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Splines and compartment models : an introduction

Author: Karl-Ernst Biebler; Michael Wodny
Publisher: New York : Springer, 2013.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Biebler, Karl-Ernst.
Splines and Compartment Models : An Introduction.
Singapore : World Scientific Publishing Company, ©2013
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Karl-Ernst Biebler; Michael Wodny
ISBN: 9789814522236 9814522236 9789814522229 9814522228
OCLC Number: 879633313
Description: 1 online resource (349 pages)
Contents: Preface; Contents; PART 1 Spline models; 1. Why spline functions?; 2. Interpolating splines of degree n; 3. Interpolating cubic splines; 3.1 Interpolating cubic splines with other extreme characteristics; 4. Smoothing natural cubic splines and the choice of the smoothing parameter; 4.1 Estimating the smoothing parameters; 5. Interpolating quadratic splines; 6. Interpolating quadratic splines and parabolas; 7. Smoothing quadratic splines; 7.1 Smoothing quadratic splines and the integral of the quadratic first derivative; 7.2 Quadratic splines smoothing the predefined first derivatives. 8. Splines and averaged functions8.1 Averaged splines in the case of common knots; 8.2 Averaged kinetics and reference ranges; 8.3 Growth curves and averaged splines without common knots; PART 2 Compartment models; 9. Concept of a context related mathematical pharmacokinetical model; 10. Compartment models; 10.1 One-compartment model; 10.2 Two-compartment models; 10.3 More-compartment models; 11. Other deterministic models; 11.1 Compartment models with delay; 11.2 Nonlinear kinetics; 12. Calculability and identifiability; 13. Compartment models and associated residence time distributions. 13.1 Unbounded residence times13.2 Properties of distributions of unbounded residence times; 13.3 Truncation; 14. Other stochastic models; 14.1 Stochastic differential equations; 14.2 Stochastic processes; 14.3 Regression attempts; 15. Calculation methods related to compartment models; 15.1 Method of least squares parameter calculations; 15.2 Statistical parameter estimation for an individual kinetics; 15.2.1 Varied minimum- X2-estimation; 15.2.2 Qualities of the varied minimum- X2-estimator; 15.3 The varied minimum- X2-method applied to population kinetics. 16. Selection of pharmacokinetic models17. Pharmacokinetics for multiple applications; PART 3 Mathematica® programs for selected problems; Program list; Bibliography; Index.
Responsibility: Karl-Ernst Biebler, Michael Wodny.

Abstract:

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 und.

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