Rate constants, pharmacokinetic

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

In practice, one will seek to obtain an estimate of the elimination constant kp and the plasma volume of distribution Vp by means of a single intravenous injection. These pharmacokinetic parameters are then used in the determination of the required dose D in the reservoir and the input rate constant k (i.e. the drip rate or the pump flow) in order to obtain an optimal steady state plasma concentration... 

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... 

R Brown, H Seifried. Extrapolation of in vivo metabolic rate constants from in vitro pharmacokinetic data. Washington, DC US Environmental Protection Agency, 1988. 

While these models simulate the transfer of lead between many of the same physiological compartments, they use different methodologies to quantify lead exposure as well as the kinetics of lead transfer among the compartments. As described earlier, in contrast to PBPK models, classical pharmacokinetic models are calibrated to experimental data using transfer coefficients that may not have any physiological correlates. Examples of lead models that use PBPK and classical pharmacokinetic approaches are discussed in the following section, with a focus on the basis for model parameters, including age-specific blood flow rates and volumes for multiple body compartments, kinetic rate constants, tissue dosimetry,... 

The pharmacokinetics of nalidixic and hydroxy-nalidixic acids have been studied by several different groups. Takasugi ejt al studied in-situ and in-vitro absorption of nalidixic acid from the gastrointestinal tracts of rats as a function of pH. They reported that the absorption of non-ionized nalidixic acid was faster than the ionized form, with the maximum absorption rate constant found when the drug was administered from a pH=3 buffer solution. The absorption in-sltu was found to be ten times the rate in-vitro, but this was dependent on several factors.(13)... 

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,... 

It appears that qualitative correlations between antibacterial activity and rate constants of HO ion catalyzed hydrolysis are fortuitous since many factors other than transpeptidase acylation contribute to antimicrobial activity. These other contributing factors include permeation of the outer membrane of the bacterial cell wall, resistance to /3-lactamase, the fit in the active site of the enzyme, stability of the acylated enzyme, and, last but not least, in vivo pharmacokinetic behavior. 

To understand the pharmacokinetic relevance of the proxibarbal-valofan equilibrium, the kinetics and thermodynamics of the reaction were carefully examined in aqueous and biphasic media. The various pseudo-first-order rate constants shown in Fig. 11.19 were determined in the pH range of 6.7 - 8.0... 

The metabolism of chloroform is well understood. Approximately 50% of an oral dose of 0.5 grams of chloroform was metabolized to carbon dioxide in humans (Fry et al. 1972). Metabolism was dose-dependent, decreasing with higher exposure. A first-pass effect was observed after oral exposure (Chiou 1975). Approximately 38% of the dose was converted in the liver, and < 17% was exhaled unchanged from the lungs before reaching the systemic circulation. On the basis of pharmacokinetic results obtained in rats and mice exposed to chloroform by inhalation, and of enzymatic studies in human tissues in vitro, in vivo metabolic rate constants (V, 3,C =15.7 mg/hour/kg, = 0.448 mg/L) were defined for humans (Corley et al. 1990). The metabolic activation of chloroform to its toxic intermediate, phosgene, was slower in humans than in rodents. 

Validation of the Model. The Corley model was validated using chloroform data sets from oral (Brown et al. 1974a) and intraperitoneal (Ilett et al. 1973) routes of administration and from human pharmacokinetic studies (Fry et al. 1972). Metabolic rate constants obtained from the gas-uptake experiments were validated by modeling the disposition of radiolabeled chloroform in mice and rats following inhalation of chloroform at much lower doses. For the oral data set, the model accurately predicted the total amounts of chloroform metabolized for both rats and mice. 

Fig. 2.6 Effect of variation in absorption rate on plasma drug concentration. The graph shows simulated plasma concentration-time curves for theophyUine after oral administration, illustrating a 20% difference in Cpmax values resulting from variation in the absorption rate constant. Absorption rate constants top curve 2.2 per h (Cpmax 20 pg/mL) middle curve 1.0 per h (Cptnax 18 M-g/mL) bottom curve 0.7 per h. Note that tmax also changes. The established therapeutic concentration of theophyUin is 10-20 pg/mL. The most rapidly absorbed formulation produces the highest concentration and greatest chance of side effects. Also, the duration for which the plasma concentration is within the therapeutic range also varies. Pharmacokinetic parameters dose, 400 mg bioavaUabiUty, 0.8 volume of distribution, 29 L half-Ufe, 5.5 h.

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... 

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.)...

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... 

Figure 19.5 Physiological pharmacokinetic model for hepatic uptake of drug constantly infused in the isolated rat liver perfusion system. Q, flow rate (mL/min) Cb, inflow concentration (pg/mL) Cs, sinusoidal concentration (pg/mL) Vs, sinusoidal volume (mL) X, binding constant (pg) Xm, maximum binding amount (pg) K, binding constant (mL/pg) kmt, internalization rate constant (min-1).

Figure 19.7 Pharmacokinetic model for analyzing drug disposition following direct intratumoral injection. ku rate constant of transfer from poorly perfused region to well perfused region k2, venous appearance rate constant k2, rate constant of leakage from the surface A, and X2, drug amounts in well perfused and poorly perfused regions, respectively.

K0 is now the zero-order rate constant and is expressed in terms of mass/time. In an active carrier-mediated transport process following zero-order kinetics, the rate of drug transport is always equal to K once the system is fully loaded or saturated. At subsaturation levels, the rate is initially first order as the carriers become loaded with the toxicant, but at concentrations normally encountered in pharmacokinetics, the rate becomes constant. Thus, as dose increases, the rate of transport does not increase in proportion to dose as it does with the fractional rate constant seen in first-order process. This is illustrated in the Table 6.1 where it is assumed that the first-order rate constant is 0.1 (10% per minute) and the zero-order rate is 10 mg/min. 

The classical compartmental and more complex PBPK models require actual pharmacokinetic data to calibrate some parameters such as metabolic rate constants. However, PBPK models are more data-intensive and require greater numbers of chemical-specific and receptor-specific inputs. Although PBPK models have been used extensively in the last 20 years to address cross-species differences and other uncertainties, there are cases in which simpler one- or two-compartment models have been sufficient for risk assessment, for example for methyl mercury (EPA 2001). 

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