MODELING OF DRUG DELIVERY TO THE HUMAN EYE A Thesis Presented to the Faculty of California State Polytechnic University, Pomona In Partial Fulfillment Of the Requirements for the Degree Master of Science In Mechanical Engineering By Withanage D. Mahathanthila 2017 SIGNATURE PAGE ii ABSTRACT The human eye can mainly be divided into two chambers in numerical modeling: anterior and the posterior lobes. The treatments for diseases in each of these sections differ. For instance, the posterior segment, being more inward involves highly invasive treatments such as surgery, whereas anterior eye diseases rely on topical drug applications. Even though it appears to be complicated, surgery can assure the direct and efficient drug delivery. Delivery of a necessary amount of topically applied drugs to the targeted site in the anterior lobe of the eye can depend on multiple factors including the temperature profile, anatomy of the sub segments as well as the fluid flow rate in the eye. In the current study, the drug transportation in the anterior eye has been studied using numerical modeling. The model considers the spatio-temporal behavior of the drugs in towards the trabecular meshwork (TM), iris and the lens when applied to the corneal surface. The aqueous humor (AH) plays a major role in the drug delivery procedure through natural convection. These movements can depend on the temperature difference between the environment (surface of the eye) and the targeted eye segment. The current study has been able to depict the temporal drug concentrations changes in the TM, iris and the lens. These predictions display that the peak average drug concentration is found within one hour after application whereas it will be completely removed after five hours. Additionally, these concentrations depend on the temperature differences, for instance the minimal peak concentration in the eye is observed when the temperature of the environment is the same as the ocular temperature. iii TABLE OF CONTENTS Signature page ..................................................................................................................... ii Abstract .............................................................................................................................. iii List of Tables ..................................................................................................................... vi List of Figures ................................................................................................................... vii Nomenclature ................................................................................................................... viii 1. Introduction ..................................................................................................................... 1 1.1 Eye components considered in the model ................................................................. 4 1.1.1 Cornea ................................................................................................................ 4 1.1.2 Sclera.................................................................................................................. 5 1.1.3 Aqueous Humor (AH)........................................................................................ 7 1.1.4 Trabecular Mesh-work ....................................................................................... 8 1.1.5 Ciliary Body ....................................................................................................... 9 1.1.6 Iris ...................................................................................................................... 9 1.2 Why topical drug delivery? ....................................................................................... 9 1.3 Common diseases treated by topical drugs ............................................................. 10 1.3.1 Glaucoma ......................................................................................................... 10 1.3.2 Cataract ............................................................................................................ 11 1.3.3 Uveitis .............................................................................................................. 13 2. Model selection ............................................................................................................. 15 3. Numerical model ........................................................................................................... 17 3.1 Eye Geometry ......................................................................................................... 17 3.2 Governing equations and initial/boundary conditions ............................................ 18 3.2.1 Transport of drug concentration....................................................................... 18 3.2.2 Aqueous Humor (AH) Flow ............................................................................ 21 3.2.2.1 The Boussinesq approximation ..................................................................... 22 iv 3.2.3 Temperature profile ......................................................................................... 22 4. Numerical results .......................................................................................................... 24 4.1 Steady State Velocity Distribution.......................................................................... 24 4.2 Steady State Temperature Distribution of entire eye .............................................. 25 (Ambient Temperature 298K)....................................................................................... 25 4.2.1 Temperature Distribution respect to different ambient temperatures .............. 26 4.3 Drug concentration distribution .............................................................................. 29 5. Validation of the results ................................................................................................ 33 6. Conclusion .................................................................................................................... 35 References ......................................................................................................................... 36 Appendix ........................................................................................................................... 39 Convergence plot for transient solver ....................................................................... 39 Convergence plot for non-linear solver .................................................................... 39 v LIST OF TABLES Table 1. Eye model Geometry Dimensions ...................................................................... 17 Table 2. Diffusion coefficients of ECA in different domains ........................................... 19 Table 3. Thermo-physical properties in different domains ............................................... 19 Table 4. Parameters to solve steady state problem ........................................................... 21 Table 5. Parameters used to find temperature profile ....................................................... 23 vi LIST OF FIGURES Figure 1.Structure of the eye and the cornea ...................................................................... 5 Figure 2.Front and side view of sclera ................................................................................ 6 Figure 3.Aqueous humor flow through trabecular meshwork ............................................ 8 Figure 4.Types of Cataracts .............................................................................................. 12 Figure 5.Schematic of the eye ........................................................................................... 13 Figure 6.Simulation domains of drug concentration......................................................... 18 Figure 7.Steady State velocity distribution of the anterior eye ......................................... 24 Figure 8.Steady State Temperature profile ....................................................................... 25 Figure 9.Temperature variation along pupillary axis of the eye ....................................... 25 Figure 10.Temperature and velocity profile at ambient temperature 308K ...................... 26 Figure 11.Temperature and velocity profile at ambient temperature 310K ...................... 27 Figure 12. Temperature and velocity profile at ambient temperature 314K ..................... 28 Figure 13.Temporal evolution of the drug at 3 different drug targets .............................. 32 Figure 14.Comparison of results with previous reports .................................................... 33 Figure 15. Comparison of velocity profiles ...................................................................... 34 Figure 16.Comparison of Drug concentration at a point (TM, Iris, Lens) ........................ 34 vii NOMENCLATURE c specific heat (J kg-1 K-1) C ECA concentration (µM) D diffusion coefficient (m2 s-1) g gravitational acceleration (m s-2) h heat transfer coefficient (W m-2 K-1) k thermal conductivity (W m-1 K-1) T temperature (K) v velocity vector (m s-1) Q volume flow rate of the aqueous humor (m3/s) p Pressure (Pa) s Non-dimensional parameter E evaporation rate (W m-2) viii Greek symbols β volume expansion coefficient (K-1) -1 -1 µ dynamic viscosity (kg m s ) -3 ρ0 reference density (kg m ) -3 ρ density (kg m ) σ Stefan-Boltzmann constant (W m-2 K-4) Subscripts ah aqueous