Pharmacokinetics and Pharmacodynamics

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4 Pharmacokinetics and Pharmacodynamics

William Banner, Jr.

image Be sure to check out the supplementary content available at http://evolve.elsevier.com/Hazinski.

Pearls

• Pharmacokinetics describes how the body alters drug concentration, including how the drug is dispersed in and removed from the body; it is the effect that the body has on the drug. Pharmacokinetics involves drug absorption, distribution, and elimination.

• Pharmacodynamics describes the relationship between drug concentration and drug effect; it is the effect the drug has on the body.

• The steady state is a state of equilibrium between how much of the drug is administered and how much is being removed from the body. In drugs with first-order kinetics (i.e., the systems that eliminate the drug are not saturated), steady state can be predicted from the drug half-life (t1/2).

• The drug half-life is the time it takes for half of the drug to be eliminated from the body. In each half-life, the drug concentration in the blood will fall by half. You can use the half-life to predict the time to steady state and to know when to anticipate drug effects or changes in effects.

• In general, when administering a drug by continuous infusion, a blood concentration of 90% of steady-state value is achieved in approximately four to five half-lives of the drug. Drugs with long half-lives will require a longer time to achieve steady state unless a loading dose is provided.

Introduction

Many drugs used in critical care, particularly vasoactive and sedative agents, must be titrated based on patient response, and both pharmacokinetics and pharmacodynamics influence that response. Pharmacokinetics describes how the body alters drug concentration, including how the drug is dispersed in and removed from the body; it is the effect that the body has on the drug. Pharmacodynamics describes the relationship between drug concentration and drug effect; it is the effect the drug has on the body.

The purpose of this chapter is to highlight principles governing both pharmacokinetic and pharmacodynamic processes and how they affect clinical decisions. This chapter is not intended to be a drug reference; it is a reference regarding principles of drug therapy.

Principles of pharmacokinetics

The effects of drug administration vary with both the drug and the patient. There have been many attempts to model these processes using mathematical equations to guide clinical therapy. In addition, understanding of developmental changes in drug metabolism and excretion and emerging information about pharmacogenetics enable more accurate prediction of pediatric drug dosing and effects.2–5

Paths of Drugs in the Body

The path of a drug in the body from administration and distribution to elimination is complex. We can break this path into individual components for better understanding (Fig. 4-1).

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Fig. 4-1 Possible paths of drugs in the body from entry to distribution and elimination. A drug will follow some of these pathways. Drug effects are caused by blood concentration, tissue concentrations, or both.

(Courtesy William Banner, Jr.)

Drug Absorption

Drugs are administered and absorbed by several routes. Bioavailability refers to the fraction of administered drug that reaches the circulation (blood); it is affected by the route of administration. The bioavailability of drugs administered orally can be altered in pediatric patients by developmental changes in the gastric pH. The gastric pH is relatively neutral in the neonate and it becomes more acidic as the child grows. In addition, some drugs (e.g., meperidine) when taken orally, are rapidly metabolized by the liver before they reach the general circulation; this is termed first pass metabolism and it reduces drug bioavailability.

Drugs administered intravenously can also be affected by the site of administration. Drugs administered through an umbilical vein catheter can flow directly into the portal circulation, where they can damage the liver. Administration of a drug into an umbilical artery catheter can cause drug precipitation in the kidneys or lower extremity vascular damage.

Drug Distribution

Drug distribution is affected by factors such as protein binding, lipid solubility, and ionization state, and by conditions such as blood pH, temperature, and other substances in the blood (e.g., blood urea nitrogen [BUN], other drugs). The volume of distribution is the ratio of the concentration of drug in the blood to the total amount of drug in the body. For example, gentamicin has a small volume of distribution; it is principally found in the blood. In contrast, digoxin undergoes widespread distribution to tissues, so the concentration in the blood represents only a fraction of the total body stores (i.e., it has a large volume of distribution). Gentamicin and digoxin are both removed by similar processes in the kidney, but the rates of elimination of the two drugs differ because the amount that is present in the blood affects how quickly the kidneys can remove the drug.

The drug’s site of action can also help predict how drug distribution will affect its efficacy and safety. Shortly after the intravenous administration of digoxin, blood concentrations can be extremely high, but the patient will not exhibit toxicity because digoxin acts on the cardiac muscle. As the blood drug concentration decreases and concentrations in the tissue (including the heart muscle) increase, the likelihood of a toxic effect increases. It is only after the drug is distributed into tissue that blood concentrations can be used to predict the likelihood of a beneficial or toxic effect.

Drug Elimination

Drugs are eliminated from the body in several ways. Some drugs such as ethyl alcohol can be exhaled through the lungs. The most common routes of elimination, however, are through the kidney and the liver. In the kidney, drugs can be filtered in the glomerulus or secreted by tubular cells. The most common method of renal excretion is through filtration. In general, the liver metabolizes drugs to change their solubility so they can be excreted through the biliary tract or the kidney.

A small number of drugs are broken down by enzymes present in plasma. These drugs, including succinylcholine, produce very short-term effects. A few drugs, such as cisatracurium, spontaneously degrade in the blood.

Mathematical modeling of drug paths

Mathematical models of drug kinetics (including elimination), called kinetic modeling, have identified several general patterns of drug behavior. The Michaelis-Menten equation describes drug kinetics, including drug elimination. According to the Michaelis-Menten equation, when the enzyme that metabolizes a drug is not saturated (i.e., there is plenty of enzyme still available to metabolize even more drug than is present), drug elimination will vary based on how quickly the drug is presented to the enzyme. If the enzyme is fully saturated (i.e., all available enzyme is being used to metabolize the drug), then drug elimination will occur at a fixed rate.

Michaelis-Menten Kinetics

A common drug governed by Michaelis-Menten kinetics is phenytoin. With even a single dose of phenytoin, the enzymes that metabolize the drug (the cytochrome P450 enzymes) are typically saturated, so the phenytoin blood concentration will initially fall slowly after administration. However, once the blood concentration falls sufficiently, the enzymes responsible for metabolism are no longer saturated and the blood concentration will then fall quickly (Fig. 4-2, curve A). Giving too much of a drug initially or giving additional doses too soon can increase the drug concentration and risk of toxicity and prolong effects and elimination time. Implications of phenytoin kinetics with repeated dosing are discussed in the next section.

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Fig. 4-2 Three general models of drug elimination. After a single dose of a drug is given, the graph of the logarithm (log) of blood concentration produced over time varies based on drug distribution and elimination (kinetics). Curve A: If the drug is primarily distributed in the blood (e.g., phenytoin) and is eliminated by enzyme systems, it demonstrates one-compartment Michaelis-Menten kinetics as shown. The log of the blood concentration over time initially declines slowly until some enzyme systems are no longer saturated. From that time, the concentration will fall more rapidly. Curve B: If the drug is largely distributed in the blood (one compartment) and the elimination systems have plenty of capacity (first-order kinetics), the graph of the log of blood concentration over time will be an inverted V. The concentration rises in a straight line and then declines in a straight line. The log of the drug concentration will fall by half during each half-life of the drug. Curve C: Drugs distributed in the tissues (e.g., vancomycin) typically demonstrate two-compartment kinetics. Immediately after administration the concentration rises. As the drug is distributed into the tissues the drug concentration falls rapidly (the first part of the downward curve). As the drug is eliminated, the drug level falls more gradually.

(Courtesy William Banner, Jr.)

First Order Kinetics

One extreme of the Michaelis-Menten equation occurs when the kidney or the liver is functioning well below its capacity to remove the drug and there is little risk of overloading the system. This extreme is referred to as first-order kinetics.

With first-order kinetics, drugs behave similarly to radioactive decay, and elimination is described in terms of the drug’s half-life (t1/2). The drug half-life is the time it takes for half of the drug to be eliminated from the body. When a half-life is listed in a drug database, the drug has first-order kinetics (see section, Half-life). See Box 4-1 for a metaphor to further explain first- and zero-order kinetics. Many of the principles described in the following sections (e.g., time to study state, volume of distribution, filtration rates) apply chiefly to drugs with first-order kinetics.

Box 4-1 Metaphor for Understanding First Order and Zero-Order Kinetics

Another way to conceptualize first-order kinetics for drug elimination is to compare drug metabolism to customers going through checkout lanes at a store. A group of cashiers has a certain capacity to process customers, much as the liver processes or metabolizes a drug. If the number of cashiers is sufficiently high, when a customer appears that customer will be processed immediately. As long as the number of cashiers exceeds the number of customers presenting at the checkout lanes, the number of customers processed through the checkout lanes will be determined by the number of customers who are present at the checkout lanes. Renal filtration or excretion and liver metabolism typically have sufficient capacity, so they have capacity (“cashiers”) available at all times to eliminate many drugs. This is called first-order kinetics.

If the capacity to process or metabolize the drug is saturated, then the rate of drug metabolism will become constant and if drug administration exceeds the rate of metabolism, the drug will begin to accumulate. Using the cashier metaphor, if the number of customers exceeds the available cashiers, the rate that customers are processed will become constant (for example, 10 customers/h), regardless of how many customers are waiting. The customers will accumulate if the number of customers exceeds the number of cashiers and the customers appear at the checkout line at a rate that is faster than they can be processed. If the capacity to metabolize the drug is saturated (zero-order kinetics) drug concentrations will increase in a manner similar to customer accumulation at the cashiers.

Volume of Distribution

Volume of distribution can be used to predict the drug concentration achieved with a drug loading dose. As noted previously, a drug like gentamicin has a low volume of distribution (it remains in the blood), so effective blood concentrations are quickly established without the need for a loading dose. By comparison, when administering a drug like digoxin, with a high volume of distribution, a relatively large initial loading dose must be given to achieve reasonable blood concentration after tissue distribution.

The volume of distribution is generally expressed as a liquid volume per body weight, such as liters per kilogram (L/kg) or milliliters per kilogram (mL/kg). The volume of distribution is used to calculate loading doses for drugs such as phenytoin, for which a loading dose of 20   mg/kg is administered to occupy the volume of distribution (0.7   L/kg) and achieve a therapeutic blood (serum) concentration.

Although it is tempting to relate anatomic places to the mathematical concept of compartments for drug distribution, the characterization is not entirely accurate. In general, we consider the group of tissues into which the drug distributes at a similar rate as occupying the same compartment, because the tissues all receive the drug at the same time.

Generally speaking, when injecting an intravenous drug, the first compartment it occupies is the blood. If the drug is primarily distributed in the blood (e.g., gentamicin), that is where the drug remains until it is eliminated; these kinetics are described as one-compartment kinetics. The graph of the logarithm of blood concentration over time shows a rise when the drug is administered and a straight line as the drug is eliminated (see Fig. 4-2, curve B).

If a drug is distributed in the blood and the tissues (e.g., vancomycin), intravenous administration temporarily increases the concentration of the drug in the blood. Initially, blood levels decline rapidly as the drug moves into tissue, and then a more gradual decline occurs as the drug is eliminated. This drug activity is called two-compartment kinetics (see Fig. 4-2, curve C).

Implications of Multicompartment Distribution

Drugs can disappear rapidly from the blood if they are distributed in the tissue. The best example of this is sodium thiopental (Pentothal). In clinical practice, a single dose of intravenous thiopental has a short effect. However, the drug has a long final half-life. The explanation for this apparent contradiction is that most thiopental elimination occurs after the drug concentration is below the level needed to keep the patient asleep (i.e., anesthetized). If several doses of thiopental are administered in a short period of time in an attempt to produce anesthesia, the tissues will become saturated and no distribution will occur. If the drug concentration increases to sufficiently high levels, the clinical effect (i.e., anesthesia) may last a long time (see Fig. 4-3).

image

Fig. 4-3 Thiopental accumulation in body compartments: single versus multiple doses. Drugs that appear to have a short duration of action may simply be rapidly distributed into tissue, allowing patients to recover from the drug effects. When pentothal is given in a single dose (solid curve), the drug concentration rises rapidly and then falls rapidly as the drug is distributed into the tissues; as a result, the patient will wake in a short time. If an additional dose is given within a short time (dotted curve), the drug effects last for a longer time. If several doses are administered over a short time, the tissues can become saturated and the drug does not have a rapid distribution phase (dashed curve). The drug accumulates in the blood (i.e., concentration is high), elimination takes more time, and the patient will take much longer to wake. The kinetics of fentanyl are similar.

(Courtesy William Banner, Jr.)

Fentanyl also has a relatively short clinical half-life when administered as a single injection. However, if continuous infusions are used over a period of days, the drug will soon have an elimination half-life of 24   hours, meaning that it will take an extended period of time for the drug levels to decrease sufficiently so the patient wakes up. This long ultimate half-life is sometimes referred to as the beta half-life.

Drug Clearance

The clearance of a drug is a measure of how quickly the drug is eliminated. Whereas half-life describes the rate of decline in drug concentration, and volume of distribution indicates where the drug is located in the body, the overall drug clearance is mathematically related to both half-life and volume of distribution. In clinical practice, half-life and clearance are used almost interchangeably, because it is unusual for the volume of distribution of a drug to change for any given drug, but many changes in development and disease states affect the drug half-life and therefore drug elimination. When comparing different drugs, it is appropriate to speak of clearance as a true measure of how a drug is eliminated from the body.

Frequently Used Terms

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