Effect site modelling and its application in TCI

E. Mortier, MD, DSc; M. Struys, MD, PhD

Department of Anaesthesiology, Ghent University Hospital, Ghent, Belgium.

 

Rational dosing of anaesthetic drugs derives from an appreciation of both the pharmacokinetics and pharmacodynamics of the compound in use (1).

Commercially available target-controlled infusion (TCI) devices for propofol incorporate an internal model of propofol pharmacokinetics to rapidly achieve and maintain a constant drug concentration in the plasma (2). For anaesthetic agents, the site of drug-effect is not the plasma (2). However, the concentration of the drug at the site of action is not measurable (3). Nevertheless, the apparent rate of drug flow into and from the site of action can be characterised by the time course of drug effect (4). Knowing this time course, the drug concentration in the biophase can be modelled with the introduction of an additional compartment, the “effect compartment” (5). The effect compartment is defined as being negligibly small (3). It is connected to the central compartment by a first-order process (3). It is characterized by a first-order  input rate constant (k1e) and a first-order output rate constant (keo) (3). Assuming that the effect compartment is negligibly small, k1e is an arbitrarily small fraction of keo (4). Knowing kco, the apparent concentration in the effect compartment can be calculated, since keo will precisely characterize the temporal effects of equilibration between the plasma concentration and the corresponding drug effect (6).

The equilibration delay between the plasma compartment and the effect compartment can be added to the pharmacokinetic model. There are several ways to do this. First of all, one can introduce an effect site model using a keo value from the available literature. However, since the value of keo is influenced by the pharmacokinetic model, it may be inappropriate to mix the keo from one published report with the pharmacokinetics from a different study (7). However, a model-independent descriptor of blood-brain equilibration exists. This is the time to peak efffect. It can be established by giving a bolus and measuring the drug effect by means of an appropriately sensitive parameter (8). A time to peak effect of 1.6 minutes has been reported by the group of Schnider using EEG (8). When using the Marsh pharmacokinetics this corresponds to a value of keo of 1.21 min–1 (9,10). In one-hunderd twenty healthy female patients we tested the performance of three TCI control algorithms (10). In all three groups the plasma concentrations were calculated by means of the Marsh pharmacokinetics (9). In group I, the plasma concentration was controlled (5.4 µg/ml). In groups II and III, the effect site concentration was controlled.

In group II the effect site was computed using a keo of 0.20 min–1 as reported by the group of Billard (11). In group III a keo of 1.21 min–1 corresponding to a time to peak effect of 1.6 minutes was used. Patients lost consciousness more slowly when the TCI device targeted the plasma. In group II, the largest doses of propofol were administered. In group III, the induction dose was simular to that in group I (table 1). Group II was associated with the largest overshoot in plasma propofol concentration. Controlling the concentration in the effect compartment was more accurate in producing the desired time course of propofol drug effect than when the plasma compartment was controlled (table 2). However, mixing the keo from a published report (Billard) with the pharmacokinetics of another report (Marsh) was highly inappropriate.

 

Table 1: Observations at loss of consciousness (mean ±SD). The dose of propofol is the amount of drug given up to the moment of loss of consciousness (10).

 

Group I

Group II

Group III

Time (s)

BIS

CeCALC  (µg/ml)

Propofol dose (ml)

90 (44-601)

67±12

not calculated

11.4±3.9D

68 (45-101)*

78±11*

1.8±0.7

20.4±3.6D

71(43-110)*

77±11*

4.7±0.6

11.7±2.0D

CeCALC = calculated effect-site concentration;  * = p< 0.05 compared to group I

  = p< 0.05 between groups II and III;  D = p< 0.05 between I and II and between II and III


Table 2: Model performance (10)

 

Group I

Group II

Group III

tpeak (s)

teq (s)

terror (s)

BIS at tpeak

CpMAX (µg/ml)

218±86

not calculated

not calculated

39±11D

5.4 ±0o

116±21*

330±36

207±73

27±11D

14.2±0.4o

120±21*

130±17

9±15

41±16D

7.5±0.2o

tpeak  = observed time necessary to reach maximal drug effect; teq = calculated time necessary to reach equilibration between plasma and effect site; terror  = teq - tpeak ; CpMAX = calculated maximum propofol concentration.

* = p< 0.05 compared to group I;  = p< 0.05 between groups II and III

D = p< 0.05 between I and II and between II and III; o = p< 0.05 between all groups

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