Expectations versus time curves

In these instances, the time of the peak in the plasma concentration versus time curve provides a convenient measure of the absorption rate. For example, if three tablets of the same drug are found to be completely absorbed and all give plasma peaks at 1 hour, it can be safely concluded that all three tablets are absorbed at essentially the same rate. (In fact, if all tablets are completely absorbed and all peak at the same time, it would be expected that all three plasma concentration versus time curves would be identical, within experimental error.)... 

Poole et al. (1968) administered ampicillin anhydrate and trihydrate to human subjects as 250 mg doses of the suspension or in capsules. The anhydrate gave higher bioavailabilities as measured by th area under the blood level versus time curves. In suspensions, the area ratio (anhydrate/trihydrate was 1.21 and in capsules, this ratio was quite comparable at 1.17. The peak in this curve also occurred earlier for the anhydrate. This was expected based on the 20% higher solubility in water at 3 C (10 mg/ml for the anhydrate and 8 mg/mL for the trihydrate). The difference in dogs was more pronounced suspensions of the anhydrate gave 1.6 times the AUC of suspensions of th< trihydrate form. 

Linear pharmacokinetics. For a simple linear pharmacokinetics case, the body can be modeled as a single drug compartment with first-order kinetic elimination—where the dose is administered and drug concentrations are drawn from the same compartment. For an intravenous bolus dose, the expected drug plasma concentration Cp versus time curves are shown in Fig. 1.10. The kinetics for this system are described by Eq. (1.6). The well-known solution to this equation is given by Eq. (1.7), and a linearized version of this solution is given in Eq. (1.8) and shown graphically in Fig. 1.13. 

If for the same one-compartment model the input is changed from an intravenous bolus to first-order kinetic input (e.g., gut absorption), the expected Cp versus time curves are shown in Fig. 1.14. The kinetics for this system are described by... 

Phenomenology of the crystallization. The conversion versus time curves obtained at three different temperatures are shown in Figure 1. With the synthesis procedure used, the sigmoid curves were characterized by shorter induction periods than the traditional method (11,12). As expected, temperature had a strong effect on the rate of crystallization. The overall crystallization rates may be approximated by the reciprocal of the times of half conversion. From these values an apparent activation energy of 22 1 kcal/mol was obtained. With respect to literature data, this value exceeds that reported, for instance, for zeolite Na-X (1,4) but compares well with the 19.8 kcal/mol found for ZSM-11 (13). 

The effects of erythromycin, an inhibitor of CYP3A4, on the pharmacokinetics of lidocaine have been studied in nine healthy volunteers. Steady-state oral erythromycin had no effect on the plasma concentration versus time curve of lidocaine after intravenous administration, but erythromycin increased the plasma concentrations of the major metabolite of lidocaine, MEGX (78). It is not clear what the interpretation of these results is, particularly since the authors did not study enough subjects to detect what might have been small but significant changes in various disposition parameters of lidocaine and did not report unbound concentrations of Udocaine or its metabolites. However, whatever the pharmacokinetic explanation, the clinical relevance is that one would expect that erythromycin would potentiate the toxic effects of lidocaine that are mediated by MEGX. 

Since many hundreds of readings were taken during a single ramp, and the expected behaviour was fairly linear, the raw data was filtered using a relatively wide 20-point window. This was re-applied several times until a smooth curve was attained for the conversion versus time curve. The smoothed data is shown in Figure 11.19. 

Consequently, it would be expected that the predictive capability of the two models will also be equivalent, and any limitations in terms of prediction of one model will reflect analogous limitations of the other model. Indeed, if the vapor pressure model fails to describe the tailing of the concentration versus time curve - which is an indication of sink effects - the mass transfer model is also unable to describe the same part of the experimental data (Tichenor et al., 1993). It should be noted, however, that the parameters of the mass transfer model have well-defined physical meanings [e.g., vapor pressure (C ), molecular diffusivity (Dy), boundary layer thickness ( )], and the parameter estimation does not rely heavily on curve fitting. The parameter estimation is the first step in the model performance and validation process, as we will see later in this Chapter. 

Add to this the societal factor that Americans seem to favor new, high-tech things, and you ve got a formula for unrealistic expectations or even, to use Alan Greenspan s famous phrase, irrational exuberance. This can be charted on a new curve that s perhaps every bit as important as the benefit-versus-time S-curve, one of expectations-versus-time. This is shown in Figure 2.10. Dr Murcko explains In the beginning there s a lot of hoopla, a lot... 

According to O Donnell et al. [130], the emulsion polymerization of vinyl acetate follows the Smith-Ewart theory of emulsion polymerization [131] because the rate of polymerization is independent of the total amount of monomer present, the rate is a function of the 0.6th power of the emulsifer concentration, and the rate of emulsion polymerization is a function of the 0.7th power of the initiator concentration instead of the expected 0.4th power. In this work poly(vinyl alcohol), 88% hydrolyzed with a medium molecular weight (i.e., Du Font s Elvanol 52-22), was used as the only externally added emulsifier. Light-scattering studies indicated that this emulsifier formed no aggregates in the aqueous solution. These latter observations may, however, have been made at room temperature and not at the reaction temperature [1]. The conversion versus time curve was essentially linear up to 80% conversion. 

Pharmacokinetic parameters, such as elimination half life (ti/2), the elimination rate constant (K), the apparent volume of distribution (V) and the systemic clearance (Cl) of most drugs are not expected to change when different doses are administered and/or when the drug is administered via different routes as a single or multiple doses. The kinetics of these drugs is described as linear, or dose-independent, pharmacokinetics and is characterized by the first-order process. The term linear simply means that plasma concentration at a given time at steady state and the area under the plasma concentration versus time curve (AUC) will both be directly proportional to the dose administered, as illustrated in Fig. 15.1. 

As shown in Figure 3.5.3, the relaxation time versus pressure curves are dramatically different from those obtained using CF4 at a temperature well above its critical point. Indeed, while the overall form of the Tx curves for CF4 in fumed silica was similar to that of the bulk gas, the shape of the Ti plots for c-C4F8 in Vycor more closely resembles that of an adsorption isotherm (Ta of CF4 in Vycor is largely invariant with pressure, as gas-wall collisions in this material are more frequent than gas-gas collisions). This is not surprising given that we expect the behavior of this gas at 291 K to be shifted towards the adsorbed phase. The highest pressure... 

Step (18) in the above is the analog of step (8), which is required for H2—D2 equilibration it is a necessary step if we view the jr-allyl as an immobile species on the surface. The products of step (19) can be viewed as propylene in the form of a loosely held w-complex which on desorption yields isomerized propylene. Readsorption of the isomerized propylene or further reaction of the x-complex would yield surface OD groups. When equilibrium is achieved, the concentration of surface OD groups should equal 40% of the initial concentration of OH groups. Figure 21 shows a plot versus time of the intensity (multiplied by a scale factor to yield concentration) of the surface OH and OD. The expected equilibrium points are indicated by arrows. Corresponding data for CD3—CH=CH2 are also shown. Except for the OH species from CD3—CH=CH2, which is a relatively weak band on the side of a surface hydroxyl, the curves approach the expected value. 

Figure 12.3. Benchmark of peer-reviewed academic reports of organic semiconductor device field-effect mobility versus time of report. All data points are for spin-coated organic semiconducting transistors. Solid points are derived from the benchmark study completed in 2002 by Brazis and Dyrc at Motorola (unpublished). The curve is a calculated estimation, based on these data, of what the expected mobility values will be in the future. The open points are data derived in 2005 from the public journals for verification of the 2002 prediction.6 38... 

Figure 1-21 Cooling history of two granitoid samples (78-419 and 78-592) from the Separation Point Batholith of New Zealand. Data are from Harrison and McDougal (1980). The emplacement age of the batholith is > 115 Ma. The curves are plotted to guide the eyes. It can be seen that cooling rate was high initially and decreases gradually as the temperature approaches surface temperature, as expected. The temperature versus time relation is roughly exponential.

Figure 3 gives plots of the rate of heat generated versus ctire time under isothermal DSC conditions, at various ten ratures, for both the Ashland polyester and the Dow vinyl ester resins. It is seen that the eunount of heat generated (i.e., the area under the dQ/dt-cure time curve) increases as the cure temperat ire increases, as would be expected for exothermic chemical reactions. 

Is the time versus concentration curve expected to be exactly Gaussian in this experiment ... 

Figure 5 Plot of variations in (which arise from the decay of the extinct nuclide versus time expressed as ppm differences from present-day compositions. An initial Stn/ Sm = 0.007 is assumed (Prinzhofer et al., 1992). If an LREE-depleted mantle (high Sm/Nd) formed within the first 200-300Ma of Earth history, then with the current 5-10 ppm analytical precision, a positive Nd deviation would be expected to be observed in any sample derived from this source. Lunar samples (Nyquist et al, 1995) and martian meteorites (Harper et al., 1995) show clear evidence of Nd variations reflecting very early differentiation on these bodies. Nd anomalies have now been suggested for some 3.7-3.S Ga terrestrial samples from southwest Greenland (Harper and Jacobsen, 1992 Boyet et al, 2002 Caro et al., 2003). Most of the 3.8 Ga gneisses that have been measured do not show these effects and recent re-measurement of the original Harper and Jacobsen sample by Papanastassiou et al. (2003) has not confirmed the original result (see text). The different/curves are for different degrees of depletion (20% and 40%) of...

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