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Ophthalmic Drug Delivery by Contact Lenses

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Title:
Ophthalmic Drug Delivery by Contact Lenses
Creator:
LI, CHI-CHUNG ( Author, Primary )
Copyright Date:
2008

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Subjects / Keywords:
Boundary conditions ( jstor )
Contact lenses ( jstor )
Cornea ( jstor )
Diffusion coefficient ( jstor )
Drug design ( jstor )
Gels ( jstor )
Hydrogels ( jstor )
Mass transfer ( jstor )
Saltwater ( jstor )
Tears ( jstor )

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Source Institution:
University of Florida
Holding Location:
University of Florida
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Copyright Chi-Chung Li. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
11/30/2007
Resource Identifier:
659871202 ( OCLC )

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1 OPHTHALMIC DRUG DELIVERY BY CONTACT LENSES By CHI-CHUNG LI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007

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2 2007 Chi-Chung Li

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3 To my mom, Theresa Ho, the most important woman in my life.

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4 ACKNOWLEDGMENTS I begin by thanking my advisor (Dr. Anuj Chauhan) for his constant guidance on my research and various aspects of my life. He is a wonderful advisor and mentor who has inspired me to strive for excellence. I w ould also like to thank my supervis ory committee members (Dr. Narayanan and Dr. Dickinson, Chemical E ngineering; and Dr. Bati ch, Materials Science and Engineering) for their suggestions and help. I would also like to thank Dr. Shah and Dr. Ren (Chemical Engineering) for being my mentors. In addition, I thank the graduate students in my lab: Derya Gulsen, Marissa Fallon, Zhi Chen, Heng Zhu, Yash Kapoor, and Jinah Kim. I have worked with them for many years, and they have been friendly and helpful. I also thank the undergraduate st udents: Mike Abrahamson helped me with synthesizing stable microemu lsions in HEMA and constructing the phase diagram of these microemulsions; and Nisita Wanakule, Weng Kin Tang, Joshua Mccarty, and Justin Thomas helped with different experiments. I also thank the department of Chemical Engineering at Univ ersity of Florida for offering an exciting PhD program and a variety of helpful resources, and the University of Florida for its bountiful and diverse cu lture and resources. I would like to thank Patrick McCavery from Technical Lab Services for his help on High Performance Liquid Chromatography (HPLC), th e people at Particle Engineering Research Center (PERC) at UF for their help with part icle sizing and imaging e quipments, the people at Major Analytical Instrument Center (MAIC) fo r SEM images, and the Brain Institute for their help with fluorescent microscopy. Most of all, I thank my dear friends who are always there fo r me, and my family for their love and support which means the world to me, and helped me become who I am.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........8 LIST OF FIGURES................................................................................................................ .........9 ABSTRACT....................................................................................................................... ............12 CHAPTER 1 INTRODUCTION..................................................................................................................14 Problems with Current Ophtha lmic Drug Delivery Vehicles.................................................14 Past Efforts on Ophthalmic Drug Delivery............................................................................15 Drug Delivery by Contact Lenses...........................................................................................15 Mathematic Model of Drug Delivery by Contact Lenses.......................................................16 Mathematic Model of Timolol Delivery by Contact Lenses..................................................17 Recent Research on Ophthalmic Drug Delivery by Contact Lenses......................................20 Drug Delivery by Particle-Laden Contact Lenses..................................................................21 2 MODELING OPHTHALMIC DRUG DELIVE RY BY SOAKED CONTACT LENSES...24 Introduction................................................................................................................... ..........24 Model.......................................................................................................................... ............25 Results and Discussion......................................................................................................... ..32 Scales for Various Parameters.........................................................................................32 Dispersion Coefficient.....................................................................................................33 Solution of the Integro-Differential Equation.................................................................35 Concentration Profiles.....................................................................................................36 Effect of P1...............................................................................................................38 Effect of P2...............................................................................................................39 Effect of P3...............................................................................................................40 Results for Timolol..........................................................................................................41 Comparison of Model Predicti ons with Clinical Data....................................................42 Conclusions.................................................................................................................... .........43 3 OCULAR TRANSPORT MODEL FOR OP HTHALMIC DELIVERY OF TIMOLOL BY P-HEMA CONTACT LENSES.......................................................................................60 Introduction................................................................................................................... ..........60 Materials and Methods.......................................................................................................... .60 Materials...................................................................................................................... ....60 Synthesis Methods...........................................................................................................61

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6 Swelling Experiments......................................................................................................61 Drug Diffusion Experiments...........................................................................................62 Results and Discussion......................................................................................................... ..63 Swelling Studies in Deionized Water..............................................................................63 Equilibrium Drug Uptake in Deionized Water................................................................63 Dynamic Drug Transport in Deionized Water................................................................66 Drug release experiments.........................................................................................66 Drug loading experiments........................................................................................69 Swelling Studies in Phosphate Buffered Saline (PBS)....................................................71 Equilibrium Drug Uptake in PBS....................................................................................71 Dynamic Drug Transport in PBS....................................................................................71 Drug release experiments.........................................................................................71 Drug loading experiments........................................................................................72 Model for Drug Release from the Contact Lens into the Eye.........................................73 Concentration profiles in the POLTF.......................................................................76 Fraction of drug that enters cornea...........................................................................77 Comparison with in vivo experiments......................................................................78 Conclusions.................................................................................................................... .........78 4 TIMOLOL TRANSPORT ACROSS MI CROEMULSION TRAPPED IN PHEMA GELS........................................................................................................................... ...........94 Introduction................................................................................................................... ..........94 Materials and Methods.......................................................................................................... .94 Materials...................................................................................................................... ....94 Methods and Procedures..................................................................................................95 Synthesis of pluronic microemulsions.....................................................................95 Entrapment of pluronic microemulsions in HEMA gels..........................................97 Synthesis of polymerizable Pluronic mi croemulsions with HEMA-water as the continuous phase...................................................................................................98 Drug release experiments for microemulsion-laden gels.........................................99 Results and Discussion.........................................................................................................100 Drug Release from HEMA Gels Loaded with Timolol (Control).................................100 Drug Release Experiments for Plur onic Microemulsion-Laden Gels...........................101 Timolol release in DI water with water replacement every 24 hours....................101 Timolol release in DI water without water replacement........................................104 Timolol release from Pluronic micr oemulsion-laden gels in PBS.........................104 Pluronic microemulsions with HEMA -water as the continuous phase..................104 Summary........................................................................................................................ .......105 5 DISPERSION OF EGDMA MICROGELS AND MICROPARTICLES IN P-HEMA CONTACT LENSES FOR OPHT LAMIC DRUG DELIVERY.........................................115 Introduction................................................................................................................... ........115 Material and Methods...........................................................................................................115 Materials...................................................................................................................... ..115 Synthesis Methods.........................................................................................................115

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7 Synthesis of p-HEMA gels loaded w ith highly crosslinked EGDMA microparticles...............................................................................................................116 Synthesis of p-HEMA gels loaded with highly crosslinked EGDMA microgels..117 Characterization Studies................................................................................................119 Gel characterization................................................................................................119 Drug release experiments.......................................................................................120 Packaging tests.......................................................................................................120 Results and Discussion.........................................................................................................121 Gel Characterization......................................................................................................121 Drug Release.................................................................................................................121 Timolol release from p-HEMA lenses (control)....................................................121 Timolol release from p-HEMA lenses loaded with highly crosslinked EGDMA microparticles.....................................................................................................124 Timolol release from p-HEMA lenses loaded with highly crosslinked EGDMA microgels.............................................................................................................125 Effect of packaging on timolol release from HEMA gels loaded with EGDMA microparticles.....................................................................................................126 Summary........................................................................................................................ .......127 6 CONCLUSION.....................................................................................................................135 7 FUTURE WORK..................................................................................................................140 Modifications of the Model..................................................................................................140 Microparticle or Microgel-Laden Contact Lenses for Ophthalmic Drug Delivery..............140 Animal Studies................................................................................................................. .....142 APPENDIX A DERIVATION OF DISPERSI ON COEFFICIENT (D*)....................................................143 Zero Order..................................................................................................................... .......150 First Order.................................................................................................................... .........150 Second Order................................................................................................................... .....152 B DERIVATION OF DRUG FLUX FROM TH E CONTACT LENS TO THE POLTF.......156 Case 1: Rapid PLTF breakup................................................................................................156 Case 2: Well-mixed PLTF.....................................................................................................158 LIST OF REFERENCES.............................................................................................................162 BIOGRAPHICAL SKETCH.......................................................................................................168

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8 LIST OF TABLES Table page 3-1 Values of parameters required in the ocular transport model............................................81 3-2 Fractional uptake by cornea (Fc) and fracti onal loss to the tear lakes (Fs), and to the pre-lens tear film (Fp) for case 1 (z ero flux to the PLTF) and case 2 (zero concentration in the PLTF)................................................................................................81 4-1 Compositions of various Pl uronic microemulsions (me).................................................107 4-2 Physical and transport properties of timolol....................................................................107 4-3 Fractional drug release in the extraction step for various types of microemulsionladen gels..................................................................................................................... ....107 5-1 Physical and transport properties of timolol....................................................................129 5-2 Transmittance at 600 nm wavelength of microparticle-laden hydrogel of 240 m thickness...................................................................................................................... .....129

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9 LIST OF FIGURES Figure page 2-1 Geometry of pre-len a nd post-lens tear films....................................................................47 2-2 The function f(ts) that characterizes the time dependence of the velocities in the POLTF (thick line) and the Fourier repres entation of the function (thin line)..................48 2-3 Comparison of the exact solution for the di spersion coefficient (s olid line) with the approximate expression (dashed line)................................................................................49 2-4 Typical concentration transients in the PO LTF at different axial locations for case 1, (i.e., no flux to the PLTF). (b) s hows a magnified view neat t = 0....................................50 2-5 Typical concentration transients in the POLTF at different axial locations for case 2, (i.e., maximum flux to the PLTF). (b)The in set shows a magnified view neat t = 0.........51 2-6 Concentration profiles in POLTF for bot h case 1 (solid) and case 2 (dashed) as a function of time. ............................................................................................................ ...52 2-7 Effect of P1 on concentr ation profiles for case 2. Th e concentration profiles are shown at three different times and for two different values of P1.....................................53 2-8 Effect of P1 on the fractions of the drug that enter cornea or are lost from the PLTF or from the POLTF. Results are shown for both case 1 (solid) and case 2 (dashed). .....54 2-9 Effect of P2 on concentr ation profiles in the POLTF for case 1. The profiles are shown at different times and fo r two different values of P2..............................................55 2-10 Effect of P2 on the fractions of the drug that enter cornea or are lost from the PLTF or from the POLTF. Results are shown for both case 1 (solid) and case 2 (dashed). .....56 2-11 Effect of P2 on concentration transients in the POLTF at x = 0 for case 1 (solid lines) and case 2 (dashed lines)....................................................................................................57 2-12 Effect of P3 on concentration transients in the POLTF at x = 0 for case 1 (solid lines) and case 2 (dashed lines)....................................................................................................58 2-13 Effect of P3 on the fractions of the drug that enter cornea or are lost from the PLTF or from the POLTF............................................................................................................59 3-1 Dependence of gel-water partition coefficient on drug c oncentration in the aqueous phase for the 1X gel. ........................................................................................................82 3-2 Dependence of gel-water partition coefficient on drug c oncentration in the aqueous phase for the 1X, 10X and 30X gels..................................................................................83

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10 3-3 Dynamic concentrations in the aqueous phase during the release experiments in water for 1X, 10X, and 30X gels.......................................................................................85 3-4 Dynamic concentrations in the aqueous phase during the loading experiments in water for 1X, 10X, and 30X gels.......................................................................................87 3-5 Dynamic concentrations in the aqueous phase during the release experiments in PBS for the 1X, 10X, and 30X gels...........................................................................................89 3-6 Dynamic concentrations in the aqueous phase during the loading experiments in PBS for the 1X, 10X, and 30X gels...........................................................................................91 3-7 Geometry of the pre-lens and post-lens tear films.............................................................92 3-8 Drug concentrations at the center of the postlens tear film for the 1X gel. (b) shows a magnified view of the short time data.............................................................................93 4-1 Cumulative percentage release from the control gels with water replacement every 24 hours. (n=2)................................................................................................................ .108 4-2 Cumulative percentage release from th e control gels withou t PBS replacement............108 4-3 Timolol released from me A laden ge l in DI water without water replacement..............109 4-4 Timolol released from me D laden ge l in DI water without water replacement..............109 4-5 Timolol released from me B laden ge l in DI water without water replacement..............110 4-6 Timolol release in DI water for me C laden PHEMA gels..............................................110 4-7 Timolol released in DI water without water replacement for meA laden PHEMA gels........................................................................................................................... ........111 4-8 Release of timolol from meA with salt la den gels into DI water (n=2), PBS, and saline......................................................................................................................... .......111 4-9 Drug release in saline for gel D.......................................................................................112 4-10 Pseudo phase diagrams for the six component microemulsion.......................................113 4-11 Comparison of release of timolol into DI water (hollow data) and release of timolol into saline. (solid data) for stabile plur onic microemulsion in HEMA/water mixture....114 5-1 Regular microscopic image of microparticles suspended in water.................................130 5-2 Fluoresecent microscopic imag e of microparticle-laden gel...........................................130 5-3 G’ (storage modulus) an d G’’ (loss modulus) for micr ogel and microparticle laden lenses......................................................................................................................... .......131

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11 5-4 Timolol base form release from PHEMA gel directly entrapped with Timolol base......131 5-5 Timolol release from microparticle laden PHEMA gels. ..............................................132 5-6 Timolol release from mi crogelA-laden PHEMA gel. .....................................................132 5-7 Timolol released from PHEMA lenses load ed with microgel B, C, and D, where well mixed extraction was implemented.................................................................................133 5-8 Timolol release from EGDMA-co-H EMA microgel laden HEMA gels ........................133 5-9 Release from EGDMA micrparticle-laden HEMA gel after soaking in packaging solution for 2 weeks.........................................................................................................134 A-1 Geometry of the post-lens tear film.................................................................................155 B-1 Geometry of the lens and the pre-lens tear film...............................................................161

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12 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy OPHTHALMIC DRUG DELIVERY BY CONTACT LENSES By Chi-Chung Li May 2007 Chair: Anuj Chauhan Major: Chemical Engineering Ophthalmic drugs are commonly delivered vi a eye drops, even though this approach is highly inefficient and leads to drug wastage and si de effects. Our study focused on investigating the feasibility of delivering eye drops by contact lenses. Contact lenses are expected to be efficient ophthalmic drug delivery vehicles because they increase the residence time of drug in the eye, an d therefore lead to larg er fractional intakes of drug by the cornea and reduce side effects. To quantify the increase in bioavailability by using contact lenses, we developed a model for drug releas e from the contact lens into the pre-lens and post-lens tear films and the later uptake by the co rnea. The motion of the contact lens driven by the eyelid motion enhances the mass transfer in the post-lens tear film (POLTF). We used regular perturbation methods to obt ain the Taylor disper sion coefficient for mass transfer in the POLTF. Results obtained from the model match c linical data in the literature, and show that drug delivery from a contact lens is much more efficient than delivery by drops. Results also show that about 50% of drug entrapped in the lens enters the cornea, which is much larger than the fractional uptake for drug delivery by drops. Our model proves that ophthalmic drug delivery is much more efficient compared to drops but it also shows that simply lo ading the drug in the lens by so aking is not adequate for long-

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13 term drug delivery. To obtain extended and controlled delivery, we developed transparent particle-laden contact lenses th at can deliver drugs for a long pe riod because of slow drug release from the particles. We explored several differe nt systems, including disp ersions of oil-in-water microemulsions and highly crosslinked micropa rticles and microgels. We showed that the pluronic surfactant covered interf ace of ethyl-butyrate in water microemulsions does not provide adequate barrier to retard transport of timolol (the drug explored in our study). The highly crosslinked micropartricles and microgels do slow down the transport, and contact lenses laden with these systems provide timolol delivery at th erapeutic dosages for a period of about 6 days.

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14 CHAPTER 1 INTRODUCTION Problems with Current Ophthalmic Drug Delivery Vehicles Drug delivery by conventional techniques such as tablets results in a relatively high drug concentration in the body, followed by a sharp decline. The rapid variations in drug concentration that result with conventional vehicles limit th e drug efficacy and cause side effects.1 This realization spawned active research in the field of controll ed drug delivery, which primarily aims to deliver drugs at a uniform rate for extended periods of time. This resulted in development of new technologies th at rendered drug delivery more convenient and efficient, and reduced side effects. Controlled drug delivery vehicles are especi ally important for ophthalmic applications because topical delivery via eye drops, wh ich accounts for about 90% of all ophthalmic formulations, is extremely inefficient, and in certain instances leads to serious side effects.1 A very low percentage (1-5%) of the drug applied as drops penetr ates the corneal epithelium and reaches the ocular tissue, while the rest of the drug is lost due to tear drainage.2 0n instillation, the drug mixes with the fluid pres ent in the tear film and has a short residence time of about 5 minutes in the film. During this time, about 1-5% of the drug gets absorbed by cornea, and the remaining gets absorbed by the conjunctiva or fl ows through the upper and the lower canaliculi into the lacrimal sac. The drug-containing tear fluid is carried from the lacrimal sac into the nasolacrimal duct, and eventually the drug gets absorbed into the bloodstream. The transnasal and conjunctival absorption leads to drug wastage, and more importa ntly, the presence of certain drugs in the bloodstream leads to undesirable side effects. For example, beta-blockers such as timolol that treat wide-angl e glaucoma have a deleterious effect on the heart.3 Furthermore, application of ophthalmic drugs as eye drops results in a rapid variation in drug delivery rates to

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15 the cornea that limits the efficacy of therapeu tic systems. Thus, there is a need for new ophthalmic drug delivery systems that increase th e residence time of the drug in the tear film, and thereby reducing wastage a nd eliminating side effects. Past Efforts on Ophthalmic Drug Delivery Previous efforts at developing new ophthalm ic drug delivery systems focused on using polymeric gels, colloidal particles, and collagen shields. 1Error! Bookmark not defined. Most of the work were done with the aim of increasing the residence tim e of the drug in the tear film by either increasing the viscosity of the tear film along with the administration of drug, or by the adhesion between the drug carrier and the mucin layer that covers ocular tissue.4 Higher residence time means a longer time of contact between drug and ocular tissue, and thus results in an increased drug uptake by ocular tissue. Mo st of them have some success in terms of increasing the fractional drug intake and reducing systemic absorption, but all of them still suffer from different problems ranging from minimal increase of bioavailability,2 discomfort, blurring of vision, damage or toxicity to cornea,16 limitations applied as to types of drugs that can be used, limitations to multi-drug applica tions, to difficulty of insertion.17 Drug Delivery by Contact Lenses A contact lens is an ideal vehi cle for delivering drugs to the eye for a number of reasons. First, present-day soft contact le nses can be worn comfortably a nd safely for an extended period of time, varying from about a day to 15 days. Second, the residence time of solutes in the POLTF is about 30 minutes, which is significantly larger than that of drugs delivered by eye drops which is about 5 minutes. 18,19 The reason for the long residence time is that once the contact lens is placed onto the ey e, the drug from the lens will diffuse into a thin fluid layer trapped between the lens and the cornea called the post-lens tear film (POLTF). There is very limited mixing between the fluid in the POLTF and the outside tear fluid, and therefore the drug

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16 stays in the POLTF for a long time before it gets drained by the regu lar tear drainage mechanism. A detailed model that describes this phenomenon is presented in chapter 2. In addition, contact lenses are made up of cross-linked gels, and thus it is easy to entrap the drug in the gel matrix either by soaking the contact lens in a dr ug solution or by adding the drug during the polymerization process.20 Finally, this system can deliver drugs to the eye while simultaneously correct vision. If no vision correc tion is needed, the lens will just be designed such that the front and the back surfaces have the same shape. There have been a number of attempts in the past to use contact le nses for ophthalmic drug delivery; and most of these focused on soaking the lens in drug solution followed by insertion into the eye,21-32 followed by the release of the drug in th e eye. A number of researchers have studied the uptake of timolol, which is a co mmon glaucoma medication, in poly hydroxyl ethyl methacrylate (HEMA), and copolymers of HEMA and methacrylic acid (MAA) or methyl methacrylate hydrogels. 33-35 Also, recently Karlgard et. al. m easured the uptake and release of a number of ophthalmic drugs by both HEMA based and silicone contact lenses in in vitro studies.36 While a number of in vitro studies have been done to study drug delivery by contact lenses, there are relatively few in vivo studies on ophthalmic drug delivery by contact lenses. There are a few clinical studies in which it was shown that the soaked contact lenses can achieve desired therapeutic results,21-24,37,38 but only a few of these studies quantified the actua l amount of drug that was taken up by the cornea.35 The lack of quantitative studies is mainly due to the difficulty of conducting these experiments in humans. Mathematic Model of Drug Delivery by Contact Lenses The dynamics of tear flow and the contact lens motion are well characterized both mathematically and experimentally. 18,39-42 Thus drug delivery from a contact lens can be

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17 modeled by coupling the models de veloped in the studies listed above with a mass transfer model for the contact lens. As described in chap ter 2, a mathematical model is developed for the process of drug delivery by soaked contact lenses and use the model to determine the effectiveness of this method in comparison to drug delivery by drops. In order to solve the drug release problem, one has to model the mass transf er in the post-lens tear film (POLTF). The dispersion in the POLTF is driven by the lid mo tion during the blink and the mass transfer model developed in chapter 2 is valid for any arbitr ary lid velocity, which can be obtained from experiments. It thus represen ts an improvement over an earlier model for dispersion in the POLTF that was developed by Creech et al., which was valid only for a specific form of blink velocity. Thus, the two main contributions of th e mass transfer model described in chapter 2 are, first, it represents the first attempt to mode l ophthalmic drug delivery by soaked contact lenses and predict the efficacy of this modality in comp arison to drops. Second, it presents a rigorous approach based on multiple time scales to develop a model for mass transfer in the POLTF, and develops an expression for dispersi on coefficient that is more accura te than those derived earlier. Also our approach clearly points out the para meter regimes in which the results for the dispersion coefficient are valid. While this mode l cannot replace clinical studies, it can serve as a very useful tool to gauge the effectiveness of soaked contact lenses and also designing these to achieve the desired therapeutic dos ages in clinical studies. We also hope that the encouraging results predicted by this model, which also match th e limited clinical data available in literature, will lead to more clinical studies in this area. Mathematic Model of Timolol Delivery by Contact Lenses In chapter 3, we developed a transport m odel for timolol delivery by PHEMA contact lenses where we modified the model described in chapter 2 to a model that is tailored for the release behavior for an ophthalmic drug, timolol maleate, by taking into account specifically the

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18 interactions between timolol and PHEMA gel. The reasons that we are interested in the release of timolol are because of the widely usage of th is drug, and the toxic side effects timolol maleate can cause. Timolol maleate is a commonly used drug for glaucoma. Glaucoma is an ocular disease typically characterized by abnormally high intraocular flui d pressure, which can lead to partial to complete loss of vision. Approxima tely three million Americans have glaucoma, and as many as 120,000 are blind from this disease. Timolol, a nonselective beta blocker, treats glaucoma by lowering the pressure inside the ey e by inhibiting the production of aqueous humor. It is known that systemic absorption of beta-blo ckers such as timolol causes a number of side effects, such as cardiac arrhythmias and seve re bronchospasms, syncopes, cerebrovascular events, heart failure, depression, states of confus ion, and impotence. These side effects can be caused simply by its ophthalmic use to treat glaucoma, and can be a voided by using a more efficient ophthalmic drug delivery system. In view of the toxic side eff ects of timolol, a number of rese archers have studied the uptake of timolol in gels composed of mixtures of various monomers that include hydroxyl ethyl methacrylate (HEMA), methacrylic acid (M AA), N,N-diethylacrylamide (DEAA), 1(tristrimethyl-siloxysilylpropyl )-methacrylate (SiMA), N,N, dimethylacrylamide (DMAA), methyl methacrylate (MMA).33-35,43-45These studies have focused on studying the effects of gel composition and ‘impriniting’ on drug uptake and release. A majority of these studies focused on drug loading into the gel by soaking in water and subsequent drug release into a tear mimic such as phosphate buffer saline (PBS). These studie s have shown that the pa rtition coefficient of timolol between gel and water depends on concen tration, and the adsorption of the drug in the polymer can be described by the Langmuir isotherm. In addition to the part ition coefficient, the diffusion coefficient of timolol in these gels was also determined by fitting the short time release

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19 data to the diffusion equation. Also an in vivo study was recently conducted in which imprinted contact lenses loaded with timolol were placed in rabbit eyes, and the dynamic concentration in the pre-lens tear film, i.e., the film in between the lens and the air was measured.43 These in vivo experiments demonstrated that timolol has a much longer residence time in the tear film when it is delivered via contact lenses compared to deliv ery by drops. However, the fraction of drug that enters the cornea cannot be computed from the pre-lens tear film measurements that were gathered in this study. The central goal of chapte r 3 is to evaluate the effectiveness of timolol delivery by contact lenses in comparison to dr ops. We accomplish this goal by developing a mathematical model for ocular tr ansport of timolol wh en it is delivered via contact lenses. A second goal of this study is to de termine the effect of a slowdown in release rates from a contact lens such as by an increased cr osslinking on the fractional uptake of timolol by cornea. In order to develop an ocular model for timolol delivery by contact lenses, we first need to develop a model to characterize tr ansport of timolol through the contact lens matrix. We accomplish this by performing in vitro experiments for uptake and release of timolol from both deionized (DI) water and PBS, and fitting the data to a mathematical model. In vitro experiments are performed for three levels of crosslinking, and the transport parameters are determined for each of these. Next, an ocular transport model is formulated that combines timolol transport in the contact lens with mass transfer in the eye. This model us es the transport parameters obtained from the in vitro experiments, and predicts the fraction of drug th at enters cornea, and also the fraction that is lost to conjunctival absorption a nd/or lacrimal drainage. By usi ng this model, we evaluate the bioavailability for timolol delivery by contact le nses, and also the effect of a slowdown in drug diffusion by increased crosslinking on bioavailabilit y. If the therapeutic needs of the cornea are known, this model can be used to determine the dr ug concentration in the solution into which the

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20 contact lens needs to be soaked. In course of developing the ocular tr ansport model, we have also investigated the binding and transport of t imolol in p-HEMA gels of various crosslinking in both DI water and PBS, and while these studies ar e not entirely new, these help in developing a better understanding of timolo l transport in hydrogels. Recent Research on Ophthalmic Dr ug Delivery by Contact Lenses A number of researches have been conducted to develop an ideal ophthalmic drug delivery vehicle using contact lenses. Most of the work can be categorized into two types of devices. One involved drug loading by soaking th e contact lens in the drug solution,21-32 followed by the release of the drug in the eye. The other involved direct entrap ment of the drug in the contact lens during the polymerization of the contact lens material.46-51 Along with some other studies involving using a compound contact lens,52 all of the above systems su ffered from limitations on drug loading as well as the drug release behavior . As described in detail by Gulsen et al.,53 the drug loading is limited by the solubility of the drug in the gel matrix. In addition, the desired drug release rates provided by these devices can only sustain in a re latively short period of time simply due to the fact that all of these devices were designed to control the release rate based on pure diffusion of the drug in the bulk hydrogel mate rial. If drugs are s imply release by simple diffusion, the time scale in which they diffuse out of the gel is h2/D, where h is the gel thickness and D is the diffusion coefficient of the drug in the gel. Since D and h ar e fixed by contact lens designers, one has no separate control over the dr ug release time scales. In the range of proper mechanical and optical propertie s, these systems can only release drugs in a matter of a few hours, and cannot offer extended drug release. Hiratani et al. recently showed that with the impr inting technique, they successfully increased the drug loading of timolol in a hydrogels made of N,N-diethylacrylamide and

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21 methacrylic acid. However, since the release mechanism is still by diffusion, they could only achieve drug release for 48 hours. Drug Delivery by Particle-Laden Contact Lenses An alternate method is to entrap the drug in nanoparticles and disperse the drug-laden nanoparticles in the gel during the polymerization.53,54 Recently, Graziacascone et al. published a study on encapsulating lipophilic drugs inside na noparticles and entrappi ng the particles in hydrogels.55 They used PVA hydrogels as hydrophilic matrices for the release of lipophilic drugs loaded in PLGA particles. They compar ed the drug release rate s from hydrogels loaded with the particles with that directly from the PLGA par ticles, and found comparable results, which implies that the release from particles is the rate limiting step and thus controlled the drug release rates. Our work , as described in ch apter 4 and 5, focuses on incorporating drug-laden particles in a p-HEMA hydrogel matrix in a manner that the hydrogel stays transparent, which is required for contact lens applic ation, while release drug at ther apeutic rates. During my PhD research, we have successfully shown that we ha ve developed transparent particle-laden contact lenses that can offer extended timol ol release at therapeutic rates. In chapter 4, we investigated the possibility of using microemu lsion laden contact lenses as ideal vehicles for ophthalmic drug delivery. Microe mulsions are dispersions of oil in water or water in oil that are thermodynamically stable du e to the significant lowe ring of the interfacial tension by the adsorption of amphiphiles on the surface. They have received considerable attention due to numerous applications in a wide variety of areas such as separations, reactions, drug delivery, and detoxification.56 In all the applications lis ted above, the process of mass transfer across the surfactant-c overed interface plays a key role. Most studies on ophthalmic use of microemulsions focused on entra pping hydrophobic drugs in the oil phase.54 Delivering ophthalmic drugs via microemulsions leads to an increase in bioavailabil ity but the effect is

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22 rather limited because the microemulsions get wa shed away by tear circulation. The elimination of microemulsions with tear circul ation can be avoided if these are trapped in soft contact lenses. In chapter 4, we synthesized ethyl butyrate/water microemulsions stabilized by Pluronic F 127 surfactant, added these to HEMA and then polym erized the solution. It was speculated that addition of HEMA to the microemulsion may lead to deastabilization and so we also synthesized six component microemulsions stabilized by Plur onic F 127 that had ethyl butyrate as the oil phase and a solution of NaCl a nd NaOH in HEMA and Water as the continuous phase. These microemulsions were polymerized to yield hydro gels. Drug release behaviors were studied in water and PBS at two different conditions. In one condition, we replace the solution every 24 hours to offer a infinite sink condition, whereas in the other condition, the same solution is used till equilibrium of the system is reached. In chapter 4, the e ffects of extraction or release temperature were also studied. In the chapter 5, novel particle laden PHEMA lenses were developed for extended timolol drug delivery. Our work focuses on dispersion of highly crosslinked microparticles of EGDMA (ethylene glycol dimethacrylat e) or EGDMA-co-HEMA (ethylen e glycol dimethacrylate-cohydroxy-ethyl methacrylate) in poly-hydroxy-ethyl methacrylate (p-HEMA) contact lenses. One of the most common treatments nowadays for glaucoma is by applying timolol maleate eye drops. The usual starting dose of timolol, whic h is a hydrophobic ophthalmic drug, is one drop of 0.25% timolol maleate in the affected eye(s) twice a day.3 Assuming a volume of 25 l for each drop, the daily dosage of timolol is 125 g each day. It is known that only about 1% of the drug applied by eye drops goes into the cornea, which means that only about 1 g/day is needed by cornea. Ophthalmic drug deliv ery by contact lenses was shown by a transport model to have a 50 fold enhancement in terms of drug release efficiency because about 50% of

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23 the applied drug goes into cornea. This means that the target drug delive ry rate is about 2~3 g/day if delivered by contact lenses. The EG DMA microparticle laden hydrogels presented in chapter 5 were shown to be able to deliver 3 g/day for about 10 days. EGDMA microparticle laden contact lenses offer a much more efficient and safer way to deliver timolol, while greatly reduced the side effects. This is a preliminary success in terms of in vitro studies. It is expected that some in vivo tests will take place in the near future, as well as the exploration of other eye drugs that can potentially be delivered by these vehicles.

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24 CHAPTER 2 MODELING OPHTHALMIC DRUG DELIVE RY BY SOAKED CONTACT LENSES Introduction While my research is mainly aimed at studyi ng the release of an ophthalmic drug timolol, in this chapter, we proposed a general model of drug release from the contact lens into the pre and the post-lens tear films and the subsequent uptake by the cornea. The motion of the contact lens, which is driven by the eyelid motion during a blink, enhances the mass transfer in the post-lens tear film (POLTF). We use regular perturbation methods to obtain the Taylor dispersion coefficient for mass transfer in th e POLTF. The diffusion of drug in the gel is assumed to obey Fick’s law and the diffusion in the gel and the mass transfer in the POLTF are combined to yield an integro-differential equation that is solved numerically by finite difference. Two extreme cases are considered in this paper. The first case corresponds to a rapid breakup of the pre-lens tear film (PLTF) that prevents dr ug loss from the anterior lens surface into the PLTF. The second case corre sponds to a situation in which the pr e-lens tear film exists at all times and furthermore the mixing and the tear draina ge in the blink ensure that the concentration in this film is zero at all times. These tw o cases correspond to the minimum and the maximum loss to the pre-lens tear film and thus represen t the highest and the lowest estimations for the fraction of the entrapped drug that diffuses into the cornea. Results show that the dispersion coefficient of the drug in the post-lens tear film is unaffected by the release of the drug from the gel. Furthermore, simulation results show that drug delivery from a contact lens is more efficient than drug de livery by drops. The fraction of drug that enters the cornea varies from about 70 to 95% for the first case (no flux to the PLTF) and from 20-35% for the second cas e (zero concentration in the PLTF ). The model predicts that

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25 delivery of pilocarpine by soaked contact lenses is about 35 times more e fficient than delivery by drops and this result matche s clinical observations. Model We develop a model to predict the drug releas e from a pre-soaked contact lens into the post-lens tear film and its subsequent uptake by the cornea. Figure 2-1 shows the real and the model geometry of the lens and th e tear film. The post-lens tear film (POLTF) is pictured as a flat, two-dimensional film bounded by an undeform able cornea and an undeformable but moving contact lens. The lens is treated as a two-dimensional body of length L and thicknessgh, and is assumed to extend infinitely in the third direc tion. The post-lens tear film has a thickness fh which may depend on x as the front surface of the eye has a complicated geometry, but for simplicity, is taken to be independent of x in th is paper. The curvatures of the cornea and the lens have been neglected because the thicknesses of the tear film (about 10 m) and of the contact lens (about 100 m) are much smaller than the cornea l radius of curvature of about 1.2 cm. The assumption of a two-dimensional geomet ry has been made to simplify the problem. The effect of gravity is negligible in the POLTF . Thus, for our purposes the pre-lens tear filmcontact lens-POLTF-cornea system is a flat, horiz ontally oriented channel. These assumptions have been utilized in the past to model mass transfer in the POLTF. 18 The drug concentrations in the gel matrix of the contact lens, and the tear film aregCand fC, respectively. To determine the drug flux to the cornea, we need to simulta neously solve the convect ive-diffusion equation in the gel matrix and in the post-lens tear film. The governing equations for the mass transfer in the tear film and lens are,

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26 2 1 f 2 2 1 f 2 f 1 f 1 f fy C x C D y C v x C u t C (21) 2 2 g 2 2 2 g 2 g gy C x C D t C (22) where x1 and y1 are the lateral and transverse coor dinates in the POLTF , respectively, x2 and y2 are the lateral and transverse coordinates in the lens, respect ively. In the above equations Df and Dg are the drug diffusivities in the tear film and the contact lens hydrogel matrix, respectively; and v , u are velocity components in x1 and y1 directions, respective ly in the post-lens tear film. The approximate values of L, fh, and gh are 1 cm, 10 m and 100 m, respectively. The diffusive time scale in the gel is 2 g gh D, which is typically a few hours. The dispersive time scale in the post-le ns tear film, i.e., the time required for a solute to leave the film by a combination of diffusion and convection is about 30 minutes. Thus, a soaked contact lens is expected to supply drug to the tear film for a period of a couple of hours. In such a short period, the diffusion in the axial (x2) direction can be neglected in the lens, and thus the diffusion equation in the lens simplifies to 2 2 g 2 g gy C D t C (23) Eq 2-2 assumes that the diffusion of the drug through the contact lens gel matrix can be modeled as a purely diffusive process. It is well known that diffusion of solutes through hydrogels exhibits complex mechanisms and is governed by an interplay of swelling of the gel, adsorption and desorption of the solute molecules on th e gel, surface diffusion along the polymer that comprises the gel and bulk diffusion through the free water. Incorporation of each of these effects into our model is feasible; however, it significantly increases the complexity of the

PAGE 27

27 problem. Since our model is the first attempt to model the process of ophthalmic drug delivery by contact lenses, we keep the gel model simple and treat diffusion in the contact lens as purely Fickian. The fluid flow in the post-lens tear film is driven by blinking. During a blink the motion of the upper eyelid drives contact lens and POLTF tear fluid moti on in both lateral (x1) and transverse (y1) directions. In the interblink pe riod both the lens and th e POLTF tear fluid are stationary. The velocity profile s in the POLTF are a combination of squeeze flow (transverse motion) and shear flow (lateral motion) and are given by Creech.18 2 1 fV'x u6f(t)Vf(t) h (24) 32vV' (23)f(t) (25) where fh is the time dependent POLTF thickness with a mean value h0 and = y1 / h0 (Figure 2-1). The POLTF thickness hf is a function of time due to the motion of the contact lens during blinking and is equal to0hV' f(t)dt. In the above expressions V and V' are the amplitude of the lens velocities in the lateral a nd the transverse directions, respectively. We now define as the blink-interblink frequency, i.e., b 2/T , where Tb is the time for a blinkinterblink cycle. The function f(t) in the above equations characteriz es the velocity of the contact lens driven by the blink and it is equal to ze ro during the interblink period and it can be approximated as bcos(t) during the blink, where bN is defined as 2 blink time) and N is therefore the ratio of the time between two b links and the actual bli nk time. The velocity amplitudes V and V' can also be related to the amplitude of lens motion by, V = and V' = 'N where and ' are the lens displacements in the lateral (x1) and the transverse (y1) directions, respectively. As discussed above, the model contact lens is not circular but

PAGE 28

28 translationally invariant in the direction out of the paper in Figure 2-1, and thus lens and the tear film are effectively semi-infinite. The flow is assumed to be periodic-steady because fh ~ 10 m and the tear kinematic viscosity = 1.5 x 10 -2 cm 2 /s,45 giving rise to a characteristic time for fully developed flow chart = 2 fh ~ 7 x 10 -5 s, much shorter than the blink period T = 2/ b ~ 0.1 s. The boundary conditions for gC are 0 y C C K ) C ( C C y C D y C D0 y 2 g h y f h y f eq , g h y g h y 1 f f h y 2 g g2 f 1 f 1 g 2 f 1 g 2 (26a-c) where K is the partition coefficient, i.e. the ratio of the concentration of th e drug in the gel and in the POLTF at equilibrium. Bounda ry conditions (eq 2-6a) and (eq 2-6b) ensures continuity of flux and equilibrium at the lenspost-lens tear film interface, respectively. The boundary condition (eq 2-6c) assumes that th ere is no loss of drug from the le ns to the pre-lens tear film (PLTF) that lies in between the lens and the air. This assumption may be reasonable because the PLTF breaks very rapidly and the breakup of the PLTF prevents any further drug loss from the front surface. Additionally, the P LTF breakup causes partial dehydrati on of the lens in the region close to the front surface, and cons equently the front surface of the c ontact lens is expected to be glassy, which may further reduce drug flux from th e front surface. This is clearly the scenario that will maximize the fraction of the drug trapped in the lens that will even tually be delivered to the cornea. To determine the fraction of trappe d drug that will go to the cornea for the other extreme, we investigate the case in which we assume that the drug can diffuse into the PLTF and

PAGE 29

29 that rapid mixing and drainage from the PLTF keep s the drug concentration in PLTF about zero. Thus the boundary condition (eq 2-6c) gets modified to g2C(y0)0 (2-6c’) The boundary conditions for fC are 1 1 11f x0 1 fx=L f fy=0cfy=0 1C 0 x C0 C DkC y (27a,c) The first boundary condition (eq 2-7a) arises due to symmetry, condition (eq 2-7b) assumes that the drug concentration in the tear meniscus is very small due to the large volume, and the last boundary condition (eq 2-7c) assumes that the dr ug flux to the cornea can be quantified as f cC k, where ck is the mass transfer coefficient for drug transport into the cornea. The mass transfer into cornea is assumed to be irreversible, whic h is reasonable because the concentration of the drug in the corneal tissue is small and the dr ug is perhaps bound to the cellular or the extracellular components. The initial conditions for the drug concentrations are i 0 t g 0 t fC C 0 C (2-8a,b) The above set of equations can be solved by fi nite-difference or finite element methods to predict the drug flux to the cornea. However, due to the disparate length and time scales involved in the problem, it is possible to reduc e the problem to a single integro-differential equation that can be solved numerically.

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30 By using a perturbation expansion in the aspe ct ratio and by using a multiple time scale analysis, the transport problem in the film can be simplified to a dispersi on equation of the form 0 0 f c 1 0 f * 1 0 fh C k j x C D x t C (29) where 0 fC is the leading order term in the regular expansion for Cf in and is independent of y1 (See Appendix A), D* is the effective dispersion co efficient, and j is the flux of the drug entering the post-lens tear film from the contact lens. The details of th e derivation are shown in Appendix 1. Now, we solve separately the transport problem in the contact lens hydrogel matrix. The transport problem in the gel is 2 gg g 2 2CC D t y (210) with the following boundary conditions, g2gf1 g 2g 2 g 2 2C(y=h)=KC(x) C -D(y=h)=j y C (y=0)=0 y (211a,c) The boundary conditions (eq 2-11a) assume equ ilibrium between the concentration in the contact lens and that in the te ar fluid in the POLTF and (eq 211b) imposes flux continuity, and thus couples the mass transfer problems in the POLTF and in the contact lens. The boundary condition (eq 2-11c) assumes that ther e is no loss of drug from the lens to the pre-lens tear film (PLTF) that lies in between the lens and the air. As described a bove we also consider the other extreme case in which the boundary condition 11c is replaced by g2C(y0)0 (2-11 c’)

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31 We solve the drug release problem for both of the extreme cases. The above set of equations can be solved by using convolution theorem to yield an analytical expression for gC in terms of f1C(x). The derivation is shown in Appendix B. As shown in the Appendix B, for case 1, which corresponds to zero flux to the PLTF, the expression for the drug flux to the POLTF, j, becomes, 22 22 g g 2 2 g g 22 22 g g 2 2 g g(2n+1)Dt(2n1)D 22 t (tt*) 4h 4h g g iff 2 n0n0 0 g g (2n+1)Dt(2n1)D 22 (tt*) 4h 4h g g if0f0 2 n0 g gD(2n+1)D j2Ce2KC(t*)edt*C(t) h4h D(2n+1)D 2Ce2KC(t*)edt*C( h4h t n0 0t)O() (212) and for case 2, which corresponds to zero conc entration in the PLTF , the expression for j becomes, 22 22 g g 2 2 g g 22 22 g g 2 2 g g-(2n+1)Dt nD 22 t (t-t*) h h ggg f igff 2 n0n1 0 gggg -(2n+1)Dt nD 22 (t-t*) h h ggg f0 igf0 2 n0 ggggD2DKnD C(t) j4Ce-DKC(t*)edt*C(t) hhhh D2DKnD C(t) 4Ce-DKC(t*)edt hhhh t f0 n1 0*C(t)O() (213) where the O( )errors in the flux are due to approx imation of the film concentration Cf by the leading order concentration Cf0. These expression can be substituted into eq (2-9) to get a single integro-differential equation which can be solved numerically to determ ine the drug concentration in the tear film as a function of x and t. We now use the followi ng scales for dedimensionalizing the integrodifferential equation: gC~iC, fC~ iC K, x1~L, D*~Df, t~ 2 g gh D, j~ gi gDC h. The dimensionless forms of the equations are:

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32 * f0f0 0f0 C C P1DP2jP3C (214) where 22 fggcg 2 gffgDhhkh P1=, P2=K, P3= DLhhD and 0j ~ is the dimensionless O(0) flux that can be determined from eqs (2-12) and (2-13). The 0j ~ for case 1 and case 2 are given below by eqs 2-15 and 2-16, respectively. 22 22 *22 (2n+1)(2n+1) () ** 44 0f0f0 n0n0 0(2n+1) j=2e2C()edC() 4 (215) 22 22*t (2n+1)22n()* 0f0f0f0 n0n1 0j4eC()2C(*)nedC() (216) Results and Discussion Scales for Various Parameters 0 0h <<1 L O() L ' O() h (217) The typical values of fh and L are 10 microns and 1 cm, respectively. Thus, is about 10-3, and is thus much less than 1. Both L and f ' h have a value of about 0.05. Thus, these too are much less than 1, and can be treated as O( ). Depending on the drug of interest, the parameters g f fgD Kh Dh and c0 fkh D could be either O() or O(2). When these parameters are O(2), the coupled POLTF-gel problem can be

PAGE 33

33 represented by eq (2-14). Also as show n in the Appendix, under the condition that c0 fkh D and g0 fgDKh Dh are O(), the coupled POLTF-gel problem is si mply a limiting case of eq 2-14 and can be obtained by setting P1=0. This occurs because if g f fgD h Dhis O(), then g f fgfD hL =O(1) Dhh, which implies that 2 2 g fggh LL ~ DDh. Thus, in this limit the time scale for lateral diffusion in the POLTF ( f 2D L ) is much larger than the time scale fo r the drug to diffuse out of the gel ( 2 g gh D), and accordingly the dispersion of the dr ug in the POLTF can be neglected. Dispersion Coefficient The expression for the dispersion coefficient that is obtained in the Appendix I is valid for any arbitrary f(t). Creech et al had analyzed the problem of dispersion in the POLTF and had obtained the dispersion coefficient for the case when f(t) = cos(Nt), where N is equivalent to defined by Creech et. al.18 They had argued that since disp ersion in the interblink period is negligible, the overall dispersion coefficient can be obtained by si mply calculating the dispersion for the case of repeated blinks without any inte rblink period in between and then multiplying the resulting dispersion coefficient by the ratio of blink time to the total time for a blink-interblink cycle. Since our approach can be used to determin e dispersion for an arbitrary f, we can test the validity of the above assumption. It is noted that for a pure cosine function, the dispersion coefficient obtained in this paper reduces to that obtained by Creech et. al. It is also noted that in the analysis of Creech et al, there was no flux of solute from the lens or to the cornea while in

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34 our problem the drug diffuses from the lens and al so enters the cornea. In fact Creech et al claimed that the dispersion coefficient of the solu te in the POLTF would change if the solute can diffuse in/out of the lens or the cornea. Howeve r, it was not clear as to how the analysis would be altered to include the flux of the drug from the lens and into the cornea. More importantly the analysis of Creech et al is only valid for a certain range of parameters but their analysis does not clearly reflect the region of applicability of th e results. Since the analysis presented in the appendix is based on the method of multiple time scales and regular expa nsions, the region of validity of the results is clear. We now compute the dispersion co efficient for the case when f(ts) is given by cos(Nts) during a blink and is zero during the interblink. The function f(ts) and the Fourier series representation of the function are shown in Figure 2-2 for N = 10. The coefficients of the Fourier series expansion can be used in eq A-58 to determine the dispersion coefficient. The dispersion coefficient for f given in Figure 2-2 is calcula ted for a range of values and is plotted in Figure 2-3 for the lateral veloci ty profile. Also the dispersi on coefficient predicted by Creech et. al., which as explained above can be obtained by setting f(ts) = cos(Nts) with no interblinks and then multiplying the dispersion coefficient by th e factor 1/N, which is the ratio of blink time to total blink-interblink cycle time. The figure also contains results for dispersion coefficient that were computed by numerically solving the O() equations in the POLTF and then computing the dispersion coefficient by computing the integral required in eq A-46 numerically. As seen in the Figure 2-3, the numerical computa tions agree with the analytical results, which is expected. Additionally, the predictions of Cr eech et. al. are only about 10% larg er than the exact solution. The results of Creech et. al. overestimate disper sion because they neglect the lateral diffusion during the interblink a nd this diffusion equilibrat es the concentration in the lateral direction, and

PAGE 35

35 thus reduces the dispersion. Since the expression of Creech et. al. is a good approximation to the exact solution, it is used to calculate dispersion for the remaining part of this chapter. It is noted that Figure 2-3 shows the results for only the lateral flow, but the matching between the numerical and the analytical re sults and the comparison between the general expressions and the predictions of Creech, et. al are simi lar for the case of squeeze flow. Solution of the Integro-Differential Equation The integro-differential equations were solved numerically by finite difference. As shown below, the convolution integrals were evaluate d by converting those to ordinary differential equations and by further solving those equations numerically. This was done to improve the convergence of the series sum of the convolution integrals. For case 1, let 22 *22 (2n+1) ( ) ** 4 nf0f0 1n0 0(2n+1) IIC( )edC() 4 (218) thus, * n-() 2** n f0 nf0nf0 0d IdC() C() C() e d d d (219) where 4 ) 1 n 2 (2 2 n We can then write an equation for solvingnI as follows, nf0 nnd I-d C( ) + I = d d (220) This equation can be solved simultaneously with eq 2-14 to determine Cf(x,t). The same procedure can be followed for case 2. Let 22* *22-n ( )* nf0f0 11 0IIC( )n ed -C( ) nn (221)

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36 As in case 1, we can write an equation for solvingnI for case 2 as follows, nf0 nndIdC( ) + I=d d (222) where 2 2 nn Concentration Profiles The concentration profiles (f0C(x,t)) in the POLTF depends on the following parameters: D*(N, 2 0 f h D , 0 ' h, L), P1, P2 and P3. In the results shown below the values of N, ' 0 ,, Lh are kept constant at 10, 6.28, 0.02 and 0.028, respectively, which correspond to normal physiological values, and the values of P1 , P2 and P3 are varied within a range of possible values. Figure 2-4 and Figure 2-5 show typical concentra tion vs. time plots at different positions for cases I and 2, respectively. The inse ts in each figure show the magnified view of the plots near t = 0. The concentration starts at zero and then very quickly increases to a value of about 0.9. Since the concentrations are dedime nsionalized by Ci/K, the maximum possible value of Cf0 in the POLTF is 1. During the period in wh ich the concentration is increasing, the drug flux from the gel is larger than the sum of the drug loss from the sides (L x ) to the outer tear lake and the drug uptake by the corn ea. The maximum value of the concentration is reached in a very short period of time because the volume of the POLTF is small as reflected in the large value of P2. At initial times, the drug flux in to the cornea and the drug loss from the sides are much less than the drug flux from the lens causing drug concentration in th e post-lens tear film to increase. However, as the drug concentra tion in the POLTF builds up, the flux of the drug from the lens decreases and the drug loss from th e sides due to dispersion and the drug flux into cornea increases. Consequently , very quickly, the drug concentr ations in the POLTF begin to

PAGE 37

37 decrease. The concentrations finally approach zero in a dimensionless time of about 8 and 2 for case 1 and case 2, which correspond to no flux and zero concentration in the PLTF, respectively. The total release time is larger for case 1 becau se there is no drug loss to the PLTF. The same data as shown Figure 2-4 and Figure 2-5 is shown as Cf0(x) plots at various times in Figure 2-6. The plots show the growth of th e dispersive boundary layer from x = L towards the lens center. The boundary layer thickness is about the same fo r both cases because the dispersion coefficient is independent of the flux from the lens. Also the concentration vs. position plots are almost identical for both the cases for short times. This is expected because the fl ux from the lens to the POLTF will be unaffected by the boundary cond ition at the lens-PLTF interface till the mass transfer boundary layers from both th e POLTF-lens and the PLTF-lens merge. We now investigate the effect of the variation of the three main parameters P1, P2 and P3 on the concentration profiles. The values of P1, P2 and P3 used in the figures are representative values for a wide variety of ophthalmic drugs. Th e variations in these pa rameters arise primarily due to variations in Dg, Df, K and kc, and each of these can vary by more than an order of magnitude. Additionally, we calculate the fractio n of the entrapped drug that enters the cornea and the fraction that is lost to the tear lake fr om the sides of the POLTF, and for case 2 also the fraction that is lost to the PLTF . The amount of drug that diffuses into the cornea is simply equal to L cf1 002kCdxdt. The mass of drug that diffuses into the tear lake from the edges of the POLTF is given by 1* f ff 0 1 x=LdC 2DDhdt dx. Finally, the amount of the drug that is lost to the

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38 PLTF is given by 2L g g2 00 2 y=0dC 2Ddxdt dy. On dedimensionalizing each of these masses by the initial mass of drug in the gel (= 2CiLhg), we get the following equations: L11 ccf1ff0 000000 02P3P3 F=kCdxdtCd d Cd d MP2P2 (223) *** fff0 sff 000 01 =1 =1 x=L2dCP1dCP1dC F=DDhdtDd Dd MdxP2d P2d (224) 21 gg Pg1 0000 02 =0 y=0dCdC 2 F=Ddxdtd d Mdyd L (225) where Fc is the fraction of the total drug that enters cornea, Fs is the fraction of the total drug wasted from the side to the outer tear lake, and FP is the fraction of the total drug wasted to the PLTF. Effect of P1 Figure 2-7 plots the f0C( ) at different locations at three different times for two different values of P1 for case 2 and Figure 2-8 plots the fractions of the drug that are either delivered to cornea or lost to the tear lake or to the PLTF for a range of P1 values. The parameter P1 is the ratio of the diffusive time scal es in the gel and the diffusive time scales in the POLTF in the lateral direction. Thus, an increase in P1 can be interpreted as an increase in the diffusion coefficient of the solute in tears. Since an increase in Df will lead to enhancement of dispersion, the thickness of the edge region will increase. This effect is shown in Figure 2-7. Also an increase in dispersion will increase the drug loss from the sides and thus the fraction of the drug that enters cornea will be reduced. The trends are the same for both the cases of no flux to PLTF and zero concentration in the PLTF.

PAGE 39

39 Effect of P2 Figure 2-9 plots the f0C( ) at four different values of dimensionless time for two different values of P2 and Figur e 10 plots the fractions of the dr ug that are either delivered to cornea or lost to the tear lake or to the PLTF for a range of P2 values. The parameter P2 is the ratio of the amount of drug present in the contact lens and the amount present in the tear film at equilibrium. Thus, an increase in P2 can be interp reted as an increase in the partition coefficient of the solute, K. As shown in Figure 2-10, for case 1, changes in P2 have a negligible effect on the fraction of drug delivered to th e cornea. The reason for this behavior is that changes in P2 change the concentrations in the POLTF but the ch ange is very similar at every axial location. Thus, the mass delivered to the cornea and the mass th at gets out from the side are affected in an almost identical way, and accordingly the fractions remain unchanged. For case 2, an increase in P2 leads to a reduction in the fluxes to the cornea and the fraction that is lost to the tear lake. The reason is that an increase in P2 is equivalent to an increase in K, and thereby a reduction in the POLTF concentrations. A ccordingly, for a given Ci, the duration of drug release into the POLTF increases with an increase in K. Thus, there is more time for the drug to diffuse into the PLTF and so the flux that goes to the PLTF increase s. The results for the temporal profiles (f0C( ) at = 0) for two different values of P2 for both case 1 and case 2 are shown in Figure 2-11. Figure 2-11 again shows that at short times (inset), the concentration profiles in the POLTF are the same for both cases. Also, the curves in th is figure show that as th e value of P2 decreases, the time to achieve the maximum concentration in the POLTF increases slightly and the value of the maximum dimensionless concentration in the f ilm decreases. To understand this issue, let us first consider the case when there is no loss of drug to the PLTF and also when the loss of the drug from the POLTF to the tear lake and also to the cornea is negligible. The parameter P2 is

PAGE 40

40 essentially the ratio of the drug carrying capacity of the lens and the drug carrying capacity of the POLTF, and as stated above, an increase in P2 can be interpreted as an increase in K. Thus, if loss to the tear lake, cornea, and the PLTF is negligible, the concentration in the POLTF will reach equilibrium, i.e., 0 fC ~ will become 1, and the time to reach equilibrium will be shorter for a larger K, or a larger P2. In the results shown in Figure 2-11, the loss to the tear lake and to the cornea is not negligible and this loss prev ents the POLTF concentration from reaching equilibrium, and thus the value for the dimensionl ess concentration stays less than 1. However, for a very small K, the flux from the lens is so large that in the time that it takes for the concentration to reach the maximum, the loss to the tear lake is negligible and thus the dimensionless concentration reaches a value very cl ose to 1. Since the loss to the PLTF does not affect the short time profiles, the reasoning for the effect of P2 on the maximum concentration and the time to attain it is the same for both case 1 (no loss to PLTF) and case 2 (maximum loss to PLTF). Effect of P3 Figure 2-12 plots the f0C( ) at the center of the lens for both the cases and for two different values of P3 and Figure 2-13 plots the fractions of th e drug that are either delivered to cornea or lost to the tear lake or to the PLTF for a range of P3 values. The parameter P3 is the ratio of the time scale for the diffusion in the lens and drug uptake by the cornea. Thus, an increase in P3 can be interpreted as an increase in the permeability of th e cornea to the solute. Accordingly, an increase in P3 leads to a larger flux into the cornea and also a reduction in the POLTF concentrations, which results in an incr ease in the fractional uptake by the cornea and a reduction in the fraction lost from the side to the tear lake. The trends are the same for the case of no flux to PLTF and zero concentration in the PLTF. As P3 becomes very large, the

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41 concentration in the POLTF is expected to be ne gligibly small, (see Figu re 2-12) and thus the boundary condition at the lens-POLTF interface beco mes almost identical to that at the lensPLTF interface for case 2. Accordingly, the diff usion from the gel become symmetric and thus about 50% of the drug goes to PLTF and the other 50% goes to the POLTF. Since the loss from the edges due to dispersion is small, as P3 beco mes very large the fracti on of drug that goes to the cornea is expected to be about 10 0% for case 1, and 50% for case 2. Results for Timolol The values of Df and Dg for timolol, which is a commonly used glaucoma drug, are 5x1010 m2/s and 5x10-12 m2/s,57,45 respectively, and the value of corneal permeability, kc, for timolol is 1.5x10-7 m/s.58 The partition coefficient for timolol in pHEMA gels depends on concentration and the average value is about 5.45 Also the values of hf and hg are 10 and 100 m, respectively. Thus, the parameters P1, P2 and P3 are 0.04, 50 and 30, respectively. The fractional flux to the cornea for these parameters is 0.1658 for the cas e of zero concentration in the PLTF and 0.7993 for the case of zero flux to the PLTF. The frac tional losses to the la ke are 0.0567 and 0.1923 for the two cases. For the case of well mixed PLTF, the loss to the PLTF is 0.8008. The durations of drug release are about 16000 and 4000 s for th e cases of rapid PLTF breakup and the wellmixed PLTF, respectively. Since the real situation is expected to be somewhere in between the two extreme cases, the fraction of timolol that enters the co rnea may be around 50%, and the release time is perhaps about 10000 s. At a saturation loading of 2 mM, 45 a contact lens can contain about 0.01 mg of drug. Thus for the mean release time of 10000 s and 50% uptake by cornea, the delivery rates to cornea are 0.04 mg/day. The usual starting dose of timolol is one drop of 0.25% timolol maleate in the affected eye(s) twice a day. Assuming a volume of 25 l for each drop, the daily dosage of timolol is

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42 0.125 mg each day. Only about 1-5% of this amount actually reaches the cornea. Thus, the dosage that needs to be delivered to cornea is at the maximum about 0.0063 mg each day, which is much smaller than the rate that can be delivered by a saturated contact lens. These results show that if a contact lens satu rated with timolol is worn for a period of about 2-3 hours, it may provide adequate dosage of timol ol and minimize side effects. Comparison of Model Predic tions with Clinical Data Most of the clinical studie s on drug delivery by contact lens es focused on delivery of a glaucoma drug pilocarpine by soft contact lenses.21-24,36,52 Pilocarpine is a hydrophilic drug that simply absorbs in the pores pres ent in the hydrogel matrix of so ft contact lenses and does not bind to the polymer matrix. Thus, the diffusion of pilocarpine through a swollen contact lens can be modeled as a purely Fickian process. Since pilocarpine simply absorb s in the soft contact lenses, the partition coefficient for this drug is eq ual to the fractional water content in the fully swollen lens and this varies from about 0.7 to 0.86 for the Sauflon lenses, which were used in most studies.23 The contact lenses used in most st udies were afocal, 0.2 mm thick, with a diameter of 13.5 or 14 mm and back central rad ii (radius of curvature) between 7.8 and 8.6 mm.21,24 Thus, these contact lenses o ccupied a volume of about 65-75 l. If these lenses are soaked in 1% pilocarpine solution then based on a saturation water content of 80%, the lenses should absorb about 560 g of drug. Hillman et. al. report ed a slightly larger value of 700 g for the drug content in the lens es soaked in 1% solution.24 Hillman et. al. compared clinical response of Sauflon lenses soaked in 1% pilocarpine so lution with that of intensive pilocarpine 4% therapy, which comprises of instilling 1 or 2 drops per min. for 5 min., every 5 min. for half an hour and then every 15 min. for 90 min.24 The pilocarpine thera py amounts to instilling of about 17 drops that contain about 30-40 l of 4% pilocarpine, which deliver about 23 mg of drug

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43 to the eyes, which is about 33 times the amount of drug present in the contact lens. Hillman et. al. reported that the clin ical response to the contact lens soaked in 1% solution was better than that for pilocarpine therapy.24 In another study with the same type of lenses and the same treatment methodologies, Hillman observed a 54.8% drop in intraocular pressure with the contact lenses and a 49.7% reduction with the 4% pilocarpine regimen 29. Thus, both of these studies suggest that drug delivery by cont act lenses is about 33 times more efficient than that by drops. As stated above, the value of the partition coeffi cient of pilocarpine in hydrophilic soft contact lenses is expected to be around 0.8. Also, the in vitro data for releas e of pilocarpine from a soaked lens into saline gives a value of about 10-12 m2/s for the diffusivity in gel, Dg.24 Since the molecular weight of pilocarpine is about 2/3 of that of timolol, its diffusivity in tears, Df , can be approximately taken as 1.5 times that of timolol, which as stated above is 5x10-10 m2/s. The corneal permeability of p ilocarpine is 1.7x10-7 m/s.36 Based on these parameters and values of 10 and 200 m for hf and hg, respectively, the values of P1, P2 and P3 are 0.003, 16 and 680, respectively. The fractional flux to the cornea for these parameters is 0.48 for the case of zero concentration in the PLTF and 0.98 for the case of zero flux to the PLTF. Since the real situation is expected to be somewhere in between the tw o extreme cases, the fraction of pilocarpine that enters the cornea may be around 70%. The fractiona l uptake for pilocarpine has been reported to be about 2%.21 Thus, the model predicts that the dr ug uptake by contact lens is about 35 times more than that by drops, and this is in r easonable agreement with the clinical results. Conclusions The model developed in this paper represents a first attempt to model drug release from a contact lens and the subsequent uptake by the co rnea. The model assumes Fickian diffusion in the contact lens and takes into account the convec tive enhancement in mass transfer in the

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44 post-lens tear film due to the flow driven by the oscillation of the contact lens during the blink. The fraction of drug that enters the cornea has be en determined for two extreme cases. The first case corresponds to a rapid breakup of the pre-lens tear film, whic h prevents drug loss from the anterior lens surface. The second case corresponds to a situation in which the pre-lens tear film exists at all times and furthermore the mixing and the tear drainage in the blink ensure that the concentration in this film is zero at all times . These two cases correspond to the minimum and the maximum loss to the pre-lens tear film a nd thus represent the highest and the lowest estimations for the fraction of the entrapped drug that diffuses into the cornea. The fraction of drug that enters the cornea varies from about 70 to 95% for the first case and from 20-35% for the second case. It is thus r easonable to assume that in normal physiological circumstances where the pre-lens tear film breaks in a few sec onds, the fraction of drug th at is absorbed by the corneal tissue will be about 50%. The tear br eakup on the anterior lens surface also causes partial dehydration of the lens near the surface a nd the dehydration results in a thin glassy layer near the surface, which might suggest that case 1, which corresponds to no-flux to the PLTF may be more applicable under normal conditions of lens wear. The model predicts that the fraction of pilocarpine that enters the co rnea may be around 70%, which is a bout 35 times larger than the reported value of about 2% for delivery by drops.18 This result is in reasonable agreement with the clinical results. The model presented in this paper takes into account the essen tial mechanisms but simplifies each one of those. For instance, the diffusion through the contact lens has been assumed to be Fickian. The diffusion of solu tes through hydrogels is complex and depends on a number of factors such as the degree of swelling and the interaction of the solute with the gel. The contact lens is swollen when it is inserted in the eye and although the water content of the

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45 lens changes after insertion, particularly near the anterior surface, this cha nge is not expected to significantly alter the drug diffusion. However, many of the ophthalmic drugs including timolol, have been shown to adsorb on the lens matrix and thus the assump tion of Fickian diffusion is not appropriate for these drugs. In fact, a partition coefficient valu e of larger than 1, which is required to achieve sufficient loading in the contact lens shows that the drug must be adsorbing to the gel. The adsorption of the drug modi fies the diffusion equation for the gel and the modified Ficks law can be incorporated into the framework proposed in this paper. In addition to the simplification of the gel diffusion, a numbe r of assumptions have been made for the mass transfer in the POLTF. Firstly, the model assumes a simplified flat 2D geometry. This assumption has been used previously to model mass transfer in the POLTF with satisfactory results, and thus is perhaps reasonable due to the thin POLTF. Additionally, the motion of the contact lens has been simplified to correspond to periodic squeeze flow and Couette flow. These assumptions have also been used previously with satisfactory results. While each of the assumptions listed above are expected to impact the drug release profiles , none of them introduce new physics or mechanisms, and furthermore, each of these can be incorporated into the framework developed in this chapter. In fu ture, we plan on incorporating some of the modifications discussed above. The results of this study show that a soaked contact lens can significantly reduce the drug wastage and the side effects associated with the entry of the drug into th e systemic circulation, and thus is a big improvement over ophthalmic drug delivery by eye drops. We note that while soaked contact lenses are more efficient than drops, they still suffer from a number of drawbacks. Firstly, when a lens is soaked in drug solution, the ma ximum drug concentration obtained in the lens matrix is limited to the equi librium concentration. Thus, a soaked lens can

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46 supply only a limited amount of drug. This techni que is especially inefficient in delivering hydrophobic drugs by HEMA based contact lenses. S econdly, even for drugs that can absorb in the lens matrix, the drug releas e times scale is only a few hours. Thus, a soaked contact lens cannot deliver drugs for extended pe riod of time. However, in spite of these defi ciencies, it is clear that a soaked contact lens is a much mo re efficient vehicle for ophthalmic drug delivery than the conventional eye drops.

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47 Figure 2-1. Geometry of pre-len and post-lens tear films. A) The geometry used in the model B) Idealized geometry.

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48 Figure 2-2. The function f(ts) th at characterizes the time depende nce of the velocities in the POLTF (thick line) and the Fourier representa tion of the function (thin line). The two functions match everywhere except at locatio ns where f(ts) is disc ontinuous. At ts = 0, 2 the Fourier series sums up to 0.5, whic h is the mean of value at ts = 0 and 2 . The value of N is taken to be 10 for the curv es in this Figure a nd everywhere else in this paper.

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49 0 1 2 3 4 5 6 7 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 2 *L N D Figure 2-3. Comparison of the exact solution for the dispersion coefficient (solid line) with the approximate expression assu med by Creech, et. al. (Ref:Error! Bookmark not defined. ) (dash line). The markers on each curve are the dispersion coefficients calculated by numerically solving the O( ) problem. In this figure the results are shown only for the component of dispersion caused by the lateral flow

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50 A B Figure 2-4. Typical concentration transients in the POLTF at different axial locations for case 1, i.e., no flux to the PLTF. B) Magnified view n eat t = 0. The values of P1, P2, and P3 are 0.5, 100 and 100, respectively. 0 0.005 0.01 0.015 0.02 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 C0x/L=0 0.5 0.95 0 1 2 3 4 5 6 7 8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 C0x/L=0 0.5 0.95

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51 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 C0x/L=0 0.95 0.5 A 0 0.005 0.01 0.015 0.02 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 C0x/L=0 0.95 0.5 B Figure 2-5. Typical concentration transients in the POLTF at different axial locations for case 2, i.e., maximum flux to the PLTF. B) Magnified view neat t = 0. The values of P1, P2, and P3 are 0.5, 100 and 100, respectively.

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52 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 x/LC0Dimensionless Time = 0.0009 0.0004 0.2069 0.2069 3.8069 1.8069, 3.8069 1.8069 Figure 2-6. Concentration prof iles in POLTF for both case 1 (solid) and case 2 (dashed) as a function of time. The values of P1, P2, and P3 are 0.5, 100 and 100, respectively.

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53 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 x/LC09E-4 0.2 0.6 Figure 2-7. Effect of P1 on c oncentration profiles for case 2. The concentration profiles are shown at three different times and for two diffe rent values of P1. (0.05 solid line; 0.5., dashed line). The values of P1, P2, and P3 are 0.5, 100 and 100, respectively.

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54 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 P1FractionsFc Fc Fp Fs Fs Figure 2-8. Effect of P1 on the fractions of the drug that enter cornea or are lost from the PLTF or from the POLTF. Results are shown fo r both case 1 (solid) a nd case 2 (dashed). The values of P2 and P3 are 100 and 100, respectively. Fc, Fs, and Fp denote the fractions of applied drug that enter the cornea, POLTF, and PLTF, respectively,

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55 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 x/LC09E-4 0.2069 0.6069 1.8069 9E-4 0.2069 0.6069 1.8069 Figure 2-9. Effect of P2 on c oncentration profiles in the POLTF for case 1. The profiles are shown at different times a nd for two different values of P2 (=20 dashed line; 100 solid line). The values of P1 a nd P3 are 0.5 and 100, respectively.

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56 50 100 150 200 250 300 350 400 450 500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 P2FractionsFp Fc Fc Fs Fs Figure 2-10. Effect of P2 on the fractions of the drug that enter co rnea or are lost from the PLTF or from the POLTF. Results are shown fo r both case 1 (solid) a nd case 2 (dashed). The values of P1 and P3 are 0.5 and 100, respectively.

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57 0 1 2 3 4 5 6 7 8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 C0P2 = 20 20 100 100 A 0 0.01 0.02 0.03 0.04 0.05 0.06 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 C020 P2 = 100 1 B Figure 2-11. Effect of P2 on concentration tran sients in the POLTF at x = 0 for case 1 (solid lines) and case 2 (dashed lines). B)A magnified view near t = 0. The values of P1 and P3 are 0.5 and 100, and the values of P2 are noted on the curves.

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58 0 1 2 3 4 5 6 7 8 9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 C0100 100 600 600 A 0 0.01 0.02 0.03 0.04 0.05 0.06 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 C0100 600 B Figure 2-12. Effect of P3 on concentration tran sients in the POLTF at x = 0 for case 1 (solid lines) and case 2 (dashed lines). B)A magnifi ed view near t = 0. The values of P1 and P2 are 0.5 and 100, and the values of P3 are noted on the curves

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59 0 100 200 300 400 500 600 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 P3FractionsFc Fs Fc Fp Fs Figure 2-13. Effect of P3 on the fractions of the drug that enter co rnea or are lost from the PLTF or from the POLTF. Results are shown for bot h case 1 and case 2. The values of P1 and P2 are 0.5 and 100, respectively.

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60 CHAPTER 3 OCULAR TRANSPORT MODEL FOR OPHTHAL MIC DELIVERY OF TIMOLOL BY PHEMA CONTACT LENSES Introduction Ophthalmic drug delivery via contact lenses should be more effective than by drops because it increases the residence tim e of the drug in the eye and is therefore expected to lead to a larger fractional intake of drug by the cornea. While a number of in vivo and some in vitro experiments have been done to design and test op hthalmic drug delivery by contact lenses, little quantitative data exists for the bioavailability, i. e., the fractional drug upta ke by cornea. In this paper we combine in vitro experiments with modeling to investigate the delivery of timolol, a commonly used glaucoma drug to the eyes. The in vitro experiments are performed to develop a transport model for release of the drug from p-HEMA contact lenses. The transport model includes adsorption of drug on the polymer and the diffusion of the drug through the bulk water. Experiments are performed at three different leve ls of crosslinker and th e transport parameters are determined for each case. The transport mode l is then incorporated into a model for the release of the drug from the c ontact lens into the pre and th e post-lens tear films and the subsequent uptake by the cornea. Results show that at least 20% of the timolol entrapped in the lens will enter the cornea, which is much larg er than the fractional uptake for drug delivery by drops. Materials and Methods Materials The HEMA monomer and the dr ug timolol (timolol maleate salt) were purchased from Sigma Chemicals (St Louis, MO) and ethylen e glycol dimethacrylat e (EGDMA), azobis-isobutrylonitrile (AIBN), and Dulbecco’s Phosphate Buffered Saline (PBS) were purchased from

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61Aldrich Chemicals (Milwaukee, WI). All the ot her chemicals were of reagent grade. All the chemicals were used wit hout further purification. Synthesis Methods The p-HEMA hydrogels were synthesized by free radical soluti on polymerization of HEMA monomer. The crosslinker EGDMA (10 l) and the monomer HEMA (2.7 ml) were added to 2 ml of distilled wa ter. The solution was then de gassed by bubbling nitrogen for 20 min. Next, 6 mg of the initiator AIBN was a dded to the polymerization mixture and the mixture was poured in between two glass plates that we re separated from each other with 0.2-mm thick spacers. The polymerization reaction was performed in an oven at 65 C for 20 hours. The gels of the composition described above are referred as 1X gels. We also synthesized gels that contained 10 times and 30 times of the EGDMA us ed in the above formul ation, and these gels are referred as 10X and 30X, respectively. Swelling Experiments The gels synthesized by following the method reported above were submerged into DI water or PBS for a period of 2 days. After co mpletion of swelling, a ci rcular piece of a fixed diameter was cut by using a cork borer. The weight and the thickness of this piece were measured, and then it was dried at room temperatur e for 2 days. Finally, the dry weight of this cylindrical gel was measured. The values of f, which is the volume fraction of water in the fully hydrated gels were computed as wet dry wetV W W f , where Wwet and Wdry are the weights of the gel in the swollen and the dry state, respectively, Vwet is the volume of the wet gel, and is the density of the swelling medium (DI water or PBS).

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62Drug Diffusion Experiments The drug diffusion experiments were conducted both in DI water and in PBS. To remove the unreacted monomer, the pure p-HEMA gels synthesized by the proc edure described above were submerged in a vial contai ning 40 ml of well-stirred water, which was changed regularly. The absorbance of the aqueous phase was monitore d, and the soaking was continued till the gain in absorbance at 332 nm in 1 day dropped below 0. 001. The gels were then submerged in a wellstirred drug solution (in DI water or in PBS) at room temperat ure and the absorbance of the solutions were measured as a function of time to determine the drug concentration. The gel thicknesses were about 200 m and the gel volumes va ried between 30 and 60 l, and the fluid volume was about 50 times the gel volume. Th e absorbance values were measured by UV-Vis spectrophotometer (Thermospectronic Genesys10 UV) at a wavelength of 332 nm. The loading experiments were conducted for four different drug concentrations in the aqueous phase (DI water or PBS) varying from 0.375 mM to 3 mM. After the gels had equilibrated in the load ing phase, these were withdrawn from the solution, blotted dry and then pla ced in fresh solution (DI water or PBS) for the release phase of the experiments. The total drug content in the gels at the beginning of the release experiments was different for each gel mainly due to the differe nces in the drug concentr ations in the loading solutions. However even for the replicate experi ments at the same loading concentration, the amount of drug uptake was slightly different for the two replicates due to small differences in gel volumes. During the release phase, the concentrat ion was monitored as a function of time by measuring the UV absorbance at 332 nm.

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63Results and Discussion Swelling Studies in Deionized Water The swelling studies were performed to determine the parameter f, which is the volume fraction of water in the fully hydrat ed gels. Table 1 lists the valu es of f for the 1X, 10X and 30 X gels. As expected, the values of f d ecrease with an increasing crosslinking. Equilibrium Drug Uptake in Deionized Water The drug molecules in the HEMA gel can either adsorb on the polymer or be present in the water phase in the hydrogel. The binding of th e drug to the gel can be modeled as a Langmuir adsorption isotherm, which relates the adsorb ed concentration of the drug on the gel ( ) to the free concentration in the aqueous phase in side the gel (C) by the following equation C k C (31) where is the surface concentration at the maximum packing on the surface and k is the ratio of the rate constants for desorp tion and adsorption of the drug on the HEMA surface. The total mass of drug (Mgel) in a gel of volume Vgel with a uniform concentration C is given by C fV V V S Mgel gel gel gel (32) where gelV S is the surface area per volume available fo r the drug to adsorb and f is the volume fraction of water in hydrated gel. The value of f for p-HEMA gels can be determined from the swelling experiments, and are listed in Table 1. The mean concentration of the drug in the gel is thus equal to fC V Sgel . Accordingly, the partition coefficient K, which is the ratio of the drug concentrations in the gel and in water at equilibrium, can be given by f C k a K (33)

PAGE 64

64where gelV S a. The parameters a and k characterize the equili brium binding of the drug to the polymer and can be obtained by fitting the equilibrium partition coefficient data to Eq. [33]. Based on Eq. [33], a plot of 1/(K-f) should be a straight lin e and the slope and the in tercept can be used to determine a and k. The partition coefficients can be determined as a function of concentration by utilizing the equilibrium concentration values in the loading experiments and in the release experiments. In these experiments the concentrat ion of the drug in water (Cw) was measured as a function of time. In the loading experiment s, the mass of the drug taken up by the gel during the loading is equal to ) C C ( Vf , w 0 , w w , where Vw is the volume of the aqueous phase, and Cw,f and Cw,0 are the final and the initial concentrations of the drug in the aqueous phase, respectively. Accordingly the part ition coefficient is defined as f , w gel f , w 0 , w wC V ) C C ( V K , where Vgel is the gel volume. After equilibrium was a ttained, the drug-loaded gels were submerged in aqueous solution for the release experiments. In the release experiments, the partition coefficient is given by f , r gel f , r f , w 0 , w wC V ) C C C ( V K , where Cr,f is the final concentration in the aqueous phase during the release experiments. It is not ed that we have implicitly assumed that at equilibrium, the concentration of timolol in the aqueous phase out side the gel is equal to the concentration in the water phase inside the gel. Figure 31 plots the partition coefficient K as a function of equilibrium concentration in the water phase (Cw,f) for the 1X crosslinked gels . The solid line is the fit obtained by assuming a linear relationship between 1/(K-f ) and the concentration. As can be seen from the figure, the Langmuir fit is not adequate to describe the data, particularly at low concentrations. We

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65speculate that the deviation from the linear relati onship between 1/(K-f) and Cw,f could be either because the adsorption cannot be described adequa tely by the Langmuir isotherm or because the drug is binding to different type s of sites on the polymer. Assuming that the deviation from the Langmuir behavior is due to pres ence of two types of sites, we attempted to fit the partition coefficient data to a sum of two Langmuir isotherms, i.e., c k a c k a f K2 2 1 1 (34) The dashed line in Figure 31 is a fit of the partition co efficient data to the above equation. The two site model fits the partition coefficient well. The partition coefficients for the 10X and 30X gels are similar to those for the 1X gels (Figure 32). We fitted the partition coefficient data for each of the two sets of 1X , 10X, and 30X gels, and the valu es of the parameters are a1 = 5.04 0.38 mM , k1 < 10-3 mM, a2 = 2.06 0.67 mM, and k2 = 0.27 0.19 mM. The thick dashdot line in Figure 32 is the partition co efficient fit based on the mean parameters. It is noted that since all the measurements were obtaine d at concentrations much larger than k1, we cannot accurately determine k1. We can only determine that k1 is less than about 10-3 mM. Also the partition coefficients are relatively insensitive to k2. In fact, increasing or decreasing k2 by a factor of 3 makes a maximum change of 10% in the partition coefficient. The weak dependence of the partition coefficient on k2 arises due to the fact th at at concentrations around k2, the dominant contribution to the partition coefficient is still fr om the first term. The value of k1 and a1 determined in here are in good agreement with the values reported in Ref 35. They reported a value of 6.6 mmol for a1 (defined as S in Ref.35) and a value of 0.005 for k1 (defined as 1/K in Ref.35). However, in this study , the authors did not explore the large concentration range, and so they were able to fit the entire partition coef ficient data with a single Langmuir isotherm.

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66It is well known that in a hydrat ed gel, only a fraction of the water is free and the rest is bound to the polymer. We speculate that one of the Langmuir term in the partition coefficient corresponds to the drug present in the bound water, which is weakly bound to the surface. It is also possible that the two terms simply correspond to the two different types of sites at which the timolol molecules can adsorb on the gel. Dynamic Drug Transport in Deionized Water We first model the release data followed by the loading data. Drug release experiments The transport of timolol in the p-HEMA ge l can be described by the modified diffusion equation that takes into account binding of the drug to the polyme r. The modified form of the diffusion equation is j y t KC (35) where KC is the total drug concentration in the gel, and the term on the right represents the divergence of the diffusive flux of the drug. In the release experiments, both the initial and the final concentrations in the gel are much larger than k1. Thus, there are no spatial gradients in the concentration of the strongly adsorbed molecule s, and accordingly the diffusive flux of these molecules is expected to be zero. The net diffu sive flux in the release experiments will then comprise of diffusion of the free drug and the weakly bound, each diffusing with individual effective diffusion coefficients. The above equation can be expressed as C K y D y C f D y t KC2 2 0 (36) where D0 is the diffusivity of the free drug, C k C a C K2 2 2 is the concentration of the bound drug that is assumed to be available for di ffusion with an effective diffusivity D2. It is noted that Eq.

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67[36] is a phenomenological equa tion, and it does not necessarily reflect the exact mechanism of binding. Here, we also assume that th e weakly bound drug does not diffuse, i.e., D2 is assumed to be negligible. With these assumptions, Eq. [36] simplifies to y C y f D C k C a C k C a fC t0 2 2 1 1 (37) Since f is a constant for a given gel, for simplicity we refer to the product D0f as the effective diffusivity D. The above equation is subj ected to the following boundary conditions: wC ) h y , t ( C 0 ) 0 y , t ( y C (38) where h is the half-thickness of the gel, the first boundary condition assumes symmetry at the center of the gel, and the second boundary conditi on assumes that the free drug concentration in the gel at the boundary with the fluid is the same as the drug concentration in the fluid. A mass balance on the fluid in the beaker yields h y gel w wy C DA 2 dt dC V (39) The initial conditions for the drug release experiments are 0 ) 0 t ( C C ) 0 t , y ( Cw r , i (310) It is noted that Ci,r should equal Cw,f which is the concentration in the aqueous phase at the end of the loading experiments. However, by using this as the initial condition, the errors in measurements during the loading phase negatively impact the re lease fits. To minimize the effect of the errors in the loading phase, Ci,r is determined by ensuring that the mass of the total drug in the gel and the fluid medium at the e nd of the release phase equals the mass at the beginning.

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68In the drug release experiments, the dynamic drug concentration in the aqueous phase was measured, and the data can be fitted to the transport model proposed above to determine the diffusion coefficients D of the drug in the gel. The values of k1 and k2 are fixed at 10-4 and 0.27 mM for each of the gels, and the values of a1 and a2 are obtained by fitting the partition coefficient data for each set of gels for a give n crosslinking. The model described above was solved by a semi-implicit finite-difference sche me with 51 spatial nodes and a dimensionless time step (D t/h2) of 0.00075. The simulations were check ed to ensure grid independence and mass conservation. The error between the mode l prediction and the experimental data was defined as N / C N / Cw 2 w (311) where Cw is the concentration in the water, wC is the difference between the experimental and the predicted concentrations, and the sum is carried over all the N experimental data points. For the three types of gels (1X, 10X, 30X), each data set was fitted to the model to obtain the diffusion coefficient. The comparison between the experimentally measured concentration and the fits are shown in Figure 3a-c for the 1X, 10X and 30X gels, respectively. The average error was less than 1% for these fits. The values of D obtained by fitting the release data are 9.46 5.14 m2/s, 6.71 5.70 m2/s and 2.45 0.94 m2/s for the 1X, 10X and 30X gels, respectively. As expected, the diffusion coeffici ent decreases with increasing crosslinking. The relatively large standard deviations in the diffus ivities arise because the partition coefficients are very sensitive to the aqueous concentration, and small measurement errors in aqueous concentration could potentially cause large errors in calculations of partition coefficients, which in turn impact the diffusivity fits.

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69Drug loading experiments In the loading experiments, the gel is fully sw ollen at t = 0 but it does not contain any drug. Thus, as the molecules diffuse into the gel, a concentration boundary layer develops, and propagates towards the center of the gel. Insi de the boundary layer, the concentration is much larger than k1, and thus there are no spatial gradients in the concentrati on of the tightly bound molecules. However, at the edge of the bounda ry layer, the concentr ation is close to k1, and thus there are gradients in the concentration of the tightly bound molecules that could lead to diffusion along the surface. The surface diffusivity of the tightly bound mol ecules is expected to be small but a very large fraction of the molecules are adsorbed in this state, and thus the tightly bound molecules may contribute to the diffusive flux in the loading experiments. As a simplification, if one neglects the diffusive flux of the adsorbed molecules, the fits between the model and the experiments are not good (curves not shown). As another extreme, one may assume that both the free and the bound molecules diffuse with the same diffusivities, and in this case, the flux simplifies to y KC Dl . By substituting this expression for flux in Eq. [35], one gets, y C y D C tg l g (312) where KC Cg is the mean gel concentration. The a bove equation is subjected to the following boundary and initial conditions: w g gKC ) h y , t ( C 0 ) 0 y , t ( y C (313) i w gC ) 0 t ( C 0 ) 0 t , y ( C (314)

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70The drug concentration in the wa ter is related to the gel con centration through the mass balance which yields h y g gel l w wy C A D 2 dt dC V (315) In the drug loading experiments, the dynamic drug concentration in the aqueous phase was measured, and the data can be fitted to the transport model proposed above to determine the diffusion coefficients Dl of the drug in the gel. The m odel described above was solved by a semi-implicit finite-difference scheme with 21 spatial nodes and a dimensionless time step (Dl t/h2) of 0.02. The simulations were checke d to ensure grid independence and mass conservation. The error between the model predic tion and the experimental data was defined by Eq. [311]. For the three types of gels (1X, 10X , 30X), each data set was fitted to the model to obtain the diffusion coefficient. The comp arison between the experimentally measured concentration and the fits are shown in Figure 3a-c for the 1X, 10X and 30X gels, respectively. The average error was less than 1% for these fits. The values of Dl obtained by fitting the loading data are 1.89 0.52 m2/s, 1.22 0.42 m2/s and 0.23 0.01 m2/s for the 1X, 10X and 30X gels, respectively. The diffusivities de crease with increasing crosslinking, which is expected. The diffusivities calculated from th e loading experiments are much smaller than the diffusivities determined from the release experiments. This could be explained by the fact that the diffusivities in the release model is the diffusivity of the free drug molecules while the diffusivity in the loading model is the mean diffusivity of both th e free and the bound drug molecules. Since the surface diff usivity of the bound molecules is expected to be smaller than the bulk diffusivity, it is reasonable that the fi tted values of diffusivities in the loading experiments are smaller than those determined from the release experiments.

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71The studies reported above were conducted in DI water, which has been reported to be a suitable medium for loading the drug into the gel. While DI water is suitable for loading, a tear mimic such as 0.9% saline or PBS are more suita ble for release studies. Accordingly, we studied the uptake and release of drug by the gels in PBS, and these studies are described below. Swelling Studies in Phosphate Buffered Saline (PBS) The swelling studies were performed to determine the parameter f, which is the volume fraction of water in the fully hydr ated gels. Table 3-1 lists the f values for the 1X, 10X and 30 X gels. The results in Table 3-1 show that the valu es of f, which correlate to the degree of swelling decreases with increasing crosslinking, and are larg er in PBS in comparison to that in DI water. Equilibrium Drug Uptake in PBS The partition coefficients for timolol in PBS were determined by using the equilibrium drug uptake, and these were relatively independent of concentration. Th e values of partition coefficient were 5.04 0.41, 5.17 1.71, and 7.96 1.55 for the 1X, 10X and 30X gels, respectively. At concentrations smaller than abou t 1 mM, the partition coefficients are smaller in PBS than in DI water because at around pH 7, a ma jority of timolol is in charged form, and thus it has a higher solubility in PBS than in DI water. Dynamic Drug Transport in PBS Drug release experiments The procedure described above for modeling the drug release in DI water (Eqs. [3-7] – [310]) was also used to fit the drug release data obtained in PBS, except that the partition coefficient is now treated as a fixed value. The fits between the model proposed above and the experimental data are shown in Figure 3a-c for the 1X, 10X a nd 30X gels, respectively. The errors in the fit are on average 5%, and the values of D obtained from the fits are 18.01 5.98, 13.42 1.89, and 4.80 0.97 m2/s for the 1X, 10X, and 30X gels respectively. We need to

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72divide these diffusivities by the partition coeffici ents to compare these with the values reported in literature that were determined by fitting the lo ading and the release data to Higuchi equation. The scaled diffusivities are 3.57, 2.60, 0.60 m2/s and these are in reas onable agreement with the value of 0.99 m2/s reported for p-HEMA gels with 2.6% (v/v) EGDMA and 0.8% (v/v) methacrylic acid. The diffusion coefficients d ecrease with increasing crosslinking, and these values are larger in PBS than in DI water due to the higher swelling in PBS compared to that in DI water. Drug loading experiments The procedure described above for modeling th e drug loading in DI water (Eqs. [312] – [315] ) was also used to fit the drug loadi ng data obtained in PBS, except that the partition coefficient is now treated as a fixed value. The fits between the model proposed above and the experimental data are shown in Figure 3a-c for the 1X, 10X a nd 30X gels, respectively. The errors in the fit are on averag e 0.5%, and the values of Dl obtained from the fits are 6.14 0.22, 2.07 0.73, and 0.30 0.03 m2/s for the 1X, 10X, and 30X gels , respectively. As expected, these diffusivity values are smaller than those obtained from the release experiments, and are larger than those obtained from the loading expe riments in DI water. Also the diffusivities decrease with increasing crosslinking. As mentioned earlier, the central goal of this paper is to compute the fractional drug uptake by cornea when a contact lens loaded with timolol is placed on an eye. In order to compute this fraction, we have to develop a combined mass transfer model for timolol release by a contact lens, and also for the transport of the drug in the tear film. Below we use the model for transport in the gels developed above, and use it to develop an ocular transport model for timolol delivery by a contact lens.

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73Model for Drug Release from th e Contact Lens into the Eye Figure 37 shows the real and the model geomet ry of the lens and the tear film. The post-lens tear film (POLTF) is pictured as a flat, two-dimensional film bounded by an undeformable cornea and an undeformable but moving contact lens. The lens is treated as a twodimensional body of length L and thicknessgh, and is assumed to extend infinitely in the third direction. The post-lens tear film has a thickness fh which may depend on x as the front surface of the eye has a complicated geometry, but for simp licity, is taken to be independent of x in this paper. The curvatures of the cornea and the lens have been neglected because the thicknesses of the tear film (about 10 m) and of the contact lens (about 100 m) are much smaller than the corneal radius of curvature of about 1.2 cm. The assumption of a two-dimensional geometry has been made to simplify the problem. The effect of gravity is negligible in the POLTF. Thus, for our purposes the pre-lens tear film-contact lens-POLTF-cornea sy stem is a flat, horizontally oriented channel. These assumptions have been u tilized in the past to model mass transfer in the POLTF. The drug concentrations in the gel matr ix of the contact lens, and the tear film aregCand fC, respectively. The time t = 0 corresponds to insert ion of the lens in the eye, and so the initial concentration in the tear film is zero, and the initial concentrat ion in the lens is the concentration obtained in the loadin g phase, which is now defined as Ci. To determine the drug flux to the cornea, we need to simultaneously solve the modified diffusi on equation in the gel matrix and the convection diffusion equation in the pre and the post-lens tear film. By using asymptotic techniques, and multiple ti me scale analysis, the transport problem in the post-lens tear film can be simplifie d to a dispersion equation of the form 0 f c f * fh C k j x C D x t C (316)

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74where D* is the effective dispersion coefficient, kc is the permeability of the cornea for the drug and j is the flux of the drug entering the post-lens tear film from the contact lens, which is determined below by solving the tr ansport problem in the lens. Th e details of this derivation of Eq. [316] are available in Ref 17. Also the expression for the dispersion coefficient, which depends on the motion of the contact lens that is caused by the blinks, is also available in Ref 17 and 18 As described in the previous section, the transport problem in the gel is 2 2y C D t KC (317) Since the value of partition coefficient is constant for timolol release in PBS, the above equation can be expressed as 2 g 2 e gy C D t C (318) where K D De , and Cg=KC is the drug concentration in the gel. The above equation is subjected to the follo wing boundary conditions, 0 ) 0 y ( y C j y C D ) x ( KC ) h y ( Cg g e f g g (319a-c) The boundary condition (eq [319a]) assumes equilibrium between the concentration in the contact lens and that in the te ar fluid in the POLTF and (eq [319b]) imposes flux continuity, and thus couples the mass transfer problems in the POLTF and in the contact lens. The boundary condition (eq [319c]) assumes that there is no loss of drug from the lens to the pre-lens tear film (PLTF) that lies in between the le ns and the air. This assumption may be reasonable because the PLTF breaks very rapidly and the breakup of the PLTF prevents any further drug loss from the

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75front surface. Additionally, the PLTF breakup causes partial dehydrat ion of the lens in the region close to the front surface, and cons equently the front surf ace of the contact lens is expected to be glassy, which may further reduce drug flux from th e front surface. This is clearly the scenario that will maximize the fraction of the drug trapped in the lens that will even tually be delivered to the cornea. This extreme case in which the drug flux to PLTF is neglected is referred as case 1. To determine the fraction of trapped drug that wi ll go to the cornea for the other extreme, we investigate the case in which we assume that th e drug can diffuse into the PLTF and that rapid mixing and drainage from the PLTF keeps the drug concentration in PLTF about zero. This case is referred as case 2, and for this case, the boundary condition eq [319c] is replaced by the following equation 0 ) 0 y ( Cg (320) Finally the initial conditions for the tear film and the contact lens are: i g fC ) 0 t ( C 0 ) 0 t ( C (321) The dimensionless forms of the equations are: f f * fC ~ P3 j ~ P2 C D ~ P1 C ~ (322) where 2 g eh t D , D * D * D ~ , L x , K / C C C ~i f , e f 2 g c f g 2 e 2 g fD h h k P3 , h h K P2 , L D h D P1 , and g i eh / C D j j ~ is the dimensionless flux from the cont act lens into the POLTF. By using convolution theorem, the gel problem can be solv ed to yield the following expressions for the dimensional flux for cases 1 and 2, 0 n 0 f 4 ) ( 1) (2n 2 2 f 0 n 4 1) (2n C d e 4 1) (2n C ~ 2 e 2 j ~2 2 2 2 (323)

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76 0 n 0 f ) ( n 2 2 f 0 n f 1) (2n C ~ d e n C ~ 2 C ~ 4e j ~2 2 2 2 (324) The values of the dimensional parameters required to calculate P1, P2 and P2 are noted in Table 3-1 and in Figure 37 caption. The parameters De and K are the values determined from the fitting of the release data in PBS, and the other parameters are obtained from literature. The values of P1, P2 and P3 for the 1X, 10X, and 30X gels are noted in Table 3-1. Below we solve the coupled mass transfer problem for drug de livery from a contact lens in the eye. Concentration profiles in the POLTF Figure 38 show concentration vs. time plots at the lens center for the 1X gel for cases 1 and 2. The inset in the figure shows the magni fied view of the plots near t = 0. The concentration starts at zero and then very quickly incr eases to a value of a bout 0.8. Since the concentrations are dedimensiona lized by Ci/K, the maximum possibl e value of Cf in the POLTF is 1. During the period in which the concentrat ion is increasing, the drug flux from the gel is larger than the sum of the drug loss from the sides (L x ) to the outer tear lake and the drug uptake by the cornea. The maximum value of the concentration is reached in a very short period of time because the volume of the POLTF is small as reflected in the large va lue of P2. At initial times, the drug flux into the corn ea and the drug loss from the sides are much less than the drug flux from the lens causing drug concentration in the post-lens tear film to increase. However, as the drug concentration in the POLTF builds up, th e flux of the drug from the lens decreases and the drug loss from the sides due to dispersion and the drug flux into cornea increases. Consequently, very quickly, the drug concentra tions in the POLTF begin to decrease. The concentrations finally approach zero in a dimensional time of about 400 and 100 minutes, for case 1 and case 2, which correspond to no flux and zero concentration in the PLTF, respectively. The total release time is larger for case 1 because there is no drug loss to the PLTF. It is noted

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77that the short time concentration profiles (insert in Figure 38) overlap for cases 1 and 2. This occurs because the flux from the lens to th e POLTF is unaffected by the boundary condition at the lens-PLTF interface till the mass transfer boundary layers from both the POLTF-lens and the PLTF-lens merge. Fraction of drug that enters cornea The amount of drug that diffuses into the cornea is simply equal to 0 L 0 f cdxdt C k 2. The mass of drug that diffuses into the tear lake from the edges of the POLTF is given by 0 f L x f fdt h dx dC D D 2. Finally, the amount of the drug that is lost to the PLTF is given by 0 L 0 0 y g gdxdt dy dC D 2. On dedimensionalizing each of thes e masses by the initial mass of drug in the gel (= 2CiLhg), we get the following equations: 0 1 0 f 0 L 0 f c 0 cd d C P2 P3 dxdt C k M 2 F (325) 00 1 f f L x f f 0 sd d dC D 2 P 1 P dt h dx dC D D M 2 F (326) 0 1 0 0 g 0 L 0 0 y g g 0 pd d d dC dxdt dy dC D M 2 F (327) where Fc is the fraction of the total drug that enters cornea, Fs is the fraction of the total drug wasted from the side to the outer tear lake, and FP is the fraction of the total drug wasted to the PLTF. After determining the concentration profiles, the various fractions can be determined by computing the integrals nume rically. The values of Fc, Fs, and Fp are listed in Table 32 for 1X, 10X and 30X gels both case 1 (no flux to PLTF ) and case 2 (zero concentration in PLTF).

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78Comparison with in vivo experiments Recently Hiratani et. al. conducted in vivo experiments with male albino rabbits in which they inserted timolol loaded imprinted c ontact lenses and measured the dynamic drug concentration in the pre-lens tear film. The re sults obtained in their st udy cannot be directly compared with our predictions because they did not measure the drug concentration in the post-lens tear film, i.e., the film in between the co rnea and the lens. However, it is expected that the concentrations in the pre-lens tear film follow trends similar to those in the post-lens tear film, and it can be seen that the trends predicted by the model (Figure 38) are similar to those observed by Hiratani et al . (Figure 2 in Ref 43). Conclusions A significant amount of recent research ha s focused on development of novel contact lenses that can provide extended drug delivery. However, ther e are only a very few studies on pharmacokinetics of drug delivery by contact lenses . This paper aims to bridge this gap by developing a mathematical model to predict the fr action of timolol that enters the corneal tissue when it is delivered by using soaked soft contac t lenses. In order to accomplish this goal, a transport model that can accurately predict the release of drug fr om the contact lenses has been developed in the first part of this paper. The drug transport has been investigated both in DI water and in PBS to develop a better understand ing of all the important mechanisms. Also studying drug uptake in DI water is useful because it may be better to load the drug into the gel by soaking in water rather in PBS because of the la rger partition coefficients in DI water. The partition coefficients in water are highly c oncentration dependent, and a single Langmuir adsorption isotherm is unable to fit the data ove r the entire concentration range. A sum of two Langmuir terms fits the data suggesting that there may be two different types of adsorption sites, or that one of the term may account for true adsorption, and the other may account for drug

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79present in the bound water in the hydrogel. The partition coefficients in PBS are smaller than those in water, and are relatively insensitive to concentration. While modeling the release of the drug from the hydrogels into both water and PBS, the interaction of the drug with the hydrogel is taken into account by including both the free a nd the bound drug in the accumulation term, and assuming that only the free form of the drug contribut es to the diffusive flux. This model fits the release data in both DI water and in PBS, and co rrectly captures the trend that the initial release in DI water is much rapid at higher concentratio ns. Physically this occurs because at higher concentrations, a larger fraction of the total dr ug is available to diffuse. When the partition coefficients are independent of concentration, this model simplifies to the diffusive model with an effective diffusivity that is a ratio of the r eal diffusivity and the partition coefficient. The diffusivity values decrease on in creasing crosslinking and are larger in PBS than in DI water, perhaps due to higher swelling of th e gels in PBS. The loading data, particularly in DI water, does not fit the model that was de veloped for the release experiment s. Instead, a simple diffusive model that assumes that both the bound and the free forms of the drug diffuse with the same diffusivities fits the data. This may be due to th e fact that during the loading experiments in DI water, there are spatial concentration gradient s in the tightly adsorbed drug, which are not present during the release experiments, because th e final equilibrium concentrations are larger than the k value. In any case, the release mode l is more pertinent because it is subsequently integrated into an ocular transport model to pr edict the fraction of drug entrapped in the contact lens that will enter the cornea afte r the lens soaked in timolol soluti on is inserted in the eye. The ocular transport model is develope d for two extreme cases. In the first case, the diffusive flux to the pre-lens tear film is assumed to be zero, and in the second case the concentration in the pre-lens tear film is assumed to be zero. Th e first and the second cases correspond to the highest

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80and the lowest bioavailability of th e drug, respectively, and in real in vivo conditions, the bioavailability may be an average of these two va lues. The ocular transport model predicts that the fraction of drug that enters the cornea increases with an increasing crosslinking, suggesting that the bioavailability will be higher for gels that release drugs slowly, such as imprinted gels, or gels loaded with drug containing nanoparticles.42,4342, 43 The fractional uptake by cornea for the 1X gel is 22% for case 2 and 92% for case 1. The predicted concentrations in the post-lens tear film qualitatively match the measured profiles in the pre-lens tear film in in vivo experiments. The results of this study show that a soaked contact lens can significantly reduce the drug wastage and the side effects associated with the entry of the drug into the systemic circulation, and thus is a big improvement over ophthalmic drug delivery by eye drops. While in vitro testing in which the concentrations in various ocular tissues and in blood are measured, are required to prove the improvements in drug delivery that can be obtained by using contact lenses, it is clear that a soaked cont act lens is a much more effi cient vehicle for ophthalmic drug delivery than the conventional eye drops.

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81Table 3-1. Values of parameters re quired in the ocular transport model Table 3-2. Fractional uptake by cornea (Fc) and fractional loss to the tear lakes (Fs), and to the pre-lens tear film (Fp) for case 1 (z ero flux to the PLTF) and case 2 (zero concentration in the PLTF). Note that all the fractions do not exactly add to 1.0 partly due to rounding off and partly due to small numerical errors. 1X 10X 30X Case 1 Fc 0.21 0.25 0.35 Fp 0.78 0.75 0.65 Fs 0.02 0.02 0.03 Case 2 Fc 0.92 0.92 0.92 Fp 0 0 0 Fs 0.07 0.07 0.07 1X 10X 30X K 5.045.177.96 D (m2/s) 3.572.600.60 P1 0.030.040.17 P2 50.4051.6679.60 P3 41.9857.74248.76 f in water 0.390.340.25 f in PBS 0.510.460.32

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82 0 0.5 1 1.5 2 2.5 3 0 50 100 150 200 250 300 Concentration (mM)K Measured 2 parameter fit 4 parameter fit Figure 31. Dependence of GelWater partition coefficient on dr ug concentration in the aqueous phase for the 1X gel. The solid line repres ents a two parameter Langmuir fit, and the dashed line represents the four paramete r (sum of two Langmuir isotherms) fit.

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83 10-2 10-1 100 101 10-1 100 101 102 103 Concentration (mM)K 1X 1X 10X 10X 30X 30X Fit Figure 32. Dependence of GelWater partition coefficient on dr ug concentration in the aqueous phase for the 1X, 10X and 30X gels. The da shed line represents the four parameter (sum of two Langmuir isotherms) fit. Two sets of replicate experiments were conducted for each degree of crosslinking.

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84 0 100 200 300 400 500 600 0 0.02 0.04 0.06 0.08 0.1 0.12 Time (min)CwA 0 100 200 300 400 500 600 0 0.02 0.04 0.06 0.08 0.1 0.12 Time (min)CwB Figure 33. Dynamic concentrations in the aqueous phase during the release experiments in water for 1X, 10X, and 30X gels. A) 1X. B) 10X. C) 30X. The solid lines represent the model fits. Different curves correspond to different amounts of drug loaded into the gels during the loading phase. Two rep licates were conducted at each loading concentration.

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85 0 100 200 300 400 500 600 0 0.02 0.04 0.06 0.08 0.1 0.12 Time (min)CwC Figure 33. Continued

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86 0 200 400 600 800 1000 0 0.5 1 1.5 2 2.5 3 Time (min)CwA Figure 34. Dynamic concentrations in the aqueous phase during the loading experiments in water for 1X, 10X, and 30X gels. A) 1X. B) 10X. C) 30X. The solid lines represent the model fits. Different curves corres pond to different values of initial drug concentrations in the solutions. Two re plicates were conducted at each loading concentration

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87 0 200 400 600 800 1000 0 0.5 1 1.5 2 2.5 3 Time (min)CwB 0 200 400 600 800 1000 0 0.5 1 1.5 2 2.5 3 Time (min)CwC Figure 34. Continued

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88 0 100 200 300 400 500 600 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Time (min)CwA Figure 35. Dynamic concentrations in the aqueous phase during the release experiments in PBS for the 1X, 10X, and 30X gels. A) 1X . B) 10X. C) 30X. The solid lines represent the model fits. Different curv es correspond to different amounts of drug loaded into the gels during the loading phase . Two sets of replicates were conducted for the 1X gels and only one set of experiments were conducted for 10X and 30X gels.

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89 0 100 200 300 400 500 600 0 0.05 0.1 0.15 0.2 0.25 0.3 Time (min)CwB 0 100 200 300 400 500 600 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (min)CwC Figure 35. Continued

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90 0 100 200 300 400 500 600 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Time (min)CwA Figure 36. Dynamic concentrations in the aqueous phase during the loading experiments in PBS for the 1X, 10X, and 30X gels. A) 1X . B) 10X. C) 30X. The solid lines represent the model fits. Different curves correspond to different values of initial drug concentrations. Two sets of replicat es were conducted for the 1X gels and only one set of experiments were conducted for 10X and 30X gels.

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91 0 100 200 300 400 500 600 0 0.5 1 1.5 2 2.5 3 3.5 Time (min)CwB 0 100 200 300 400 500 600 0 0.5 1 1.5 2 2.5 3 3.5 Time (min)CwC Figure 36. Continued

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92 Drug laden contact lens Cornea Post Lens Tear Film (POLTF) Pre-Lens Tear Film(PLTF) ) A lens cornea C kcCf jghPOLTF PLTF x y CgfhB Figure 37. Geometry of the pre-lens and postlens tear films. A) Real geometry B) The geometry utilized in the model for th e PLTF-lens-POLTF system. Values of parameters used in the ocular transport model were obtained from literature. ( Df = 5x10-10 m2/s 39; hg = 100 m; hf = 10 m; kc = 1.510-5 cm/s40,41; L = 0.7 cm )

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93 A B Figure 38. Drug concentrations at the center of the post-lens tear film for the 1X gel. B) Magnified view of the short time data.

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94 CHAPTER 4 TIMOLOL TRANSPORT ACROSS MICRO EMULSION TRAPPED IN PHEMA GELS Introduction While eye-drops are convenient and well acc epted by patients, about 95% of the drug contained in the drops is lost due to absorption through the co njunctiva or through the tear drainage. A major fraction of the drug eventual ly enters the blood stre am and may cause side effects. 1,2,59 The drug loss and the side effects can be minimized by using microemulsion laden soft contact lenses for ophthalmic drug delivery.53,54 In order for microemulsion-laden gels to be effective, these should load sufficient quantiti es of drug and should release it a controlled manner. The presence of a tightly packed surfact ant at the oil-water inte rface of microemulsions may provide barrier to drug transpor t, and this could be used to c ontrol the drug delivery rates. In this chapter, we focus on trapping ethylbu tyrate in water microemulsion stabilized by pluronice F127 surfactant in hydr oxyl ethyl methacrylate (HEMA) gels and measuring the transport rates of timolol, which is a beta bloc ker drug that is used for treating a variety of diseases including glaucoma. The results descri bed here show that microemulsion-laden gels could have high drug loadings, particularly for dr ugs such as timolol base which can either be dissolved in the oil phase or it can form the o il phase of the microemulsions. However the surfactant covered interface of the pluronic microe mulsions does not provide sufficient barrier to impede the transport of timolol, which is perhaps due to the small size of this drug. Materials and Methods Materials HEMA monomer and ethylene glycol dimeth acrylate (EGDMA) were purchased from Aldrich Chemicals (St Louis, MO); ethylbutyr ate and Benzoyl peroxi de (BP) (97%) was purchased from Aldrich Chemicals (Milwaukee, WI); timolol maleate, Pluronic F127,

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95 Dulbecco’s phosphate buffered saline (PBS), sodium caprylate, and sodium hydroxide pellets (99.998%) were purchased from Sigma Chemical s (St Louis, MO); Darocur TPO was kindly provided by Ciba (Tarrytown, NY). Cyclosporin e A was purchased from LC Laboratories (Woburg, MA). Methods and Procedures Synthesis of pluronic microemulsions The first step in synthesis of gels loaded w ith drug containing mi croemulsions requires synthesis of an oil-in-water microemulsion. H ydrophobic drugs such as cyclosporine or even the base form of timolol can be dissolved in the oil phase of the microemulsion. The microemulsions are then added to HEMA monome r and polymerized to form a HEMA gel laden with drug containing microemulsion drops. The microemulsions described below utilize et hyl butyrate as the oil phase, Pluronic F 127 as the surfactant, and sodium caprylate as the co-s urfactant. In these studies, the base form of timolol is entrapped in the oil drops of the micr oemulsions. The fraction of drug in the oil phase and also the fraction of the oil phase in the microemulsions are varied to develop systems with different drug loadings. Four t ypes of microemulsions are descri bed below. They are referred to as meA, meB, meC, and meD. To make meA, we first dissolved 0.0831 g of timolol maleate salt in 6 ml of 0.77M NaOH solution. The pH of the result ing solution is above the pKa of timolol (pKa~ 9.2), and thus the base form of timolol separated out from the a queous solution. After allowing the mixture to phase separate, we pipetted out 5 ml of the aqueous phase, and added 400 l of ethyl butyrate to extract the timolol base. After extraction, we separated the upper oi l phase (timolol base dissolved in ethyl butyrate) and and the lo wer aqueous phase. The upper phase (timolol

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96 containing ethyl butyrate which is referred as T/E below) was used as the oil phase of the microemulsions. MeA is water-in-oil (W/O) microemulsion stabilized by Pluronic F127 surfactant and sodium caprylate co-surfactant. To make the su rfactant solution, we diss olved 1.2 g of Pluronic F127 and 0.0163 g of sodium caprylate in 9 ml saline (0.85 wt% NaCl in DI wa ter). In order to dissolve the surfactant in the aqueous solution, the mixture had to be stirred at about 600 rpm at room temperature for a period of about 5 hours. We then added 0.1 ml T/E and 0.5 ml of 1.5M NaOH solution to 4.5 ml of the surfactant soluti on, and stirred the mixture at 600 rpm at room temperature. After about 3 hours, the solution turned clear, which indicated microemulsion formation. MeB was made by the same procedures as me A, except that meB has a slightly higher content of oil phase than meA. To synthesize me B, 0.15 ml instead of 0.1 ml T/E was added to 4.5 ml of surfactant solution. MeC was also made by similar procedures as meA. For preparing meC, pure timolol base was used as the oil phase instead of a mixture of timolol and ethyl butyrate. To synthesize meC, 0.1642 g of timolol maleate was added to 6 ml of 1.5 M NaOH solution to generate timolol base, and the mixture was allowed to phase separate. We then pipetted out and discarded 5 ml of the top aqueous phase, and the rest of the mixt ure was dried by blowing nitrogen for about 30 minutes. We separately dissolved 2.145 g of Pl uronic F127 and 0.016 g of sodium caprylate in 8 ml saline (0.85 wt% NaCl in DI water) for use as the surfactant solution fo r meC. In order to dissolve the surfactant in the aqueous solution, the mixture had to be stirred at about 600 rpm at room temperature for a period of about 5 hours. We then added 1 ml of 2.31 M NaOH solution,

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97 4 ml surfactant solution, and 0.383 g more Pluronic F127 to th e “dried” timolol base, and stirred the mixture at 600 rpm at room temperature for 3 hours. MeD was also made by similar procedures as meA, except that it had a slightly higher content of timolol in T/E mixture, a slightly higher oil content in the microemulsion, as well as a higher total amount of surfactan t added to the microemulsion while keeping the ratio of surfactant to oil constant . In addition, there was no co-surfactant added. Specifically, 0.1222 g of timolol maleate was added to 6 ml of 0.77 M NaOH solution to generate timolol base, and the mixture was allowed to phase separate. We then pipetted out and disc arded 5 ml of the top aqueous phase, and extracted timolol base with 230 l ethyl butyrate. We separately dissolved 1.64 g of Pluronic F127 in 9 ml saline (0.85 wt% Na Cl in DI water) as the surfactant solution for meD. In order to dissolve the surfactant in the aqueous solution, the mixture had to be stirred at about 600 rpm at room temperature for a period of about 5 hours. We then added 0.1 ml T/E and 0.5 ml of 1.5 M NaOH solution to 4.5 ml of the su rfactant solution, and stirred the above solution at 600 rpm at room temperature for 3 hours. The compositions of the four types of microemulsions desc ribed above are summarized in Table 4-1. The relevant physical and transport properties of timo lol are presented in Table 4-2. Entrapment of pluronic micr oemulsions in HEMA gels The microemulsion-loaded p-HEMA hydrogels were synthesized by free radical solution polymerization with UV initiation. 1.35 ml of the monomer hydroxyl ehtyl methacrylate (HEMA), 5 l of ethylene glycol dimethacrylate (EGDMA) , and 1 ml of the microemulsion were mixed together in a glass tube. This soluti on was degassed by bubbling nitrogen for 15 minutes to reduce the amount of dissol ved oxygen which can be a scavenger of both initiating and

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98 propagating species in free radical polymerization. Next, 3 mg of the photoinitiator, Darocur TPO, was added to the mixture, and the solu tion was stirred for 10 minutes. The resulting mixture was poured in between two glass plates separated by a 200 m plastic spacer. The mold was then put on a UVB-light illuminator for 40 minut es for gel curing. Pure p-HEMA gels were synthesized by replacing the microemulsion by an equal volume of DI wa ter. Control (without microemulsion) HEMA gels were prepared by following the same pro cedure described above, except that the microemulsion was replaced by an equal volume of DI water. The base form of timolol was loaded into the control gels by direct dissolving the drug in the polymerizing mixture. Synthesis of polymerizable Pluronic microemu lsions with HEMA-water as the continuous phase The microemulsions described above (MeA, B, C and D) could poten tially get destabilized after addition of the HE MA monomer. To eliminate this issue, it was decided to polymerize microemulsions that already c ontain HEMA in the continuous pha se. The procedure used to prepare these microemulsions is essentially iden tical to that described above for synthesizing ethyl butyrate in water microemulsions. The major difference is that the water phase was replaced by a mixture of water, HEMA, NaOH a nd NaCl. Several experiments were conducted to determine the suitable ratios of these four components. The composition of the continuous phase was eventually fixed to be HEMA/H2O/NaCl/(2N NaOH solution) = 53.6 : 35.8 : 1.6 : 9. The fraction of oil and the surfactants was vari ed to investigate the compositions at which microemulsions form. The phase behavior of these 6 component systems was investigated at two different temperatures. Since these microe mulsions contain HEMA in the continuous phase, these can be polymerized simply by adding initi ator (TPO) to the microemulsion. These

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99 microemulsions were polymerized by pouring th em between two glass plates separated by a 200 m plastic spacer, and then exposing the mold to UVB-light for 40 minutes for gel curing. Drug release experiments for microemulsion-laden gels Timolol release in DI water with water replacement every 24 hours. After polymerization, each gel was removed from the gl ass mold, and was cut into pieces that were above about 1.5 cm in length and width and about 200 m in thickness. Each piece of gel was dried in the air overnight and then weighed the ne xt day. The gel was then submerged in 200 ml deionized (DI) water bath under minimal stirring and at room temperature for 5 hours to extract the unreacted monomer. This step is referred to as the extraction or the initial soaking step. The extraction step was typically conducted at room temperature, but in some instances a higher temperature was used to invesrtigate the effect of temperature on drug release rates. The fraction of drug that diffused out during the extraction step was determined by measuring the absorbance at wavelengths near the absorban ce peak of timolol (295 nm). Th e fractions of drug released in the extraction step for various types of gels are listed in Table 4-3. After the extraction step, the gels were transferred into 3 ml of DI water for the drug release experiments. The DI water was replaced ev ery day, and the absorbance of the sample was measured right before water replacement. The drug release experiments with water replacement were typically conducted at room temperature, but in some instances a higher temperature was used to investigate the effect of temperature on drug release rates. In some experiments, the extraction step wa s eliminated and the drug release experiments described above were conducted immedi ately after polymerizing the gel.

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100 Timolol release in DI water without water replacement. These experiments were performed to determine the equilibrium release time for the microemulsion-laden gels. The protocols for these experiments we re identical to those describe d above, except that the gel was kept in the same 3 ml DI water during the entire course of the drug rel ease experiments. These experiments were conducted only for gels loaded with Me A, and only at room temperature. Timolol release from Pluronic micr oemulsion-laden gels in PBS. Since DI water may not be a good mimic of tears and so it was deci ded to perform timolol release experiments from Pluronic microemulsion-laden gels in PBS. Protocols identical to those described above were followed, except that the DI water was replaced by PBS or saline both in the extraction and the drug release steps. Results and Discussion Drug Release from HEMA Gels Loaded with Timolol (Control) Control HEMA gels do not contain any microe mulsion and these were loaded with the drug by directly dissolving the timolol base in th e polymerization mixture. Figure 4-1 plots the cumulative percentage release from the control ge ls with water replacement every 24 hours. The data shows a very slow release with about 1% of the drug diffusing out each day. Also Figure 42 plots the cumulative percentage release from th e control gels in 3.5 ml PBS without any fluid replacement for two days, and the second cumulativ e percentage release af ter replacing 3.5 ml PBS. The results in Figure 4-2 are in sharp cont rast with those in Figur e 4-1 as the entire drug amount diffuses out into the PBS in about 4 hours. The cause of the large difference between the release behavior in DI water and in PBS can be explained by the difference in partition coefficients of timolol base between the gel a nd DI water and between the gel and PBS. The partition coefficients of timolol maleate in DI wa ter and PBS were measured by Li, etc. In DI water, the partition coefficients are concentration dependent, and its values in the concentration

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101 range of our experiments are much greater than the partition coefficient in PBS, which is relatively independent of concentr ation and has a value of about 5.60 The partition coefficients in DI water become larger than 100 at concentr ations comparable to those in the release experiments described above and co nsequently a majority of the drug in the gel is bound to the polymer matrix and is not available to diffuse. This explains the slow release in DI water compared to PBS in which the partition coeffici ent is only about 5 and so a much larger amount of drug is available for diffusion. The significant differences in partition coefficients between PBS and DI water are due to the fact that in PBS almost the entire drug is e xpected to exist in the protonated form which is highly soluble in water but in DI water a fraction of the drug will exist as the base form, which has a ve ry limited solubility in water. Drug Release Experiments for Pluronic Microemulsion-Laden Gels Timolol release in DI water with water replacement every 24 hours Figure 4-3 plots the cumulative percentage release during the drug release experiments from a gel loaded with MeA as a function of time. The results show that the gel releases drug for about 25 days, during which about 55% of the dr ug has diffused out. The type MeA gel (gel loaded with MeA) loses about 17.5% of the dr ug in the extraction step. Thus the total drug release amounts to about 75% of th e drug loading. Since the rele ase rates are nonzero even after 25 days, the remaining fraction may continue to diffuse out over a long period of time. Also a fraction of the loaded drug may be irreversibly tr apped in the gel. Additionally, a fraction of the drug may be lost in the process of extracting the timolol base into the oil phase. The cumulative drug release profiles are sigmoida l in shape, which implies that the drug release rates first increase with time and then decrease. This be havior is interesting because typically in a diffusive system, the release rates decrease with tim e because of the reductions in concentration. Furthermore the release rates from these microemulsion-laden systems are faster than those from

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102 the HEMA control. This is very surprising because the surfactant-l aden interface of the microemulsion drops is expected to impede tran sport. Both of these interesting observations could be explained by considering the transport of ethyl butyrate which is the oil phase of the microemulsion. Since the oil has a finite solubi lity in the HEMA matrix it may also diffuse and this diffusion could lead to enha nced drug transport due to the high solubility of the drug in oil. Also the oil transport may increase with time due to depletion of the surfactant at the microemulsion interface. The increased oil tr ansport could cause the increase in the drug transport rates. Finally, the drug release profiles have to level off as all the trapped drug diffuses out. This leads to the sigmoidal drug releas e profiles evident in Figure 4-3 to Figure 4-5. In order to test this hypothesis it was deci ded to measure drug transport at elevated temperatures at which both the oil and the surfactant have higher solubilities in water and in HEMA. Figure 4-3 also shows the effect of an increase in the extraction temperature on the subsequent drug release which wa s conducted at room temperature. It was speculated that an increase in the extraction temperature will result in a larger loss of oil and surfactant in the extraction step, and that should lead to a fast er drug release in the subsequent drug release experiments. The data in Figure 4-3 is in agreement with this speculation. The release rates are faster for the gels which were exposed to a hi gher extraction temperature. Furthermore, the increase in the release rates occu rs at an earlier time for these gels which is perhaps due to a larger loss of surfactant during the extraction step. To further understand the contri butions from oil transport to the drug transport, it was decided to entrap microemulsions with differe nt oil and drug loadings. Figure 4-4 plots the cumulative drug release profiles for gels loaded with microemulsion D, which have similar amount of oil (ethyl butyrate + tim olol base) as microemulsion A but it has a higher ratio of drug

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103 to ethyl butyrate. Based on the above hypothesis it could be specu lated that a re duction in ethyl butyrate loading will lead to slow er transport. The gels loaded with MeD release drug for about 35 days which is longer than the release time for MeA gels. The effect of an increase in extraction temperature for MeD gels is similar to that for MeA ge ls. These gels release for about 20 days which is longer than the MeA gels e xposed to the higher extr action temperature. For MeD gels, additional drug release experiments we re conducted at elevated temperatures with extraction at room temperature. This data is also shown in Figure 4-4. An increase in temperature during the release experiments leads to faster release withou t changing the sigmoidal shape of the curve. The measured cumulative re lease in this case exceed s 100% which is due to errors in measurements. Figure 4-5 plots the cumulative drug release profiles for gels loaded with microemulsion B which have the same ratio of drug to oil as MeA but a higher microemulsion loading in the gel. Since the o il to drug ratio for MeA and MeB are similar their drug release profiles are expected to also be similar, which is indeed the case. To further understand the role of oil in drug transport and al so to determine whether the surfactants provide any barrier to transport it was decided to en trap microemulsions of timolol base (MeC) in the gels. Since th ese systems have no ethyl butyrate the drug transport is expected to be slower than that for MeA and MeD gels, a nd furthermore if the surfactants do not provide any barrier to transport, the rel ease rates from these systems are expected to be similar to those from the control p-HEMA gels. The release ex periments for gel C were stopped after about 50 days during which only about 20% of the drug diffused out (Figure 4-6). The drug release profiles from gels loaded with MeC are very similar to those from the control gels with no surfactant, and this suggests th at the surfactant covered interface does not retard transport.

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104 Timolol release in DI wat er without water replacement These experiments were performed to determ ine the equilibrium re lease time for the microemulsion-laden gels. These equilibrium experiments were only done on gel A. These gels lost 17.5% of the entrapped drug during the ex traction phase. The results of drug release experiments (Figure 4-7) show that about 8% of the entrapped drug diffuses out in a period of about 10 days. Based on this data the partition coefficient of timolol in gel A is about 800. Timolol release from Pluronic microemulsion-laden gels in PBS To better mimic tears, it was decided to perf orm timolol release experiments from Pluronic microemulsion-laden gels in PBS. The rel ease in saline and PBS was much more rapid compared to the release in DI water. The ex traction phase for these studies was conducted in 10 ml of saline. In both PBS a nd saline, about 90% of the drug diffused out during the extraction phase, and the remaining amount is released in th e first 1.5 hours of the drug release experiments (Figure 4-8, Figure 4-9). This result is expected because the surfactants do not retard transport and so the higher solubility of the drug in the PBS is expected to lead to a rapid release. Pluronic microemulsions with HEMA-water as the continuous phase It may be possible that the surfactant cove red interface does not pr ovide any barrier to transport because the microemulsions may be getting destabilized after HEMA addition to the microemulsion. To ensure that the microemuls ions are stable after HEMA addition, it was decided to synthesize microemulsion in HEMA -water solutions, and then polymerize the continuous phase of the microemulsions. However, ethyl butyrate which is the oil phase in the microemulsions is highly soluble in HEMA-water mix. In order to minimize the solubility of the oil in the continuous phase, it was decided to fo rm the Pluronic microemulsions at a high pH and with salt added to the continuous phase. So th ese microemulsions contain six components which are water, NaCl, NaOH, HEMA, Ethyl butyrate, and F 127. The fraction of oil and the

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105 surfactants was varied to investigate the compos itions at which microemulsions form. The phase behavior of these 6 component systems was inve stigated at two different temperatures. The compositions explored in these experiments are i ndicated in the phase diagrams shown in Figure 4-10 a-b. In all of these figures a ‘X’ mark indicates phase sepa ration, and a ‘o’ marks formation of a single phase microemulsion. It was th en decided to add timolol to a few of these compositions, polymerize the system into 200 m thick gels, and then measure the drug release rates. After polymerizing the microemulsions, drug release studies were conducted both in PBS and in DI water with protocols identical to t hose described above. These experiments showed that these systems also had a very rapid release in PBS and a slow release in DI water. (Figure 4-11) These results therefore eliminated the dest ruction of the microemulsions, or reduction in the packing at the interface as a po tential reason for the lack of any barrier to transport. Thus it seems logical to conclude that the pluronic mi croemulsions do not impede the transport of timolol from inside the oil drops to the continuous phase. The rapid release of timolol from these syst ems makes them unsuitable for contact lens applications. However, it is very encouraging that these systems have a very large timolol loading, and thus these may find some applications in other areas such as transdermal patches for delivery of timolol or other drugs. These sy stems may also be useful for loading hydrophobic molecules that have a low solubility both in HE MA and in PBS. Furthermore, these systems may offer resistance to transport of larger molecules and so th e pluronic microemulsion-laden gels could be useful for controlle d release of larger molecules. Summary Our study focused on measuring timolol transp ort from pluronic microemulsions trapped in pHEMA gels. These gels could be useful for drug delivery applications because of large drug

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106 loading. To fabricate the microemulsion-la den gels, ethyl butyrate/ water microemulsions stabilized by Pluronic F 127 surf actant were prepared, and thes e were then added to HEMA followed by polymerization. It was speculated that addition of HEMA to the microemulsion may lead to deastabilization and so we also synthesized six component microemulsions stabilized by Pluronic F 127 that had ethyl butyrate as the oil pha se and a solution of NaCl and NaOH in HEMA and Water as the continuous phas e. These microemulsions were polymerized to yield hydrogels. Both of these systems yi elded transparent hydrogels with mechanical properties similar to those for HEMA gels. It was possible to obtain very large loading of timolol in these systems by dissolving the base form of timolol in the oil phase. Gels that had timolol loaded microemulsions exhibited a slow and extended drug release in DI water. In DI water, the transport of drug was faster in microe mulsion-laden gels compared to control due to coupling between the oil (ethyl butyrate) and dr ug (timolol) transport. The transport rates showed a sigmoidal shape which was also attributed to ethyl butyrate trans port in the gel. The transport rates for gels loaded with timolol microemulsions were comparable to those for the control suggesting that the surfactan t does nor retard drug transport in DI water. All of the gels exhibited a very rapid release in PBS and in saline due to higher solubility of timolol in these solutions compared to that in DI water. Thus these systems are of limited utility for ophthalmic drug delivery. However it is encouraging that these systems can have a very high timolol loading, and so these may find applications in ot her areas such as transdermal drug delivery, and also for delivery of hydrophobic molecules to eyes.

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107 Table 4-1. Compositions of various Pluronic microemulsions (me) ID Oil % in me Surf % in me Drug % in oil Drug % in me A 1.73 10.4 14.76 0.254 B 2.48 10.3 14.6 0.362 C 2.18 15.5 100 2.18 D 1.96 13.4 30 0.58 Table 4-2. Physical and tr ansport properties of timolol Timolol Molecular weight 316 Diffusivity in tears x 1012 (m2/s) 500 Dosage (drops/day) 2 (0.25%) Corneal permeability (m/s) 1.5x10-7Fraction that enters eye 1.3% Therapeutic requirement (g/day) 1.5 Table 4-3. Fractional drug release in the extr action step for various types of microemulsionladen gels Gel Gel weight Initial timolol input Released during initial soaking type g mg mg % A 0.060 0.095 0.016 17.5 B 0.064 0.144 0.018 12.55 C 0.072 0.848 0.064 7.56 D 0.049 0.179 0.023 12.67

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108 0 1 2 3 4 5 6 7 8 9 05101520 time (days)% of timolol released Figure 4-1. Cumulative percentage release from the control gels with water replacement every 24 hours. (n=2) 0 10 20 30 40 50 60 70 80 90 00.511.522.5 time (days)% of timolol released Figure 4-2. Cumulative percenta ge release from the control ge ls without PBS replacement. Solid data shows the cumulative percentage release from the control gels into 3.5 ml PBS without PBS replacement. After two days, PBS was replaced with fresh 3.5 ml PBS, and the second cumulative release is shown as the lower curve represented by hollow triangles.

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109 0 10 20 30 40 50 60 051015202530 time (days)% of timolol released0 5 10 15 20 25 30 35 40amount of timolol released ( g) for 40 mg gel Figure 4-3 Timolol released from me A laden gel in DI water without water replacement. Solid data represent experiments done with extrac tion at room temperature. (n=4) Hollow data represent experiments done with extraction at 60 C. (n=2) 0 20 40 60 80 100 051015202530354045 time (days)% of timolol released0 20 40 60 80 100 120 140 160amount of timolol released ( g) for 40 mg gel Figure 4-4. Timolol released from me D laden gel in DI water without water replacement. Solid data represent experiments done with extrac tion at room temperature. (n=2) Hollow circular data represent experiments done with extraction at 60 C. (n=2) Hollow triangular data represent releas e experiments done at 50 C.

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110 0 10 20 30 40 50 60 70 80 0:00:00120:00:00240:00:00360:00:00480:00:00600:00:00720:00:00 time (days)% of timolol released0 10 20 30 40 50 60 70amount of timolol released ( g) for 40 mg gel Figure 4-5. Timolol released from me B laden ge l in DI water without water replacement. Solid data represents release experiment done at room temperature. (n=2) Hollow triangular data represents release experi ment done at 50 C. Hollow circular data represent experiments done with extraction at 60 C. (n=2) 0 2 4 6 8 10 12 14 16 18 20 0102030405060 time (days)% of timolol released Figure 4-6. Timolol release in DI water for me C laden PHEMA gels. The errors bars denote standard deviation, n = 2.

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111 0 1 2 3 4 5 6 7 8 0510152025 time (days)% of timolol released Figure 4-7. Timolol released in DI water without water replacement for meA laden PHEMA gels (n = 4). 0 2 4 6 8 10 12 14 012345 time (days)% of timolol released 64% 67% 40% PBS saline DI Figure 4-8 Release of timolol from meA with salt laden gels into DI water (n=2), PBS, and saline. The numbers represent the percenta ge of timolol loss dur ing 5 hour extraction in DI water, PBS, and saline, respectivel y. Solutions were changed every 24 hours.

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112 0 1 2 3 4 5 6 7 0:00:0012:00:0024:00:0036:00:0048:00:0060:00:0072:00:0084:00:00 time (days)% of timolol released Figure 4-9. Drug release in saline for gel D. Gels were first soaked in 10 ml saline for 5 hours followed by fresh 3 ml saline (replace every 24 hours) for four days which is shown in this figure. 89% of timolol was lost during extraction. (n=2)

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113 3-Component Plot0.80 0.85 0.90 0.95 1.00HEMA / Water FracSurfactant Oil HEMA / Water Solnat 22.8 deg CA 3-Component Plot0.80 0.85 0.90 0.95 1.00HEMA / Water FracSurfactan t Oil HEMA / Water Solnat 5.3 deg CB Figure 4-10. Pseudo phase diagrams for the six component microemulsion at A) room temperature and B) 5 oC.

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114 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 00.10.20.30.40.50.60.70.8 time (days)mg of timolol released 2.4 mg/g 1.5 mg/g 2.4 mg/g 1.5 mg/g Figure 4-11. Comparison of release of timolol into DI water (hollow data) and release of timolol into saline. (solid data) for stabile pluronic microemulsion in HEMA/water mixture. Absorbance data taken at 3.5, 5.5 , and 18 hour s after gels were put in 10 ml DI water or saline. Two loadings of timolol in gel were used for these experiments. (1.5 and 2.4 mg timolol/g dry gel). No timolol re lease observed after 3.5 hours in saline but release continues in DI water

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115 CHAPTER 5 DISPERSION OF EGDMA MICROGELS AND MICROPARTICLES IN P-HEMA CONTACT LENSES FOR OPHTLAMIC DRUG DELIVERY Introduction Particle-laden contact lenses can minimi ze drug loss and side effects and thus are considered to be very promising candidate s as ideal ophthalmic drug delivery vehicles.53,54 The essential idea is to encapsulate the ophthalmic dr ug formulations in particles, and to disperse these drug-laden particles in the lens material. Upon insertion into the eye, the lens will slowly release the drug into the pre-lens (the film betw een the air and the lens) and the post-lens (the film between the cornea and the lens) tear f ilms, and thus provide drug delivery for extended periods of time. This paper focuses on disper sion of highly crossli nked microparticles of EGDMA (ethylene glycol dimethacrylate) or EGDMA-co-HEMA (ethylene glycol dimethacrylate-co-hydroxy-ethyl methacrylate) in poly-hydroxyethyl methacrylate (p-HEMA) contact lenses. Material and Methods Materials HEMA monomer and ethylene glycol dimeth acrylate (EGDMA) were purchased from Aldrich Chemicals (St Louis, MO); ethylbutyr ate and Benzoyl peroxi de (BP) (97%) was purchased from Aldrich Chemicals (Milwaukee, WI); timolol maleate, Pluronic F127, Dulbecco’s phosphate buffered saline (PBS), sodium caprylate, and sodium hydroxide pellets (99.998%) were purchased from Sigma Chemical s (St Louis, MO); Darocur TPO was kindly provided by Ciba (Tarrytown, NY). Cyclosporin e A was purchased from LC Laboratories (Woburg, MA). Synthesis Methods Relevant physical and transport properties of timolol are presented in Table 5-1.

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116 Synthesis of p-HEMA gels loaded with highly crosslinked EGDMA micro-particles The first step in synthesis of gels loaded with highly crosslinked EGDMA microparticles requires synthesis of an emulsion of EGDMA in water. EGDMA is hydrophobic, and so it forms the oil phase in the emulsion. Hydrophobic drug s such as cyclosporine, dexamethasone, or the base form of timolol can be dissolved in the EDGMA drops. The drug containing EGDMA drops are then polymerized to yield the drug loaded crosslinke d EGDMA microparticles. Since EGDMA monomer contains 2 viny l groups, it is expected to fo rm a highly crosslinked gel on polymerization. The details of the process are as follows: Add 6 g of 1.04M NaOH (purged with nitrogen ) to 120 mg of timolol maleate. At such high pH, timolol maleate forms the base form of timolol that is relatively hydrophobic. To concentrate the base form, 5 ml of the upper wate r phase was pipetted out. To the remaining mixture, 1 g of EGDMA and 7.5 mg of Benzoyl Peroxide were a dded, followed by addition of 5 g of water (purged with nitrog en) and 1.65 g of 2.08 M NaOH. Timolol base dissolved in the EGDMA phase resulting in the formation of dr ug-laden emulsion. The emulsion was next heated in an 80C hot water ba th and stirred at 1100 rpm for 6.5 hours. This resulted in polymerization of the emulsion drops to form dr ug-containing EGDMA particles. The particles were then allowed to settle for a day, and the cross-linked EGDMA phase was withdrawn and used as the concentrated particle suspension in the gel synthesis. Next, the drug laden EGDMA micro-particle s were loaded in p-HEMA hydrogels by adding the concentrated particle disper sion to the HEMA monomer mix followed by polymerization. Specifically, 1.35 ml of the HEMA monomer, 0.5 ml DI water, 5 l of ethylene glycol dimethacrylate (EGDMA), and 0.1 g of the concentrated particle suspension were mixed

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117 together in a glass tube. This solution wa s degassed by bubbling nitrogen for 15 minutes to reduce the amount of dissolved oxygen. Next, 3 mg of the photoinitiator, Darocur TPO, was added to the mixture, and the solution was stirred for 15 minutes . The mixture was then poured in between two glass pl ates separated by a 200 m thick plastic spacer. The glass plates were then placed on a UV-light illuminator (UVB) for 30 minutes for gel curing. Synthesis of p-HEMA gels loaded with highly crosslinked EGDMA microgels It is well known that free radi cal polymerization leads to form ation of micron sized gels at short times, and these subsequently grow larger , and eventually depending on the water fraction, join to form one contiguous gel. If the polymer ization is terminated at short times by quenching, one may obtain a dispersion of microgels in the continuous phase which could be purely monomer (bulk polymerization) or a mix of the monomer in the solvent (solution polymerization). Below we de scribe a process for formati on of EGDMA microgels, and the subsequent entrapment of these microgels in HE MA gels to yield a HE MA gel that contains small but highly crosslinked EGDMA microgels . Since EGDMA monomer contains 2 vinyl groups, the microgels of EGDMA are expected to be highly crosslinked. The degree of crosslinking can be reduced by incorporating some fraction of HEMA into the microgels. As mentioned above, micro-gels were synthe sized with pure EGDMA and also a mixture of EGDMA and HEMA. To synthesize micro-gels of pure EGDMA, first, timolol base was generated by adding 6 g of 1.04M NaOH to 240 mg of timolol maleate. Next 11 ml of the upper water phase was pipetted out to in crease the fraction of the timolol base in the mixture. From the remaining mixture, we extracted timolol base with 0.85 g of Benzoyl Peroxide/EGDMA mixture (2.9:97.1 ratio by weight). Next, the solution was heated at 80C for 15 minutes, followed by quenching in a 0C water bath. Th e solution at this stage is a di spersion of EGDMA microgels in

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118 monomeric EGDMA with some linear polymeric or weakly crosslinked chains. Next, 7.2 ml of un-purged DI water was added to the solution to completely stop the reaction. The solution with micro-gels was then stirred at 600 rpm for 12 minutes, vortexed for 30 seconds, and then left stationary on the counter over night. The procedure for synthesizing EGDMA-co-HEM A micro-gels is identical to the one described above except that 1.1 g of Benzoyl Peroxide/EGDMA/HEMA mixture (2.8/78/19.2 wt%) was added to the high pH drug solution in stead of the 0.85 g of Benzoyl Peroxide/EGDMA mixture (2.9:97.1 ratio). Another minor difference was that 7 ml of DI water was added to stop the reaction instead of 7.2 ml. To incorporate the microgels into the HEMA matrix, we followed the same procedure as the one utilized to incorporate the EGDMA particle s into the gel. The only difference was that the microgel solution replaced the particle susp ension. Specifically, 1.35 ml of the HEMA monomer, 5 l of ethylene glycol dimethacrylate (EGDMA), and 1 g of the microgel solution were mixed together in a glass tube. This solution was degassed by bubbling nitrogen for 15 minutes to reduce the amount of dissolved oxygen which can be a scavenger of both initiating and propagating species in radical polymerization. Next, 3 mg of the photoinitiator, Darocur TPO, was added to the mixture, and the solutio n was stirred for 15 minutes. The mixture was then poured in between two gl ass plates separated by a 200 m thick plastic spacer. The glass plates were then placed on a UV-light illumina tor (UVB) for 40 minutes for gel curing.

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119 Characterization Studies Gel characterization The transparency of the hydrogels was meas ured by light transmittance tests on hydrogels of 200 m in thickness using Thermospectronic Gene sys 10 UV-Vis spectrometer at a visible wavelength of 600 nm. The mechanical properties of the gels were characterized by rheological measurements using a Dynamic Mechanical Analyzer (DMA Q 800, TA Instruments, New Castle, DE). Gels were measured in compression mode while submerged in Dulbecco’s phosphate buffered saline (PBS) at ambient temperature (24. 8.3C). For each sample, the gel was cut into a flat-sheet and mounted in the DMA chamber which was filled with PBS to keep the sample hydrated during the measurement. Right on top of the chamber is the moving clamp which has a flat bottom surface and will clamp the gel sample in between the bottom of the chamber during DMA measurements. The rheological response was measured with a periodic force at frequencies 1, 2, and 5 Hz. At the beginning of each run, a static preload force of 0.1 N was applied to ensure adequate contact between the clamps and the sample. The thicknesses of the samples were measured automatically by DMA du ring the application of preload force. A “Force Track” of 115% was used, as suggested by the manual, to ensure the adequate contact between the samples and the clamps. We manually input strain values to be 1 m for pure PHEMA gels, 2 or 2.2 m for microgel laden gels, 2 m for microparticles, and 1.6 or 1.8 m for EGDMA-co-HEMA microgel laden gels. The storage modulus (G’) and loss modulus (G”) were obtained and compared.

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120 Drug release experiments All particle-laden lenses were cut into circ ular pieces with 1.65 cm diameter and 0.2 mm thickness, dried out in the air ov ernight, and then weighed the ne xt day before the drug release experiment. The gel was then submerged in 200 ml PBS under minimal stirring (140 rpm) and at room temperature for 15-24 hours to extract the unr eacted monomer. This step is referred to as the extraction or the initial soaking or the extrac tion step. At the end of the extraction step, PBS aliquots were collected and the concentration of timolol was measured to determine the fraction of drug that is released in the extraction step. Next the gels were withdrawn from the PBS used in the extraction step and soaked in fresh 3.5 PB S. During this stage the drug concentration was measured every 24 hours without replacing the PB S. The time-dependent concentrations of timolol in PBS were determined by measuring the absorbance as a function of time by UV-Vis spectrophotometer in the 261-309nm wavelength ra nge. For some experiments, the timolol concentrations were also measured by a HPLC using a reverse phase C18 column (SymmetryR C18, Waters). The mobile phase used was 10% pH=2.5 phosphate buffer, 65% DI water, and 25% acetonitrile. The samples were measured with a flow rate of 1 ml/min of the mobile phase at 30 C, and detected at 280nm. Packaging tests Typically contact lenses are packaged in blister packs that contain about 1-1.5 ml solution. Preliminary tests were done to estimate the e ffects of packaging on drug release behavior of these particle-laden hydrogels. For these tests, drug loaded microparticle laden lenses were cut into circular pieces with 1.65 cm diameter a nd 0.2 mm thickness and then subjected to the extraction step for 15 hours. The gel piece is then stored in 1.5 ml of packaging solution (DI water or PBS) and sealed for two weeks. DI water was chosen to be the packaging solution

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121 because the solubility of timolol in DI water is low and thus the drug loss during packaging can be minimized. However, typically contact lenses are packaged in tear mimics such as PBS to minimize the changes in tear composition after in sertion of contact lens es in the eyes. Accordingly, it was decided to also perform packag ing tests in PBS. Afte r two weeks of storage in the packaging solution, the gel piece is take n out and put into 3.5 ml fresh PBS for the subsequent drug release studies. Th e timolol concentration of the packaging solution and that of PBS as a function of time were analyzed by UVVis spectrophotometer and HPLC at the same conditions as used for drug release experiments. Results and Discussion Gel Characterization The transparency of the hydrogels was meas ured by light transmittance tests on hydrogels of 200 m in thickness using Thermospectronic Gene sys 10 UV-Vis spectrometer at a visible wavelength of 600 nm. The resu lts are shown in Table 5-2. Figure 5-1 shows a regular microscopic image of microparticles suspended in DI water. Figure 5-2 shows flurorescent microscopic imag e of p-HEMA gel loaded with the same microparticles. The storage modulus (G’) and loss modulus (G ”) were obtained for all the microgel and microparticle laden lenses. The results are shown in Figure 5-3. Drug Release Timolol release from p-HEMA lenses (control) The control experiments involve d synthesizing pure p-HEMA gels of the same thickness as the particle-laden gels. Timolol was loaded into the gels by directly adding it to the polymerizing mixture. The initial extraction st ep was not performed for these systems because as the duration of the initial extrac tion is longer than the total releas e time for these gels and so it

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122 is expected that if the initial extraction step is performed, the entire drug w ill be released in this step. The drug release experiments for these gels were conducted with protocols identical to those described in the Methods section for the particle-laden gels in PBS. The drug release profiles for these control p-HEMA gels are shown in Figure 5-4. The results show that 80% of the drug comes out in 5 hours, and that the system reaches equilibrium in 5 hours. The drug release from the p-HEMA gel into PBS or DI water can be modeled by assuming that the transport can be describe d by the diffusion equation, i.e., 2 2y C D t C Eq. 5-1 The boundary conditions for the drug release experiment are wKC ) h y , t ( C 0 ) 0 y , t ( y C Eq. 5-2 where h is the half-thickness of the gel, the first boundary condition assumes symmetry at the center of the gel and the s econd boundary condition assumes equilibrium between the drug concentration in the gel and that in the PBS phase. A mass balance on the PBS in the beaker yields h y gel w wy C DA 2 dt dC V Eq. 5-3 where Vw is the PBS volume (=3.5 ml), Agel is the cross-sectional area of the gel, and C is the drug concentration in the release medium. Fina lly the initial conditions for the drug release experiments are 0 ) 0 t ( C C ) 0 t , y ( Cw i Eq. 5-4 Since the fluid volume is much larger than the gel volume the concentration Cw is negligible, and in this perfect sink condition the above set of equations can be solved analytically to yield

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123 ) e 1 ( 1 n 2 1 V ) V C ( 8 C e ) y h 2 ) 1 n 2 ( cos( ) 1 n 2 ( C 4 ) 1 ( CDt h 4 ) 1 n 2 ( 0 n 2 f gel i 2 w 0 n Dt h 4 ) 1 n 2 ( i n2 2 2 2 2 2 Eq. 5-5 In the long time limit the mass of drug released into the PBS (=VfCw) can be approximated as Dt h 4 i2 2e 1 M M Eq. 5-6 The drug release from a microgel/micropartic le laden gel can be modeled simply by assuming that the release time scal e from the microdomains are much longer than that of bulk gel time scales, and furthermore the concentration in th e gel is essentially zero at the particle time scales because the entire drug present in the bulk gel has already diffused into the PBS on a much shorter time scale. With these assumptions the release from each particle can be modeled by treating the particles as sphe res. The total mass of drug re leased by the particles become ) e 1 ( n 1 6 1 M Mt D R n 0 n 2 2 0 , p pP 2 2 2 Eq. 5-7 where MP,0 is the total mass of drug tr apped in the particles and Dp and R are the diffusivity of the drug in the particles and the particle radius , respectively. The above equation assumes that the particles are monodisperse. The drug release from microdomain laden gels is expected to be a sum of the release from the bulk gel and the particles, and thus can be obtained by combining Equation 5-6 and, i.e., ) e 1 ( M ) e 1 ( M M2 1T / t 0 , p T / t i Eq. 5-8 where M is the mass of drug released, and T1 and T2 are the time constants for release from gel and domains, respectively, and can be related to the diffusivities and geometric parameters by Equation 5-6 and 5-7. The values of the four pa rameters are obtained by fitting the experimental data to the above equation, and these parameters are noted in th e figure caption for each of the

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124 release profiles and the solid lines are the best fits to the experimental data based on the above equation. The time scale for release is similar in DI water is slightly longer than that in PBS, which is expected because the diffusion coefficient is expected to be slightly smaller for gels soaked in DI water due to smaller degree of swelling. Timolol release from p-HEMA lenses loaded with highly crosslinked EGDMA microparticles The gels loaded with highly crosslinked EGDMA microparticles lost about 60 % of the initially loaded drug in the extraction stage. This fraction is presum ably the drug that was present outside the microparticles. The drug release profiles for th e subsequent release experiments conducted in 3 ml PBS are shown in Figure 5-5, in which the mass of drug released into the solution is plotted as a function of time. The data in Figure 5-5 clear ly shows that there is an extended drug release from the gel which last s for about 10 days. The drug release occurs on two different time scales; there in an initial burst releas e in the first 2 hours, which accounted for 5-20% of initially loaded timolol, followed by a slow release, for about 10 days, with an average rate of 1 g/day. The values of T1 are about 0.1 da y = 2 hours for all the gels, and the value of T2 ranges from about 4-6 days. The value of A/(A+B) and B/(A+B), which represent the fractional release in the burst phase and the ex tended release phase, respectively, are about 0.6 and 0.4, respectively. It may be speculated that the burst release arises due to transport of the drug that is outside the particle s but this hypothesis is contradict ed by the fact th at the release time scale for the burst release is larger than th e time scale for drug release from control gels. Furthermore the initial extraction step was perfor med in 200 ml of PBS and considering the fact that the gel volume is only about 50 l, it is unlikely that the bulk of the gel can retain the amount of drug that is subsequent ly released as a burst in the drug release experiments. The origin of the burst release will be discussed in more details later.

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125 The rate at which the EGDMA microparticles ca n deliver is about half to a third of the therapeutically required rates. However, it is exp ected that this rate can be very easily adjusted by controlling the particles size a nd degree of crosslink of these emulsion particles which is a function of the relative amount of surfactant, EGDMA, and water. Timolol release from p-HEMA lenses loaded with highly crosslinked EGDMA microgels The drug release results for hydrogel loaded with bulk polymerized EGDMA micro-gels A are shown in Figure 5-6. The four curves corresp ond to four gels that were prepared identically. The fraction of drug released in the extraction phases are noted on each curve. These values range from 73-79%, which is much larger than the drug released during the extraction phase for the microparticle-laden gels. The higher loss in the extraction stage can be explained by the differences in the procedures used to fabricate these two types of systems. These systems also exhibit an initial burst followed by a slow release for a period of about 10 days. The origin of the initial burst in these experiments is unclear. Interestingly the extent of initial burst is different for the four different re peat runs but the subs equent long term release is very similar. The total drug release from these systems is about 20 g in 10 days, and if the initial burst is excluded the released amount is about 1 g/day. It is noted that in these systems about 20% of the initially loaded drug is present inside the gels even after 10 days of release. However, after about 7 days the release rates are almost ne gligible suggesting that 20% of the drug is irreversibly trapped inside th e highly crosslinked microgels. To study the effect of drug loading and pol ymerization time of microgel on timolol drug release by microgel-laden PHEMA lenses, we conducted drug release experiments on three systems, microgel B, C, and D, where timolol load ings are 28, 28, and 32 mg of timolol /g of dry gel, and the polymerization times are 17, 19.5, and 14.5 minutes, respectively. The results of

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126 PHEMA lenses loaded with these microgels are sh own in Figure 5-7. The results show that for all three systems, the drug loss dur ing extraction is about 78%. Th e total drug release from these systems are about 110, 50, and 30 g in 10 days, and if the initial bursts are excluded, the release rates are about 2, 1, and 4.5 g/day for microgel B, C, and D, respectively. The results suggest that the longer polymerization time applied for th e synthesis of microgels, the slower the release of timolol out of these microgels. This makes sense because the larger the highly crosslinked domains, the longer it takes for drug to diffuse out of these domains. The results for hydrogel loaded with bulk polymerized EGDMA-co-HEMA microgels, are shown in Figure 5-8. To see the effect of extr action phase on the drug release, we employed two different time periods of extraction phase, 6 hour s (represented by solid li ne in Figure 5-8) and 22 hours (represented by dashed line in Figure 5-8) on the same microgel-laden lenses. For systems where 22 hours of extraction was used, about 90% of the initially loaded drug was lost during the extraction phase. These system exhib it an initial burst which accounts for about 0.5% of initially loaded timolol, follo wed by a slow release for 10 days . For systems where 6 hours of extraction was used, about 70-80% of the initially loaded drug was lost during the extraction phase. Two of the systems exhibit an initial burst which accounts for about 13% of initially loaded timolol, the other has an initial burst wh ich accounts for 1.5% of in itially loaded timolol. All of the systems have slow release of 1-1.5 g/day for 10 days. For this system, the cumulative release including the release in the extraction phase is about 90 % of the entrapped drug. Effect of packaging on timolol releas e from HEMA gels loaded with EGDMA microparticles A typical contact lens first undergoes an extraction and is then stored in packaging solution for an extended period of time. To include the e ffects of release in the packaging solution it was

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127 decided to soak the gels with EGDMA micropart icles in 1.5 ml of packaging solutions for a period of 2 weeks and then conduct drug release studies. Two different types of packaging solutions were explored in this study: DI water (solid lines) and PBS (dashed lines) solution. The results of these studies are presented in Figure 5-9. The three numbers on each curve indicate the fraction of drug lost in the extraction phase (extraction in 200 ml for 3 hours), in the packaging solution, and final releas e in 3 ml PBS solution, respectively. The drug loss in the packaging medium is more for gels soaked in PB S. Each gel exhibits a burst release followed by an extended release for about 10 days at a rate of about 0.4 g/day if packaged in DI water, and 0.2 g/day if packaged in PBS. These results are very encouraging because ev en after soaking in the packaging solution for 2 weeks, these lenses retain extend ed timolol release for about 10 days. Summary Since the diffusivity of a drug in a polymer matrix depends on the degree of crosslinking, we synthesized hydrogel microparticles of pure EGDMA by suspension polymerization and then entrapped these in a HEMA matrix. We also synthesized dispersions of EGDMA microgels in HEMA by first polymerizing pure EGDMA and then adding HEMA to the mix, and continuing polymerization till gelation. The base form of timolol was dissolved in EGDMA, and thus it got entrapped in the highly crosslinked micropartic les/microgels. These microparticles/microgels are a few microns in size, but the dispersion of these particles in HEMA gel are transparent, perhaps due to the small refractive index di fference between HEMA and EGDMA. These systems release timolol for about 10 days at a rate of 1 to 4.5 g per day. Experiments were conducted to simulate release in two different p ackaging liquids, and results showed that if DI water is used as packaging solutions for contact lenses made of these materials, the lenses will

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128 release timolol into the eyes for a period of about 10 days at a rate of about 0.5 g/day. The drug delivery rate offered by these systems can be very easily adjusted by controlling the particles size and degree of crosslink of these emulsion particle s which is a function of the relative amount of surfactant, EGDMA, and water. These systems ar e therefore very promisi ng, and it is speculated that the amount of drug rel ease could be further increased be controlling the degree of crosslinking in these microgels to minimize th e irreversible entrapment of timolol. These systems could be adapted for a wide variety of drugs . It is also advantageous that these systems can be fabricated in non-aqueous solutions and t hus can be directly inte rfaced with the current methods of contact lens manufacturing.

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129 Table 5-1. Physical and tr ansport properties of timolol Timolol Molecular weight 316 Diffusivity in tears x 1012 (m2/s) 500 Dosage (drops/day) 2 (0.25%) Corneal permeability (m/s) 1.5x10-7 Fraction that enters eye 1.3% Therapeutic requirement ( g/day) 1.5 Table 5-2. Transmittance at 600 nm wavele ngth of microparticle-laden hydrogel of 240 m thickness. (n=2 for PHEMA, n=3 for micr oparticle-laden gel, n=3 for microgelAladen gel, and n=3 for EGDMA-co-HEMA microgel-laden gel) Sample ID Microparticle Mi crogel Microgel-co-HEMA PHEMA Transimittance at 600 nm (%) 92.8 97.29797.9

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130 1 m 1 m Figure 5-1. Regular microscopic image of microparticles suspended in water Figure 5-2. Fluoresecent microscopi c image of microparticle-laden gel

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131 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.070123456 frequency(MPa) HEMAs HEMAl 6XHs 6XHl Cr9s Cr9l 6XH_25ps 6XH_25pl Figure 5-3. G’ (storage modul us) and G’’ (loss modul us) for microgel and microparticle laden lenses 0 10 20 30 40 50 60 70 80 90 00.511.522.5 time (days)% of timolol released Figure 5-4. Timolol base form release from PH EMA gel directly entrapped with timolol base

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132 0 0.005 0.01 0.015 0.02 0.025 0.03 0510152025 time (days)mg of timolol released 61.5% 60.6% 47.2% 51.7% Figure 5-5. Timolol release from microparticle laden PHEMA gels. (data shown in the hollow diamond ( ) represents the case where well mixe d extraction is implemented.) As shown in the figure, it matched the curves with lowest initial burst fairly well. (T1 =0.22, T2=4.37 ) 0 0.005 0.01 0.015 0.02 0.025 0510152025 time (days)mg of timolol released 73% 70% 79 % 74.7% Figure 5-6. Timolol release from microgelA-l aden PHEMA gel. Data shown in the hollow diamond ( ) represents the case where well mixe d extraction is implemented. As shown in the figure, it matched the curves w ith lowest initial burst fairly well in the first day, and then has a sl ower release afterwards. (T1 =0.07, T2=3.62 )

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133 0 0.02 0.04 0.06 0.08 0.1 0.12 02468101214 time (days)mg of timolol released 77.8% 78.8% 79.5% Figure 5-7. Timolol released from PHEMA lenses loaded with microgel B, C, and D, where well mixed extraction was implemented. (T1 =0.28, 0.27, 0.10 and T2=5.15, 3.33, 1.56 for microgel B, C, and D, respectively. ) 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0510152025 time (days)mg of timolol released 70% 81% 69% 90% 93% Figure 5-8. Timolol release from EGDMA-co-HEM A microgel laden HEMA gels . Data of gels where 6 hours of extraction phase was used ar e represented by solid line (n=3), and 22 hours by dashed line. (n=2) (T1 =0.15, T2=3.55 for the curves with greater initial burst.) (T1 =0.08, T2=2.15 for the bottom three curves. )

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134 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0510152025 time (days)mg of timolol released (64, 4.5, 9%) (54, 4, 8%) (63, 4, 8%) (54, 10.5, 5%) (67, 8, 4%) Figure 5-9. Release from EGDMA micrparticle -laden HEMA gel after soaking in packaging solution for 2 weeks. In the parenthesis show s the percentage release of initial loaded timolol during extraction phase, packaging pha se, and final drug release in 3 ml of PBS, respectively. (T1 =0.10, T2=4.10 )

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135 CHAPTER 6 CONCLUSION Approximately 90% of all ophthalmic drug form ulations are now applied as eye-drops. While eye-drops are convenient and well accepte d by patients, about 95% of the drug contained in the drops is lost due to absorption through the conjunctiva or thr ough the tear drainage. Ophthalmic drug delivery via contact lenses shou ld be more effective than by drops because it increases the residence time of the drug in the eye and is therefore expected to lead to a larger fractional intake of drug by the co rnea. In chapter 1, a mathem atic model that describes drug delivery by contact lenses to the cornea is developed. The model represents a first attempt to model drug release from a contac t lens, transport through the PO LTF, and the subsequent uptake by the cornea. The model assumes Fickian diffusi on in the contact lens and takes into account the convective enhancement in mass transfer in th e post-lens tear film due to the flow driven by the oscillation of the contact le ns during the blink. The fracti on of drug that enters the cornea has been determined for two extreme cases. Th e first case corresponds to a rapid breakup of the pre-lens tear film, which prevents drug loss from the anterior lens surface. The second case corresponds to a situation in which the pre-lens tear film exis ts at all times and furthermore the mixing and the tear drainage in th e blink ensure that the concentra tion in this film is zero at all times. These two cases correspond to the minimu m and the maximum loss to the pre-lens tear film and thus represent the highest and the lowe st estimations for the fraction of the entrapped drug that diffuses into the cornea. The fraction of drug that enters the cornea varies from about 70 to 95% for the first case and from 20-35% for the second case. It is thus reasonable to assume that in normal physiological circumstances where th e pre-lens tear film breaks in a few seconds, the fraction of drug that is abso rbed by the corneal tissue will be about 50%. The tear breakup on the anterior lens surface also causes partial dehydration of the lens near the surface and the

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136 dehydration results in a thin glassy layer near the surface, which mi ght suggest that case 1, which corresponds to no-flux to the PLTF may be more applicable under normal conditions of lens wear. The model predicts that the fraction of pilocarpine that enters the cornea may be around 70%, which is about 35 times larger than the repo rted value of about 2% for delivery by drops.21 This result is in reasonable agr eement with the clinical results. In chapter 2 we combine in vitro experiments with m odeling to investigat e the delivery of timolol, a commonly used glaucoma drug to the eyes. The in vitro experiments are performed to develop a transport model for rel ease of the drug from p-HEMA contact lenses. The transport model includes adsorption of drug on the polymer and the diffusion of the drug through the bulk water. Experiments are performed at three diffe rent levels of crosslinker and the transport parameters are determined for each case. The transport model is then incorporated into a model for the release of the drug from the contact lens into the pre and the post-lens tear films and the subsequent uptake by the cornea. Results show that at least 20% of the timolol entrapped in the lens will enter the cornea, which is much larg er than the fractional uptake for drug delivery by drops. The results of our studies show that a soaked contact lens can signi ficantly reduce the drug wastage and the side effects associated with the entry of the drug into the systemic circulation, and thus is a big improvement over ophthalmic drug delivery by eye drops. We note that while soaked contact lenses are more efficient than drops, they still suffer from a number of drawbacks. Firstly, when a lens is soaked in drug solution, the ma ximum drug concentration obtained in the lens matrix is limited to the equi librium concentration. Thus, a soaked lens can supply only a limited amount of drug. This techni que is especially inefficient in delivering hydrophobic drugs by HEMA based contact lenses. S econdly, even for drugs that can absorb in

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137 the lens matrix, the drug releas e times scale is only a few hours. Thus, a soaked contact lens cannot deliver drugs for extended pe riod of time. It is thus impor tant to develop a system that can deliver ophthalmic drugs at a controlled rate for an extended period of time. With the aim of developing a ophthalmic drug delivery vehicle that can delivery ophthalmic drugs for an extended period of time, we pioneered the idea of using particle-laden contact lenses for ophthalmic drug delivery. The particles investig ated in this dissertation are microemulsions and EGDMA microparticles an d microgels. Microemulsion-laden contact lenses were first developed for ophthalmic drug delivery by Gulsen, et al in our group.53,54 The essential idea is to encapsulate the ophthalm ic drug formulations in the microemulsion nanoparticles, and to disperse these drug-laden part icles in the lens materi al. Upon insertion into the eye, the lens will slowly release the drug into the pre-lens (the film between the air and the lens) and the post-lens (the film between the co rnea and the lens) tear films, and thus provide drug delivery for extended periods of time. In chapter 4, we synthesized ethyl butyrate/water microemuls ions stabilized by Pluronic F 127 surfactant, added these to HEMA and then polym erized the solution. It was speculated that addition of HEMA to the microemulsion may lead to deastabilization and so we also synthesized six component microemulsions stabilized by Plur onic F 127 that had ethyl butyrate as the oil phase and a solution of NaCl a nd NaOH in HEMA and Water as the continuous phase. These microemulsions were polymerized to yield hydroge ls. Both of these systems yielded transparent hydrogels with mechanical properties similar to those for HEMA gels. It was possible to obtain very large loading of timolol in these systems by dissolving the base form of timolol in the oil phase. Gels that had timolol loaded microemuls ions exhibited a slow and extended drug release in DI water. In DI water, the transport of dr ug was faster in microemulsion-laden gels compared

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138 to control due to coupling between the oil (ethyl butyrate) and drug (timolol) transport. The transport rates showed a sigmoidal shape which was also attributed to ethyl butyrate transport in the gel. The transport rates for gels loaded with timolol microemulsions were comparable to those for the control suggesting that the surfactant does not retard drug trans port in DI water. All of the gels exhibited a very rapid release in PBS and in saline due to higher solubility of timolol in these solutions compared to that in DI wate r. Thus, these systems are of limited utility for ophthalmic drug delivery. However, it is encour aging that these systems can have a very high timolol loading, and so these may find applica tions in other areas such as transdermal drug delivery. Other types of particle laden systems that we studied are described in chapter 5. We synthesized hydrogel micropartic les of pure EGDMA by suspensi on polymerization and then entrapped these in a HEMA matrix. We also synthesized dispersions of EGDMA microgels in HEMA by first polymerizing pure EGDMA and then adding HEMA to the mix, and continuing polymerization till gelation. The base form of timolol was dissolved in EGDMA, and thus it got entrapped in the highly crosslinked micropartic les/microgels. These microparticles/microgels are a few microns in size, but the dispersion of these particles in HEMA gel are transparent, perhaps due to the small refractive index di fference between HEMA and EGDMA. These systems release timolol for about 10 days at a rate of 1 to 4.5 g per day. Experiments were conducted to simulate release in two different p ackaging liquids, and results showed that if DI water is used as packaging solutions for contact lenses made of these materials, the lenses will release timolol into the eyes for a period of about 10 days at a rate of about 0.5 g/day. The drug delivery rate offered by these systems can be very easily adjusted by controlling the particles size and degree of crosslink of these emulsion particle s which is a function of the relative amount of

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139 surfactant, EGDMA, and water. These systems ar e therefore very promisi ng, and it is speculated that the amount of drug rel ease could be further increased be controlling the degree of crosslinking in these microgels to minimize th e irreversible entrapment of timolol. These systems could be adapted for a wide variety of drugs . It is also advantageous that these systems can be fabricated in non-aqueous solutions and t hus can be directly inte rfaced with the current methods of contact lens manufacturing.

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140 CHAPTER 7 FUTURE WORK Modifications of the Model The model presented in chapter 2 and 3 take s into account the essential mechanisms but simplifies each one of those. For instance, a number of assumptions have been made for the mass transfer in the post-lens tear film (POLTF). Firstly, the model assumes a simplified flat 2D geometry. This assumption has been used previous ly to model mass transfer in the POLTF with satisfactory results, and thus is perhaps reasona ble due to the thin POLTF. Additionally, the motion of the contact lens has been simplifie d to correspond to periodic squeeze flow and Couette flow. These assumptions have also been used previously with satisfactory results. While each of the assumptions listed above are exp ected to impact the drug release profiles, none of them introduce new physics or mechanisms , and furthermore, each of these can be incorporated into the framework developed in chapter 2 and 3. In future, we plan on incorporating some of the modifications discussed above. In addition, it w ill also be interesting to study the bioavailabilty of diffe rent drugs to the cornea, and to different parts of the eye. Microparticle or Microgel-Laden Contact Lenses for Ophthalmic Drug Delivery The preliminary success shows the great pote ntial that microgel or microparticle-laden contact lenses have as ideal ophthalmic drug deliv ery vehicles. However, our results show that these systems exhibit short initial burst release af ter packaged in PBS or DI water. To prevent drug from getting out of the particles during packag ing which leads to the initial burst release, it is planned in the future, to make particle-lad en contact lens where the matrix is positively charged. Since timolol is positively charged in its ionized form, it is expected that due to electrostatic repulsion, timolol will tend to stay in side the particles during packaging. Synthesis of these positively charged particle-laden lenses will be similar as our current systems, except

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141 that positively charged monomers will be incorporated in the monomer mix before polymerization of the lens. Although it is generally perceived that burst release is undesirable for drug delivery devices, burst release might be beneficiary in th e case of timolol delivery to the eye because of the substantial binding of timolol to the ciliary body.61 In this case, the initial delivery of timolol will mostly be bound to ciliary body before it can r each other parts of the eye in a substantial amount. Therefore, a higher initial release rate of timolol will be used to saturate the binding of timolol on the ciliary body while still providing dr ug to other parts of the eye at required drug concentrations. In the future, we plan to unders tand better the pharmacokinetics of timolol in the eye, and combine pharmacokinetics of timolol in de signing a system that delivers at the most efficient rates. We plan also to investigate the effectiveness of microparticle/microgel-laden lenses at delivering other ophthalmic drugs, su ch as cyclopsporin A and dexamethasone, which are commonly used ophthalmic drugs for dry eyes and inflammations, respectively. In addition, all the particle-laden lenses st udied in this disserta tion are p-HEMA based lenses. Although p-HEMA lenses are worn comfortably by a large population, they are recommended to be used as daily wear contact lenses, meaning that the contact lenses are designed to be removed prior to sleeping. On th e other hand, silicone based contact lenses have been developed and used for extended wear in the United Stats sin ce 2001 due to the high oxygen permeability of theses lenses.62 Although there ar e still problems associated with extended wear lenses, it has gathered growi ng acceptance by the public, and will serve as the ideal lens matrix for extended ophthalmic drug deliver y. In the future, we plan to investigate the effectiveness of particle-laden silicone le nses for extended ophthalmic drug delivery.

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142 Furthermore, the bioavailability of drug delivered by contact lenses can be further increased (Chapter 2) if the drug loss to the prelens tear film (PLTF) is reduced. In reality, PLTF breaks up in a few seconds, and thus stops the drug loss to the PLTF. We can further prevent drug loss to the PLTF by highly crosslinki ng a thin layer on one side of the contact lens, that is, the side in cont act with PLTF. It is expected that this will substantially increase the bioavailability of drug delivered by contact lenses while keeping the mechanical properties roughly unchanged. Animal Studies In the future, we plan to start animal studies with these particle-laden lenses. We will start with adult rabbits (8 to 11 pounds) which are common subjects for ophthalmic studies. The size (diameter) and shape (curvature) of corneas of adult rabbits are significantly different than that in adult humans. Thus, contact lenses that are desi gned to fit normal huma n eyes do not fit rabbit eyes well, and they frequently pop out when the ra bbits blink or squint. As part of extensive experiments that Dr. Schultz conducted previ ously with Vistakon, the optimal values for diameter (15 mm) and base curve (8.0 mm) were de termined for contact lenses for adult rabbits. Using these special diameter and base curve parame ters, soft contact lenses (Etafilcon A lenses) were retained in >90% of rabbit eyes for 3 da ys. Thus, all lenses containing nanoparticles will all be produced with a 15 mm diameter and an 8. 0 mm base curve. Toxicology tests of particleladen contact lenses will be conducted. The bioa vailability of timolol delivered by particle-laden contact lenses will be measured as well.

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143 APPENDIX A DERIVATION OF DISPERSI ON COEFFICIENT (D*) The geometry of the POLTF is shown in Figur e A-1. For convenience, the coordinates x1 and y1 have been replaced by x and y in this Appendix. The governing equation for mass transfer in the POLTF is 2 1 f 2 2 1 f 2 f 1 f 1 f fy C x C D y C v x C u t C (A-1) As noted in the main text, the fluid flow in th e post-lens tear film is driven by blinking and the velocity profiles are given by 2 t 0 0N' u6xf(t)Nf(t) h'f(t)dt (A-2) 32vN' (23)f(t) (A-3) There are four main time scales for mass-tr ansfer in the POLTF: time scale for axial diffusion (L2/Df), time scale for lateral diffusion (h0 2/Df), the time scale for the oscillatory blink (1/ ) and the time scale for drug uptake by the cornea (h0/kc). The time scale for the blink is comparable to the time scale for lateral diffusion, i.e., ) 1 ( O D hf 2 0 and both of these time scales are significantly smaller than the time scal e for lateral diffusion. The ratio for the time scale for lateral equilibration and that for axial equilibration is 2 2 2 0f0 2 fh/Dh L/DL . Since 0h 1 L , it can be used as a parameter for regular expansion and the mass transfer problem can be expanded in and then solved to different orders in . The time scale for drug uptake by cornea varies and for typical ophthalmic drugs the ratio of the time scale for corneal uptake and

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144 that for axial equilibration, i.e., 0 f 2 ch D kL can be either O( ) or O(1). Below we consider these two cases separately. First we consider the case when 0 f 2 ch D kL is O( ). In this case since there are three different time scales, we use the method of multiple time scal es and define the concentration to be of the form ffsml C=C(t, t,t, , ) (A-4) where cff smlf 2 00iktD tyxC tt, t,t, , ,C hLhL(C/K) (A-5) In the above expressions Ci is the initial drug concentration in the contact lens and K is the partition coefficient, i.e., the ratio of concen tration in lens and in fluid at equilibrium. We dedimensionalize u and v given in A-2 and A-3 by L and h0 , respectively. The dimensionless velocities are 2 t 0 0uN' u6f(t)Nf(t) LL h'f(t)dt (A-6) 32 00v' vN (23)f(t) hh (A-7) For normal blinking both L and 0h are much less than 1, and thus these can be treated as O( ). Accordingly, we define and ' ' , and thus both Land 0 ' h are O(1). After substituting = and = in the expressions for dimensionless velocity A-6, A-7 and then using Taylor expansions, the dimensionless velocities can be expanded as

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145 2 12 2 12u = u+ u+.... v = v+ v+.... (A-8) where 2 1s 0 2 2 2sss 2 0 32 1s 0N N ' u +6 ( )f(t) Lh N ' u6 ( ) f(t)f(t)dt h N ' v =( 2 -3 ) f(t) h (A-9) The concentration can also be expanded as a regular expansion in , i.e., 2 ff0f1f2 CC C C... (A-10) By using the dedimensionalization described above, and the multiple time scale form for concentration given in A-4, the c onvection diffusion equation becomes, 22 22 fffffff c 22 sml C C C C CCC +K+u+v=+ t t t (A-11) where f 2 0D h and f c cD L k K . The concentration Cf in the above equation can be expressed as a regular expansion in A-10 to yield a series of diffe rential equations to different orders in . The boundary condition at the POLTF-corn ea interface, i.e., at y = 0 is f fc C D= kC y (A-12) After dedimensionalizing the a bove equation and substituting the regular expansion for Cf, we get the following boundary conditio ns for different orders in :

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146 f0 f1 cf0 f2 cf1 C ( =0) =0 C ( =0) =KC C ( =0) =KC (A-13) The boundary condition at the lens-cor nea interface, i.e., at y = hf is gi f f gDC C D= jj yh (A-14) which in dimensionless form becomes g0 ffs 0fg DKh Ch(t) = = jj hDh (A-15) where the dimensionless parameter g0 fgDKh Dh has been assumed to be O( ) and thus g fgDKL Dh is O(1). Since the boundary at y = hf(ts) moves in time, we expand the boundary condition in a Taylor series to convert the problem to a stationary boundary. As noted in the main text fs00ssh(t) = h N ' f(t)dt =h N ' f(t)dt (A-16) Thus the lens-POLTF boundary is located at sssss 22 000N ' ' L ' L = 1f(t)dt=1N()f(t)dt1N()g(t) hhh (A-17) where 2 0 ' L () ~ O(1) h and sssg(t)f(t)dt

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147 By utilizing A-17 in A-15 and then expanding f s 2 0 C ' L =1N() g(t) h around = 1 gives 23 ff 23 222 f ss 22 00 CC ( =1)( =1) C ' L ' L ( =1) + N()g(t) + (N) g(t) 1 !h2 !h +... =j (A-18) By substituting the regular expansion of f C in the above equation , and comparing various powers of in the above equation, we get the following boundary conditions at 1 for different orders of the concentration in f0 2 f1f0 s 22 0 2 f2f1 s1 22 0 C =0 CCN ' L =()g(t)+j h CCN ' L =()g(t)+j h (A-19) where 1 j is the O( ) flux from the contact lens into the POLTF. Now we substitute the regular expansion for f C from A-10 into the governing equati on A-11 and then obtain differential equations to different orders in . We then solve these equa tions subject to the boundary conditions at the same order in as given by A-13 and A-19 Order: O() 2 f0f0 2 s CC = t (A-20) Boundary conditions:

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148 f0 f0 C ( =0) = 0 C ( =1) = 0 (A-21) f0f0l C= C( t , ) (A-22) Order: O() 2 f1f0f0f1 c1 2 sm C C CC +K u = t t (A-23) Boundary conditions: f1 cf0 f1 C ( =0) = KC C (=1)=j (A-24) Integrating A-23 in st over a period (0-2 )and in over the domain (0-1) and applying the boundary conditions A-24 gives f0 ccf0 m C K= KCj t (A-25) Differentiating the multiple time scale form of the concentration A-4 with time gives l f m f c s f ft C L D t C h k t C t C 2 0 (A-26) Now substituting the regular expansion for f C into A-26 gives O0 0 0 1 0 0 m f c l f c m f m f c ft C h k t C K t C t C h k t C (A-27) Combining A-27 and A-25, gives th e following to leading order in

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149 j C K Lh D t Cf C f f 0 0 0 (A-28) The above equation in dimensional form becomes f0cf0 0Cj-kC th (A-29) If the flux coming out of the lens j is known, the above equation can be solved to determine the concentration in the POLTF as a function of time. It can be seen that when g0 fgDKh Dh and 2 c f 0L k D h are O( ), the concentration profile in the POLTF is independent of the axial direction. Now we consider the case when the time s cale for drug uptake by the cornea and that for drug release by the lens are both comparable to the time scale for axial equilibration, i.e., g0 fgDKh Dh and 2 c f 0L k D h are both O(1). In this case mlt~t and accordingly, we define the concentration to be of the form ffsl C=C(t, t, , ) (A-30) In this case the dimensionless c onvection diffusion equation becomes 22 22 ffffff 22 sl C C C CCC ++u+v=+ t t (A-31) The boundary conditions for this case are: f0 f1 f2 cf0 C ( =0) =0 C ( =0) =0 C ( =0) = KC (A-32)

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150 and f0 2 f1f0 s 22 0 2 f2f1 s 22 0 C =0 CCN ' L =()g(t) h CCN ' L =()g(t)+j h (A-33) where in this case g0 fgDKh Dh and 2 c c 0fkL K hD. Now we solve the governing equations to different orders in Zero Order The zero order solution is unchanged. f0f0l C= C( t , ). (A-34) First Order 2 f1f0f0f1 11 2 s C C CC +u+v= t (A-35) Since f0 Cis not a function of , the above equation simplifies to 2 f1f0f1 1 2 s C CC + u = t (A-36) Based on the form of the differential equation and 1u A-9 , we assumef1 Cto be of the form: 0 f11s2s 0 C NN C G(,t)6G(,t) Lh (A-37) On substituting the chosen form of f1 C A-36 in we get the following equations for G1 and G2: 2 1 2 s s 1G ) t ( f t G (A-38)

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151 2 22 s 2 sGG (1)f(t) t (A-39) with boundary conditions: 0 ) 1 ( G ) 1 ( G 0 ) 0 ( G ) 0 ( G2 1 2 1 (A-40) Since f is a periodic function and 2 0 s0 fdt, it can be expressed in the Fourier series as sint nsnsn n1n n0fasin(nt)bcos(nt)de (A-41) Thus G1 can also be expressed as sint 11s,ns1c,ns1,n n1n n0GG()sin(nt)G()cos(nt)G()e (A-42) Substituting G1 from the above expression into A38 and then solving the resulting differential equation for G1,n gives nn 1,nnn sinh(1i)1cosh(1i) 22 ididn Gcosh(1i) nn2 n nn (1i) (1i)sinh(1i) 2 22 (A-43) Similarly G2 can be expressed in a complex Fourier series as sint 22,n n n0GG()e (A-44) and solving A-39 gives the following expression for G2,n.

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152 2 n 2,n nn sinh(1i) 2 id2i G nn n (1i) 2 n 1cosh(1i) 2 id n cosh(1i) n2 nn (1i)sinh(1i) 22 (A-45) Second Order f2f0f0f1f1f0 2112 sl 22 f0f2 22 C C C C C C + + u + u + v + v t t CC = + (A-46) We use continuity to write th e above equation in the form f2f0f0 f0 21f11f12 s 22 f0f2 22 C C C C u (uC) (vC) v t t CC (A-47) We now integrate the above equation over a period with respect to ts and over 0 to 1 with respect to . After some algebraic manipulations the above equation reduces to the form f0f0f0 l C C C + u = D* + R ( ) t (A-48) where 2 2 * 1sss2sss 0 2s1sss 0NN DG(,t;)f(t)dtd61G(,t;)f(t)dtd 2L2h NN 6G(,t;)(1)G(,t;)f(t)dtd 2Lh

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153 (A-49) 2s1sss 0NN u6G(,t;)(1)G(,t;)f(t)dtd 2Lh (A-50) and 22 c f0 0f0fLjLk R( ) = C hDhD (A-51) By multiplying A-38 by G2 and A-39 by G1 and then adding and integrating the equation gives d dt G G t G G G G d dt ) t ( f G ) 1 ( Gs 2 1 s 2 2 2 1 2 1 2 2 s s 1 2 (A-52) The above expression can be simplified by noting that d dt G G ts 2 1 s= 0 due to periodicity. Furthermore, integrating by parts and using the boundary conditions gives d G G 2 d G G G G2 1 2 2 2 1 2 1 2 2 (A-53) To evaluate the above expressi on is useful to rewrite eqs A-38 and A-39 in a transformed coordinate 2 1 and then differentiate th e equations wit respect to . After the coordinate transformation and differentiati on eqs A-38 and A-39 become 1 2 2 s 1 sG ) t ( f G t (A-54) 2 2 2 s 2 sG ) t ( f 2 G t (A-55) with boundary conditions: 0 ) 2 / 1 ( G ) 2 / 1 ( G2 1 (A-56)

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154 From the above differential equations and the boundary conditions, it is clear that G1 and G2 are symmetric and antisymmetric, respectively and thus 0 d G G 2 d G G 2 d G G G G2 1 2 1 2 2 2 1 2 1 2 2 (A-57) The above derivation shows that the interaction of the latera l and the squeeze flows in the POLTF do not contribute to dispersion and thus the dispersion coefficient for mass transfer in the POLTF is simply a sum of the dispersion coe fficients for the lateral and the squeeze flow. Thus the expressions for *D and u simplify to the following: 2 2 * 1ss2ss 0NN DGf(t)dtd61Gf(t)dtd 2L2h (A-58) 0 u (A-59) Substituting the Fourier expansions for G1, G2 and f in the above equations gives 2 2 n1,nn2,n n0 0NN dGd6d1Gd Lh (A-60) After considerable algebra th e above expression reduces to 22 * nn 2 n1(ab) D* = 1+D(n) n (A-61) where (A-62) where 2 . The average equation in this case is

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155 22 f0f0c f0 l0f0f C CLjLk = D* +C t hDhD (A-63) which in dimensional form becomes f0f0cf0 f 0 C Cj-kC = D D* + t x xh (A-64) Thus it can be seen that the av erage equation for the case of O( ), i.e., Eq. A-28 is simply a special case of Eq. A-64 in the limit of negligible dispersion. contact lens cornea POLTF PLTFxy Gravity ' 0h L Figure A-1 Geometry of the post-lens tear film.

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156 APPENDIX B DERIVATION OF DRUG FLUX FROM THE CONTACT LENS TO THE POLTF The geometry of the contact lens is shown in Figure B-1. For conve nience, the coordinates x2 and y2 have been replaced by x and y in this Appendix. Case 1: Rapid PLTF breakup The governing equation and the boundary and the initial conditions for diffusion in the gel are 2 gg g 2 CC D t y (B-1) g ggf C (y0) 0 y C(yh) K C(t) (B-2) giC (t0)C (B-3) Taking Laplace transform of the governing eq uation and the boundary conditions, we get, 2 g ggg 2 dC s C C(t0) D d y (B-4) g ggf C (y0)0 y C(yh)KC (B-5) where g C is the Laplace transform of gC. The solution to the above set of differ ential equation and boundary conditions is

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157 g ii gf g g gg i f gg ggs cosh y D CC C (K C ) ss s cosh h D ss cosh ycosh y DD C1 (1) (s K C ) ss ss cosh hcosh h DD (B-6) The above solution can also be expressed as gg if g f gg ggss cosh ycosh y DD CdC1 C (1) K C (0) sd ts ss cosh hcosh h DD (B-7) The solution in the Laplace domain can now be inve rted to give the soluti on in the time domain. The inverted solution is 22 g 2 g 22 g 2 g 2(2n1) n Dt 4h gi l (2n1) n Dt 4h f g (2n1) n t f 0 g(1) 4(2n1) C C cos y e (2n1)2 h (1) 4(2n1) K C (0) 1 cos y e (2n1)2 h d C(1) 4(2n1) K () 1 cos y e d (2n1)2 h 2 g 2 gD(t) 4h d (B-8) To simplify the above expression, we integrate th e convolution integral by parts. This gives

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158 22 g 2 g(2n1) n t D(t) 4h f 0 g n f g (2n1 n f gd C(1) 4(2n1)y K () 1 cos e d d (2n1)2 h (1) 4(2n1)y K C (t) 1 cos (2n1)2 h (1) 4(2n1)y K C (0) 1 cos e (2n1)2 h 22 g 2 g 22 g 2 g) Dt 4h (2n1) 22 n t D(t) 4h g 2 0 gg (2n1)D (1) 4(2n1)y K C() cos e (2n1)2 h4 h (B-9) Thus, the concentra tion profile becomes 22 g 2 g 22 g 2 g(2n1) n Dt 4h gi g n f g (2n1) 22 n D(t 4h g f 2 gg(1) 4(2n1)y C C cos e (2n1)2 h (1) 4(2n1)y K C(t) 1 cos (2n1)2 h (2n1)D (1) 4(2n1)y K C() cos e (2n1)2 h4 h t ) 0d (B-10) Thus, the flux j can be expressed as g 22 22 g g 2 2 g g 22 g 2 gg g yh (2n1) (2n1) 22 t Dt D(t) 4h 4h gi g gfgf 3 0 ggg (2n1) 2 Dt 4h gg i n0 ggC j D y 2 DC(2n1)D 2 () e D K C(t) DK C() e d hh2 h 2 D2 D K(2n1) C e C() hh 22 g 2 g (2n1) 2 t D(t) 4h g f 2 n0 0 gD e d C(t) 4 h (B-11) Case 2: Well-mixed PLTF The governing equation, the boundary conditions, and the initial condition of the mass transfer problem for case II are the following.

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159 2 gg g 2 CC D t y (B-12) g ggf C(y0) 0 C(yh) K C(t) (B-13) giC (t0) C (B-14) After taking the Laplace transfor m of the differential equation and the boundary conditions, we get, 2 g ggg 2 dC sCC(t0) D d y (B-15) g gg C (y0) 0 1 C (yh) s (B-16) The solution to the above set of differ ential equation and boundary conditions is, g g0 i ggg gg g g gg igg gg gg ggs sinh y D C Cs1s C (1-coshh) (1-coshh) sDssD s sinh h D ss sinh ysinh y DD 1s1s1 C(1-coshh) (1-coshh) sDsDs ss sinh hsinh h DD (B-17) The solution in the Laplace domain can now be inve rted to give the soluti on in the time domain. The inverted solution is

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160 22 g 2 g 22 g 2 g 2 g 2 gn n Dt h gi n0 g n n t D(t) h f f n0 0 gg (2n1) Dt h i n0 g2(1(1))ny C C sin e nh d Cy2(1(1))ny K ()C(0) sin e d d hnh 4(2n1)y = C sin e (2n1)h 22 g 2 g 22 g 2 g 22 g 2 gn n Dt h f n1 gg t n n D(t) h f n1 gg 0 (2n1) 22 n t D(t) 4h g f 2 n1 0 ggy2(1)ny KC (t) sin e hnh y2(1)ny C () sin e hnh K nD 2(1)ny C() esin d nhh (B-18) Thus, the concentrati on profile becomes, 2 g 2 g 22 g 2 g(2n1) Dt h gi n0 g n f n1 gg n t D(t) h g n f 2 n1 0 gg4(2n1)y C C sin e (2n1)h y2(1)ny KC (t) sin hnh nD ny K C() 2(1)sin ed hh (B-19) Thus, the flux j can be expressed as, g 22 22 g g 2 2 g gg g yh (2n1) n 22 t Dt D(t) 4h h gigg f gff 2 n0n1n1 0 gggg C j D y 4DC2DKnD C(t) e DK C()edC(t) hhhh (B-20)

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161 lens cornea C kcCf jghPOLTF PLTF x y Cgfh Figure B-1: Geometry of the lens and the pre-lens tear film.

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162 LIST OF REFERENCES (1) Bourlais, C., Acar L, Zia H, Sado PA, Nee dham, T, Leverge R Ophthalmic drug delivery systems. Progress in retinal and eye research, 1998. 17 (1), 33-58. (2) Lang, J. C. Ocular Drug-Deliver y Conventional Ocular Formulations. Adv Drug Deliver Rev, 1995. 16 (1), 39-43. (3) TIMPOTIC prescribing information, supplied by MERCK (http://www.merck.com/product/usa/pi_c irculars/t/timoptic/timoptic_xe_pi.pdf) (4) Saettone MF, C. P., Torraca MT, Burgalas si S, Giannaccini, B. Evaluation of mucoadhesive properties and in vivo activity of ophthalmic vehicles based on hyaluronic acid. Int. J. Pharm, 1989. 51, 203-212. (5) Saettone MF, T. A., Savigni P, Tellini N. Vehicle effects on ophthalmic bioavailability. The influence of different polymers. J. Pharm. Pharmacol., 1982. 34, 464-466. (6) Davies NM, F. S., Hadgraft J, Kellaway, IW. Evaluation of mucoadhesive polymers in ocular drug delivery. I. Viscous Solutions. Pharm. Res., 1982. 9 (9), 1137-1144. (7) Greaves JL, Olejnik O, Wilson CG. Poly mers and the precorneal tear film. S.T.P. Pharm. Sco.,1992. 2(1), 13-33. (8) Kyyronen K, U. A. Improved ocular: system ic absorption ratio of Timolol by viscous vehicle and phenylephrine. Invest. Ophthalmol. Vis. Sci., 1990. 31 (9), 1827-1833. (9) Hiementz PC, R. R.. "Principles of colloid and surface chemistry, 1997, 3rd ed.,." (10) Calvo P, V.-L. J., Al onso MJ, Comparative in vitro ev aluation of several colloidal systems, nanoparticles, nanocapsules, and nanoemulsiuons as oc ular drug carriers. J. Pharm. Sci, 1996. 85 (5), 530-536. (11) Marchal-Heussler L, S. D., Hoffman M, Maincent P. Poly ( -caprolactone) nanocapsules in carteolol ophthalmic drug delivery. Pharm. Res., 1993. 10 (3), 386-390. (12) Calvo P, S. A., Martinez J, Lopez MI , Calonge M, Pastor JC, Alonso MJ. Polyster nanocapsules as new topical ocular delivery systems for cyclosporin A. Pharm. Res., 1996. 13 (2), 311-315.

PAGE 163

163 (13) Li VHK, W. R., Kreuter J, Harmia T, R obinson JR. Ocular drug delivery of progesterone using nanoparticles. J. Microencapsulation, 1986. 3 (3), 213-218. (14) Sawusch MR, O. B. T., Dick JD, Otts ch JD. Use of collagen corneal shields in the treatment of bacterial kearatitis. Am. J. Ophthalmol., 1988. 106, 279-281. (15) Vasantha R, S. P., Panduranga Rao K. Collagen ophthalm ic inserts for pilocarpine drug delivery systems. Int. J. Pharm., 1988. 47, 95-102. (16) Zimmer AK, K. J., Robinson JR. Studies on transport pathways of PBCA nanoparticles in ocular tissues. J. Microencapsulation, 1991. 8 (4), 497-504. (17) Li, C. C.;Chauhan, A. Modeling ophtha lmic drug delivery by soaked contact lenses. Ind Eng Chem Res, 2006. 45 (10), 3718-3734. (18) Creech, J. L.; Chauhan, A.;Radke, C. J. Dispersive mixing in the posterior tear film under a soft contact lens. Ind Eng Chem Res, 2001. 40 (14), 3015-3026. (19) Mc Namara, N. A., Polse, K.A., Brand, R.D., Graham, A.D., Chan, J.S., Mc Kenney, C.D. Tear mixing under a soft contac t lens: Effects of lens diameter. Am. J. of Ophth, 1999. 127 (6), 659-665. (20) N.A. Peppas . "Hydrogels in medici ne and pharmacy." v.1 & 2, CRC Press inc., Boca Raton, FL. 1986 (21) Hillman, J. S. Management of acute glaucoma with Pilocarpine-soaked hydrophilic lens,. Brit. J.Ophthal., 1974. 58, 674-679. (22) Ramer, R., Gasset, A. Ocular Penetration of Pilocarpine. Annals of Ophthalmology, 1974. 6, 1325-1327. (23) Montague, R., Watkins, R. Pilocarpine dispensation fo r the soft hydrophilic contact lens. Brit.J.Ophthal, 1975. 59, 455-458. (24) Hillman, J., Masters, J., Broad, A. Pilocarpine delivery by hydrophilic lens in the management of acute glaucoma. Transactions of the ophthalmol ogical societies of the United Kingdom, 1975, 79-84. (25) Giambattista, B., Virno, M., Pecori-Giraldi, Pellegrino, N., Motolese, E. Possibility of Isoproterenol Therapy with Soft Contact Le nses: Ocular Hypotensi on Without Systemic Effects. Ann. Ophthalmol, 1976. 8, 819-829.

PAGE 164

164 (26) Marmion, V. J. a. Y., S. P ilocarpine administration by contact lens,. Trans. Ophthal. Soc., U.K, 1977. 97, 162-163. (27) Arthur, B. W., Hay, G.J., Wasan, S.M., Willis, W.E. Ultra-structural Effects of Topical Timolol on Rabbit Cornea. Archives of Ophthalmology, 1983. 10, 1607-1610. (28) Wilson, M. C., Shields, M.B A Comparison of Clinical Variations of the Iridocorneal Endothelial Syndrome. Arch. Ophthalmol., 1989. 107, 1465-1468. (29) Fristrom, B. A 6-month, randomized , double-masked comparison of latanoprost with timolol in patients with open angl e glaucoma or ocular hypertension. Acta Opthalmol. Scand. (Acta ophthalmologica Scandinavica), 1996. 74, 140-144. (30) Schultz, C. L., Mint, J.M. Drug de livery system for antiglaucomatous medication. 2000 (31) Rosenwald, P. L. Ocular device. United States Patent: 4,484,922, 1981 (32) Schultz, C. L., Nunez, I.M., Silor, D. L ., Neil, M. L., Contact lens containing a leachable absorbed material. 1995, -. (33) Garcia, D. M.Escobar, J. L.Noa, Y. Bada, N.Hernaez, E. Katime, I. Timolol maleate release from pH-sensible pol y(2-hydroxyethyl methacrylateco-methacrylic acid) hydrogels. Eur Polym J, 2004. 40 (8), 1683-1690. (34) Alverez-Lorenzo, C.Hi ratani, H.Gomez-Amoza, J. L.Ma rtinez-Pacheco, R.Souto, C. Concheiro, A. Soft cont act lenses capable of sustained delivery of timolol. J Pharm Sci, 2002. 91 (10), 2182-2192. (35) Hiratani, H.;Alvarez-Lorenzo, C. The nature of backbone monomers determines the performance of imprinted soft contact lenses as timolol drug delivery systems. Biomaterials, 2004. 25 (6), 1105-1113. (36) Prausnitz, M. R.;Noonan, J. S. Perm eability of cornea, sclera, and conjunctiva: A literature analysis for drug delivery to the eye. J Pharm Sci, 1998. 87 (12), 1479-1488. (37) Giambattista, B., Virno, M., Pecori-Giraldi, Pellegrino, N., Motolese, E. Possibility of Isoproterenol Therapy with Soft Contact Le nses: Ocular Hypotensi on Without Systemic Effects. Ann. Ophthalmol, 1976. 8, 819-829. (38) Marmion, V. J. a. Y., S. P ilocarpine administration by contact lens,. Trans. Ophthal.

PAGE 165

165 Soc., U.K, 1977. 97, 162-163. (39) Mc Namara, N. A., Polse, K.A., Brand, R.D., Graham, A.D., Chan, J.S., Mc Kenney, C.D. Tear mixing under a soft contac t lens: Effects of lens diameter. Am. J. of Ophth, 1999. 127 (6), 659-665. (40) Chauhan, A.; Radke, C.;Polse, K. Settling and deformation of a soft contact lens. Invest Ophth Vis Sci, 2001. 42 (4), S589-S589. (41) Chauhan, A.;Radke, C. J. The role of fenestrations and channels on the transverse motion of a soft contact lens. Optometry Vision Sci, 2001. 78 (10), 732-743. (42) Chauhan, A.;Radke, C. J. Modeling the vertical motion of a soft contact lens. Curr Eye Res, 2001. 22 (2), 102-108. (43) Hiratani, H.; Fujiwara, A.; Tamiya, Y.; Mizutani, Y.;Alvarez-Lorenzo, C. Ocular release of timolol from molecularly imprinted soft contact lenses. Biomaterials, 2005. 26 (11), 12931298. (44) Hiratani, H.; Mizutani, Y.;Alvarez-Lor enzo, C. Controlling drug release from imprinted hydrogels by modifying the character istics of the imprinted cavities. Macromol Biosci, 2005. 5 (8), 728-733. (45) Hiratani, H.;Alvarez-Lo renzo, C. Timolol uptake and re lease by imprinted soft contact lenses made of N,N-diethylacrylamide and methacrylic acid. Journal of Controlled Release, 2002. 83 (2), 223-230. (46) Elisseeff, J.McIntosh, W.Anseth, K.Riley, S.Ragan, P. Langer, R. Photoencapsulation of chondrocytes in poly(ethylene oxide)based semi-interpe netrating networks. Journal of Biomedical Materials Research, 2000. 51 (2), 164-171. (47) Ward, J. H., Peppas, N.A. Preparati on of controlled release systems by free-radical UV polymerizations in the presence of a drug. Journal of Controlled Release, 2001. 71 (2), 183192. (48) Scott, R. A., Peppas, N.A Highly crosslinked, PEG-containing copolymers for sustained solute delivery. Biomaterials, 1999. 20 (15), 1371-1380. (49) Podual, K., Doyle F.J., Peppas, N.A. Preparation and dynamic response of cationic copolymer hydrogels cont aining glucose oxidase. Polymer, 2000. 41 (11), 3975-3983.

PAGE 166

166 (50) Colombo, P., Bettini, R., Peppas, N.A. Observation of swelling process and diffusion front position during swelling in hydroxypropyl methyl cellulose (HPMC) matrices containing a soluble drug. Journal of Controlled Release, 1999. 61 (1,2), 83-91. (51) Ende, M. T. A.;Peppas, N. A. Transpor t of ionizable drugs and proteins in crosslinked poly(acrylic acid) and poly(a crylic acid-co-2-hydroxyethyl methacrylate) hydrogels .2. Diffusion and release studies. Journal of Controlled Release, 1997. 48 (1), 47-56. (52) Nakada, K., Sugiyama, A. Process for producing controlled drugrelease contact lens, and controlled drug-release contact lens ther eby produced. United States Patent: 6,027,745, May 29, 1998. (53) Gulsen, D.;Chauhan, A. Dispersion of lip osomes in soft contact lens for ophthalmic drug delivery. Abstr Pap Am Chem S, 2004. 227, U875-U875. (54) Gulsen, D.;Chauhan, A. Ophtha lmic drug delivery through contact lenses. Invest Ophth Vis Sci, 2004. 45 (7), 2342-2347. (55) Cascone, M. G.; Zhu, Z. H.; Borselli, F.;Lazzeri, L. Poly(vinyl alcohol) hydrogels as hydrophilic matrices for the release of li pophilic drugs loaded in PLGA nanoparticles. J Mater Sci-Mater M, 2002. 13 (1), 29-32. (56) Varshney, M.Morey, T. E.Shah, D. O.Flint, J. A.Moudgil, B. M.Seubert, C. N. Dennis, D. M. Pluronic microemulsions as nanoreservo irs for extraction of bupivacaine from normal saline. J Am Chem Soc, 2004. 126 (16), 5108-5112. (57) Fantini, S.Clohessy, J.Gorgy, K.Fusa lba, F.Johans, C.Kontturi, K. Cunnane, V. J. Influence of the presence of a gel in the wate r phase on the electrochemical transfer of ionic forms of beta-blockers across a large water vertical bar 1,2-dichloroethane interface. Eur J Pharm Sci, 2003. 18 (3-4), 251-257. (58) Edwards, A.;Prausnitz, M. R. Predicted permeability of the cornea to topical drugs. Pharmaceut Res, 2001. 18 (11), 1497-1508. (59) Segal, M. P. .Pumps and timed release. FDA Consumer magazine October, 1991. (60) Li, C. C. and Chauhan, A., Ocular Transport Model for Ophthalmic Delivery of Timolol by Soaked p-HEMA Contact Lenses, J. of Drug Del. Sci. Tech., 2007. 17 (1), 69-79. (61) Menon, I. A.; Trope, G. E.; Basu, P. K.; Wakeham, D. C.;Persad, S. D. Binding of Timolol to Iris-Ciliary Body and Melanin an Invitro Model for Assessi ng the Kinetics and Efficacy of Long-Acting Antiglaucoma Drugs. J. Ocul. Pharmacol., 1989. 5 (4), 313-324.

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167 (62) Dumbleton, K. Adverse Events with Silicone hydrogel Continuous Wear. Contact Lens & Ant. Eye , 2002 25, 137-146.

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168 BIOGRAPHICAL SKETCH The author was born in December 8th 1980 in Taipei, Taiwan. She did her undergraduate study in Chemical Engineering at National Taiwan University a nd graduated in May 2002. She then came to the University of Florida for her master’s degree in chemical engineering and received her degree in August 2003. She joined th e PhD program in Chemi cal Engineering at the University of Florida and received her PhD degr ee in May 2007. After graduation, she joined Merck in West Point Pennsylvania as a Senior Research Pharmacoki neticist in May 2007