|aIncludes bibliographical references (pages 319-330) and index.
|a1. Why spline functions? -- 2. Interpolating splines of degree n -- 3. Interpolating cubic splines -- 4. Smoothing natural cubic splines and the choice of the smoothing parameter -- 5. Interpolating quadratic splines -- 6. Interpolating quadratic splines and paraboles -- 7. Smoothing quadratic splines -- 8. Splines and averaged functions -- 9. Concept of a context related mathematical pharmacokinetical model -- 10. Compartment models -- 11. Other deterministic models -- 12. Calculability and identifiability -- 13. Compartment models and associated residence time distributions -- 14. Other stochastic models -- 15. Calculating methods related to compartment models -- 16. Selection of pharmacokinetic models -- 17. Pharmaacokinetics for multiple applications -- Mathematica® programs for selected problems.
|aThis 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.