PHARMACOKINETICS AND BIOPHARMACEUTICS (46:138)

LECTURE TUTORIAL

Noncompartmental Pharmacokinetics

 

Key Terms:

 

Statistical moment: A mathematical description of a discrete distribution of data. Statistical moments calculated from a set of concentration-time data represent an estimate of the true moment (or the true probability density function that describes the true relationship between concentration and time), much like the mean of a sample population represents an estimate of the true mean of the entire population.

 

Extraction ratio: The ratio of the rate of xenobiotic elimination and the rate at which xenobiotic enters the organ. It is a measure of the efficiency of drug removal by an organ.

 

Clearance: The volume of blood from which all of a xenobiotic would appear to be removed per unit time.

 

Systemic clearance: The overall clearance of drug from the body, represented by the sum of all organ clearance.

 

Mean residence time (MRT): The average total time molecules of a given dose spend in the body. Thus, this can only be measured after instantaneous administration.

 

Mean transit time (MTT): The average time molecules of a given dose spend in the kinetic system. When determined after non-instantaneous administration, the MTT will be the sum of the MRT and the MAT (see below).

 

Mean absorption time (MAT): Technically, MAT is really the mean arrival time; that is, the average time it takes for drug molecules to enter a kinetic space (such as the systemic circulation). However, since the most common condition under which MAT is determined is after oral administration, many (perhaps most) authors of texts and journal articles refer to it as the mean absorption time. In general, it makes little practical difference which terminology one uses. If it is viewed as absorption time, one is considering the time drug molecules spend at the site of absorption. The problem with this notion is that rarely is this measured. Instead what is measured is the appearance of drug in the systemic circulation. The mean arrival time and mean absorption time will only be the same if 100% of the drug is absorbed. If some is degraded in the gut or eliminated unabsorbed in the fecal stream, the average total time molecules spend in the site of absorption may be different than the average total arrival time into the systemic circulation.

 

Systemic availability: The fraction of administered drug that reaches the systemic circulation. Commonly used to measure the extent to which drug is available in the body after non-intravenous administration.

 

Key Principles:

 

Noncompartmental analysis reduces the assumptions that must be made in modeling concentration versus time data: An advantage of noncompartmental analysis is that it requires fewer assumptions than that which is necessary with compartmental analysis. It also avoids some of the common problems seen with compartmental analysis. For example, if one administers i.v. procainamide to 10 subjects, pharmacokinetic analysis would reveal the kinetics of the drug in some subjects is best described using a two-compartment model, while it is best described with a three-compartment model in other subjects. Should the data for all subjects be ‘forced’ into a single model, or should every subject be modeled based upon the fit of their individual plasma concentration-time data? These and related questions pose real problems in the use of compartmental analysis – problems that are largely avoided with noncompartmental analysis. However, it is important to realize that noncompartmental analysis is not ‘model-independent’ (though it is erroneously stated to be by numerous authors). There are still assumptions that are made with noncompartmental analysis, which may or may not be correct (and often the available data does not allow us to definitively determine the accuracy of the assumptions). The number and implication of those assumptions are, however, less than that seen with compartmental analysis.

 

Additivity of clearance: It is unusual for a drug to be eliminated by a single route. Most commonly, drug elimination occurs via several organs of elimination; though one may predominate. Since blood is fractionally distributed to various potential organs of elimination in parallel, the clearance of drug from the various organs of elimination is additive. This is extremely useful in determining organ specific elimination, the impact of organ specific pathology, and the mechanism of drug interactions. One exception to this principle is when the lung represents a significant organ of elimination – because the lung is in series rather than parallel with all other organs.

 

Mean residence time is independent of route: It is commonly stated in the literature (including several noted textbooks) that MRT is route-dependent. This is incorrect and arises from a misunderstanding of the difference between the definition of MRT and one means by which it may be calculated. After an intravenous bolus dose, the MRT may be calculated as

 

MRT = AUMC/AUC

 

Since the ratio of AUMC/AUC will change with route of administration, some have concluded that MRT also changes with route of administration. However, this overlooks the definition of MRT that is specific for the average total time molecules spend in the body. Thus, MRT is a measure of the rate of elimination of a xenobiotic. AUMC/AUC is not a definition of MRT, it is only one means of calculating MRT when administration is instantaneous and CL is constant. The ratio of AUMC/AUC is a valid means to calculate the MTT after any route of administration. After an intravenous bolus dose, MRT = MTT. However, after non-instantaneous forms of administration, the mean transit time is the sum of the mean residence time and the mean arrival time; such that

 

AUMC/AUC = MTT = MRT + MAT

 

For a further discussion of this concept, see Karol MD. Mean residence time and the meaning of AUMC/AUC. Biopharm Drug Dispos 11:179-181, 1990. For an indepth discussion of mean time parameters, see Veng-Pedersen. Mean time Parameters in Pharmacokinetics. Definition, Computation and Clinical Implications: Parts I and II. Clin Pharmacokinet 17:345-366, 424-440, 1989.

           

Practice Problems:

 

1.         A dose of 300 mg of a drug was administered to a subject via an intravenous bolus. Blood samples were obtained and the following concentrations obtained at the indicated times:

 

 

Using noncompartmental methods, calculate the CL, Vss, and MRT of this drug in this patient. Answer

 

 

2.                  A study is conducted in which a drug is administered as an i.v. bolus dose of 500 mg, a 500mg oral tablet made by Manufacturer 1, and a 500 mg oral tablet made by Manufacturer 2. The AUC and AUMC values obtained are indicated below:

 

 

 

 

                     From this data, calculate the MAT for each manufacturer’s oral product. Do they exhibit a similar rate of absorption? Answer 

 

 

 

Last revised 07/13/05

 

ã 2005 - Craig K. Svensson, Pharm.D., Ph.D.

 

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