Pharmacodynamics linear

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... 

In silico modeling of non-linear drug absorption for the P-gp substrate talinolol and of consequences for the resulting pharmacodynamic effect. Pharmaceutical Research, 23, 1712-1720. 

In contrast to unfractionated heparin, LMWHs bind weakly to endothelial cells and are cleared mainly by renal excretion. A consequence of this is that their pharmacokinetics and pharmacodynamics are linear and the pharmacodynamics effect is proportional to the dose. This makes them more predictable than standard heparin, and is the main reason why routine monitoring is not needed. Because of the predominantly renal excretion there is a risk of accumulation in patients with reduced renal function. In this group of patients it may be advisable to monitor the anti-Xa activity. 

Many time-dependent processes appear to be nonlinear, yet when the drug concentration is measured carefully relative to the time of dose, the underlying dose-to-drug-concentration relationship is directly proportional to the dose and therefore is linear (see Time- and State-Varying Pharmacokinetics and Pharmacodynamics ). 

In the simplest case, drug effects are directly related to plasma concentrations, but this does not necessarily mean that effects simply parallel the time course of concentrations. Because the relationship between drug concentration and effect is not linear (recall the Emax model described in Chapter 2 Drug Receptors Pharmacodynamics), the effect will not usually be linearly proportional to the concentration. 

Pharmacokinetics Usually linear Usually independent from dynamics Often nonlinear Often dependent on pharmacodynamics and HAxA... 

Insulin Diabetes Human (18 type-I diabetic patients) Inhalation (AERx ) Pharmacodynamic system efficiency 12.7%. Dose-response relationship close to linear [64]... 

A mechanism-based PK/PD model for rHu-EPO was used to capture the physiological knowledge of the biological system. An open, two-compartment disposition model with parallel linear and nonlinear clearance, and endogenous EPO at baseline, was used to describe recombinant human erythropoietin (rHu-EPO) disposition after intravenous administration [35]. The pharmacodynamic effect of rHu-... 

Other simpler empirical models have also been used since the early days of pharmacodynamics [412,413] to describe the drug concentration-effect relationship. The linear model relies on a linear relationship between E and c ... 

Under the assumptions of the direct-link model, neither a counterclockwise (Figure 10.2) nor a clockwise hysteresis loop (Figure 10.4) will be recorded in an effect vs. concentration plot. In principle, the shape of the effect vs. concentration plot for an ideal direct-link model will be a curve identical to the specific pharmacodynamic model, relating effect with concentration, e.g., linear for a linear pharmacodynamic model, sigmoid for the sigmoid Emax model (cf. Table 10.1 and following paragraphs and sections), etc. 

From a modeling point of view, the last equilibrium assumption that can be relaxed, for the processes depicted in Figure 10.1, is H4, between the activated receptors (v variable in the occupancy model) and the response E. Instead of the activated receptors directly producing the response, they interfere with some other process, which in turn produces the response E. This mechanism is usually described mathematically with a transducer function T which is no longer linear (cf. Section 10.4.1). This type of pharmacodynamic model is called indirect response and includes modeling of the response process usually through a linear differential equation of the form... 

Using the approach of Sheiner and Verotta [452], a large number of pharmacodynamic models can be considered as hierarchical models composed of a series of submodels. These submodels are linear or nonlinear, static or dynamic input-output, elementary models. Several possible combinations of such submodels have been considered, but they have systematically associated the linear with dynamic features, and the nonlinear with static ones. Is there hesitation or fear of using nonlinear dynamics in the traditional pharmacokinetic-dynamic modeling context ... 

Population pharmacodynamic data, i.e., observed 24-hour efficacy scores were modeled as a function of individual predicted 24-hour steady state AUCs. Various pharmacodynamic models were explored including linear, Emax, and sigmoidal Emax models. Fixed and random-effect parameters were used to describe the PK/PD relationship. The results of the model development are presented in Table 7. 

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. 

Pharmacodynamic models mathematically relate a drug s pharmacological effect to its concentration at the effect site. Examples of the types of pharmacodynamic models that have been employed include the fixed-effect model/ maximum-effect models (Emax and sigmoid Emax)/ and linear and log-linear models (11). Unlike pharmacokinetic modelS/ pharmacodynamic models are time independent. However these models can be linked to pharmacokinetic modelS/ as discussed in Chapter 19. 

Several of the PK/PD models described in Chapter 19 have been employed to explore the relationship between circulating protein concentrations and pharmacodynamic endpoints. For example, a dog model of hemophilia was used to study the activity of recombinant FIX (79). Activity was determined in a bioassay, a modified one-stage partial thromboplastin time assay with pooled human plasma as the internal standard. As shown in Figure 32.14, the relationship between activity and recombinant FIX (BeneFIX) concentration was linear (r = 0.86), suggesting that for every 34.5 ng/mL of FIX, there would be a corresponding 1% increase in FIX activity. In 11 males with hemophilia B, it was necessary to use a sigmoid Emax... 

Ko, H.C. Jusko, W.J. Ebling, W.F. Non-linear perpendicular least-squares regression in pharmacodynamics. Biopharm. Drug Dis. 1997,18, 711-716. 

This approach is called the first order (FO) method in NONMEM. This is the most widely used approach in population pharmacokinetic and pharmacodynamic data analysis, and has been evaluated by simulation. The use of the first-order Taylor series expansion to approximate the non-linear model in r], and, possibly,... 

Biopharmaceutical research often involves the collection of repeated measures on experimental units (such as patients or healthy volunteers) in the form of longitudinal data and/or multilevel hierarchical data. Responses collected on the same experimental unit are typically correlated and, as a result, classical modeling methods that assume independent observations do not lead to valid inferences. Mixed effects models, which allow some or all of the parameters to vary with experimental unit through the inclusion of random effects, can flexibly account for the within-unit correlation often observed with repeated measures and provide proper inference. This chapter discusses the use of mixed effects models to analyze biopharmaceutical data, more specihcally pharmacokinetic (PK) and pharmacodynamic (PD) data. Different types of PK and PD data are considered to illustrate the use of the three most important classes of mixed effects models linear, nonlinear, and generalized linear. 

Pharmacokinetics usually independent of pharmacodynamics Usually linear pharmacokinetics Metabolic breakdown Renal clearance often important... 

FIGURE 5-16. The linear model (E = S x C + I) is often used as a pharmacodynamic model when the measured pharmacologic effect is 20% to 80% of fmax- In this situation, the determination of fmax and ECso is not possible. To illustrate this, effect measurements from Fig. 5-14 between 20% and 80% of fmax are graphed using the linear pharmacodynamic model. 

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