Stochastic Compartmental Models

Resumons nos conclusions... C est done en termes probabilistes que les lois de la dynamique doivent etre formulees lorsqu elles concer-nent des systemes chaotiques. 

The real world of compartmental systems has a strong stochastic component, so we will present a stochastic approach to compartmental modeling. In deterministic theory developed in Chapter 8, each compartment is treated as being both homogeneous and a continuum. But  

In deterministic theory we started with the definition of a compartment as a kinetically homogeneous amount of material. The equivalent definition in stochastic theory is that the probability of a unit participating in a particular transfer out of a compartment, at any time, is the same for all units in the compartment. 

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Matis, J. and Wehrly, T., Generalized stochastic compartmental models with Erlang transit times, Journal of Pharmacokinetics and Biopharmaceutics, Vol. 18, No. 6, 1990, pp. 589-607. 

Matis, J., An introduction to stochastic compartmental models in pharmacokinetics, Pharmacokinetics-Mathematical and Statistical Approaches in Metabolism and Distribution of Chemicals and Drugs, edited by A. Pecile and A. Rescigno, Plenum Press, New York, 1988, pp. 113-128. 

Gardenas, M. and Matis, J., On the time-dependent reversible stochastic compartmental model. II. A class of n-compartment systems, Bulletin of Mathematical Biology, Vol. 37, 1975, pp. 555-564. 

The first term in the above equation represents the rate of osteoblast transformation into osteocjrtes, and the last term represents Ae rate of deaA of osteocytes. Reddy and Joshi (1987) simulated the stochastic compartmental model of bone cells in which Ae equation for the population means are the same as Ae above equations. In adAticm, the stochastic analysis provides information about the variations and covariences of cellular populations. Figure 1.5 shows the normalized number of osteoblasts plotted as a fimction of age of Ae mdividual when C, and are assumed to be sinusoidal... 

Reddy, N. P., and Joshi, A. (1987). A Stochastic Compartmental Model of Bone Cells, International Journal... 

Nassar et al. [20] proposed a stochastic compartmental model to simulate the concentration dynamics of suspended particles in the liquid and solid parts over the different section of flow. In their work, a deep-bed filter is considered to be an open system composed of an arbitrary number of sections or compartments distributed in the axial direction. 

In this section, a stochastic compartmental model is employed to estimate the number of compartments (necessary to characterize the flow) and the intensities of forward and backward flows between compartments in an open-flow adsorber without adsorbate. In addition, this model and the linear batch model are combined into one for predicting breakthrough curves in an open-... 

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