Pharmacokinetics and Pharmacodynamics

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4 Pharmacokinetics and Pharmacodynamics

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.25

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).

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.

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.

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).

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.

Frequently Used Terms

Drug concentration is affected by drug administration rate and dose, drug absorption and drug elimination. To evaluate a drug concentration, providers must be familiar with common terms such as half-life, steady state, and loading dose, and they must be familiar with drug metabolism and excretion patterns.

Steady State

When multiple doses of any medication are given, there is a period of accumulation before the drug reaches what is referred to as steady state. The steady state is a state of equilibrium between the amount of drug administered and the amount of drug 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. When a drug is administered as a continuous infusion, 50% of steady state is achieved during the first half-life of the drug. By the end of the second half-life of the drug, 75% of steady state will be achieved. If there is a need to achieve steady state more rapidly, administer a bolus prior to initiation of the drug infusion (see section, Bolus Plus Infusion Kinetics). Note that the average blood concentration at which steady state ultimately is achieved is the same regardless of whether the drug is given by continuous infusion or intermittent dosing (see Fig. 4-4).

Bolus Plus Infusion Kinetics

Critical care nurses often administer analgesics, sedatives, and vasoactive agents by continuous infusion, and these drugs are titrated to clinical effect. As a result, nurses should be familiar with the effects of continuous infusions and loading doses on drug concentration, as shown in Fig. 4-5.

As noted previously, if a drug is administered by either loading dose or continuous infusion, drug concentration will increase over time and achieve 90% of steady state over approximately four to five half-lives of the drug.

To avoid a delay in the onset of effective therapy by continuous infusion, a bolus dose can be given. The bolus dose is followed by the continuous infusion. Note that the same steady-state concentration will ultimately be achieved whether or not a bolus is given; the bolus shortens the time required to achieve this steady state.

A continuous infusion may be erroneously referred to as a maintenance dose. However, the continuous infusion will not maintain the therapeutic level if the infusion is not correctly calculated in light of elimination and other factors affecting blood concentration.

If the patient is unable to eliminate a drug normally (i.e., the patient has a decrease in clearance), a continuous infusion can contribute to drug accumulation (i.e., an elevated steady-state concentration) and toxicity. This can occur, for example, when a neonate is given the same bolus plus infusion dose as an older child. See section, Additional Factors Affecting Drug Elimination for further information.

Michaelis-Menten or Non-linear Kinetics and Dosing

A few common drugs do not obey the basic rules of steady-state equilibrium and can produce toxicity in unexpected ways. The most common of these is phenytoin and its precursor fosphenytoin. At low concentrations, phenytoin has a predictable relationship of dose to steady-state concentration (Fig. 4-6). However, as the dose increases, enzymes that normally inactivate the drug eventually become saturated. At that point, the steady-state concentration begins to rise out of proportion to the increase in dose, and even small increases in dose are then likely to substantially increase drug concentration and produce toxicity.

Total versus free concentration

The drug concentration typically measured in the clinical laboratory is the total concentration of drug present in blood (actually in the serum). For most drugs it is adequate to monitor the blood/serum concentration when monitoring effects and when toxicity is a concern. Some drugs, however, bind avidly to protein binding sites in the serum. For these drugs, the drug level that most closely correlates with drug benefits and side effects is the “free” concentration of drug—that is, the concentration of drug that is not bound to protein.

Anticonvulsants, particularly phenytoin, have a high degree of protein binding; typically approximately 10% of the drug is free in the serum. It is only this unbound fraction that passes through the blood brain barrier and produces effects in the brain. For these drugs, at a blood concentration of x, the actual active amount of drug available is only 10% of x.

If protein binding sites are diminished (e.g., in hypoalbuminemia) or protein binding sites are occupied by another substance (e.g., BUN), the percent of free or unbound drug available at a given total concentration can be higher than normal. Thus, a patient with a normal amount of protein binding can exhibit therapeutic effects at a given concentration, but that same patient can develop toxic effects at the same total concentration if they develop conditions producing a higher amount of free drug (see Evolve Fig. 4-1 in the Chapter 4 Supplement on the Evolve Website).

When evaluating the concentration of drugs such as phenytoin, providers can request that the laboratory measure only the free, or unbound, concentration if conditions such as a low albumin or high BUN are present. This free portion is interpreted with a different therapeutic scale, usually available from the clinical laboratory.

Additional factors affecting drug elimination

The rate of drug excretion can accelerate or decelerate and still be considered a first-order (nonsaturated) model. Many developmental factors, diseases, and additional drugs can affect enzyme and organ function and influence the rate of drug metabolism

Maturation of Kinetic Processes

Developmental changes associated with hepatic drug metabolism and renal secretion or filtration can accelerate or decelerate drug elimination. Several metabolic processes mature during the first months of life (Fig. 4-7); many drug elimination pathways continue to mature during the first years of life. Failure to recognize these developmental changes in children can lead to drug complications.

By the end of the first year of life, liver metabolism and drug clearance is similar to that reported in older children and adults. The child’s glomerular filtration rate does not reach adult levels (in mL/min per m2 body surface area) until approximately 3 years of age (Table 4-1)1,6.

Table 4-1 Changes in Glomerular Filtration Rate with Age

Age Glomerular Filtration Rate (mL/min per 1.73   m2)
Premature infant 6
Full-term newborn 8-60
1 month 26-90
1 year 63-150
3 years 89-179
6 years 79-170
Adult male 110-152

Consistent with values from Barakat AY, Ichikawa I: Laboratory data. In Ichikawa I, editor: Pediatric textbook of fluids and electrolytes, Baltimore, 1990, Williams and Wilkins; and Tan JM: Nephrology. In Custer JW, Rau RE, editors: The Johns Hopkins Hospital Harriet Lane Handbook, ed 18, Philadelphia, 2009, Mosby-Elsevier.

Practical clinical considerations

Drug Monitoring and Dosing

Although it is important to understand principles of pharmacokinetics to interpret drug concentrations, few clinicians understand the actual mathematical theories and calculations underpinning the kinetics. Fortunately, most drug databases provide relatively simple dosing recommendations and equations that factor in the kinetics. Recommended drug doses often differ based on postconceptual age, weight, and parameters of renal function.

There are two basic reasons to determine drug levels or concentration: to judge safety or efficacy, and to predict future dosing. Drug levels are most often used to monitor for safety and efficacy and are rarely used to attempt to calculate future dosing.

When a sample is obtained to evaluate drug concentration, it is critical to know the timing of the sampling in regard to drug administration. For drugs that require a timed infusion, failure to accurately time both the drug administration and the blood sampling can yield a falsely high or low drug concentration that can cause erroneous decisions about future dosing. The following general approaches to drug dosing and monitoring form a basis for drug use.

Wait Until Steady State

Identify the time to steady state for a drug. In general, 90% of the steady-state concentration will be achieved in four to five half-lives for a drug. The drug concentration after the third dose will only approximate steady state if the drug (e.g., aminoglycosides or vancomycin) has a relatively short half-life. Drugs with long half-lives will require a longer time to achieve steady state unless a loading dose is provided.

It may be appropriate to evaluate a drug concentration before steady state, to provide additional safety in situations where drug elimination is likely to be compromised by immaturity of the drug elimination system, disease, or organ failure. The best example is a small newborn or infant with renal insufficiency. In this patient, the drug kinetics might be markedly altered, so evaluation of the drug concentration after a small number of doses could provide useful information.

It may also be reasonable to check a drug concentration after a loading dose if a desired drug effect (pharmacodynamic) has not been achieved. For example, if a loading dose of phenytoin does not stop seizure activity, the phenytoin drug level can be checked to predict the benefit of administering an additional loading dose, and to determine the size of such a dose. For phenytoin, a loading dose of 20   mg/kg usually creates a blood concentration of 15 to 20   mcg/mL. A drug level of 12   mcg/mL the day after a loading dose might prompt administration of an additional 10   mg/kg loading dose to raise the concentration to 20   mcg/mL. Note that the drug levels from samples drawn before achieving the predicted steady state are not useful to predict maintenance dosing.

Drug information in databases

Several well-researched databases are available to guide pediatric drug therapy. These databases contain core information that will be useful to guide therapy.

Pharmacokinetic Parameters

The drug’s volume of distribution, protein binding, clearance, and drug half-life may be listed. A drug with a volume of distribution less than 1   L/kg is chiefly distributed in the blood, with only a small amount of tissue distribution. Larger volumes of distribution (>1   L/kg) reflect greater tissue distribution. The greater the tissue distribution, the more likely that administration of a loading dose will be needed, if it can be tolerated. If a loading dose is recommended, it should be listed with the dosing information.

Protein binding (listed as a percent of total) and its clinical importance may be noted in this section. Highly bound drugs can be displaced from proteins by other drugs or in some clinical conditions (e.g., a high BUN). Providers should consider the degree of protein binding when evaluating drug levels; measurement of the free (unbound) drug concentration may be needed.

The drug clearance reflects changes that occur with disease and maturation of organ function. Such data should also be included with dosing information. If a drug’s clearance is altered by disease states or organ function, it may be necessary to alter initial doses to avoid toxicity.

As noted previously, the drug half-life is an extremely useful piece of information. The nurse can use the half-life to predict time to steady state and to know when to anticipate drug effects or changes in effects. Estimates of time of achievement of steady state (typically four to five half-lives of the drug, unless a bolus is administered), will help determine when to obtain blood levels and when to expect a response to therapy.

The drug half-life can be used to help the nurse anticipate clinical changes when drugs are initiated or discontinued. Intravenous milrinone has a half-life of approximately 3   hours in infants, whereas dopamine has a half-life of approximately 2   minutes. If milrinone is discontinued, the drug concentration will decrease by half every 3   hours in the infant (and more rapidly in children and adults), so the benefits of the milrinone will likely decrease over the same time period. By comparison, if a dopamine infusion is discontinued, the drug concentration will halve in approximately 2   minutes, so clinical changes can be observed in that time.

Some databases will list a half-life for short-term administration and a half-life for long-term administration; these may also be termed the distributional effect (or t1/2-alpha) and terminal elimination (or t1/2-beta), respectively. The terminal elimination half-life will ultimately determine the time to steady state and may be responsible for prolonged effects observed in children after long-term use of sedatives.

Pharmacodynamics

Pharmacodynamics is the description of the effects of the drug on the body. Mathematically there is a sigmoidal (S-shaped) relationship between the receptor activation causing a drug response (i.e., clinical effects) and the logarithm of its blood concentration. This relationship is relatively flat at low concentrations, until enough of the drug is present to produce effects. The relationship is also flat at high concentrations, once receptors are saturated and maximal effects are obtained. At moderate doses (i.e., the center part of this S), there is a nearly direct relationship between drug concentration and drug effects. In other words, increasing the dose increases the effects (see Pharmacodynamics in the Chapter 4 Supplement on the Evolve Website for more information and Chapter 6 for additional information about titration of vasoactive infusions).

Critical care providers monitor pharmacodynamics in both concrete and subtle ways. Many of the drugs used in critical care have fairly solid endpoints that are used to titrate a dose (e.g., a target systolic blood pressure when titrating vasopressors such as norepinephrine). However, other drugs can be used to produce more qualitative clinical effects. For example, during milrinone therapy, nurses cannot readily monitor the child’s cardiac output at the bedside, but they monitor quality of systemic perfusion by evaluating a variety of subjective factors including signs of end-organ function (e.g., urine output).

One of the most complex drugs that requires pharmacodynamic assessment is dopamine. Dopamine interacts with three different receptors: the dopamine receptor, the beta-1 receptor, and the alpha receptor. It has a different range of affinities for binding to these three receptors. For each receptor there is a typical S-shaped relationship between the logarithm of dopamine concentration and receptor binding that produces drug effects (Fig. 4-8). As dopamine blood concentration increases, one receptor nears saturation; at the same time, dopamine begins to bind with another receptor, producing additional clinical effects. The net effect on a variable such as systemic vascular resistance is not a typical S because stimulation of different receptors will produce different effects. The key to dopamine titration is understanding that dopamine’s pharmacodynamic effect is modulated by three receptor systems (see Chapter 6).