Distribution rate constant

Equation 5 was actually derived for the case where reaction occurs at some contact distance r = a. A derivation of eq 5 for the present case of a volume distributed rate constant k(r) is approximate and is given elsewhere (28). 

Fig. 14. Schematic description of pharmacokinetic and pharmacodynamic determinants of drug action. Distribution from the measurement site (Cp) to the biophase (Ce), determined by a distribution rate constant is followed by drug-induced inhibition or stimulation of the production (k ) or removal (A out) of a mediator (R), transduction of the response R and further transformation of R to the measured effect E, if the measured effect variable is not R. (Modified from Jusko WJ, Ko HC, Ebling WF. Convergence of direct and indirect pharmacodynamic response models. J Pharmacokinet Biopharm 1995 23 5-6.)...

A basic assumption related to both methods of analysis is that the elimination of drug from the body is exclusively from the sampling compartment (i. e., blood/ plasma), and that rate constants are first order. However, when some or all of the elimination occurs outside the sampling compartment - that is, in the peripheral or tissue compartment(s) - these types of analysis are prone to error in the estimation of Vss, but not CL. In compartmental modeling, the error is related to the fact that no longer do the exponents accurately reflect the inter-compartmental and elimination (micro) rate constants. This model mis specification will result in an error that is related to the relative magnitudes of the distribution rate constants and the peripheral elimination rate constant. However, less widely understood is the fact that this model mis specification will also result in errors in noncompartmental pharmacokinetic analysis. 

Note that the effect equilibration rate constant (ke0) may be viewed as a first-order distribution rate constant. It can also be thought of in terms of the rate of presentation of a drug to a specific tissue, determined by, for example, tissue perfusion rate, apparent volume of the tissue and eventual diffusion into the tissue. The results of the data fitting in this exercise with the analgesic are Emax 4.5 EC50 0.61 ng-ml 1 and e0 0.07 h1. 

A multiple compartment system would probably be necessary to obtain a rate constant for metabolism, distribution rate constant, rate constant for absorption, etc. Sulfonylurea drugs may lower blood sugar by stimulating the beta cells of the pancreatic islets to release endogenous insulin. Also, it has been reported that the sulfonylureas block the degradation of insulin by the enzyme insulinase13. 

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. 

The plasma concentration versus time relationship in Equation (10.198) contains two exponential decay terms. The first exponential decay term contains the larger hybrid rate constant (/li), which dominates at early times during the distribution phase. Hence Xi is called the hybrid distribution rate constant. The second exponential decay term contains the smaller hybrid rate constant (/I2) which dominates at later times during the elimination phase. The slope of the terminal line is equal to —I2 rather than the negative value of the micro elimination rate constant (—kio), and hence I2 called the hybrid elimination rate constant. The relationships for the two-compartment elimination half-life are then written in terms of I2... 

Figure 10.62 Illustration of how In(Cp) versus t changes with an increase or decrease in the hybrid distribution rate constant (2i) or distribution half-life (fi/2,d/sf)-...

The postinfusion plasma concentration versus time relationship in Equation (10.241) contains two exponential decay terms. The first exponential decay term contains the larger hybrid rate constant (/li), which dominates during the distribution phase. Hence Xi is called the hybrid distribution rate constant. The second exponential decay term contains the smaller hybrid rate... 

Figure 1 shows a schematic depiction of the potential energy surface for a generic bi-molecular reaction. Within the realm of classical mechanics the thermal, or equilibrium (i.e., reactants in a Boltzmann distribution), rate constant is given by (1,3,5)... 

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... 

Determination of the distribution half life ti/2)a and distribution rate constant (a). 

Relationship between the slow disposition (or post-distribution) rate constant (fi) and the elimination rate constant (ICio), the apparent... 

For ordinary pharmacokinetics, the distribution rate constant (a) is greater than the slow disposition, or post-distribution rate constant (/ )... 

Figure 13.10 A plasma concentration (Cp) versus time profile for a drug that obeys a two-compartment model following intravenous bolus administration plotted on semilogarithmic paper, p, slow disposition, or post-distribution, rate constant 6, empirical constant 4, apparent volume of distribution for the central compartment /C21, transfer rate constant Xq, administered dose a, distribution rate constant.

When an administered drug exhibits the characteristics of a two-compartment model, the difference between the distribution rate constant (a) and the slow (post-) distribution rate constant (/ ) plays a critical role. The greater the difference between these, the more conspicuous is the existence of a two-compartment model and, therefore, the greater is the need to apply all the equations for a two-compartment model. Failure to do so will, undoubtedly, result in inaccurate clinical predictions. If, however, the difference between the distribution and the slow post-distribution rate constant is small and will not cause any significant difference in the clinical predictions, regardless of the model chosen to describe the pharmacokinetics of a drug, then it may be prudent to follow the principle of... 

Is it possible for the rate constant associated with elimination to have a greater value than that for the distribution rate constant The answer to this is "Yes." This type of flip-flop kinetics occurs for the aminoglycoside antibiotic gentamicin. In the case of gentamicin, the terminal (fi) portion of the curve, which represents the slower process, corresponds to distribution while the steep feathered line, whose slope is -a/2.303, corresponds to the faster process (the elimination process in this case). Ordinarily, for most drugs, this is not the case, and we can refer to a as the distribution rate constant and to jS as the postdistribution rate constant. 

Once the values of distribution rate constant and the post-distribution rate constant, as well as the values of the two empirical constants A andU (the two y-axis intercepts) are obtained by the methods described above, or are taken to be the values reported in the literature, the micro rate constants for elimination and inter-compartmental transfer can be generated using Equation 13.6 ... 

Note that A + B = (Cp)o-The distribution rate constant, the post-distribution rate constant and the empirical constants A and B can be determined from the plasma concentration versus time data. Using these values and Eq. 13.14, the inter-compartmental rate constant (IC21) can be calculated. Note that this is a first-order rate constant associated with the transfer of a dmg from compartment 2 (i.e. peripheral or tissue) to the central compartment (compartment 1). 

Please note that in Eq. 13.31 the last observed plasma concentration is divided by the post-distribution rate constant (/3) because of the presence of a two-compartment model. Compare Eq. 13.31 with Eq. 4.26 (p. 66) and Eq. 7.15 (p. 134), which were employed when the administered drug exhibited the characteristics of a one-compartment model. 

Since both the a and p rate constants depend on the pure distribution rate constants (Ki2 andlCai) and on the pure elimination rate constant (ICio), they are termed "hybrid" rate constants. 

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... 

Determination of the distribution rate constant and the empirical constant A... 

Table 13.4 gives data for the difference between the observed and the extrapolated plasma concentrations (Cp)diff at various times, from which the distribution rate constant (a) and the empirical constant A can be obtained. 

Ratio of the inter-compartmental transfer rate constant associated with the transfer of drug from the peripheral compartment to the central compartment over the distribution rate constant. 

Please note that the distribution rate constant a is greater than the disposition rate constant j3. 

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