Distributions from Steady-State Data

DISTANCE DISTRIBUTIONS FROM STEADY-STATE DATA 

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DISTANCE DISTRIBUTIONS FROM STEADY-STATE DATA... 

Dynamic simulations for an isothermal, continuous, well-mixed tank reactor start-up were compared to experimental moments of the polymer distribution, reactant concentrations, population density distributions and media viscosity. The model devloped from steady-state data correlates with experimental, transient observations. Initially the reactor was void of initiator and polymer. 

It is possible to predict what happens to Vd when fu or fur changes as a result of physiological or disease processes in the body that change plasma and/or tissue protein concentrations. For example, Vd can increase with increased unbound toxicant in plasma or with a decrease in unbound toxicant tissue concentrations. The preceding equation explains why because of both plasma and tissue binding, some Vd values rarely correspond to a real volume such as plasma volume, extracellular space, or total body water. Finally interspecies differences in Vd values can be due to differences in body composition of body fat and protein, organ size, and blood flow as alluded to earlier in this section. The reader should also be aware that in addition to Vd, there are volumes of distribution that can be obtained from pharmacokinetic analysis of a given data set. These include the volume of distribution at steady state (Vd]SS), volume of the central compartment (Vc), and the volume of distribution that is operative over the elimination phase (Vd ea). The reader is advised to consult other relevant texts for a more detailed description of these parameters and when it is appropriate to use these parameters. 

In this section, we describe a quantitative VD model on 118 chemically diverse drugs comprising neutral and basic compounds. VD data were collected from literature by Lombardo et al. [19]. In the vast majority of cases, these data represent VDss values, i.e. volume of distribution at steady state. 

Another class of problems of which only the surface has been scratched is offered by mixed systems in which a Fischer-Tropsch type catalyst is combined with a solid acid such as a zeolite. Such systems have been used in recent attempts to produce narrower product distributions, and indeed deviations from the normal Schulz-Flory distribution have been reported (82-84). However, at the closing date of this review it was still unclear whether the results are characteristic of the running-in or of the steady-state behavior of the catalyst. In particular, the selective retention of the heavier products within the pores of the support might falsify the apparent catalyst selectivity. Only accurate mass-balancing and/or steady-state data can provide information on true product patterns unspoiled by this running-in phenomenon. 

In many cases additional work may be required to reparameterize models into the form required for the current analysis. This may involve, for example, a reparameterization between rate constants and clearance and volume terms or between derived parameters, such as volume of distribution by area (E ) and volume of distribution at steady state (Ess), or even extraction of parameter values from data summary variables (such as peak concentration, Cmaxi time to peak concentration, and area under the concentration curve, Af/C). The latter process is sometimes not straightforward and ultimately some data summaries may provide little useful information. See Dansirikul et al. (20) for methods of conversion of data summary variables into model-based parameters. 

Fig. 4 Allometric plots of the pharmacokinetic parameters clearance, volume of the central compartment ( /c), volume of distribution at steady state Vss), and elimination half-life of rPSGL-lg. Each data point within the plot represents an averaged value ofthe pharmacokinetic parameter with increasing weight from mouse, rat, monkey (3.74 kg), monkey (6.3 kg), and pig, respectively. The solid line is the best fit with a power function to relate pharmacokinetic parameters to body weight (from [54]).

Gillespie, W. R., Simple methods for estimation of mean residence time and steady-state volume of distribution from continuous-infusion data, Pharm. Res., 8(2) 254-258, 1991. 

Resource energy transfer is also used to study macro-molecular systems in which a single D-A distance is not preset, such as assemblies of proteins and membranes or Unfolded proteins where there is a distribution of D-A distances. The extent of energy transfer can also be influenced by the presence of donor-to-acceptor diffusion during the donor lifetime. Although information can be obtained from the steady-state data, such systems are usually studied using time-resolved measurements. These... 

Wajima T, Fukumura K, Yano Y, Oguma T. 2003. Prediction of human pharmacokinetics from animal data and molecular structural parameters using multivariate regression analysis volume of distribution at steady state. J Pham Phamacol 55 939-949. 

The present clinical data indicate that the pharmacokinetics of MCC-465 differ from those of the free doxombicin but are very similar to doxil in humans. Also, MCC-465 shows peak plasma levels and AUCs similar to the doxil. The increased AUCs result from the increased plasma levels. The volume of distribution at steady state (Vdss) ofMCC 65 is also similar to that reported for doxil (8). These pharmacokinetics data indicate that the stability in blood circulation of MCC-465 is similar to doxil. These results suggest that the conjugation of the F(ab )2 of GAH did not interfere with the stealth effect of the pegylated liposomes. Until now, we have not reached MTD yet. 

Model equations can be augmented with expressions accounting for covariates such as subject age, sex, weight, disease state, therapy history, and lifestyle (smoker or nonsmoker, IV drug user or not, therapy compliance, and others). If sufficient data exist, the parameters of these augmented models (or a distribution of the parameters consistent with the data) may be determined. Multiple simulations for prospective experiments or trials, with different parameter values generated from the distributions, can then be used to predict a range of outcomes and the related likelihood of each outcome. Such dose-exposure, exposure-response, or dose-response models can be classified as steady state, stochastic, of low to moderate complexity, predictive, and quantitative. A case study is described in Section 22.6. 

In PAMPA measurements each well is usually a one-point-in-time (single-timepoint) sample. By contrast, in the conventional multitimepoint Caco-2 assay, the acceptor solution is frequently replaced with fresh buffer solution so that the solution in contact with the membrane contains no more than a few percent of the total sample concentration at any time. This condition can be called a physically maintained sink. Under pseudo-steady state (when a practically linear solute concentration gradient is established in the membrane phase see Chapter 2), lipophilic molecules will distribute into the cell monolayer in accordance with the effective membrane-buffer partition coefficient, even when the acceptor solution contains nearly zero sample concentration (due to the physical sink). If the physical sink is maintained indefinitely, then eventually, all of the sample will be depleted from both the donor and membrane compartments, as the flux approaches zero (Chapter 2). In conventional Caco-2 data analysis, a very simple equation [Eq. (7.10) or (7.11)] is used to calculate the permeability coefficient. But when combinatorial (i.e., lipophilic) compounds are screened, this equation is often invalid, since a considerable portion of the molecules partitions into the membrane phase during the multitimepoint measurements. 

From these data, aquatic fate models construct outputs delineating exposure, fate, and persistence of the compound. In general, exposure can be determined as a time-course of chemical concentrations, as ultimate (steady-state) concentration distributions, or as statistical summaries of computed time-series. Fate of chemicals may mean either the distribution of the chemical among subsystems (e.g., fraction captured by benthic sediments), or a fractionation among transformation processes. The latter data can be used in sensitivity analyses to determine relative needs for accuracy and precision in chemical measurements. Persistence of the compound can be estimated from the time constants of the response of the system to chemical loadings. 

A system of N continuous stirred-tank reactors is used to carry out a first-order isothermal reaction. A simulated pulse tracer experiment can be made on the reactor system, and the results can be used to evaluate the steady state conversion from the residence time distribution function (E-curve). A comparison can be made between reactor performance and that calculated from the simulated tracer data. 

Another issue is how much of a contribution from two sites is required to produce nonlinear Stem-Volmer plots Figure4.14 shows Stem-Volmer plots for another dual distribution data set. r huri = 5, riong = 15, / iong = tfshon = 0.25, and Short = I -0 and k ong = 0.025. However, the fractional contribution of the short-lived component to the total unquenched steady-state luminescence was varied. Clearly, the curvature is pronounced and experimentally detectable from 0.1 to 0.9 not surprisingly, it is more pronounced for comparable contributions from both sites. This last feature is due to the fact that in the limit of pure fast or slow components, the plots become linear. 

The axial screw temperature profiles for the screw speeds are shown in Fig. 10.21. These profiles were constructed from the data set shown in Fig. 10.20 by using the data collected at steady state. As shown in this figure, the temperature profile would approximate the model developed by Cox and Fenner [30], but the temperature distribution is more complicated than this simple model. 

The polystyrene data were collected from a steady state, continuous, well-mixed reactor. The initiator was n-butylli-thlum for data of Figure 2 and was azobisisobutylnitrile for data of Figure 3. Toluene was used as a solvent. The former polymerizatl n y ields an exponential population density distribution ( ), M /M = 1.5 the latter yields a molar distribution defined as th product of degree of polymerization and an exponential ( ), M /M = 2.0. Standards utilized in calibration of both instrumen s ftere polystyrene supplied by Pressure Chemical Company. 

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. 

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