Pharmacokinetic concepts for TCI anaesthesia

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1 Pharmacokinetic concepts for TCI anaesthesia E. Gepts Department of Anaesthesiology, UVC Sint Pieter, 322 Hoogstraat, 1000 Brussels, Belgium Summary The development of new short-acting anaesthetic drugs, improved drug assay techniques and the availability of reliable infusion systems opened the field of clinical pharmacokinetics and pharmacodynamics. The tri-exponential drug concentration decay complicates the definition of therapeutic dosage regimens and prevents straightforward prediction of recovery from drug effects. The context-sensitive half-time, the time required for drug blood concentration to decrease to half its value, provides a useful comparative predictor of drug concentration decline after infusion. The effect-site equilibration time contributes to the delay of drug effect and intensifies the disequilibrium between drug blood concentrations and obtained effect following incremental dosage. The rationale for drug infusion is reduction of fluctuating drug concentrations and drug effects. A variability similar to that observed with the use of inhalation agents, must be achieved by the choice of an appropriate pharmacokinetic model. The use of a target controlled infusion device, delivering proportional changes based on pharmacokinetic principles, allows titration of the concentration against clinical effect in individual patients. Keywords Equipment; Diprifusor, target controlled infusion. Anaesthetics, intravenous; propofol. Pharmacokinetics.... Correspondence to: Dr E. Gepts Diprifusor is a trademark, the property of Zeneca Ltd For many years, pharmacotherapeutic management was a matter of trial and error following observation of drug dose effect relationships. Dosage regimens were adjusted empirically until a maximum desired effect for the correct time with minimal toxicity was achieved. Many questions remained unanswered. For example, why is the duration of the hypnotic effect of a single dose of thiopentone short, while after repeated doses it is prolonged? For most intravenous anaesthetics, after repetitive or continuous administration, duration of drug effect was unpredictable. Clinical experience suggested drug accumulation and supported the administration of intravenous anaesthetics as small incremental doses upon clinical signs of awakening. Indeed, optimal intravenous anaesthetic drug dosing was more of an art than a science. Anaesthetists needed short-acting drugs that did not have cumulative effects. Over the past 20 years a number of new drugs have been introduced. The awakening times of patients after multiple dosing with these drugs showed great promise, with propofol (formulated as an emulsion) having one of the most attractive pharmacological profiles. Anaesthesia maintenance, even by empirically defined propofol infusion schemes, was accompanied by a rapid and clear recovery from drug effect [1]. Improved drug assay techniques have opened the field of clinical pharmacokinetics, the quantitative study of the small drug concentrations in body fluids resulting from clinical drug dosages. The mathematical models developed are used as descriptive statistics for the processes that govern drug distribution and elimination. Pharmacokinetic modelling can also predict what might happen with multiple bolus injections, intravenous infusions or a combination of both. The availability of reliable infusion systems has led to an increasing interest in continuous infusion administration as an alternative to bolus injections of short-acting drugs. In vitro and in vivo studies show that the magnitude of the response is a function of the concentration of drug in the fluids bathing the site of action. These observations suggest that the therapeutic objective can be achieved by maintaining an adequate concentration of drug at the site of action for the duration of therapy. Evidently, a close Blackwell Science Ltd

2 E. Gepts Pharmacokinetic concepts relationship exists between anaesthetic drug blood or plasma concentration and effect [2]. As a consequence, anaesthesia is thought to be more adequately maintained by continuous administration, compared with bolus injections which lead to fluctuating blood, plasma and tissue concentrations and produce a fluctuating drug effect. However, concern exists about the drug concentration decline after cessation of infusion and the prediction of the time to recovery of normal consciousness. Pharmacokinetic definitions Most drugs exhibit multicompartment pharmacokinetic behaviour. The simpler one- or two-compartment models can be used to calculate drug dosage regimens for drugs with a large therapeutic window that are administered once, as a single dose, to relieve, for example, occasional headaches or that are administered daily, for about a week, to maintain a bacteriostatic effect. For the most simple pharmacokinetic model, the one-compartment model, three useful parameters are defined: X the volume of distribution (V ): the volume in which the drug instantaneously dilutes after intravenous administration and from which the drug is irreversibly removed; X the clearance value (Cl ): the amount of blood or plasma from which the drug is entirely cleared in one unit of time; X the half-life (t 1/2 ): the time required for the drug concentration to decrease to half of its value. A therapeutic concentration (C ther ) can be achieved with a loading dose that equals the desired concentration multiplied by the volume of distribution (V ) [3]: Loading dose ¼ C ther :V The maintenance infusion rate that compensates for the irreversible loss of drug by clearance is defined as C ther (Cl ): multiplied by the clearance value Maintenance infusion rate ¼ C ther :Cl Drug concentration decay The pharmacokinetics of propofol have been studied extensively in human volunteers and patients following various administration schemes [4 6]. Most investigators agree that the propofol blood concentration decay (Fig. 1) is best described by a tri-exponential equation, irrespective of the size of the bolus dose. A three-compartment model is therefore needed to describe adequately the distribution, redistribution and elimination of propofol (Fig. 2). The initial distribution half-life is short, ranging from 2 to 3 min, and the intermediate distribution has a half-life of min. The terminal phase levels off, with a half-life of 3 8 h. The central volume of distribution, in which propofol might dilute instantaneously after injection, is about 228 ml.kg ¹1, but steady-state volumes of distribution range from 800 l in healthy volunteers to 1900 l in elderly patients. The metabolic clearance of propofol is similar to or exceeds liver blood flow, suggesting a possible extra-hepatic site of biotransformation. The pharmacokinetics of propofol, as for most anaesthetics, appear to be linear. Within clinical dosage ranges, the shape of the drug concentration decay is unaffected by the dose (Fig. 1) and the derived pharmacokinetic parameters are similar for different doses [7]. Therefore, the derived pharmacokinetic parameters can be used to predict the concentrations generated by any clinical propofol administration scheme, or to calculate an administration scheme to obtain and maintain any desired propofol concentration. Figure 1 Blood propofol concentration decay following intravenous administration of 70 mg and 175 mg propofol showing parallel curves independent of dose. The decay is described by a tri-exponential equation where A, B and C are the intercepts with the y-axis and a, b and g are the slopes of the composite curves Blackwell Science Ltd 5

3 E. Gepts Pharmacokinetic concepts Anaesthesia, 1998, 53, Supplement 1, pages 4 12 Figure 2 The three-compartment model with drug input in the central compartment (V c ), distribution to a shallow compartment (V 2 ) and to a remote compartment (V 3 ). K 12,K 21,K 13 and K 31 are the intercompartmental rate constants that govern drug distribution and K 10 is the rate constant for elimination from the central compartment. The decay is described by a tri-exponential equation where A, B and C are the intercepts with the y-axis and a, b and g are the slopes of the composite curves. The three-compartment model The therapeutic prerequisite in anaesthesia is complex. The requirements of an effective administration regimen are smooth induction, easy transition to anaesthesia maintenance with the ability to control the depth of anaesthesia rapidly in response to changing levels of surgical stimulation, and rapid recovery from drug effect. The appropriate time factor can range from minutes to hours and the therapeutic window is variable. The disposition of anaesthetic drugs must be known from immediately following administration to several hours thereafter. A three-compartment model is therefore needed to calculate dosage regimens and to predict drug concentrations. Drug dilutes initially in a central volume of distribution (V c ) and this can be used to calculate the loading dose. Thereafter, the maintenance infusion rate has to compensate for drug clearance and for the transient loss of substance by distribution to the peripheral compartments governed by the intercompartmental time constants K 12,K 21,K 13 and K 31 (Fig. 2). Drug distribution contributes much more to the loss of substance available for effect than does drug elimination, particularly in the early phase of drug administration. Drug blood concentrations might decrease rapidly below the therapeutic level if distribution characteristics are not taken into account (Fig. 3). The compensation required to account for drug distribution is difficult to determine accurately. The calculation of the maintenance infusion rate at any time after dosing initiation is rather imposing: Maintenance infusion rate ðtþ ¼ C ther :V c :ðk 10 þ½k 12 :e ¹K21:t ÿþ½k 13 :e ¹K31:t ÿþ The three-compartment model behaviour of anaesthetic drugs with complex distribution dynamics makes the calculation of accurate dosing regimens and the prediction of recovery from drug effect difficult. The halflives of a three-compartment pharmacokinetic model have been shown to be poor predictors of duration of effect. The lack of a reliable predictive parameter for duration of drug effect after continuous drug administration is a major drawback of infusion techniques in clinical anaesthesia. Figure 3 Propofol blood concentrations following a dosage regimen calculated to obtain a blood concentration of 3 mg.ml ¹1 by using the central volume of distribution for the loading dose and the clearance value for the maintenance dose Blackwell Science Ltd

4 E. Gepts Pharmacokinetic concepts Figure 4 The time required for drug concentration (fentanyl, alfentanil, sufentanil) to decrease by half of its value, as a function of infusion duration. [Computer simulations created using the Stanpump recovery program (SL Shafer).] The context-sensitive half-time Hughes et al. introduced the concept of context-sensitive half-time as the time required for drug concentration to decrease to half of its value after a given duration of drug infusion (the context) [8]. The context-sensitive halftime is thus not a fixed value but a curve representing the half-times as a function of the duration of drug infusion. Each drug exhibits a characteristic contextsensitive half-time curve that is a better comparative predictor of drug concentration decay than the traditional elimination half-life. The context-sensitive half-times for three routinely used opioids (fentanyl, alfentanil and sufentanil) indicate that all three exhibit comparable and reasonably short 50% drug declining times following a drug infusion of up to 15 min. Thereafter, the time for fentanyl increases rapidly towards clinically unreasonable half-times. The curve for alfentanil is specific, showing how the rapidly increasing context-sensitive half-times reach a plateau after 3 h of infusion (Fig. 4) at approximately 60 min, two-thirds of its elimination half-life. This is because of its small volume of distribution which means that equilibrium is rapidly achieved. Sufentanil, initially advocated to be used for long-lasting invasive surgery, shows short context-sensitive half-times, shorter than alfentanil, for infusion times of up to 10 h. Most hypnotic agents exhibit short context-sensitive half-times, with the exceptions of thiopentone and midazolam (Fig. 5). Despite the fact that the elimination halflife of midazolam is comparatively short, its context-sensitive half-time increases rapidly with increasing durations of infusion, probably because of its low clearance rate. The context-sensitive half-time curves appear to provide better comparisons of the pharmacokinetic profiles of anaesthetic drugs in the clinical context than the traditional pharmacokinetic parameters. Compared with the opioids, the context-sensitive half-time of the routinely used hypnotic, propofol, is significantly shorter for any duration of infusion, thus ensuring a more rapid decline in Figure 5 The time required for drug concentrations of propofol, thiopentone, midazolam, ketamine and etomidate to decrease by half of their value, as a function of infusion duration. [Computer simulations created using the Stanpump recovery program (SL Shafer).] 1998 Blackwell Science Ltd 7

5 E. Gepts Pharmacokinetic concepts Anaesthesia, 1998, 53, Supplement 1, pages 4 12 Figure 6 Calculated (simulated) blood and effect-site concentrations, expressed as percentages of the initial blood concentration, during the first 20 min after bolus administration of (a) propofol and (b) midazolam. blood concentrations. Thus, it might be advisable to terminate opioid infusion well before propofol infusion. However, the context-sensitive half-time is not a reliable predictor for recovery from drug effect. The difference between the drug concentration at which the clinician expects recovery to occur and the actual drug concentration is an important determinant for the delay of recovery. There is no evidence that this difference is 50%. Therefore, the Diprifusor device provides an awakening time that is the time calculated for the actual propofol concentration to decrease to a definable concentration at which recovery is supposed to occur. The mean effect time The mean effect time, as described by Bailey, quantifies the duration of drug effect using the logistic distribution of the probability of drug effect [9]. This parameter includes clinical drug effect modelling. The discrepancy between mean effect time and the context-sensitive half-time increases with decreasing steepness of the drug concentration effect curve. However, the gradient of the drug concentration effect curve may be less steep when derived by logistic regression of data from a patient population compared with data from a single individual because of interindividual variability. Furthermore, extrapolations are made from the model beyond the observed data, which might introduce an artefact [10]. The mean effect time offers an average population value for recovery from drug effect but necessitates further prospective validation concerning its clinical usefulness. Effect-site equilibration time Anaesthetic agents seldom produce immediate effect; their physicochemical characteristics and molecular structure determine the time to enter biophase. In fact, the concentration at the effect-site, the biophase concentration, governs the drug effect, not the plasma concentration. However, the actual anatomical site of the biophase may be difficult to identify and direct physical measurement of drug concentrations in the biophase is impossible. By measuring the drug effect and blood concentrations accurately and frequently, one can characterise the time for equalisation of drug concentrations in the biophase with that in blood. The mathematical first order rate constant derived, k eo, determines the time delay between changes in drug concentration in the blood and measured changes in drug effect. This rate constant and its corresponding half-life are important descriptors of the rate of onset and end of drug effect. They are of particular relevance in anaesthesia, giving an indication of the time lag the anaesthetist may expect between peak plasma concentration and the maximum effect from a given dose. The simulations of Shafer & Varvel on bolus and infusion administrations of opioids clearly demonstrate the properties of each type of administration and of each drug and their relationship with the biophase rate constant and pharmacokinetic profile [11]. After bolus administration, drugs exhibiting a long time lag between blood concentration and effect and a rapid concentration decline, show an important delay of biophase peak concentration and an effective biophase concentration at a low percentage of the initial blood concentration achieved. Ultimately, a too small bolus dose might induce no effect at all. A comparison of the blood and apparent biophase concentrations after bolus administration of propofol with midazolam is seen in Fig. 6. For propofol, peak effect concentration is obtained after about 4 min and at 40% of the initial blood concentration. For midazolam, the delay is 7 min and the biophase concentration achieved Blackwell Science Ltd

6 E. Gepts Pharmacokinetic concepts Figure 7 Propofol blood and effect-site concentrations after a propofol bolus injection of 70 mg followed by (a) two incremental bolus doses of 35 mg each or (b) a continuous infusion of 70 mg over 30 min (2.33 mg.min ¹1 ). represents only 25% of the initial blood concentration, indicating a waste of active substance. When propofol anaesthesia is maintained by infusion instead of intermittent bolus administration, the biophase concentrations parallel the blood concentrations more closely (Fig. 7). The rationale for using drugs by infusion The rationale for drug infusion is based on three sound principles. The first principle concerns the closer relationship between drug concentrations compared with drug doses and the observed degree of drug effect. The second principle concerns the guidelines for intermittent drug administration, signs of awakening or insufficient analgesic protection, which do not meet the therapeutic end point of continuity of an appropriate level of anaesthesia. The third principle includes the effect-site equilibration time and the largely fluctuating drug concentrations in the biophase during bolus injections. For drugs with close concentration effect relationships, infusion offers advantages over administration via bolus injections and the side-effect profile is more likely to be limited. However, such benefits are more evident for short-acting drugs that might show large peak and trough concentrations and fluctuating effects during on-demand administration. The choice of the drug used must include the prediction of the desired recovery from drug effect. Although the clinician can easily increase the drug concentration in blood by increasing drug administration, the decrease in drug concentration after cessation of drug administration is entirely dependent on distribution and elimination processes. Recovery from drug effect after infusion administration is dependent on the drug concentration response curve and the contextsensitive half-time. The definition of an adequate infusion regimen for an individual patient remains cumbersome. Manual infusion schemes have been proposed, based either on the concept of minimum infusion rate or approximations of computergenerated infusion regimens and have proved useful in clinical anaesthesia [1, 12]. However, they are rigid and lack versatility and accuracy when the level of anaesthesia is considered inappropriate and adjustments need to be made rapidly. Most manual infusion schemes also require incremental bolus doses to increase the drug concentration. The rationale for target controlled infusion Target controlled infusion (TCI) includes the instantaneous calculation of the infusion rates necessary to obtain and maintain a given therapeutic drug blood concentration based on average pharmacokinetic parameters. For drugs whose pharmacokinetics are described by a two-compartment model, Kruger-Thiemer described the theoretical infusion regimen required to achieve and maintain a constant plasma drug concentration [13]. Based on the concept of additivity, the required dosage includes a bolus to fill the central compartment (C ther.v ) followed by an infusion to compensate for the loss of drug by elimination processes (C ther.cl ) and superimposed as an exponentially declining infusion to replace drug transfer into the peripheral compartment (C ther.v.[k 12.e ¹K21.t ]). This infusion scheme is commonly referred to as the boluselimination-transfer (BET) scheme. The first clinical application of this theory was published in 1981 by Schwilden [14]. He demonstrated that a computerised pharmacokinetic model-driven continuous infusion was able to reach the desired plasma levels of an intravenous anaesthetic drug. Since then, other research groups have written algorithms including the threecompartment model which, for most anaesthetic drugs, 1998 Blackwell Science Ltd 9

7 E. Gepts Pharmacokinetic concepts Anaesthesia, 1998, 53, Supplement 1, pages 4 12 Figure 8 Propofol blood concentration and infusion rates generated following an initial TCI with a Stanpump (SL Shafer) with target concentrations set at 3 mg.ml ¹1, followed by 5 mg.ml ¹1 and finally 2 mg.ml ¹1. is more appropriate than the two-compartment model [15 21]. In designing these algorithms, it is necessary to consider the physical limitations of the infusing device. It is not possible to implement any derived scheme precisely, because infusion pumps do not have infinite resolutions for drug infusion rates and for response times. The algorithm is a set of instructions that control the infusion rates to obtain predicted drug concentrations that are as close as possible to the set end-point value, the target concentration. Infusion rates are generally updated at intervals of 15 s, although more frequent updates occur in the Diprifusor system [22]: the calculated prediction is compared to the end point and the infusion rate is adapted accordingly. In fact, the drug infusion rate changes at discrete time intervals. The resulting fluctuations in predicted drug concentrations are not clinically significant. Figure 8 illustrates the infusion rates and the calculated drug concentrations obtained following propofol TCI with a Stanpump (SL Shafer) system. At the starting target concentration a bolus dose is administered to fill the central compartment, followed by an initially high infusion rate to compensate for rapid drug distribution and, thereafter, an infusion rate that decreases with time. When a higher target concentration is asked for, an additive bolus dose is administered followed by an appropriate infusion and, when a lower target concentration is asked for, the infusion stops until the desired concentration is attained and then a new appropriate maintenance rate is initiated. Individual variability Much criticism has been expressed at the extent of pharmacokinetic variability. The choice of an appropriate pharmacokinetic model has been the concern of many investigators [23]. When individuals are given identical doses of a drug, or even identical doses per kg of body weight, large differences in pharmacological response may be seen. Also, the dose required to produce a specific response may vary between individuals. Two sources contribute to this variability: differences in plasma or blood drug concentrations (pharmacokinetic variability) and differences in effect produced by a given drug concentration (pharmacodynamic variability). For many drugs, the intensity of response correlates well with the drug concentrations, suggesting a relatively low degree of pharmacodynamic variability. Several factors affect drug disposition. Drug distribution, metabolism and excretion processes are subject to a great deal of individual variation from body weight and age-related phenomena, genetic and environmental factors, the consequences of disease and concomitant administration of other drugs. Body weight The volume of distribution of a drug is determined by the anatomical space into which it distributes and its relative degree of vascular and extravascular binding. In adults with normal fat content, the volumes of both total body water and extracellular fluid are directly proportional to body weight. Therefore, a relationship might exist between the volume of distribution and body weight, particularly for the central volume of distribution. Whenever peak blood levels are of concern during drug administration, body weight should be considered in determining the appropriate dose. Most anaesthetists feel that obese patients may be at risk of overdose when weight-normalised infusion schemes are used. A lean body mass correction has been proposed to take account of this, but it did not find many converts. The Diprifusor TCI system takes body weight into account when determining the central volume of distribution. This is appropriate for patients with normal fat content but for morbidly obese patients I use a corrected body weight of the ideal weight plus 0.4 excess weight. However, a study by Servin et al. has demonstrated that Blackwell Science Ltd

8 E. Gepts Pharmacokinetic concepts the pharmacokinetics of propofol in obese patients are unaltered and clearance values and volumes of distribution correlate well with body weight [24]. Further clinical investigations are required. In contrast, the relationship between drug clearance and body weight in normal young adults is poor. Studies that include children and elderly patients are compromised by the well known age effect on drug clearance. There are no general guidelines to relate maintenance doses of drugs to body weight. Age Evidence indicates that children require and tolerate larger weight-adjusted doses of drugs compared with adults [25 30]. Total body water and extracellular fluid make up a larger percentage of total body weight in children than in adults and age-related differences in drug metabolism have been demonstrated. The lean body mass per unit surface area decreases as a function of age from 21 to 81 years in healthy humans and is probably responsible for decreasing volumes of drug distribution in elderly patients [2, 31, 32]. In general, drug elimination is impaired in new-borns because of the immaturity of several enzyme systems. However, it improves with age and tends to be most efficient in older infants and children, declining with age. Disease Pharmacokinetic variability is much greater in sick compared with healthy people [24, 33 36]. Disease affects various organ functions and the way drugs are distributed, metabolised and excreted. Renal disease directly affects drug excretion but it also has an effect on drug binding. Hepatic disease alters drug metabolism but some drugs are affected more than others. Cardiovascular disease can substantially interfere with the transport of drugs to eliminating organs but also influences the rate of distribution and redistribution. A degree of uncertainty about the pharmacokinetics for any individual patient is apparent because of the interindividual variability of the disposition of drugs. It is unlikely that this variability can be reduced below a minimum level, even when using population kinetics and introducing multiple factors that might influence drug disposition such as weight, height, sex, age and quantified renal, hepatic or cardiac function. Moreover, pharmacodynamic variability might be several times greater than pharmacokinetic variability in any individual [37]. Conclusion If variability similar to that experienced with inhalational anaesthetics, administered by a vaporiser, can be achieved TCI will perhaps provide a comparable comfortable administration tool for intravenous anaesthetics. It produces proportional changes based on pharmacokinetic principles and allows the titration of the achieved concentration against the required clinical effect in each patient. The microprocessor only controls the infusion device: the anaesthetist continues to control the choice of the drugs and the level of anaesthesia. References 1 Fragen RJ, Hanssen EHJH, Denissen PAF, Booij LHDJ, Crul JF. Disoprofol (ICI 35868) for total intravenous anaesthesia. Acta Anaesthesiologica Scandinavica 1983; 27: Shafer A, Doze VA, Shafer SL, White PF. Pharmacokinetics and pharmacodynamics of propofol infusions during general anesthesia. Anesthesiology 1988; 69: Norman J. The I.V. administration of drugs. British Journal of Anaesthesia 1983; 55: White PF. Propofol pharmacokinetics and pharmacodynamics. Seminars in Anesthesia 1988; 7: Kanto J, Gepts E. Pharmacokinetic implications for the clinical use of propofol. Clinical Pharmacokinetics 1989; 17: Gepts E, Camu F. Pharmacokinetics of intravenous induction agents. In: White PF, ed. Baillere s Clinical Anaesthesiology: Kinetics of Anaesthetic Drugs in Clinical Anaesthesiology. Philadelphia: WB Saunders, 1991; Gepts E, Camu F, Cockshott ID, Douglas EJ. Disposition of propofol administered as constant rate intravenous infusions in humans. Anesthesia and Analgesia 1987; 66: Hughes MA, Glass PS, Jacobs JR. Context-sensitive halftime in multicompartment pharmacokinetic models for intravenous anesthetic drugs. Anesthesiology 1992; 76: Bailey JM. Technique for quantifying the duration of intravenous anesthetic effect. Anesthesiology 1995; 83: Schnider TW, Shafer SL. Evolving clinically useful predictors of recovery from intravenous anesthetics. Anesthesiology 1995; 83: Shafer SL, Varvel JR. Pharmacokinetics, pharmacodynamics, and rational opioid selection. Anesthesiology 1991; 74: Roberts FL, Dixon J, Lewis GT, Tackley RM, Prys- Roberts C. Induction and maintenance of propofol anaesthesia. A manual infusion scheme. Anaesthesia 1988; 43 (Supplement): Kruger-Thiemer E. Continuous intravenous infusion and multicompartment accumulation. European Journal of Pharmacology 1968; 4: Schwilden H. A general method for calculating the dosage scheme in linear pharmacokinetics. European Journal of Clinical Pharmacology 1981; 20: Blackwell Science Ltd 11

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