The first requirement for a pharmacokinetic approach is to know what the suitable concentrations are for each drug. The target concentrations for most modern hypnotics and narcotics sufficient to suppress the response to a given surgical stimulus have been studied. This slite, for example, shows the target plasma concentrations for respectively 50% and 95 % chance of loss of consciousness for several hypnotics. It may be noticed that the differences between ED50 and ED95 are much larger than what we are used to when using volatile agents: titration to effect in the idividual patient will thus remain necessary.
This slite summarizes data on the Effective Concentrations 50% for different endpoints for modern narcotics, as well as the recommended range of infusion rates necessary to achieve these concentrations. The end-points reported are surgical incision, 50% decrease in EEG activity, 50% of decrease in minimal alveolar concentration of isoflurane, and analgesia in the post anesthesia care unit.
Once we know the adequate concentration to suppress the response to a given stress stimulus, we need to establish the dose of the drug needed to obtain that concentration. The relationship between dose administered and concentration obtained in the plasma unfortunately is not a simple one, since drugs are extensively redistributed between so called distribution volumes, depending of the relative blood flow to the tissues and the physicochemical characteristics of the drug, mainly its lipophylicity, its degree of ionisation at a certain pH, and its binding to proteins. Depending on the concentration of drug already present in each of the compartments, a certain amount administered will have a different effect on the concentration in the plasma. For all drugs, pharmacokinetic models have been developed that enable us to calculate the change of the concentration of drug in all hypothetical body compartments over time. For most drugs used in anaesthesia the pharmacokinetic behaviour can be described by a three comparment open model, with a redistribution phase followed by the elimination phase. By filling in numerics for the volumes of distribution and the rate constants for exchange of drug betweens compartments and for elimination, we can construct a formula which allows us to calculate the concentrations obtained over time.
This slite depicts some pharmacokinetic data sets for propofol. Several authors took different populations of study subjects, gave them a known dose of propofol, measured the plasmaconcentrations achieved over time and tried to fit a model to the result, calculating the central volume of distribution and the compartment exchange rate constants necessary to predict the plasmaconcentration changes observed. NONMEM
So far we are able to calculate the plasma concentration. It is obvious though in clinical practice that there is a time lag between the concentration change of a drug in the plasma and its effect in the central nervous system. One of the first investigators to clearly demonstrate this by simultaneously measuring the change in plasmaconcentration and the EEG effect of opioids were Scott and Stanski in 1985. They nicely pictured the hysteresis loop between plasma concentration and effect.
The effect is proportional to the concentration reached at the effect site. If we can measure the effect, we can measure the time delay to reach the peak concentration in the central nervous system. For drugs with similar effects, for example fentanyl, alfentanil and sufentanil, this delay can differ substantially, depending on the time to reach and to leave the effect site.
If we want to take into account the time lag between plasma concentration change and effect, we can adapt our pharmacokinetic model by adding an effect-site compartment with a negligible distribution volume, but with a rate constant Keo, that is an indicator for the speed of redistribution between the blood and the effect-site compartment. The keo can be calculated for each drug for which we have a measure of the effect.
What is the practical utility of pharmacokinetic models ? For each drug for which the pharmacokinetic data set has been determined, we can make a simulation of the concentrations obtained with a given dosage of the drug. We are also able to use drugs more rationally. First, for drugs with similar effects we are able to choose the drug which best serves our clinical purpose. Second, we can calculate optimal dosing schemes to obtain a blood or effect site concentration in the therapeutic window as fast as possible and with minimal overshooting of the desired concentration. The logical step in the era of microcomputers is to couple the pharmacokinetic information with a computer-controlled administration device: the target controlled infusion systems, which can be either blood concentration or effect-site concentration controlled.
This is an example of a simulation with the TIVA trainer developed by Frank Engbers. You notice the difference in the calculated first compartment (in red) and effect-site concentration (green) when administering respectively 0.25 µg/kg sufentanil or 0.5 µg/kg remifentanil. In brown and orange are depicted the caculated second and third compartment concentrations respectively.
This a the same comparison for alfentanil and remifentanil.
In this simulation we can see that there is almost no accumulation with repetitive bolus doses of remifentanil.
In contrast with what happens if you administer consecutive bolus doses of fentanyl.
How to handle continuous infusions? If we use an infusion with a constant speed the final steady state concentration is only approached after 4 to 5 half-lifes, a very impractical solution to obtain an adequate concentration during anaesthesia, because even with drugs with a relatively short half-life it would take hours to reach the desired concentration. A solution to the problem is to give a bolus dose followed by a progressively decreasing infusion rate to create a pseudo-plateau. Some 25 years ago the Bolus Elimination Transfer or BET was developed as a better strategy to create a concentration plateau that more ideally approached the target concentration. With computer controlled infusion systems the computer can calculate the infusion rate necessary to obtain and maintain a desired concentration. Several times a minute it calculates how much drug has to be added in the next time block to obtain a given concentration and to maintain this concentration at the same level by replacing the drug that is lost from the targeted compartment by redistribution and elimination.
These is a simulation of what happens when a conctant rate infusion of alfentanil is adminstered: after 60 minutes the concentration is still far below the final steady state concentration. A drug with an extremely short elimination half-life like remifentanil can be adequately used as a constant rate infusion since the desired concentration is approached after a relatively short time.
Until now we have focused on the question how to obtain and maintain a desired concentration. What about the end of anaesthesia? The time needed for a drug to decrease its concentration after an infusion depends on the infusion time. When the infusion time was short, drug can disappear from the central compartment and the effect site by redistribution to the peripheral compartments and by definitive elimination. Once the redisribution phase is finished, the peripheral compartments are saturated. As a result the effect site concentration can only decrease by definitive elimination and the time to awakening from anaesthesia increases. Pharmacokinetic simulation has lead to the development of the concept context-sensitive half-life, which graphically depicts the time needed for the plasma concentration to decrease by 50% after stopping an infusion in relation to the duration of the infusion. This concept helps in comparing the suitability of drugs for use as a continuous infusion to maintain anaesthesia. In the example we notice that fentanyl is hardly suited for this purpose since after 2 hours of infusion it will take another 2 hours for the concentration to decrease by 50%. Elimination of alfentanil becomes independent of the infusion duration after 2 hours. There appears to be an advantage for using sufentanil for infusions with a duration up to 6 hours. Remifentanil is the ideal opioid for use as a continuous infusion.
This slite depicts a comparison of the context sensitive half-times of the intravenous hypnotics. Notice the favourable position of propofol.
What is a target controlled infusion? Simply put, TCI is using pharmacokinetics in reverse. The anaesthesiologist chooses the desired concentration. The computer calculates the administration rate using a pharmacokinetic model for the drug. For each time unit the computer calculates the amount of drug needed to keep the desired concentration constant, this is the amount of drug leaving the target compartment as a result of elimination and redistribution. At each moment the computer takes into account what the concentration in each compartment is at that given moment. The calculations are made several times each minute. This information drives the infusion pump.
Schematically: the anaesthesiologists chooses the target concentration; the computer does the calculation of the amount of drug necessary and delivers this information to the infusion pump; the infusion pump administers the calculated amount to the patient; for safety reasons a pharmacokinetic simulation is made, calculating the concentration that should be reached with the amount of drug administered by the pump: this number should be approximately the same as the desired concentration. Since the pharmacokinetic model uses the mean numbers for a population, the actual concentration in the individual patient may differ; moreover the pharmacodynamic response to a given concentration may differ individually. On top of that the desired intensity of effect is not constant during the course of an operation. Therefore the anaesthesiologist must judge the response of the patient, either clinically or with the aid of some technical device, in order to adapt the desired concentration according to the needs of the patient.
These are 2 examples of plasma concentration target controlled infusions with sufentanil and remifentanil respectively. The thin red line indicates the target concentrations choosen and the changes made over time. The fat red line represents the actual calculated plasma concentration and the green line the corresponding calculated effect-site concentration. The black area represents the infusion rate for each time block. It can be noticed that the infusion rate changes exponentially due to the redistribution of drug. When the target concentration is decreased, the infusion rate drops to zero to restart as soon as necessary to keep the newly choosen concentration constant. At the end of the infusion it is possible to calculate the time necessary for the concentration to fall below the treshold for spontaneous breathing (or waking up in the case of an hypnotic).
The concentration can also be targeted to the effect-site in stead of the plasma. The desired effect is obtained faster but the blood concentrations will be higher at the start since a higher blood concentration results in a higher concentration difference between plasma and brain with as a result faster diffusion. The pharmacokinetic model choosen and the corresponding keo will be of the utmost importance: a fast keo results in a small overshoot in blood concentration, a slow keo in a large overshoot.
This slite depicts the difference in rate controlled, blood compartment concentration controlled, and effect site controlled infusions. In red the blood concentration, in green the effect site concentration, in blue the infusion rate. Notice how slowly the blood and effect site concentrations are reached with a classical infusion. With blood concentration controlled systems the effect site concentration is reached relatively slowly. In the effect site controlled system the effect-site concentration is reached very fast but at the expence of temporary high blood concentrations.
Another example of propofol effect-site TCI with infusion rate, plasma concentration and effect-site concentration.
This is a simulation of effect-site TCI with a large overshoot in plasma concentration when using a slow keo, and a smaller overshoot when using a fast keo in the Marsh model for propofol.
Drugs characterized by fast diffusion to the central nervous system are best suited for effect-site concentration controlled infusions However, the largest advantage in time to reach the desired effect is to be expected for drugs with slow diffusion
Of course TCI has limitations. The first question that arises is: how accurate is TCI ? Do the target concentrations correpond to reality ? The pharmacokinetic parameter set is determined in a limited number of patients. In how far does the PK parameter set correspond to reality ? The second question is: Is the pharmacokinetic model used applicable to the individual patient: in other words does the patient correspond to the population sample used to determine the PK data
First I want to make a remark. Is it absolutely necessary that the prediction is 100 % accurate to make TCI a useful tool ? Titration to effect remains necessary: corrections in administration rate will be made if needed. In every case swings in concentration will be less important that with manual systems. Modifications in the desired concentration will at least result in proportional changes in real concentration and in effect
This slite is a demonstration of these statements. The 2 upper drawings represent identical manual infusion shemes of remifentanil. Notice the very different concentrations obtained in 2 patients with the same weight, but different age and height. The lower drawing represents TCI with remifentanil in the second of the 2 patients. Notice the much smoother concentration profile.
The validity of the pharmacokinetic models used in TCI has been studied extensively using the following tools: median prediction error (MDPE): median of the procentual difference, positive or negative, thus the bias of the system median absolute prediction error (MDAPE): median of the procentual difference between the measured and the predicted concentration in absolute value (this value should be smaller than 30%) divergence : the slope of the linear regression analysis of the evolution in time of the MDAPE wobble : median of the variability comparing measured and calculated values in individual patients.
This study by Vuyck, for example, compares the calculated and measured propofol concentrations using three different parameter sets. On the right the evolution of the performance error over time in individual patients is depicted. It can be noticed that the PK values determined by Shafer result in the least bias.
This table summarizes the results of performance studies for 2 propofol models and three opioids. We can see that the accuracy lies within in an acceptable 30% limit for al drugs.
The performance in the individual patient may differ for several reasons. Age, weight and body composition, disease and hydratation status all influence the individual pharmacokinetics. To solve this problem we can adapt the target value. Alternatively we can use kinetic libraries: we feed the important cofactors to the computer and the computer determines the most suitable parameter set. Such a system already exists for paediatric TCI for propofol that uses age and weight.
Two examples of kinetics adapted to age and weight in children.
What if we use several interacting drugs ?
Of course the use of interactive drugs has profound effects on the targets choosen for both drugs. Think about the interaction of opioids and volatile anaesthetics, for example the effect of the concentration of remifentanil on the isoflurane concentration needed to maintain anaesthesia.
The most complete way of representing drug interactions is by way of response surface modelling that gives a representation of the combined drug effect of any combination of 2 drug concentrations. The concentration of drug A is represented on one axis, the concentration of drug B on a second axis, and the degree of effect on the third axis. The three-dimentional graph gives the effect of any combination of drug concentrations.
This is an example of response surface modelling in practice from a study by Mertens. It represents the probability of not responding to laryngoscopy with any combination of propofol and remifentanil. It can be seen that with a high concentration of remifentanil, the concentration of propofol guaranteeing unresponsiveness may be as low than 2 µg/ml.
The same study looked at the probability of unconsciousness.
This study looked a awaking times following a combination of propofol and alfentanil used at different concentrations to maintain a 300 minutes anaesthetic. From the graph the combination of concentrations resulting in the shortest wake-up time can be determined.
What are to be expected future developments in TCI ? We probably will see more multidrug infusors on the market, combining hypnotics and narcotics. It will become possible to make use of kinetic libraries to obtain a greater accuracy of the predicted concentration in the individual patient. Computer programms may make target suggestions for dosing according to interaction data of surface modelling studies. Studies on closed-loop systems with automated effect evaluation for depth of anaesthesia and paincontrol are ungoing and probably will be introduced as a titration tool in the future.
Target Controlled Infusion: totally intravenous anesthesia made simple J. VAN HEMELRIJCK K. U. Leuven
duration of surgery stress theoretic concentration needed for adequate anesthesia apprehension intubation prep. incision awakening
Anesthesia = titration to needs <ul><li>Pharmacodynamic approach : titrating drugs to effect </li></ul><ul><ul><li>Clinical signs, hemodynamics </li></ul></ul><ul><ul><li>EEG parameters or other techniques to measure “depth” of anesthesia </li></ul></ul><ul><li>Pharmaceutical approach : choosing “forgiving drug” </li></ul><ul><li>Pharmacokinetic approach : knowledge of concentration-effect relationship </li></ul><ul><ul><li>MAC </li></ul></ul><ul><ul><li>Therapeutic window concentrations </li></ul></ul><ul><ul><li>Dosage schemes that pretend to achieve these concentrations </li></ul></ul><ul><ul><li>Target Controlled Infusions </li></ul></ul>
Three-compartiment open model time concentration V 1 V 2 V 3 k 12 k 21 k 13 k 31 DOSE k 10 C = . e - t + A . e - t + B . e - t
Pharmacokinetic data-sets for propofol NONMEM: nonlinear mixed effect modeling
Hysteresis between changes in plasmaconcentration and effect Scott JC et al. Anesthesiology 1985;62:234-241
Shafer SL, Varvel JR. Anesthesiology 1991;74:53-63
Effect site effect keo V 1 V 2 V 3 k 12 k 21 k 13 k 31 DOSIS k 10
Pharmacokinetics in practice <ul><li>Simulation of concentrations that are obtained with dosage scheme used </li></ul><ul><li>Rational use of drugs: </li></ul><ul><ul><li>Which drug best serves the clinical purpose </li></ul></ul><ul><ul><li>Calculating optimal dosage and mode of administration </li></ul></ul><ul><li>Pharmacokinetically controlled infusors: TCI </li></ul><ul><ul><li>Blood concentration controlled </li></ul></ul><ul><ul><li>Effect-site concentration controlled </li></ul></ul>
Target Controlled Infusion <ul><li>PK- model used in reverse </li></ul><ul><li>Choosing a desired concentration and the computer calculates the administration rate using the PK-model </li></ul><ul><li>For each time unit the computer calculates the amount of drug needed to keep the desired concentration in the target compartment constant (= the amount of drug leaving the target compartment as a result of elimination and redistribution) </li></ul><ul><li>Several times each minute </li></ul><ul><li>This information drives the infusionpump </li></ul>
EEG/MLAEP/BIS/.... ANESTHESIST POMP-CONTROL ALGORITHM pharmacokinetic simulation Cp predicted Cp desired Infusion pump delta t infusion rate reported IR PATIENT RESPONSE of PATIENT
Effect-site TCI <ul><li>TCI but effect-site concentration controlled vs. blood concentration. </li></ul><ul><li>Desired effect is obtained faster (no hysteresis). </li></ul><ul><li>Blood concentration will be higher at the start: the higher the difference in concentration between blood and effect site (brain), the faster the effect site concentration increases </li></ul><ul><li>The Pk-model choosen and the keo is of utmost importance </li></ul><ul><ul><li>fast keo: small overshoot of blood concentration </li></ul></ul><ul><ul><li>slow keo: large overshoot of blood concentration </li></ul></ul>
Effect-site TCI <ul><li>Drugs characterized by fast diffusion to the central nervous system are best suited for effect-site concentration controlled infusions </li></ul><ul><li>The largest gain in time to reach the desired effect is to be expected for drugs with slow diffusion </li></ul>
Limitations of TCI <ul><li>How ACCURATE ???: do the target concentrations correspond to reality ? </li></ul><ul><ul><li>Pk set is determined in a limited number of patients. In how far does the PK parameter set correspond to reality ? </li></ul></ul><ul><ul><li>Is the pharmacokinetic model used applicable to the individual patient: does the patient correspond to the population sample used to determine the PK data ? </li></ul></ul>
Is it absolutely necessary that the prediction is accurate ? <ul><li>Titration to effect remains necessary </li></ul><ul><li>“ swings” in concentration will be less important than with manual systems </li></ul><ul><li>Modifications in the desired concentration will at least result in proportional changes in real concentration and in effect </li></ul>
Investigating the validity of the model <ul><li>median prediction error (MDPE): median of the procentual difference, positive or negative, thus the bias of the system </li></ul><ul><li>median absolute prediction error (MDAPE): median of the procentual difference between the measured and the predicted concentration in absolute value (< 30%) </li></ul><ul><li>divergence : the slope of the linear regression analysis of the evolution in time of the MDAPE </li></ul><ul><li>wobble : median of the variability in individual patients </li></ul>
Performance in individual patients <ul><li>Age: children and elderly persons have different PK </li></ul><ul><li>Weight and body composition: importance depends on the drug </li></ul><ul><li>Disease and hydratation influence PK </li></ul><ul><li>Adapt target to the situation or </li></ul><ul><li>Kinetic libraries: PK-set according to circumstances </li></ul><ul><ul><li>Feed cofactors to the computer: age, weight, height, sex, renal disease… </li></ul></ul><ul><ul><li>Computer determines suitable kinetic parameter set </li></ul></ul><ul><ul><li>E.g. PAEDfusor for propofol: age and weight </li></ul></ul>
The future of TCI <ul><li>Multidrug TCI apparatus </li></ul><ul><li>Kinetic libraries: adaptation of the PK model to the individual patients needs </li></ul><ul><li>Pharmacodynamic interactions: suggestions for dosing according to the data of surface modelling </li></ul><ul><li>Closed-loop systems with automated effect evaluation for depth of anesthesia and paincontrol (?) </li></ul>