Pharmacokinetic parameter

It was noted in the previous section that both pharmacokinetics and pharmacodynamics are concerned with relationships over time. One illustration of the fundamental importance of the rates of these processes can be seen in the plasma concentration-time profile (also known as the plasma-concentration curve) for an administered drug. This was introduced in Section 4.2.1, along with several quantitative pharmacokinetic terms used to describe and quantify aspects of the plasma concentration-time profile  

However, while informative, this description is only a starting point. Understanding and prediction are more important than simple description (Rolan 

The term absorption refers to the rate and extent to which an administered dose of a drug is taken into the body. In the case of oral administration, interest lies with the rate and extent of systemic absorption from the gastrointestinal tract following administration. If a drug is taken into the intestinal cells, it is deemed to have been absorbed, regardless of the extent to which it is metabolized. In contrast, the term bioavailability refers to the proportion of an administered dose that reaches the systemic circulation unchanged. 

While the therapeutic outcomes of low absorption and low availability can be similar (both lead to low concentrations of the drug in the blood), separate investigation and quantification of these factors can be beneficial. For example, a drug that is well absorbed but experiences a very high first-pass metabolism can demonstrate low bioavailability. Low absorption and low bioavailability are likely to be improved in different ways, including chemical modification, reformulation, and changing the route of administration (see Rolan and Molnar, 2006). 

Most drugs require access to tissues to exert their therapeutic effects. Therefore, when investigating the time course of a drug s action, understanding the rate and extent of transfer from blood plasma to the target tissues is essential. The pharmacokinetic profile can provide quantitative clues indicating that the drug is extensively distributed outside the plasma. 

One can now appreciate why conventional definitions of pharmacokinetics are a little different from the definition given here. The conventional definitions make references to events other than temporal and spatial distribution. These events are, in fact, consequences of a drug s kinetics, and thus the two should be separated. The processes of drug absorption, distribution, metabolism, and elimination relate to parameters that can only be estimated from a mathematical model describing the kinetics of the drug. The point is that, to understand the mathematical basis of pharmacokinetic parameter estimation, it is necessary to keep in mind the separation between kinetics per se and the use of data to estimate pharmacokinetic parameters. 

Using the definition of pharmacokinetics given in terms of spatial and temporal distributions, one can easily progress to a description of the underlying assumptions and mathematics of noncompartmental and compartmental analysis, and, from there, proceed to the processes involved in estimating the pharmacokinetic parameters. This will permit a better understanding of the domain of validity of noncompartmental vs compartmental parameter estimation. 

What is desired from the pharmacokinetic parameters is a quantitative measure of how a drug behaves in the system. To estimate these parameters, one must design an experiment to collect transient data that can then be used to estimate the parameters of interest. 

To design such an experiment, the system must contain at least one accessible pool that is, the system must contain a pool that is available for drug input and data collection. As we will see, this pool must have 

The pharmacokinetic parameters descriptive of the accessible pool are as follows (these definitions apply 

Chemical Analysis of Antibiotic Residues in Food, First Edition. Edited by Jian Wang, James D. MacNeil, and Jack F. Kay. 2012 John Wiley Sons, Inc. Published 2012 by John Wiley Sons, Inc. 

PHARMACOKINETICS, DISTRIBUTION, BIOAVAILABILITY, AND RELATIONSHIP TO ANTIBIOTIC RESIDUES 

Abbreviation Dimension (Typical Units) Estimation/Computation 

From raw data with trapezoidal rule or AUC = F dose/Cl 

Generally obtained from raw data simple analytical solution for a 

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Lack of favorable ADME properties (absorption, distribution, metabolism, elimination) can preclude therapeutic use of an otherwise active molecule. The clinical pharmacokinetic parameters of clearance, half-life, volume of distribution, and bioavailability can be used to characterize ADME properties. 

Taken together ABC-transporters represent a large family of proteins affecting the pharmacokinetic parameters of various drugs. Here, P-gp is currently the best characterized member and it may also be one of the most important ABC-transporters with regard to drug transport. However, it becomes more and more apparent that ABC-transporter act in a coordinated... 

Toluene, volatile nitrites, and anesthetics, like other substances of abuse such as cocaine, nicotine, and heroin, are characterized by rapid absorption, rapid entry into the brain, high bioavailability, a short half-life, and a rapid rate of metabolism and clearance (Gerasimov et al. 2002 Pontieri et al. 1996, 1998). Because these pharmacokinetic parameters are associated with the ability of addictive substances to induce positive reinforcing effects, it appears that the pharmacokinetic features of inhalants contribute to their high abuse liability among susceptible individuals. 

Sheiner LB, Beal SL. Evaluation of methods for estimating population pharmacokinetic parameters. II. Biexponential model and experimental pharmacokinetic data. / Pharmacokinet Biopharm 1981 9 635-51. 

Simulation methods have also been developed that include physiologically based pharmacokinetic modeling (PBPK) and methods such as Cloe PK, OMPPPlus, GastroPlus , SimCYP , and others [122] that are described elsewhere in this book. It is likely that the computational metabolism predictions could be integrated with these to assist in deriving more accurate predictions of human pharmacokinetic parameters. 

One example of such constructive cross talk can be found in the growing literature on quantitative structure-pharmacokinetic relationships (QSPKR). Reports on how to predict pharmacokinetics from molecular information, or how to link pharmacokinetic parameters with molecular features, have appeared in both the pharmacokinetic [61] and the toxicological [62] literature. Others are extending this to pharmacodynamics as well [63], and the approaches look promising. 

Analysis of most (perhaps 65%) pharmacokinetic data from clinical trials starts and stops with noncompartmental analysis (NCA). NCA usually includes calculating the area under the curve (AUC) of concentration versus time, or under the first-moment curve (AUMC, from a graph of concentration multiplied by time versus time). Calculation of AUC and AUMC facilitates simple calculations for some standard pharmacokinetic parameters and collapses measurements made at several sampling times into a single number representing exposure. The approach makes few assumptions, has few parameters, and allows fairly rigorous statistical description of exposure and how it is affected by dose. An exposure response model may be created. With respect to descriptive dimensions these dose-exposure and exposure-response models... 

Obach RS, Baxter JG, Liston TE, Silber BM, Jones BC, MacIntyre F, Ranee DJ, Wastall P. The prediction of human pharmacokinetic parameters from precl-inical and in vitro metabolism data. J Pharmacol Exp Ther 1997 Oct 283(l) 46-58... 

Research of the pharmacokinetic parameters of lipid emulsion of paclitaxel 91... 

The half-life time t of a drug is an important pharmacokinetic parameter. In this simple model it can be obtained immediately from the solution in eq. (39.6) ... 

From the AUC and knowing the dose, one can immediately derive from eq. (39.12) an important pharmacokinetic parameter which is the clearance Cl of the drug from the plasma ... 

An important pharmacokinetic parameter is the time of appearance of the maximum t of the plasma concentration. This can be derived by setting the first derivative of the plasma concentration function in eq. (39.16) equal to zero and solving for t, which yields ... 

The pharmacokinetic parameters of the model are then readily derived from the defining equations and the results of the regression ... 

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... 

Usually, one has obtained an estimate for the elimination constant and the distribution volume Vp from a single intravenous injection. These pharmacokinetic parameters, together with the interval between administrations 0 and the single-dose D, then allow us to compute the steady-state peak and trough values. The criterion for an optimal dose regimen depends on the minimum therapeutic concentration (which must be exceeded by and on the maximum safe... 

The truncated part of the integral can be obtained by numerical integration (e.g. by means of the trapezium rule) of the function rCp(r) between times 0 and T. The mean residence time MRT is an important pharmacokinetic parameter, especially when a substantial fraction of the drug is excreted or metabolized during its first pass through an organ, such as the liver. 

Although most CF patients have shorter half-lives and larger volumes of distribution than non-CF patients, some patients exhibit decreased clearance. Possible causes include concomitant use of nephrotoxic medications, presence of diabetic nephropathy, history of transplantation (with immunosuppressant use and/or procedural hypoxic injury), and age-related decline in renal function in older adult patients. Additionally, CF patients are repeatedly exposed to multiple courses of IV aminoglycosides, which can result in decreased renal function. Evaluation of previous pharmacokinetic parameters and trends, along with incorporation of new health information, is key to providing appropriate dosage recommendations. 

Drug Mechanism of Action Dose Pharmacokinetic Parameters Usual Serum Concentration Range Dose-Related Adverse Effects Idiosyncratic Adverse Effects... 

Pharmacokinetic parameters of the newer antidepressants are shown in Table 35— 5.9,29 Several antidepressants are not very highly protein bound, and the most notable of these is venlafaxine. The elimination half-lives of nefazodone and... 

Drugs can be cleared from the body by metabolism as well as renal excretion, and when this occurs it is not possible to measure directly the amount cleared by metabolism. However, the total clearance rate (TCR), or total body clearance, of the drug can be calculated from its pharmacokinetic parameters using the following equation ... 

The RCR can be determined from urine and plasma data using Eq. (18), and the TCR can be determined from the pharmacokinetic parameters using Eq. (19). Alternately, the RCR can be calculated by multiplying the TCR by the fraction of the dose excreted unchanged into urine,/), ... 

In Sec. VII we dealt with methods of determining the rate (and mechanism) of absorption. In this section we will deal with methods of determining the extent of absorption. In every example, the calculation will involve a comparison between two studies carried out in the same group of volunteers on different occasions. Usually it will be necessary to assume that the volunteers behaved identically on both occasions, especially with regard to their pharmacokinetic parameters. 

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... 

Studies interested in the determination of macro pharmacokinetic parameters, such as total body clearance or the apparent volume of distribution, can be readily calculated from polyexponential equations such as Eq. (9) without assignment of a specific model structure. Parameters (i.e., Ah Xt) associated with such an equation are initially estimated by the method of residuals followed by nonlinear least squares regression analyses [30],... 

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