Central compartment, volume

Finally, the method used to calculate the volume of distribution may be influenced by renal insufficiency. The three most commonly used volume of distribution terms are volume of the central compartment (Ec), volume of the terminal phase (E, E jea). and volume of distribution at steady state (Eis). The central compartment volume is calculated as the intravenous bolus dose divided by the initial plasma concentration. E for many drugs approximates extracellular fluid volume and thus may be increased or decreased by shifts in this physiologic volume. Renal insufficiency, especially oliguric acute renal failure, is often accompanied by fluid overload and a resultant increased Ec due to reduced renal elimination of water and sodium. Uaiea Or E is Calculated as the total body clearance divided by the terminal elimination rate constant (k or /3). This volume term represents the proportionality constant between plasma concentrations in the terminal elimination phase and the amount of drug remaining in the body. E is affected by both distribution characteristics, as well as by the elimination rate constant. The third volume term, the steady-state volume of distribution (Ess), is calculated as (AUMC x dose)/AUC , where AUMC is the area under the first moment of the concentrationtime curve and AUC is the area under the concentration-time curve... 

The AUC is a measure of bioavailability, i.e. the amount of substance in the central compartment that is available to the organism. It takes a maximal value under intravenous administration, and is usually less after oral administration or parenteral injection (such as under the skin or in muscle). In the latter cases, losses occur in the gut and at the injection sites. The definition also shows that for a constant dose D, the area under the curve varies inversely with the rate of elimination kp and with the volume of distribution V. Figure 39.6 illustrates schematically the different cases that can be obtained by varying the volume of distribution Vp and the rate of elimination k both on linear and semilogarithmic diagrams. These diagrams show that the slope (time course) of the curves are governed by the rate of elimination and that elevation (amplitude) of the curve is determined by the volume of distribution. 

This model is an extension of the one-compartment model for intravenous injection (Section 39.1.1) which is now provided with a peripheral buffering compartment which exchanges with the central plasma compartment. Elimination occurs via the central compartment (Fig. 39.12). The model requires the estimation of the plasma volume of distribution and three transfer constants, namely for... 

Methods for calculating volume of distribution (VD) can be influenced by renal disease. Of the commonly used terms (i.e., volumes of central compartment, terminal phase, and distribution at steady state [ Vss]), Vss is the most appropriate for comparing patients with renal insufficiency versus those with normal renal function because Vss is independent of drug elimination. 

The term refers to the distribution volume of the effect compartment and thus the effect compartment becomes S5monymous with the central compartment. The above equation contains three unknown parameters making it impossible to predict the concentration or the effect (E(t)) as a function of time if we define the ratio of concentration in the effect compartment and the central compartment, or the partition coefficient, at equilibrium. 

In this equation, we now have the term for the volume of central compartment, V, instead of the volume term in the effect compartment. If we use the term Ce t)/K rather than Ce t) in the effect model, we can rewrite the effect as a function of time ... 

Figure 13.1. Compartmental model based on clearance and volume (Section 13.2.4.1). The drug is administered at a rate Ri into the central compartment, which is characterized by a volume of distribution K. The drug is transported to and from the peripheral compartment with inter-compartmental clearance CL12 and CL21, respectively (usually it is assumed that there is no net transport between the two compartments if the concentrations in both compartments are equal in this case CL21 = CLi2)- The peripheral compartment is characterized by a volume of distribution 1 2-Elimination may take place from both compartments and is characterized by clearance CL o and CL20, respectively.

Figure 13.2. Compartmental model based on rate constants (Section 13.2.4.1). The drug is administered at a rate into the central compartment, which is characterized by a volume of distribution V. The drug is transported to and from the peripheral compartment with rate constants and feii, respectively.

Figure 13.3. Model of Stella and Himmelstein, adapted from reference [5] (Section 13.3.1). The drug-carrier conjugate (DC) is administered at a rate i c(DC) into the central compartment of DC, which is characterized by a volume of distribution Fc(DC). DC is transported with an inter-compartmental clearance CLcr(DC) to and from the response (target) compartment with volume Fr(DC), and is eliminated from the central compartment with a clearance CZ.c(DC). The active drug (D) is released from DC in the central and response compartments via saturable processes obeying Michaelis-Menten kinetics defined by Fmax and Km values. D is distributed over the volumes Fc(D) and Fr(D) of the central and response compartment, respectively. D is transported with an inter-compartmental clearance CLcr(D) between the central compartment and response compartment, and is eliminated from the central compartment with a clearance CLc(D).

Distribution - The volume of distribution of the drug in the central compartment is approximately 14 L per 70 kg ideal body weight. Treprostinil was 91% bound to human plasma protein. 

Pharmacokinetics Population pharmacokinetic analysis gave the following values for a reference patient (white male, 45 years of age, with a body weight of 80 kg and no proteinuria) Systemic clearance is 15 mL/h, volume of central compartment is P.1160... 

PK model (Fig. 7). This compartment does not influence the pharmacokinetics of the drug because its volume is assumed to be negligibly small. The parameter eO serves to characterise the time needed to equilibrate the effect compartment with the central compartment where drug concentrations are measured. 

Clearance (Cl) and volumes of distribution (VD) are fundamental concepts in pharmacokinetics. Clearance is defined as the volume of plasma or blood cleared of the drug per unit time, and has the dimensions of volume per unit time (e.g. mL-min-1 or L-h-1). An alternative, and theoretically more useful, definition is the rate of drug elimination per unit drug concentration, and equals the product of the elimination constant and the volume of the compartment. The clearance from the central compartment is thus VVklO. Since e0=l, at t=0 equation 1 reduces to C(0)=A+B+C, which is the initial concentration in VI. Hence, Vl=Dose/(A+B-i-C). The clearance between compartments in one direction must equal the clearance in the reverse direction, i.e. Vl.K12=V2-k21 and VVkl3=V3-k31. This enables us to calculate V2 and V3. 

Although 17d>extrap i s the same as Vd from the one-compartment disposition model, one should apply this volume term cautiously to systems greater than one compartment. As Eq. (1.37) shows, V extrap is dependent on the elimination rate from the central compartment (k, 0) in a complex interaction between a and p. Of all the volume terms, V extrap overestimates the volume to the greatest degree and is probably the least useful in the design of controlled release delivery systems. 

It is possible to predict what happens to Vd when fu or fur changes as a result of physiological or disease processes in the body that change plasma and/or tissue protein concentrations. For example, Vd can increase with increased unbound toxicant in plasma or with a decrease in unbound toxicant tissue concentrations. The preceding equation explains why because of both plasma and tissue binding, some Vd values rarely correspond to a real volume such as plasma volume, extracellular space, or total body water. Finally interspecies differences in Vd values can be due to differences in body composition of body fat and protein, organ size, and blood flow as alluded to earlier in this section. The reader should also be aware that in addition to Vd, there are volumes of distribution that can be obtained from pharmacokinetic analysis of a given data set. These include the volume of distribution at steady state (Vd]SS), volume of the central compartment (Vc), and the volume of distribution that is operative over the elimination phase (Vd ea). The reader is advised to consult other relevant texts for a more detailed description of these parameters and when it is appropriate to use these parameters. 

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. 

Cl plasma concentration at time zero fi/2a, distribution half-life f1/2jg, elimination half-life Kej, elimination rate constant from central compartment Ki2/.K2i, transfer rate constant between peripheral and central compartments AUC(o ), total area under plasma drug concentration time curve Vd(area> apparent volume of distribution GB, total body clearance. 

In general, the volume of distribution of the central compartment (Vc), in which peptides and proteins initially distribute after an IVadministration, is typically equal to or slightly larger than the plasma volume of 3-8 L (approximate body water volumes for a 70-kg person interstitial 12 L, intracellular 27 L, intravascular 3 L). Furthermore, the steady-state volume of distribution (Vss) is usually no more than twice the initial volume of distribution, or approximately 14-20 L [13, 37, 43]. This distribution pattern has been described for the somatostatin analogue octreotide (Vc 5.2-10.2 L Vss 18-30 L), and t-PA analogue tenecteplase (Vc 4.2-6.3 L Vss 6.1-9.9 L) [52]. Epoetin-a also has a volume of distribution estimated to be close to the plasma volume at 0.0558 L/kg after an IVadministration to healthy volunteers [53]. Similarly, Vss for darbepoetin-a has been reported as 0.0621 L/kg after an IV administration in patients undergoing dialysis [54], and distribution of thrombopoie-tin has also been reported to be limited to the plasma volume (-3 L) [55]. 

In contrast to noncompartmental analysis, in compartmental analysis a decision on the number of compartments must be made. For mAbs, the standard compartment model is illustrated in Fig. 3.11. It comprises two compartments, the central and peripheral compartment, with volumes VI and V2, respectively. Both compartments exchange antibody molecules with specific first-order rate constants. The input into (if IV infusion) and elimination from the central compartment are zero-order and first-order processes, respectively. Hence, this disposition model characterizes linear pharmacokinetics. For each compartment a differential equation describing the change in antibody amount per time can be established. For... 

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