Abstract
The recently introduced open-target-controlled infusion (TCI) systems can be programmed with any pharmacokinetic model, and allow either plasma- or effect-site targeting. With effect-site targeting the goal is to achieve a user-defined target effect-site concentration as rapidly as possible, by manipulating the plasma concentration around the target. Currently systems are pre-programmed with the Marsh and Schnider pharmacokinetic models for propofol. The former is an adapted version of the Gepts model, in which the rate constants are fixed, whereas compartment volumes and clearances are weight proportional. The Schnider model was developed during combined pharmacokinetic–pharmacodynamic modelling studies. It has fixed values for V1, V3, k13, and k31, adjusts V2, k12, and k21 for age, and adjusts k10 according to total weight, lean body mass (LBM), and height. In plasma targeting mode, the small, fixed V1 results in very small initial doses on starting the system or on increasing the target concentration in comparison with the Marsh model. The Schnider model should thus always be used in effect-site targeting mode, in which larger initial doses are administered, albeit still smaller than for the Marsh model. Users of the Schnider model should be aware that in the morbidly obese the LBM equation can generate paradoxical values resulting in excessive increases in maintenance infusion rates. Finally, the two currently available open TCI systems implement different methods of effect-site targeting for the Schnider model, and in a small subset of patients the induction doses generated by the two methods can differ significantly.
When TCI devices first became commercially available in 1997, the concept was new to clinicians and regulatory authorities, many of whom feared the possible complications arising from use of a device that changed infusion rates automatically. A strong emphasis on safety was thus necessary to ensure regulatory approval and the confidence of clinicians. The systems all contained the Diprifusor® (Astra Zeneca, UK) microprocessor, programmed with the Marsh adult pharmacokinetic model for propofol.15 The Diprifusor contained two microprocessors—one 16 bit and the other 8 bit (G.N.C. Kenny, personal communication), the former to calculate and implement the required infusion rates, and the latter to monitor the driving motor to calculate the volume of propofol actually being administered and to perform a simple calculation of the estimated plasma concentration from this. The system was designed to shut down if there was a significant discrepancy between the plasma calculations estimated by the two microprocessors.
The first generation systems only allowed the user to target the plasma concentration. At the time of their release the significance of an effect-site anatomically and temporally separate from the plasma was only just being fully appreciated. Early models only displayed the target and estimated plasma concentrations. Later on a keo value was incorporated allowing an estimate of the effect-site concentration to be made and to be displayed as additional information.
In addition to controlling the user interface, and calculating and implementing the infusion rates required to achieve the target concentration, the Diprifusor microprocessor also controlled a syringe recognition system that only allowed the use of glass pre-filled 50 ml syringes of 1% or 2% propofol (Diprivan 1%™ or Diprivan 2%™, AstraZeneca, UK).
Open TCI systems do not contain the Diprifusor microprocessor and do not have a syringe and drug recognition system. They contain a single processor that the manufacturer can program with any pharmacokinetic model for any drug, and allow the use of a wide variety of syringes of sizes between 10 ml and 50 ml supplied by several different manufacturers. The chief benefit of these systems is that cheaper, generic formulations of propofol can be used for TCI.
At the time of publication, there are two open TCI systems commercially available: the Alaris Asena PK™ (Cardinal Health, Alaris Products, Basingstoke, UK) and the Base Primea™ (Fresenius, France). These systems provide the user with a potentially confusing range of choices. Generally they are supplied with pre-loaded and activated models for remifentanil (Minto model),16,18 sufentanil,9 and two models for propofol. With the Base Primea system the user has a choice of the modified Marsh22 and Schnider19,20 models, whereas with the Asena PK system, the choice is between the Marsh15 and Schnider19,20 adult models and the Kataria paediatric model.11 With all these drugs and models both plasma and effect-site targeting are possible (except with the Marsh model implemented in the Asena PK). To further add to the confusion the two systems use two different methods of implementing effect-site targeting with the Schnider model.
Failure to appreciate the differences between the different propofol models and implementation methods may result in administration of excessive or inadequate doses of propofol with potentially harmful results.
Plasma vs effect-site targeting
Early TCI systems were designed to achieve a user-defined plasma ‘target concentration’. It soon became apparent that there was hysteresis in the relationship between plasma concentration and clinical effect, caused by the temporal delay in equilibration between plasma concentrations and the concentration at the sites of action within the central nervous system, referred to as the ‘effect-site’.
The rate of plasma/effect-site equilibration depends on factors that determine the rate of drug delivery to the effect-site (such as cardiac output and cerebral blood flow) and pharmacological properties that determine the rate of drug transfer across the blood–brain barrier (lipid solubility, degree of ionization, etc). The time course of plasma/effect-site equilibration can be mathematically described by a first-order rate constant typically referred to as the keo. Strictly speaking, this term should be used to describe the rate of removal of drug from the effect-site out of the body, but the effect-site is regarded as having negligible volume, so that there is no need for separate constants describing the rate constants for movement into and out of the effect compartment (the keo defines the proportional change in each unit of time of the concentration gradient between the plasma and effect-site).
With effect-site targeting, the TCI system manipulates the plasma concentration to achieve the effect-site concentration as rapidly as possible. When the effect-site target concentration is increased, the TCI system briefly increases the plasma concentration to an optimal level above the target effect-site concentration before temporarily stopping the infusion to allow the plasma concentration to decrease to the level of the target effect-site concentration. Most systems use mathematical iterations to determine the magnitude of the optimal plasma concentration overshoot—the peak plasma concentration that generates a gradient sufficient to cause the most rapid increase in effect-site concentration but without an overshoot of the effect-site concentration above its target (Fig. 1).
Effect-site targeted TCI. At time zero the target is set at 3 µg ml−1, at 5 min it is increased to 6 µg ml−1, and at 10 min it is reduced to 3 µg ml−1. At each target change the system manipulates the blood concentration to rapidly achieve the target effect-site concentration.
If the target effect-site concentration is reduced the system stops the infusion, allowing the plasma concentrations to fall, thereby generating a concentration gradient out of the effect-site, until the estimated effect-site concentration has fallen to the new target. At this stage the plasma concentration will be less than the effect-site concentration, and so the system has to administer a small bolus to increase the plasma concentration to the target concentration.
With effect-site targeting, the magnitude of the plasma concentration overshoot estimated by the system depends critically on the keo and also on the estimated rate of decline in the plasma concentration. If a slower (smaller) keo is used, a greater overshoot in the peak plasma concentration will be required to produce a larger concentration gradient between the blood and the effect-site and thereby to hasten plasma-effect-site equilibration (Fig. 2).
Effect-site targeted TCI for propofol (Marsh model), showing the effect of the choice of keo. If a slow keo is used, then a large overshoot in plasma concentration will result when the target concentration is increased.
The estimated rate of decline of the plasma concentration also has an influence on the overshoot. A system that estimates a slower decline in plasma concentrations will administer a lesser plasma overshoot than a system estimating a faster decline, to avoid an eventual effect-site concentration overshoot. After a bolus dose, the rate of decline in plasma concentrations mostly depends on the rate of fast re-distribution, but is also influenced by the rate of drug metabolism and of slow re-distribution. Naturally, the net rate of decline caused by re-distribution depends on the concentration gradients between compartments. If a system estimates that the plasma drug concentration will fall rapidly after a bolus at a given time, then a greater overshoot is necessary to optimize the gradient driving drug into the effect-site, and the flux of drug into the effect-site, than if a slow rate of decline were estimated.
Since the accuracy of the estimated plasma concentration itself and the degree of overshoot required depend on the accuracy of several parameters and assumptions, there are multiple potential sources of error. Model errors resulting in excessively high plasma concentrations may well be tolerated by young fit patients, but in frail, elderly subjects, they may result in significant cardiovascular instability.
Methods for estimating keo
Unlike isoflurane, for which the brain concentration can be estimated with reasonable accuracy by magnetic spectroscopy,13,14 there are currently no methods of directly estimating the effect-site concentrations of i.v. anaesthetic agents. The time course of changes in effect-site concentration can however be estimated by recording a measure of clinical effect and then used to generate an estimate of the keo. Ideally, a combined pharmacokinetic–pharmacodynamic (PK/PD) modelling technique should be used, in which concomitant measurements of plasma drug concentrations and clinical effect are performed in a study population during and after administration of a bolus, an infusion, or a combination of the two. The result is a combined model that estimates plasma and effect-site concentrations.
When pharmacodynamic and pharmacokinetic data are not available from the same subject group, then a model-independent parameter called ‘Time to peak effect’ (TTPE) can be used to estimate the keo for a PK model and patient group.17 After any bolus, maximal clinical effects will occur when the effect-site concentration reaches its maximum. Since transfer of drug between blood and effect-site is gradient-driven, when the plasma concentration is greater than the effect-site concentration, net transfer is from plasma to effect-site and vice versa. When depicted graphically, this peak occurs when the effect-site concentration curve crosses the plasma concentration curve, reaching a local maximum. TTPE is defined as the time delay between a bolus injection and the peak clinical effect. It is considered to be independent of the size of the bolus dose.
The effect-site compartment is assumed to have negligible volume. Hence uptake of drug into the effect-site should have negligible influence on the plasma concentration of a drug, so that the calculated plasma concentration profile following an infusion of drug is identical for any value of keo. With this assumption, determination of the keo becomes a simple one-dimensional mathematical minimization problem. This process is illustrated in Figure 3, in which measured or estimated plasma concentrations (following a bolus dose) are plotted over time alongside an observed measure of clinical effect. Different keo values are then used to estimate the effect-site concentration. Smaller keo values result in the estimated peak in effect-site concentrations being smaller and occurring later than if faster (larger) keo is used. In this case, a keo of 0.38 min−1 results in a peak effect-site concentration at 100 s which matches best with the observed maximal clinical effect.
Estimation of keo using TTPE methodology. Estimated plasma concentrations and a measure of anaesthetic effect are plotted over time. The estimated effect-site concentrations resulting from different keo values are then calculated and plotted, to determine which keo value is associated with a peak effect-site concentration that matches the peak clinical effect.
A disadvantage of this approach is that it requires precise observation of TTPE, whereas in real clinical situations noise and other factors make the observation of a single ‘peak effect’ difficult. Rather than relying mainly on one observation an alternative approach is to plot the relationship between the measure of clinical effect and the estimated effect-site concentrations arising from different keo values (Fig. 4). Simple mathematical techniques can then be used to determine the keo value which limits the area within the loop caused by the hysteresis effect. In this hypothetical example, a keo of 0.38 min−1 is selected since it completely collapses the hysteresis curve. This methodology can also be applied to studies involving infusions.
Optimization of keo value. A measure of anaesthetic effect is recorded continuously after a bolus dose, or during and after an infusion. Estimated effect-site concentrations are calculated from the estimated plasma concentration, and different keo values. Mathematical techniques are used to determine the keo value which best collapses the hysteresis curve (i.e. most limits the area between the two limbs of the curve).
Difference between Marsh and Schnider models
These models were derived in different ways, have quite different parameters, and when used to determine the infusion rates of a TCI system during effect-site TCI, can result in significantly different propofol infusion rates. In normal and mildly obese patients, the differences mainly occur within the first 10 min after a target concentration increase (Fig. 5), whereas in more obese patients, the differences can be greater throughout the infusion.
Comparison of the cumulative dose of propofol 1% infused when a TCI system uses the Marsh and Schnider models at a target blood concentration of 4 µg ml−1 in a 40-yr-old male patient who weighs 70 kg and is 170 cm tall.
Marsh model
The Marsh model parameters were published with the results of a study of its predictive performance, and that of an adapted model, in children in 1991.15 Compartmental volumes are proportional to weight, whereas rate constants for slow and fast redistribution are fixed (Table 1). It was pragmatically adapted from the Gepts three-compartmental model,8 which was developed from a study involving three groups of six patients who each received constant rate infusions of propofol at either 3, 6, or 9 mg kg−1 h−1. Although full details were not published it appears that the study included few elderly or obese patients. The Marsh model is identical to the Gepts model in all respects except that the central compartmental volume was increased to 0.228 litre kg−1. There is no published explanation of the rationale for this adjustment.
Adult propofol models
| Marsh15 | Schnider19,20 | |||
|---|---|---|---|---|
| General model | 70 kg | General model (LBM calculated using weight, height, gender) | 70 kg, male height 170 cm | |
| V1 | 0.228 litre kg−1 | 15.9 litre | 4.27 litre | 4.27 litre |
| V2 | 0.463 litre kg−1 | 32.4 litre | 18.9−0.391×(age−53) litre | 24.0 litre |
| V3 | 2.893 litre kg−1 | 202.0 litre | 238 litre | 238 litre |
| k10 (min−1) | 0.119 | 0.119 | 0.443+0.0107×(weight−77)−0.0159×(LBM−59)+0.0062×(height−177) | 0.384 |
| k12 (min−1) | 0.112 | 0.112 | 0.302−0.0056×(age−53) | 0.375 |
| k13 (min−1) | 0.042 | 0.042 | 0.196 | 0.196 |
| k21 (min−1) | 0.055 | 0.055 | [1.29–0.024×(age−53)]/[18.9–0.391×(age−53)] | 0.067 |
| k31 (min−1) | 0.0033 | 0.0033 | 0.0035 | 0.004 |
| keo (min−1) | 0.26 | 0.26 | 0.456 | 0.456 |
| TTPE (min) | 4.5 | 4.5 | 1.69 | 1.69 |
| Marsh15 | Schnider19,20 | |||
|---|---|---|---|---|
| General model | 70 kg | General model (LBM calculated using weight, height, gender) | 70 kg, male height 170 cm | |
| V1 | 0.228 litre kg−1 | 15.9 litre | 4.27 litre | 4.27 litre |
| V2 | 0.463 litre kg−1 | 32.4 litre | 18.9−0.391×(age−53) litre | 24.0 litre |
| V3 | 2.893 litre kg−1 | 202.0 litre | 238 litre | 238 litre |
| k10 (min−1) | 0.119 | 0.119 | 0.443+0.0107×(weight−77)−0.0159×(LBM−59)+0.0062×(height−177) | 0.384 |
| k12 (min−1) | 0.112 | 0.112 | 0.302−0.0056×(age−53) | 0.375 |
| k13 (min−1) | 0.042 | 0.042 | 0.196 | 0.196 |
| k21 (min−1) | 0.055 | 0.055 | [1.29–0.024×(age−53)]/[18.9–0.391×(age−53)] | 0.067 |
| k31 (min−1) | 0.0033 | 0.0033 | 0.0035 | 0.004 |
| keo (min−1) | 0.26 | 0.26 | 0.456 | 0.456 |
| TTPE (min) | 4.5 | 4.5 | 1.69 | 1.69 |
Adult propofol models
| Marsh15 | Schnider19,20 | |||
|---|---|---|---|---|
| General model | 70 kg | General model (LBM calculated using weight, height, gender) | 70 kg, male height 170 cm | |
| V1 | 0.228 litre kg−1 | 15.9 litre | 4.27 litre | 4.27 litre |
| V2 | 0.463 litre kg−1 | 32.4 litre | 18.9−0.391×(age−53) litre | 24.0 litre |
| V3 | 2.893 litre kg−1 | 202.0 litre | 238 litre | 238 litre |
| k10 (min−1) | 0.119 | 0.119 | 0.443+0.0107×(weight−77)−0.0159×(LBM−59)+0.0062×(height−177) | 0.384 |
| k12 (min−1) | 0.112 | 0.112 | 0.302−0.0056×(age−53) | 0.375 |
| k13 (min−1) | 0.042 | 0.042 | 0.196 | 0.196 |
| k21 (min−1) | 0.055 | 0.055 | [1.29–0.024×(age−53)]/[18.9–0.391×(age−53)] | 0.067 |
| k31 (min−1) | 0.0033 | 0.0033 | 0.0035 | 0.004 |
| keo (min−1) | 0.26 | 0.26 | 0.456 | 0.456 |
| TTPE (min) | 4.5 | 4.5 | 1.69 | 1.69 |
| Marsh15 | Schnider19,20 | |||
|---|---|---|---|---|
| General model | 70 kg | General model (LBM calculated using weight, height, gender) | 70 kg, male height 170 cm | |
| V1 | 0.228 litre kg−1 | 15.9 litre | 4.27 litre | 4.27 litre |
| V2 | 0.463 litre kg−1 | 32.4 litre | 18.9−0.391×(age−53) litre | 24.0 litre |
| V3 | 2.893 litre kg−1 | 202.0 litre | 238 litre | 238 litre |
| k10 (min−1) | 0.119 | 0.119 | 0.443+0.0107×(weight−77)−0.0159×(LBM−59)+0.0062×(height−177) | 0.384 |
| k12 (min−1) | 0.112 | 0.112 | 0.302−0.0056×(age−53) | 0.375 |
| k13 (min−1) | 0.042 | 0.042 | 0.196 | 0.196 |
| k21 (min−1) | 0.055 | 0.055 | [1.29–0.024×(age−53)]/[18.9–0.391×(age−53)] | 0.067 |
| k31 (min−1) | 0.0033 | 0.0033 | 0.0035 | 0.004 |
| keo (min−1) | 0.26 | 0.26 | 0.456 | 0.456 |
| TTPE (min) | 4.5 | 4.5 | 1.69 | 1.69 |
Later on, a keo value of 0.26 min−1 came to be used with this model in first generation TCI pumps, to enable effect-site concentration estimations to be made. The data on which this keo value was based were never published in the peer-reviewed literature, although it is quite similar to the value of 0.2 min−1 found by Billard and colleagues.3
Struys and colleagues23 later published evidence that a keo of 1.2 min−1 used in conjunction with the Marsh pharmacokinetic parameters more accurately predicted the time course of clinical effect (as assessed by the Bispectral Index) than the keo of 0.26 min−1. A keo of 1.2 min−1 used with the Marsh model results in an estimated TTPE of approximately 1.6 min, which is consistent with the findings of other groups.19 This combination (sometimes referred to as the ‘modified Marsh’ model) is used in the Base Primea TCI system, and results in more gentle manipulations of the plasma concentration (above and below the target concentration) when effect-site targeting mode is used.
Schnider model
This model was derived during a combined pharmacokinetic and pharmacodynamic study in a single set of 24 volunteers (11 female, 13 male; weight range 44–123 kg; age range 25–81 yr; height range 155–196 cm).19,20 The co-variates are total body weight, age, height, and lean body mass (LBM) (calculated from total weight, gender, and height) (Table 1).
V1 and V3 (and thus k13 and k31) are fixed, whereas the size of V2 (and thus k12 and k21) is influenced only by age, being smaller with advancing age. The implications of this are that after a bolus of a given size, the Schnider model will estimate that the same peak plasma concentration is achieved for all patients, irrespective of their age, height, or weight. After the peak, the initial rate of decrease in plasma concentration will depend on the age of the patient. This is in contrast to the Marsh model, where estimated plasma concentrations after a given bolus are proportional to the patient's weight, whereas the estimated rate of decline of the plasma concentration is the same for all patients.
The elimination rate constant, k10, is the only parameter influenced by body mass. It varies in a complex manner with total body weight, height, and LBM but does not vary with age. Thus, these only influence the rate at which drug metabolism is estimated to occur, and thus the rate at which propofol is infused to replace these losses during the maintenance phase.
The Schnider model incorporates a keo of 0.456 min−1 derived from the combined PK/PD study mentioned earlier, in which a rapidly calculated EEG parameter was used as a measure of clinical effect. This keo, in conjunction with the PK parameters, predicts a TTPE, after a bolus dose, of 1.69 min.
LBM calculation formula used in Schnider model
In the Schnider model, LBM is calculated using the James formula,10 which performs satisfactorily in normal and moderately obese patients, but paradoxically in the severely obese.
The James formula calculates LBM as follows:
Figure 6 illustrates the relationship between total body weight, LBM, and ideal body mass (IBM). Note that for males, the calculated LBM increases with total body mass until it reaches a maximum value slightly greater than the ideal body mass [Males: ideal body weight (kg)=49.9+0.89 x (height in cm−152.4); Females: ideal body weight (kg)=45.4+0.89 x (height in cm−152.4)].1 Thereafter [when the body mass index (BMI) is >42 kg m−2], with increasing total body weight, the calculated LBM decreases paradoxically. A similar paradoxical situation exists with females. The calculated LBM increases with total body weight, and reaches a peak when the BMI is approximately 37 kg m−2. This maximum LBM value is slightly less than the ideal body mass (for the appropriate height) except in very short females in whom it is similar to ideal body mass.
Relationship between body weight, height, and lean body mass (LBM) for males (a) and females (b), as calculated by the James formula. Each line shows the change in LBM for a given height (indicated on the right). Ideal body mass (IBM) for each height is indicated by a cross – read the value off the y-axis – or by text and arrows when the IBM does not fall on the LBM curve.
The effect of the calculated LBM value on the k10, and hence on maintenance infusion rates, is not immediately obvious. As shown in Table 1, increasing total body weight and height tend to increase the k10, whereas increasing LBM will tend to decrease the k10. Thus, total body weight and LBM have opposing effects on the k10, with the LBM value moderating the influence of total body weight on the k10. In severely obese patients, the paradoxically low calculated LBM causes a large increase in calculated k10. As a result, as BMI increases beyond 42 kg m−2 in males, and 37 kg m−2 in females, the infusion rates required (to replace the estimated drug metabolism) increase exponentially. The relationship between total body weight and calculated k10 for patients of different heights is illustrated in Figure 7 (solid lines).
Relationship between total body weight and k10 for males with the Schnider model.
The manufacturers of current open TCI systems have implemented compromise solutions that may improve safety. In the Asena PK system, if the user enters a body weight and height combination that falls on the declining portion of the total body weight (TBW) vs LBM curve, then the maximal LBM figure for that height is used. A similar solution in implemented in the Base Primea system: for a given height, the system will not accept a TBW figure that falls on the declining portion of the curve, and the user is required to enter a total body mass at or below the value generating the maximum LBM. The influence of increasing total body weight on the calculated k10, when these limits in LBM are applied in the severely obese, are illustrated in Figure 7 (dashed lines).
The influence of total body weight on maintenance infusion rates in the morbidly obese are discussed in greater detail in what follows.
Effect-site targeting implementation with the Schnider model
Schnider used semi-linear canonical correlation to calculate the ‘canonical univariate parameter’ from EEG data recorded from the volunteers in his study, and used this to track the time course of the pharmacodynamic effect of propofol.20 The median TTPE of a propofol bolus, determined by this parameter, was 1.69 min. Based on visual inspection of the EEG the TTPE ranged from 1.0 to 2.4 min (median 1.6 min). When a TTPE of 1.6 min was used to calculate the keo for each of their volunteers, the median keo was 0.456 min−1. The authors concluded that a keo of 0.456 min−1 used with the pharmacokinetic parameters determined in the same group of volunteers19 provided the best description of the time course of clinical effect of propofol.
After a standard bolus dose (e.g. 2 mg kg−1), the Marsh model estimates the same peak concentration, and the same rate of decline in plasma concentration, in all subjects, since the compartment volumes and clearances are all weight-proportional. As a result, use of a single keo value generates the same estimated TTPE in all patients. The converse is also true: if a single TTPE is used, then the calculated keo will be the same for all patients.
The situation is different with the Schnider model. A weight-adjusted dose will result in different estimated peak plasma concentrations for patients of different weight, since the volume of V1 is the same for all patients. After the peak is reached, the rate of decline in plasma concentrations will vary from patient-to-patient, depending on the age, gender, height, and weight. If a fixed keo is used to calculate the TTPE in patients who differ in one or more of these parameters, then different TTPE values will result. Likewise, a single TTPE value used to calculate individual keo values will result in different values in different patients. This latter approach is illustrated in Figure 8, which shows the estimated plasma and effect-site propofol concentrations arising after a 2 mg kg−1 propofol bolus in two different male patients, both weighing 70 kg, but one being older and taller than the other. In this example, the keo has been adjusted in each case to cause the effect-site concentration to reach local maxima at 1.6 min. In the case of the elderly patient a faster (larger) keo value is required, and results in a greater estimated peak effect-site concentration.
Predicted blood and effect-site concentration profiles, based on the Schnider model and a TTPE of 1.6 min, for two different patients who both weigh 70 kg and who have each received a 2 mg kg−1 i.v. bolus dose of propofol. In the older patient, plasma propofol concentrations will fall at a slower rate. To produce an estimated TTPE that is the same as in the younger patient, a faster keo value is required.
The Asena PK open TCI system incorporates many of the software routines that are used in the Rugloop II software, developed by T.D.S. and M.M.R.F.S.7 Alternative implementations can be found in Stanpump, developed by Steven L. Shafer, MD at Stanford University.22 Thus, in common with Rugloop and Stanpump, when implementing effect-site targeting for the Schnider model, the Asena PK uses a fixed time to peak approach to calculate a unique keo for each patient. The Base Primea system on the other hand uses a fixed keo (0.456 min−1), and this results in different times to peak effect for different patients.
For non-obese and mildly obese patients, fixed TTPE approach results in a keo that is in the vicinity of 0.456 min−1. For some severely obese patients this approach can generate a significantly faster (larger) keo. As mentioned earlier, the choice of keo will influence the degree of plasma concentration over- and under-shoot when the target concentration is changed, and thus also influences the overall dose.
Practical consequences of differences between the Marsh and Schnider models
Plasma vs effect-site targeting
In general, for non-obese or mildly obese patients, the cumulative dose administered by the two models using the two modes of operation will follow a similar pattern. The highest total dose will be given by the Marsh model in effect-site targeting mode (with a keo of 0.26 min−1), followed by the Marsh model in plasma targeting mode, then the Schnider model in effect-site targeting mode, and finally the lowest dose will be administered by the Schnider model in plasma targeting mode. Figure 5 shows the cumulative dose administered to a 40-yr-old man, who weighs 70 kg and is 170 cm tall, by systems implementing the Marsh and Schnider models in effect-site and plasma targeting mode (target concentration 4 µg ml−1).
The important question is not, of course, which model delivers the largest or smallest dose of drug, but which one produces the most accurate predictions of plasma and effect-site concentration. Plasma concentrations can be measured directly offline using chromatography. While several studies have assessed the predictive performance of the Marsh model,2,5,6,24 other than the initial study from which the Schnider model was derived, there is a paucity of published data of the ability of the latter model to predict plasma propofol concentrations accurately.
There are very few situations in which use of the Schnider model in plasma targeting mode may be recommended. When a TCI system is used in plasma targeting mode, and the target plasma concentration is increased, the size of the initial bolus dose (in mg) required to increase the plasma concentration to the new target is calculated mathematically as follows:
Thus the size of the initial bolus is directly proportional to the value of V1 in the model. In the Marsh model, V1 varies with weight of the patient (15.9 litre for a 70 kg patient), whereas in the Schnider it is fixed at 4.27 litre irrespective of the patient's weight. As a result, when plasma targeting k10 mode is used with the Schnider model, the small fixed V1 results in the same initial bolus being given to all patients, for a given plasma target concentration, regardless of their age, weight or height. This is counter-intuitive and contrary to the clinical experience of anaesthetists, who observe that induction requirements increase with body weight.
In effect-site targeting mode, a system implementing the Schnider model calculates a plasma concentration overshoot. The exact extent of the overshoot will depend on the age, weight, and height of the patient, and will generally be of the order of 300% of the target concentration. In almost all situations where the Schnider model is used, it should be used in effect-site targeting mode.
Few would recommend the use of the Marsh model in effect-site targeting mode with a keo of 0.26 min−1. Although this keo value is slower (smaller) than the keo used with the Schnider model, the degree of overshoot of the estimated plasma concentration is far less than with the Schnider model. This is because the estimated rate of decline of plasma concentrations after a bolus is far slower with the Marsh model than the Schnider model, resulting in a more modest overshoot of ∼150%. Nonetheless, the much larger V1 value in the Marsh model results in much greater initial doses being administered in this mode. For example, for an initial target concentration of 4 µg ml−1, the initial bolus will be 172 mg for a 70 kg patient, whereas for the Schnider model the initial dose will be 77 mg.
The Base Primea system allows effect-site targeting with the Marsh model with a faster keo value of 1.2 min−1, resulting in smaller overshoots (of the order of 50%). In effect-site targeting mode at an initial target of 4 µg ml−1, it will administer an initial dose of 98 mg to a 70 kg man (age 40 yr, height 170 cm).
In fit, healthy, young patients, the use of the modified Marsh model in effect-site targeting mode may be safe and justifiable. With currently available evidence, in almost all other situations, the safest options, and those most commonly chosen by clinicians are either of the Marsh in plasma mode or the Schnider model in effect-site mode. Thus in the following sections, we will compare the initial and subsequent doses administered with these two options.
Size of the initial dose on starting an infusion
Figure 9 illustrates the influence of choice of model and implementation, total body weight and height on the cumulative dose administered during the first 15 min of a TCI, for males and females aged 20, 40, and 80 yr. The target concentration is 5 µg ml−1, and the figure illustrates the doses administered by the Marsh model in plasma targeting mode and the Schnider model in effect-site targeting mode (both fixed keo method and fixed TTPE implementation). For the Schnider implementations, the dotted lines indicate the doses administered if the original LBM equations are used in the morbidly obese without the corrections mentioned earlier.
Influence of total body weight, height, age, and gender on the cumulative propofol dose administered during the first 15 min at a target concentration of 5 µg ml−1. The figures illustrate the doses administered by the Marsh model in plasma targeting mode (green) and the Schnider model in effect-site targeting mode (fixed keo method red, fixed TTPE implementation blue). The solid lines represent the doses implemented by current infusion systems, whereas dashed lines indicate the doses that would be administered to severely obese patients if the systems did not correct for the paradoxical decrease in LBM (see text). (a) Female age 20 yr; (b) Male 20 yr; (c) Female 40 yr; (d) Male 40 yr; (e) Female 80 yr; (f) Male 80 yr.
As can be seen in the figure, the dose administered by the Marsh model is unaffected by age or height. For the Schnider model, increasing age decreases the dose, whereas increasing height increases the dose, except in the morbidly obese in whom shorter patients may sometimes receive larger doses than taller patients of the same weight. In shorter patients, increasing total weight causes the dose administered to increase more steeply.
For the Marsh model (in plasma-targeting mode), the dose administered increases linearly with total body mass, and will be greater than the Schnider model (effect-site-targeting mode) in all patients except those adults with a very low body weight.
For the Schnider model at any given height, the initial dose increases with increasing total body weight. This increase is modest in the normal and mildly obese patient, to whom far less drug would be administered than with the Marsh model. In these patients, the doses resulting from the two different implementations of the Schnider model are very similar. In the severely obese, the increase in total dose is much more rapid, and can be significantly different with the two different implementations of the Schnider model. In particular, in young, tall, obese patients, the fixed TTPE method will result in a greater initial propofol dose (as a result of a slower keo value, and thus a significantly higher peak plasma concentration for the same effect-site target concentration).
‘Maintenance’ infusion rates
After the initial dose, the infusion rate administered by a TCI system depends of course on the estimated rates of redistribution and metabolism. As time passes, and the concentrations in the different compartments equilibrate, eventually the infusion rate gradually decreases to that required to replace drug lost by metabolism.
As mentioned before, for the Marsh model, the fast and slow re-distribution rate constants are proportional to the weight of the patient, whereas for the Schnider model, the fast re-distribution rate constant depends only on age, whereas the slow re-distribution rate constant is independent of age, weight, or height. In the Marsh model, the metabolic rate constant varies with weight only, whereas in the Schnider model it varies according to LBM and total body weight.
Figure 10 illustrates the influence of choice of model, age, gender, weight, and height on the total propofol dose that would be administered to patients during the period between 15 min and 60 min after starting an infusion with a target 5 µg ml−1. The dose administered by the Marsh model is unaffected by age or height, and is a linear function of body weight. For the Schnider model, increasing age decreases the dose, whereas increasing height increases the dose (except in morbidly obese patients where shorter patients of the same weight will receive greater doses). Except in very thin patients, increasing weight increases the dose.
Influence of total body weight, height, age, and gender on the cumulative ‘maintenance dose’ administered from 15 min to 60 min after starting an infusion of propofol at a target concentration of 5 µg ml−1. The figures illustrate the doses administered by the Marsh model in plasma targeting mode (green) and the Schnider model in effect-site targeting mode (fixed keo method red, fixed TTPE method blue). The solid lines represent the doses implemented by current infusion systems, whereas dashed lines indicate the doses that would administered to severely obese patients if the systems did not correct for the paradoxical decrease in LBM (see text). (a) Female age 20 yr; (b) Male 20 yr; (c) Female 40 yr; (d) Male 40 yr; (e) Female 80 yr; (f) Male 80 yr.
Despite these differences, for most patients the choice of model (and effect-site targeting implementation method) does not result in significantly different maintenance infusion rates.
Comment
With current knowledge, there is little conclusive evidence to demonstrate the superiority of any particular model or method of effect-site targeting implementation. In general, it is best for anaesthetists to use the model and methods with which they are most familiar, and to only use a different model or method of effect-site implementation if they understand the differences of the new model or method. Most experts would agree that if the Schnider model is used it should be used in effect-site targeting mode, whereas if the Marsh model is used it should be used in plasma targeting mode or if it is used in effect-site targeting mode, then it should be used with the faster keo for propofol recommended by Struys and colleagues23 (1.2 min−1).
Anaesthetists using the Marsh model in the years after TCI systems were first available quickly learnt by experience that target concentrations appropriate for younger patients were associated with haemodynamic instability in elderly patients. This is because of both pharmacokinetic and pharmacodynamic changes with age. The Marsh model does not make any adjustments for age, and has been shown to under-predict plasma propofol concentrations in the elderly.24 Advancing age is also associated with increased pharmacodynamic sensitivity to the effects of propofol.
A major benefit of the Schnider model is that it adjusts doses and infusion rates according to patient age. This provides a strong argument for using the Schnider model in elderly and unwell patients, in whom smaller bolus doses will be given after target increases, and this may improve haemodynamic stability and safety.
The situation is less clear for morbidly obese patients. The clinical experience of anaesthetists using TCI systems is that if the total body mass of severely obese patients is used with the Marsh model, the resulting large doses at induction often result in adverse haemodynamic consequences. This observation probably results from the fact that the initial volume of distribution (V1) has been shown not to be significantly increased in obesity,21 and that induction dose requirements are more closely related to LBM.4
The problem for clinicians using the Marsh model is that although induction requirements are more closely related to LBM, maintenance requirements do increase significantly with severe obesity, and are more closely related to total body mass. As a result, for the Marsh model there remains controversy over what value the user should input into the TCI system for patient weight. Most anaesthetists do not input the real total body weight with morbidly obese patients, when using the Marsh model. Many input a weight calculated using a formula recommended by Servin:21 ‘Input weight’=IBM+0.4×(TBW–IBM).
Albertin used this formula with the Marsh model during TCI propofol in obese patients, with IBM calculated using the Lemmens formula.12 Predictive accuracy was good for the first 20 min, which is not surprising since the input weight is generally closer to the LBM than total body weight. For samples taken after 40 min, however, measured blood concentrations were significantly lower than predicted concentrations.
The problems for clinicians using the Schnider model in obese patients relate, as indicated earlier, to the problems with the LBM calculation, and the differences between the two methods of effect-site targeting implementation. The equipment manufacturers have implemented a pragmatic solution to the problem of the paradoxical decrease in LBM in the morbidly obese. In the severely obese, maintenance dose requirements do increase with increasing body weight, and the linear increase in k10 in the severe obese resulting from the ‘fixing’ of LBM at the maximum value, seems to be a reasonable and logical solution. Further studies are required to provide the scientific evidence for this.
For most patients, the different methods of Schnider effect-site targeting implemented in the Asena and Base Primea systems result in clinically insignificant differences in dose administered. In a very small subset of the population, the fixed TTPE method will result in significantly higher induction doses. This is because, in these patients, the system will estimate larger values for k10 and k12 than for older, shorter, thinner patients. As a result, it will estimate more rapid falls in plasma concentration after a bolus dose, which with a fixed keo results in an earlier TTPE. If the TTPE is fixed, a slower (smaller) keo is required to delay the TTPE, and this slower keo then results in the requirement for a greater plasma concentration overshoot and thus a much large initial bolus size. It is not clear at present which method of effect-site targeting implementation is safest and most appropriate.
The studies from which the Marsh and Schnider pharmacokinetic models were developed did not include severely obese patients. Until there is good scientific evidence showing reasonable predictive performance of either of these, or a new pharmacokinetic model, target-controlled infusions should be used with caution in severely obese patients, regardless of which model or effect-site implementation method is used.
Funding
A.R.A. receives funding from the Royal College of Anaesthetists/British Oxygen Company Chair of Anaesthesia.
Comments
Dear Sir, We are pleased that our article has generated discussion and thank Dr. Engbers and colleagues for their constructive comments.
We have sought clarification once more from the main manufacturers of ‘open TCI’systems on how their pumps deal with the calculation of the Schnider model elimination rate constant (k10) in morbidly obese patients, and based on this we agree that our figure 7 is not in keeping with the latest software versions implemented in these pumps. For the sake of clarity, we would like to explain the current situation in some detail.
The Base Primea system (Fresenius-Kabi, Brezins, France) allows the user to input the actual patient parameters, but will not operate in TCI mode if the user enters a combination of height and total body weight (TBW) that yields a body mass index (BMI) >35 for females or a BMI >42 for male patients (personal communication, Mr. S. Ruton, Fresenius- Kabi). On the other hand, the Alaris Asena PK system (Carefusion, Basingstoke, UK) requires the user to first input the patient height and gender, and then will not allow the user to input a TBW value that generates a paradoxical LBM value based on the James equation1 (i.e. TBW and height combination that generate a LBM value that falls on the portion of the TBW vs. LBM curve with a negative slope) (personal communication, Mr. M. Richardson, Carefusion).
The nett effect of these software solutions implemented in the currently available open TCI systems is to prevent the system microprocessors from applying paradoxical or absurd parameters. The heavy solid lines in figure 1(a) and l(b) indicate the range of TBW values within which both systems will operate for males and females respectively who are 160 cm or 190 cm tall, and the resulting k10 values with the Schnider model. The light continuous lines indicate the range of values for these heights, over which paradoxically decreasing LBM values would result in excessive k10 values if the Schnider model was implemented as published.2;3
View Image
Whether models are generated by formal mixed-effects modeling procedures or by more pragmatic methods, we agree with Engbers that it is dangerous to extrapolate a model beyond the boundaries of the important characteristics of the population from which it was developed. By observing the range of TBW values within which the systems will operate (indicated by the heavy solid lines in figure 1), the reader will notice that these software solutions also prevent the use of the Schnider model in morbidly obese patients whose characteristics are significantly different from those of the subjects from the studies from which the original Marsh and Schnider models were developed.2-4
We are aware of strategies that clinicians have developed to enable them to use open TCI systems with the Schnider model for TCI in morbidly obese patients. Although we do not recommend these practices, we feel that it is important to mention this issue, to illustrate the inherent and significant dangers. One option for clinicians who wish to use the Schnider model in morbidly obese patients is to input a ‘corrected’ TBW value – typically the user will input the maximum TBW value that the system will allow for a patient of that height (i.e. a falsely low TBW is used). As illustrated by the dotted lines in figures 1(a) and 1(b), the result of this strategy is that all morbidly obese patients of a given height and gender will be assigned the same TBW, LBM and k10 values, and all will thus receive the same amount of propofol for a given target concentration profile. By fixing k10 this strategy fixes the only Schnider model parameter that usually varies with weight (the only other parameters with co-variates are the fast re-distribution rate constants which vary with age). Thus anaesthetists who use the Schnider model in morbidly obese patients, should know that by inputting falsely low TBW values, they have generated a model where the infusion rates no longer scale according to the patient weight. Since propofol is a highly lipid-soluble agent, maintenance doses are likely to be related to total body weight. There is thus a real danger that with this strategy insufficient maintenance doses will be administered to morbidly obese patients. At present clinicians who wish to administer intravenous anaesthesia to morbidly obese patients are ‘between the devil and the deep blue sea’ (we promise not to re-invoke the satanic analogy!). Our personal view is that with current evidence and knowledge, the most prudent approach is to manually administer an induction bolus based on an estimate of lean body mass, and thereafter to administer a manually controlled infusion, carefully titrated to clinical effect.
We have focused on obese patients, but there are several other groups who fall outside of the boundaries of the original research, such as the very young or old, and the critically ill, and in whom the utility of different models is uncertain. In his letter, Engbers has also touched on the issue of which model is best in ‘normal’ patients. The study of Glen and Servin5 which he mentions, is a valuable contribution, but cannot be regarded as conclusive evidence. A goal of the ‘WorldSIVA Open TCI’ initiative (www.opentci.org) is to attempt to answer precisely these sorts of questions, by harnessing the statistical benefits of combining data sets derived from different studies. A recent study resulting from this initiative, involving a very large dataset, has shown results at odds with those of Glen and Servin.6 There is clearly some way to go yet.
Finally, we apologise for the error in figure 6. We were aware of it and have asked the editor to publish an erratum.
A.R. Absalom V. Mani T. de Smet M.M.R.F Struys
References
1. Research on obesity. London: Her Majesty's Stationary Office; 1976. 2. Schnider TW, Minto CF, Gambus PL, Andresen C, Goodale DB, Shafer SL et al. The influence of method of administration and covariates on the pharmacokinetics of propofol in adult volunteers. Anesthesiol 1998; 88(5):1170-1182. 3. Schnider TW, Minto CF, Shafer SL, Gambus PL, Andresen C, Goodale DB et al. The influence of age on propofol pharmacodynamics. Anesthesiol 1999; 90(6):1502-1516. 4. Gepts E, Camu F, Cockshott ID, Douglas EJ. Disposition of propofol administered as constant rate intravenous infusions in humans. Anesthesia and Analgesia 1987; 66(12):1256-1263. 5. Glen JB, Servin F. Evaluation of the predictive performance of four pharmacokinetic models for propofol. Br J Anaesth 2009; 102(5):626-632. 6. Masui K, Upton RN, Doufas AG, Coetzee JF, Kazama T, Mortier EP et al. The Performance of Compartmental and Physiologically Based Recirculatory Pharmacokinetic Models for Propofol: A Comparison Using Bolus, Continuous, and Target-Controlled Infusion Data. Anesth Analg 2009; Oct 27. [Epub ahead of print](PMID: 19861357).
Legend to Figure 1: Influence of total body weight and height on the k10 calculated by the Schnider model (males - figure 1a, females figure 1b) as implemented in the latest versions of commercially available ‘open TCI’ systems. The heavy black and blue lines indicate the range of TBW values within which the systems will operate for patients who heights are 160 and 190 cm respectively. The light black and blue lines indicate the k10 values which result from application of the original Schnider equation for k10 outside of the aforementioned ranges. Finally, the dotted lines indicate the k10 values that result if the systems use the maximum allowed TBW values, and fix the LBM at the maximum value, for patients whose heights are 160 and 190 cm.
Conflict of Interest:
None declared
To the Editor. We congratulate the authors in their effort to address this complex topic and trying to explain the problems, controversies and differences that come with the current commercial Target Controlled infusion devices. There have been surprisingly few published papers about the differences between the pharmacokinetic models since they were introduced in so called open TCI systems several years ago(1). However, there is clearly confusion amongst anaesthetists since the introduction of multiple models for the delivery of propofol by TCI. That such confusion exists is confirmed by a recent paper from Enlund and an editorial in the EJA.(2,3) We feel that this current article only partially resolves this confusion and leaves other important points unaddressed. There are also some errors in the paper: -The x axis in figure 6 is wrongly labeled, it should be Wt and not time. -In the text, the authors suggest that the pumps compensate for the erroneous calculation of the Lean Body Mass for obese people by offering “a pragmatic solution”, fixing the LBM to the maximum while allowing the weight and length to increase (figure 7). We are unable to confirm this statement using the latest software version in commercial available infusion pumps. Dependent on the height of the patient the maximum weight is simply limited to the maximum Lean Body Mass. Therefore the graph in figure 7 should be changed as illustrated in figure 1 below. Note that now in the area above the maximum Lean Body Mass, the influence of the height of the patient is inverted.
-Also figures 9 and 10 are confusing: the legend states that the solid line represents what the pumps are giving and the dotted line what would be administered if the systems ‘did not correct’ for the paradoxical decrease in LBM. In the range of the dotted line however there is no solid line and this corresponds with reality because the systems will not operate with parameters in this range and hence do not correct for any error.
The second remark we want to make is more conceptual. There is no magic to pharmacokinetics: it predicts the right concentration and dose or it does not. In a recent publication(4) it has been shown, by measuring blood concentrations, that the Schnider model over-predicts the concentration and therefore under-predicts the dose in the initial (induction) phase. We agree with authors that it makes the Schnider model unsuitable for blood control TCI. When the model is used in effect site control, as advocated by the authors, the control modality is used for compensating the dose under- prediction of the model. The logical consequence of this is that it makes the information of the effect site concentration at induction useless as it will predict accomplishment of the effect concentration much faster than reality because the predicted high peak blood concentration(overpressure) in fact will not occur. This seems a high price to pay for the automatic adaptation to the age of the patient which is built into the Schnider model. We feel that this is a step backwards in the development of TCI. Lastly, after the excellent publication of one of the authors on the relationship between the keo and the mode of administration (bolus or infusion)(5), we challenge the use of the Time to Peak effect(TPE), which is based on a bolus, to ‘calibrate’ the keo for different pharmacokinetic models when used in Target controlled infusion mode.
In our opinion the irregularity in the details are only signs of the hidden devil. Satan is the extrapolation of nonlinear model-effects outside the boundaries of the original, limited research data and the lack of appropriate validation of models, concepts and control modalities.
1 Barakat AR, Sutcliffe N, Schwab M. Effect site concentration during propofol TCI sedation: a comparison of sedation score with two pharmacokinetic models. Anaesthesia, 2007, 62, pages 661–666. 2 Enlund M. TCI : Target Controlled Infusion, or Totally Confused Infusion? Call for an Optimised Population Based Pharmacokinetic Model for Propofol. Upsala J Med Sci 113 (2): 161–170, 2008
3 Coetzee JF. Total intravenous anaesthesia to obese patients: largely guesswork? Eur J Anaesth. 2009;26:359-61.
4 Glen JB, Servin F. Evaluation of the predictive performance of four pharmacokinetic models for propofol. British Journal of Aaesthesia 102(5): 626-32(2009). 5 Struys MRF, Coppens MJ De Neve N Mortier EP Doufas AG, Van Bocxlaer JFP, Shaver SL.Influence of Administration Rate on Propofol Plasma–Effect Site Equilibration. Anesthesiology 2007; 107:386 –96
Figure 1 View Image The inverse relationship of k10 (and clearance) with LBM causes a non linear increase(solid line). If only LBM would be fixed on its maximum the increase becomes lineairly related to weight only, as suggested in the article(intermittend line).The pumps fix the weight at the maximum LBM, therefore with increasing weight there is no further change in k10 (dotted line).
Conflict of Interest:
None declared