{"product_id":"closedform-solutions-for-drug-transport-through-controlledrelease-devices-in-two-and-three-dimensions-9781118947258","title":"Closedform Solutions for Drug Transport through","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eProvides solutions for two- and three-dimensional linear models of controlled-release systems\u003cbr\u003e\u003cbr\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003eReal-world applications are taken from used to help illustrate the methods in Cartesian, cylindrical and spherical coordinate systems\u003c\/li\u003e \u003cli\u003eCovers the modeling of drug-delivery systems and provides mathematical tools to evaluate and build controlled-release devices\u003c\/li\u003e \u003cli\u003eIncludes classical and analytical techniques to solve boundary-value problems involving two- and three-dimensional partial differential equations\u003c\/li\u003e \u003cli\u003eProvides detailed examples, case studies and step-by-step analytical solutions to relevant problems using popular computational software\u003c\/li\u003e \u003c\/ul\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003eAcknowledgements xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Steady-State Analysis of a Two-Dimensional Model for Percutaneous Drug Transport 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Separation of Variables in 2-D Cartesian Coordinates1\u003c\/p\u003e \u003cp\u003e1.2 Model for Drug Transport across the Skin 3\u003c\/p\u003e \u003cp\u003e1.3 Analytical Solution of the Diffusion Model in 2-D Cartesian Systems 4\u003c\/p\u003e \u003cp\u003e1.4 Summary 6\u003c\/p\u003e \u003cp\u003e1.5 Appendix: Maple, Mathematica, and Maxima Code Listings 6\u003c\/p\u003e \u003cp\u003eProblems 10\u003c\/p\u003e \u003cp\u003eReferences 12\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Constant Drug Release from a Hollow Cylinder of Finite Length in Two Dimensions 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Separation of Variables in 2-D Cylindrical Coordinates 13\u003c\/p\u003e \u003cp\u003e2.2 Model for Drug Release from a Hollow Cylinder 15\u003c\/p\u003e \u003cp\u003e2.3 Analytical Solution of the Transport Model in 2-D Cylindrical Coordinates 15\u003c\/p\u003e \u003cp\u003e2.4 Summary 19\u003c\/p\u003e \u003cp\u003e2.5 Appendix: Maple Code Listings 19\u003c\/p\u003e \u003cp\u003eProblems 20\u003c\/p\u003e \u003cp\u003eReferences 20\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Analysis of Steady-State Growth Factor Transport Through Double-Layered Scaffolds 23\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Governing Steady-State Transport Equations 23\u003c\/p\u003e \u003cp\u003e3.2 Solution Procedure for Transport Through a Two-Layered Scaffold 25\u003c\/p\u003e \u003cp\u003e3.3 Concentration Profile of Vascular Endothelial Growth Factor in Two Layers 31\u003c\/p\u003e \u003cp\u003e3.4 Summary 32\u003c\/p\u003e \u003cp\u003e3.5 Appendix: Maple Code Listings 33\u003c\/p\u003e \u003cp\u003eProblems 37\u003c\/p\u003e \u003cp\u003eReferences 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Steady-State Two-Dimensional Diffusion in a Hollow Sphere 39\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Separation of Variables and Legendre Polynomials in 2-D Spherical Coordinates 39\u003c\/p\u003e \u003cp\u003e4.2 Model For 2-D Diffusion in a Sphere 43\u003c\/p\u003e \u003cp\u003e4.3 Analytical Solution of 2-D Diffusion in Spherical Coordinates 46\u003c\/p\u003e \u003cp\u003e4.4 Summary 49\u003c\/p\u003e \u003cp\u003e4.5 Appendix: Maple, Mathematica, and Maxima Code Listings 49\u003c\/p\u003e \u003cp\u003eProblems 56\u003c\/p\u003e \u003cp\u003eReferences 57\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Steady-State Three-Dimensional Drug Diffusion through Membranes from Distributed Sources 59\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Separation of Variables in 3-D Cartesian Coordinates 59\u003c\/p\u003e \u003cp\u003e5.2 Transport across the Membrane 61\u003c\/p\u003e \u003cp\u003e5.3 Analytical Solution of the Diffusion Model in 3-D Cartesian Systems 63\u003c\/p\u003e \u003cp\u003e5.4 Summary 68\u003c\/p\u003e \u003cp\u003e5.5 Appendix: Maple Code Listings 69\u003c\/p\u003e \u003cp\u003eProblems 73\u003c\/p\u003e \u003cp\u003eReferences 73\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Constant Drug Release from a Hollow Cylinder of Finite Length in Three Dimensions 75\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Separation of Variables in 3-D Cylindrical Coordinates 75\u003c\/p\u003e \u003cp\u003e6.2 Model For 3-D Drug Release from a Hollow Cylinder 77\u003c\/p\u003e \u003cp\u003e6.3 Analytical Solution of the Transport Model in 3-D Cylindrical Coordinates 78\u003c\/p\u003e \u003cp\u003e6.4 Summary 84\u003c\/p\u003e \u003cp\u003e6.5 Appendix: Maple Code Listings 85\u003c\/p\u003e \u003cp\u003eProblems 87\u003c\/p\u003e \u003cp\u003eReferences 87\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Sustained Drug Release from a Hollow Sphere in Three Dimensions 89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Method of Green’s Function in 3-D Spherical Coordinates 89\u003c\/p\u003e \u003cp\u003e7.2 Model for Molecular Transport across the Wall of a Hollow Sphere 95\u003c\/p\u003e \u003cp\u003e7.3 Analytical Solution of the Transport Model in 3-D Spherical Coordinates 96\u003c\/p\u003e \u003cp\u003e7.4 Summary 97\u003c\/p\u003e \u003cp\u003e7.5 Appendix: Maple, Mathematica and Maxima Code Listings 98\u003c\/p\u003e \u003cp\u003eProblems 105\u003c\/p\u003e \u003cp\u003eReferences 105\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Analysis of Transient Growth Factor Transport Through Double-Layered Scaffolds 107\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Laplace and Fourier-Bessel-based Methods in 2-D Cylindrical Coordinates 107\u003c\/p\u003e \u003cp\u003e8.2 Governing Equations for Transport through Double-Layered Scaffolds 112\u003c\/p\u003e \u003cp\u003e8.3 Concentration Profile of Vascular Endothelial Growth Factor in Two Layers 114\u003c\/p\u003e \u003cp\u003e8.4 Summary 119\u003c\/p\u003e \u003cp\u003e8.5 Appendix: Maple Code Listings 120\u003c\/p\u003e \u003cp\u003eProblems 126\u003c\/p\u003e \u003cp\u003eReferences 126\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Molecular Diffusion through the Stomach Lining and into the Bloodstream 129\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Laplace Transforms, Legendre Functions and Spherical Harmonics129\u003c\/p\u003e \u003cp\u003e9.2 Spherical Diffusion in Three Dimensions 132\u003c\/p\u003e \u003cp\u003e9.3 Analytical Solution of the Transient Transport Model in 3-D Spherical Coordinates 133\u003c\/p\u003e \u003cp\u003e9.4 Summary 138\u003c\/p\u003e \u003cp\u003e9.5 Appendix: Maple Code Listings 138\u003c\/p\u003e \u003cp\u003eProblems 141\u003c\/p\u003e \u003cp\u003eReferences 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Diffusion-Controlled Ligand Binding to Receptors on Cell Surfaces 145\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Weber’s Integral 145\u003c\/p\u003e \u003cp\u003e10.2 Steady-State Diffusion-Limited Ligand Binding 148\u003c\/p\u003e \u003cp\u003e10.3 Transient Diffusion-Controlled Ligand Binding in 2-D Cylindrical Coordinates 151\u003c\/p\u003e \u003cp\u003e10.4 Summary 156\u003c\/p\u003e \u003cp\u003e10.5 Appendix: Maple, Mathematica and Maxima Code Listings 156\u003c\/p\u003e \u003cp\u003eProblems 167\u003c\/p\u003e \u003cp\u003eReferences 168\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Two-Dimensional Analysis of a Cylindrical Matrix Device with a Small Hole For Drug Release 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Mathematical Modeling of Drug Transport through the Device 169\u003c\/p\u003e \u003cp\u003e11.2 Drug Concentration Profile inside the Matrix 171\u003c\/p\u003e \u003cp\u003e11.3 Normalized Cumulative Percentage of Drug Released 177\u003c\/p\u003e \u003cp\u003e11.4 Summary 178\u003c\/p\u003e \u003cp\u003e11.5 Appendix: Maple Code Listings 178\u003c\/p\u003e \u003cp\u003eProblems 182\u003c\/p\u003e \u003cp\u003eReferences 183\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Three-Dimensional Drug Diffusion through Membranes from Distributed Sources 185\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Governing Equations of the Transport Model 185\u003c\/p\u003e \u003cp\u003e12.2 Analytical Solution of the Diffusion Model in 3-D Cartesian Systems 187\u003c\/p\u003e \u003cp\u003e12.3 Average Dimensionless Concentration and Flux 194\u003c\/p\u003e \u003cp\u003e12.4 Summary 194\u003c\/p\u003e \u003cp\u003e12.5 Appendix: Maple and Mathematica Code Listings 195\u003c\/p\u003e \u003cp\u003eProblems 207\u003c\/p\u003e \u003cp\u003eReferences 207\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Effective Time Constant for Two- and Three-Dimensional Controlled-Released Drug-Delivery Models 209\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Effective Time Constant in Controlled-Release Drug-Delivery Systems 209\u003c\/p\u003e \u003cp\u003e13.2 Intravitreal Drug Delivery using a 2-D Cylindrical Model 210\u003c\/p\u003e \u003cp\u003e13.3 Analysis of a Rectangular Parallelepiped-Shaped Matrix with a Release Area 218\u003c\/p\u003e \u003cp\u003e13.4 Summary 225\u003c\/p\u003e \u003cp\u003e13.5 Appendix: Maple and Mathematica Code Listings 225\u003c\/p\u003e \u003cp\u003eProblems 232\u003c\/p\u003e \u003cp\u003eReferences 232\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Data Fitting For Two- and Three-Dimensional Controlled- Release Drug-Delivery Models 233\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Data Fitting in Controlled-Release Drug-Delivery Systems 233\u003c\/p\u003e \u003cp\u003e14.2 Estimation of Diffusion Coefficient in a Solid Cylinder of Finite Length 234\u003c\/p\u003e \u003cp\u003e14.3 Estimation of Diffusion Coefficient in a Rectangular Parallelepiped-Shaped Matrix 240\u003c\/p\u003e \u003cp\u003e14.4 Summary 243\u003c\/p\u003e \u003cp\u003e14.5 Appendix: Maple and Mathematica Code Listings 244\u003c\/p\u003e \u003cp\u003eProblems 256\u003c\/p\u003e \u003cp\u003eReferences 258\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Optimization of Two- and Three-Dimensional Controlled-Released Drug-Delivery Models 259\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Optimum Design of Controlled-Released Drug-Delivery Systems 259\u003c\/p\u003e \u003cp\u003e15.2 Design of a 2-D Cylindrical Dosage Form with a Finite Mass Transfer Coefficient 260\u003c\/p\u003e \u003cp\u003e15.3 Design of a Rectangular Parallelepiped-Shaped Matrix with a Finite Mass Transfer Coefficient 265\u003c\/p\u003e \u003cp\u003e15.4 Summary 268\u003c\/p\u003e \u003cp\u003e15.5 Appendix: Maple and Mathematica Code Listings 268\u003c\/p\u003e \u003cp\u003eProblems 282\u003c\/p\u003e \u003cp\u003eReferences 283\u003c\/p\u003e \u003cp\u003eIndex 285\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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