Preface ix Acknowledgements xi 1 Steady-State Analysis of a Two-Dimensional Model for Percutaneous Drug Transport 1 1.1 Separation of Variables in 2-D Cartesian Coordinates1 1.2 Model for Drug Transport across the Skin 3 1.3 Analytical Solution of the Diffusion Model in 2-D Cartesian Systems 4 1.4 Summary 6 1.5 Appendix: Maple, Mathematica, and Maxima Code Listings 6 Problems 10 References 12 2 Constant Drug Release from a Hollow Cylinder of Finite Length in Two Dimensions 13 2.1 Separation of Variables in 2-D Cylindrical Coordinates 13 2.2 Model for Drug Release from a Hollow Cylinder 15 2.
3 Analytical Solution of the Transport Model in 2-D Cylindrical Coordinates 15 2.4 Summary 19 2.5 Appendix: Maple Code Listings 19 Problems 20 References 20 3 Analysis of Steady-State Growth Factor Transport Through Double-Layered Scaffolds 23 3.1 Governing Steady-State Transport Equations 23 3.2 Solution Procedure for Transport Through a Two-Layered Scaffold 25 3.3 Concentration Profile of Vascular Endothelial Growth Factor in Two Layers 31 3.4 Summary 32 3.5 Appendix: Maple Code Listings 33 Problems 37 References 38 4 Steady-State Two-Dimensional Diffusion in a Hollow Sphere 39 4.
1 Separation of Variables and Legendre Polynomials in 2-D Spherical Coordinates 39 4.2 Model For 2-D Diffusion in a Sphere 43 4.3 Analytical Solution of 2-D Diffusion in Spherical Coordinates 46 4.4 Summary 49 4.5 Appendix: Maple, Mathematica, and Maxima Code Listings 49 Problems 56 References 57 5 Steady-State Three-Dimensional Drug Diffusion through Membranes from Distributed Sources 59 5.1 Separation of Variables in 3-D Cartesian Coordinates 59 5.2 Transport across the Membrane 61 5.3 Analytical Solution of the Diffusion Model in 3-D Cartesian Systems 63 5.
4 Summary 68 5.5 Appendix: Maple Code Listings 69 Problems 73 References 73 6 Constant Drug Release from a Hollow Cylinder of Finite Length in Three Dimensions 75 6.1 Separation of Variables in 3-D Cylindrical Coordinates 75 6.2 Model For 3-D Drug Release from a Hollow Cylinder 77 6.3 Analytical Solution of the Transport Model in 3-D Cylindrical Coordinates 78 6.4 Summary 84 6.5 Appendix: Maple Code Listings 85 Problems 87 References 87 7 Sustained Drug Release from a Hollow Sphere in Three Dimensions 89 7.1 Method of Green''s Function in 3-D Spherical Coordinates 89 7.
2 Model for Molecular Transport across the Wall of a Hollow Sphere 95 7.3 Analytical Solution of the Transport Model in 3-D Spherical Coordinates 96 7.4 Summary 97 7.5 Appendix: Maple, Mathematica and Maxima Code Listings 98 Problems 105 References 105 8 Analysis of Transient Growth Factor Transport Through Double-Layered Scaffolds 107 8.1 Laplace and Fourier-Bessel-based Methods in 2-D Cylindrical Coordinates 107 8.2 Governing Equations for Transport through Double-Layered Scaffolds 112 8.3 Concentration Profile of Vascular Endothelial Growth Factor in Two Layers 114 8.4 Summary 119 8.
5 Appendix: Maple Code Listings 120 Problems 126 References 126 9 Molecular Diffusion through the Stomach Lining and into the Bloodstream 129 9.1 Laplace Transforms, Legendre Functions and Spherical Harmonics129 9.2 Spherical Diffusion in Three Dimensions 132 9.3 Analytical Solution of the Transient Transport Model in 3-D Spherical Coordinates 133 9.4 Summary 138 9.5 Appendix: Maple Code Listings 138 Problems 141 References 143 10 Diffusion-Controlled Ligand Binding to Receptors on Cell Surfaces 145 10.1 Weber''s Integral 145 10.2 Steady-State Diffusion-Limited Ligand Binding 148 10.
3 Transient Diffusion-Controlled Ligand Binding in 2-D Cylindrical Coordinates 151 10.4 Summary 156 10.5 Appendix: Maple, Mathematica and Maxima Code Listings 156 Problems 167 References 168 11 Two-Dimensional Analysis of a Cylindrical Matrix Device with a Small Hole For Drug Release 169 11.1 Mathematical Modeling of Drug Transport through the Device 169 11.2 Drug Concentration Profile inside the Matrix 171 11.3 Normalized Cumulative Percentage of Drug Released 177 11.4 Summary 178 11.5 Appendix: Maple Code Listings 178 Problems 182 References 183 12 Three-Dimensional Drug Diffusion through Membranes from Distributed Sources 185 12.
1 Governing Equations of the Transport Model 185 12.2 Analytical Solution of the Diffusion Model in 3-D Cartesian Systems 187 12.3 Average Dimensionless Concentration and Flux 194 12.4 Summary 194 12.5 Appendix: Maple and Mathematica Code Listings 195 Problems 207 References 207 13 Effective Time Constant for Two- and Three-Dimensional Controlled-Released Drug-Delivery Models 209 13.1 Effective Time Constant in Controlled-Release Drug-Delivery Systems 209 13.2 Intravitreal Drug Delivery using a 2-D Cylindrical Model 210 13.3 Analysis of a Rectangular Parallelepiped-Shaped Matrix with a Release Area 218 13.
4 Summary 225 13.5 Appendix: Maple and Mathematica Code Listings 225 Problems 232 References 232 14 Data Fitting For Two- and Three-Dimensional Controlled- Release Drug-Delivery Models 233 14.1 Data Fitting in Controlled-Release Drug-Delivery Systems 233 14.2 Estimation of Diffusion Coefficient in a Solid Cylinder of Finite Length 234 14.3 Estimation of Diffusion Coefficient in a Rectangular Parallelepiped-Shaped Matrix 240 14.4 Summary 243 14.5 Appendix: Maple and Mathematica Code Listings 244 Problems 256 References 258 15 Optimization of Two- and Three-Dimensional Controlled-Released Drug-Delivery Models 259 15.1 Optimum Design of Controlled-Released Drug-Delivery Systems 259 15.
2 Design of a 2-D Cylindrical Dosage Form with a Finite Mass Transfer Coefficient 260 15.3 Design of a Rectangular Parallelepiped-Shaped Matrix with a Finite Mass Transfer Coefficient 265 15.4 Summary 268 15.5 Appendix: Maple and Mathematica Code Listings 268 Problems 282 References 283 Index 285.