DOSE–RESPONSE RELATIONSHIPS

Most drugs exert their effects by binding to receptors¹ 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:

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:

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:

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