Drug distribution data calculation

Liposome partitioning of ionizable drugs can be determined by titration, and has been correlated with human absorption [102-104]. A new absorption potential parameter has been suggested, as calculated from liposome distribution data and the solubility-dose ratio, which shows an excellent sigmoidal relationship with human passive intestinal absorption (Eq. 2) [102, 103]. 

Figure 6.3 Quantal effects. Typical set of data after administration of increasing doses of drug to a group of subjects and observation of minimum dose at which each subject responds. Data shown are for 100 subjects dose increased in 0.2 mg/kg of body weight increments. Mean (ji) (and median) dose is 3.0 mg/kg standard deviation (v) is 0.8 mg/kg. Results plotted as histogram (bar graph) showing number responding at each dose smooth curve is normal distribution function calculated for ji of 3.0 and v of 0.8.

For a drug administered by the oral, or any other extravascular, route of administration, the apparent volume of distribution cannot be calculated from plasma drug concentration data alone. The reason is that the value of F (the fraction of administered dose that reaches the general circulation) is not known. From Eqs 6.7 and 6.8 ... 

The (AUC)g has been shown above to be the 0th statistical moment. It can be calculated for plasma drug concentration data that are not describable by an explicit pharmacokinetic equation, even in cases when the curve has an irregular shape. If the assumption is made that all the underlying processes of absorption, distribution, and elimination follow linear kinetics (are monoexponential functions), (AUC)o can provide us with the most important parameter in all pharmacokinetics, the systemic clearance of drug (CIJ. Here is the relationship ... 

The latter approach—completely drying the aerosol— while valid, is diffi-cnlt to perform experimentally (29). The low solids content of pharmaceutical nebulizer solutions results in dry aerosols that are too fine for reliable enough measurements to be made to allow back calculation with any accuracy. For example a typical nebulizer droplet distribution with a mass median diameter of 3 pm generated from a 0.1% drug solution would result in a dry particle distribution with a mass median diameter of 0.1 pm. Obtaining size distribution data with any reasonable resolution at this size is very problematic. A further issue is that the solids content of the original droplets must be known in order to perform the calculation, and this can vary considerably during the course of nebulization. This technique has therefore not been used extensively. 

The volume of distribution is a parameter that can be calculated from plasma drug concentration versus time data (expressed as area under the curve or AUC), according to the two equations shown below, for terminal or steady-state volume of distribution, respectively. 

The volume of distribution (Vd) of a drug may be simply calculated under the one-compartment model from Cp-time data. Extrapolation of the In Cp-time line back to the y-intercept provides the hypothetical Cp°. As long as the drug mass in the original dose (D0) is known, Equation 7.13 can calculate Vd. 

The preceding discussion has been intent upon breaking down equations and making sense of different variables and how each may be calculated from experimental Cp-time data. At the outset of this chapter, two parameters—clearance and volume of distribution—were set apart as the key pharmacokinetic variables for a drug. This brief section tries to establish the importance and utility of these two variables. The highlight of this subsection is Equation 7.12, which is shown again here. A rearranged form of Equation 7.12 is Equation 7.33. 

In pharmaceutical research and drug development, noncompartmental analysis is normally the first and standard approach used to analyze pharmacokinetic data. The aim is to characterize the disposition of the drug in each individual, based on available concentration-time data. The assessment of pharmacokinetic parameters relies on a minimum set of assumptions, namely that drug elimination occurs exclusively from the sampling compartment, and that the drug follows linear pharmacokinetics that is, drug disposition is characterized by first-order processes (see Chapter 7). Calculations of pharmacokinetic parameters with this approach are usually based on statistical moments, namely the area under the concentration-time profile (area under the zero moment curve, AUC) and the area under the first moment curve (AUMC), as well as the terminal elimination rate constant (Xz) for extrapolation of AUC and AUMC beyond the measured data. Other pharmacokinetic parameters such as half-life (t1/2), clearance (CL), and volume of distribution (V) can then be derived. 

The choice of the concentration of the drug to be tested should consider therapeutic levels that could be attained with clinically employed doses. In the case of a compound under pre-clinical evaluation for a potential antitumor activity, a concentration limit of 100 pg/ml is recommended. Pharmacokinetic data are available for various anti-neoplastic clinically used drugs, with information about their maximum plasma concentration, concentration versus time, and pharmaceutical half-life in plasma. When these data are not available, an approximation of plasma levels could be obtained by calculating the theoretical concentration obtained when the administered dose is uniformly distributed throughout the body fluid. 

Equation 2.4 was derived by substituting CLR/Vi for k in Equation 2.13. Although Ud and CLr are the two primary parameters of the single-compartment model/ confusion arises because k is initially calculated from experimental data. However/ k is influenced by changes in distribution volume as well as clearance and does not reflect just changes in drug elimination. 

However, experimental determination of logP does include correlation with such properties. For example, the ElogD method developed by Lombardo et al. [67] uses RP-HPLC retention data to determine octanol-water distribution coefficients at pH 7.4 for neutral and basic drugs in Pfizer. Moreover the authors used the same method to determine ElogD at pH 6.5, thus calculating important parameters for intestinal absorption [68],... 

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