TCI : Target controlled infusion, or totally confused infusion? Call for an optimised population based pharmacokinetic model for propofol.

Different pharmacokinetic models for target controlled infusion (TCI) of propofol are available in the recently launched open TCI systems. There is also a compelling choice to work with either plasma- or effect-site targets. Knowledge about the clinical consequences of different alternatives is of importance. We aimed to illustrate the potential differences in the actual drug delivery/output between three present commercially available and clinically used pharmacokinetic models: the original Marsh model, which is also implemented in the Diprifusor®, the “modified Marsh-” and the Schnider models. Simulations were made in the TivaTrainer program (eurosiva.com). Firstly, our standard plasma target regimen was simulated, and secondly an effect-site target of 3.5 μg/mL was chosen. Thirdly, real infusors were used for measuring the time to reach defined predicted effect-site concentrations when aiming at a plasma target of 6 μg/mL. Identical patient characteristics were used in all simulations: male, 170 cm, 70 kg, 40 years of age. Resulting predicted effect-site peak concentrations, and used bolus doses were recorded, as were the resulting plasma over-shoot, and time frames. The plasma target regimen gave predicted effect-site peaks in the different models ranging from 3.6 to 7.2 μg/mL, reached after 2¾ to 4 minutes. To reach the same effect-site target, the three models used bolus doses ranging from 68 to 150 mg given during 22 to 46 seconds. The predicted plasma concentration over-shoots varied from 5.0 to 13.4 μg/mL. There were obvious differences between the models in the time taken to reach defined effect-site concentrations. We observed clinically significant different results between the models. The choice of model will make a difference for the patient. To eliminate confusion – not necessarily to improve precision – we call for an optimised population based pharmacokinetic model for propofol – a consensus model!


Introduction
Target controlled infusion (TCI) of propofol was introduced with the Diprifusor in Europe in 1996 and made propofol based anaesthesia easier to perform (1). The Diprifusor algorithm seems to work well in clinical practice, although the underlying population based pharmacokinetic model relied upon two small populations, 18 and 20 patients, with a quite narrow range of ages and weights (2,3). In 2003 so called open TCI became available, making TCI remifentanil feasible and making TCI propofol possible to perform with generic alternatives. Additionally, alterna-tive pharmacokinetic models for propofol were offered (4,5). A new feature was also that the effect-site, i.e. the CNS, could be chosen as the target, in contrast to plasma target only with the Diprifusor. Effect-site targeting is more logical to use, and it should decrease the time needed for achieving the desired effect when concentration adjustments are made.
The first model by Marsh (Marsh I) for plasma targeting, included in the Diprifusor, was replaced by a "modified Marsh" model (Marsh II) for effect-site targeting in the commercially available open TCI systems (4). Also, a propofol model from Schnider was included in these systems (5). The values of important pharmacokinetic/pharmacodynamic (Pk/Pd) parameters vary a lot between the three models (Table 1). Different alternatives increase the need of pharmacokinetic knowledge.
The lower k eo and thus the higher t ½ k eo in the Diprifusor, compared with the other two models, demand a higher concentration gradient between plasma and effect-site to achieve a certain effect-site target concentration, i.e. the dose must be relatively higher. This is a drawback for the elderly and fragile patients leading to a pronounced over-dosing, especially if Marsh I would be used for effect-site targeting. Ways to come around this problem are to take time and titrate to the optimum target, or to modify the model, or to do both. On the other hand, young fit patients need higher effect site target concentrations, otherwise they receive too little of the drug and will not become unconscious within a reasonable time.
The potential clinical differences between the three models were investigated in this study by performing two types of simulations in the TivaTrainer program (eurosiva.com). Also, the time frames, with which the three models display a predicted effect-site concentration during plasma target mode, were simulated in different infusors.

Methods
The pharmacokinetic parameters listed in Table 1 (read V c and t ½ k eo ) were used in the TivaTrainer simulation program. Two different situations were simulated. We used identical patient variables in all simulations, including a third simulation for evaluating the time to reach certain effect-site concentrations with the three models in real infusors: male 170 cm, 70 kg, 40 years of age.
1. Plasma target, "The way we use the Diprifusor" The starting point was the way we use the plasma target controlled Diprifusor. The procedure may be described as effect-site targeting with the anaesthetist as an inter-face, cf.: Appendix. Identical output was programmed in the TivaTrainer for the three different models, i.e. the same bolus dose and the same infusion flow profile of propofol. The predicted effect-site concentration peak, the time to reach the peak, and the predicted plasma concentration over-shoot were noted.

Effect-site target
Simply, in the second type of simulation an effect-site target concentration of 3.5 μg/mL was set in the three different propofol models. The calculated bolus dose used by the model, the time for delivering it, and the predicted plasma over-shoot were noted.

Time to reach a displayed predicted effect-site target in infusors
A syringe containing propofol (Diprivan 10 mg/mL pre-filled 50 mL syringe, Astra-Zeneca, Södertälje, Sweden) was connected to either a Diprifusor (Fresenius Vial S.A., Brezins, France) for testing the Marsh I model, or a Base Primea (Fresenius Vial S.A., Brezins, France) for testing the Marsh II-, and the Schnider models. The infusors were programmed for a plasma target of 6 μg/mL and started. The time point, at which different predicted effect-site concentrations (0.1, 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 μg/mL) were displayed, was recorded.

Statistics
No statistical evaluation was made. Purely clinical considerations were made when comparing the outcome variables.  The predicted plasma-and effect-site concentration peaks ranged from 6.0 to 17.5 μg/mL and from 3.6 to 7.2 μg/mL, respectively, when the same infusion profile was simulated. The time to reach the predicted effect-site peak concentration ranged from 2¾ to 4 min.
2. Effect-site target, Table 2 The bolus dose given, the extent of plasma over-shoot, and the time to reach a predicted effect-site concentration of 3.5 μg/mL differed more than twofold between the three pharmacokinetic models. The models used bolus doses ranging from 68 to 150 mg infused during 22 to 46 seconds. The predicted plasma over-shoot concentrations varied from 5.0 to 13.4 μg/mL.
3. Time to reach a displayed predicted effect-site target in infusors, Fig. 2 The infusor with the Schnider-and Marsh II models started to indicate an increasing effect-site concentration sooner than the Diprifusor with the Marsh I model. E.g. after 30 seconds of infusion the predicted effect-site concentration displayed by the Diprifusor was less than 0.4 μg/mL, while the Schnider-and the Marsh II models in the Base Primea displayed 1.0 and 1.5 μg/mL, respectively. A predicted effect-site concentration of 1.0 μg/mL was displayed after almost 60 seconds with the Marsh I model. 3.75 1.5 1.5 Figure 1a. A simulation of plasma target directed propofol infusion with the original Marsh model with an initial plasma target of 6 μg/ mL, reduced to 3 μg/mL just before the predicted effectsite concentration reached 3 μg/mL, cf.: Appendix. A predicted effect-site peak concentration of 3.6 μg/mL was reached after 4 min.  Figure 1a. The model predicted the plasma peak concentration to 6.2 μg/mL, which was reached after a bit more than 1 min. A predicted effect-site peak concentration of 5.8 μg/mL was reached after approx.

Discussion
The three population Pk-models for target controlled infusion of propofol differ considerably in critical Pk-parameters (Table 1). These differences had apparent effects in the simulations, to an extent that must be considered of major clinical importance (Fig 1a-c, Table 2, Fig 2). E.g. the maximum predicted effect-site concentrations varied twofold with an identical infusion regimen (Fig 1a-c). Likewise, the initial dose used to reach the same effect-site target (3.5 μg/mL) varied more than twofold (Table 2). Thus, the choice of model in a clinical situation may make a difference for the patient. Of important pharmacological factors only drug plasma or blood concentrations (at intervals) and the time to peak effect (TTPE) can be measured, while information on the actual drug dose is easily accessible. All other factors (= parameters) are calculated based on these values. TTPE for propofol has to be measured by introducing surrogate endpoints, like processed EEG, introducing additional physiological variability. TTPE was not measured for the Marsh I model (3). The value of 4.5 min was estimated in later simulations (4). Obviously, the Marsh I model comprises a much longer TTPE than the other two models (Table 1). Which TTPE is the most accurate one? As observed in the infusor simulation, the Marsh II-or the Schnider models indicated a small, increasing predicted effect-site concentration already after a few seconds of infusion. This is a well-known and essential model simplification. Pk-modelling assumes that the central compartment is well mixed. This leads to the false indication of a concentration gradient between the plasma and the effect-site already after a few seconds of infusion. If considering an armbrain circulation time of 30-40 seconds and an undetermined time for transfer of the drug across the blood-brain-barrier for further transport to the regions of interest, no drug should have had time to reach the effect-site until a minimum of 40 seconds. After 30 seconds the predicted effect-site concentration displayed by the Diprifusor was less than 0.4 μg/mL, while the Schnider-and the Marsh II models in the Base Primea displayed 1.0 and 1.5 μg/mL, respectively (Fig 2). This may be interpreted as an over-estimation of the effect-site concentration and an under-estimation of TTPE in the latter models. In a recent clinical trial, changes in the sedation score and Bispectral index correlated better with effect site concentration predictions by the original Marsh model than with the Schnider model (6). Additionally, when comparing with the k eo and t ½ k eo reported for sevoflurane (with clinical on-and off set similar to propofol), the Marsh I model harmonised better (7,8).
On the other hand, the Marsh II-and Schnider models seem to have a stronger scientific base of Pk/Pd-modelling with the use of EEG measurements and actual measurement of TTPE (4,5). However, the presumption that different EEG responses reflect clinically purposeful measures is not unchallenged (9). The median effective concentration (EC 50 ) of propofol for loss of consciousness (LOC) differs significantly from EC 50 for immobility, indicating that different effects are mediated at different levels of the central nervous system (10). This supports the discussed clinical finding. Anatomically, EEG reflects the electrical activity in superficial cortical structures, and from a functional point of view EEG reflects LOC rather than immobility. It may be that the defined TTPE of 1.6 min in the later models is the time to initial effect rather than the time to true peak effect?
Potential benefits with the Marsh II-and Schnider models are reduced hemodynamic-and respiratory effects, especially in the elderly and fragile patients (5). Age is included as a pharmacokinetic co-factor in the Schnider model, which may have a value, although the impact of age on pharmacodynamics is much stronger (5). This unavoidable fact will be best handled by drug titration, starting with a low target and by increasing the infusion time, irrespective of the model used. If we accept to use the Marsh II-and Schnider models, we have to learn about and agree to higher initial targets, especially to young and fit patients. The potential hemodynamic benefit may then be lost or decreased.
It should be noted that the TivaTrainer is in some details programmed with values that differ from those presented in Table 1. The TivaTrainer uses a fixed-k eo method to calculate a patient-individualised TTPE for each patient for the Schnider model. In contrast, a modern infusor such as Alaris Asena PK uses a fixed-TTPE method to calculate a patient-individualised k eo for each patient for the same model (personal communication, Dr Anthony Absalom, Camebridge, UK). In the present simulations, we used the t ½ k eo values presented in table without bracket, and the fixed TTPE values (from the simulation program) are shown within parentheses. Thus, t ½ k eo was the "leading" parameter. The reason for using the lower TTPE, suggested in the simulation program, was that the probable "true" TTPE would be lower than 4.5 min. As suggested, the TTPE should be used when kinetic and dynamic models have been calculated from different study populations (11,12). Therefore, we also did the other way around (not in Table) and used the listed TTPE of 4.5 min in the Marsh I model, accepting another value of t ½ k eo suggested by the simulation program. Then, the time to reach peak effect-site concentration in Marsh I was prolonged in the plasma-and the effect-site target simulations with 13 and 25%, respectively. Otherwise, only minor deviations in results were found (1.7-9.5%).
After the introduction of open TCI, different models and their different attached numbers for targets may confuse enthusiasts of total intravenous anaesthesia, not to mention new users. This is more than an academic question; it also includes aspects of patient safety. Therefore, we call for an optimised population based pharmacokinetic model for propofol -a consensus model!