Pharmacokinetic-pharmacodynamic model dosing parameters

Dose-response models describe a cause-effect relationship. There are a wide range of mathematical models that have been used for this purpose. The complexity of a dose-response model can range from a simple one-parameter equation to complex multicompartment pharmacokinetic/pharmacodynamic models. Many dose-response models, including most cancer risk assessment models, are population models that predict the frequency of a disease in a population. Such dose-response models typically employ one or more frequency distributions as part of the equation. Dose-response may also operate at an individual level and predict the severity of a health outcome as a function of dose. Particularly complex dose-response models may model both severity of outcome and population variability, and perhaps even recognize the influence of multiple causal factors. 

Since dose tolerance studies usually produce adverse events, pharmacokinetic evaluation should include an assessment of the dose-concentration-toxicity relationship. In addition to regularly scheduled plasma samples obtained to calculate pharmacokinetic parameters, it is common to obtain a plasma sample at the time an adverse event is observed. Often it is possible to correlate acute toxicity with plasma concentrations as well as with dose, and occasionally even to develop a pharmacokinetic/pharmacodynamic model for acute or subchronic toxicity. 

C(t) modeled according to two-compartment model with zero-order and first-order absorption Pharmacokinetic/pharmacodynamic relationship modeled using Hill model with first-order absorption. Modeled parameters matched experimental parameters when bicompartmental model with zero-order input was used. Linear PKs, anticlockwise hysteresis loop established for all doses studied. Apomorphine and growth hormone concentration predicted with good accuracy... 

The approach involves a semimechanistic or mechanistic model that describes the joint probability of the time of remedication and the pain relief score (which is related to plasma drug concentrations). This joint probability can be written as the product of the conditional probability of the time of remedication, given the level of pain relief and the probability of the pain relief score. First, a population pharmacokinetic (PK) model is developed using the nonlinear mixed effects modeling approach (16-19) (see also Chapters 10 and 14 of this book). With this approach both population (average) and random (inter- and intraindividual) effects parameters are estimated. When the PK model is linked to an effect (pharmacodynamic (PD) model), the effect site concentration (C ) as defined by Sheiner et al. (20) can be obtained. The effect site concentration is useful in linking dose to pain relief and subsequently to the decision to remedicate. 

Complex pharmacokinetic/pharmacodynamic (PK/PD) simulations are usually developed in a modular manner. Each component or subsystem of the overall simulation is developed one-by-one and then each component is linked to run in a continuous manner (see Figure 33.2). Simulation of clinical trials consists of a covariate model and input-output model coupled to a trial execution model (10). The covariate model defines patient-specific characteristics (e.g., age, weight, clearance, volume of distribution). The input-output model consists of all those elements that link the known inputs into the system (e.g., dose, dosing regimen, PK model, PK/PD model, covariate-PK/PD relationships, disease progression) to the outputs of the system (e.g., exposure, PD response, outcome, or survival). In a stochastic simulation, random error is introduced into the appropriate subsystems. For example, between-subject variability may be introduced among the PK parameters, like clearance. The outputs of the system are driven by the inputs... 

Risk Assessment. This model successfully described the disposition of chloroform in rats, mice and humans following various exposure scenarios and developed dose surrogates more closely related to toxicity response. With regard to target tissue dosimetry, the Corley model predicts the relative order of susceptibility to chloroform toxicity consequent to binding to macromolecules (MMB) to be mouse > rat > human. Linking the pharmacokinetic parameters of this model to the pharmacodynamic cancer model of Reitz et al. (1990) provides a biologically based risk assessment model for chloroform. 

Exposures of newborns to PAHs depend on pharmacokinetic processes operating in the mother, and transfer through breast milk. Since it is difficult to characterize these pathways in humans, physiologically based pharmacokinetic (PBPK) and pharmacodynamic (PD) models need to be developed using appropriate animal models, and incorporating key parameters such as dose, exposure duration, and developmental stage (Dorman et al, 2001). Thus, development of PBPK and PBPD models for PAHs is an immediate need that will help in not only characterizing the dose-response relationship, but also extrapolation of results from animal studies to humans. 

Relatively few PBPK models have been developed to describe the pharmacokinetics and pharmacodynamics of chemical warfare nerve agents. Maxwell et aV developed a PBPK-PD model for GD in the rat, describing the inhibition of AChE and carboxylesterase (CaE) in blood and tissues with mass balance equations based on parameters for blood flow, tissue volumes, GD metabolism and tissue/plasma partition coefficients. The resulting model gives accurate predictions of AChE activity in the blood and seven different tissues following intramuscular dosing with 90 pg GD kg bodyweight (BW), and was able to reproduce dose-response AChE inhibition from 10 to 100% in the brain. 

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