Cp versus Time curve

Table 6 illustrates the steps involved in carrying out the Wagner-Nelson calculation. The third column (f 0 Cp dt) shows the area under the Cp versus time curve calculated sequentially from t = 0 to each of the time points using the trapezoidal rule (see Sec. VIII.A). The fourth column (kei f 0 Cp di) shows each of the preceding areas multiplied by k.ei (as estimated from the tail )... 

Estimate the initial rate of reaction from the Cs or CP versus time curves for different initial substrate concentrations. 

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... 

Area under Cp versus time curve (pg/mL) h pgmL h... 

Figure 4.6 Application of the trapezoidal rule to determine the area under the plasma concentration (Cp) versus time curve (AUC). (Rectilinear plot of plasma or serum concentration versus time following the administration of an intravenous bolus of a drug fitting a one-compartment model.)...

Figure 7.6 The area under the plasma concentration (Cp) versus time curve (AUC)o against dose of a drug administered by the intravascular route. Please note that slope of the graph permits the determination of the systemic clearance (Cl), of the drug. (Review how to calculate the slope.) K, elimination rate constant V, apparent volume of distribution.

Equation (35) describes the line in Fig. 10, which is a semilog plot of Cp versus time for an orally administered drug absorbed by a first-order process. The plot begins as a rising curve and becomes a straight line with a negative slope after 6 hours. This behavior is the result of the biexponential nature of Eq. (35). Up to 6 hours, both the absorption process [exp(—kat) and the elimination process [exp( keil)] influence the plasma concentration. After 6 hours, only the elimination process influences the plasma concentration. 

Equation (57) can be used to calculate the Cmax and Cmin values on the plasma concentration plateau by substituting values for t that correspond to the peaks and valleys in the Cp versus t curve. Thus, if t = tmax (the time of the peak), Eq. (57) gives Cmax ... 

Figure 6.13 (a) Semilog plot of plasma concentration for (Cp) versus time representative of a two-compartment model. The curve can be broken down into an a or X i distribution phase and ft or k2 elimination phase, (b) Two-compartment model with transfer rate constants, Kn and K2, and elimination rate constant, Ke. ... 

A lower creatinine clearance value will affect other so-called "constant" parameters such as the elimination and/or excretion rate constants (K or jy, the elimination half life (ti/2) and, possibly, the apparent volume of distribution. These, in turn, will influence the value of any other pharmacokinetic parameter mathematically related to them. (This example is for a one-compartment model). These parameters include plasma concentration (Cp) at any time t, the area under the concentration versus time curve from t— 0 to t= °°, and clearance. 

Figure 7.1 Plasma concentration (Cp) versus time data following the administration of a dose of a drug as an intravenous bolus (a) or by an extravascular route (b). (AUC)q, area under the plasma concentration versus time curve from time zero to t. ...

The interpretation of impedance measurements, i. e. curves C = C(v) in adsorption equilibria, or capacitance versus time curves C = C(t) at constant frequency (v = const) for adsorption processes, is not easy and still a field for analytic and simulative investigations. Also the dielectric equation of state (EOS) (Cr = 8r(T, p, m ))of an adsorption system does not seem to have been investigated in a systematic way -except some virial like series expansions considered in [3.40]. Correspondingly interrelations between the dielectric EOS and the adsorption isotherm or the heat of adsorption are - though they must exist, cp. [6.16, 6.17] - unknown to the best knowledge of the authors. 

By computing values from the above equations, a curve of T versus time may be plotted. This information may be used to design heating systems or evaluate the performance of existing ones. The input parameters required for the analysis are T, U, A, W, Cp, and T,. 

Fig. 39.8. (a) Semilogarithmic plot of plasma concentration Cp (pg I" ) versus time t. The straight line is fitted to the later part of the curve (slow 3-phase), with the exception of points that fall below the quantitation limit. TTte intercept B of the fitted line is the extrapolated plasma concentration that would have been obtained at time 0 with an intravenous injection. The slope sp is proportional to the transfer constant of elimination k. (b) Semilogarithmic plot of the residual plasma concentration C (pg r ) versus time t, on an expanded time scale t. The straight line is fitted to the first part of the residual curve (fast a-phase), with the exception of points whose residuals fall below the quantitation limit. The intercept B of the fitted line, is the same as that in panel a. The slope is proportional to the transfer constant of absorption from the extravascular compartment. 

The effects of different model parameters on the plasma concentration versus time relationship can be demonstrated by mathematical analysis of the previous equations, or by graphical representation of a change in one or more of the variables. Equation (10.95) indicates that the plasma concentration (Cp is proportional to the dose (Av) inversely proportional to the volume of distribution (V)- Thus an increase in Aw or a decrease in Fboth yield an equivalent increase in Cp as illustrated in Figure 10.20. Note that the general shape of the curve, or more specifically the slope of the line for ln(Cp versus t, is not a function of Av or V. Equations (10.98) and (10.99) show that the... 

Bioequivalence. This is the statistical equivalence between the generic and the standard (brand name) formulation of drug for the "big three" parameters peak plasma drug concentration [(Cp)max]/ time of peak plasma drug concentration (tmax)/ and area under the plasma drug versus time concentration curve (AUC). The FDA looks at the data of the study and decides whether these have proved bioequivalence or not. 

Figure 15.1 Relationship between the plasma concentration (Cp) at a time at steady state (a) and the area under the plasma concentration versus time (ADC) curve (b) against the administered dose for a drug that exhibits dose-independent pharmacokinetics.

Though the accuracy of description of flow curves of real polymer melts, attained by means of Eq. (10), is not always sufficient, but doubtless the equation of such a structure based on the idea of relaxation mechanism of non-Newtonian polymer flow, correctly reflects the main peculiarities of viscous properties. Therefore while discussing the effect a filler has on the viscosity properties of polymer melts, besides the dependences Y(filler modifies the characteristic time of relaxation. According to [19], a possible form of the X versus

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