Cp*TiMe

Iterative method Formulation Number of iterations CP time (seconds) Comments... 

The central processor (CP) time is based on a CDC Cyber 73 computer. 

The 13C NMR spectra were measured regularly over 6 months (190 days) and the polymer structure became almost stable after this period. After 6 months, the relative intensities in the unsaturated carbon region were independent of CP time. The alkyl signal positions became constant after 11 days (Figure 38(b)). However, their line width gradually broadened to double the width after 6 months. 

Since the intensities of the resonances in the CPMAS experiment depend upon strengths of the dipolar couplings and molecular motions in the solid, it is not straightforward to obtain quantitative spectra. However, one may adjust the time during which magnetization is transferred from the proton to the carbon resonances, the CP time, and determine the time for which the solid state and solution integrals are equal. One can thereby obtain measurements of the aromatic to ethynyl ratio during the course of the cure. 

Know how to derive pharmacokinetic parameters from Cp-time data... 

Cp is the plasma concentration of the drug at time t. The elimination rate constant is keb with units of inverse time. Cp° is the plasma concentration at t = 0. Cp° is a special case that is more theoretical than real. At the time of the injection (t = 0), the drug bolus hits the bloodstream. At this instant, the drug has not mixed with the entire blood supply. The concentration at the site of injection is very high, but blood in other parts of the body still has a Cp of 0. For this reason, Cp° cannot be directly measured experimentally but must be determined by extrapolation of the Cp-time line back to the y-axis. 

With real Cp-time data (clinical data), the first data point is normally collected approximately 15 minutes after administration. Therefore, the value of In Cp° is determined by extrapolation of the In Cp-time line back to t0 rather than as an experimental data point. 

Calculating Half-Life from Cp-Time Data... 

PROBLEM The following table presents Cp-time data for a drug. Use the data to construct a In Cp versus time graph. Determine the best-fit line of the graph to calculate the half-life of the drug. 

SOLUTION To generate a In Cp graph, we need In Cp data. Taking the natural logarithm of Cp gives new In Cp-time data points. 

Knowing total clearance for a drug is important. Clearance is determined from Cp-time plot data for an IV bolus. Cp-time data for an IV bolus can be used to determine the elimination rate constant of a drug ( el) as well as the hypothetical Cp°. These two values allow direct calculation of the area under the curve (AUC) of the Cp-time plot with Equation 7.10 (Figure 7.5).1... 

PROBLEM The following table present some Cp-time data points for an IV bolus dose of 325 mg. What is CL for this drug ... 

In practice, clinical Cp-time data is used to determine el, which in turn is used to calculate CL and Fd of a drug. However, physiologically, ty2 and el are determined by CL and Vd. 

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 early discussion on IV bolus administration was completely based on the one-compartment model. The discussion somewhat avoided covering exactly what was happening to the drug immediately after the injection. Most Cp-time data is not recorded until 15 minutes after injection of the drug. Why Because interpreting data for the first 15 minutes requires the two-compartment model. 

Mathematically, the Cp-time relationship of a two-component model can be expressed as shown in Equation 7.15, a two-term version of Equation 7.1. 

FIGURE7.13 Transdermal Cp-time data for ethinyl estradiol (7.8)5... 

FIGURE 7.14 Single-dose oral Cp-time plot... 

Equation 7.21 contains a number of variables. Experimentally, fcel and Vd for a drug can be readily determined from analysis of Cp- or In Cp-time data from an IV bolus. As long as the administrator knows the amount of drug that he or she gave a patient, then D0 is known as well. That leaves F and kah as the only unknown terms in Equation 7.21. 

Bioavailability (/ ), or more precisely the absolute bioavailability, is a property of a drug, its formulation, and its route of administration. Bioavailability is a measure of drug exposure that results from oral dosing of a drug relative to drug exposure by an IV bolus. As has already been discussed, drug exposure is related to the area under the curve (AUC) of a Cp-time plot. 

In a clinical setting, AUComl is determined by trapezoidal estimation of experimental Cp-time data points. From AUComl and D0oral and information from an IV bolus, oral bioavailability can be determined through Equation 7.22. 

A particularly significant Cp-time point for an oral drug is Cpmax and tmax. Cpmax occurs during a transition between the absorption and elimination phases. At Cpmax, dCp/dt is 0, and the rate of absorption is balanced by the rate of elimination (Equation 7.29). Through analysis and rearrangement of the first derivative of Equation 7.21 with respect to time, Equation 7.30 can be obtained and used for simple calculation of tmax. Substitution of tmax into Equation 7.21 then provides Cpmax. 

While tmax can be directly calculated with Equation 7.30, tmax can also be estimated from a set of clinical Cp-time data points. With both el and an estimated tmax, one may... 

Larger, less frequent doses afford a broader range of Cp values. If Cp strays outside the therapeutic window, smaller, more frequent doses provide a narrower gap between the peaks and valleys of the Cp-time graph (Figure 7.17). The number of doses required to reach a pseudo Css range depends on kch kah, dose size, and dose frequency. 

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. 

Regardless of where a metabolite forms, Cp-time plots for metabolites often closely resemble Figure 7.20. The metabolite s Cp (Cpm) starts at 0 and rises to a peak. First-order elimination then becomes the predominant process, and Cpm begins to fall. Overall, the shape of the Cpm-time curve somewhat resembles Cp-time curve of an oral drug. 

The behavior of metabolites may often be modeled reasonably well, but determining the various parameters for metabolites is a challenge. Specialized pharmacokinetic curve-fitting software frequently can tease the parameters from clinical Cp-time data. If necessary, metabolites may be synthesized in lab and then administered directly to animals. From these studies, key parameters such as Vd, CL, F, and kah may be determined in the absence of the parent drug. Keep in mind that a pharmaceutical company may not administer a metabolite into humans without the metabolite s being classified as an investigational new drug (IND). 

If the kel of a drug is much greater than its metabolite, how might one determine the kel of the metabolite Before answering this question, sketch a superimposed Cp-time plot of both the drug and metabolite. 

Cp-time data points for a 100-mg IV bolus are given in the following table for a hypothetical drug and a 70-kg patient. Assume a one-compartment model. Determine keh t /2, and Vd for the drug. 

The same drug as in question 6 was administered as a 100-mg oral dose to the same patient. The Cp-time data is shown in the following table. Determine and then F. 

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