Plasma drug concentration profile

PK models (Section 13.2.4), PD models (Section 13.2.5), and PK/PD models (Section 13.2.6) can be used in two different ways, that is, in simulations (Section 13.2.7) and in data analysis (Section 13.2.8). Simulations can be performed if the model structure and its underlying parameter values are known. In fact, for any arbitrary dose or dosing schedule the drug concentration profile in each part of the model can be calculated. The quantitative measures of the effectiveness of drug targeting (Section 13.4) can also be evaluated. If actual measurements have been performed in in-vivo experiments in laboratory animals or man, the relevant model structure and its parameter values can be assessed by analysis of plasma disappearance curves, excretion rate profiles, tissue concentration data, and so forth (Section 13.2.8). 

Figure 5.9. Dose-response profile in a population. (A) Relationship between responding patients, expressed as percentage of individuals, and plasma drug concentrations. With increasing drug concentration, the proportion of patients who derive therapeutic benefit, without concentration-limited side effect peaks, and then declines. (B) A schematic representation of dose-response curves. Typical therapeutic and lethal responses at indicated doses are evaluated in animal models to estimate therapeutic index, TI. ED50, effective dose needed to produce a therapeutic response in 50% of animals, exhibiting therapeutic response LD50, effective dose needed to produce lethal effects in 50% of animals.

The mean in vitro dissolution time is compared to either the mean residence time or the mean in vivo dissolution time. Level B correlation, like Level A correlation, uses all of the in vitro and in vivo data but is not considered to be a point-to-point correlation and does not uniquely reflect the actual in vivo plasma level curve, since several different in vivo plasma level-time curves will produce similar residence times. A Level C correlation is the weakest IVIVC and establishes a single point relationship between a dissolution parameter (e.g., time for 50% of drug to dissolve, or percent drug dissolved in two hours, etc.) and a pharmacokinetic parameter (e.g., AUC, Cmax, Tmax). Level C correlation does not reflect the complete shape of the plasma drug concentration-time curve of dissolution profile. 

FIGURE 23.2 Simulated response profiles (solid lines) for cell proliferation model with irreversible inactivation (Figure 23.1), where g R) and /(C) are given by Eqs. (23.4) and (23.8). Plasma drug concentrations are shown (dashed lines) for increasing intravenous doses ranging from 10 to 10,000 units. Parameter values are = 0.3 h , = 10,000 units,... 

Both the rate and extent of drug distribution across tissue barriers can have a profound impact on pharmacokinetic and pharmacodynamic properties. The extent of drug distribution manifests itself locally as the tissue to plasma (or blood) concentration ratio. Collectively, the extent of distribution into all the tissues results in the apparent volume of distribution. Simply put, the pharmacokinetic parameter volume of distribution reflects the ratio of individual tissue to plasma drug concentration weighed for tissue volume. The rate of distribution (together with the extent of distribution) can influence the shape of the plasma versus time profile for a drug, which can give rise to differences in elimination half-life as well as onset and duration of action. 

Intravenous Drug Disposition. The estimation of primary pharmacokinetic parameters using noncompartmental analysis is based on statistical moment theory [45, 46]. The relationships dehned by this theory are valid under the assumption that the system is linear and time-invariant. For simplicity, we further assume that drug is irreversibly removed only from a single accessible pool (e.g., plasma space). Regardless of the route of administration, the temporal profile of plasma drug concentrations, Cp(t), can represent a statistical distribution curve. As such, the zeroth and first statistical moments (Mo and Mi) are defined as ... 

The peak plasma drug concentration (units = ag/ml or ng/ml, etc.) The Cniax is also a measure of the extent of bioavailability or peak exposure and indicates concentrations required for a therapeutic or toxic response. It relates to peak exposure of the drug. is obtained directly from the plasma concentration time profile. 

In Fig. 10.11, the plasma concentration versus time profile shows a trough. This might be attributed to an elapse in time between the completion of an intravenous bolus loading dose and the commencement of the infusion rate. The magnitude of the nadir observed in the plasma concentration versus time profile will be influenced by the elapsed time and the elimination half life of the drug. However, there is no bolus/infusion combination for a two-compartment drug that will produce a total plasma drug concentration that is constant over time the profile will have peaks and/or nadirs. This, therefore, could be an alternative explanation for the deviation from a horizontal line in Fig. 10.11. 

Figure 11.6 Plasma drug concentration (Cp) versus time profile following the intravenous bolus administration of many equal doses at an identical dosing interval (t). In this representation, the dosing regimen has been designed so that the plasma drug concentrations will fall within the therapeutic range at steady state.

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... 

The CAT model estimates not only the extent of drug absorption, but also the rate of drug absorption that makes it possible to couple the CAT model to pharmacokinetic models to estimate plasma concentration profiles. The CAT model has been used to estimate the rate of absorption for saturable and region-depen-dent drugs, such as cefatrizine [67], In this case, the model simultaneously considers passive diffusion, saturable absorption, GI degradation, and transit. The mass balance equation, Eq. (51), needs to be rewritten to include all these processes ... 

In spite of its limitations, the ACAT model combined with modeling of saturable processes has become a powerful tool in the study of oral absorption and pharmacokinetics. To our knowledge, it is the only tool that can translate in vitro data from early drug discovery experiments all the way to plasma concentration profiles and nonlinear dose-relationship predictions. As more experimental data become available, we believe that the model will become more comprehensive and its predictive capabilities will be further enhanced. 

The second situation when IVIVC is not likely for class II drugs is where the absorption is limited by the saturation solubility in the gastrointestinal tract rather than the dissolution rate, as discussed in more detail above. In this situation, the drug concentration in the gastrointestinal tract will be close to the saturation solubility, and changes of the dissolution rate will not affect the plasma concentrationtime profile and in vivo bioavailability. Standard in vitro dissolution tests are carried out under sink conditions , i.e., at concentrations well below the saturation solubility. Thus, only effects related to dissolution rate can be predicted in vitro. If more physiologically relevant dissolution media are used, which do not necessarily provide sink conditions , the possibility for IVIVC could be improved, as has been indicated by the results of recent studies using simulated intestinal medium [76],... 

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