be ill identified. For example, E contours for D 3 D 1 pair shown in Figure 2 6 A where two contours have same values of error. This implies that the parameter estimation might depend on the initial guesses of the param eters. However, the minima are relatively close to each other. Similarly, for the k 3 K 3 pair, the parameter estimation might depend on starting parameter values ( Figure 2 6 B). The plots involving parameter in Figs. 2 6 C and 2 6 D show that the y axis parameter is not well defined because the contour plots are vertical lines. We have next quantified the information implied in contour plots above in terms of correlation coefficients between all the parameter s of the model. The calculated values for the possible 55 combinations of parameters pairs are given in Table 2 3. For the purposes of emphasizing the importance of E contours vis vis Table 2 3, the coefficients for the parameter pairs employed E contou rs shown in Figs. 2 5 and 2 6 are highlighted (shaded and bold text). A parameter is well identified if its regression coefficient with all other parameters lies between 0.9 < r < 0.9  As per this criterion,
38 it is evident from Table 2 3 that most of the parameters are well identified, with the exception of and K 3 This conclusion is consistent with those drawn on the basis o f the contour plots in Figures 2 5 and 2 6 2.4.2 Single Parameter Sensitivity Analysis We next determined the sensitivity of each parameter vis vis total error E defined by Equation 2 13. Since all parameters except one are fixed in this calculation, the error function is expanded as a Taylor ser ies at the point of minimum error, ( 2 14) where E min is the minimum error or the error corresponding to the optimum parameter. The parameter u in the above denotes any one of the el even model parameters. u min is the value of u at which the error is minimum. In Equation 2 14, the linear term is absent as the first derivative (dE/du) is zero at the minimum. We further define a dimensionless sensitivity parameter derived from Eq uation 2 14: ( 2 15) where the index quantifies the changes in E due to changes in u. For instance, a value of 5 for implies that 10% change in the parameter from its optimal estimate (i.e., u u min = 0.1 u min ) gives a 5% change in error (E E min ). To calculate for a specific value of u, we determined the second derivative in Equation 2 15 computing E around u min
39 and then fitting the resulting data to a quadratic polynomial. The calculated values of show n in Table 2 2 indicates that and the parameters involving endothelium (i.e., K 3 k 3 and D 3 ,) are << 5, suggesting that the model is insensitive to these parameters indicating that they may be poorly identified. This is consistent with the conclusions drawn from the contour plots (Figs. 2 5 and 2 6 ) and the correlation matrix (Table 2 3). The lack of sen sitivity of the parameters involving endothelium could be attributed to limited sampling of RhB in the monolayer given its smaller thickness compared to other layers; sampling interval was 0.5 m. The lack of sensitivity to occurs be cause the transport from the epithelium to the stroma is limited by the barrier offered by the epithelium stroma interface and so small changes in the stromal concentration have a negligible impact on the flux at the epithelium stroma interface. 2.5 Predi ction of In Vivo Pharmacokinetics Guss et al .,  instilled a drop of 0.1% RhB on surface of the cornea of rabbits and measured the concentration transients in the epithelium, stroma, and aqueous humor. However, the study did not report the concentration profiles across each of the layers due to lack of high depth resolution ion their measurements. Therefore, the measured values represent spatial averages in different layers. The model described in Eq uation s 2 1 to 2 10 can be employed to predict the in vivo pharmacokinetics with the caveat that RhB conc entration in tears decreases exponentially after administration of a drop  Therefore, we assume tear RhB concentration as ( 2 16)
40 where C 0 is the initial concentration of RhB (after accounting for dilution in the tears) and is the time constant of elimination from the corneal surface. This modifies the boundary condition at y = 0 as ( 2 17) Additionally, we incorporate the anterior chamber dynamics into the in vitro model to account for RhB clearance in vivo which occurs largely through aqueous humor outflow. Thus, the mass balance in the anterior chamber can be given by ( 2 18) where C aq is the concentration of RhB in the anterior chamber (which is assumed to be well mixed ), V aq is the volume of anterior chamber, K clearance is the total clearance from anterior chamber, and A cornea is the surface area of corne a. The values of V aq and A cornea for rabbits were assumed to be 0.311 mL and 1.54 cm 2 respectively  K clearance is approximated as the aqueous humor outflow in rabbits, which is reported as 0.411 l/min  while the d rop volume is assumed to be 30 l  The value of was taken to be 1 min based on the fact that the tear concentration drops to negligible values a few minutes af ter instillation [1,4,64,69,72] Based on these considerations, we computed the concentration transients for spatially averaged con centration in epithelium. The comparison of the predicted to the values reported by Guss et al .,  is presented in Figure 2 7 The comparison is not exact but is comparable, despite the variability in the physiological parameters and the uncertainty in the tear concentrations. The value of K clearance is also uncertain because of binding to various tissues and
41 diffusion through the lens (shown significant RhB accumulation in lens  ) ; however, its uncertainty has very little impact on the concentration transients in epithelium as the concentration in anterior chamber is sufficiently close to perfect sink conditions for most of the time. 2.6 Discussion In this study, we established a kinetic model for characterizing transport of a lipophilic solute across the cornea. Most models on the trans corneal penetration kinetics reported to date are based on the method of compartmental modeling [8 10] A few studies that attempted to characterize the diffusive transport across each of the corneal layers were lacked experimental evidence of trans corneal concentrati on profiles [12 14] The model developed in this study accounts not only for the multi laminate structure of the cornea ( Figure 1 1 ) but also is based on temporal and spatial exp erimental concentration profile of a fluorescent dye, RhB, as a lipophilic drug analog. Because of corneal transparency, we measured unsteady state trans corneal profiles of RhB. This novel data provide experimental evidence for a mechanistic description o f the trans corneal transport, and as a result enabled development of a physiology based pharmacokinetic model. It is worthy to note that the fluorescent dye RhB has been previously used as a model drug surrogate for characterizing transport across the sk in [73,74] cornea/lens [15,75] conjunctiva/sclera  2.6.1 Modeling Interphase and Intraphase Tran sport A novel aspect of our model is the integration of the muIti laminate view of the cornea illustrated in Figure 1 1 Although this model is well known [1,4,5,77] models for topical pharmacokinetics, in general, have failed to include the existence of heterogeneous nature (i.e., presence of three distinct phases) across the cornea. RhB,
42 being a lipophilic molecule (octanol water partition coefficient: 100 310) [15,74] turned out to be very useful in mimicking a lipophilic drug analog. Its trans corneal distribution lipophilic layer) but also demonstrated a unique mechanism of intra phase transport within the cellular layers, namely the epithelium and endothelium. To accommodate inter phase transport, we formulated partitioning at the interface ( Equation 2 4, 2 5, an d 2 7) and also modeled interfacial resistance ( Equation 2 5) for transport across the epithelium stroma interface. For describing intra phase transport in the stroma, we assumed homogeneous transport properties but the solute transport is by diffusion ( Eq uation 2 3). For transport across the cellular layers, we incorporated an additional length scale in describing the diffusive transport. In this approach, the transport is modeled as diffusion across the bilayers of plasma membrane and partitioning into in tracellular lipophilic domains. Since the concentration in the cytoplasm is expected to be small for lipophilic solutes, partitioning into such domains is likely to be prolonged (as discussed previously in the model section). We believe that the slow accu mulation of RhB in the cellular layers ( Figure 2 1 ) and a continuous increase in the observed RhB fluorescence at the tear epithelium interface shown in Figure 2 1 support our reasoning. Therefore, we conclude that the transport of lipophillic molecules across the cellular layers is rate limited by transport across the hydrophilic cytoplasm. 2.6.2 Model Validation In terms of model validation, uncertainties in the model from the point of view of estimated parameters have been analyzed extensively. However, model verification with multiple fluorescent dyes was beyond the scope of current study and need to be considered in further studies. As a first step in the succe ss of our model, we note that
43 the parameters Table 2 2 predicted the experimental data accurately. Secondly, the calculated parameters exhibited high sensitivity and the estimated values were independent of starting initial estimate. This conclusion is bas ed on the sensitivity analysis presented in error (E) contour plots ( Fig ure 2 5 and 2 6 ) and the correlation coefficients between the parameters (Table 2 3). As noted earlier, three of the parameters, namely and k 3 showed poor sensitivities, indicating a need for additional experiments to accurately determine their values. As noted earlier, it is possible that this can be overcome by overcoming the inadequate sampling across the endothelium given its small th ickness (4 m)  A principal set of parameters relating to transport and phase equilibrium at tear epithelium, epithelium stroma, and stroma endothelium interphase are given in Table 2 1. To establish the validity of these parameters, it is instructive to compare the values reported in Table 2 1 with values previously reported in literature. The parameters K 1 and K 3 have never been measured or estimated previously so we cannot compare o ur fitted values to any prior measurements. The parameter 1/k 1 the time constant of transfer of drug from lipid bilayer to other hydrophobic domains in epithelium, also has not been reported, and thus a direct comparison with measurements is not feasible A scaling analysis shows that this parameter is about 5 R 2 /D 1C where R is the radius of the epithelial cell and D 1C is the diffusivity of RhB in the cytoplasm of the epithelial cells. Setting R = 8.3 m D 1C = 4 10 12 m 2 /s (base d on Stokes Einstein equation  ) and = 10, we get 1/k 1 = 800 s, which is significantly lower than the fitted value of 2500 s (Table 2 2). None the less, the value obtained from the scaling analysis is of the same order of magnitude as the fitted value, which is encouraging, particularly
44 considering the assumptions implicit in the scaling analysis and the uncertainty in the values of the parameters utilized in the scaling calculations. The time constant of transfer of drug from lipid bilayer to other hydrophobic domains in endothelium is about 5 R 2 /D 3C which should be approximately be equal to the value obtained for t he epithelium, i.e., 2500 s due to similarities in the structure of the epithelium and endothelium cells. This value is in reasonable agreement with the fitted value of 3330 s (Table 2 2). Based on a model reported by Zhang et al., the diffusivity of a 0 .55 nm size lipophillic molecule in epithelium should be ~ 210 12 m 2 /s. Our fitted value of 7.9 10 12 m 2 /s is in reasonable agreement with the value predicted by the model. Similarly, based on Zhang et al.  the diffusivity in endothelium should be ~ 2 10 12 m 2 /s, which is in good agreement with the fitted value of 1.5 10 12 m 2 /s. Zhang et al.,  also reported a value of diffusivity in stroma as 2.210 10 m 2 /s, which is a n order of magnitude higher than the fitted value of 2.3 10 11 m 2 /s. The discrepancy between the value estimated from the model of Zhang et al .,  and that obtained by fitting the transient profiles is likely due to significant binding of the drug in stroma to collagen and proteoglycans. The value of the partition coefficient between the stroma and tears = x is ~ 100, which is much larger than 1, even though stroma is almost water like, supporting the hypothesis that a large fraction of RhB in stroma is bound. The bound and the free concentrations are in stroma are likely in equilibrium due to fast binding unbinding kinetics, but the bound fraction do es not diffuse leading to a reduction in the value of the diffusivity by the ratio of the free drug to the total drug present locally  To our knowledge, there is no reported value of the barrier at the epithelium str oma interface, and so a direct comparison with experiments is not feasible. The experimental
45 profiles for fluorescence show a slight shoulder/peak at the interface between the epithelium and stroma, which appears to support the hypothesis that a thin layer at this interface presents a barrier to transport. Alternatively, the resistance could also be due to an additional transport step of RhB from inside the lipid bilayers of the epithelium to the stroma. Further investigations are needed to examine this is sue. 2.6.3 Asymptotic Behavior In order to obtain further insights on the penetration kinetics, we examined the pseudo steady state behavior after a prolonged time after topical instillation. For this purpose, we have the time derivatives in the model to zero and then calculated concentration profiles. Under these conditions, the concentration in each layer is linear so that the transport across the cornea can be modeled by a lumped model with an overall permeability coefficient given by ( 2 19) where L epi L stroma and L endo are the thicknesses of epithelium, stroma, and endothelium, respectively. To determine the time after which this lumped model can be employed, we calculated the diffusive time scales of each layer (L 2 /D) and also for transport into the interior lipophilic domains given by 1/k 1 and 1/k 3 These characteristic times for the estimated parameters (Table 2 2) are given in Table 2 4. The time required to reach pseudo steady state was found to be ~ 6 0 min. This implies that for t < 60 min, the lumped model is unsuitable for assessing the trans corneal penetration. In other words, for time up to 60 min, the unsteady terms in the mass balances must be
46 included. Since the residence time of topical drugs is only a few minutes, it is clear that lumped model is a poor representation of clinical relevant pharmacokinetics. However, the lumped model could be employed for describing transport in vitro experiments with diffusion chambers as the topical concentrat ion can be maintained constant over an extended time period. Additional insights on trans corneal transport can be obtained by comparing the transport resistance of each layer. Thus, using the estimated parameters, the transport resistance of stroma, epith elium, and endothelium and the interfacial resistance at the epithelium stroma interface, respectively, are: We note that that each layer, with the exception of the endothelium, offers significant resistance. The effective permeability of the cornea to RhB, based on Equation 2 19, is 0.41 10 6 m/s, and is in reasonable agreement with permeability values reported in the literature for molecules with similar size and hydrophobicity  However, it should be emphasized that the overall permeability coefficient is not relevant for predicting
47 pharmacokinetics of drugs delivered through eye drops because the residence time of drug is far less than the time required for reaching pseudo steady state. 2.7 Conclusions The mathematical model developed here accurately characterizes the transient solute transport through the cornea. Th e fitted values are reliable with a low level of uncertainty for all parameters except the endothelium parameters and the partition coefficient The model can predict the in vivo pharmacokinetics of RhB with reasonable accuracy. The model developed here is a significant improvement over conventional approaches using a lumped permeability approach because the drug residence time is much small er than the time needed for establish in g pseudo steady T hus the lumped overall permeability is not a useful measure of total transport resistance. The experimental data show s a slow accumulation of hydrophobic solutes in epithelium and endothelium, and we ascribe this to the slow transport fr om the bilayers to interior hydrophobic sites.
48 Figure 2 1 Trans corneal penetration of RhB after topical administration across rabbit cornea mounted in vitro ; Y axis represents fluorescence in arbitrary units (AU). The fluorescence scans were obtained with a custom built scanning microfluorometer (see Methods) with a depth resolution of ~ 8 m using a 40x objective (Zeiss, Inc. 0.75 NA; water immersion).
49 Figure 2 2 Transport across the cellular layers: The main mechanism for transport of lipophilic solutes is through the lipid bilayers of the plasma membrane (dark arrow). Another important but slower mechanism leads to continu ed accumulation of hydrophobic solute in the intracellular hydrophobic domains (e.g., membrane associated with endoplasmic reticulum). This mechanism can be resolved into following steps in sequence: (1) transport by partition into the bilayer of the plasm a membrane from tears, (2) partitioning of the drug into cytoplasm from the bilayer, and (3) partitioning into intracellular hydrophobic domains. Hydrophilic solutes can pass through paracellular pathways, independently of their partition coefficient and d egree of ionization which permit an alternative route for trans cellular movement of the lipophilic solutes.
50 Figure 2 3 Partition equilibrium of a l ipophilic topical drug: Suppose C 0 is the concentration of the topical drug in the tears at an instant t. Then, partitioning of the drug into the epithelium results in a concentration C 1 (at y = 0) at its outer boundary given by (PC x C 0 ), where PC is the partition coefficient between tears (equivalent to a buffer) and lipid rich epithelial layer (equivalent to octanol). Once the drug is in the epithelium, it diffuses down along its concentration gradient in the epithelium. Abbreviations. C 1 : Concentration in epithelium; C 2 : Concentration in stroma; C 3 : Concentration in endothelium; C a : Concentration in the anterior chamber; y: Depth across cornea.
51 Figure 2 4 Comparison of model predictions (solid lines) and experimental me asurements (circles) for transient fluorescence profiles in cornea at t = 6, 30, 60, and 140 min.
52 Figure 2 5 Contour plots of error, i.e., square of the difference between the model predictions and experimental values for Rh odamine B concentration in cornea (eq 13). The parameters on the x and the y axes are varied in a range of 50% around the optimal values, while keeping all other variables fixed at the optimal values. The contours in each case show a single minimum and contours converge proving that the fitting is robust and the pair of parameters [ D 2 in (a); k 1 D 2 in (b) K 1 in (c) K perm D 1 in (d)] are uncorrelated [a d are clockwise starting from top left]
53 Figure 2 6 Contour plots of error, i.e., square of the difference between the model predictions and experimental values for Rhodamine B concentration in cornea (eq 13). The parameters on the x and the y axes are varied in a range of 50% around the optimal values, while keeping all other variables fixed at the optimal values. The contour plots in Panels A and B show closely spaced multiple minima, implying that the value of the optimal parameters predicted by the error minimization (D 3 D 1 in Panel A) and k 3 K 3 in Panel B) would vary slightly depending on the initial guess of the parameters. The contours in Panels C and Panel D are straight lines, proving that variation of has a negligible effect on error if > 10.
54 Figure 2 7 Comparison of experimental data by Guss et al.,  and model prediction for spatially averaged transient epithelium concentration of RhB in rabbit cornea. In the experiment, a single drop of 1% RhB was instilled in the rabbit eye.
55 Table 2 1 Description of the model parameters Parameter Units Definition Ratio of the average concentration in the epithelium bilayers (based on total cell volume) and the concentration in tears at equilibrium K 1 Ratio of the average concentration in the epithelial bilayers (based on total cell volume) and that in the internal hydrophobic regions (based on total cell volume) at equilibrium k 1 s 1 Permeability of the cytoplasmic medium separating the lipid bilayers and the internal hydrophobic regions in the epithelium D 1 m 2 /s Diffusion coefficient of RhB in the lipid bilayers in the e pithelium k perm m/s Permeability coefficient of epithelium stroma interface Ratio of the concentration in stroma and the average concentration in the epithelium bilayers (based on total cell volume) at equilibrium D 2 m 2 /s Diffusion coefficient of RhB in s troma Ratio of the average concentration in the endothelium bilayers (based on total cell volume) and the concentration in stroma at equilibrium K 3 Ratio of the average concentration in the endothelium bilayers (based on total cell vol ume) and that in the internal hydrophobic regions (based on total cell volume) at equilibrium k 3 s 1 Permeability of the cytoplasmic medium separating the lipid bilayers and the internal hydrophobic regions in the endothelium D 3 m 2 /s Diffusion coefficient of RhB in the lipid bilayers of the e ndothelium
56 Table 2 2 The optimal values of the model parameters obtained by minimizing the total error between the model prediction and experimental data for RhB concentration in cornea at various times. Sensitivity analysis of the transport model. Values of the sensitivity i ndex larger than 5 indicates that error between the experimental data and the model fit increased by less than 5% for a 10% change in the model parameter, and implies a robust fit and a reliable value of the fitted parameter. Parameter Estimated value Units Sensitivity Index 9.8 100.27 K 1 1.6 6.39 k 1 4 10 4 s 1 4.48 D 1 7.9 10 12 m 2 /s 3.01 k perm 6 10 8 m/s 10.36 10.6 0.11 D 2 22.8 10 12 m 2 /s 4.92 2.8 0.54 k 3 3 10 4 s 1 0.01 K 3 1.2 0.02 D 3 1.5 10 12 m 2 /s 0.78
57 Table 2 3 Coefficient of correlation between all the model parameters obtained by fixing all parameters except the two chosen parameters. Correlation coefficient is calculated for the limiting contours encompassing the minima. Coefficient of correlation should lie between 0.9 and 0.9 for variables to be uncorrelated. High values of correlation coefficients have been marked with an asterisk in the table. The blank entries in the table correspond to the cases of vertical or horizontal contours for which the correlat ion coefficient is undefined, ex., contour plots in Fig 2 6 (c d). K 1 k 1 D 1 k perm D 2 K 3 k 3 D 3 1 0.13 0.32 0.42 0.05 0.06 0.12 0.2 0.33 0.22 K 1 1 0.53 0.14 0.12 0.32 0.12 0.04 0.35 0.34 0.01 k 1 1 0.54 0.02 0.91 0.09 0.25 0.61 0.35 0.08 D 1 1 0.19 0.55 0.82 0.01 0.14 0.19 k perm 1 0.19 0.61 0.16 0.11 0.03 0.19 1 0.03 0.60 0.15 0.16 0.03 D 2 1 0.28 0.98 0.03 0.2 1 0.30 0.31 0.90 K 3 1 0.1 0.71 k 3 1 0.81 D 3 1
58 Table 2 4 Characteristic time scales for the principal mechanisms included in the model. Mechanism Time Scale Time ( min ) Diffusion in the Epithelium (L epithelium ) 2 / D 1 4.3 Diffusion in the Stroma (L stroma ) 2 / D 2 68.2 Diffusion in the Endothelium (L endothelium ) 2 / D 3 2.2 Transport from bilayers of the plasma membrane into intracellular lipophilic domain in the epithelium 1 / k 1 41.6 Transport from bilayers of the plasma membrane into intracellular lipophilic domain in the endothelium 1 / k 3 55.6
59 CHAPTER 3 TRANSCORNEAL PENETRATION OF FLUORESCEIN ACROSS RABBIT CORNEA 3 .1 Introduction Most of the eye medications delivered topically have to have to transport across cornea to reach the target tissues. Fluorescein is used as a drug analog for hydrophilic drugs to understand the transport mechanism of these molecules across cornea. This ch apter focuses on developing a mechanistic model to explain the transient kinetics of fluorescein, when endothelium side is exposed to a fixed concentration of sodium fluorescein. 3.2 Materials and Methods Sodium fl u orescein and reagents for ringers solutio n were obtained from S igma C hemical C ompany (St. Louis, MO). Eyes were obtained from freshly killed albino (New Zealand White) rabbits of either sex. All procedures for animal handling were followed in accordance with the guidelines set by the Association for Research in Vision and Ophthalmology (ARVO) and were approved by Laboratory Animal Care Committee in the laboratory of (late) Prof. David Maurice, Ophthalmology at Stanford University (SP. Srinivas). The corneas were isolated, mounted and were maintai ned at 34 C by circulating water through the jacket and perfused with HCO 3 Ringers (containing reduced glutathione, glucose, adenosine, 40 mM HEPES, and 40 mM NaHCO 3 ) at the anterior and posterior surfaces. The trans co r neal profiles of fluorescein were obtained using a custom built confocal scanning microfluorometer, as has been described previously [61,62] About 30 minutes after mounting the cornea, the endothelium was exposed to fluo rescein dissolved ( 0.0 1 g/mL) in the Ringers. Depth scanning was performed through a stepper motor mechanically coupled to the fine focus knob of the
60 microscope. Depth resolution was ~ 8 m at a sensitivity of 10 6 gm/mL of fluorescein (SNR > 20) using a 40x water immersion objective of 0.75 NA (Zeiss Inc) [62,64] Excitation wavelength used in the experiments was 48510 nm while emission wavelength was 530 10 nm Scanning was performed at ~ 6 00 m/min over 800 m depth. Scatter and fluorescence scans were measu red to obtain corneal thickness and trans corneal concentration profile of fluorescein respectively. More than 6 experiments were performed and data from one typical experiment is consi dered in this study for analysis. The experimental data alone were presented in an abstract form by Srinivas and Maurice previously at the Association of Research in Vision 3.3 Results and Discussion 3.3.1 Fluorescence P rofiles The spatially resolved flu orescence profiles in cornea are plotted in Figure 3 1 for various times. It is reiterated that the cornea is exposed to fluorescene (FL) on the anterior chamber side, and fluor e scein then diffuses across the three layers of the cornea. Since FL is hydrophilic, it is expected to face significant barrier to transport in the endothelium and epithelium. The profiles show elevated concentration of FL in stroma, which is expected bec ause of hydrophilic nature of FL and stroma. Additionally, there are a few key aspects of the experimental data which are important to understanding the mechanisms of transport through each of the cornea layers: (i) The concentration of FL in endothelium is only slightly smaller than that in the stroma; (ii) The fluorescence at the stroma endothelium interface increases with time; (iii) The fluorescence boundary layer in stroma is about 175 m thick at 41 min utes and it
61 reaches the stroma epithelium bounda ry, which is about 350 m from the endothelium, in less than 120 min. The first observation suggests that FL is able to diffuse across the lipid bilayers of the endothelial cells and accumulate in the cytoplasm of the endothelial cells. The fluorescence at the stroma endothelium interface is plotted as a function of fluorescence from the endothelium (cytoplasm) with time as a parameter in Figure 3 2 This figure suggests that the ratio is relatively constant suggesting that the concentration in the endot helium and that in stroma at the stroma endothelium boundary are in equilibrium. The first and the second observation suggest that the dominant mechanism for transport of FL across the endothelium is transcellular transport through the lipid bilayers. The thickness of a purely diffusive boundary layer changes as square root of time, and thus the time taken for the boundary layer to reach 350 m depth should be about 4 times the time that it took to reach the 175 m depth The third observation listed abov e clearly shows that the time to reach epithelium is less than 4 times the time for the boundary layer to traverse half of the stroma, suggesting that FL transport in stroma must be due to a combination of diffusion and convection. The convection in strom a is generated due to the pressure difference created across the cornea during the experiment. The fluid is continuously pumped in and out of the anterior chamber and thus the pressure in the aqueous chamber is larger than the atmospheric pressure, wherea s the pressure on the epithelium tear interface is atmospheric. This pressure gradient leads to convection through the cornea.
62 3.3.2 Swelling of C ornea Water transport in cornea can occur due to a number of driving forces including pressure, osmosis, ele ctro osmosis, and water channels aquaporins. The thickness of various corneal layers particularly stroma is controlled by a balance between water fluxes from various mechanisms. These driving forces persist even after a cornea is excised, but their balan ce likely gets disturbed, and thus various layers of cornea could swell during the experiment. The thickness of various layers of cornea can easily be determined by utilizing the dynamic concentration profiles because each layer has a different affinity f or fluorescein and thus the fluorescence is expected to be discontinuous at the interface between various layers. The discontinuity in fluorescence implies infinite slope at the interface. The discontinuities are smoothened in the experimental profiles ( Figure 3 1.) because the fluorescence measurement at a spatial location includes contributions from the fluorophores in the vicinity, with the contribution from each fluorophore decreasing as a Gaussian away from its location. This effect, also known as th e instrument response function (IRF) smoothes the profiles; yet, the slopes at the interfaces is larger than those in the vicinity. Thus, the location of each of the interfaces can be detected by calculating the slope of the concentration profiles and det ermining the local maxima of slope. After the interfaces are located, the thickness of each layer can easily be determined as the distance between the pertinent interfaces. The thicknesses of epithelium, stroma, and endothelium are denoted by L e L s and L en respectively. The thickness of stroma and epithelium are plotted as a function of time in Figure 3 3 A and Figure 3 3B respectively The thickness of stroma is relatively unchanged in the first 200 minutes, after which it swells at a relatively cons tant rate of micron per min. The thickness of epithelium is also relatively constant for the first 200
63 minutes, after which it swells rapidly by about 10 microns in an hour, followed by a more gradual swelling. The swelling of cornea could be due to th e changes in water in flow and outflow, but it could also be a manifestation of degradation of the physical integrity of the cornea. Since the details of the mechanisms of the corneal swelling are not the focus of this paper, we only utilize the data for time less than 3 hours to model transport in stroma and endothelium. However, during this period the fluorescence in the epithelium is negligible, therefore data from longer times are utilized. These details are discussed in the next section on model deve lopment. 3.3.3 Mathematical Model for Fl T ransport in Cornea 184.108.40.206 Transport in s troma As discussed above, Fl transport in cornea occurs through a combination of diffusion and convection due to the fluid movement from endothelium towards the epithelium ( Equation 3 1 ). The corneal stroma is composed of ~ 260 lamellae of collagen fibrils bound with glycosaminoglycans (GAGs). The solute molecules could bind to collagen and GAGs. However, the binding unbinding events typically occur on a faster time scale com pared to that of diffusion, and thus we assume that the bound and the unbound forms are in equilibrium so that one only needs to write the mass balance for the total solute amount. Therefore, the governing equation for Fl transport in stroma can be written as ( 3 1 ) where C 2 is the total concentration of Fl (or equivalently fluorescence) in stroma, D is the average diffusivity in stroma, and v is the velocity of fluid. The above differential
64 equation needs t o be supplemented by boundary conditions at the interfaces with endothelium and epithelium. 220.127.116.11 Transport in endothelium Transport across endothelium can occur through two routes paracellular i.e., transport through the space in between the cells; or transcellular i.e., transport across the cells. Due to the hydrophilic nature and relatively small molecular weight of 332 Da, the permeability of molecules through the paracellular route is expected to be larger as compared to the permeability through th e transcellular route which requires the molecules to traverse the lipid bilayers of the endothelial cells. However, the area of the space in between the cells available for paracellular transport is much smaller than the area available for transcellular transport, and thus the net transcellular flux could be the leading transport mechanism. While measuring permeability of endothelium through macroscropic experiments using diffusion cells, it is not feasible to determine the dominant mechanism. However, accumulation of F L in the endothelium evident in the profiles in Figure 3 1 shows that the solute must be cross ing the lipid bilayers to accumulate inside the cytoplasm because the paracellular volume in the endothelium is not sufficient to contribute to the measured fluorescence in endothelium. Also, as mentioned earlier, the fact that the ratio of the fluorescence in endothelium and that in stroma at interface with endoth e lium is relatively constant suggesting that the two concentrations are in equilibr ium due to transport through the lipid bilayers of the cells. Further evidence regarding the dominance of the trans cellular transport is that if a constant permeability is assumed for the endothelium, the models fits do not agree with the experimental dat a (fits not shown).
65 To model the endothelium transport, we propose the following mass balance on the endothelial cells, ( 3 2 ) where C 1 is the concentration in endothelium, Co is the concentration in anterior 10 is the partition coefficient of drug between cytoplasm in endothelium and 12 is the partition coefficient between cytoplasm in endothelium and stroma, and k is the permeability of the endothelia l lipophillic membranes. In the above equation, the LHS represents the accumulation; the first term on the RHS account for net transport from anterior chamber to endothelium, and the last term accounts for the net transport from endothelium to stroma. The surface area S is the transcellular area available for transport, and V is the volume of epithelial cells. The endothelium is coupled to stroma through the following boundary condition (3 3 ) The diffusion resistance in s troma (D/L s ) is much smaller than that in endothelium (k) because of the large thickness of the stroma in comparison to that of endothelium (this statement will be tested after values for the parameters are determined). Accordingly, the above boundary con dition can be simplified to ( 3 4) This simplification implies that the stroma concentration at the interface is in equilibrium with the endothelium concentration, which is clearly supported by the data in Figure 3 2 This simplified boundary condition can now be applied in the governing equation for
66 endothelium ( Equation 3 2 ) to yield the following simplified mass balance for endothelium ( 3 5) The above eq uation can be solved by using C 1 =0 as an initial condition to give the following expression for the endothelium concentration ( 3 6 ) where By utilizing the above equ ation into boundary condition ( Equation 3 4 ), we get the following boundary condition for stroma at the stroma endothelium inteface, ( 3 7 ) 21 12 ) is the partition coefficient of drug between stroma and cytoplasm in endothelium. It is to be noted tha t 21 10 is the effective partition coefficient of drug between stroma and aqueous humor. 18.104.22.168 Transport in epithelium The epithelium consists of 5 6 layers of cells with multi stranded tight junctions Based on the mechanism for F L transport in endothelium, the likely mechanism in epithelium is transcellular transport through the cell layers. The cornea transport can thus be modeled as 6 layers of cells with transport barriers between each layer. This model is described in details later, but a simpler approximation is utilized to model the fluorescence profiles in stroma at short times. Due to the multilayer nature of epithelium, it is expected to offer significantly larger resistance to transport, and thus, it
67 can be assumed that in the short time regime, the flux from the stroma to the epithelium is essentially zero, i.e., ( 3 8 ) This simplified model cannot predict the epithelium concentrations, and the detailed epithelial model that will be utilized to fit the epithelium data is presented later. The governing equation for transport in stroma ( Equation 3 1 ) along with the boundary conditions ( Equation 3 7 and Equation 3 8 ) can be solved numerically by finite difference to obtain the concentrat ion profiles as a function of time in stroma, and also the concentration transients in endothelium. It is noted that the model presented above has no non linear terms and so the response is linearly proportional to the solute concentration in the tears. F urthermore, if the fluorescence is linearly proportional to concentration with the same constant of proportionality in each layer, the concentration can simply be expressed in fluorescence units. Based on these assumptions, below we interchangeably use th e terms fluorescence signal and the solute concentration. 22.214.171.124 Parameter e stimation The fluorescence at any location x is contributed by fluorophores located in the vicinity of x, with the contribution from any fluorophore decaying away from its locatio n as a Gaussian. Thus, the measured fluorescence profiles are a convolution of the concentration profiles and the Instrument Response Function (IRF) which given by the following expression,
68 ( 3 9 ) where (2.36 ) represents full width of the Gaussian, which is 20 m for the experiments reported here. The predicted concentration profiles can be convoluted with the IRF to predict the fluorescence profiles, i.e., ( 3 10 ) The four unknown model parameters (D, v, k 1 ) can be obtained by matching the model prediction to the experimental data by minimizing the following objective function E, which is the sum of squares of the difference between model and the experimental results. ( 3 11 ) where C exp and C Model are the measured and predicted concentrations at given position and time, and N represents the total number of data points. The four unknown parameters can be obtained by fitting the entire data in stroma and endothelium, or alternatively t he parameter k 1 can first be determined by fitting the endothelium data, and the rema ining three parameters can be o btained by fitting the stroma l data. We adopt the second approach as the endothelium data is highly sensitive to the parameter k 1 and thus more reliable values of k 1 can be obtained by fitting endothelium concentration, or equivalently the stroma concentration at the stroma endothelium interface. The remaining three parameters were obtained by minimizing the sum of squares ( Equation 3 9 ) in stroma. The values of the fitted parameters are presented in
69 Table 3 1 and the best fit fluorescence profiles are compared with the experimental data in Fig 3 4. 3. 4 Sensitivity Analysis Since the model has a relatively large number of parameters it is i mportant to determine whether the parameter values listed in Table 3 1 are unique or a number of different combinations of the parameters can fit the data. We adopted various approaches to test the reliability of the three parameters (D, v, ) including c onstructing contour plots, obtaining correlation coefficients, and sensitivity indices. 3.4.1 Contour Plots and C orrelation C oefficients The contour plots were constructed by picking any two parameters, varying them within 50% of their estimated values and plotting contours along which the error is constant. The shapes of the contour plots reflect the correlation between the two parameters that are varied for that contour plot. For instance, if the contour plots around the minimum are concentric and cu lminate in a point or a small line segment, it implies that parameters are not correlated around the estimated values of the parameter. However if the contours are elliptic culminating in a line, it implies that the parameters are correlated, i.e., changes in one parameter can be compensated by changes in the other parameter, and thus accurate determination of the parameters is not possible. If one the other hand, the contours are vertical (or horizontal lines), the error is independent of the parameter o n the x axis (or y axis for horizontal contours). The contour plots in Figure 3 5A and 3 5B v pair converge towards a single point, which mean that these parameters are well identified. The contour plots for the D v pair (Figure 3 5C) show that close to the global minimum, there are multiple contours that have the similar values of error, which implies
70 existence of multiple local minima. In this case, the parameter estimation might depend on the initial guesses of parameters. However the three minima are relatively close to each other, and thus the best fit value is reliable. The qualitative information visible in the contour plots can be quantified by computing the correlation coefficients between various pairs of parameters. The correlation coefficient s for each pair of parameters are presented in Table 3 2. All the correlation coefficients between the parameters lie between 0.9 and 0.9 which proves that parameters are not correlated. 3.4.2 Sensitivity Index To further examine the sensitivity of each model parameter, we obtain a sensitivity index which is a measure of the relative incr ease in error for changes in that parameter. A large value of the index implies that small changes in the parameter lead to rela tively large changes in the error, and thus the parameter value is robust. Since all parameters except one are fixed in this analysis, the error can be expanded as a Taylor series around the point of minimum error, ( 3 1 2 ) where E min is the minimum error or the error corresponding to the predicted parameter, u is the specific parameter (any one of the eleven model parameters), and u min is the value of u at which the error is minimum or the estimated value of u. It is noted that the li near term is absent from the above expansion because the first derivative dE/du is zero at the minimum. As discussed in the previous chapter (chapter 2), t he sensitivity index is defined by the following equation
71 ( 3 1 3 ) The second derivative of E was obtained by computing E around u min in the range 0.05 E min
72 epithelium permeability reported in  justifies our assumption of negligible permeability to solve the model for short time scales. 3.6 Conclusion A mechanistic pharmacokinetic model has been developed to explain the transient concentration profiles of FL in rabbit cornea. Apart from traversing through paracellular route, FL molecules also transports i tself across the cells through transcellular route. Model developed could play a major role in developing better ocular formulations and is a significant improvement over previously existing compartmental models.
73 Figure 3 1 T r ansient concentration profiles of Fluorescein in rabbit cornea, when endothelium side was exposed to a fixed concentration of the dye.
74 Figure 3 2 P lot of concentration of fluorescein at stroma endothelium interface vs concentration in endothelium(cytoplasm in endothelium) with time as parameter.
75 Figure 3 3 Transient swelling of corneal layers specifically, (A)Stroma and (B) Epithelium.
76 Figure 3 4 Comparison of model predictions and experimental profiles of fluorescein concentration in stroma for short times (t < 3 hours). Here x=0 represents endothelium stroma interface while x=334m represents stroma epithelium interface.
77 Figure 3 5 Contour plots are plotted by picking two parameters and fixing all other parameters. Value of the objective function, error, is the third dimension. Along a particular contour error remains constant. A B C
78 Table 3 2 Values of parameter in the model and their sensitivity to the model Parameter Estimated value Units Sensitivity Index 1.79 132.8 k 1 0.1176 hr 1 94.0 D 7.76 10 12 m 2 /s 17.8 V 1.38 10 8 m/s 4.32 Table 3 3 Correlation coefficients are calculated for limiting contours encompassing the minima. Parameter D V 1 0.58 0.087 D 1 0.3274 V 1
79 CHAPTER 4 DRUG TRANPORT IN HEMA CONJUNCTIVAL INSERTS CONTAINING PRECIPITATED DRUG PARTICLES 4 .1 Introduction This chapter focuses on development of polymeric conjunctival inserts for delivery of cyclosporine A for dry eye treatment. Inserts will be placed in conjunc tival sac of the eyes and will release drug in tears which will go towards cornea or conjunctiva. Drug exists as particles in these devices which is verified using imaging techniques. Also a mechanism of transport of drug in these HEMA inserts has been dis cussed. Although the mathematical equations describing the model have been proposed for cylindrical geometry, similar mechanism could be used to propose a model for any polymeric system containing drug as particles. 4 2 Materials and Methods Hydro xyl ethy l methacrylate (HEMA), E thylene glycol dimethacrylate (EGDMA), and A zobisisobutylonitrile (AIBN) were purchased from Sigma Aldrich (St. Louis, MO); Cyclosporine A was purchased from LC Labs (Woburn, MA); and Silastic laboratory tubing of two different siz es (ID 1.02 mm and 1.47 mm) were purchased from Dow drug release experiments was purchased from Sigma Aldrich (St Louis, MO). 4 .2.1 Fabrication of Inserts The inserts were fabricated in two different designs using p HEMA and p EGDMA, which are common materials for commercial contact lenses. The basic structure of the design I inserts is shown in Figure 4 1A, with a p HEMA core, which is loaded with cyclospo core, about 1.35 mL of HEMA monomer was mixed with EGDMA monomer in various
80 mixture was purged with N 2 for about 10 minutes to remove the O 2 in the monomer. Next, 10 wt% of cyclosporine A and about 0.03 g of AIBN (initiator) were added and the mixture was stirred for about 5 minutes. The resulting solution was filled into Silastic tubing with 1.02mm ID that served as the molds for the polymerization. The filled molds minutes for polymerization. After the polymerization, the p HEMA core was taken out of the mold to obtai n a drug loaded design I insert of 1.02 mm diameter with 1X crosslinking and 10% drug loading. The degree of crosslinking was increased or decreased by changing the amount of EGDMA in the polymerization mixture to obtain inserts with 0X, 10X or 20X crossli nking, which contain 0, 10 and 20 times the EGDMA utilized in the procedure described above. Also the amount of drug loading was altered to prepare inserts with drug loading varying from about 0 to 30%. The inserts without drug (0% drug loading) were soa ked in drug PBS solutions to load drug into the inserts. Subsequently, drug release studies were conducted with these inserts, and fitted to a diffusion model to obtain diffusivity and partition coefficient of cyclosporine in the inserts. The design II in sert shown in Figure 4 1B consists of drug loaded 1.02 mm dia p HEMA core and a concentric 0.225 mm thick EGDMA shell. To prepare the monomer mix for the shell, 0.03 g of AIBN was added to purged 1.35 mL of EGDMA, and the mixture was stirred for 5 minute s. The 1.02 mm diameter p HEMA core loaded with cyclosporine A (design I insert) was first inserted into Silastic tubing with a 1.47 mm ID, and the gap between the core and the tube was filled with the EGDMA solution, while ensuring that the p HEMA core w as centered. The tubing was sealed with office
81 polymerization. The end product had a substantially cylindrical shaped core shell structure, with a 1.02 diameter p HEMA core loaded wi th cyclosporine A, surrounded by a 0.225 mm thick shell of p EGDMA. In some cases, the shell of the design II insert was prepared with a mixture of HEMA and EGDMA to reduce the degree of crosslinking in the shell. 4 .2.3 Drug Release After the inserts were fabricated, they were cut into cylinders of variable lengths using a surgical blade, and then used in drug release studies. The drug release was measured in 3.5ml of phosphate buffer saline (PBS), which was replaced every 24 hours to simulate perfect sink conditions. The concentration of cyclosporine A in the release medium was determined with an HPLC (Waters, Milford, MA) equipped with a reverse phase C18 column (Waters, Milford, MA) and a UV detector. The mobile phase was 70% acetonitrile and 30% deioniz ed water at a flow rate of 1.2 mL/min. The column 4 3 Results and Discussion The diffusivity of cyclosporine A through the p HEMA inserts will play an important role in the drug release dynamics. Accordingly, before discussing the drug release profiles from the inserts, we report results for diffusivity obtained by theoretical models and by release studies from inserts in which drug was loaded by soaking in drug PBS solution 4 3. 1 Estimation of Diffusivity in the p HEMA I nserts A number of researchers have developed theoretical models for estimating diffusivities of solutes through porous hydrogels such as p HEMA. Brinkman developed
82 the following relationship between the hy draulic permeability of the hydrogel an d the solute diffusivity given  ( 4 1) where D th is the theoretically determined diffusivity of the molecule through a porous medium of hydr aulic permeability k, water, T is the temperature and k B ynam ics and also by experime nts  It has however been suggested tha t Equation 4 1 is valid only for diffusion in pressure driven flows and in its absence, the coefficient of should be 1/9 instead of 1/3  Due to the absence of pressure driven flow in our experiments, we use the eq uation by replacing 1/3 with 1/9. The parameters required for estimating cyclosporine A diffusivity thr ough a p HEMA gel are listed in Table 4 1. Based on Equation 4 1 the cyclosporine A diffusivity in the p HEMA gels was estimated to be 10.210 12 m 2 /s. 4 3.2 Measurement of Diffusivity in the p HEMA inserts To measure diffusivity of cyclosporine A in ins erts, we prepared inserts without drug, and then loaded drug by soaking the inserts in drug PBS solution. Subsequently, drug release profiles were measured and fitted to the diffusion equation to determine the diffusivity. Specifically, 7.5 mm long inser ts were fabricated and three such inserts were soaked together in 7 ml of drug PBS solution with a concentration a period of 6 days. The three drug loaded inserts were then removed from the drug solution and soaked in 2 m l of PBS which was changed at regular intervals to maintain
83 perfect sink conditions. The concentration of drug in the release medium was measured every time the fluid was replaced. The cumulative drug release from these experiments is plotted as a functi on of time in Figure 4 2A. Drug transport from the cylindrical inserts can be modeled as a 1 dimensional diffusion because the length of the inserts is much longer than the radius, i.e., ( 4 2) where C(r,t) is the total drug concentration in the insert at position r and time t, and D is the diffusivity of the drug in the insert. The drug release profiles showed that the loading duration of 6 days was not sufficiently long to reach equilibrium, and thus dynamics of both loadin g and release phase need to be simulated. The drug uptake can be simulated by solving the differential equation ( Equation 4 2.) with the following boundary and initial conditions: at r = R ( 4 3) at r = 0 ( 4 4) at t = 0 ( 4 5) where K is the partition coefficient of drug in HEMA, is concentration of drug in solution in which uptake experiments were conducted and R is the radius of the insert. The bou ndary conditions are based on the negligible change in concentration during the uptake due to large volume of fluid used ( Equation 4 3 ) and symmetry about the centerline ( Equation 4 4). The differential equation ( Equation 4 2 ) along with conditions Eq uati ons.4 3 to 4 5 can be solved analytically to yield the following solution for the concentration profiles C(r,t) in the insert
84 ( 4 6) where J 0 and J 1 n are the zeroes of J 0 i.e., roots of the equation J 0 n ) = 0. Based on the above solution, the concentration in the insert at the end of the loading duration, i.e., t = t 1 = 6 days is given by the above equation with t = 6 days. The drug release from th e inse r ts can be simulated by solving the differential equation ( Equation 4 2) with the following boundary and initial conditions at r = R ( 4 7) at r = 0 ( 4 8) at t = 0 ( 4 9) where C 1 ( r ) is defined by Equation 4 6 with t = 6 days. The boundary conditions are based on the perfect sink ( Equation 4 7) and symmetry about the centerline ( Equation 4 8). Equation 4 2 along with Eq uations 4 7 to 4 9 can be solved analytically to yield the following solution for the concentration profiles C(r,t) in the insert during release experiments ( 4 10) The cumulative mass of drug released into the solution M(t) can be related to flux of drug at the boundary, i.e. at r = R by th e following equation ( 4 11)
85 Substituting Equation 4 10 in Equation 4 11 and integrating with respect to t yields the following equation for M(t) ( 4 12) where V insert is the volume of inserts soaked in pbs. Diffusivity, D, and partition coefficient, K, are unknown and are therefore used as a fitting parameter to fit the experimental data for cumulative amount released M(t) to Equation 4 12 to yield values of (0.95 0. 29) 10 13 m2/s and 41.8 4.73 for D and K, respectively. The simulated profile with average values of D and K is plotted in Figure 4 2B. along with the experimental profile. The value of the measured diffusivity D = (0.95 0.29) 10 13 m2/s is more t han an order lower than the value of Dth = 10.210 equation. This difference between the diffusivity values could potentially be attributed to the binding of the drug molecules on the p HEMA polymer chains. A majority of the cyclosporine A that is absorbed into the p HEMA inserts during soaking is absorbed on the polymer as evident from the high partition coefficient. The free cyclosporine A molecules can diffuse through the pores in the p HEMA hydrogel, and the bound molecules could potentially diffuse along the polymer chains Additionally, there is a very rapid exchange of the bound and the free cyclosporine A molecules. Assuming that the exchange between the bound and free molecules is more rapid than diffusive ti me scales, an effective diffusivity, D, can be defined taking into account both surface and free diffusion of the bou nd and the free forms  ( 4 13)
86 where f is volume fraction of water in hyd rated HEMA insert, D f is the bulk diffusivity of cyclosporine A inside the gel i.e., through the porous structure in the polymer, and D su is the diffusivity of cyclosporine A on the surface of polymer. The value of f was determined to be approximately 40% by water swelling experiments as discussed later ( Figure 4 12). Assuming negligible surface diffusion, the expression for effective diffusivity simplifies to Using the value of estimated diffusivity based on easured values of f and K yields a value of D = (0.98 0.11) 10 13 m 2 /s, which is in reasonable agreement with the measured value of (0.95 0.29) 10 13 m 2 /s. Using a t test analysis, we can say that the difference in diffusivities obtained from two different methods is statistically insignificant. This reasonable agreement suggests that the discrepancy between the measured and predicted values for diffusiv ity arose due to drug binding to the polymer, and that this effect can be taken into account by defining an effective diffusivity through Equation 4 13 Below we discuss cyclosporine A release from inserts in which the drug was loaded by direct addition to the polymerizing mixture. 4 3.3 Design I I nsert 4 .3.3.1 Effect of length on drug release Figure 4 3A shows the cumulative amount of drug released as a function of time from three 1.02 mm diameter inserts of different lengths (4, 7.5 and 10 mm for the shor t, medium and long inserts, respectively) with 20% drug loading and 0 X crosslinking. The release profiles appear to be approximately zero order for the first 15 days for all the three cases. The release rates increase with increasing length and in fact are linear in length for longer inserts as shown in Figure 4 3B in which the % release (cumulative
87 release/ initially loaded amount x 100) overlap for the medium and the long inserts. The ear dependence of released amount of drug on length is expected because the curved surface areas of the longer (7.5 and 10 mm long) devices are much larger than their cross sectional areas; therefore majority of the drug flux is in the radial direction. A ccordingly, the axial transport can be neglected while modeling drug release from these systems, which is described in a later section. 4 .3.3.2 Effect of drug loading To explore the effect of drug loading on the drug release profiles, we prepared 1.02 mm diameter and 7.5 mm long inserts with 0 X crosslinking and several different drug loadings such as 5%, 10%, 20% and 30%. The results in Figure 4 4A show that the cumul ative release curves are linear in time and independent of drug loadings for certain period. The instant of time at which a curve deviates from the other overlapping curves depends on the drug loading, with higher loadings inserts exhibiting linear, loadin g independent behavior for longer times. We propose that the independence of the release rate on drug loading at short times arises from the fact that the drug release rates are initially controlled by the mass transport resistance on the fluid side. The resistance in the gel increases with time due to the thickening of the mass transfer boundary layer, and beyond certain time, the release is controlled by the gel, and subsequently the drug release rates begin to depend on the drug loading. The details o f this mechanism will be described and validated later in the section on model development.
88 4 .3.3.3 Effect of crosslinking To explore the effect of crosslinking on release profiles, inserts were prepared with crosslinking of 0X, 10X and 100X respectively, with 0X, 10X and 100X crosslinking referring to 0%, 2.25% and 22.5% by wt of EGDMA in the monomer mix, respectively. These inserts were each 7.5 mm long, 1 mm in diameter and contained 20% drug. The results in Figure 4 4B show that increasing the crossli nking from 0X to 10X does not have a significant effect on the drug release, but increasing crosslinking to 100X the drug release rates are relatively similar for th e 0X and 10X inserts does not imply that the drug diffusivity is the same for both systems. As mentioned above, at short times the drug release rates are controlled by the fluid, and accordingly the release rates are independent of both drug loading and g el crosslinking. For the 100X crosslinking, the gel begins to control release at an earlier time and so its release rates are different than those for 0X and 10X systems. In fact at longer times, the release rates from the 10X systems are expected to be less than that for the 0X systems. The above results show that the drug release rates from these devices can be controlled by manipulating the geometry, crosslinking, and drug loading or a combination of these parameters. 4 .3.3.4 Effect of convection The e xperiments described above were performed without forced stirring to simulate the limited mixing conditions in the conjunctival sac. To explore the transport mechanisms, drug release experiments were conducted with 7.5 mm long, 1mm diameter plugs with 5%, 10%, 20% and 30% drug in presence of forced stirring. Comparison of the cumulative release profiles in presence of convection shown in
89 Figure 4 4C with those in absence of convection ( Figure 4 4A) clearly show that stirring increases the drug release rate s, further supporting the hypothesis that that limited mixing in the release medium is impacting the release from the inserts and it must be taken into account while modeling the drug release. 4 .3. 3.5 SEM imaging of i nserts The drug solubility in the mono mer mixture is much higher than that in the HEMA polymer and thus the drug molecules are likely to form precipitates during the polymerization process. The presence and sizes of the precipitates were verified directly through imaging of the cross sections of the drug loaded inserts in JEOLJSM 6400 scanning electron microscopy (X SEM). The X SEM images for pure HEMA insert (0% drug loading) along with the images for inserts with 5%, 10% and 15% drug loading are presented in Figure 4 5. The imaging clearly proves the existence of precipitates, which are fairly non uniform in size, with the largest aggregates about 5 10 microns in size for all drug loadings. Although the precipitate sizes are in the micron range, the particles are much smaller than the devic e size, which is about 1 mm, and thus in the model developed below, the particles can be considered as point sources uniformly dispersed in the gel matrix. 4 .3. 3.6 Model The X SEM images prove that cyclosporine A drug is present as particles inside the con junctial inserts. Also, prior experimental studies and models for materials that contain drug as particles show that the plots of % drug released as function of where t is the time and Cp is the drug loading overlap for different d rug loadings. The plots of % release from the inserts as a function of ( Figure 4 6) do overlap for
90 conjunctival inserts, which is consistent with release rates from devices that contain drugs di spersed as particles  Therefore conjunctival inserts can be modeled as cylinders which contain drug embedded in a polymer matrix as particles. Additionally, the curves in Figure 4 4 are linear at long times, which is expected  but each curve has a non linear curved portion at short times which is quite interesting. In fact, in the non linear portion, the rate of drug released from each insert is the same, and is thus independent of the drug loading. Further more, the amount released in this non linear portion increases with increased mixing, suggesting that the short time behavior is caused because of the mass transfer resistance on the fluid side. In general, drug transport from inside the insert to the bul k fluid faces two mass transfer resistances in series resistance due to diffusion in the gel and that due to diffusion in the fluid. The resistance in each phase is directly proportional to the boundary layer thickness. The boundary layer thickness in t he fluid depends on the extent of mixing and is independent of time, whereas, the boundary layer thickness in the insert is zero at initial times, and it then grows as square root of time. Accordingly, at short times the resistance in fluid will dominate because of very small mass transfer boundary layer, and hence negligible resistance in the gel, and at long times the resistance in gel will dominate because of thickening of the boundary layer in the gel. Below, we develop a mathematical model for drug re lease from the inserts that takes both resistances into account and explains all the observed trends in the drug release profiles. Since the drug loading is above the solubility limit, the hydrated conjunctival inser ts contain drug in three forms  (i) free drug dissolved in the fluid that hydrates the gel, (ii) drug adsorbed on the polymer surface, and (iii) drug present as
91 aggregates/particles. On exposing the inserts to PBS, the un aggregated drug diffuses out of the insert to reduce the free concentration of the drug below the solubility limit, which leads to dissolution of the drug particles. The breaking up of aggregates will form a depletion zone near the surface, whose length is denoted by which will incre ase in time. To model the problem, we assume that the concentration profile in the depletion zone is in pseudo steady state, i.e., the time scale for transport is controlled by the time scale for the growth of the depletion zone. This is a reasonable ass umption because the total drug loading is significantly above the solubility limit, and so a very large fraction of the drug exists as aggregates. To develop a mass balance equation, consider the interface between the region that is depleted of all the dr ug particles due to drug transport into the PBS and the core of the insert that still has drug as particulates. The thickness of the depletion zone is denoted by thus this interface is located at a distance (R ) from the axis of cylinder, where R is t he radius of the insert. A graphical representation of the model is presented in Figure 4 7. The radial diffusive flux of the ( 4 14) where C = C(r, t) is concentration at time t and distance r inside the depletion layer ; D is the effective diffusivity of cyclosporine A inside the gel, L is the length of the cylinder, and C p is the initial loading of drug inside the cylinder. Equation 4 14 can be simplified to yield ( 4 15) The above governing equation is subjected to the following boundary conditions:
92 at ( 4 16) at ( 4 17) at ( 4 18) where K is the partition coefficient for the gel, i.e., the ratio between the equilibrium concentrations of drug in the gel and that in the aqueous phase. Furthermore, C is the solubility limit of cyclosporine A in the aqueous phase, D and D fluid are the effective diffusivities of cyclosporine A in the insert and in the release medium (PBS), respectively, C f is the drug concentration at any instant t in the fluid at the boundary with the insert, i.e., at r = R, and f is the boundary layer thickness of the mass transfer boundary layer in the fluid that depends on the extent of mixing. C b is the concentration of cyclosporine A in the bulk in PBS (release medi um) which would be zero if perfect sink conditions were assumed. The boundary conditions in Equation 4 16 defines equilibrium at r = R between the concentration in the aqueous phase in the gel, which must be the solubility limit C and the total drug co ncentration in the gel, which is accordingly KC Similarly, at r = R, i.e., on the surface of the cylinder in contact with the release medium, the gel concentration C will be in equilibrium with the fluid concentration at r = R, which is denoted by C f ( E quation 4 17 ). It is noted that the drug concentration in the mass transfer boundary layer on the fluid side decreases from C f at r = R to the bulk concentration C b at r = R + f where f is the mass transfer boundary layer thickness in PBS. Accordingly, the diffusive flux in the mass transfer boundary layer in fluid is This expression assumes that the boundary layer
93 thickness is much smaller th a n the insert radius. A slightly more accurate expression that accounts for the curvatu re can be easily include, if desired. The diffusive flux in fluid at r = R must equal the diffusive flux inside the gel at r = R, which is given by the expression By equating these two fluxes, we obtain the boundary condition given by Equation 4 18 The above sets of equations are consistent with the observation that the release profiles for all drug loadings overlap when plotted as a function of The diffusion of drug into the fluid leads to an increase in concentration of cyclosporine A in the bulk in PBS (release medium) C b which can be determined from the following mass balance ( 4 19) where V b is the volume of PBS in which release experiments were conducted. The concentration C b increases with time but it is reset to be zero every time the pbs is replaced. Equation 4 15 can be integrated with respect to r to get Equation 4 20 constant that needs to be determined. ( 4 20) B y utilizing the three boundary conditions ( Equation 4 16 to Equation 4 18) in Equation 4 20, we obtain the following ordinary differential equation for (t), ( 4 21)
94 Equations 4 19 and Equation 4 21 now represent a set of coupled ordinary differential equations that can be solved simultaneously to obtain and C b as a function of time. As stated above C b is assigned to be zero every time the fluid is replaced. The values of the known parameters th at are needed to solve the model are listed in Table 4 2. The diffusivity of cyclosporine A in aqueous phase, D fluid was obtained by using Stokes Einstein equation for cyclosporine A using a radius of 9.5  and temperature 298 K. The rate of the drug diffusing from the insert into the release medium N is given by the following expression ( 4 22) The cumulative mass of cyclosporine A released into the release medium, P, is related to can be obtained by integrating the release rate N with respect to time. The values of P obtained as a function of time from the model can be fitted to experimental data to f Since the effecti ve diffusivity D was earlier shown to be equal to the parameter KD can be simplified to It is noted that while the amount of drug loaded into the insert is known, a fraction of it was lost during fabrication, and some fraction may be irreversibly trapped. Accordingly, the total amount of drug released from an insert was also utilized as a parameter to fit the data. The fit was done by minimizing the least square error between the predicted and measured cumulat ive release profiles. A few sample comparisons between the predicted and the experimental profiles for the cumulative release are presented in Figure 4 8A (without convection) and Figure 4 8B (with convection). The model predictions match the data well pr oving the validity of the proposed mechanisms and the model.
95 We estimate KD (= ) by fitting the model to the release data with low drug loadings (for the case of without convection) and use that value to fit all the release profiles ( Figure 4 8A.). We estimate a value of KD = = (10.93 2.37) 10 12 m 2 /s f, to be 0.47 0.06 mm. The values of the diffusivity in an insert with a particular drug loading should be independent of degree of mixing and must be same for the case of convection and without convection. Also, mass transfer boundary layer in fluid which is a representation of amount of convection in fluid should be different for the cases o f convection and without convection. Therefore we use the same value of diffusivity and different value of thickness of the mass transfer boundary layer to fit the data with convection ( Figure 4 f obtained from the fits for the case of convection is 0.154 0.05 mm. A t test analysis showed that the boundary layer thicknesses for the case of convection and without convection are significantly different statistically (p<0.01) and that the values decrease on increasing mixing. Utilizing a value of 41.8 4.73 for K and the fitted value of KD = = (10.93 2.37) 10 12 m 2 /s yields D (= ) to be (2.62 0.27) 10 13 m 2 /s, which is of the same order but more than twice the values of effective diffusivity obtained from the direct measurements described previously. This difference could potentially be due to the impact of drug on the polymerization. Alternatively, the val ue of C* in the gel could be different from the solubility limit of the drug in bulk fluid reported in Table 4 2.
96 4 3.4 Design II Insert 4 .3.4.1 Effect of length The design II insert comprises of a 1.02 mm diameter HEMA core with a concentric 0.235 mm thi ck EGDMA shell. Figure 4 9A shows drug release profile from 3 inserts of different lengths (4mm, 7.5mm and 10mm) containing 20% drug. The drug release is approximately zero order for first 10 days and its magnitude increases linearly with length as clearly evident in Figure 4 9B in which the % Release ((cumulative release/ initially loaded amount) x 100) overlap for the 7.5 and 10 mm inserts. The 7.5 rate from the design I insert of same length and drug loading. The linear dependence of released amounts on length is expected because the curved surface of the devices is much larger than the cross section area for the 7.5 and 10 mm inserts. 4 .3.4.2 Effect of drug loading Fig ure 4 10A shows the release profiles of three 7.5 mm long design II inserts with drug loadings of 5%, 20% and 30%. The release profiles overlap within error bars for first few days and start deviating as time increases suggesting that here again at short t imes the drug release rates are controlled by the transport in the fluid. 4 .3.4.3 Effect of c onvection The drug release experiments reported above were conducted without stirring or mixing to mimic the limited mixing in the conjunctival sac. The effect of convection was explored by conducting release experiments with stirring from 7.5 mm long design II conjunctival inserts of diameter 1.47mm with core diameter of 1.02mm ( Figure 4 10B). On comparing the results in Figure 4 10B and in Figure 4 10A, one can conclude that
97 convection increases the amount of drug release showing that the mass transfer in the fluid controls the release rates in early part of drug release. 4 .3.4.4 Mechanisms A 0.235 mm thick EGDMA shell is expected to provide significant resistanc e to drug transport and so only a 60% reduction in drug release rates (reduced from 20 g/day to 8 g/day) may be surprising. However the drug that is released from the design II inserts with pure EGDMA shell does not diffuse through the shell but through the cracks that form in the shell due to stress developed in the shell because of differences between the swelling behavior of the EGDMA shell and the HEMA core. Image of the cracks formed in a design II conjunctival insert with 20% drug loading taken fr om a sony DSC T700 digital camera is presented in Figure 4 11A. An enlarged image of the largest crack in insert taken from an optical microscope at a resolution of 10X is presented in Figure 4 11B. Cracks are formed in the radial direction and have varying sizes, largest one having a size of about 0.2mm. The EGDMA water content is almost negligible and the HEMA water content is about 40%. Thus swelling of the HEMA core leads to stresses in the EGDMA shell leading to cracks that occupy roughly 40% of the surface. Accordingly, the design II inserts are expected to release drug at a rate of about 40% of the Type I insert, which is close to the experimentally observed value. Furthermore, the drug r elease rates are independent of drug loading and are zero order in time because the rate limiting step is drug transport in the fluid. At longer times, the drug release rates will depend on drug loading and will cease to be zero order. A mathematical mod el for the design II inserts is more complex than that for the design I insert because the drug transport occurs both in radial and axial directions
98 around the cracks, which are of complex shapes distributed randomly along the length, and is not presented here. 4 .3.4.5 Effect of crosslinking in shell Figure 4 10C shows release profiles for four design II inserts of length 7.5 mm, overall diameter 1.47 mm, and drug loading of 20% in the core, with different degrees of crosslinking in the shell. The ratio of HEMA and EGDMA was varied to observe the effect of degree of crosslinking in the shell on the drug release. We observe that as we increase HEMA fraction in shell from 0% to 25%, the rate of drug release decreases, but on further increasing the HEMA fractio n to 50%, the release rates begin to increase. This behavior occurs because of dual transport mechanisms in parallel: diffusion through the shell and diffusion through the cracks. As explained above, the inserts with pure EGDMA shell release drug through t he cracks that form on the surface due to differential swelling between the HEMA core and the EGDMA annulus. The drug transport through the EGDMA shell is negligible because of the negligible drug diffusivity through the EGDMA matrix. As the HEMA content i n the shell increases from 0 to 25%, the swelling difference between the core and the annulus decreases leading to a reduction in the crack formation, and a consequent reduction in the drug release rates. As the HEMA fraction in the shell increases beyond 25%, the crack formation further reduces, and thus the amount of drug that diffuses through the crack likely reduces. However this reduction in drug transport through the cracks is compensated by the increased drug diffusion through the shell due to the in creased pore size of the HEMA + EGDMA matrix, and thus the total transport rates increase with HEMA addition to the core.
99 To quantitatively validate the proposed mechanism on the effect of HEMA addition to the shell, we measured the water content of HEMA + EGDMA gels with HEMA fraction varying from 0 to 100% ( Figure 4 12). The data shows that the water content (based on increase in weight due to hydration) increases from about 0% for the pure EGDMA gels to about 45% for pure HEMA gels. The differential sw elling defined as the difference in water content of the core material (pure HEMA) and the shell material is about 45% for the pure EGDMA shell and about 40% for the 25% HEMA shell. Since the crack formation is expected to be proportional to the different ial swelling, the inserts with 0 and 25% HEMA in the shells are expected to have about 45% and 40%, respectively of the surface occupied by cracks. Consequently, the 0% HEMA and 25% HEMA shell inserts should release drug at rates that are about 45% and 40 %, respectively of the rates for the design I insert with same length, core diameter and drug loading, which is consistent with the data shown in Figure 4 10C. With further increase in the HEMA fraction, the water content in the shell becomes high enough ( ~ 10% for the 50% HEMA shells) to allow diffusion of the drug through the shell, thus leading to an increase in the release rates with increasing HEMA fraction in the shell. 4 3.5 Bioavailability of C onjunctival Inserts The inserts developed here can rel ease about 10 20 g/day depending on time, length, loading, coating, and degree of mixing in the fluid surrounding the insert. The mixing in the inferior conjunctival sac is expected to be small, and thus the in vivo release rates may be smaller than the values obtained in the in vitro experiments. The exact release rates and the therapeutic efficacy of these devices can only be
100 established through in vivo experiments, but a simple pharmacokinetic model could be useful to obtain a rough estimate of the ef ficacy of these systems. To develop the pharmacokinetic model, we perform a mass balance on the drug released from a device placed in the inferior conjunctival sac of an eye. A human eye has a tear volume V of about 7 10 l, and this volume is maintained through a balance between tear secretion from the lacrimal glands and conjunctiva and tear elimination through drainage through the canaliculi into the nasal cavity and also through evaporation. The tear volume increases after eye drop instillation and th en decreases to the baseline value in about 5 10 minutes depending on the viscosity of the instilled fluid. The drug released from the conjunctival insert into the tear film can either diffuse into the ocular tissue through the cornea and the conjunctiva, or exit the tear volume with tears that drain into the nasal cavity. Thus, a mass balance on the drug released from the insert gives the following equation, ( 4 23) where V is total volume of fluid on ocular surface, F is the drug r elease rate by conjunctival inserts (~ 10 20 g/day), kA is the sum of the product of the area and the permeability for the cornea and the conjunctiva, and C is the dynamic drug concentration. Since the time scale for release from the inserts is a few days which is much longer than the time scale for concentrations in the eyes to reach a steady state, one can assume that the drug release from the inserts could be considered to be at a pseudo steady state, i.e., ( 4 24)
101 The details o f the mechanism of the therapeutic action of cyclosporine A and the exact site of action are not exactly known and so for simplicity we assume that both the drug that enters the cornea and also the conjunctiva can lead to therapeutic benefits. Accordingly we define bioavailability as the ratio of the drug that enters the ocular tissue (cornea or conjunctiva) and the amount released by the insert, i.e., ( 4 25) We assume corneal and conjunctival permeability to be similar and equal to 1.110 6 cm/s  and corneal and conjunctival area to be 1.04 cm 2 and 17.65 cm 2 respectively  Using q drainage ranging from 110 11 m 3 /s to 410 11 m 3 /s  we obtain bioavailability values of conjunctival inserts ranging from 34% to 67%. The typical dry eye treatment based on cyclosporine A involves delivery of two drops of Restasis each day. Restasis contains 0.05% drug, and th us two 28 l drops of this cyclosporine A delivered via eye drops is expected to be small due to the small residence time o f about 10 minutes in the eyes  and thus a release of about 10 15 bioavailability for inserts. This simple pharmacokinetic model suggests that the release from the inserts develo ped here may be therapeutically efficacious. 4 .4 Conclusion We have explored the mechanisms of cyclosporine transport in HEMA rods for developing conjunctival inserts. The diffusivity of the drug in the inserts can be correctly predicted by using Brinkman been taken into account. The release of the drug from the inserts exhibits some
102 interesting trends that cannot be explained by simple diffusive transport in the gel. For instance, the release rate s are zero order in time and are independent of drug loading and crosslinking for certain duration, beyond which the rates decrease in time and are lower for lower loadings and higher crosslinking. All of these effects arose due to limited mixing in the f luid that resulted in creation of a mass transfer boundary layer in release medium. In general, drug transport from inside the insert to the bulk fluid faces two mass transfer resistances in series resistance due to diffusion in the gel and that due to diffusion in the fluid. The resistance in each phase is directly proportional to the boundary layer thickness. The boundary layer thickness in the fluid depends on the extent of mixing and is independent of time, whereas, the boundary layer thickness in the insert is zero at initial times, and it then grows as square root of time. The boundary layer thickness scales as in inserts in which the drug is below the solubility limit but scales as in inserts in which the drug is dispersed as particles (all notation used here is described previously in the text). In inserts or other gels that do not contain drug particles, the boundary layer in the device grows rapidly and thus control the overall release behavior except for extremely short times in which fluid mixing may play a role. However, the very slow growth of the mass transfer boundary layer in gels that contain drug particles ensures that the mass transfer resistance in the fluid will be r ate limiting for a larger duration of time. Enhanced mixing reduces the mass transfer barrier in the fluid, but cannot completely eliminate it. Thus, the behavior of zero order release will likely be observed from all gels in which drug concentration is so high such that drug is dispersed as particles. In all such cases, the simple diffusion model will not
103 match the data but the modified model proposed here that incorporates the presence of the particles and the mass transfer boundary layer in the fluid will be needed. The proposed model can be used to determine the release rates for any degree of mixing. The extent of mixing is not yet established in eyes; therefore in vivo experiments would have to be conducted to determine the release profiles under ph ysiological equation and also directly measured by loading and releasing drug into inserts that were prepared without any drug. The values of diffusivity measured agreed wi th the value assumed to diffuse, i.e., the drug adsorbed on the polymer was assumed to be in equilibrium with the free form but not diffusible along the surface. Both, the directly value obtained from fitting the model to drug release from the design I insert. The difference could be due to the effect of the drug directly added to the mon omer mixture on the polymerization, and/or the differences between the solubility limit of the drug in the pores of the gel and solubility limit in bulk fluid. compared to abou t 28 g/day delivered by Restasis. The duration of release and the amount released each day can be increased by increasing the drug loading and/or crosslinking, and length, respectively. The release depends on the extended of mixing, which is limited in the lower conjunctival sac, but not yet established definitively; therefore in vivo experiments would have to be conducted to determine the release profiles under physiological mixing. It is noted that although the devices proposed here
104 seem promising, bu t their potential for medical applications needs to be demonstrated through in vivo animal and human trials to determine the degree of comfort, biocompatibility, in vivo release profiles, and therapeutic efficacy.
105 Figure 4 1 Schematic representation of Design I (A) and Design II (B) inserts (not to scale). HEMA + EGDMA + Drug 1mm A 1.47mm 1mm EGDMA or EGDMA+HEMA Shell HEMA core + Drug B
106 Figure 4 2. Estimation of diffusivity of cyclosporine A in p HEMA insert (A) Drug Release from the inserts which were soaked in a cyclosporine A solution for 4 days to load the drug. (B) Comparison of model and experimental results for release experiments using the mean value of fitted diffusivity A B
107 Figure 4 2 Effect of length on release profiles from design I conjunctival inserts (drug loading =20%) (A) Cumulative release. (B) % Release (amount released / total drug loading). A B
108 Figure 4 3 Effect of drug loading (A), degree of crosslinking (B) and release with enhanced convection (C) on release profiles for design I conjunctival inserts (L=7.5mm). A B
109 Figure 4 4. Continued C
110 Figure 4 4 X SEM images of Inserts loaded with cyclosporine A. Drug loadings are indicated in each figure 10% X 2500 10 m 10 m A B 0% X 1500 0% X 2500 5% X 1500 5% X 2500 10 m 10 m 10 m 10 m 15% X 2500
111 Figure 4 5 Scaled drug Release profiles from Design I inserts with various drug loadings, i.e., plots of % release data plotted vs which are expected to overl ap for all drug loadings based on the model predictions.
112 Figure 4 6 Model for drug release from a cylindrical rod (conjunctival insert) that contains drug at concentrations C p which is above the solubility limit, and so a fraction of the drug precipitates as particles. The model combines mass transfer in the insert and that in the surrounding fluid boundary layer of thickness f The insert contains drug particles distributed uniformly at t = 0. Dissolution of the particles and subsequent diffusion of the drug creates a particle free zone ne ar the periphery, whose thickness growth with time. R f C = C b 3.5 ml of PBS C(r,t)=Concentration of drug inside the depletion zone in insert. D=Diffusivity of drug in the depletion zone C p =Drug loading K=Partition coefficient of cyclosporine A in the insert C b = Concentration of cyclosporine A in bulk (release medium) R = Radius of insert = Thickness of depletion zone in the insert f = Boundary layer thickness in the fluid
113 Figure 4 7 Comparison of model predictions and experimental measurements of drug release without convection (A) and with convection (B) from Design I inserts. A B
114 Figure 4 8 Effect of length on release profile of design II insert (drug loading 20%) on (A) Cumulative release, and (B) % release. A B
115 Figure 4 9 Release profiles from 7.5 mm long design II conjunctival inserts. (A) Effect of drug loading (5%, 20% and 30%) (B) Drug release with enhanced convection. (C) Effect of EGDMA % in the shell. A B
116 Figure 4 10. Continued C
117 Figure 4 10 Image of a soaked design II insert with (A) a sony T 700 digital camera and an (B) enlarged image of the crack taken at higher resolution by an optical microscope. A B
118 Figure 4 11 Dependence of % change in weight of gels due to swelling in water on HEMA % in HEMA:EGDMA gels.
119 Table 4 1 Values of parameters used to estimate theoretical diffusivity inside HEMA Parameter Value K 7.510 21 m 2  r 1 9.510 10 m  8.910 4 Pa s T 298 K Table 4 2 Values of parameters used in fitting the model to experimental results for release of drug from design I insert Parameter Value C p 10 4 x [% loading] gm/m 3 R 0.510 3 m L 7.510 3 m D fluid 2.29 x 10 10 m 2 /s C* 25 gm/m 3 
120 CHAPTER 5 DRUG DELIVERY BY PUNCTAL PLUGS 5.1 Introduction This chapter focuses on delivery of cyclosporine A drug via punctal plugs that are to be placed in canaliculi which connects eyes to the nose. A novel design of punctal plugs has been proposed and mechanism of transport of drug in these systems has been discussed. A pharmacokinetic model has been developed to compare the effectiveness of Restasis emulsion (commercially existing eye drop) and th e punctal plugs. 5. 2 Materials and Methods Cyclosporine A was bought from LC Labs (Woburn, MA); and Silastic laboratory tubing of size (ID 0.51 mm and OD 0.94mm) and size (ID 1.47mm and OD 1.96mm) were purchased from Dow corning (Midland, MI). Hydroxyl Et hyl Methacrylate (HEMA), ethylene glycol dimethacrylate (EGDMA), and Azobisisobutylonitrile (AIBN) were purchased from Sigma Aldrich (St. Louis, MO); while Acetonitrile (HPLC grade) and deionized water (HPLC grade) used as mobile phase in HPLC were bought from Fisher experiments was purchased from Sigma Aldrich (St Louis, MO). 5.2.1 Punctal Plug F abrication Punctal plugs were made of HEMA, EGDMA and silicone, all of which ar e biocompatible. The basic structure of the plugs is shown in Figure 1 2 ., with a p HEMA EGDMA 2 for
121 10 minutes to remove the O 2 in the monomer. Subsequently, 20 wt% of cyclosporine A and 0.03 g of AIBN (initiator) were added and the mixture was stirred for 5 minutes. The resul ting solution was filled into Silastic tubing with 0.51 mm ID and 0.94mm OD. After the tubing was sealed at both ends with office clamps, it was submerged into a water t he tubing leads to formation of a compound rod with a p HEMA core surrounded by an annulus of the silicone tubing. The compound rod was cut into segments of desired length and then the silicone annulus was cut off from a part of the plug to create the des igns illustrated in Figure 1 2 The degree of crosslinking was increased by increasing the amount of EGDMA in the polymerization mixture to obtain plugs with 100X crosslinking, which contains 100 times the EGDMA utilized in the procedure described above. Also the amount of drug loading was altered to prepare plugs with drug loading of 20% and 40%. 5.2.2 Drug Release In vitro drug release profiles were measured by soaking a plug in 3.5ml of phosphate buffer saline (PBS) which was replaced at regular interv als. The concentration of cyclosporine A in the release medium was determined with an HPLC (Waters, Milford, MA) equipped with a reverse phase C18 column (Waters, Milford, MA) and a UV detector. The mobile phase was 70% acetonitrile and 30% deionized wate r at V detector wavelength was 210 nm. 5. 3 Results Commercial plugs are about 1 mm in diameter and 2 mm in length. The plugs described here comprise of a 0.51 mm diameter p HEMA core with a fraction of the
122 core coated with a silicon shell of outer diameter 0.94 mm. The length of the plug was chosen to be 3.2 mm with about 50% of the length covered with the shell, which is larger than the commercial plugs, but the length can easily be reduced to 2 mm while keeping other design parameter same. The solubility of cyclosporine A in the polymer is less than tha t in the monomer mixture; therefore the drug is expected to form precipitates during the polymerization. The cross section of punctal plugs with 20% drug loading and 0X crosslinking were imaged through JEOLJSM 6400 Scanning electron microscope (X SEM) at different magnifications ( Figure 5 1 .). The drug clearly forms particles with a non uniform size distribution with largest particles of size ~10 m. The drug release profile from a plug with a drug loading of 20% and 0X crosslinking is shown in Figure 5 2 The core of the plug weighs about 0.67 mg, and about a month without any initial burst, and a relatively zero order release for the first 10 days. Since, typical p lugs are worn for a period much longer than a month; it is desirable to increase the duration of release from the plugs, possibly by increasing the crosslinking. An increase in crosslinking from 0X to 100X results in a decrease in the release rate to abou order for the entire duration ( Figure 5 2 ). Thus increased crosslinking has the desired effect of increased release duration but the daily release amount decreases, and the duration of zero order release also decr eases. To increase the daily release, plugs were prepared with 40% drug loading while keeping 100 X crosslinking. The effect of increased drug loading while keeping crossl inking at 100X is shown in Figure 5 3 The plugs with 40% drug loading release at a constant rate of about 3 g/day for about a month and then the rate
123 decreases slightly. The plugs contain about 225 g of drug so these are expected to release for about 3 months, which is the typical duration of plug wear. 5.3.1 Mechanisms of R elease The results described above show that the cumulative release curves are linear in time for certain duration. We propose that the independence of the release rate on drug loading at short times arises from the fact that the drug release rates are initially controlled by the mass transport resistance on the fluid side. In general, drug transport from inside of the plug to the bulk fluid faces two mass transfer resistances in series resistance due to diffusion in the core and that due to diffusion in the f luid. The resistance in each phase is directly proportional to the boundary layer thickness. The boundary layer thickness in the fluid depends on the extent of mixing and is independent of time, whereas, the boundary layer thickness in the core is zero a t initial times, and it then grows as square root of time. Accordingly, at short times the resistance in fluid will dominate because of very small mass transfer boundary layer and hence negligible resistance in the gel, and at long times the resistance in gel will dominate because of thickening of the boundary layer in the gel. The resistance in the gel increases with time due to the thickening of the mass transfer boundary layer, and beyond certain time, the release is controlled by the gel, and subsequen tly the drug release rates begin to depend on the drug loading. These mechanisms suggest that an increase in convection in the release medium will lead to an increase in the release rates. This hypothesis was tested by conducting release experiments with mixing in the release medium.
124 5.3.2 Effect of Convection Figure 5 4 A shows the effect of convection on drug release profiles from plugs with 20% drug loading and 100X crosslinking. Similarly, the effect of convection on plugs with 40% drug loading and 10 0X crosslinking is shown in Figure 5 4 B. In both cases, increased convection clearly increases the drug release rates proving that at short times, the release rates are controlled by the mass transfer resistance in the fluid. These results support the me chanisms proposed above. The mixing in the canaliculus in the tears surrounding the exposed section of the plug is expected to be very small, and thus the results provided in previous sections may be close to the physiological conditions. However in vivo experiments are necessary to determine the release profiles after insertion of plugs in the canaliculi. 5. 4 Model for the Zero Order Release In the previous section, the zero order profiles at early times were attributed to the diffusion through the mass transfer boundary layer in the fluid. To prove this hypothesis, we predict the release profiles based on this hypothesis and compare the results with the measurements. If mass transfer is limited by diffusion in the fluid, the rate of drug released from the device is given by ( 5 1) where C* is the concentration of drug in fluid at solid liquid interface and is assumed to be equal to solu bility limit of drug (=25g/ml  ) in the release medium. Also, D f (=2.29 10 10 m 2 /s  ) is the drug diffusivity in the fluid, refers to boundary layer thickness in the fluid, and N and A refer to cumulative amount of drug released from the
125 insert and total surface area for drug release respectively. It is to be noted that drug is released from the plugs through two distinct surfaces, the cylindrical curved surface and the circular cross section surfaces. Since streamlines of convection in the fluid greatly d epend on surface geometry, the boundary layer thicknesses in the fluid for the two surfaces would be independent of each other and have to be evaluated separately. As a result, Equation 5 1 can be modified as ( 5 2) where S 1 and S 2 a re the curved surface and cross 1 2 are the respective boundary layer thickness. Each of the boundary layer thicknesses could be determined by designing the plug such that one of the surface areas for diffusion is blocked. For example, if a plug is designed such that the silicon shell cov ers the entire length of the plug, the drug can diffuse out only from the circular cross sections. Equation 5 2 can then be simplified by eliminating the term corresponding to S 1 The release data from such a plug could then be fitted to the simplified E quation 5 2 2 Similarly, a plug with no shell and circular faces covered, or a long plug in which the curved surface area far exceeds the cross section 1 2 drug loaded p HEMA cores of dia meter 1.02 mm were first coated with an EGDMA shell of thickness 0.225 mm, and were then surrounded by a silicon shell of thickness 0.25 mm to eliminate any possibility of drug release from the curved areas. Results not reported here showed that only a si licon shell was not sufficient to completely eliminate all radial transport of drug. Plugs were prepared with several different drug loadings to ensure that the release rates were independent of the
126 drug loadings which is expected on the basis of the mode l proposed above ( Equation 5 2 ). The data in Figure 5 5 clearly shows that the release profiles are independent of loadings and is zero order for first 8 10 days. The solid line shows the fitted release profiles based on Equation 5 2 with S 1 = 0 and S 2 = 2 (0.5) 2 mm 2 and a fitted value of 2 The value of the boundary layer thickness in fluid surrounding the 1 has been determined to be 0.47mm in chapter 4. The values of 1 and 2 can n ow be utilized in Equation 5 2 with the appropriate values of S 1 (=5.65 10 6 m 2 ) and S 2 (1.56 10 6 m 2 ) to predict rate of drug release from the plugs. The predicted profiles are plo tted as the solid lines in Figure 5 2 and Figure 5 3 The prediction is in good agreement with the release from the systems with 20% drug lo ading and 0X crosslinking ( Figure 5 2 ) and 40% drug loadi ng and 100 X crosslinking ( Figure 5 3 .). The release from 20%, 100X cannot be compared with the model because the profiles are non zero order as the gel resistance is comparable to the resistance in fluid at early times because of high crosslinking in gel leading to non zero order behavior. A general model that includes both fluid and gel resistance can be developed in a similar way as discussed in previous chapter (chapter 4) but is not presented here as we are primarily interested in plugs with high drug loadings, and long durations of zer o order release due to their suitability for therapeutic use as drug eluding punctal plugs. 5. 5 Pharmacokinetics of Cyc losporine A D elivery via Restasis and Punctal P lugs The typical dry eye treatment based on cyclosporine A involves instillation of two
127 The plug with 40% drug loading and 100X crosslinking release cyclosporine A at a rate of about 3 g/day. Since the length of the commercial plugs are about half of those developed here, and only one of the circular cross sections will contact tears, the release rates from a plug inserted in the canaliculus could be about 1.5 g/day, which is only about 5% of the rate of drug delivered through Restasis emulsion. However, the bioavailability of cyclosporine A delivered via eye drops is expected to be small due to the small residence time of about 5 minutes in the eyes and thus a release of about 1.5 rmine the therapeutic release rates from plugs, we obtain a rough approximation of the desired rates by developing a pharmacokinetic model for ocular delivery of cyclosporine A both through Restasis and plugs. 5. 5. 1 Phar macokinetics of Cyclosporine A D eli very via Restasis This pharmacokinetic model is based on the tear balance model  and the tear drainage model  which predicts the dynamic aqueous concentration of drugs after in stillation through eye drops. After an eye drop is instilled in the eyes, the components in the drop are eliminated through three routes: evaporation, transport into the cornea and the conjunctiva, and tear drainage into the lacrimal sac. The Restasis f ormulation is an emulsion that contains 0.625% castor oil and 0.05% cyclosporine A by weight, and formulation are typically instilled in each eye every day. To devel op a pharmacokinetic model for Restasis, one has to perform mass balances for the three main components of the Restasis eye drop: drug cyclosporine A, castor oil, and water. The drug cyclosporine A is present both in the oil and the water phase, and the concentrations in
128 the two phases are expected to be in equilibrium due to the large surface area of the oil drops. In the model presented below, it is assumed that the oil phase only acts as a reservoir of the drug and does not directly penetrate into the corneal or the conjunctival epithelia, which is reasonable due to the relatively large size of the drops. The oil phase also cannot evaporate and so it is eliminated only through the tear drainage pathway. 126.96.36.199 Aqueous phase mass balance A mass balance on the aqueous fraction of the tears yield ( 5 3) where V aq refers to total volume of aqueous phase on ocular surface, q production is rate of tears produced, q evaporation is rate of tears evaporated, q absorbed is the rate of absorption of tears by conjunctiva and q drainage is the rate of tears drained from the eyes aqueous is the fraction of aqueous phase in tears. Here it is assumed that the tear production rate, the evaporation rate and absorption rate are not affected by the instillation of eye drops. Ba sed on the tear drainage model  if the viscosity of the eye drop formulation is less than about 10 cp, which is the case for Restasis, the drainag e rate is given by the following expression, ( 5 4) where L is the canaliculus length, t c is the duration of a blink interblink cycle, R 0 is the or tears, R m is the radius of curvature of the tear meniscus, b and E are the thickness and
129 the modulus of the canaliculus respectively, p o is imposed on the canaliculus during a blink and p sac is pressure in the lacrimal sac, which can be taken as zero (a tmospheric pressure). The details of the derivation of the expressions and the values of all the pa rameters are available in Ref.  5.5.1. 2 Oil phase mass balance A mass balance for oil phase in the tear film yield s ( 5 5) where V oil oil represents the fraction of oil present. 188.8.131.52 Drug balance The mass balance for drug on the ocular surface yield ( 5 6) where C oil is concentration of drug in oil phase and C aq is concentration of drug in aqueous phase. The parameters k 1 and k 2 are permeabilities of cornea and conjunctiva, respectively for cyclosporine A, and A 1 and A 2 are the areas of cornea a nd conjunctiva, respectively. Finally, the aqueous and oil fractions are defined by Equation 5 7 ( 5 7) Also, the oil concentration and aqueous phase concentration at any instant of time are assumed to be in equilibrium, i,e., ( 5 8)
130 Due to lack of available data for partition coefficient of cyclosporine A in castor oil K partition its value is assumed to equal the octanol water parti tion coefficient for the drug. 184.108.40.206 Geometric relationship The radius of meniscus, R m required in Equation 5 4 to obtain the drainage rates is a function of total ocular volume V total (=V aq +V oil ) at any instance of time and can be related to the meniscus curvature through the fo llowing geometric relationship  ( 5 9) Here V total is total volume including oil volume and aqueous phase volume of fluid, V film is fluid in the exposed and unexposed tear film, and L lid is per imeter of the lid margin. Total tear volume at steady state is assumed to be 10 l  and using a steady state radius of meniscus of 0.37 mm, V film is determined to be 8.3 l. By solving the above equations simultaneously using finite difference method we can obtain the ocular volume, oil and aqueous volume fractions, and the drug concentration as a function of time. The parameters used to solve the above set of equations are available in [22,93] and are also presented in Table 5 1. The initial emulsion to the ocular film that has the steady state radius of meniscus of 0.37mm, 220.127.116.11 Bioavailability After determining the aqueous and oil volume fractions, and the drug concentration as a function of time, one can determine the bioavailability (F) of cyclosporine A. The deta ils of the mechanism of the therapeutic action of cyclosporine A and the exact site of action are not exactly known and so for simplicity we assume
131 that both the drug that enters the cornea and also the conjunctiva can lead to therapeutic benefits. Accord ingly, we define bioavailability as the ratio of the drug that enters the ocular tissue (cornea or conjunctiva) and the amount administered into the eye. It can thus be defined as ( 5 10) where Mo is the initial amount of drug in the formulation. By solving the equations in MATLAB we obtain a value of 2.8 % for the bioavailability of cyclosporine A delivered 5. 5.2 Phar macokinetics of Cyclosporine A D elivery via Punctal Plugs To develop the pharmacokinetic model for drug released from a plug, we perform a mass balance on the drug released into the ocular tear film. A human eye has a tear volume V of about 10 l, and this volume is maintained fixed thr ough a balance between tear secretion from the lacrimal glands and conjunctiva and tear elimination through drainage through the canaliculi into the nasal cavity and also through evaporation. The drug released from the plug into the tear film can either d iffuse into the ocular tissue through the cornea and the conjunctiva, or exit the tear volume with tears that drain into the nasal cavity. Thus, a mass balance on the drug released from the insert gives the following equation, ( 5 1 1) where V is total volume of fluid on ocular surface, F is the drug release rate by plug (~ 1.5 g/day), kA is the sum of the product of the area and the permeability for the cornea and the conjunctiva, and C is the dynamic drug concentration.
132 Since the t ime scale for release from the inserts is a few days, which is much longer than the time scale for concentrations in the eyes to reach a steady state, one can assume that the drug release from the inserts could be considered to be at a pseudo steady state, i.e., ( 5 12) Based on the definition of bioavailability (F) described above, the value of F for drug released from the plug can be computed as ( 5 13) The presence of a punctal plugs in one of the canaliculus reduces the drainage rate to roughly about half of the normal value. Based on Equation 5 4 the drainage rate under normal physiological conditions from both canaliculi is 1.4l/min. This value is in reasonable agreement with reported values of 1 2l/min for tear drainage  Using half of this value in Equation 5 13 (since one of the puncta is blocked by punctal plug) gives a value of 64% for bioavailability of cyclosporine A released from a plug. Based on the model for pharmacokinetics of Restasis developed above, the therapeutic requirement of cyclosporine A is about 0.7 g/day, and thus a release of 1.5 g/day of cyclosporine A from the plug with a bioavai lability of 64% may be adequate. 5. 6 Conclusion Dry eyes are a major health care problem in the United States and worldwide. These are frequently treated either by instillation of eye drops, drugs such as Restasis, and/or by blocking tear drainage throug h insertion of punctal plugs. Here we propose to combine the two approaches by delivering cyclosporine A through punctal plugs that also block tear drainage. In addition to serving as a dual approach for
133 treating dry eyes, drug delivery through punctal p lugs will likely increase compliance and reduce side effects due to systemic uptake of ophthalmic drugs. The ocular requirements of cyclosporine A are estimated by developing a pharmacokinetic model for Restasis, which contains 0.05% drug, and two 25 l d rops and the bioavailability of the drug delivered through Restasis is determined to be about 2.8 % suggesting that the therapeutic requirements of ocular tissue is ab out 0.7 Punctal plugs with dimensions similar to commercial plugs and with 40% drug do not have any initial burst effect, thereby minimizing the chances of having any toxic effects due to sudden release of a large quantity of drug. Also, drug release profiles are approximately linear for more than 40 days, which is an added asset for a drug delivery system. A model has been proposed to predict the linear release pr ofile or zero order release at short times. The degree of convection plays a prominent role in controlling the release rates particularly at short times. The extent of mixing is not yet established in eyes; therefore in vivo experiments would have to be do ne to determine the drug release profiles from these drugs under physiological mixing. Also, the results presented in this paper are for cyclosporine A but the concept can be applied to fabricate drug loaded punctal plugs for other eye diseases. Although t he devices proposed here are prepared with biocompatible materials, the degree of comfort and biocompatibility is needed to be explored for these devices through testing in animal models.
134 Figure 5 1 X SEM images of punctal plugs with 20% drug loading. Figure 5 2 Effect of crosslinking on cumulative drug release profiles from the punctal plugs with 20% drug loading (131 g). Data represented as mean SD (n=3). The solid line is the prediction of the profile for the 20%, 0X system based on the model described below. 20% X 1500 20% X 2500 10 m 10 m
135 Figure 5 3 Effect of increased drug loading on cumulative drug release profil es from the punctal plugs with 100X crosslinking. Data represented as mean SD (n=3). The solid line is the prediction for the 40%, 100X system based on the model described below. Fig ure 5 4 Effect of increased convection on cumulative drug release profiles from the punctal plugs with crosslinking of 100X and drug loading of (A) 20% (131 g) and (B) 40% (225 g). Data represented as mean SD (n=3).
136 Figure 5 5 Drug release profile of plugs totally covered with silicon (only ends are exposed, sides are covered) Total dia=1.96mm, EGDMA shell dia=1.47mm, core dia=1.02mm. f = 0.2mm
137 Table 5 1 Physiological parameters used for the pharmacokinetic model Parameter Value L 1.210 2 m t c 6s R 0 2.510 4 m 43.010 3 N/m p 0 400Pa p sac 0(atmospheric) tear 1.510 3 Pa s L lid 5710 3 m k cornea 1.110 8 m/s  k conj 1.110 8 m/s  A cornea 1.0410 4 m 2 A conj 17.6510 4 m 2 K partition 831.76 
138 CHAPTER 6 CONCLUSION Millions of people in the United States are suffering from severe eye problems; therefore effective ways of delivering drugs is an area of current research. Bioavailability of drugs delivered via eye drops has been reported to be low (< 5%) due to their ra pid elimination from eyes through tear drainage. Therefore our work has focused on understand ing the transport of drugs in front surface of the eyes specifically in cornea, which could be of immense help in designing better ophthalmic formulations. Also, w e have developed drug delivery devices such as conjunctival inserts and punctal plugs which would not only improve bioavailability of drugs but would also greatly enhance patient compliance. Conventional pharmacokinetic models that depict cornea as compar tment s are un suitable to determine bioavailability of topical drugs. The mechanistic model developed in this thesis accurately characterizes the transient transport behavior of drugs across cornea. Chapter 2 in the thesis presents the mechanism and model d evelopment of transport of hydrophobic molecules while chapter 3 deals with presenting the phenomenon for hydrophilic drugs. Lipophilic drugs exhibit slow accumulation in cellular layers presumably due to the ir slow transport from the membrane bilayers to intracellular hydrophobic sites. While, for hydrophilic drugs transport across the transcellular layer plays a rate determining step in transport across the endothelial layer of cornea. Sensitivity analysis of the parameters obtained from the model clearly indicates that the parameters are sensitive to the model and are well identified.
139 Drug delivery devices such as cylindrical conjunctival HEMA inserts (chapter 4) and punctal plugs (chapter 5) were prepared and presented as an alterna te solution for the treatment of dry eyes. The devices were fabricated via thermal polymerization in presence of cyclosporine A drug at high loadings to create a system containing particles of drug dispersed in the matrix. The drug release rates were measu red to explore the effect of length, drug loading, crosslinking, and mixing in the release medium. The inserts release the drug for a period of about a month while punctal plugs release drug for more than two months at therapeutic rates. The rates of drug release are zero order and independent of drug loading and crosslinking for certain period of time. These effects were shown to arise due to a mass transfer boundary layer in the fluid and a mathematical model was developed by coupling mass transfer in th e devices with that in the boundary layer in the surrounding fluid. The model with diffusivity in the polymer matrix and boundary layer thickness as parameters fits the experimental data and explains all trends in release kinetics. The fitted diffusivity i s about twice that obtained by direct measurements, which agreed well with the value obtained by using the Pharmacokinetic models are also developed for Restasis commercially existing ophthalmic emulsion to obtain the bioavailability of the drugs delivered through these eye drops. T hese models suggest that the amount delivered by our devices is therapeutically sufficient and similar to the commercially existing ophthalmic solu tions.
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147 BIOGRAPHICAL SKETCH Chhavi Gupta completed his undergraduate studies from Indian Institute of Technology, Guwahati (IITG), India in May 2006. He joined Department of Chemical E ngineering at the University of Florida in a Ph.D. program in Fall 2006. He joined Dr. s ince then began working on his thesis titled