Compartmental specificity, description

The process was considered as continuous and compartmental models were used to approximate the continuous systems [335]. For such applications, there is no specific compartmental model that is the best the approximation improves as the number of compartments is increased. It order to put compartmental models of continuous processes in perspective it may help to recall that the first step in obtaining the partial differential equation, descriptive of a process continuous in the space variables, is to discretize the space variables so as to give many microcompartments, each uniform in properties internally. The differential equation is then obtained as the limit of the equation for a microcompartment as its spatial dimensions go to zero. In approximation of continuous processes with compartmental models one does not go to the limit but approximates the process with a finite compartmental system. In that case, the partial differential equation... 

As we rise to higher levels of organization through cells, tissues, and organs, the calculations we did at any simpler level become more challenging if we stick to that level of description. For example, concentrations can be much higher in the cell, interact with many other molecules, and different substrates can be compartmentalized, immobilized on specific structures within the cell, or otherwise moved around in the cell by complicated processes driven by energy consumption. 

As stated, a number of PBPK/PD models have been developed for individual nerve agents (sarin, VX, soman, and cyclosarin) in multiple species. Chapter 58 in the current volume discusses tiie development of such models. Standalone PBPK or compartmental models have also been developed that describe the pharmacokinetics of certain countermeasures, such as diazepam (Igari et al., 1983 Gueorguieva et al., 2004) and oximes (Stemler et al., 1990 Sterner et al., 2013). However, to date, few models for specific countermeasures have been harmonized and linked to NA PBPK/PD models to be able to quantitatively describe their pharmacokinetic and pharmacodynamic interactions. This is partly due to the fact that most PBPK/ PD models developed for NAs and other OPs focus on the inhibition of ChEs as the critical endpoint. The lack of a mathematical description of the disruption of other complex biochemical pathways presents a problem for linking these NA models to those of many countermeasures. For example, the conventional NA countermeasures, atropine and diazepam, as well as many novel countermeasures, do not directly impact ChE kinetics because they act at sites distinct from the active site of the esterases, such as muscarinic, GABA, or NMDARs (Figure 69.2). 

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