Using Pharmacodynamic and Pharmacokinetic Concepts to Optimize Treatment of Infectious Diseases

Richard Quintiliani, MD

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Other PD Concepts

One of the simplest models in pharmacokinetics describes the body as a single homogeneous compartment into which the drug appears to dissolve. The volume of this compartment, called the apparent volume of distribution (VD), rarely relates to physiologic volumes but serves as a proportionality constant between the dose of drug administered and the observed plasma or serum concentration just after the intravenous administration of a bolus dose.

This concept can be more easily understood using a hydrodynamic, or "bathtub," model. In the bathtub model, we add a known amount of dye to water in a bathtub of known volume. Clearly, a large bathtub yields a lower concentration than a small bathtub if the same quantity of dye is placed in each one. Drugs that distribute widely through the body tend to have large volumes of distribution and low serum concentrations; drugs that remain only in the blood volume typically have small volumes of distribution and high serum concentrations.

In general, drugs with a high level of serum protein binding penetrate to a lesser extent into the interstitial spaces; produce higher peak serum concentrations; and exhibit a slower rate of elimination from the body, especially if the major elimination mode is by glomerular filtration. Thus, an inverse relationship exists between protein binding and VD. There is no relationship between renal tubular secretion and protein binding.

The value of VD for the clinician is that this term roughly describes whether or not the antibiotic will be widely distributed in tissue. Drugs that have poor tissue penetration (eg, β-lactam antibiotics) typically have a low (less than 20 L) VD at steady state, whereas agents with widespread tissue distribution (eg, fluoroquinolones) have a high (greater than 100 L) VD at steady state.

Drug concentrations decline in the body as a result of elimination, usually by the kidneys, liver, or both. The term "clearance" is used to describe the intrinsic ability of the body to remove drug. Clearance represents a theoretic volume of blood or plasma that is cleared of drug within a period of time. It is expressed as units of volume per time.

The clearance volume for a drug is generally constant during a dosing interval. The amount of drug removed per unit of time can be determined if we recall that concentration and volume are related. Because the clearance of a drug remains constant after distribution is complete but the serum concentration declines as the drug is removed from the body, the amount of drug removed per unit of time is highest when the serum concentration is highest (ie, just after administration of a dose).

In the one-compartment PK model, which most antibiotics follow, drug distribution is assumed to be instantaneous and elimination from the body follows first-order (log linear) decline. A semilogarithmic plot of drug concentration versus time yields a linear graph. This type of plot can be used to determine the T1/2 of a drug, which refers to the amount of time required for the drug concentration to decrease by 50%. A simple rule for drugs that follow a one-compartment model is to multiply the T1/2 by 5; this will predict the time the serum concentration will decline to its lowest, or trough, concentration.

Antibiotics with very short half-lives, such as penicillin, nafcillin, oxacillin, and cephalothin, require very frequent dosing (eg, every 4 hours), since their half-lives are only 30 minutes. Antibiotics with long half-lives, such as the respiratory quinolones (eg, levofloxacin, gatifloxacin, moxifloxacin), ceftriaxone, and azithromycin, allow once-daily dosing.

If we know the T1/2 of a drug, we can predict the time required to reach steady state, in which all the peak and trough concentrations are the same after the dose. Fifty percent of the final steady-state concentration accumulates during each T1/2, so that after 5 half-lives, approximately 97% of the final steady-state concentration has been achieved. For example, an antibiotic with a T1/2 of 2 hours (eg, ceftazidime) would take about 10 hours to attain steady state, whereas as an agent with an 8-hour T1/2 (eg, ceftriaxone) would reach steady state in about 40 hours.

Clearly, the longer the T1/2 of a drug, the longer it takes to achieve a steady-state concentration. This can be particularly important for patients receiving drugs that have long half-lives and narrow therapeutic ranges of serum concentrations. In these patients, a loading dose is often used to quickly achieve therapeutic drug concentrations.

The post-antibiotic effect (PAE) describes the persistent suppression of bacterial growth after exposure of a microorganism to an antibiotic. The term should not be confused with the effects of bacterial suppression by subinhibitory antibiotic concentrations. Antibiotics that kill bacteria by interfering with protein synthesis (eg, aminoglycosides) or DNA replication (eg, quinolones) usually demonstrate prolonged PAEs (eg, 1 to 5 hours) against gram-negative bacteria, while agents that kill bacteria by interfering with cell wall synthesis (eg, β-lactam antibiotics, glycopeptides) have little, if any, PAE against these types of organisms. Against gram-positive bacteria, both types of antibiotics typically exhibit short PAEs of about 1 hour.

The clinical relevance of the PAE is related to its use in establishing dosing regimens that are directed against a specific pathogen. The PAE has been one of many explanations for the success of intermittent dosing with drugs that exhibit short half-lives.

Bioavailability, or the degree of absorption of an antibiotic, is an extremely important characteristic, since a high level of bioavailability often allows for inexpensive and effective treatment of an infection without the use of injectable agents or hospitalization. Of course, there are many advantages to rapidly replacing an intravenous antibiotic with an oral formulation. Probably the most important one is the avoidance of intravenous line sepsis, the major source of hospital-acquired bacteremia and fungemia. Proactive programs to rapidly switch patients from intravenous to oral therapy are often designated as sequential, transitional, or switch therapy.

To replace an intravenous antibiotic with an oral formulation, the oral drug should have a high degree of bioavailability, preferably over 90%. In this situation, the concentrations of the oral antibiotic in tissue or serum can rival the levels that would be obtained if the patient continued treatment with the intravenous formulation. Table 2 lists the oral antibiotics that exhibit bioavailability of greater than 90%. Replacing an intravenous antibiotic with an oral drug is probably unwise for oral agents with less than 50% bioavailability.

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