Pharmacokinetics first-order absorption rate

The changes in a drug s plasma concentration with time may be calculated for a specific pharmacokinetic model by substituting of the appropriate rate expressions into Equation (8.29). For example, for a one compartment model in which the drug exhibits first order absorption and elimination (Figure 8.10), it is possible to show that ... 

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... 

Even though the absorption rate constant (kf) defines the rate of absorption, its accurate determination is largely dependent on the adequacy of the plasma concentration-time data associated with the absorption phase of the drug. When a drug is administered orally, as a conventional (immediate-release) dosage form, or injected intramuscularly as an aqueous parenteral solution, the absorption and disposition kinetics can often be analysed in terms of a one-compartment pharmacokinetic model with apparent first-order absorption. The plasma concentration-time curve is described by the equation... 

The principal parameter used to indicate the rate of drug absorption is Cmax, even though it is also influenced by the extent of absorption the observed fmaX is less reliable. Because of the uncertainty associated with Cmax, it has been suggested (Endrenyi Yan, 1993 Tozer, 1994) that Cmax/AUCo-loq/ where AUCo-loq is the area under the curve from time zero to the LOQ of the acceptable analytical method, may more reliably measure the rate of drug absorption, except when multiexponential decline is extensive. Estimation of the terms should be based on the observed (measured) plasma concentrationtime data and the use of non-compartmental methods rather than compart-mental pharmacokinetic models. MRTs, from time zero to the LOQ of the analytical method, for the test and reference products can be compared, assuming that first-order absorption and disposition of the drug apply (Jackson Chen, 1987). 

A new molecular entity exhibiting one-compartment pharmacokinetics with first-order absorption was assumed. The typical (mean) values of the population PK parameters for the NME were 1 h 17.5L/h, and SOL for absorption rate constant (Ka), apparent clearance (CLIP), and apparent volume of distribution (V/F), respectively. An intersubject variability of 45% (coefficient of variation) was assumed for each of these parameters, and this was assumed to be lognormally distributed with a mean of zero. A proportional error model was assumed for the residual error of 15%. 

Cmax and fmax are used as characteristics of the absorption rate and may thereby be affected by the drug dissolution and release, as discussed above. However, both variables are affected by several pharmacokinetic properties other than the absorption rate (Ka) as shown in equations 4 and 5, which describe Cmax and tmax, respectively, for a first-order absorption process ... 

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. 

If we let K = (D Sa Pc/d), then, since A is present in the equation, n must equal 1, so we have a first-order rate process. Fick s law of diffusion, which is important for quantitating rates of absorption, distribution, and elimination, is thus the basis for using first-order kinetics in most pharmacokinetic models. 

In conclusion, pharmacokinetics is a study of the time course of absorption, distribution, and elimination of a chemical. We use pharmacokinetics as a tool to analyze plasma concentration time profiles after chemical exposure, and it is the derived rates and other parameters that reflect the underlying physiological processes that determine the fate of the chemical. There are numerous software packages available today to accomplish these analyses. The user should, however, be aware of the experimental conditions, the time frame over which the data were collected, and many of the assumptions embedded in the analyses. For example, many of the transport processes described in this chapter may not obey first-order kinetics, and thus may be nonlinear especially at toxicological doses. The reader is advised to consult other texts for more detailed descriptions of these nonlinear interactions and data analyses. 

Conceptual models of percutaneous absorption which are rigidly adherent to general solutions of Pick s equation are not always applicable to in vivo conditions, primarily because such models may not always be physiologically relevant. Linear kinetic models describing percutaneous absorption in terms of mathematical compartments that have approximate physical or anatomical correlates have been proposed. In these models, the various relevant events, including cutaneous metabolism, considered to be important in the overall process of skin absorption are characterized by first-order rate constants. The rate constants associated with diffusional events in the skin are assumed to be proportional to mass transfer parameters. Constants associated with the systemic distribution and elimination processes are estimated from pharmacokinetic parameters derived from plasma concentration-time profiles obtained following intravenous administration of the penetrant. 

As stated in the introduction, the submodels may differ in fixed or random effects. The task is to learn how to communicate our ideas about the submodels to NONMEM. Suppose that during a population pharmacokinetic (PK) analysis of an orally administered drug, a model is used where the absorption and elimination rates are first order. The model is parameterized in terms of elimination rate (K), apparent volume of distribution (Vd) and absorption rate (KA), such that both K and KA are allowed to vary between subjects. Specifically, the values of K and KA for the th subject (Kj and KAj) are specified as follows ... 

Note This is a conceptuai representation of a physioiogicaiiy based pharmacokinetic (PBPK) modei for a hypotheticai chemicai substance. The chemicai substance is shown to be absorbed by inhaiation, by ingestion, or via the skin metaboiized in the iiver and excreted in the urine, biie, feces, sweat, or by exhaiation. Lymphatic absorption from the gastrointestinai tract avoids the first-pass effect of iiver metaboiism and is very important for iipophiiic chemicais (e.g., PCBs). important first-order rate constants are (eiimination) and K (metaboiism). 

We studied the in vivo pharmacokinetics of transscleral delivery of IgG. We used an osmotic pump, the tip of which was secured flush against bare sclera in rabbits to facilitate unidirectional movement, to deliver fluorescently labeled IgG (150kDa) at rates on the order of pL/hr. Biologically relevant concentrations in the choroid and retina were attained for periods of up to four weeks with negligible systemic absorption (6). Levels in the vitreous and aqueous humors, and orbit were negligible. Although there was a spatial concentration gradient, the IgG concentration in the choroidal hemisphere distal to the footprint of the osmotic pump tip was half of that in the proximal hemisphere. The elimination of IgG from the choroid and retina followed first-order kinetics with half-lives of approximately two to three days. 

For the pharmacokinetics of rhG-CSF in humans, it has been reported that the absorption and clearance of rhG-CSF follow first-order kinetics without any apparent concentration dependence [114], When rhG-CSF was administered by 24-h constant i.v. infusion at a dose level of 20pg/kg, the mean serum concentration achieved 48ng/mL. Constant i.v. infusion for 11 to 20 days produced steady-state serum concentrations over the infusion period. Subcutaneous administration of rhG-CSF at doses of 3.45 and 11.5pg/kg resulted in peak serum concentrations of 4 and 49ng/mL, respectively. The mean value of volume of distribution was 150mL/kg. The elimination half-life was 3.5h after either i.v. routes or s.c. routes, with a clearance rate of 0.5-0.7 mL/min/kg. The administration of a daily dose for 14 consecutive days did not affect the half-life. 

Carbamazepine is known to exist in both an anhydrate and a dihydrate form, with the anhydrate spontaneously transforming to the dihydrate upon contact with bulk liquid water [34]. The anhydrous phase is reported to be practically insoluble in water, but this observation is difficult to confirm owing to its rapid transition to the dihydrate phase. The rates associated with the phase transformation process have been studied and appear to follow first-order kinetics [35]. Interestingly, the only difference in pharmacokinetics between the two forms was a slightly higher absorption rate for the dihydrate [36]. The slower absorption of anhydrous carbamazepine was attributed to the rapid trans-... 

FIGURE 1.1 The three most commonly used pharmacokinetic models in explaining the pharmacokinetic behavior of drugs. The symbols C, P, S, and D represent central, peripheral, shallow, and deep compartments, whereas the first-order rate constants, symbolized by k j, represent drug transport from compartment i to compartment j. ka, and kd represent a bolus rV dose, the absorption rate constant, and constant rate infusion, respectively. 

Km the first-order rate constant for metabolism of dmg or [in context] the Michaelis constant in non-linear pharmacokinetics Ko the zero-order elimination rate constant Mother the first-order rate constant for elimination of dmg by a process other than metabolism or renal excretion Kio for a two-compartment dmg, the first-order rate constant for elimination of dmg from the central compartment Ki2 for a two-compartment drug, the first-order rate constant for transfer from the central to the peripheral compartment K21 for a two-compartment drug, the first-order rate constant for transfer from the peripheral to the central compartment MAT mean absorption time mean residence time in the gastrointestinal tract synonymous with MRTgit... 

An ideal pharmacokinetic model of the percutaneous absorption process should be capable of describing not only the time course of penetration through skin and Into blood (or receptor fluid In a diffusion cell), but also the time course of disappearance from the skin surface and accumulation (reservoir effect) of penetrant within the skin membrane. Neither Pick s Plrst Law of Diffusion nor a simple kinetic model considering skin as a rate limiting membrane only Is satisfactory, since neither can account for an accumulation of penetrant within skin. To resolve this dilemma, we have analyzed the In vitro time course of absorption of radiolabeled benzoic acid (a rapid penetrant) and paraquat (a poor penetrant) through hairless mouse skin using a linear three compartment kinetic model (Figure 5). The three compartments correspond to the skin surface (where the Initial dose Is deposited), the skin Itself (considered as a separate compartment), and the receptor fluid In the diffusion cell. The Initial amount deposited on the skin surface Is symbolized by XIO, and K12 and K23 are first order rate constants. 

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