Single-compartment distribution

The importance of these equations is that drugs can have different half-lives due either to changes in clearance or changes in volume (see Section 2.7). This is illustrated in Figure 2.3 for a simple single compartment pharmacokinetic model where the half-life is doubled either by reducing clearance to 50 % or by doubling the volume of distribution. 

Fig. 2.3 Effect of clearance and volume of distribution on half-life for a simple single compartment pharmacokinetic model.

When a drug of single compartment distribution is given intravenously, a. semilog plasma concentration time plot is obtained (Fig. 1.3.4), which has two slopes, one is due to distribution and another which is due to the drug elimination. 

The bioconcentration process can be modeled by an organism-water two-compartment toxicokinetic model where the organism is described as a single compartment in which the chemical is homogeneously distributed. 

In a pioneer work, Marcus established the link between some usual time-varying forms of h ( ) and / (a) in a single compartment [300]. For instance in h(t) = (f +/ ), a = 1 leads to A Gam(A,/3) and 1 < a < 2 defines the standard extreme stable-law density with exponent a. In the case of a = 1.5, the obtained distribution is known as the retention-time distribution of a Wiener process with drift. 

Pharmacokinetics provides the scientific basis of dose selection, and the process of dose regimen design can be used to illustrate with a single-compartment model the basic concepts of apparent distribution volume (Vd), elimination half-life (b/2) and elimination clearance (CLg). A schematic diagram of this model is shown in Figure 2.4, along with the two primary pharmacokinetic parameters of distribution volume and elimination clearance that characterize it. 

FIGURE 2.4 Diagram of a single-compartment model in which the primary kinetic parameters are the apparent distribution volume of the compartment (V ) and the elimination clearance (CLg). 

As shown in Figure 2.5 the back-extrapolated estimate of Co can be used to calculate the apparent volume (Vdiextrap)) hypothetical single compartment into which digoxin distribution occurs ... 

Equation 2.4 was derived by substituting CLR/Vi for k in Equation 2.13. Although Ud and CLr are the two primary parameters of the single-compartment model/ confusion arises because k is initially calculated from experimental data. However/ k is influenced by changes in distribution volume as well as clearance and does not reflect just changes in drug elimination. 

In the disposition model shown in Figure 4.9, the kinetics of drug distribution and elimination are represented by a single compartment with first-order elimination as described by the equation... 

A 70-kg patient is treated with an intravenous infusion of lidocaine at a rate of 2 mg/min. Assume a single-compartment distribution volume of 1.9 L/kg and an elimination half-life of 90 minutes. 

The distribution volume of a drug is the volume in which it appears to distribute (or which it would require) if the concentration throughout the body were equal to that in plasma, i.e. as if the bod/ were a single compartment. 

Lidocaine pharmacokinetics tend to follow a single compartment model in neonates, with an increased half-life, and substantially reduced protein binding, leading to a much larger volume of distribution than in adults, but an increased proportion of unbound drug (56). 

For simplicity, the intravenous bolus one-compartment model is used for illustrative purposes. After introduction of an intravenous bolus dose (Dq) into the single compartment, the drug is assumed to distribute instantaneously through all fluids and tissues of the body. The property of kinetic homogeneity is also assumed. 

The simplest model is where (a) the drug distributes into a single compartment, represented by plasma, and (b) the effect is an instantaneous, direct function of the concentration in that compartment. In this situation, the relationship between drug concentration (O and a pharmacological effect (E) can be simply described by the linear function ... 

What the analysis of distribution makes evident is that the body is a heterogenous collection of compartments. This is reflected in the fact that the elimination of a drug, as described in Figure 9.15 as a simple first order process, often does not, in fact, follow such simple kinetics. The first order process shown in Figure 9.15 assumes that the drug enters and leaves a single compartment. However, if the drug enters and leaves a more complex system (such as a system of two or three compartments in series or... 

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... 

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. 

Standard PK models represent the body as either a single compartment, which assumes instantaneous distribution to all tissues or as two compartments, which assumes instantaneous distribution throughout the central compartment (containing the systemic circulation) and slower first-order distribution to the second compartment (representing tissues that equilibrate slowly). 

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