Stochastic Models and Linear Tracer Kinetics
The purpose of a model is to verify whether some hypotheses made on a real system are valid (Rescigno and Beck, 1987), and subordinately to determine the values of some of the parameters that represent specific properties of the system under study (Zierler, 1981). For instance the model commonly used when dilution phenomena are expected, is a set of ordinary differential equations with constant coefficients, while when diffusion phenomena are the case, partial differential equations are to be used, finite difference equations for delay phenomena, etc.
KeywordsProbability Density Function Moment Generate Function Tracer Kinetic Finite Difference Equation Absolute Moment
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- H. Bateman, 1954. Table§ of Integral Transforjn, Vol. I. McGraw-Hill, New York, pages 303–366.Google Scholar
- J.H.Matis, T.E.Wehrly and K.B.Gerald, 1983. The statistical analysis of pharmacokinetic data. Tracer Kinetics and _Physiologic Modeling (R.M.Lambrecht and A.Rescigno editors). Springer-Verlag, Berlin, pages 1–58.Google Scholar
- A.Rescigno, 1987. Image analysis and the method of moments..Phyßiçs -rid Engineering of Medical Imaging (R. Guzzardi editor). Martinus Nijhoff, The Hague, in press.Google Scholar
- A.Rescigno and J.S.Beck, 1987. The use and abuse of models. J,_ Pharmaç,Qk in. Biopharm in press.Google Scholar
- A.Rescigno and C. C. Duncan, 1985. Tracer kinetics and stochastic models: from compartment analysis to image reconstruction. Bathematics and Compçter_in Biomedical Application s (J. Eisenfeld and C. DeLisi editors). Elsevier, Amstermam, pages 205–218.Google Scholar
- A.Rescigno and R.M.Lambrecht, 1985. An algorithm for reconstruction of count rate curves from total counts. _Mathematics in Biploay and Medicine (V.Capasso, E. Grosso and S.L.Paveri-Fontana editors). Berlin, Springer-Verlag, pages 399–408Google Scholar
- A.Rescigno and L.D.Michels, 1973. Compartment modeling from tracer experiments. Bull. Bath.Biol. 35: 245–257.Google Scholar
- A.Rescigno and G.Segre, 1961. The precursor-product relationship. J. Theor.Biol 1: 498–513.Google Scholar
- A.Rescigno and G.Segre, 1964. Drug and Tracer Kinetics Blaisdell, Waltham, Mass.Google Scholar
- A.Wald, 1939. Limits of a distribution function determined by absolute moments and inequalities satisfied by absolute moments. Trans. Amnr. Math. Soc. 46: 280–306.Google Scholar