Compartment models catenary

As an example application, we will develop the master equation for a fragment of a two-way catenary compartment model around three compartments spaced by Az, as illustrated in Figure 9.24. By assuming only one particle in movement, the master equation gives... 

Fig. 39.14. (a) Catenary compartmental model representing a reservoir (r), absorption (a) and plasma (p) compartments and the elimination (e) pool. The contents X, Xa, Xp and X,. are functions of time t. (b) The same catenary model is represented in the form of a flow diagram using the Laplace transforms Xr, Xa and Xp in the j-domain. The nodes of the flow diagram represent the compartments, the boxes contain the transfer functions between compartments [1 ]. (c) Flow diagram of the lumped system consisting of the reservoir (r), and the absorption (a) and plasma (p) compartments. The lumped transfer function is the product of all the transfer functions in the individual links. 

This result can be generalized in the case of a catenary irreversible m-compartment model [347] the state probability in the compartment i (i = 2, rn) at t is given by... 

A good review of the master equation approach to chemical kinetics has been given by McQuarrie [383]. Jacquez [335] presents the master equation for the general ra-compartment, the catenary, and the mammillary models. That author further develops the equation for the one- and two-compartment models to obtain the expectation and variance of the number of particles in the model. Many others consider the m-compartment case [342,345,384], and Matis [385] gives a complete methodological rule to solve the Kolmogorov equations. 

Fig. 39.7. (a) Two-compartment catenary model for extravascular (oral or parenteral) administration of a single dose D which is completely absorbed. The transfer constant of absorption is (b) Time courses of the amount in the extravascular compartment Xa, the concentration in the plasma compartment Cp and the content in the elimination pool X. ... 

The synthetic data have been computed from a theoretical two-compartment catenary model with the following parameters ... 

Two-compartment catenary model for extravascular administration with incomplete absorption... 

In the catenary model of Fig. 39.14a we have a reservoir, absorption and plasma compartments and an elimination pool. The time-dependent contents in these compartments are labelled X, X, and X, respectively. Such a model can be transformed in the 5-domain in the form of a diagram in which each node represents a compartment, and where each connecting block contains the transfer function of the passage from one node to another. As shown in Fig. 39.14b, the... 

One of several general models for metabolite compart-mentation in which a central compartment is directly linked to or feeds from (hence the name) other compartments that do not communicate with each other aside from their connection to the central pool. See Catenary Model Compartmental Analysis... 

Farquhar, j. W., R. C. Gross, R. M. Wagner, and G. M. Reaven Validation of an incompletely coupled two-compartment nonrecycling catenary model for turnover of liver and plasma triglyceride in man. J. Lipid Res. 6, 119—134 (1965). 

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