Instantaneous absorption models distribution

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. 

Other drug delivery situations that do not closely mimic true instantaneous absorption can still be approximated by this absorption model, as long as the absorption process occurs much more quickly than all other processes. For example, an orally ingested drug for which absorption is essentially complete after one or two hours could be approximated as instantaneous absorption if the distribution, metabolism, and excretion processes all take several days to approach completion. Note that even if an extravascular drug delivery can be treated as instantaneous absorption, the bioavailability F) can still range from 0 to 100%. Specific criteria for when the instantaneous absorption approximation can be used will be provided later in... 

The two-compartment model scheme is applied to the steady delivery of drug into the systemic circulation (zero-order absorption) in this section. The only difference between the instantaneous absorption and zero-order absorption two-compartment models is in the type of drug absorption. Thus all descriptions of what is included in each compartment, the use of micro and hybrid rate constants, and the different types of distribution volumes are identical to the two-compartment bolus IV model values. As was done previously for zero-order absorption, the model equations are written specifically for the case of IV infusion, with modifications for other types of zero-order absorption described in Section 10.11.5. 

Standard linear regression and method of residual analyses of two-compartment IV infusion (zero-order absorption) data is limited to samples collected during the postinfusion period. Plasma concentrations during the infusion period do not lend themselves to a linear analysis for a two-compartment model. Estimation of parameters from measured postinfusion plasma samples is quite similar to the two-compartment bolus IV (instantaneous absorption) case. Proper parameter evaluation ideally requires at least three to five plasma samples be collected during the distribution phase, and five to seven samples be collected during the elimination phase. Area under the curve (AUC) calculations can also be used in evaluating some of the model parameters. 

A separate mass balance equation is written in the form of Section 10.6.2 for each compartment in the model. Thus a total of n mass balance equations must be written and solved for an n compartment model. The details of these equations and their solution are not provided in this chapter. However, it will be noted that absorption, distribution, and elimination rates are written in the same form as in the previous one- and two-compartment models. The absorption rate for instantaneous, zero-order, or first-order absorption is identical to the previous forms for one- and two-com-partment models. Distribution and elimination rates are written as first-order linear rate equations using micro rate constants. So the distribution rate from compartment 1 to compartment n is given by kj Aj, the distribution rate from compartment n back to compartment 1 equals k i A , and the elimination rate from any compartment is written k o A schematic diagram for the generalized n compartment model is illustrated in Figure 10.90. 

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 rates of movement of foreign compound into and out of the central compartment are characterized by rate constants kab and kei (Fig. 3.23). When a compound is administered intravenously, the absorption is effectively instantaneous and is not a factor. The situation after a single, intravenous dose, with distribution into one compartment, is the most simple to analyze kinetically, as only distribution and elimination are involved. With a rapidly distributed compound then, this may be simplified further to a consideration of just elimination. When the plasma (blood) concentration is plotted against time, the profile normally encountered is an exponential decline (Fig. 3.24). This is because the rate of removal is proportional to the concentration remaining it is a first-order process, and so a constant fraction of the compound is excreted at any given time. When the plasma concentration is plotted on a logio scale, the profile will be a straight line for this simple, one compartment model (Fig. 3.25). The equation for this line is... 

The distribution transport rate (r is ) is a measure of how quickly drug molecules are exchanged between the plasma and the tissues. A rapid distribution transport rate causes the plasma and tissues to come quickly into equilibrium with each other, whereas a slower rate will cause a prolonged approach to equilibrium. As with the rate of absorption, different types of PK modeling approaches can be employed to approximate distribution rates. In the case of distribution there are essentially two types of models, instantaneous distribution and first-order distribution. The difference between the two types of models is in the number of compartments used to represent the drug disposition in the body. 

Instantaneous distribution is represented by considering the body as a single compartment. This type of PK model can have parameters associated with how fast drug reaches the systemic circulation by absorption... 

Linear (or first-order) kinetics refers to the situation where the rate of some process is proportional to the amount or concentration of drug raised to the power of one (the first power, hence the name first-order kinetics). This is equivalent to stating that the rate is equal to the amount or concentration of drug multiplied by a constant (a linear function, hence linear kinetics). All the PK models described in this chapter have assumed linear elimination (metabolism and excretion) kinetics. All distribution processes have been taken to follow linear kinetics or to be instantaneous (completed quickly). Absorption processes have been taken to be instantaneous (completed quickly), follow linear first-order kinetics, or follow zero-order kinetics. Thus out of these processes, only zero-order absorption represents a nonlinear process that is not completed in too short of a time period to matter. This lone example of nonlinear kinetics in the standard PK models represents a special case since nonlinear absorption is relatively easy to handle mathematically. Inclusion of any other type of nonlinear kinetic process in a PK model makes it impossible to write the... 

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