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Splines and compartment models : an introduction /
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...
| Cote: | Libro Electrónico |
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| Auteur principal: | |
| Autres auteurs: | |
| Format: | Électronique eBook |
| Langue: | Inglés |
| Publié: |
New York :
Springer,
2013.
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| Sujets: | |
| Accès en ligne: | Texto completo |
Table des matières:
- 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.