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# Splines and Compartment Models

An Introduction

## 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.

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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 n
• Interpolating Cubic Splines
• Smoothing Natural Cubic Splines and the Choice of the Smoothing Parameter
• Interpolating Quadratic Splines and Parabolas
• Splines and Average Functions
• Compartment Models:
• Concept of a Context Related Mathematical Pharmacokinetical Model
• Compartment Models
• Other Deterministic Models
• Calculability and Identifiability
• Compartment Models and Associated Residence Time Distributions
• Other Stochastic Models
• Calculation Methods Related to Compartment Models
• Selection of Pharmacokinetic Models
• Pharmacokinetics for Multiple Applications
• Mathematica® 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.
Key Features:
• This book treats modeling and data interpretation as a whole, and the qualities of the developed methods are mathematically characterized
• New application of the varied minimum chi-square method for the parameter calculation and the model choice in the pharmacokinetics
• The developed methods are ready for application. The reader/user will be able to modify the given solutions

Date release: July 23, 2013

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