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Splines And Compartment Models

Author: Karl-Ernst Biebler
Publisher: World Scientific
ISBN: 9814522244
Size: 51.33 MB
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This book presents methods of mathematical modeling from two points of view. Splines provide a general approach while compartment models serve as examples for context related to modeling. The preconditions and characteristics of the developed mathematical models as well as the conditions surrounding data collection and model fit are taken into account. The substantial statements of this book are mathematically proven. The results are ready for application with examples and related program codes given. In this book, splines are algebraically developed such that the reader or user can easily understand and vary the numerical construction of the different kinds of spline functions. The classical compartment models of the pharmacokinetics are systematically analyzed and connected with lifetime distributions. As such, parameter estimation and model fit can be treated statistically with a varied minimum chi-square method. This method is applicable for single kinetics and also allows the calculation of average kinetics. Contents:Spline Models:Why Spline Functions?Interpolating Splines of Degree nInterpolating Cubic SplinesSmoothing Natural Cubic Splines and the Choice of the Smoothing ParameterInterpolating Quadratic SplinesInterpolating Quadratic Splines and ParabolasSmoothing Quadratic SplinesSplines and Average FunctionsCompartment Models:Concept of a Context Related Mathematical Pharmacokinetical ModelCompartment ModelsOther Deterministic ModelsCalculability and IdentifiabilityCompartment Models and Associated Residence Time DistributionsOther Stochastic ModelsCalculation Methods Related to Compartment ModelsSelection of Pharmacokinetic ModelsPharmacokinetics for Multiple ApplicationsMathematica® Programs for Selected Problems Readership: Graduate students in biomathematics, medicine, pharmacy and human biology. Professionals like bio-mathematicians, pharmacologists, clinical pharmacologists, pharmacists, doctors engaged in clinical research, scientists in pharmaceutical R&D and scientific staff in the life sciences. Keywords:Mathematical Modeling;Model Selection;Pharmacokinetics;Compartment Models;Minimum Chi-square Estimation;Pharmacokinetics for Multiple Applications;Residence Time DistributionsKey Features:This book treats modeling and data interpretation as a whole, and the qualities of the developed methods are mathematically characterizedNew application of the varied minimum chi-square method for the parameter calculation and the model choice in the pharmacokineticsThe developed methods are ready for application. The reader/user will be able to modify the given solutionsReviews: “Part 2 is very pleasant reading which is completely suited for both course segments in teaching numerical analysis and seminars on the topics in the curriculum of applied mathematicians… I warmly recommend the book for applied mathematicians working in collaboration with medical, pharmacological and chemical institutes. Also, it is an excellent auxiliary material in the education of numerical mathematics.” Acta Scientiarum Mathematicarum

Spline Functions

Author: Larry L. Schumaker
Publisher: SIAM
ISBN: 1611973902
Size: 49.50 MB
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This book describes in detail the key algorithms needed for computing with spline functions and illustrates their use in solving several basic problems in numerical analysis, including function approximation, numerical quadrature, data fitting, and the numerical solution of PDE's. The focus is on computational methods for bivariate splines on triangulations in the plane and on the sphere, although both univariate and tensor-product splines are also discussed. The book contains numerous examples and figures to illustrate the methods and their performance. All of the algorithms in the book have been coded in a separate MATLAB package available for license. The package can be used to run all of the examples in the book and also provides readers with the essential tools needed to create software for their own applications. In addition to the included bibliography, a list of over 100 pages of additional references can be found on the book's website.

Comprehensive Biomedical Physics

Publisher: Newnes
ISBN: 0444536337
Size: 51.30 MB
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Comprehensive Biomedical Physics is a new reference work that provides the first point of entry to the literature for all scientists interested in biomedical physics. It is of particularly use for graduate and postgraduate students in the areas of medical biophysics. This Work is indispensable to all serious readers in this interdisciplinary area where physics is applied in medicine and biology. Written by leading scientists who have evaluated and summarized the most important methods, principles, technologies and data within the field, Comprehensive Biomedical Physics is a vital addition to the reference libraries of those working within the areas of medical imaging, radiation sources, detectors, biology, safety and therapy, physiology, and pharmacology as well as in the treatment of different clinical conditions and bioinformatics. This Work will be valuable to students working in all aspect of medical biophysics, including medical imaging and biomedical radiation science and therapy, physiology, pharmacology and treatment of clinical conditions and bioinformatics. The most comprehensive work on biomedical physics ever published Covers one of the fastest growing areas in the physical sciences, including interdisciplinary areas ranging from advanced nuclear physics and quantum mechanics through mathematics to molecular biology and medicine Contains 1800 illustrations, all in full color

Nonlinear Regression

Author: George A. F. Seber
Publisher: John Wiley & Sons
ISBN: 9780471471356
Size: 80.35 MB
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WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. From the Reviews of A User?s Guide to Principal Components "The book is aptly and correctly named?A User?s Guide. It is the kind of book that a user at any level, novice or skilled practitioner, would want to have at hand for autotutorial, for refresher, or as a general-purpose guide through the maze of modern PCA." ?Technometrics "I recommend A User?s Guide to Principal Components to anyone who is running multivariate analyses, or who contemplates performing such analyses. Those who write their own software will find the book helpful in designing better programs. Those who use off-the-shelf software will find it invaluable in interpreting the results." ?Mathematical Geology

Comparative Pharmacokinetics

Author: Jim E. Riviere
Publisher: John Wiley & Sons
ISBN: 9780470959886
Size: 42.36 MB
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Now in a revised edition, Comparative Pharmacokinetics: Principles, Techniques, and Applications presents the principles and techniques of comparative and veterinary pharmacokinetics in a detailed yet practical manner. Developed as a tool for ensuring that pharmacokinetics studies are properly designed and correctly interpreted, the book provides complete coverage of the conceptual basis of pharmacokinetics as used for quantifying biological processes from the perspectives of physiology and medicine. New chapters have been added on quantitative structure permeability relationships and bioequivalence, and a number of existing chapters have been significantly revised and expanded to provide a current resource for veterinary and comparative pharmacokinetics.

Physics Of Pet And Spect Imaging

Author: Magnus Dahlbom
Publisher: CRC Press
ISBN: 1315356783
Size: 74.46 MB
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PET and SPECT imaging has improved to such a level that they are opening up exciting new horizons in medical diagnosis and treatment. This book provides a complete introduction to fundamentals and the latest progress in the field, including an overview of new scintillator materials and innovations in photodetector development, as well as the latest system designs and image reconstruction algorithms. It begins with basics of PET and SPECT physics, followed by technology advances and computing methods, quantitative techniques, multimodality imaging, instrumentation, pre-clinical and clinical imaging applications.


Author: Ene I. Ette
Publisher: John Wiley & Sons
ISBN: 1118679512
Size: 39.69 MB
Format: PDF
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Pharmacometrics is the science of interpreting and describing pharmacology in a quantitative fashion. The pharmaceutical industry is integrating pharmacometrics into its drug development program, but there is a lack of and need for experienced pharmacometricians since fewer and fewer academic programs exist to train them. Pharmacometrics: The Science of Quantitative Pharmacology lays out the science of pharmacometrics and its application to drug development, evaluation, and patient pharmacotherapy, providing a comprehensive set of tools for the training and development of pharmacometricians. Edited and written by key leaders in the field, this flagship text on pharmacometrics: Integrates theory and practice to let the reader apply principles and concepts. Provides a comprehensive set of tools for training and developing expertise in the pharmacometric field. Is unique in including computer code information with the examples. This volume is an invaluable resource for all pharmacometricians, statisticians, teachers, graduate and undergraduate students in academia, industry, and regulatory agencies.

Energy Metabolism

Author: Patrick Christian Even
Publisher: Frontiers E-books
ISBN: 288919308X
Size: 28.29 MB
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Energy metabolism is central to life and altered energy expenditure (EE) is often cited as a central mechanism responsible for development of the obese phenotype. Resting EE, EE of physical activity, cold induced thermogenesis and thermic effect of feeding add to produce total EE but can also affect each other. It is thus very important that each component be well measured. Measuring energy expenditure by indirect calorimetry is extremely simple in theory but the practice if far more difficult. Taking into account temperature in small sized animals, measuring accurately the effect of activity on EE, correcting EE for body size body composition, age sex etc… add difficulties in producing reliable data. The goal of this Research Topic was to call for the practical experience of main investigators trained to practice calorimetry in order to get their feedback and the way they deal with the various and specific problems of humans and animal calorimetry. The goal is to share the questions/solutions experienced by the contributors to inititate a “guide of the good practices” that can be periodically updated and used by all those who are and will be interested in measuring energy metabolism from the 20g mouse to the human and large farm animals.