Multi-compartment models

Usually, the buffer compartment is not accessible and, consequently, the absolute amount of X cannot be determined experimentally. For this reason, we will only focus our discussion on the plasma concentration Cp. It is important to know, however, that the time course of the contents in the two compartments is the sum of two exponentials, which have the same positive hybrid transfer constants a and p. The coefficients A and B, however, depend on the particular compartment. This statement can be generalized to mammillary systems with a large number of compartments that exchange with a central compartment. The solutions for each of n compartments in a mammillary model are sums of n exponential functions, having the same n positive hybrid transfer constants, but with n different coefficients for each particular compartment. (We will return to this property of linear compartmental systems during the discussion of multi-compartment models in Section 39.1.7.)... 

In the previous section we found that the hybrid transfer constants of a two-compartment model are eigenvalues of the transfer constant matrix K. This can be generalized to the multi-compartment model. Hence the characteristic equation can be written by means of the determinant A ... 

The general structure of a low-resolution multi-compartment model of mercury circulation in the environment was formulated. The atmospheric part of the model was developed and tested. 

Figure 1. General scheme of MSCE-POP multi-compartment model (Mantseva et al., 2004).

Legierse, K. C. H. M., W. H. J. Vaes, T. Sinnige, and J. L. M. Hermens, Distribution of chlorobenzenes and the organophosphorous pesticide chlorthion in the pond snail (Lymnaea stagnalis) A multi-compartment model based on partitioning to polar lipids, neutral lipids and pond snail protein, Ph.D. thesis, University of Utrecht, Utrecht, 1998,... 

POP concentrations in the European atmosphere can be estimated from these national emission inventories by using model calculations, such as the MSCE-POP model. This is a three-dimensional Eulerian multi-compartment model operating within the geographical scope of EMEP region with a spatial resolution of 50 km x 50... 

Figure 19.1 Physiological pharmacokinetic model for evaluating in vivo disposition of a macromolecular drug. (A) A multi-compartment model in which every tissue compartment is connected with the plasma pool by blood flow. (B) Tissue uptake of a drug from vascular space to tissue parenchyma.

Figure 6.14 (a) Semilog plot of plasma concentration for (Cp) versus time representative of a three- or multi-compartment model. The curve can be broken down into three phases, A.i, X2, and X2. (b) Three-compartment model with transfer rate constants, K 2, K2, K 2, K- i, and elimination rate constant, Ke. As these models can get more complicated, the a, ft. and y nomenclature may get replaced with Xn as indicated in the profile. 

Shargel L, Multi-compartment models, In Applied biopharmaceutics and pharmacokinetics, Shargel E,Wu Pong S,Yu A, editors,... 

A mathematical model of long-term toxicokinetics in humans has been developed [14,15]. Subsequently, a more detailed description of Cd toxicokinetics was formulated considering additional events that modify the behavior of Cd in humans [16,17]. The kidney and particularly the cortex, is considered the critical target tissue for Cd and its accumulation is of decisive importance for risk assessment. In long-term exposures (life-long) either a simple one-compartment model or a more multi-compartment model predicts that 1/3 to 1/2 of the total body burden accumulates in the kidney and that the concentration of Cd in the kidney cortex is 1.25 times higher than the average concentration in the whole kidney [8]. 

Arundel P. 1997. A multi-compartment model generally applicable to physiologicaUy-based pharmacokinetics. 3rd IFAC Symposium Modelling and control in biomedical systems, Warwick, UK, March 23-26,1997. 

This multi-compartment model was used by Kocher to calculate collective committed dose equivalent versus time following the release of 1 Ci of to each of several compartments. Of interest here is the conclusion that the long term (> 10 year) collective doses are essentially the same whether the is released to the atmosphere (over land or water), to the surface soil compartments, or the mixed ocean layer. 

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