Elimination rate constant defined

A9.5.2.3.1 The bioconcentration factor is defined as the ratio on a weight basis between the concentration of the chemical in biota and the concentration in the surrounding medium, here water, at steady state. BCF can thus be experimentally derived under steady-state conditions, on the basis of measured concentrations. However, BCF can also be calculated as the ratio between the first-order uptake and elimination rate constants a method which does not require equilibrium conditions. 

Given a zero time blood drug concentration (Co), a nonzero time concentration (Cf), and a defined time (t), then k can be readily determined either algebraically, graphically, or with appropriate software. For example, in a graphical plot of In Cf versus f, the slope of the linear relationship is k. The elimination rate constant k represents the fraction of drug removed per unit of time and has units of reciprocal time (min h" day" ). The overall elimination rate constant (k) includes the renal constant (fccR)> the biliary constant (fccs)) the metabolic constant (kcM)> and others such that k kcR "i kcB 3" kcM. 

Total body clearance (Clr) is defined as the theoretical total volume of blood, serum, or plasma completely cleared of drug per unit of time. It is usually expressed in units of mL/min, L/hr, mL/min/kg, or L/hr/kg. Like the elimination rate constant, CIt is the sum total of all the clearances contributed by each elimination route (i.e., Cfr = CIcr + CIcb + ClcM+ Clearance is a most important parameter, because it provides a better representation than does k of the body s abflity to eliminate a drug. In addition, Clj has more physiological meaning and is readily used to relate the dosing rate to steady-state concentration. 

For example, suppose the terminal elimination rate constant ( z,) was estimated using four observations. If the mean and variance of z was 0.154 per hour and 6.35E — 4 (per hour)2, respectively. Then the mean and variance for half life O1/2) defined as Ln(2)/ z, would be 4.5 h and... 

Equation (6.4) corresponds to the mathematical form of the second phase of the blood concentration-time curve in Figure 6.8, which is a semilogarithmic plot, i.e., it plots the logarithm of changing blood concentration against time. The slope of the second phase of the curve in Eigure 6.8 is defined by the elimination rate constant, k. The larger the elimination rate constant k, the steeper the slope and the faster the chemical is eliminated from the bloodstream. 

High reaction temperatures can cause numerical overflow problems in the computer calculation of k, owing to the very large values generated by the exponential term. This can often be eliminated by defining a value of the rate constant, kg, for some given temperature, Tq. Thus... 

Finally, to conclude our discussion on coupling with chemistry, we should note that in principle fairly complex reaction schemes can be used to define the reaction source terms. However, as in single-phase flows, adding many fast chemical reactions can lead to slow convergence in CFD simulations, and the user is advised to attempt to eliminate instantaneous reaction steps whenever possible. The question of determining the rate constants (and their dependence on temperature) is also an important consideration. Ideally, this should be done under laboratory conditions for which the mass/heat-transfer rates are all faster than those likely to occur in the production-scale reactor. Note that it is not necessary to completely eliminate mass/heat-transfer limitations to determine usable rate parameters. Indeed, as long as the rate parameters found in the lab are reliable under well-mixed (vs. perfect-mixed) conditions, the actual mass/ heat-transfer rates in the reactor will be lower, leading to accurate predictions of chemical species under mass/heat-transfer-limited conditions. 

A model based on the assumption that a metabolite is present within a single compartment with defined rate constants for absorption and elimination of the metabolite. The rate of appearance of a tracee and the infusion of tracer are assumed to take place in a single pool that is instantly well-mixed. Wolfe has described in detail how the constant tracer infusion method allows one to calculate half-life, pool size, turnover time, mean residence time, and clearance time. 

Using rate data from IR experiments on the overall elimination reaction from [Rh(C(0)Me)(C0)l3] in the absence of Mel and the equilibration of Rh( C(0) Me)(CO)l3] with [Rh(C(0)Me)( C0)l3] in neat Mel it was possible to estimate the two further rate constants that defined the system. Putting these together showed that [RhMe(CO)2l3] is unstable both with respect to reductive elimination and migratory insertion at 35 °C in MeI/CH2Cl2 [32]. 

When a compound is administered by a route other than intravenously, the plasma level profile will be different, as there will be an absorption phase, and so the profile will be a composite picture of absorption in addition to distribution and elimination (Fig. 3.26). Just as first-order elimination is defined by a rate constant, so also is absorption kab. This can be determined from the profile by the method of residuals. Thus, the straight portion of the semilog plot of plasma level against time is extrapolated to the y axis. Then each of the actual plasma level points, which deviate from this during the absorptive phase, are subtracted from the equivalent time point on the extrapolated line. The differences are then plotted, and a straight line should result. The slope of this line can be used to calculate the absorption rate constant kab (Fig. 3.26). The volume of distribution should not really be determined from the plasma level after oral administration (or other routes except intravenous) as the administered dose may not be the same as the absorbed dose. This may be because of first-pass metabolism (see above), or incomplete absorption, and will be apparent from a comparison of the plasma... 

We can find the hysteresis and isola boundaries from the above equations by applying conditions (7.46) and (7.55) respectively. In each case we have three equalities. Two of these can, in principle, be used to determine the values for x and tres. Eliminating these, the third equation then defines a surface in the k2 P0-ku space. Alternatively, we can also specify a particular value for, say, the uncatalysed rate constant ku and then use the third equation to give the boundaries in the k2 P0 plane. This latter procedure has... 

Traditionally, linear pharmacokinetic analysis has used the n-compartment mammillary model to define drug disposition as a sum of exponentials, with the number of compartments being elucidated by the number of exponential terms. More recently, noncompartmental analysis has eliminated the need for defining the rate constants for these exponential terms (except for the terminal rate constant, Xz, in instances when extrapolation is necessary), allowing the determination of clearance (CL) and volume of distribution at steady-state (Vss) based on geometrically estimated Area Under the Curves (AUCs) and Area Under the Moment Curves (AUMCs). Numerous papers and texts have discussed the values and limitations of each method of analysis, with most concluding the choice of method resides in the richness of the data set. 

Figure 6.2 shows the standard mechanism of substitution reactions carried out on carboxylic acid derivatives in neutral or basic solutions. The tetrahedral intermediate—formed in the rate-determining step—can be converted to the substitution product via two different routes. The shorter route consists of a single step the leaving group X is eliminated with a rate constant Ad. In this way the substitution product is formed in a total of two steps. The longer route to the same substitution product is realized when the tetrahedral intermediate is proto-nated. To what extent this occurs depends, according to Equation 6.1, on the pH value and on the equilibrium constant Kcq defined in the middle of Figure 6.2 ...

The experimental technique controls how the mass transport and rate law are combined (and filtered, e.g. by removing convective transport terms in a diffusion-only CV experiment) to form the overall material balance equation. Migration effects may be eliminated by addition of supporting electrolyte steady-state measurements eliminate the need to solve the equation in a time-dependent manner excess substrate can reduce the kinetics from second to pseudo-first order in a mechanism such as EC. The material balance equations (one for each species), with a given set of boundary conditions and parameters (electrode/cell dimensions, flow rate, rate constants, etc.), define an I-E-t surface, which is traversed by the voltammetric technique. 

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