Pharmacokinetic-pharmacodynamic model structure

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... 

FIGURE 51.1. PBPK-PD model schematic of sarin in Hartley guinea pig. This model structure allows for the simulation of experimental studies with dosing hy intravenous or subcutaneous dosing, and inhalation exposure. This model design was after Gearhart et al. (1990) and was adapted to simulate the pharmacokinetics and pharmacodynamics of sarin in the guinea pig. 

Many types of modeling techniques are available in the discovery phase of drug development, from structure activity relationships (SAR) to physiology based pharmacokinetics (PBPK) and pharmacokinetics-/pharmacodynamics (PK/PD) to help choosing some of the lead compounds. Some tests that are carried out by discovery include techniques related to structure determination, metabolism, and permeability NMR, MS/MS, elemental analysis, PAMPA, CACO-2, and in vitro metabolic stability. Although they are important as a part of physicochemical molecular characterization under the biopharmaceutics umbrella, they will not be discussed here. The reader can find relevant information in numerous monographs [9,10]. 

Assumptions are included in all of the elements of any pharmacokinetic/pharma-codynamic (PK/PD) model. Some examples of common assumptions made for these models include the structure of the models for pharmacokinetics, pharmacodynamics, and their respective covariate influences, the models for the clinical effect of the drug, the parameter values of all these models, and the variance structures for model components (11). Assumptions reduce inferential certainty because if the assumptions are wrong, then the model-based conclusions are wrong. Therefore, it is the quality of the attendant assumptions, and not their existence, that is the issue with assumptions in modeling (12). 

While ejqierimental methods always require sufficient amount of chemicals for the estimation of drag absorption, computational in silico) methods can lead to the prediction of intestinal absorption based on chemical structure, and can thus be used before synthesis of compoimds. In silico predictions could be based both on relatively simple quantitative structure-activity relationships (QSAR) analysis and more complex physiologically based pharmacokinetic and/or pharmacodynamic models. Whichever the approach used for model building, computational methods should be based on experimental data that were obtained for a wide range of structurally diverse compoimds (training set). It should be noted, however, that current in silico methods, are not as reliable as experimental models. 

Herbette, L. G., Pharmacokinetic and pharmacodynamic design of lipophilic drugs based on a structural model for drug interactions with biological membranes, Pest. Sci. 35, 363-368 (1992). 

Nestorov, I. A. (1999). Sensitivity analysis of [4iarmacokinetic and pharmacodynamic systems 1. A structural approach to sensitivity analysis of physiologically based pharmacokinetic models. J Pharmacokinet Biopharm 27, 577-596. 

Linear mixed effects models are primarily used in pharmacodynamic analysis or in the statistical analysis of pharmacokinetic parameters. Linear mixed effects models could also be used to analyze concentrationtime data from a 1-compartment model with bolus administration after Ln-transformation. The advantages to using mixed effects in an analysis are that observations within a subject may be correlated and that in addition to estimation of the model parameters, between- and within-subject variability may be estimated. Also, the structural model is based on the population, not on data from any one particular subject, thus allowing for sparse sampling. Most statistical packages now include linear mixed effects models as part of their analysis options, as do some pharmacokinetic software (Win-Nonlin). While linear mixed effects models are not cov-... 

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