Other Pharmacodynamic Models

When one looks into the basic functions of the link and indirect response models, it is clear that one of the differences resides in the input functions to the effect and the receptor protein site, respectively. For the link model a linear input operates in contrast to the indirect model, where a nonlinear function operates. For the link model the time is not directly present and the pharmacological time course is exclusively dictated by the pharmacokinetic time, whereas the indirect model has its own time expressed by the differential equation describing the dynamics of the integrated response. 

A number of other pharmacodynamic approaches focusing either on prereceptor or postreceptor events have been proposed in the literature and are discussed below. 

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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... 

The UEL for reproductive and developmental toxicity is derived by applying uncertainty factors to the NOAEL, LOAEL, or BMDL. To calculate the UEL, the selected UF is divided into the NOAEL, LOAEL, or BMDL for the critical effect in the most appropriate or sensitive mammalian species. This approach is similar to the one used to derive the acute and chronic reference doses (RfD) or Acceptable Daily Intake (ADI) except that it is specific for reproductive and developmental effects and is derived specifically for the exposure duration of concern in the human. The evaluative process uses the UEL both to avoid the connotation that it is the RfD or reference concentration (RfC) value derived by EPA or the ADI derived for food additives by the Food and Drug Administration, both of which consider all types of noncancer toxicity data. Other approaches for more quantitative dose-response evaluations can be used when sufficient data are available. When more extensive data are available (for example, on pharmacokinetics, mechanisms, or biological markers of exposure and effect), one might use more sophisticated quantitative modeling approaches (e.g., a physiologically based pharmacokinetic or pharmacodynamic model) to estimate low levels of risk. Unfortunately, the data sets required for such modeling are rare. 

At times, the effect measured during a pharmacodynamic study has a value before the drug is administered to the patient. In these cases, the drug changes the patient s baseline value. Examples of these types of measurements are heart rate and blood pressure. In addition, a given drug may increase or decrease the baseline value. Two basic techniques are used to incorporate baseline values into pharmacodynamic data. One way incorporates the baseline value into the pharmacodynamic model the other way transforms the effect data to take baseline values into account. 

What this equation shows is that the F-test and AIC are not independent and that given one of them the other can be determined. These equations also show that sometimes the two criteria can lead to different conclusions. Suppose a modeler fit an Emax model with two estimable parameters and a sigmoid Emax model with three estimable parameters to a data set with 14 observations, such as might be the case when fitting a pharmacodynamic model to individual data. In this case, an F-test greater than 3.84 is required to declare the sigmoid Emax model the superior model at the 0.05 level, which is equivalent to a AAIC of —2.19. An F-test value less than 3.84 is considered to be not statistically significant at the 0.05 level and the reduced model is chosen as the superior model. However, any AAIC less than 0, even values between 0 and —2.19, is still considered to be indicative that the full model is the superior model. Hence, the possibility exists for the two criteria to reach different conclusions. 

A model is nonlinear if any of the partial derivatives with respect to any of the model parameters are dependent on any other model parameter or if any of the derivatives do not exist or are discontinuous. For example, the Emax pharmacodynamic model,... 

What are the strengths and weaknesses of these approaches The use of intrinsic clearance in vitro permits predictions between species for the particular enzyme/route of metabolism concerned. If humans have qualitatively different routes of metabolism for any particular compound, then this will weaken the predictive value of the in vitro observation. Similarly, allometric scaling works best for compounds with a high component of non-enzymatic elimination, such as our model compound with approximately 90% excretion as unchanged drug. This prediction weakens as variations in rates of enzymatic reactions become more important. The pharmacokinetic-pharmacodynamic modelling approaches use existing in vivo data to calculate constants which can be applied to other in vivo data, but does not, in its present form, link in vitro and in vivo data. 

The curve of therapeutic effect as a function of time may be temporally displaced with respect to the curve of plasma drug concentration over time, requiring the use of indirect pharmaco-kinetic/pharmacodynamic modeling. Other complicating factors may he at play. For example, over time the formation of antibodies to a protein may neutralize the protein or change its pharmacokinetic profile. At times, the blood concentration-effect relationship is so inaccessible for a particular therapeutic... 

RNAi has had an important impact on the development of novel disease models in animals, and it is likely that siRNAs, the trigger molecules for RNA silencing, will become an invaluable tool for the treatment of genetic disorders. The rational design of siRNAs, the introduction of chemical modifications into siRNAs to improve their pharmacokinetic and pharmacodynamic properties for in vivo application with high specificity, and the development of efficient delivery system will foster the therapeutic application of RNAi in AD and other neurodegenerative disorders (413,417). 

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