Model indirect response

The rate equation describes the variation in response variable R (with initial value of Rq) the measure response appears at a constant rate (zero order) of and is eliminafed by the first-order constant. The indirect response models will generally fall info fwo caf-egories inhibition or stimulation function. The inhibition response is classically described in ferms of IC q, fhe drug concenfration fhaf produce 50% of maximal inhibition (e.g., action of S5mfhefic glucocorticoid on adrenal glands or effecf of furosemide on sodium absorption in fhe loop of Henley) and is a number from 0 fo 1 where 1 represents total inhibition ... 

Pharmacokinetic/pharmacodynamic evaluated using indirect response modeling with inhibition of input... 

Jusko, W.J. and Ko, H.C., Physiologic indirect response models characterize diverse types of pharmacodynamic effects, Clin. Pharmacol. Ther., 56, 406-419,1994. 

An instructive example is the physiological variable serum creatinine. Creatinine is an endogenous metabolite formed from, and thus reflecting, muscle mass. Total body muscle mass is sufficiently constant to render measurement of serum creatinine useful for assessing actual renal function. The serum value of creatinine (R) is namely dependent on the continuous (zero-order) input of creatinine into the blood (A in) and its renal elimination rate, which is a first-order rate process (A out x ) In case of an extensive muscle breakdown, kin will temporarily increase. It may also be permanently low, for example in old age when muscle mass is reduced. Likewise, creatinine clearance may decrease for various reasons, described by a decrease in A out- An increase in creatinine clearance may occur as well, for example following recovery from renal disease. According to pharmacodynamic indirect response models. 

Indirect response models have been successfully applied for a number of drugs that display a relatively slow onset of effect compared to their distribution to the site of action. Examples are corticosteroids, warfarin, furosemide and terbutalin. Such models are also particularly appropriate if the measured response is a change in circulating blood cells or endogenous proteins (e.g. hormones or cytokines). 

Sheiner LB, Verotta D. Further notes on physiologic indirect response models. Clin Pharmacol Ther 1995 58 238-40. 

The standard effect-compartment model, usually characterized as an atypical indirect-link model, also constitutes an example of what we will call a direct-response model in contrast to the indirect-response models. Globally, the standard direct-response models are models in which c(t) affects all dynamic processes only linearly. 

Ariens [432] was the first to describe drug action through indirect mechanisms. Later on, Nagashima et al. [433] introduced the indirect response concept to pharmacokinetic-dynamic modeling with their work on the kinetics of the anticoagulant effect of warfarin, which is controlled by the change in the prothrombin complex synthesis rate. Today, indirect-response modeling finds extensive... 

It is rather obvious that an indirect response mechanism, whatever the detailed processes involved, results in a counterclockwise hysteresis loop for the effect-concentration relationship, Figure 10.2. Here, however, the elaboration of the observed response is usually secondary to a previous time-consuming synthesis or degradation of an endogenous substance(s) or mediator(s). Since both the indirect-link and indirect response models have counterclockwise hysteresis effect-concentration plots, an approach based on the time of the maximum effect has been applied to furosemide data [440] for indirect (link or response) model selection. 

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 very general scheme for relating effects to concentration, of which both the effect-compartment and the indirect-effect models are special cases, was outlined by Sheiner and Verotta [452], The models presented in the study can be considered to be a special case of that unified scheme. As judiciously presented by these authors, both direct-response and indirect-response models are composed of one nonlinear static submodel and one dynamic submodel, but the placement of the submodels in the global model differs ... 

In an indirect-response model, the above order of models is reversed and now the static model precedes the dynamic one. The dynamic model describes the formation and loss of the response variable through a linear differential equation whose parameters are nonlinear saturable forms of the driving concentration c (t). 

Chakraborty, A., Krzyzanski, W., and Jusko, W., Mathematical modeling of circadian cortisol concentrations using indirect response models Comparison of several methods, Journal of Pharmacokinetics and Biopharmaceutics, Vol. 27, No. 1, 1999, pp. 23-43. 

Minami, H., Sasaki, Y., Saijo, N., Ohtsu, T., Fujii, H., Igarashi, T., and Itoh, K., Indirect-response model for the time course of leukopenia with anticancer drugs, Clinical Pharmacology and Therapeutics, Vol. 64, No. 5, 1998, pp. 511-521. 

In contrast to the aforementioned direct relationships/ the indirect response model shown in Figure 32.16 was used to describe the relationship between the administration of GH and IGF-1 in nonhuman primates (88). It was assumed in this model that the production of IGF-1 varied over time/ a reasonable... 

For example, such simple PK/PD models as described in Fig. 13 have been used to describe the effects of beta-2-adrenergic drugs on the heart rate, but models incorporating an effect-compartment [106] or indirect-response model [105] are necessary for other drug actions, such as the effects of glucocorticoids on lymphocytes and endogenous cortisol suppression (for review see Ref. 107). 

Transit Models The development of indirect effect models (32) facilitated the evaluation of many disease-mediated processes such as changes in biomarker levels over time. Control streams and example databases for these models are presented elsewhere in Chapters 22 and 23 and will not be covered here. However, as was discussed, when applying these indirect response models, it is possible to increase the delay in response by the addition of extra compartments. The addition of these extra effect compartments also creates additional parameters that need to be estimated, which are often not identifiable. 

Dayneka et al. (6) characterized the four basic indirect response models—the first set of mechanistic PK/PD models to describe a diverse array of drug responses. Shortly thereafter, the importance (7) and initial applications (8,9) of these models were described using data obtained from the literature. Since then, numerous applications and advancements of these models have been published. 

Indirect response models have been extended to drugs that alter the generation of natural cells (41). Unlike cancerous cells and embryonic stem cells, the lifespan of primary human cells is finite. Thus, cells live for a specific duration known as the cell lifespan and then undergo apoptosis (programmed cell death). Cell lifespan models assume that, for a given cell type, each cell lives for the same period of time Tr and then disappears (Figure 22.3). Thus, cells are produced at a zero-order rate kin and are lost at the same rate, but Tr units of time later ... 

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