Elimination, pharmacokinetics rate constant

The pharmacokinetics (elimination rate constant, half-life, AUC) of a single 400-mg dose of erythromycin ethyl succinate were not significantly altered by a single 1-g dose of sucralfate in 6 healthy subjects. It was concluded that the therapeutic effects of erythromycin are unlikely to be affected by concurrent use. ... 

Pharmacokinetics. Figure 1 Main pharmacokinetic processes and parameters Half-life (T1/2), volume (Vd), elimination rate constant (Ke), and clearance (Cl). 

Other applications of the previously described optimization techniques are beginning to appear regularly in the pharmaceutical literature. A literature search in Chemical Abstracts on process optimization in pharmaceuticals yielded 17 articles in the 1990-1993 time-frame. An additional 18 articles were found between 1985 and 1990 for the same narrow subject. This simple literature search indicates a resurgence in the use of optimization techniques in the pharmaceutical industry. In addition, these same techniques have been applied not only to the physical properties of a tablet formulation, but also to the biological properties and the in-vivo performance of the product [30,31]. In addition to the usual tablet properties the authors studied the following pharmacokinetic parameters (a) time of the peak plasma concentration, (b) lag time, (c) absorption rate constant, and (d) elimination rate constant. The graphs in Fig. 15 show that for the drug hydrochlorothiazide, the time of the plasma peak and the absorption rate constant could, indeed, be... 

Elimination Rate Constant, (Kd), is a crucial pharmacokinetic parameter which measures the rate of elimination of drugs from the body. Kd is specific for a given drug, and has the units of time"1. When the Kd is greater, the drug is eliminated rapidly. It is calculated from the slope of the terminal portion of the log plasma concentration versus time profile. From the terminal portion of the plasma concentration versus time profile, Kd is calculated as,... 

Single-dose pharmacokinetics including relationship among dose and plasma concentration, absorption rate, total, metabolic and renal clearance, volume of distribution, elimination rate constant and half-life... 

Pharmacokinetics According to product label, analysis of data from a study in healthy men and women who received intravenous and subcutaneous Neumega revealed that following subcutaneous administration absorption is the rate-limiting step. Hence the elimination rate constants... 

In pharmaceutical research and drug development, noncompartmental analysis is normally the first and standard approach used to analyze pharmacokinetic data. The aim is to characterize the disposition of the drug in each individual, based on available concentration-time data. The assessment of pharmacokinetic parameters relies on a minimum set of assumptions, namely that drug elimination occurs exclusively from the sampling compartment, and that the drug follows linear pharmacokinetics that is, drug disposition is characterized by first-order processes (see Chapter 7). Calculations of pharmacokinetic parameters with this approach are usually based on statistical moments, namely the area under the concentration-time profile (area under the zero moment curve, AUC) and the area under the first moment curve (AUMC), as well as the terminal elimination rate constant (Xz) for extrapolation of AUC and AUMC beyond the measured data. Other pharmacokinetic parameters such as half-life (t1/2), clearance (CL), and volume of distribution (V) can then be derived. 

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. 

Further support for the thesis that the observed drug-membrane interaction directly or indirectly affects the receptor and does not represent pharmacokinetic influences can be derived from preliminary data of a small set of five derivatives for which some pharmacokinetic parameters were determined in rats [41]. The pharmacokinetic parameters - area under the curve (AUC), elimination rate constant (kd ), half-life (to 5), the time of maximal concentration (tmax), and maximal concentration (cmax) - did not correlate significantly with either log 1/ED50(MES), log Al/T2, or log fC0i t. Instead, even for this small set of compounds, log 1 /ED50(MES) correlated again significantly with both parameters log Al/T2 and log K ocL (r = 0.998 and 0.973 respectively). 

Pharmacokinetic studies are in general less variable than pharmacodynamic studies. This is so since simpler dynamics are associated with pharmacokinetic processes. According to van Rossum and de Bie [234], the phase space of a pharmacokinetic system is dominated by a point attractor since the drug leaves the body, i.e., the plasma drug concentration tends to zero. Even when the system is as simple as that, tools from dynamic systems theory are still useful. When a system has only one variable a plot referred to as a phase plane can be used to study its behavior. The phase plane is constructed by plotting the variable against its derivative. The most classical, quoted even in textbooks, phase plane is the c (f) vs. c (t) plot of the ubiquitous Michaelis-Menten kinetics. In the pharmaceutical literature the phase plane plot has been used by Dokoumetzidis and Macheras [235] for the discernment of absorption kinetics, Figure 6.21. The same type of plot has been used for the estimation of the elimination rate constant [236]. 

Un the classical pharmacokinetic-pharmacodynamic literature, the effect site concentration and the effect site elimination rate constant are denoted by eg and kgq, respectively. Here, the symbols y (t) and ky are used instead. 

Fig. 9. Semilogarithmic plots of plasma concentrations versus time for 3 doses of salicylate administered to the same subject, illustrating capacity-limited elimination. At low plasma concentrations, parallel straight lines are obtained from which the first-order elimination rate constant can be estimated. As long as concentrations remain sufficiently high to saturate the process, elimination follows zero-order kinetics (C. A. M. van Ginneken et al., J. Pharmacokinet. Biopharm., 1974,2, 395-415).

In the absence of concentration-time profiles after IV administration, it is impossible to estimate the actual elimination rate constant, and the interpretation of absorption and elimination rates after SC administration of macromolecules must be done cautiously. It is for this reason surprising that so few published pharmacokinetic studies include IV administration to assess whether or not the macromolecule follows flip-flop pharmacokinetics. 

For a number of years, computers have been successfully utilized in pharmacokinetics to 1) fit blood-level data to the appropriate model (single, two, or multiple compartments) and to calculate model parameters, such as absorption rate constant, elimination rate constant, half-life, and volume of distribution 2) evaluate... 

To facilitate the understanding of the pharmacokinetic concepts, the examples given previously are for the simplest and the most effective route of administration, that is, intravenous administration. When exposure is to toxic compounds (e.g., occupational or environmental exposure), however, other routes are frequently involved. These routes include respiratory, cutaneous, mucous, or oral uptake. In such cases, pharmacokinetic analyses are more complex since they should take into account the various processes responsible for the uptake of a xenobiotic. Usually, this consists of introducing into equations an additional term that contains a rate constant describing the uptake, operating in a direction opposite to, yet not conceptually different from the elimination rate constant. 

The advantages of using non-compartmental methods for calculating pharmacokinetic parameters, such as systemic clearance (CZg), volume of distribution (Vd(area))/ systemic availability (F) and mean residence time (MRT), are that they can be applied to any route of administration and do not entail the selection of a compartmental pharmacokinetic model. The important assumption made, however, is that the absorption and disposition processes for the drug being studied obey first-order (linear) pharmacokinetic behaviour. The first-order elimination rate constant (and half-life) of the drug can be calculated by regression analysis of the terminal four to six measured plasma... 

In a study of the disposition of antipyrine (20 mg/kg, i.v.) in eight healthy Standardbred mares aged between six and nine years, the following values (mean + SD or median (range)) were obtained for the major pharmacokinetic parameters Pd(ss) (mL/kg) 864 (731-952), CZb (mL/minkg) 6.2 (4.3-8.6), MRT (h) 2.3 (1.7-3.5), and the overall elimination rate constant (per hour) 0.37 + 0.09 (Dyke et al, 1998). It was established that renal clearance accounts for < 2% of systemic clearance, which implies that hepatic clearance exceeds 98%, and that 4-hydroxyantipyrine (formed by hepatic microsomal oxidation) is the major... 

As discussed previously, clearance and volume of distribution are the primary fundamental parameters required to describe pharmacokinetics. They are related to the elimination rate constant by... 

The first step is to estimate this patient s pharmacokinetic parameters of tobramycin on the basis of published population data. The volume of distribution in this patient is 23.1 L (0.33 L/kg x 70 kg), and his residual total body clearance (CLres) estimated from the relationship between CL and creatinine clearance [CLres = CLcr X 0.98] is 3 mL/min or 0.176 L/h. The elimination rate constant can be approximated as ... 

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. 

For example, Wu (2000) computed the AUC, AUMC, and MRT for a 1-compartment model and then showed what impact changing the volume of distribution and elimination rate constant by plus or minus their respective standard errors had on these derived parameters. The difference between the actual model outputs and results from the analysis can then be compared directly or expressed as a relative difference. Alternatively, instead of varying the parameters by some fixed percent, a Monte Carlo approach can be used where the model parameters are randomly sampled from some distribution. Obviously this approach is more complex. A more comprehensive approach is to explore the impact of changes in model parameters simultaneously, a much more computationally intensive problem, possibly using Latin hypercube sampling (Iman, Helton, and Campbell, 1981), although this approach is not often seen in pharmacokinetics. 

Zhi, J. Unique pharmacokinetic characteristics of the 1-compartment first-order absorption model with equal absorption and elimination rate constants. Journal of Pharmaceutical Sciences 1990 79 652-654. 

Half-life. In pharmacokinetics, the time it takes for the concentration of a drug to be reduced to a half. It is related to the elimination rate constant. 

Some pharmacokinetic software packages perform noncompartmental analysis without fitting the entire response curve. These programs compute the elimination rate constant (k) for the terminal elimination phase of the data, and then use a trapezoidal rule with this elimination rate constant to compute AUC and AUMC. With these terms, the total body clearance, the steady-state volume of distribution, and the mean residence time in the body can be calculated. Without C , it is not possible to calculate the volume of distribution of the central compartment or the mean residence time of the sampling compartment. The latter term is therefore critical in accurately determining these parameter values and depends on an unbiased and close fit of the data to Equations 13.2 and 13.6. 

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