## Abstract

Modern anaesthesia and sedation consists of giving combinations of hypnotic and analgesic drugs to obtain the desired anaesthetic effect. Understanding how these drugs interact to create the anaesthetic state improves the precision of anaesthetic drug dosing and physiological stability of the patient.

### Summary

Modern anaesthesia and sedation consists of giving combinations of hypnotic and analgesic drugs to obtain the desired anaesthetic effect. Understanding how these drugs interact to create the anaesthetic state improves the precision of anaesthetic drug dosing and physiological stability of the patient.

Anaesthetic drugs often interact synergistically, which is important because greater sedative effect occurs at lower doses when combined and concentration-dependent side effects may be reduced if total drug dosage is adjusted appropriately. Propofol and opioids, and volatile anaesthetics and opioids, interact synergistically in suppressing movement and haemodynamic responses to noxious stimulus, but additively for reduction of bispectral index (BIS), and are commonly combined for anaesthesia.

Traditionally, pharmacodynamic interactions have been studied using shifts in dose–response curve or isobolographic analysis. These methods provide useful markers of the magnitude of interaction between various combinations of agents, but do not inform us of the time course of combined drug effect. The adoption of response surface methodology allows continuous prediction of drug effect for any dose combination to be derived in real-time. Interaction models can be incorporated into population models for syringe pump drivers, to guide closed-loop anaesthesia and to display predicted effects of drug combinations. Using measures of depth of hypnotic effect such as the processed EEG or blood pressure to adjust dosage, these population models are surprisingly accurate in individuals and enhance the precision of drug dosage in clinical practice.

### The Importance of Drug Interactions in Anaesthesia

Anaesthetic pharmacology teaching has emphasized the actions of individual drugs. However, modern anaesthesia consists of giving combinations of drugs to achieve the desired balance of hypnosis, analgesia, immobility and reflex suppression in our patients. Common drug combinations include a hypnotic such as propofol with an opioid such as fentanyl or remifentanil, or a volatile anaesthetic such as sevoflurane with an opioid analgesic. The individual actions of these drugs have been well described and are familiar to all anaesthetists, but how they interact to produce the anaesthetic state is less well appreciated: combinations can be synergistic in their hypnotic and analgesic effects, but also can increase the incidence of hypotension and respiratory depression. A good understanding of the pharmacology of commonly used drug combinations allows more precise drug dosing and hopefully safer anaesthesia. Modern anaesthetic displays and anaesthesia delivery systems have incorporated these interaction models into their predictions of drug effect.

In this chapter we outline the methods used to study drug interactions, briefly describe the important interactions that occur between commonly used classes of drugs and illustrate how this methodology is incorporated into some practical applications in modern anaesthesia.

### Pharmacokinetic Interactions

Interactions may affect a drug’s pharmacokinetic (PK) profile, its pharmacodynamic (PD) profile, or both. A PK interaction occurs when a co-administered drug changes the absorption, distribution or elimination of another drug, altering its concentration–time relationship. To describe whether an interaction is due to changes in its PK profile requires the measurement of drug concentrations. Common examples in anaesthesia exist: when midazolam and propofol are combined there is reduced clearance of both drugs, resulting in a 25% increase in propofol concentration and a 27% increase in midazolam concentration in the blood [1, 2]; similarly, alfentanil and sufentanil reduce the clearance of propofol [3].

### Pharmacodynamic Interactions

A PD interaction occurs when one drug alters the concentration–effect relationship of another drug. When the two drugs work at the same site on a receptor, then the interaction between the two drugs may be additive or antagonistic, depending on the affinity of each drug for the receptor site and whether it is an agonist or antagonist (efficacy). However, even when drugs have different modes of action, they may also interact, so that the required dose of each drug to produce the same effect is reduced when the combination is given. For example, the dose of propofol to cause hypnosis is reduced by an opioid such as fentanyl, and similarly propofol reduces the dose of fentanyl required to suppress movement to a noxious stimulus.

Most drug combination research in anaesthesia has been based on observational studies of patients without blood sampling, so that the relative contribution of PK and PD interactions to the overall drug effect of the combination has not necessarily been studied.

### Methods to Study Drug Interactions

#### Shift in the Dose–Response Curve

The simplest way to study an interaction is to determine whether one drug alters the dose– or concentration–response curve of a second drug. To do this, a response curve in either the dose or concentration domain is constructed for the first drug when given alone, and this is then repeated in the presence of a fixed dose of the second drug (Fig. 3.1a). If the dose–response curve for the first drug is altered after adding the second drug, then this suggests that the drugs interact. This method has been used extensively for the study of combinations of volatile anaesthetics with opioids and shows a large reduction in the concentration of volatile anaesthetic required to suppress movement to a noxious stimulus (i.e. MAC, the minimum alveolar concentration) and a small reduction in the concentration of volatile anaesthetic required to produce hypnosis (i.e. MACawake). This interaction is often referred to as MAC-reduction. For instance a concentration of remifentanil of 1.25 ng/mL halves the sevoflurane partial pressure required to suppress movement to a noxious stimulus, and is also sufficient to completely eliminate response to a light stimulus such as prodding or shaking [4]. A limitation of this method is that it only describes the interaction for one dose combination and does not determine whether the interaction is additive or synergistic. It is however a useful method when one of the drugs is not capable of reliably causing the effect under observation in all patients when given alone.

Fig. 3.1 Different methods for studying drug interactions in anaesthesia.

(a)Shift in dose–response curve.

A shift in dose–response curve of drug A in the presence of a constant concentration of drug B indicates an interaction. Shifts to the left (resulting in reduced dose or concentration requirements) indicate synergy. Dose–response curves for both individual drugs (at the outer-faces of the surface) and combinations of dose pairs are displayed on the response-surface (c) as vertical slices (purple lines).

(b)The isobologram.

An isobologram shows concentration (or dose) pairs that cause the same effect (often called iso-effect lines, usually these relate to some clinically useful index such as 50% or 95% of the maximal response for the endpoint in question). Additivity is suggested by a linear relationship (a), while supra-additivity [or synergism, (b)] and infra-additivity (c) are displayed by curves bowing towards or away from the origin. Isobolograms are visible on the response-surface (c) as horizontal slices (blue lines).

(c)Response surface.

A response surface for the effects of a two-drug combination is shown. All possible concentration combinations of the two drugs and their resulting effects are incorporated into the surface. Bowing of the surface towards the reader (as highlighted by the blue line at the 50% effect level) indicates synergy; a flat surface (i.e. when the isobolograms contained within the surface and depicted by the horizontal lines appear straight or flat) indicates additivity (not shown); and bowing away from the reader indicates infra-additivity (not shown). The two other techniques, shift in dose–response curve (purple line) and the isobologram (blue line), can be seen as individual slices of the surface.

#### Isobolograms

To determine the nature of a PD interaction, we must first define additivity (or the ‘expected’ effect) and synergism. The best definition of additivity is that proposed by Loewe [5]. It is based on the concept that a drug cannot interact with itself. If we have a drug that, at a dose of 2 mg, causes 50% of the maximal drug effect (defined as the C_{50}), then it is obvious that two 1 mg doses, or any other combination of doses that equals 2, will also produce the same effect. This can be depicted visually by using an isobologram (Fig. 3.1b). The line connects the dose pairs that together cause the same effect and is called an isoeffect line; if the line is straight then the drugs are additive. Additivity can be defined mathematically as:

where *a* and *b* are the doses of two drugs that when given together cause the target effect, *A* and *B* are the doses of each drug that when given alone cause the same target effect, and *I* is the interaction index. *I* = *1* for an additive relationship. If *I < 1,* there is inward bowing of the isobologram curve (i.e. towards the origin of the graph where the concentration of both drugs is zero) and synergy (or supra-additivity) exists. If *I > 1,* there is outward bowing of the isobologram curve and infra-additivity exists. The term infra-additivity is used rather than antagonism to distinguish between those drugs that simply act via different mechanisms, and consequently have contrasting effects, and those that display true pharmacological antagonism in which the dose requirement of one drug is increased by the presence of a second drug (e.g. fentanyl in the presence of naloxone, an opioid antagonist).

Isobolographic methods are robust when both drugs can achieve the target endpoint when given alone, and confidence intervals can be calculated for the line of additivity to assess the precision with which we know the shape of the curve. Multiple isobolograms can be studied for a drug, each determining a different level of effect, but the method suffers from the disadvantage that only one level of effect can be studied at a time. Isobolograms have been drawn for a variety of hypnotic pairs; for instance midazolam–thiopentone and midazolam–propofol combinations have both been found to be synergistic for hypnosis [6, 7].

#### Response Surface Models

Response surface modelling describes the complete dose–response relationship for a combination of two drugs (Fig. 3.1c). A response surface model incorporates the shift in dose–response curve and isobologram techniques already mentioned. There are several methods based on a standard sigmoid dose–response curve (or Hill equation, Equation 2) used to describe the PD dose–response relationship for an anaesthetic drug, to two or more drugs [8]:

where *E _{0}* is the baseline response,

*Ce*is the concentration in the effect compartment,

*C*is the concentration producing 50% of the maximal effect

_{50}*E*, and

_{MAX}*γ*relates to the steepness of the curve.

*E*and

_{MAX}, C_{50}*γ*are parameters to be estimated. Although shown here for

*Ce*, this equation can also be used for

*Cp*, concentration in the plasma, or for dose.

Three main methods of deriving a response surface have been used in anaesthesia. They are known as the Minto, Greco and hierarchical methods [9–11]. The Minto and Greco models both normalize the concentration of each drug to account for differences in dose required to achieve the same effect:

_{A}= Ce/C

_{50A}

They then introduce an interaction parameter to describe the combined drug effect. The Greco model introduces a first order interaction term (ε):

_{A}+ U

_{B}+ ε ⋅ U

_{A}⋅ U

_{B})

The Minto model expresses the drugs as a ratio and introduces a polynomial function containing an interaction term (β) that can be applied to the EC_{50} (or E_{MAX} or γ).

Both models then introduce these terms into the standard sigmoid curve equation (Equation 2).

Optimal model parameters are then estimated and additive and non-additive interactions compared to determine statistical significance using log likelihood. The Greco model can also be reduced further to account for interactions where one drug is not capable of reaching the end-point in question at any reasonable dose when given alone (e.g. ablation of movement with an opioid) [12, 13]. The Minto model can also be readily adapted to account for three-drug interactions [10].

The Hierarchical model takes a different approach, which does not require the inclusion of an interaction parameter. The effect of drug A on the chosen endpoint, such as ablation of response to a noxious stimulus, is first estimated:

where E_{0} in this case is the pre-drug or baseline effect. The effect of drug B on the remaining effect not accounted for by drug A is then estimated:

All these models readily allow covariates such as age, weight, body mass index and sex to be incorporated, improving their accuracy and allowing us to individualize both the PK and PD components of drug response for a combination of drugs. Models can be readily created for both continuous variables such as bispectral index (BIS) and also bivariate (dichotomous) responses such as lack of movement to verbal command (‘hypnosis’) or to a noxious stimulus (‘anaesthesia’). It is important to note that all these models are empirical as they do not reflect any true underlying physiological process and also assume that interactions are constant over time. There have been few studies of whether PD interactions vary with the age or sex of a patient.

When drugs are additive, the isobolograms (horizontal lines) within the response surface appear flat. When the interaction is synergistic, the surface takes on a sail-like shape, bowing outwards (i.e. towards the reader, refer to Fig. 3.1), and when the interaction is infra-additive, the surface bows inwards. Response surfaces incorporate earlier study designs using shifts in dose–response curves (refer to Fig. 3.1), which can now be seen as vertical slices of the surface, and isobolograms, which are horizontal lines along the response surface. The parameters of the response surface are estimated simultaneously using all available data points, so that information can be interpolated to inform effect levels or concentration ranges where information is sparse, and outlier data points become less influential. With robust trial design and continuous measures of effect, a response surface can be drawn with data from as few as 20 subjects [14]. These models can then be used to predict effects for all portions of the concentration–response curve for both drugs. They have become incorporated into modern anaesthesia displays and intravenous anaesthesia using twin infusion pumps as described in Chapter 6 of this book. Simulation analysis can be used to estimate the optimal concentration pairs for a certain endpoint, such as those that give the most rapid recovery or least respiratory depression during conscious sedation or total intravenous anaesthesia [15, 16]. The technique was used by LaPierre to identify optimal regions of the propofol–remifentanil response surface that provide reliable loss of responsiveness without ventilatory depression by combining response surface models for the individual end-points [15] (Fig. 3.2).