Two-compartment model of distribution

The one-compartment model of distribution assumes that an administered drug is homogeneously distributed throughout the tissue fluids of the body. For instance, ethyl alcohol distributes uniformly throughout the body, and therefore any body fluid may be used to assess its concentration. The two-compartment model of distribution involves two or multiple central or peripheral compartments. The central compartment includes the blood and extracellular fluid volumes of the highly perfused organs (i.e., the brain, heart, liver, and kidney, which receive three fourths of the cardiac output) the peripheral compartment consists of relatively less perfused tissues such as muscle, skin, and fat deposits. When distributive equilibrium has occurred completely, the concentration of drug in the body will be uniform. 

Rat studies using radiolabeled EGb 761 have revealed that the extract follows a two-compartment model of distribution (19). The radiolabeled extract was distributed into glandular and neuronal tissues, as well as the eyes. 

This approach is presented for the two-compartment model of Section 9.2.7. At the second level in (9.16), we assume that A is a gamma-distributed random variable, A Gam(A2,p2)- The Laplace transform of the state probability is... 

Physiologically based toxicokinetic models are nowadays used increasingly for toxicological risk assessment. These models are based on human physiology, and thus take into consideration the actual toxicokinetic processes more accurately than the one- or two-compartment models. In these models, all of the relevant information regarding absorption, distribution, biotransformarion, and elimination of a compound is utilized. The principles of physiologically based pharmaco/ toxicokinetic models are depicted in Fig. 5.41a and h. The... 

Whether the chemical distributes evenly throughout the body (one-compartment model) or differentially between different compartments (models of two or more compartments). 

The pharmacokinetic behaviour of all hydrophiUc, NS-CA is well known. They all follow an open two-compartment model characterized by rapid distribution into the extracellular space volume and are excreted almost exclusively by glomerular filtration. 

For a two-compartment model C=0 and the equation is bi-exponential. The exponents o, jSand y are related to the intercompartmental transfer rate constants by complex formulae. They are related to the half-lives for each of the distribution and terminal phases by the relationship ... 

Figure 3.28 Log10 plasma concentration against time profile for a foreign compound after intravenous administration. The distribution of this compound fits the two-compartment model. The dotted 1 line is determined by the method of residuals as described in the text. (Thus, R" = R - R, etc.)...

A two-compartment open linear model has been described for the pharmacokinetic profile of cocaine after intravenous administration.14 The distribution phase after cocaine administration is rapid and the elimination half-life estimated as 31 to 82 min.14 Cone9 fitted data to a two-compartment model with bolus input and first-order elimination for the intravenous and smoked routes. For the intranasal route, data were fitted to a two-compartment model with first-order absorption and first-order elimination. The average elimination half-life (tx 2 3) was 244 min after intravenous administration, 272 min after smoked administration, and 299 min after intranasal administration. 

A.2 Two-Compartment Open Model When the dmg concentration -time profile demonstrates a biexponential decline following IV dosing, a two-compartment model that is the sum of two first-order processes (distribution and elimination) best describe the data (Fig. 2.4). A dmg that follows the PK of a... 

The central compartment represents the blood/plasma and any other tissue that rapidly equilibrates, relative to the distribution rate, with the blood/plasma (e.g., liver or heart tissue). The tissue compartment represents all other tissues that keep the drug and reach steady-state concentrations more slowly than the tissues of the central compartment. Since the two-compartment model is fairly robust in describing a bulk of all drugs, we will limit our discussion to two compartments with elimination... 

Figure 6.13 (a) Semilog plot of plasma concentration for (Cp) versus time representative of a two-compartment model. The curve can be broken down into an a or X i distribution phase and ft or k2 elimination phase, (b) Two-compartment model with transfer rate constants, Kn and K2, and elimination rate constant, Ke. ... 

PK modeling can take the form of relatively simple models that treat the body as one or two compartments. The compartments have no precise physiologic meaning but provide sites into which a chemical can be distributed and from which a chemical can be excreted. Transport rates into (absorption and redistribution) and out of (excretion) these compartments can simulate the buildup of chemical concentration, achievement of a steady state (uptake and elimination rates are balanced), and washout of a chemical from tissues. The one- and two-compartment models typically use first-order linear rate constants for chemical disposition. That means that such processes as absorption, hepatic metabolism, and renal excretion are assumed to be directly related to chemical concentration without the possibility of saturation. Such models constitute the classical approach to PK analysis of therapeutic drugs (Dvorchik and Vesell 1976) and have also been used in selected cases for environmental chemicals (such as hydrazine, dioxins and methyl mercury) (Stem 1997 Lorber and Phillips 2002). As described below, these models can be used to relate biomonitoring results to exposure dose under some circumstances. 

The structure of a compartmental PK model is given by the number of compartments being used and the way the compartments are connected. For most drugs the plasma concentration-time profiles can be sufficiently described by one-, two-or three-compartment models. A one-compartment model assumes that no time is necessary for the distribution of the drug and the whole distribution occurs within this one compartment. The two-compartment model implements in addition to a central compartment a peripheral compartment which allows the description of distribution processes of the compound in, e.g. tissues with different physicochemical properties. The three-compartment model provides an additional compartment for distribution processes. The use of more than three compartments is quite rare, but there are some situations where the model can get quite difficult, e.g. if the concentration-time profile of metabolites are also considered within the model. For more information regarding compartment models, refer to Rowland and Tozer... 

Consider the irreversible two-compartment model with survival, distribution, and density functions starting time, the molecules are present only in the first compartment. The state probability p (t) that a molecule is in compartment 1 at time t is state probability p2 (/,) that a molecule survives in compartment 2 after time t depends on the length of the time interval a between entry and the 1 to 2 transition, and the interval I, a between this event and departure from the system. To evaluate this probability, consider the partition 0 = ai < a.2 < < o.n 1 < an = t and the n — 1 mutually exclusive events that the molecule leaves the compartment 1 between the time instants a, i and a,. By applying the total probability theorem (cf. Appendix D), p2 (t) is expressed as... 

To illustrate the process uncertainty, we present the case of the two-compartment model, Figure 9.1. Equations (9.5) associated with the transfer-intensity matrix H were used to simulate the random distribution of particles, which expresses the process uncertainty. 

Fig. 2. (Continued) method (regression model) third row SUV image (SUV), global metabolic rate (influx), and distribution volume (DV). The parametric images are obtained by applying the Patlak model to the data fourth row SUV image (SUV), phosphorylation rate (k3), and transport rate (kl). The images are obtained by a voxel-based application of the two-compartment model.

FIGURE 3.6 Serum gentamicin concentrations measured in a patient during and after a 10.5-day course of therapy (80 mg every 36 hrs). Data were analyzed with the two-compartment model shown in the figure. The half-life of serum levels during therapy is primarily reflective of renal elimination. The terminal half-life seen after therapy was stopped is the actual distribution phase. (Reproduced with permission from Schentag JJ, Jusko WJ, Plant ME, Cumbo Tj, Vance JW, Abrutyn E. JAMA 1977 238 327-9.)... 

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