{"product_id":"method-of-lines-pde-analysis-in-biomedical-science-and-engineering-isbn-9781119130482","title":"Method of Lines PDE Analysis in Biomedical Science and Engineering","description":"\u003cp\u003e\u003cb\u003ePresents the methodology and applications of\u003c\/b\u003e \u003cb\u003eODE and PDE models within biomedical science and engineering \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eWith an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration\u003ci\u003e, Method of Lines PDE Analysis in Biomedical Science and Engineering \u003c\/i\u003edemonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE). Written by a well-known researcher in the field, the book provides an introduction to basic numerical methods for initial\/boundary value PDEs before moving on to specific BMSE applications of PDEs.\u003c\/p\u003e \u003cp\u003eFeaturing a straightforward approach, the book’s chapters follow a consistent and comprehensive format. First, each chapter begins by presenting the model as an ordinary differential equation (ODE)\/PDE system, including the initial and boundary conditions.  Next, the programming of the model equations is introduced through a series of R routines that primarily implement MOL for PDEs. Subsequently, the resulting numerical and graphical solution is discussed and interpreted with respect to the model equations. Finally, each chapter concludes with a review of the numerical algorithm performance, general observations and results, and possible extensions of the model. \u003ci\u003eMethod of Lines PDE Analysis in Biomedical Science and Engineering\u003c\/i\u003e also includes:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eExamples of MOL analysis of PDEs, including BMSE applications in wave front resolution in chromatography, VEGF angiogenesis, thermographic tumor location, blood-tissue transport, two fluid and membrane mass transfer, artificial liver support system, cross diffusion epidemiology, oncolytic virotherapy, tumor cell density in glioblastomas, and variable grids\u003c\/li\u003e \u003cli\u003eDiscussions on the use of R software, which facilitates immediate solutions to differential equation problems without having to first learn the basic concepts of numerical analysis for PDEs and the programming of PDE algorithms\u003c\/li\u003e \u003cli\u003eA companion website that provides source code for the R routines\u003c\/li\u003e \u003c\/ul\u003e \u003ci\u003eMethod of Lines PDE Analysis in Biomedical Science and Engineering\u003c\/i\u003e is an introductory reference for researchers, scientists, clinicians, medical researchers, mathematicians, statisticians, chemical engineers, epidemiologists, and pharmacokineticists as well as anyone interested in clinical applications and the interpretation of experimental data with differential equation models. The book is also an ideal textbook for graduate-level courses in applied mathematics, BMSE, biology, biophysics, biochemistry, medicine, and engineering. \u003cp\u003ePreface xi\u003cbr\u003eAbout the Companion Website xiii\u003cbr\u003e\u003cbr\u003e1 An Introduction to MOL Analysis of PDEs: Wave Front Resolution in Chromatography 1\u003cbr\u003e1.1 1D 2-PDE model, 2\u003cbr\u003e1.2 MOL routines, 7\u003cbr\u003e1.2.1 Main program, 7\u003cbr\u003e1.2.2 MOL\/ODE routine, 16\u003cbr\u003e1.2.3 Subordinate routines, 20\u003cbr\u003e1.3 Model output, single component chromatography, 21\u003cbr\u003e1.3.1 FDs, step BC, 21\u003cbr\u003e1.3.2 Flux limiters, step BC, 39\u003cbr\u003e1.3.3 FDs, pulse BC, 48\u003cbr\u003e1.3.4 Flux limiters, pulse BC, 50\u003cbr\u003e1.4 Multi component model, 53\u003cbr\u003e1.5 MOL routines, 54\u003cbr\u003e1.5.1 Main program, 54\u003cbr\u003e1.5.2 MOL\/ODE routine, 62\u003cbr\u003e1.6 Model output, multi component chromatography, 67\u003cbr\u003eReferences, 68\u003cbr\u003e\u003cbr\u003e2 Wave Front Resolution in VEGF Angiogenesis 69\u003cbr\u003e2.1 1D 2-PDE model, 70\u003cbr\u003e2.2 MOL routines, 72\u003cbr\u003e2.2.1 Main program, 72\u003cbr\u003e2.2.2 MOL\/ODE routine, 81\u003cbr\u003e2.2.3 Subordinate routines, 85\u003cbr\u003e2.3 Model output, 86\u003cbr\u003e2.3.1 Comparison of numerical and analytical solutions, 86\u003cbr\u003e2.3.2 Effect of diffusion on the traveling-wave solution, 88\u003cbr\u003e2.4 Conclusions, 88\u003cbr\u003eReferences, 89\u003cbr\u003e\u003cbr\u003e3 Thermographic Tumor Location 91\u003cbr\u003e3.1 2D, 1-PDE model, 92\u003cbr\u003e3.2 MOL analysis, 94\u003cbr\u003e3.2.1 ODE routine, 94\u003cbr\u003e3.2.2 Main program, 100\u003cbr\u003e3.3 Model output, 105\u003cbr\u003e3.4 Summary and conclusions, 110\u003cbr\u003eReferences, 111\u003cbr\u003e\u003cbr\u003e4 Blood-Tissue Transport 113\u003cbr\u003e4.1 1D 2-PDE model, 114\u003cbr\u003e4.2 MOL routines, 115\u003cbr\u003e4.2.1 MOL\/ODE routine, 115\u003cbr\u003e4.2.2 Main program, 119\u003cbr\u003e4.2.3 Bessel function routine, 128\u003cbr\u003e4.3 Model output, 129\u003cbr\u003e4.4 Model extensions, 133\u003cbr\u003e4.5 Conclusions and summary, 142\u003cbr\u003eReferences, 143\u003cbr\u003e\u003cbr\u003e5 Two-Fluid\/Membrane Model 145\u003cbr\u003e5.1 2D, 3-PDE model, 146\u003cbr\u003e5.2 MOL analysis, 147\u003cbr\u003e5.2.1 MOL\/ODE routine, 148\u003cbr\u003e5.2.2 Main program, 153\u003cbr\u003e5.3 Model output, 160\u003cbr\u003e5.4 Summary and conclusions, 162\u003cbr\u003e\u003cbr\u003e6 Liver Support Systems 165\u003cbr\u003e6.1 2-ODE patient model, 166\u003cbr\u003e6.2 Patient ODE model routines, 167\u003cbr\u003e6.2.1 Main program, 167\u003cbr\u003e6.2.2 ODE routine, 172\u003cbr\u003e6.3 Model output, 174\u003cbr\u003e6.4 8-PDE ALSS model, 176\u003cbr\u003e6.4.1 Membrane unit MU1, 177\u003cbr\u003e6.4.2 Adsorption unit AU1, 177\u003cbr\u003e6.4.3 Adsorption unit AU2, 178\u003cbr\u003e6.4.4 Membrane unit MU2, 179\u003cbr\u003e6.5 Patient-ALSS ODE\/PDE model routines, 180\u003cbr\u003e6.5.1 Main program, 180\u003cbr\u003e6.5.2 ODE routine, 188\u003cbr\u003e6.6 Model output, 195\u003cbr\u003e6.7 Summary and conclusions, 196\u003cbr\u003eAppendix - Derivation of PDEs for Membrane and Adsorption Units, 200\u003cbr\u003eA.1 PDEs for Membrane Units, 200\u003cbr\u003eA.2 PDEs for Adsorption Units, 202\u003cbr\u003eReferences, 203\u003cbr\u003e\u003cbr\u003e7 Cross Diffusion Epidemiology Model 205\u003cbr\u003e7.1 2-PDE model, 205\u003cbr\u003e7.2 Model routines, 207\u003cbr\u003e7.2.1 Main program, 207\u003cbr\u003e7.2.2 ODE routine, 215\u003cbr\u003e7.3 Model output, 218\u003cbr\u003e7.3.1 ncase = 1, time-invariant solution, 218\u003cbr\u003e7.3.2 ncase = 2, transient solution, no cross diffusion, 220\u003cbr\u003e7.3.3 ncase = 3, transient solution with cross diffusion, 222\u003cbr\u003e7.4 Summary and conclusions, 224\u003cbr\u003eReference, 225\u003cbr\u003e\u003cbr\u003e8 Oncolytic Virotherapy 227\u003cbr\u003e8.1 1D 4-PDE model, 228\u003cbr\u003e8.2 MOL routines, 229\u003cbr\u003e8.2.1 Main program, 230\u003cbr\u003e8.2.2 MOL\/ODE routine, 240\u003cbr\u003e8.2.3 Subordinate routine, 245\u003cbr\u003e8.3 Model output, 246\u003cbr\u003e8.4 Summary and conclusions, 273\u003cbr\u003eReference, 274\u003cbr\u003e\u003cbr\u003e9 Tumor Cell Density in Glioblastomas 275\u003cbr\u003e9.1 1D PDE model, 276\u003cbr\u003e9.2 MOL routines, 277\u003cbr\u003e9.2.1 Main program, 277\u003cbr\u003e9.2.2 MOL\/ODE routine, 286\u003cbr\u003e9.3 Model output, 289\u003cbr\u003e9.3.1 Output for ncase = 1, linear, 290\u003cbr\u003e9.3.2 Output for ncase = 2, logistic, 295\u003cbr\u003e9.3.3 Output for ncase = 3, Gompertz, 296\u003cbr\u003e9.4 p-refinement error analysis, 299\u003cbr\u003e9.5 Summary and conclusions, 301\u003cbr\u003eReferences, 301\u003cbr\u003e\u003cbr\u003e10 MOL Analysis with a Variable Grid: Antigen-Antibody Binding Kinetics 303\u003cbr\u003e10.1 ODE\/PDE model, 303\u003cbr\u003e10.2 MOL routines, 306\u003cbr\u003e10.2.1 Main program, 306\u003cbr\u003e10.2.2 MOL\/ODE routine, 314\u003cbr\u003e10.3 Model output, 318\u003cbr\u003e10.3.1 Uniform grid, 318\u003cbr\u003e10.3.2 Variable grid, 321\u003cbr\u003e10.4 Summary and conclusions, 325\u003cbr\u003eAppendix: Variable Grid Analysis, 327\u003cbr\u003eA.1 Derivation of numerical differentiators, 327\u003cbr\u003eA.2 Testing of numerical differentiators, 331\u003cbr\u003eA.2.1 Differentiation matrix, 331\u003cbr\u003eA.2.2 Test functions, 332\u003cbr\u003eReferences, 340\u003cbr\u003e\u003cbr\u003eAppendices\u003cbr\u003eAppendix A Derivation of Convection-Diffusion-Reaction\u003cbr\u003ePartial Differential Equations 341\u003cbr\u003eAppendix B Functions dss012, dss004, dss020, vanl 345\u003cbr\u003eIndex 351\u003c\/p\u003e \u003cp\u003e\"This book demonstrates the use of numerical methods for the computer solution of partial differential equations (PDEs) as applied to biomedical science and engineering...The book is worth reading not only for mathematicians but also for, e.g., chemical engineers, medical researchers, clinicians, epidemiologists and statisticians.\" (\u003ci\u003eMathematical Reviews\/MathSciNet\u003c\/i\u003e June 2017)\u003c\/p\u003e \u003cb\u003eWilliam E. Schiesser, PhD, ScD (hon.)\u003c\/b\u003e, is Emeritus McCann Professor of Biomolecular and Chemical Engineering and Professor of Mathematics at Lehigh University. His research interests include numerical software; ordinary, differential algebraic, and partial differential equations; and computational mathematics. Dr. Schiesser is the author or coauthor of fifteen books, including \u003ci\u003eDifferential Equation \u003c\/i\u003e\u003ci\u003eAnalysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R\u003c\/i\u003e and \u003ci\u003eDifferential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation\u003c\/i\u003e \u003ci\u003eApplications with R\u003c\/i\u003e, both published by Wiley. \u003cp\u003eWith an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, \u003ci\u003eMethod of Lines PDE Analysis in Biomedical Science and Engineering \u003c\/i\u003edemonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE). Written by a well-known researcher in the field, the book provides an introduction to basic numerical methods for initial\/boundary value PDEs before moving on to specific BMSE applications of PDEs.\u003c\/p\u003e \u003cp\u003eFeaturing a straightforward approach, the book’s chapters follow a consistent and comprehensive format. First, each chapter begins by presenting the model as an ordinary differential equation (ODE)\/PDE system, including the initial and boundary conditions. Next, the programming of the model equations is introduced through a series of R routines that primarily implement MOL for PDEs. Subsequently, the resulting numerical and graphical solution is discussed and interpreted with respect to the model equations. Finally, each chapter concludes with a review of the numerical algorithm performance, general observations and results, and possible extensions of the model\u003ci\u003e. Method of Lines PDE Analysis in\u003c\/i\u003e \u003ci\u003eBiomedical Science and Engineering \u003c\/i\u003ealso includes:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eExamples of MOL analysis of PDEs, including BMSE applications in wave front resolution in chromatography, VEGF angiogenesis, thermographic tumor location, blood-tissue transport, two fluid and membrane mass transfer, artificial liver support system, cross diffusion epidemiology, oncolytic virotherapy, tumor cell density in glioblastomas, and variable MOL grids\u003c\/li\u003e \u003c\/ul\u003e \u003cul\u003e \u003cli\u003eDiscussions on the use of R software, which facilitate immediate solutions to differential equation models without having to first learn the basic concepts of numerical analysis for PDEs and the programming of PDE algorithms\u003c\/li\u003e \u003c\/ul\u003e \u003cul\u003e \u003cli\u003eA companion website that provides source code for the R routines\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eMethod of Lines PDE Analysis in Biomedical Science and Engineering \u003c\/i\u003eis an introductory reference for researchers, scientists, clinicians, medical researchers, mathematicians, statisticians, chemical engineers, epidemiologists, and pharmacokineticists as well as anyone interested in clinical applications and the interpretation of experimental data with differential equation models. The book is also an ideal textbook for graduate-level courses in applied mathematics, BMSE, biology, biophysics, biochemistry, medicine, and engineering.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989614510309,"sku":"NP9781119130482","price":128.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119130482.jpg?v=1761784816","url":"https:\/\/k12savings.com\/es\/products\/method-of-lines-pde-analysis-in-biomedical-science-and-engineering-isbn-9781119130482","provider":"K12savings","version":"1.0","type":"link"}