Author | Anderson, David H. author |
---|---|
Title | Compartmental Modeling and Tracer Kinetics [electronic resource] / by David H. Anderson |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1983 |
Connect to | http://dx.doi.org/10.1007/978-3-642-51861-4 |
Descript | IX, 304 p. online resource |
Section 1. Compartmental Systems -- 1A. Introduction -- 1B. Preliminary definitions -- 1C. Tracer experiments -- 1D. History of compartmental analysis -- Section 2. Elementary Compartmental Models -- 2A. Drug kinetics -- 2B. Leaky fluid tanks -- 2C. Diffusion -- 2D. Solute mixture -- Section 3. First-Order Chemical Reactions -- Section 4. Environmental Studies -- 4A. Kinetics of lead in the body -- 4B. The Aleut ecosystem -- Section 5. Nonlinear Compartmental Models -- 5A. Continuous flow chemical reactor -- 5B. Reaction order -- 5C. Other nonlinear compartmental models -- Section 6. The General Compartmental Model -- Section 7. Tracer Kinetics in Steady-State Systems -- 7A. The tracer equations -- 7B. Linear compartmental models. -- Section 8. Uptake of Potassium by Red Blood Cells -- Section 9. Standard Types of Tracer Experiments -- 9A. Tracer concentration equations -- 9B. Tracer specific activity equations -- Section 10. Analytical Solution of the Tracer Model -- 10A. The general solution of the model -- 10B. Nonnegativity of the solution -- Section 11. System Structure and Connectivity -- 11A. The connectivity diagram -- 11B. Common compartmental systems -- 11C. Strongly connected systems -- Section 12. System Eigenvalues and Stability. -- 12A. Nonpositive eigenvalues . -- 12B. The smallest magnitude eigenvalue -- 12C. Symmetrizable compartmental matrices and real eigenvalues -- 12D. Distinct eigenvalues -- 12E. Compartmental model stability -- 12F. Bounds on the extreme eigenvalues -- Section 13. The Inverse of a Compartmental Matrix -- 13A. Invertibility conditions -- 13B. A Neumann series for the inverse matrix -- 13C. Matrix inequalities -- Section 14. Mean Times and the Inverse Matrix -- 14A. Mean residence times -- 14B. The compartmental matrix exponential -- 14C. Further properties of mean residence time -- 14D. System Mean residence time -- Section 15. Solution of the Steady-State Problem for SEC Systems -- 15A. The tracer steady-state problem -- 15B. Ill-conditioned SEC systems -- 15C. An iterative procedure for SEC systems -- 15D. Updating the algorithm -- Section 16. Structural Identification of the Model -- 16A. The system (A, B, C) -- 16B. The structural identification problem -- 16C. A simple identification example -- 16D. Realizations of impulse response functions -- 16E. Impulse response function structure -- 16F. Nonlinear identification equations -- 16G. A three compartment model -- 16H. A four compartment model -- Section 17. Necessary and Sufficient Conditions for Identifiability -- 17A. Model identifiability -- 17B. Necessary conditions -- 17C. Sufficient conditions -- Section 18. A Simple Test for Nonidentifiability -- 18A. Counting nonzero transfer function coefficients -- 18B. Coefficient structure -- 18C. Further refinements of formula (18.4) -- 18D. The nonidentifiability test -- 18E. Tighter bounds on the number of independent equations -- Section 19. Computation of the Model Parameters -- 19A. Local identifiability -- 19B. Newtonโs method and modifications -- 19C. The Kantorovich conditions -- 19D. An example -- Section 20. An Alternative Approach to Identification -- 20A. A new identification method -- 20B. The component matrices of A -- 20C. The identification technique using component matrices -- 20D. Identification of a lipoprotein model -- 20E. The identification technique using modal matrices -- 20F. Identification of a pharmacokinetic system -- 20G. Spectral sensitivity of a linear model -- Section 21. Controllability, Observability, and Parameter Identifiability -- 21A. The control problem -- 21B. Completely controllable systems -- 21C. Completely observable systems -- 21D. Realizations and identifiability -- 21E. A third method of identifiability -- Section 22. Model Identification from the Transfer Function Equations -- 22A. Form of the nonlinear equations -- 22B. Coefficients of the transfer fuction -- 22C. The nonlinear algebraic equations for the identification problem -- 22D. Necessary conditions for positive solutions of the nonlinear system -- 22E. Refined necessary conditions -- 22F. Additional properties of the nonlinear algebraic system -- 22G. An iterative scheme for solving F(?) = 0 -- 22H. Triangularization of F(?) = 0 -- 22I. Uniqueness of solution F(?) = 0 -- Section 23. The Parameter Estimation Problem -- 23A. The basic estimation problem -- 23B. A lipoprotein metabolism model -- 23C. Nonlinear least-squares -- 23D. Initial parameter estimates -- 23E. Method of moments -- 23F. Other methods of parameter estimation -- 23G. Positive amplitudes -- 23H. Curve-fitting sums of exponentials is ill-posed -- 23I. Fitting the differential equation model directly to data -- 23J. Modulating function method -- 23K. An antigen โ antibody reaction example -- 23L. Additional literature on fitting of differential equations to data -- Section 24. Numerical Simulation of the Model -- 24A. Compartmental model simulation -- 24B. A three compartment thyroxine model -- 24C. Numerical integration methods and some inadequacies -- 24D. Implicit methods . -- 24E. Determining model stiffness -- Section 25. Identification of Compartment Volumes -- 25A. The basic single exit compartmental model -- 25B. Readily identifiable parameters -- 25C. The catenary single exit system -- 25D. Estimation of compartmental volumes -- 25E. Creatinine clearance model -- 25F. Shock therapy -- 25G. Bounds and approximations on compartmental volumes -- Section 26. A Discrete Time Stochastic Model of a Compartmental System -- 26A. The Markov chain model -- 26B. The liver disease model -- 26C. Simulation of the hepatic system -- 26D. Mathematical analysis of the model -- 26E. Parameter estimation -- 26F. Discussion -- Section 27. Closing Remarks