Pharmacokinetic/pharmacodynamic model basics

M. O. Karlsson, T. Anehall, L. E. Friberg, A. Henningsson, C. Kloft, M. Sandstrom, and R. Xie, Pharmacokinetic/pharmacodynamic modelling in oncological drug development. Basic Clin Pharmacol Toxicol 96 206-211 (2005). 

The basic problem in nonlinear least squares is finding the values of 0 that minimizes the residual sum of squares which is essentially a problem in optimization. Because the objective functions used in pharmacokinetic pharmacodynamic modeling are of a quadratic nature (notice that Eq. (3.13) is raised to the power 2), they have a convex or curved structure that can be exploited to find an estimate of 0. For example, consider the data shown in Fig. 3.1. Using a 1-compartment model with parameters 0 = (V, CL, volume of distribution (V) can be systematically varied from 100 to 200 L and clearance (CL) can be systematically varied from 2 to 60 L/h. With each parameter combination, the residual sum of squares can be calculated and plotted... 

Meibohm, B., and Derendorf, H. (1997). Basic concepts of pharmacokinetic/ pharmacodynamic (PK/PD) modelling. Int. J. Clin. Pharmacol. Ther. 35 401-413. 

As discussed earlier, high-affinity anti-drug antibodies produce effects on the pharmacokinetics and pharmacodynamics of drugs in animals and humans. For new therapeutic applications, these effects need to be fully tested in animals before administration to humans. In addition, from a basic science viewpoint, it will be necessary to develop relevant pharmacokinetic and pharmacodynamic models of... 

W. Krzyzanski, R. Ramakrishnan, and W. J. Jnsko, Basic pharmacodynamic models for agents that alter production of natural cells. J Pharmacokinet Biopharm 27 467-489... 

One of the more common PD models used to describe the time course of a biomarker is the simple indirect effect model. In this example, drug concentrations increase the rate of degradation of the biomarker and act to reduce the biomarker concentration. Such a model has been used to characterize the pharmacokinetics/ pharmacodynamics of PEGylated interferon (55) and other proteins. A fragment of an example control stream for this basic PK/PD model is presented and explained in Table 41.5. Explanations for the different commands used are provided as well. 

Sharma, A. and Jusko, W.J., Characterization of four basic models of indirect pharmacodynamic responses, /. Pharmacokinet. Biopharm., 24,611-635,1996. 

Dayneka, N., Garg, V., and Jusko, W., Comparison of four basic models of indirect pharmacodynamic response, Journal of Pharmacokinetics and Biopharmaceutics, Vol. 21, No. 4, 1993, pp. 457-478. 

Biopharmaceutics, pharmacokinetics, and pharmacodynamics are the most important parts of pharmaceutical sciences because they bridge the gap between the basic sciences and the clinical application of drugs. The modeling approaches in all three disciplines attempt to ... 

N. L. Dyneka, V. Garg, and W. J. Jusko, Comparison of fonr basic models of indirect pharmacodynamic responses. J Pharmacokinet Biopharm 4 457-478 (1993). 

W. Krzyzanski and W. J. Jusko, Mathematical formalism and characteristics of four basic models of indirect pharmacodynamics responses for drug infusions. J Pharmacokinet Biopharm 26 385-408 (1998b). 

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