MODELING IN PHARMACOKINETICS

Consider a tablet that is taken regularly once a day. We want to find the optimal quantity of the drug (i.e., the only active ingredient) in the tablet in order to keep the drug concentration in the blood within a given therapeutic range [Cj, Cy] as strictly as possible. To predict the drug concentration we use the linear compartmental model shown in Fig. 2.9, one of the most popular models in pharmacokinetics. 

Matis, J., An introduction to stochastic compartmental models in pharmacokinetics, Pharmacokinetics-Mathematical and Statistical Approaches in Metabolism and Distribution of Chemicals and Drugs, edited by A. Pecile and A. Rescigno, Plenum Press, New York, 1988, pp. 113-128. 

R., Hauck, W.W. et al., An individual bioequivalence criterion regnlatory considerations, Stat. Med. 19, 2821-2842, 2000 Meyer, M.C., United States Food and Drug Administration requirements for approval of generic drug products, J. Clin. Psychiatry 62 (Suppl. 5), 4-9, 2001 Temple, R., Policy developments in regulatory approval, Stat. Med. 21, 2939-3048, 2002 Gould, A.L, Substantial evidence of effect, J. Biopharm. Stat. 12, 53-77, 2002 Chen, M.L., Panhard, X., and Mentre, F, Evaluation by simulation of tests based on nonlinear mixed-effects models in pharmacokinetic interaction and bioequivalence cross-over clinical trials, Stat. Med. 24,1509-1524,2005 Bolton, S., Bioequivalence studies for levothy-roxine, AAPS J. 7, E47-E53, 2005. 

Bonate PL. Compartmental models. In Pharmacokinetics in Drug Development, Volume 1 Clinical Smdy Design and Analysis. Bonate PL, Howard DR, eds. 2004. AAPS Press, Arlington, VA. pp. 291-320. 

In modeling, observed data is frequently taken and a model developed, which is then used to draw inferences about the data used to develop the model—a circular process to be sure. In order for valid inference to be drawn, however, a proper model must be used. But what is the proper model In pharmacokinetic modeling, one often has a set of candidate models to choose from, such as a 1-, 2-, or 3-compartment model after bolus administration. Which model is most appropriate With today s software it s is an easy matter to obtain parameter estimates for most any model. Choosing an appropriate model is often far more difficult than estimating the parameters of a model. It is the choice of model, the formulation of the model, where science and intuition meet and therein lies the art of modeling. 

The study of pharmacokinetics may be pursued at a number of levels. Considering the detail of the mathematical models involved one may use a noncompartmental, classical, or physiologically based approach. All three approaches require some measure of mathematical description or assumptions with the classical, compartmental approach intermediate in complexity. This chapter describes the development and use of compartmental models in pharmacokinetic research. Noncompartmental and physiologically based pharmacokinetic models are discussed in Chapters 13 and 14, respectively. 

Bischoff, K. B. (1987). Physiologically based pharmacokinetic modeling. In Pharmacokinetics in Risk Assessment—Drinking Water and Health, Vol. 8, pp. 36-61. National Academy Press, Washington DC... 

Because of the complexity of ADME processes, an adequate description of the observations is sometimes possible only by assuming a simplified model the most useful model in pharmacokinetics is the compartment model. The body is conceived to be composed of mathematically interconnected compartments. 

A. M. ter laak, N. P. E. Vermeulen, Molecular-modeling approaches to predict metabolism and toxicity, in Pharmacokinetic Optimization in Drug Research, B. Testa, H. van de Water-beemd, G. Folkers, R. Guy (Eds.), Wiley-VCH, Weinheim, 2001,... 

Leung H-W. 1993. Physiologically-based pharmacokinetic modelling. In Ballentine B, Marro T, Turner P, eds. General and applied toxicology. New York, NY Stockton Press, 153-164. 

KrishnanK, Andersen ME. 1994. Physiologically-based pharmacokinetic modeling in toxicology. In Wallace Hayes, ed. Principles and methods of toxicology. 3rd edition. New York, NY Raven Press, Ltd. 

Sheiner LB, Steimer JL. Pharmacokinetic/pharmacodynamic modeling in drug development. Annu Rev Pharmacol Toxicol 2000 40 67-95. 

Blakey GE, Nestorov lA, Arundel PA, Aarons LJ, Rowland M. Quantitative structure-pharmacokinetics relationships I. Development of a whole-body physiologically based model to characterize changes in pharmacokinetics across a homologous series of barbiturates in the rat. J Pharmacokinet Biopharm 1997 Jun 25(3) 277-312. Erratum in J Pharmacokinet Biopharm 1998 Feb 26(l) 131. 

Charnick SB, Kawai R, Nedelman JR, Lemaire M, Niederberger W, Sato H. Perspectives in pharmacokinetics. Physiologically based pharmacokinetic modeling as atoolfor drug development./P/jarmacokmefTEop/jarm 1995 Apr 23(2) 217-29. Review. 

Krishnan K, Andersen ME. 1994. Physiologically based pharmacokinetic modeling in toxicology. In ... 

Parrott, N Paquereau, N Coassolo, P Lave, Th. An evaluation of the utility of physiologically based models of pharmacokinetics in early drug discovery. f Pharm. Sci. 2005, 94, 2327-2343. 

When we apply these two properties of the Laplace transform to differential equations of our pharmacokinetic model in eq. (39.46), we obtain ... 

Children s Susceptibility. No studies were located in which comparisons were made between the sensitivity of children and adults to the toxicity of americium. Animal studies indicate that juvenile dogs are less susceptible than adults to americium-induced bone cancer (Lloyd et al. 1999). No direct evidence was located to indicate that the pharmacokinetics of americium in children may be different from that in adults. Based on dosimetric considerations related to differences in the parameters of available models, as well as studies in animals, it seems likely that children may be more susceptible to americium toxicity than are adults by virtue of age-related differences in pharmacokinetics. Absorption of ingested americium may be as much as 200 times greater in neonatal animals than in adults. (Bomford and Harrison 1986 David and Harrison 1984 Sullivan et al. 1985). 

Readers interested in such advanced topics are referred to a number of texts that describe these more complex pharmacokinetic models in detail [1-5] and to the website http //www.boomer.org/pkin/. 

Stirred tank models have been widely used in pharmaceutical research. They form the basis of the compartmental models of traditional and physiological pharmacokinetics and have also been used to describe drug bioconversion in the liver [1,2], drug absorption from the gastrointestinal tract [3], and the production of recombinant proteins in continuous flow fermenters [4], In this book, a more detailed development of stirred tank models can be found in Chapter 3, in which pharmacokinetic models are discussed by Dr. James Gallo. The conceptual and mathematical simplicity of stirred tank models ensures their continued use in pharmacokinetics and in other systems of pharmaceutical interest in which spatially uniform concentrations exist or can be assumed. 

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

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