Abstract
In this paper biological compartmental models are considered which take into account the intrinsic randomness of the transport rate parameters and their possible variability in time. An identification procedure is presented for the estimation of the stochastic processes representing the transport rate parameters of a compartmental model from a noisy input-output experiment. The problem is formulated in terms of nonlinear filtering. A simple model is discussed for the case in which the transport rate parameters are independent of each other. The possibility of testing possible important features of the behavior of the transport rate parameters is also evidenced.
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Literature
Bernard, S. R., L. R. Shenton and V. R. R. Uppuluri. 1965. “Stochastic Models for the Distribution of Radioactive Material in a Connected System of Compartments.” InProceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, IV, pp. 481–510. Berkeley: University of California Press.
Bierman, G. J. 1977.Factorization Methods for Discrete Sequential Estimation. New York: Academic Press.
Cardenas, M. and J. H. Matis. 1974. “On the Stochastic Theory of Compartments: Solution forn-Compartment Systems with Irreversible, Time-Dependent Transition Probabilities.”Bull. Math. Biol.,36, 489–504.
— and J. H. Matis. 1975a. “On the Time-Dependent Reversible Stochastic Compartmental Model—I. The General Two Compartment System.”Bull. Math. Biol.,37, 505–519.
— and J. H. Matis. 1975b. “On the Time-Dependent Reversible Stochastic Compartmental Model—II. A Class ofn-Compartment Systems.”Bull. Math. Biol.,37, 555–564.
Campello, L. and C. Cobelli. 1977. “Parameter Estimation of Biological Stochastic Compartmental Models. An Application.”IEEE Trans. Biomed. Engng, in press.
Chuang, S. and H. H. Lloyd. 1975. “Analysis and Identification of Stochastic Compartment Models in Pharmacokinetics: Implication for Cancer Chemotherapy.”Math. Biosci.,22, 57–74.
Cobelli, C. and G. Romanin-Jacur. 1976a. “Controllability, Observability and Structural Identifiability of Multi Input-Multi Output Biological Compartmental Systems.”IEEE Trans. Biomed. Engng,23, 93–100.
— and G. Romanin-Jacur. 1976b. “On the Structural Identifiability of Biological Compartmental Systems in a General Input-Output Configuration.”Math. Biosci.,30, 139–151.
Gelb, A., Ed. 1974.Applied Optimal Estimation. Cambridge: M.I.T. Press.
Jacquez, J. A. 1972.Compartmental Analysis in Biology and Medicine, pp. 182–189. Amsterdam: Elsevier.
Jazwinski, A. H. 1970.Stochastic Processes and Filtering Theory. New York: Academic Press.
Kalman, R. E. and R. S. Bucy. 1961. “New Results in Linear Filtering and Prediction Theory.”Transactions of the ASME, Ser. D, J. Basic Engng,83, 95–107.
Kapadia, A. S., B. C. McInnis and S. A. El-Asfouri. 1975. “Analysis and Parameter Identification of Stochastic Compartmental Models.”Proceedings of the IEEE Conference on Decision and Control, pp. 516–519. Houston, Texas, U.S.A.
Kapadia, A. S. and B. C. McInnis. 1976. “A Stochastic Compartmental Model with Continuous Infusion.”Bull. Math. Biol.,38, 695–700.
Kodell, R. L. and J. H. Matis. 1976. “Estimating the Rate Constants in a Two-Compartment Stochastic Model.”Biometrics,32, 377–380.
Marcus, A. H. 1975. “Power Laws in Compartmental Analysis. Part I: A Unified Stochastic Model.”Math. Biosci.,23, 337–350.
Matis, J. H. and H. O. Hartley. 1971. “Stochastic Compartmental Analysis: Model and Least Squares Estimation from Time Series Data.”Biometrics,27, 77–102.
— M. Cardenas and R. L. Kodell. 1974. “On the Probability of Reaching a Threshold in a Stochastic Mamillary System.”Bull. Math. Biol.,36, 445–454.
— R. L. Kodell and M. Cardenas. 1976. “A Note on the Use of a Stochastic Mamillary Compartmental Model as an Environmental Safety Model.”Bull. Math. Biol.,38, 467–478.
Purdue, P. 1974a. “Stochastic Theory of Compartments.”Bull. Math. Biol.,36, 305–309.
— 1974b. “Stochastic Theory of Compartments: One and Two Compartment Systems.”Bull. Math. Biol.,36, 577–587.
— 1975. “Stochastic Theory of Compartments: an Open, Two Compartment, Reversible Systems with Independent Poisson Arrivals.”Bull. Math. Biol.,37, 269–275.
Soong, T. T. 1971. “Pharmacokinetics with Uncertainties in Rate Constants.”Math. Biosci.,12, 235–243.
— 1972. “Pharmacokinetics with Uncertainties in Rate Constants—II: Sensitivity Analysis and Optimal Dosage Control.”Math. Biosci.,13, 391–396.
— and J. W. Dowdee. 1974. “Pharmacokinetics with Uncertainties in Rate Constants—III: The Inverse Problem.”Math. Biosci.,19, 343–353.
Thakur, A. K., A. Rescigno and D. Schafer. 1972. “On the Stochastic Theory of Compartments. I.A Single-Compartment System.”Bull. Math. Biophys.,34, 53–63.
— A. Rescigno and D. Schafer. 1973. “On the Stochastic Theory of Compartments. II. Multicompartment Systems.”Bull. Math. Biol.,35, 263–271.
— and A. Rescigno. 1977. “On the Stochastic Theory of Compartments. III. General Time-Dependent Reversible Systems.”Bull. Math. Biol.,40, 237–246.
Tsokos, J. O. and C. P. Tsokos. 1976. “Statistical Modeling of Pharmacokinetics Systems.”Transactions of the ASME. Ser D. J. Dynamic Systems, Measurement and Control,98, 37–43.
Uppuluri, V. R. R. and S. R. Bernard. 1967. “A Two Compartment Model With a Random Connection.” InCompartments, Pool and Spaces in Medical Physiology, Eds P. E. E. Bergner and C. C. Lushbaugh, pp. 175–188. Oak Ridge, Tennesse, USA: USAEC.
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Cobelli, C., Morato, L.M. On the identification by filtering techniques of a biologicaln-compartment model in which the transport rate parameters are assumed to be stochastic processes. Bltn Mathcal Biology 40, 651–660 (1978). https://doi.org/10.1007/BF02460736
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DOI: https://doi.org/10.1007/BF02460736