{"product_id":"closed-form-solutions-for-drug-transport-through-controlled-release-devices-in-two-and-three-dimensions-isbn-9781118947258","title":"Closed-form Solutions for Drug Transport through Controlled-Release Devices in Two and Three Dimensions","description":"\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 \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 \u003cb\u003eLaurent Simon\u003c\/b\u003e, 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).\u003cbr\u003e\u003cbr\u003e\u003cb\u003eJuan Ospina\u003c\/b\u003e 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. \u003cp\u003eProvides solutions for two- and three-dimensional linear models of controlled-release systems\u003cbr\u003e\u003cbr\u003eDesigned to administer an exact dosage of an API to a target site during a treatment period, controlled-release drug-delivery systems regulate the therapeutic agent release rate while it is being delivered to a particular location\u003cbr\u003e\u003cbr\u003e\u003ci\u003eClosed-form Solutions for Drug Transport through Controlled-Release Devices in Two and Three Dimensions \u003c\/i\u003ecovers various classical and analytical techniques to solve boundary-value problems involving two- and three-dimensional partial differential equations (PDEs.) These methods are applied to study drug-transport mechanisms in 2-D and 3-D coordinate systems and result in a detailed picture of the evolution of active pharmaceutical ingredients (APIs) through a controlled-released (CR) device or a membrane.\u003cbr\u003e\u003cbr\u003eMathematical modeling platforms, that can represent the transport mechanisms adequately, are important assets in the fabrication of these products, as well. This book shows how analytical tools, routinely used by physicists, mathematicians and engineers, can be implemented to guide the design of CR devices. A host of diverse real-world applications are taken from the literature to help illustrate the methods in Cartesian, cylindrical and spherical coordinate systems. \u003cbr\u003e\u003cbr\u003e\u003ci\u003eClosed-form Solutions for Drug Transport through Controlled-Release Devices in Two and Three Dimensions \u003c\/i\u003efeatures:\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 \u003c\/ul\u003e \u003cul\u003e \u003cli\u003eModeling of drug-delivery systems and provide mathematical tools to evaluate and build controlled-release devices\u003c\/li\u003e \u003c\/ul\u003e \u003cul\u003e \u003cli\u003eClassical and analytical techniques to solve boundary-value problems involving two- and three-dimensional partial differential equations\u003c\/li\u003e \u003c\/ul\u003e \u003cul\u003e \u003cli\u003eDetailed examples, case studies and step-by-step analytical solutions to relevant problems using popular computational software\u003c\/li\u003e \u003c\/ul\u003e \u003cbr\u003eThe textbook is presented in a manner to help the reader apply the theory to their problems. For researchers in the field, the integration of modeling and simulations at an early design stage is crucial in the development of new technologies. The materials covered in the book will help provide a good foundation for anyone who wishes to be involved in cutting-edge drug-delivery research.\u003cbr\u003e\u003cbr\u003eLaurent 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).\u003cbr\u003e\u003cbr\u003eJuan Ospina is currently an Assistant Professor at EAFIT University in the Logic and Computation Group, Physics Engineering Program. He has published numerous article on the topic of mathematical physics.","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988936179941,"sku":"NP9781118947258","price":128.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118947258.jpg?v=1761782120","url":"https:\/\/k12savings.com\/products\/closed-form-solutions-for-drug-transport-through-controlled-release-devices-in-two-and-three-dimensions-isbn-9781118947258","provider":"K12savings","version":"1.0","type":"link"}