Linear pharmacokinetics

The mid and low doses for a carcinogenicity study are to provide information for assessing the relevance of the study findings to humans. The low dose should be equal to, or a multiple of, the maximum dose proposed for human testing. The rationale for the selection of the low and mid dose needs to be provided on the basis of pharmacokinetic linearity and saturation of metabolic pathways, human exposure and therapeutic dose, pharmacodynamic response in the test species, alteration in the normal physiology of the test species, mechanistic information and the potential for threshold effects, and the unpredictability of toxicity progression observed in other toxicology studies. 

The following discussion will describe how AUC and AUMC are estimated, how they are used to estimate specific pharmacokinetic parameters (including the assumptions), and what their relationship is to specific pharmacokinetic parameters estimated from compartmental models. Both moments, however, are used for other purposes. For example, AUC acts as a surrogate for exposure, and values of AUC from different dose levels of a drug have been used to justify assumptions of pharmacokinetic linearity. These uses will not be reviewed. 

Balani, S.K. et al., Evaluation of microdosing to assess pharmacokinetic linearity in rats using liquid chromatography-tandem mass spectrometry, Drug Metab. Dispos., 34(3), 384, 2006. 

After Phase I studies have established the safety of the drug candidate for continued development, there are numerous pharmacokinetic questions that need to be answered in addition to the basic questions of safety and efficacy addressed by Phase II and III clinical studies. These questions are answered with focused pharmacokinetic studies, the exact timing of which depends on the specifics of the drug and disease, as well as resources available and financial risks a sponsor is willing to take. Around the time of Phase II, pharmacokinetic studies are usually conducted to answer questions about metabolism in humans, pharmacokinetic linearity, and bioavailability. 

Crossover studies in healthy volunteers examining pharmacokinetic linearity, time dependency, and intra- and intersubject variability over the anticipated clinical dose range are generally required to ensure that the pharmacokinetic model developed for the drug candidate is suitable and predictive. Exceptions could include drugs with such low variability that definitive data on linearity are obtained from dose tolerance studies, or in cases where Phase 11b studies use crossover designs with extensive pharmacokinetic sampling. 

Studies of the pharmacokinetics of this deHvery system in two animal models have been reported in the Hterature. After iajection of these microspheres at three doses, leuproHde concentrations were sustained for over four weeks foUowing an initial burst (116). The results iadicated that linear pharmacokinetic profiles in absorption, distribution, metaboHsm, and excretion were achieved at doses of 3 to 15 mg/kg using the dmg loaded microspheres in once-a-month repeated injections. 

Generic applications for chiral medicinal products should be supported by bioequivalence studies using enantiospecific bioanalytical methods unless both products contain the same, stable, single enantiomer or both products contain a racemate where both enantiomers show linear pharmacokinetics. 

The data are also represented in Fig. 39.5a and have been replotted semi-logarithmically in Fig. 39.5b. Least squares linear regression of log Cp with respect to time t has been performed on the first nine data points. The last three points have been discarded as the corresponding concentration values are assumed to be close to the quantitation limit of the detection system and, hence, are endowed with a large relative error. We obtained the values of 1.701 and 0.005117 for the intercept log B and slope Sp, respectively. From these we derive the following pharmacokinetic quantities ... 

Thus far we have only considered relatively simple linear pharmacokinetic models. A general solution for the case of n compartments can be derived from the matrix K of coefficients of the linear differential equations ... 

This general approach for solving linear pharmacokinetic problems is referred to as the y-method. It is a generalization of the approach by means of the Laplace transform, which has been applied in the previous Section 39.1.6 to the case of a two-compartment model. 

A. Rescigno, Mathematical foundations of linear kinetics. In Pharmacokinetics Mathematical and Statistical Approaches to Metabolism and Distribution of Chemicals and Drugs. (J. Eisenfeld and M. Witten, Eds.), North-Holland, Amsterdam, 1988. 

Also, if conversion of drug to active metabolite shows significant departure from linear pharmacokinetics, it is possible that small differences in the rate of absorption of the parent drug (even within the 80-125% range for log transformed data) could result in clinically significant differences in the concentration/ time profiles for the active metabolite. When reliable data indicate that this situation may exist, a requirement of quantification of active metabolites in a bioequivalency study would seem to be fully justified. 

The drug should show linear pharmacokinetics and should not be converted to an active metabolite that plays a substantial role in the therapeutic or toxic properties of the product. 

M. L. Chen and A. J. Jackson, The role of metabolites in bioequivalency assessment, I. Linear pharmacokinetics without first pass effect, Pharm. Res, 8, 25 (1991). 

P Veng-Pedersen. Linear and nonlinear systems approach in pharmacokinetics How much do they have to offer I. General considerations. J Pharmacokin Biopharm 16 413-472, 1988. 

LZ Benet. General treatment of linear mammillary models with elimination from any compartment as used in pharmacokinetics. J Pharm Sci 6 536-541, 1972. 

K Yamaoka, T Nakagawa, T Uno. Application of Akaike s information criteria (AIC) in the evaluation of linear pharmacokinetic model. J Pharmacokin Biopharm 6 165-175, 1978. 

Shaw et al. [64] described a (D)-penicillamine detection method in blood samples that had been treated with EDTA, deproteinized with trichloroacetic acid, and analyzed within 1 h. Penicillamine was detected at a vitreous-carbon electrode operated at +800 mV after HPLC separation. A linear calibration graph was obtained, and the method had a limit of detection equal to 5-20 ng. The method was useful in clinical and in pharmacokinetic studies. 

According to USP 28 [1], the range of an analytical method can be defined as the interval between upper and lower levels (in the Pharmaceutical Industry usually a range from 80 to 120% of the target concentrations tested) of the analyte that have been demonstrated to be determined with a acceptable level of precision, accuracy, and linearity. Routine analyses should be conducted in this permitted range. For pharmacokinetic measurements, a wide range should be tested, where the maximum value exceeds the highest expected body fluid concentration, and the minimum value is the QL. 

---