Elimination rate constant determination

One sure way is to have an rmambiguous value of the drug s elimination half life (and therefore of the elimination rate constant) determined from a study in which the drug is administered intravenously. Another strong indication that the regular model is the correct model is the situation where the extravascular administration is of a type that should not have any kind of slow, extended absorption. An example of this is an immediate release tablet or a capsule. This type of dosage form should not have an absorption half life that is slower than its elimination half life. 

In addition to the elimination rate constant, the half-life (T/i) another important parameter that characterizes the time-course of chemical compounds in the body. The elimination half-life (t-1/2) is the time to reduce the concentration of a chemical in plasma to half of its original level. The relationship of half-life to the elimination rate constant is ti/2 = 0.693/ki,i and, therefore, the half-life of a chemical compound can be determined after the determination of k j from the slope of the line. The half-life can also be determined through visual inspection from the log C versus time plot (Fig. 5.40). For compounds that are eliminated through first-order kinetics, the time required for the plasma concentration to be decreased by one half is constant. It is impottant to understand that the half-life of chemicals that are eliminated by first-order kinetics is independent of dose. ... 

The area under the PCP concentration-time curve (AUC) from the time of antibody administration to the last measured concentration (Cn) was determined by the trapezoidal rule. The remaining area from Cn to time infinity was calculated by dividing Cn by the terminal elimination rate constant. By using dose, AUC, and the terminal elimination rate constant, we were able to calculate the terminal elimination half-life, systemic clearance, and the volume of distribution. Renal clearance was determined from the total amount of PCP appearing in the urine, divided by AUC. Unbound clearances were calculated based on unbound concentrations of PCP. The control values are from studies performed in our laboratory on dogs administered similar radioactive doses (i.e., 2.4 to 6.5 pg of PCP) (Woodworth et al., in press). Only one of the dogs (dog C) was used in both studies. 

The data used are given in Table I. The elimination rate constants included were determined at 20° C. (5). The toxicity to mosquito larvae, given as median lethal dosages (concentration in parts per million of water required to cause 50% mortality in 48 hours), was estimated from the data of Deonier et al. (9) and is probably reproducible to within 30%. 

Thus after 6 hours the semilog plot of Cp versus time shown in Fig. 10 becomes a straight line and kei can be determined from the slope. Therefore, the overall elimination rate constant for a drug may be accurately determined from the tail of a semilog plot of plasma concentration versus time following extravascular administration if ka is at least five times larger than kei. 

The ratio (Q) of the estimated elimination rate constant or total body clearance relative to normal renal function is used to determine the dose or dosing interval alterations needed (CLfaii is the clearance with impaired renal function). 

The determination of the bioconcentration factor (BCF) can be performed in two different ways computationally with quantitative structure activity relationship (QSAR) methods, or from experimental measurements [2], The QSAR methods estimate BCF from the structural or physicochemical properties of the compound, whereas the experimental methods use measured values of uptake and elimination rate constants or concentrations in the steady state. 

The equilibration of drug between plasma and biophase is determined by the parameter KeQ and the equilibration half-time In 21 Keg, and T ITEe is the length of time it takes for plasma concentration and effective concentration to reach equilibrium this time can range from a few minutes to several hours. For drugs with short half-time, the value of KCq is large and an equilibration is reached fast, and thus the plasma concentration is a good indicator of biophase levels for drugs with low Kcg (lower than the terminal elimination-rate constant), an equilibrium will never be reached. The time at which peak concentration is achieved (Te ) is expressed as... 

Table 7.2 Comparison of Elimination Rate Constants (/CeS d M and Halflives (fi/2s d) Determined in SPMDs and Bivalves... 

At other times the compound is found to have significant protein binding. Again this can lead to an increase in the solubility of the compound. If the binding occurs in the blood, it could lead to reduced elimination rate constants. Whenever the pharmacology studies indicate some type of interaction is happening additional studies should be conducted to try and elucidate the interactions. If the compound has a particularly low solubility it can lend itself to solubility studies which can be used to determine the interaction equilibrium constants and effect on the overall solubility. 

The elimination process is represented by the elimination rate constant ke, which may be determined from the gradient of the plasma profile (Fig. 3.25). The reasons for the overall process of elimination being first order are that the processes governing it (excretion by various... 

Figure 3.25 Log10 plasma concentration time profile for a foreign compound after intravenous administration. The plasma half-life (fo) and the elimination rate constant (fce ) of the compound can be determined from the graph as shown.

The first-order elimination rate constant K can be determined as shown in Eq. (1.4) and has units of 1/time. The larger the value of K, the more rapidly elimination occurs. Once K has been determined, then calculating the half-life t1/2 is straightforward (Eq. 1.5). 

Cp is the plasma concentration of the drug at time t. The elimination rate constant is keb with units of inverse time. Cp° is the plasma concentration at t = 0. Cp° is a special case that is more theoretical than real. At the time of the injection (t = 0), the drug bolus hits the bloodstream. At this instant, the drug has not mixed with the entire blood supply. The concentration at the site of injection is very high, but blood in other parts of the body still has a Cp of 0. For this reason, Cp° cannot be directly measured experimentally but must be determined by extrapolation of the Cp-time line back to the y-axis. 

Knowing total clearance for a drug is important. Clearance is determined from Cp-time plot data for an IV bolus. Cp-time data for an IV bolus can be used to determine the elimination rate constant of a drug ( el) as well as the hypothetical Cp°. These two values allow direct calculation of the area under the curve (AUC) of the Cp-time plot with Equation 7.10 (Figure 7.5).1... 

Volume of distribution and clearance are both properties of a drug. These two properties determine a drug s elimination rate constant and half-life (Equation 7.12). 

SOLUTION The only equation we have that contains Cpss is Equation 7.18. To use this equation, we need to determine the elimination rate constant (kel) for morphine. Fortunately, with Equation 7.12 we can calculate el from the two parameters we have been given V d and CL. Convert CL to liters to make the units match and switch up the final time units to hours instead of minutes. 

From these simulations based on a two-compartment model with both plasma and tissue elimination, a Vss determined by utilizing noncompartmentai methods will have a value less than the true Vss. These simulations also show that the shape of the plasma concentration-time curve and the relative magnitudes of the plasma and tissue elimination rate constants do not correlate with the error. However, this error does tend to be greater for hypothetical drugs that are more extensively eliminated by tissue routes. 

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). 

Since drug elimination mechanisms in humans generally follow first-order kinetics (nonsaturated), an elimination rate constant (Kt) can be determined according to the following formula (assuming a one-compartment model) ... 

Based on measured DNOC blood levels of a worker exposed to DNOC by a combination of inhalation and dermal routes (Pollard and Filbee 1951), an elimination rate constant of 0.002 hour and a half- life of 153.6 hours were determined (King and Harvey 1953b). A peak urinary quantity of 22 mg DNOC was found on the third day after the employee was admitted to the hospital and 5 weeks after his initial exposure (Pollard and Filbee 1951). About 89.9 mg of DNOC was eliminated via the urine over the 20 days after admission. The data suggest that humans have a relatively inefficient mechanism for eliminating DNOC and this may be due to slow detoxification and excretion or storage of DNOC in the body. 

In the only inhalation study located for animals, an elimination rate constant of 0.01 hour 1 was determined for female hooded rats exposed to 2 mg/m of DNOC aerosols for 5 hours (King and Harvey 1954). This was determined to correspond to an initial blood level of 60 pg/g that would result in essentially complete elimination of DNOC in 182 hours. 

Elimination rate constant (k) determines the rate of decline of a concentration and the rate of accumulation to steady state. It depends on CL and V. 

Elimination rate constants study for non-, mono-, and di-ortho CBs in rainbow trout showed that substitution pattern influenced the elimination kinetics for example, CB-126 was more slowly eliminated than di- and mono-ortho congeners of similar kow, supporting the conclusion that toxic CBs declined more slowly in biota than other congeners [140]. Non- and mono-ortho CBs have been determined in 16 species of fishes from Netherlands coast and inland waters [141], In all these species, potential toxicity (as represented TEQs) arise from CBs-126, CB-156, and CB-118 and the TEQs are at least four times higher than those derived from PCDD/Fs. Reports carrying congener-specific PCB data on various fish species from all around the world are available. 

Following the dosage administration, blood samples (10-15) are withdrawn from the volunteers. The idea behind selecting the sampling times is that one would be able to accurately determine the Cmax- Therefore, generally more frequent sampling times are needed at the lower part of the curve. Similarly, the terminal phase should have a sufficient number of sample times to establish the elimination rate constant. The duration of sampling should be such that most (at least 80%) of... 

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