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Splines and Compartment Models: An Introduction

by Biebler Karl-Ernst

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Mathematical modeling through splines and compartments

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AlbakiReads Editorial

Mathematical modeling through splines and compartments

Biebler introduces mathematical modeling through two connected approaches: splines as a general framework and compartment models as a field of application. The book develops spline construction algebraically, with attention to how numerical forms can be understood and varied. Its applied examples focus on classical pharmacokinetic compartment models, linking them to lifetime distributions and examining parameter estimation and model fit. The discussion also addresses model assumptions and data-collection conditions, and includes mathematical proofs, examples, and program code. A varied minimum chi-square method is presented for analyzing single kinetics and calculating average kinetics.

Good fit for readers who enjoy

  • Readers seeking an introduction to spline methods and mathematical modeling.
  • Those studying pharmacokinetic compartment models, parameter estimation, or model fit.
  • Practitioners interested in worked examples and related program code.

Themes

Mathematical modelingSpline functionsPharmacokinetic compartment modelsStatistical parameter estimationModel fit and data collection

Based on publisher information and book metadata.

Book overview

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.
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