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Splines And Compartment Models

Author: Karl-Ernst Biebler
Publisher: World Scientific
ISBN: 9814522244
Size: 45.20 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: 77.53 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.

Compartmental Modeling And Tracer Kinetics

Author: David H. Anderson
Publisher: Springer Science & Business Media
ISBN: 3642518613
Size: 11.60 MB
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This monograph is concerned with mathematical aspects of compartmental an alysis. In particular, linear models are closely analyzed since they are fully justifiable as an investigative tool in tracer experiments. The objective of the monograph is to bring the reader up to date on some of the current mathematical prob lems of interest in compartmental analysis. This is accomplished by reviewing mathematical developments in the literature, especially over the last 10-15 years, and by presenting some new thoughts and directions for future mathematical research. These notes started as a series of lectures that I gave while visiting with the Division of Applied ~1athematics, Brown University, 1979, and have developed in to this collection of articles aimed at the reader with a beginning graduate level background in mathematics. The text can be used as a self-paced reading course. With this in mind, exercises have been appropriately placed throughout the notes. As an aid in reading the material, the e~d of a proof is indicated by ~. Sub section titles are utilized to make it easier for the reader to skim over detailed material on a first reading and make the entire manuscript somewhat more accessible, especially to nonmathematicians in the biosciences. The preparation of this monograph has been a long task that would not have been completed without the influence of a number of individuals. I am especially indebted to H. T. Banks, J. W. Drane, J. Eisenfe1d, J. A. Jacquez, D. J.

An Introduction To Differential Equations

Author: Anil G Ladde
Publisher: World Scientific Publishing Company
ISBN: 9814397393
Size: 12.39 MB
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Volume 1: Deterministic Modeling, Methods and Analysis For more than half a century, stochastic calculus and stochastic differential equations have played a major role in analyzing the dynamic phenomena in the biological and physical sciences, as well as engineering. The advancement of knowledge in stochastic differential equations is spreading rapidly across the graduate and postgraduate programs in universities around the globe. This will be the first available book that can be used in any undergraduate/graduate stochastic modeling/applied mathematics courses and that can be used by an interdisciplinary researcher with a minimal academic background. An Introduction to Differential Equations: Volume 2 is a stochastic version of Volume 1 (“An Introduction to Differential Equations: Deterministic Modeling, Methods and Analysis”). Both books have a similar design, but naturally, differ by calculi. Again, both volumes use an innovative style in the presentation of the topics, methods and concepts with adequate preparation in deterministic Calculus. Errata Errata (32 KB)

Applications Of Epidemiological Models To Public Health Policymaking

Author: Zhilan Feng
Publisher: World Scientific
ISBN: 9814522368
Size: 34.27 MB
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Mathematical models can be very helpful to understand the transmission dynamics of infectious diseases. This book presents examples of epidemiological models and modeling tools that can assist policymakers to assess and evaluate disease control strategies. Contents:Mathematical Modeling in Epidemiology:Epidemic ModelsEndemic ModelsApplications to Public Health Policymaking:Applications of Models to Evaluations of Disease Control StrategiesDevelopment of Interactive Tools to Assist Public Health Policymaking Readership: Researchers in mathematical biology, mathematical modeling, infectious diseases and complex systems. Keywords:Epidemiological Model;Population Dynamics;Disease Control StrategyKey Features:Development of modeling tools that are user-friendly to policymakersConsideration of heterogeneities that are not analyzed in detail previouslyConnection of model analyses to real disease data to improve understanding

Modeling In Biopharmaceutics Pharmacokinetics And Pharmacodynamics

Author: Panos Macheras
Publisher: Springer
ISBN: 3319275984
Size: 74.87 MB
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The state of the art in Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics Modeling is presented in this new second edition book. It shows how advanced physical and mathematical methods can expand classical models in order to cover heterogeneous drug-biological processes and therapeutic effects in the body. The book is divided into four parts; the first deals with the fundamental principles of fractals, diffusion and nonlinear dynamics; the second with drug dissolution, release, and absorption; the third with epirical, compartmental, and stochastic pharmacokinetic models, with two new chapters, one on fractional pharmacokinetics and one on bioequivalence; and the fourth mainly with classical and nonclassical aspects of pharmacodynamics. The classical models that have relevance and application to these sciences are also considered throughout. This second edition has new information on reaction limited models of dissolution, non binary biopharmaceutic classification system, time varying models, and interface models. Many examples are used to illustrate the intrinsic complexity of drug administration related phenomena in the human, justifying the use of advanced modeling methods. This book will appeal to graduate students and researchers in pharmacology, pharmaceutical sciences, bioengineering, and physiology. Reviews of the first edition: "This book presents a novel modelling approach to biopharmaceutics, pharmacokinetics and pharmacodynamic phenomena. This state-of-the-art volume will be helpful to students and researchers in pharmacology, bioengineering, and physiology. This book is a must for pharmaceutical researchers to keep up with recent developments in this field." (P. R. Parthasarathy, Zentralblatt MATH, Vol. 1103 (5), 2007) "These authors are the unique (or sole) contributors in this area that are working on these questions and bring a special expertise to the field that is now being recognized as essential to understanding biological system and kinetic/dynamic characteristics in drug development...This text is an essential primer for those who would envision the incorporation of heterogeneous approaches to systems where homogeneous approaches are not sufficient to describe the system." (Robert R. Bies, Journal of Clinical Pharmacology, Vol. 46, 2006)