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Blood arriving at an organ of extraction normally contains only a fraction of the total drug present in the body. The flow through the major extraction organs, the liver and kidneys, is about 3 % of the total blood volume per minute, however, for many
20 | 2 Pharmacokinetics
drugs, distribution out of the blood into the tissues will have occurred. The duration of the drug in the body is therefore the relationship between the clearance (blood flow through the organs of extraction and their extraction efficiency) and the amount of the dose of drug actually in the circulation (blood). The amount of drug in the circulation is related to the volume of distribution and therefore to the elimination rate constant (kel) which is given by the relationship:
kel = Cl/Vd (2.7)
The elimination rate constant can be described as a proportional rate constant. An elimination rate constant of 0.1 h-1 means that 10 % of the drug is removed per hour.
The elimination rate constant and half-life (fy2), the time taken for the drug concentration present in the circulation to decline to 50 % of the current value, are related by the equation:
*1/2 = b2/fcd (2.8)
Half-life reflects how often a drug needs to be administered. To maintain concentrations with minimal peak and trough levels over a dosing interval a rule of thumb is that the dosing interval should equal the drug half-life. Thus for once-a-day administration a 24-h half-life is required. This will provide a peak-to-trough variation in plasma concentration of approximately two-fold. In practice the tolerance in peak-to-trough variation in plasma concentration will depend on the therapeutic index of a given drug and dosing intervals of two to three half-lives are not uncommon.
The importance of these equations is that drugs can have different half-lives due either to changes in clearance or changes in volume (see Section 2.7). This is illustrated in Figure 2.3 for a simple single compartment pharmacokinetic model where the half-life is doubled either by reducing clearance to 50 % or by doubling the volume of distribution.
Fig. 2.3 Effect of clearance and volume of distribution on half-life for a simple single compartment pharmacokinetic model.
Intravenous Administration: Infusion
With linear kinetics, providing an intravenous infusion is maintained long enough, a situation will arise when the rate of drug infused = rate of drug eliminated. The
2.5 Intravenous Administration: Infusion 21
Fig. 2.4 Plasma concentration profile observed after intravenous infusion.
plasma or blood concentrations will remain constant and be described as “steady state”. The plasma concentration profile following intravenous infusion is illustrated in Figure 2.4.
The steady state concentration(Css) is defined by the equation:
Css = ko/Clp (2.9)
where ko is the infusion rate and Clp is the plasma (or blood) clearance. The equation which governs the rise in plasma concentration is shown below where the plasma concentration (Cp) may be determined at any time (t).
Cp = ko / Clp (1 - e”kel' ‘) (2.10)
Thus the time taken to reach steady state is dependent on kel. The larger kel (shorter the half-life) the more rapidly the drug will attain steady state. As a guide 87 % of steady state is attained when a drug is infused for a period equal to three half-lives. Decline from steady state will be as described above, so a short half-life drug will rapidly attain steady state during infusion and rapidly disappear following the cessation of infusion.
22 2 Pharmacokinetics
Increasing the infusion rate will mean the concentrations will climb until a new steady state value is obtained. Thus doubling the infusion rate doubles the steady state plasma concentration as illustrated in Figure 2.5.
When a drug is administered orally, it has to be absorbed across the membranes of the gastrointestinal tract. Incomplete absorption lowers the proportion of the dose able to reach the systemic circulation. The blood supply to the gastrointestinal tract (GIT) is drained via the hepatic portal vein which passes through the liver on its passage back to the heart and lungs. Transport of the drug from the gastrointestinal tract to the systemic circulation will mean the entire absorbed dose has to pass through the liver.
On this “first-pass” the entire dose is subjected to liver extraction and the fraction of the dose reaching the systemic circulation (F) can be substantially reduced (even for completely absorbed drugs) as shown in the following equation:
F =1- E (2.11)
Again E is the same concept as that shown in Figure 2.1. This phenomenon is termed the first-pass effect, or pre-systemic metabolism, and is a major factor in reducing the bioavailability of lipophilic drugs. From the concept of extraction shown in Figure 2.1, rapidly metabolized drugs, with high Cli values, will have high extraction and high first-pass effects. An example of this type of drug is the lipophilic calcium channel blocker, felodipine. This compound has an hepatic extraction of about 0.80, leading to oral systemic drug exposure (AUC) of only about one-fifth of that observed after intravenous administration . Conversely, slowly metabolized drugs, with low Cli values, will have low extraction and show small and insignificant first-pass effects. The class III anti-dysrhythmic drug, dofetilide, provides such an example. Hepatic extraction of this compound is only about 0.07, leading to similar systemic exposure (AUC) after oral and intravenous doses .