Elimination rate constant from central compartment

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. 

A clear distinction must be made between the elimination rate constant (Kio) and the slow disposition or post-distribution rate constant ip). The constant ICio is the elimination rate constant from the central compartment at any time while the disposition or post-distribution... 

Xi and X2 represent the doses of drug in the central compartment (1) and the peripheral compartments, respectively, k 2 represents the intercompartment rate constant from the central to the peripheral compartment, 21 represents the intercompartment rate constant from the peripheral back to the central compartment, and k o is the elimination rate constant. 

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. 

Another approach to make a model identifiable is to change the experimental design and collect additional data from another compartment. But this may not always resolve the problem. One common perception is that collecting urine is a useful aid in resolving identifiability problems. This is true only if the rate constants from all other losses from the central compartment are known. For example, if loss in Compartment 1 via k in Model A in Fig. 1.13 were entirely to urine, collecting urine from Compartment 3, in addition to the sample from Compartment 1, would not resolve the model s unidentifiability because k2o still remains nonsensical. In Model B in Fig. 1.13, suppose Compartments 3 and 4 represent urine, i.e., loss from Compartments 1 and 2 is entirely by renal elimination. Collecting urine from Compartments 3 and 4, in add-... 

In Equations 1.5 and 1.6, is a bolus intravenous dose P is the terminal elimination rate constant representing elimination out of the body when the drug follows a two-compartment model a, which is larger than p, is the distribution rate constant AUC is the area under the concentration-time curve for drug in plasma following the intravenous dose and k2i is a model parameter representing distribution of drug from the peripheral compartment into the central compartment. In both of the above equations, the term is equated to an elimination term, P in Equation... 

Cl = dose/AUC = Kiq V , where K q is first-order rate constant of elimination from central compartment... 

If, after the attainment of distribution equilibrium, the fraction of drug in the central compartment is equal to 1, then, from Eq. 13.38, /3 Kio- That is, the slow disposition rate constant would be equal to the elimination rate constant. What does this mean ... 

Km the first-order rate constant for metabolism of dmg or [in context] the Michaelis constant in non-linear pharmacokinetics Ko the zero-order elimination rate constant Mother the first-order rate constant for elimination of dmg by a process other than metabolism or renal excretion Kio for a two-compartment dmg, the first-order rate constant for elimination of dmg from the central compartment Ki2 for a two-compartment drug, the first-order rate constant for transfer from the central to the peripheral compartment K21 for a two-compartment drug, the first-order rate constant for transfer from the peripheral to the central compartment MAT mean absorption time mean residence time in the gastrointestinal tract synonymous with MRTgit... 

The terminology for the so-called central compartment is Q. There are various rate constants that should be included in the diagram K01 is the rate constant for a drug moving from the outside of the body (compartment 0) to the central compartment (compartment 1) K10 is the rate constant of elimination from Ci to C o- Single-compartment models do not occur physiologically. 

Figure 13.5. Model of Boddy, adapted from reference [7] (Section 13.3.3). The drug-carrier conjugate (DC) is administered at a rate i c(DC) into the central compartment, which is characterized by a volume of distribution To DC is transported by blood flow Qcr to and from the response (target) compartment, characterized by a volume of distribution Vr, and by blood flow Qct to and from the toxicity compartment, characterized by a volume of distribution VV- DC is eliminated from only the central compartment with a clearance CLc(DC). The active drug (D) is released from DC in the central, response and toxicity compartments with first-order rate constants kc, k and fcr> respectively. The D is distributed over these compartments in a manner similar to the DC. The D is eliminated from these compartments with a clearance of CLc(D), CLr(D) and CLt(D), respectively. Conventional drug administration can be simulated by the input of D at a rate i c(D) into the central compartment.

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. 

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... 

As stated above, the Vss calculation using Eqs. (5) or (10) is valid only when elimination exclusively occurs from the sampling (plasma/blood) compartment. When some or all elimination occurs from the tissue compartment (Fig. 7.1), the concentration versus time profile will still be characterized by a bi-exponential equation however, the ability of modeling systems to quantify the micro rate constants is lost. That is to say, essentially identical bi-exponential concentration time profiles are possible with and without elimination from the tissue compartment. Therefore, when modeling from a plasma profile only, there is no way of determining if the exit of drug from the body is exclusive to the central compartment. 

The in vitro study did not use adequate controls (e.g., pH, vehicle used, volume of test agent given, and samples taken from sham-operated animals), resulting in artifacts of methods rather than results in vitro data cannot predict the volume of distribution in central or in peripheral compartments in vitro data cannot predict the rate constants for chemical movement between compartments in vitro data cannot predict the rate constants of chemical elimination... 

Finally, the same result is obtained by applying Eq. A. 15 to this case. In this instance, the coefficients Af are A and B and A equals the rate constant for elimination from the central compartment, namely kiQ. 

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