Closed-form Solutions for Drug Transport through Controlled-Release Devices in Two and Three Dimensions

Laurent Simon, PhD, is Associate Professor of Chemical Engineering and served as the Associate Director of the Pharmaceutical Engineering Program at New Jersey Institute of Technology. Dr. Simon is the author of Laboratory Online, a series of educational and interactive modules that help engineers build a strong understanding of drug delivery technologies and their underlying engineering principles. During his time at NJIT, Dr. Simon has received the Excellence in Teaching Award, Master Teacher Designation, Newark College of Engineering Saul K. Fenster Innovation in Engineering Education Award and a Distinguished Teaching Award from the American Society of Engineering Education (ASEE).Juan Ospina is currently an Assistant Professor at EAFIT University in the Logic and Computation Group, Physics Engineering Program. He has published numerous articles on the topic of mathematical physics.

• Preface ixAcknowledgements xi1 Steady-State Analysis of a Two-Dimensional Model for Percutaneous Drug Transport 11.1 Separation of Variables in 2-D Cartesian Coordinates11.2 Model for Drug Transport across the Skin 31.3 Analytical Solution of the Diffusion Model in 2-D Cartesian Systems 41.4 Summary 61.5 Appendix: Maple, Mathematica, and Maxima Code Listings 6Problems 10References 122 Constant Drug Release from a Hollow Cylinder of Finite Length in Two Dimensions 132.1 Separation of Variables in 2-D Cylindrical Coordinates 132.2 Model for Drug Release from a Hollow Cylinder 152.3 Analytical Solution of the Transport Model in 2-D Cylindrical Coordinates 152.4 Summary 192.5 Appendix: Maple Code Listings 19Problems 20References 203 Analysis of Steady-State Growth Factor Transport Through Double-Layered Scaffolds 233.1 Governing Steady-State Transport Equations 233.2 Solution Procedure for Transport Through a Two-Layered Scaffold 253.3 Concentration Profile of Vascular Endothelial Growth Factor in Two Layers 313.4 Summary 323.5 Appendix: Maple Code Listings 33Problems 37References 384 Steady-State Two-Dimensional Diffusion in a Hollow Sphere 394.1 Separation of Variables and Legendre Polynomials in 2-D Spherical Coordinates 394.2 Model For 2-D Diffusion in a Sphere 434.3 Analytical Solution of 2-D Diffusion in Spherical Coordinates 464.4 Summary 494.5 Appendix: Maple, Mathematica, and Maxima Code Listings 49Problems 56References 575 Steady-State Three-Dimensional Drug Diffusion through Membranes from Distributed Sources 595.1 Separation of Variables in 3-D Cartesian Coordinates 595.2 Transport across the Membrane 615.3 Analytical Solution of the Diffusion Model in 3-D Cartesian Systems 635.4 Summary 685.5 Appendix: Maple Code Listings 69Problems 73References 736 Constant Drug Release from a Hollow Cylinder of Finite Length in Three Dimensions 756.1 Separation of Variables in 3-D Cylindrical Coordinates 756.2 Model For 3-D Drug Release from a Hollow Cylinder 776.3 Analytical Solution of the Transport Model in 3-D Cylindrical Coordinates 786.4 Summary 846.5 Appendix: Maple Code Listings 85Problems 87References 877 Sustained Drug Release from a Hollow Sphere in Three Dimensions 897.1 Method of Green’s Function in 3-D Spherical Coordinates 897.2 Model for Molecular Transport across the Wall of a Hollow Sphere 957.3 Analytical Solution of the Transport Model in 3-D Spherical Coordinates 967.4 Summary 977.5 Appendix: Maple, Mathematica and Maxima Code Listings 98Problems 105References 1058 Analysis of Transient Growth Factor Transport Through Double-Layered Scaffolds 1078.1 Laplace and Fourier-Bessel-based Methods in 2-D Cylindrical Coordinates 1078.2 Governing Equations for Transport through Double-Layered Scaffolds 1128.3 Concentration Profile of Vascular Endothelial Growth Factor in Two Layers 1148.4 Summary 1198.5 Appendix: Maple Code Listings 120Problems 126References 1269 Molecular Diffusion through the Stomach Lining and into the Bloodstream 1299.1 Laplace Transforms, Legendre Functions and Spherical Harmonics1299.2 Spherical Diffusion in Three Dimensions 1329.3 Analytical Solution of the Transient Transport Model in 3-D Spherical Coordinates 1339.4 Summary 1389.5 Appendix: Maple Code Listings 138Problems 141References 14310 Diffusion-Controlled Ligand Binding to Receptors on Cell Surfaces 14510.1 Weber’s Integral 14510.2 Steady-State Diffusion-Limited Ligand Binding 14810.3 Transient Diffusion-Controlled Ligand Binding in 2-D Cylindrical Coordinates 15110.4 Summary 15610.5 Appendix: Maple, Mathematica and Maxima Code Listings 156Problems 167References 16811 Two-Dimensional Analysis of a Cylindrical Matrix Device with a Small Hole For Drug Release 16911.1 Mathematical Modeling of Drug Transport through the Device 16911.2 Drug Concentration Profile inside the Matrix 17111.3 Normalized Cumulative Percentage of Drug Released 17711.4 Summary 17811.5 Appendix: Maple Code Listings 178Problems 182References 18312 Three-Dimensional Drug Diffusion through Membranes from Distributed Sources 18512.1 Governing Equations of the Transport Model 18512.2 Analytical Solution of the Diffusion Model in 3-D Cartesian Systems 18712.3 Average Dimensionless Concentration and Flux 19412.4 Summary 19412.5 Appendix: Maple and Mathematica Code Listings 195Problems 207References 20713 Effective Time Constant for Two- and Three-Dimensional Controlled-Released Drug-Delivery Models 20913.1 Effective Time Constant in Controlled-Release Drug-Delivery Systems 20913.2 Intravitreal Drug Delivery using a 2-D Cylindrical Model 21013.3 Analysis of a Rectangular Parallelepiped-Shaped Matrix with a Release Area 21813.4 Summary 22513.5 Appendix: Maple and Mathematica Code Listings 225Problems 232References 23214 Data Fitting For Two- and Three-Dimensional Controlled- Release Drug-Delivery Models 23314.1 Data Fitting in Controlled-Release Drug-Delivery Systems 23314.2 Estimation of Diffusion Coefficient in a Solid Cylinder of Finite Length 23414.3 Estimation of Diffusion Coefficient in a Rectangular Parallelepiped-Shaped Matrix 24014.4 Summary 24314.5 Appendix: Maple and Mathematica Code Listings 244Problems 256References 25815 Optimization of Two- and Three-Dimensional Controlled-Released Drug-Delivery Models 25915.1 Optimum Design of Controlled-Released Drug-Delivery Systems 25915.2 Design of a 2-D Cylindrical Dosage Form with a Finite Mass Transfer Coefficient 26015.3 Design of a Rectangular Parallelepiped-Shaped Matrix with a Finite Mass Transfer Coefficient 26515.4 Summary 26815.5 Appendix: Maple and Mathematica Code Listings 268Problems 282References 283Index 285