Chapter 79 Pharmacokinetics, pharmacodynamics and drug monitoring in critical illness

Richard N. Upton, John A. Myburgh, Raymond G. Morris

Pharmacokinetics (PK) is the study of the absorption, distribution, metabolism and elimination (ADME) of drugs, usually by measurement of drug concentrations in blood or plasma. Pharmacodynamics (PD) is the study of the effects of a drug on the body. The pharmacokinetics of a drug is one determinant of its pharmacodynamics. Pharmacokinetic-pharmacodynamic (PK-PD) analysis seeks to summarise the behaviour of a drug in the body, to understand the sources of variability in this behaviour, and to use this knowledge to design rational, and ideally individualised, dosing regimens. The aim of this chapter is to review some basic PK and PD principles, to introduce the concepts that an intensive care physician may encounter when reading a contemporary PK-PD paper, and to consider the influence of critical illness on the pharmacokinetics and pharmacodynamics of drugs used in intensive care.

DOSE–RESPONSE RELATIONSHIPS

Most drugs exert their effects by binding to receptors ¹ such as an enzyme or membrane ion channel. The binding to the receptor directly or indirectly triggers a chain of biological events leading to the observable effects of the drug. The magnitude of effect is a function of:

• the number of receptors present

• the willingness of a drug to associate with a receptor (receptor affinity)

• the presence of other compounds competing for the binding site on the receptor (agonists/antagonists)

• the concentration of the free (unbound) drug in the vicinity of the receptor

As the number of receptors present is finite, drugs have a maximum achievable effect. Classically, a plot of drug effect versus the logarithm of a wide range of doses will be described by a sigmoid-shaped dose–response curve (Figure 79.1). In practice, the range of doses used in patients is often narrower, and is confined to a smaller section of the dose–response curve.

Figure 79.1 The basic concepts of dose–response curves for the therapeutic and toxic effects of a hypothetical drug. Each curve can be described by the maximum effect (E_max) and the dose at which half of the maximum effect is achieved (ED₅₀). The Hill coefficient (n) controls the steepness of the linear section of the curve. When this is very steep, drugs have a threshold effect and behave in an ‘on or off’ manner.

Note that a drug effect can be plotted in individuals (e.g. mean arterial pressure vs. drug concentration) or for a population of individuals (e.g. % of patients responding to increasing doses of an antihypertensive). The shape of dose–response curves is often defined by three parameters:

• the maximum possible effect (E_max)

• the dose at which 50% of E_max is achieved (the median effective dose, or ED₅₀)

• a parameter controlling the steepness of the linear section of the curve (sometimes called the Hill coefficient, Figure 79.1)

Analogous curves can often be drawn for each of the adverse or toxic effects of a drug. The ratio of the median toxic dose and the median effective dose is termed the therapeutic index. The smaller the therapeutic index of a drug, the greater the potential to do harm rather than good.

Any drug should be administered with a clear understanding of the expected benefits to the patient. While it is more difficult to cause drug toxicity by administering a drug with a high therapeutic index, careless use can result in treatment failure and unnecessary cost. Drugs with a low therapeutic index should be used with considerable caution, with the assistance of titration to measured drug effects, dose nomograms or measurements of drug concentrations (therapeutic monitoring).

TITRATION

Many drugs used in intensive care have a relatively rapid onset of a directly measurable physiological effect (Table 79.1). They can therefore be used by a process of titration of dose versus effect to achieve the desired therapeutic outcome. While titration can be an empirical process, efficient titration strategies are guided by an understanding of the kinetics and dynamics of a drug. Important issues include an understanding of:

• the time required for the drug to achieve peak effect after intravenous bolus administration; multiple doses within this time period may result in ‘overshoot’ of effect

• potential for drug accumulation with repeated bolus doses that may manifest as a stronger, longer action for subsequent doses

• potential range of dose sizes for titration

• optimisation of initiating, increasing or decreasing the rate of an intravenous infusion

• the effects of evolving pathophysiology and tolerance

• potential kinetic and dynamic interactions with coadministered drugs

Table 79.1 PK-PD summary for some commonly used drugs

Developing this understanding requires knowledge of some fundamental pharmacokinetic and pharmacodynamic concepts.

PHARMACOKINETICS

Key pharmacokinetic concepts include volume of distribution (V) and clearance (CL). These can be applied to individual organs or to the whole body.

VOLUME OF DISTRIBUTION IN AN ORGAN

A drug administered to a patient will directly or indirectly enter the blood and be distributed by the blood circulation around the body. Drug enters the organs of the body via the afferent arterial blood supply. Any given molecule can then either diffuse into the organ or leave via the efferent venous blood (Figure 79.2). At steady state (when the arterial concentrations are constant and the net rates of diffusion into and out of the organ are equal), the total amount of drug in the organ (A) will often be a fixed ratio of the afferent arterial concentration (C). This ratio is known as an apparent volume of distribution (V):

Figure 79.2 Processes governing drug entry into a tissue.

(1)

The process of normalising amount (e.g. mg) for concentration (e.g. mg/l) produces a constant with the units of volume (l).

A given organ is characterised by the size of defined ‘physiological’ spaces and its relative proportions of water, lipids and drug-binding sites (Figure 79.2). The important physiological spaces are:

• the intravascular space (about 3% of the total mass of the organ)

• the interstitial space (about one-third of total organ mass). It is separated from the intravascular space by the endothelium, which has pores of sufficient size to allow the passage of most drugs (transcapillary exchange) but not (effectively) plasma proteins

• the intracellular space (about two-thirds of total organ mass). It is separated from the interstitial space by the lipid barriers of the parenchymal cell membranes

A drug may act on receptors in any of these spaces. The physicochemical properties of a drug dictate which physiological spaces are accessible to the drug. A drug can exist in blood in several forms: ionised or unionised (governed by the local pH and the pKa of the drug), and bound or unbound to plasma proteins.

• Only unbound (free) drug can diffuse into the interstitial space via capillary pores or via a paracellular route

• Only unbound, unionised drug can diffuse across cell membranes (transcellular route)

Consequently, drugs that are highly bound or highly ionised in blood generally have smaller distribution volumes in an organ. For example, the distribution volume of propofol in the brain is less than expected based on its high lipophilicity because it is highly bound in plasma. Paradoxically, highly lipophilic drugs in general do not penetrate tissues as extensively as moderately lipophilic compounds, as high lipophilicity is correlated with high binding in plasma.³³

A distribution volume (V) provides information about how much drug is in an organ at steady state, but provides no information about how quickly steady-state concentrations in the organ would be achieved. The fastest possible rate is when diffusion across the endothelium and cell membranes is significantly faster than organ blood flow (Q). In this case, the uptake into the organ is ‘flow-limited’, and the half-life of organ equilibration is given by:

(2)

Note that if the distribution volume of an organ is relatively large or the organ blood flow is low, the time required for an organ to completely equilibrate (at least five times t_t1/2) with the blood can be quite long despite flow-limited kinetics.

When the diffusion rate across the endothelium and cell membranes is significantly less than organ blood flow (Q), the uptake into the organ is ‘membrane-limited’ and less affected by changes in organ blood flow. Morphine shows membrane-limited uptake into the brain.³⁴

THE SPECIAL CASE OF THE BRAIN

Drug penetration into the brain is further restricted compared to that of other organs because of passive and active defence mechanisms collectively known as the blood–brain barrier (BBB). The passive component is the tight junctions of endothelial cells in the brain, which means that passage across the endothelium is solely by the transcellular route, and therefore restricted to lipophilic compounds. The active component is a range of transmembrane transporters. Some of these allow the uptake of endogenous compounds (e.g. amino acids and glucose). Of more pharmacological importance are a range of efflux transporters that actively pump drugs from the brain to the blood.³⁵ The clinical significance of these transporters is currently being defined, but may be particularly important for some drugs. For example, loperamide is a potent opioid, but has no central effects at normal doses because it is excluded from the brain by P-glycoprotein.³⁶ Similarly, the concentration of morphine in the brain is kept low by active transport. When the BBB is damaged, morphine concentrations in the brain are found to be higher.²⁶

CLEARANCE IN AN ORGAN

The liver and the kidney have the special (but not exclusive) role of removing drug from the body. The liver can either transport a drug from the blood into the bile or metabolise a drug into another chemical entity (metabolite). Metabolism can be Phase I (e.g. by oxidation or reduction by enzymes of the cytochrome P-450 (CYP) family, or hydrolysis by esterases) or Phase II (e.g. conjugation with another compound to form a glucuronide or sulphate). The kidney excretes drug by filtration, and potentially active secretion, into the urine. Usually metabolites are less active than their parent compound, are more polar and more readily excreted in bile or urine.

The rate (R) that the liver or kidney can remove drug from the body is usually proportional to the concentration of drug in the blood (C) (i.e. first-order kinetics). This proportionality constant is known as drug clearance (CL):

(3)

The process of normalising rate (e.g. mg/min) for concentration (e.g. mg/l) produces a constant with the units of flow (l/min). For an organ, the clearance can be shown to be equal to the blood flow (Q) through the organ multiplied by the extraction ratio of the drug across the organ (E). If the liver, for example, completely removes all drug passing through it, then E = 1 and the clearance of the drug is hepatic blood flow. If half the drug is removed, E = 0.5 and the clearance is half the hepatic blood flow. Clearance can also be calculated for the whole body, where it represents the total rate of removal of the drug from the body.

HEPATIC DRUG CLEARANCE

There are a number of factors that affect drug metabolism by the liver, but they can be classified by the extraction ratio of the drug across the liver: high (> 0.7), intermediate or low (< 0.3).

• High extraction drugs: There is a relative excess of the enzymes that metabolise a drug (i.e. a high intrinsic clearance). The rate-limiting step is supply of the drug to the liver, so hepatic clearance depends on hepatic blood flow (which is proportional to cardiac output ³⁷) and is unaffected by changes in the amount of active enzyme (and therefore enzyme inhibition or enzyme induction) and changes in free fraction of the drug.

• Low extraction drugs: There is a relative shortage of the enzymes that metabolise the drug (i.e. a low intrinsic clearance) and the rate-limiting step is the activity of the enzymes themselves. Hepatic clearance is independent of hepatic blood flow but is affected by enzyme inhibition or enzyme induction, other competing drugs, and changes in free fraction of the drug (the form accessible to the enzyme).

When the concentration of some drugs is relatively high (e.g. ethyl alcohol, phenytoin, high-dose barbiturates), the metabolic pathway becomes saturated, and the drug is slowly eliminated at a fixed rate (i.e. a zero-order process). A corollary is that small increases in a dose of a drug will cause marked sustained increases in plasma concentration during zero-order kinetics compared with administration during first-order elimination kinetics.

RENAL DRUG CLEARANCE

Three processes govern the net clearance of a drug or metabolite by the kidneys: glomerular filtration, tubular secretion and tubular reabsorption. Filtration in the glomerulus normally allows the passage of the free but not protein-bound drug into the renal tubules. Therefore, drugs that are not subject to tubular secretion or reabsorption have a renal clearance that equals the glomerular filtration rate (normally 0.1 l/min). Drugs that are actively secreted into the tubules (usually charged molecules) can have higher renal clearances up to a theoretical maximum of renal blood flow (1.2 l/min). Drugs that are lipophilic and uncharged are filtered, but rapidly diffuse back across the tubule into the blood stream so that their net renal clearance is zero.

HALF-LIFE IN THE BODY

For a given drug, each organ of the body has characteristic rates of distribution (equilibration half-life) or clearance (extraction). When these complex processes are summed together, however, the sum appears to reduce to changes in blood concentrations that can be described by one, two or three exponential functions, each with an associated half-life term. Half-lives can describe the rate of decline of the blood drug concentration following a dose, or the rate of increase in concentration during an infusion. Half-life is defined as the time taken for the drug concentration in the blood to decrease (or increase) by 50%, and when only one half-life is evident it is related to distribution volume and clearance as follows:

(4)

In this case, clearance and distribution volume describe the apparent behaviour of the drug in the body as a whole. This volume and clearance can be used to calculate dose regimens for this special case.

• Intravenous bolus dose: Shortly after a bolus dose of A mg, the initial blood concentration will be:

(5)

It will decline to 50% of this concentration in one half-life, and to 6% of this concentration in four half-lives.

• Intravenous infusion: For a constant rate infusion of X mg/min, the final steady-state concentration during the infusion will be:

(6)

It will reach 50% of this concentration in one half-life, and 94% of this concentration in four half-lives.

The distribution volume can sometimes provide information about the location of a drug in the body:³⁸ a drug that distributes only in the intravascular space (e.g. one that is tightly bound to plasma proteins, such as indocyanine green) will have a distribution volume of about 0.075 l/kg; a drug that distributes into the extracellular space (e.g. one that is charged and cannot cross cell membrane, such as furosemide) will have a distribution volume of about 0.21 l/kg; and a drug that distributes into the total water space (e.g. one that is uncharged, lipophilic but does not bind to proteins, such as antipyrine) will have a distribution volume of about 0.6 l/kg. Drugs with higher distribution volumes can be assumed to be bound in blood and/or tissues.