Instantaneous absorption models assumptions

The one-compartment bolus IV injection model is mathematically the simplest of aU PK models. Drug is delivered directly into the systemic circulation by a rapid injection over a very short period of time. Thus the bolus rV injection offers a near perfect example of an instantaneous absorption process. Representation of the body as a single compartment implies that the distribution process is essentially instantaneous as well. The exact meaning of the assumptions inherent in this model are described in the next section. Model equations are then introduced that allow the prediction of plasma concentrations for drugs with known PK parameters, or the estimation of PK parameters from measured plasma concentrations. Situations in which the one-compartment instantaneous absorption model can be used to reasonably approximate other types of drug delivery are described later in Section 10.7.5. 

The standard one-compartment bolus IV (or instantaneous absorption) model makes three inherent assumptions about the ADME processes that occur after drug delivery. The specific nature and implications of each of these assumptions are described in this section. 

As in all instantaneous absorption models, the entire absorbed dose of drug is taken to enter the systemic circulation instandy at time zero (< = 0). This provides an excellent approximation of the rapid drug delivery direcdy into the systemic circulation provided by a bolus IV injection, which truly occurs over a very short period of time (typically several seconds). However, this assumption does not actually require a strict interpretation of the word instantaneous. Even if an absorption process takes a substantial period of time (minutes or hours), it can still be approximated as instantaneous as long as absorption occurs quickly relative to other ADME processes. Thus, other routes of drug delivery besides a bolus IV injection can be approximated by instantaneous absorption if the time it takes for the absorption process to be essentially complete is very small compared to the half-life of elimination. The equations throughout most of this section are written specifically for a bolus IV injection, but modifications that can be employed to apply the equations to other drug delivery methods are described in Section 10.7.5. 

This assumption is the same for all instantaneous absorption models. See Section 10.7.1.1 for the details regarding this assumption. 

The enhancement factors are either obtained by fitting experimental results or are derived theoretically on the grounds of simplified model assumptions. They depend on reaction character (reversible or irreversible) and order, as well as on the assumptions of the particular mass transfer model chosen [19, 26]. For very simple cases, analytical solutions are obtained, for example, for a reaction of the first or pseudo-first order or for an instantaneous reaction of the first and second order. Frequently, the enhancement factors are expressed via Hatta-numbers [26, 28]. They can be used in combination with the HTU/NTU-method or with a more advanced mass transfer description method. However, it is generally not possible to derive the enhancement factors properly from binary experiments, and a theoretical description of reversible, parallel or consecutive reactions is based on rough simplifications. Thus, for many reactive absorption processes, this approach appears questionable. 

Multicompartment model equations can be written for instantaneous absorption, zero-order absorption, or first-order absorption. For any of these particular absorption situations, the assumptions described previously for the corresponding absorption in one- and two-compartment models remains exactly the same for multicompartment models. 

Because of the assumption of instantaneous absorption in the model, Cmax tended to be slightly overpredicted, which may be the most reassuring prediction to make from a toxicology point of view. 

The second approach to the calculation of spectra in solutions is based on the assumption that the ground and excited states are intimately coupled in an instantaneous absorption process.In this model, the solute ground state electron distribution responds to the electron distribution in the excited state through the instantaneous polarization of the solvent. In such a case, the energy of the absorbing (ground) state is shifted by the following amount... 

The basis for all CAT models is the fundamental understanding of the transit flow of drugs in the gastrointestinal tract. Yu et al. [61] compiled published human intestinal transit flow data from more than 400 subjects, and their work showed the human mean small intestinal transit time to be 199 min. and that seven compartments were optimal in describing the small intestinal transit process using a compartmental approach. In a later work, Yu et al. [58] showed that between 1 and 14 compartments were needed to optimally describe the individual small intestine transit times in six subjects but in agreement with the earlier study, the mean number of compartments was found to be seven. This compartmental transit model was further developed into a compartmental absorption and transit (CAT) model ([60], [63]). The assumptions made for this CAT model was that no absorption occurs in the stomach or in the colon and that dissolution is instantaneous. Yu et al. [59] extended the CAT model... 

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