Rate of distribution

Absorbed lead is distributed in various tissue compartments. Several models of lead pharmacokinetics have been proposed to characterize such parameters as intercompartmental lead exchange rates, retention of lead in various pools, and relative rates of distribution among the tissue groups. See Section 2.3.5 for a discussion of the classical compartmental models and physiologically based pharmacokinetic models (PBPK) developed for lead risk assessments. 

To characterize the kinetic stabilities of complexes, the rate constants should be used, determined for the exchange reactions occurring between the complexes and endogenous metal ions (e.g. Cu2+ and Zn2+). Similarly to the equilibrium plasma models, the development of a kinetic model is needed for a better understanding of the relation between the extent of in vivo dissociation and the parameters characterizing the rates of dissociation, the rates of distribution in the extracellular space and the rates of excretion of the Gd3+ complexes. 

Figure 9.1 illustrates the processes of chemical uptake and elimination via the respiratory surface for fish. These processes result from the combination of the water ventilation rate, the rate of chemical permeation across the membranes of the respiratory surface, and the rate of distribution of the chemical within the organism. 

From these studies it is evident that the rates of distribution depend greatly on the nature of the alkoxyl groups and the number of alkyl groups bonded to aluminum. 

The pharmacokinetic properties of the benzodiazepines in part determine their clinical use. In general, the drugs are well absorbed, widely distributed, and extensively metabolized, with many active metabolites. The rate of distribution of benzodiazepines within the body is different from that of other antiseizure drugs. Diazepam and lorazepam in particular are rapidly and extensively distributed to the tissues, with volumes of distribution between 1 L/kg and 3 L/kg. The onset of action is very rapid. Total body clearances of the parent drug and its metabolites are low, corresponding to half-lives of 20-40 hours. 

The classification of barbiturates as ultrashort-acting, short-acting, intermediate-acting, and long-acting refers to the duration of effect and not to the elimination half-life. The duration of action is determined by the rate of distribution into brain and subsequent redistribution to other tissues. ... 

As far as the rate component of bioavailability is concerned, it is estimated by two parameters, Cmax and tmax. The maximum plasma concentration (Cmax) is related to (a) total plasma clearance (b) the fraction of dose that reaches the general circulation without being metabolized (c) the rate of absorption and (d) the rates of distribution and elimination. The time to reach Cmax (tmax) depends on (a) the rate of absorption and (b) the rates of distribution and elimination. 

When a drug is administered as an i.v. bolus, the entire dose of the drug is injected straight into the blood. Therefore, the absorption process is considered to be completed immediately, and the concentration-time profile of fhe drug in plasma will be determined by the rate of distribution and elimination. When the distribution of the drug is very fast, the plasma concentration-time curve is determined only by the elimination rate and shows a mono-exponential (first-order) decline (a theoretical example is shown in Figure 31.7a ... 

FIGURE 3.6 Compartmental analysis for different terms of volume of distribution. (Adapted from Kwon, Y., Handbook of Essential Pharmacokinetics, Pharmacodynamics and Drug Metabolism for Industrial Scientists, Kluwer Academic/Plenum Publishers, New York, 2001. With permission.) (a) Schematic diagram of two-compartment model for compound disposition. Compound is administrated and eliminated from central compartment (compartment 1) and distributes between central compartment and peripheral compartment (compartment 2). Vj and V2 are the apparent volumes of the central and peripheral compartments, respectively. kI0 is the elimination rate constant, and k12 and k21 are the intercompartmental distribution rate constants, (b) Concentration versus time profiles of plasma (—) and peripheral tissue (—) for two-compartmental disposition after IV bolus injection. C0 is the extrapolated concentration at time zero, used for estimation of V, The time of distributional equilibrium is fss. Ydss is a volume distribution value at fss only. Vj, is the volume of distribution value at and after postdistribution equilibrium, which is influenced by relative rates of distribution and elimination, (c) Time-dependent volume of distribution for the corresponding two-compart-mental disposition. Vt is the starting distribution space and has the smallest value. Volume of distribution increases to Vdss at t,s. Volume of distribution further increases with time to Vp at and after postdistribution equilibrium. Vp is influenced by relative rates of distribution and elimination and is not a pure term for volume of distribution. 

Kinetics of Effects. Many rate constants may affect the activities of antisense oligonucleotides, such as the rate of synthesis and degradation of the target RNA and its protein the rates of uptake into cells the rates of distribution, extrusion, and metabolism of an oligonucleotide in cells and similar pharmacokinetic considerations in animals. Fortunately, in the past several years, many more careful dose-response and kinetic studies have been reported and in general they demonstrated a relatively slow onset of action and a duration of response consistent with the elim-. ination rates of the drugs tested (see below). 

Both the rate and extent of drug distribution across tissue barriers can have a profound impact on pharmacokinetic and pharmacodynamic properties. The extent of drug distribution manifests itself locally as the tissue to plasma (or blood) concentration ratio. Collectively, the extent of distribution into all the tissues results in the apparent volume of distribution. Simply put, the pharmacokinetic parameter volume of distribution reflects the ratio of individual tissue to plasma drug concentration weighed for tissue volume. The rate of distribution (together with the extent of distribution) can influence the shape of the plasma versus time profile for a drug, which can give rise to differences in elimination half-life as well as onset and duration of action. 

Since the target site of a drug is rarely at the site of administration or in the systemic circulation, delivery of the drug to the target tissue by the distribution process is often a critical determinant of the drug s effectiveness. Many of the physiochemical and physiological factors involved in the distribution process have been discussed previously in Section 10.2 or in Chapter 7. This section will focus on the means by which the distribution process is incorporated and represented in PK models. This involves mathematical terms to represent both the extent of distribution and the rate of distribution transport. 

Analogous to first-order absorption, first-order distribution indicates that the rate of distribution from one location to another is proportional to the amount of drug remaining to be distributed (A ) raised to the power of one. This could be written for distribution in a manner analogous to first-order absorption (Section 10.3.2.3) in the form... 

Figure 10.16 Graphical representation of the rates of distribution between two compartments.

By convention, compartment 1 is taken to include the systemic circulation, and compartment 2 represents the tissue or tissues that are exchanging drug molecules with the circulation. The amount of drug remaining in compartment 1 is labeled Ai, and the amount remaining in compartment 2 is A2. The rate constant for distribution from 1 2 is labeled ki2, and the rate constant for distribution from 2 1 is 1. The rate of distribution from 1 2 can then be written as... 

All these conventional notation terms are illustrated in Figure 10.16. The overall net rate of distribution (taken as positive for net distribution from 1 2) can finally be expressed as... 

It should be noted that as in absorption, first-order distribution represents linear kinetics, as the net rate of distribution is a linear function of the amount of drug remaining in compartment 1 (Ai) and the amount of drug remaining in compartment 2( 2). Also as in the absorption case, a half-life of distrihution tvz,dist) be defined in terms of the distrihution rate constants. However, because distribution occurs in more than one direction, and due to other model complications that will be explained later, the distribution half-life cannot be written as a simple function of ki2 and 1. It turns out that the distribution half-life is defined in terms of a hybrid rate constant (/Ij) by the equation... 

Each of the exponential decay terms in the generalized multicompartment models represent a distinct phase or change in shape of the plasma concentration versus time curve. The extra (n+l) exponential term for first-order absorption always has the absorption rate constant (ka) in the exponent, and always represents an absorption phase. The exponential term with the smallest rate constant (A ) always represents the elimination phase, and this rate constant always represents the elimination rate constant and always equals the terminal line slope m= — A J. All other exponential terms represent distinct distribution phases caused by the different rates of distribution to different tissue compartments. 

As soon as a drug finds its way into the blood stream, it tries to approach the site of biological action. Hence, the distribution of a drug is markedly influenced by such vital factors as tissue distribution and membrane penetration, which largely depends on the physico-chemical characteristics of the drug. For instance, the effect of the ultra-short acting barbiturate thiopental may be explained on its dissociation constant and lipid solubility. It is worthwhile to observe here that the dmation of thiopental is not influenced by its rate of excretion or metabolism, but by its rate of distribution. 

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