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Effect of the mode of administration of inhaled anaesthetics on the interpretation of the [F.sub.A]/[F.sub.I] curve--a GasMan[R] simulation.


The pharmacokinetics of inhaled anaesthetics are usually described by the [F.sub.A]/[F.sub.I] over time ([[F.sub.A]/[F.sub.I]]/dt) curve. This curve describes the evolution of the alveolar partial pressure (expressed as fraction of 1 atmosphere, [F.sub.A]) towards the inspired partial pressure ([F.sub.I]) over time (1). Factors affecting the kinetics of inhaled anaesthetics affect the rise (curve shift upwards or downwards) and rate of rise ([[F.sub.A]/[F.sub.I]]/dt, the steepness of the upslope) of the [F.sub.A]/[F.sub.I] curve. The effects of blood solubility, cardiac output and ventilation on the [F.sub.A]/[F.sub.I] curves are basic kinetic concepts that are learned early during anaesthesia training (1). The effect of these parameters on the course of [F.sub.A]/[F.sub.I] is thought to reflect how these factors affect wash-in of the central nervous system and, therefore, speed of induction because [F.sub.A] is the partial pressure that corresponds closest to the central nervous system inhaled agent level. Therefore, [F.sub.A] is related to the clinical end-points of immobility and hypnosis as described by minimum alveolar concentration (MAC) and MACawake 'concepts', respectively (2,3). Anaesthetists are thoroughly familiar with all these concepts and multi-gas analysers readily display [F.sub.A] and [F.sub.I] in the operating room. However, the classical [F.sub.A]/[F.sub.I] curves are based on the delivery of anaesthetics using a high fresh gas flow (FGF) and a constant vaporiser setting, which results in a constant [F.sub.I]. Therefore, the [F.sub.A]/[F.sub.I] curves may not reflect the underlying organ kinetics in the same way when closed-loop end-expired feedback administration is used, which focuses on maintaining a certain (constant) [F.sub.A] by manipulating [F.sub.I]. This technology is implemented, for example, in the Zeus anaesthesia machine (Drager, Lubeck, Germany) (4). In this paper, GasMan[R] (Med Man Simulations Inc., Chestnut Hill, MA, USA) was used to examine whether differences in blood solubility, cardiac output and ventilation independently affect the relationship between [F.sub.A]/[F.sub.I] and the partial pressure in the vessel-rich group ([F.sub.VRG]) during constant [F.sub.I] and constant [F.sub.A] control. For the purposes of this paper, the partial pressure in the central nervous system is considered to be the same as that in the vessel-rich group (VRG) and the terms alveolar and end-expired are used interchangeably because the GasMan[R] program does not incorporate a separate dead space ventilation correction function. Although the simulation only approximates actual in vivo conditions, the purpose of this paper is to provide additional insight into the kinetics of potent inhaled anaesthetics. More specifically, we examine how changes in solubility, cardiac output and ventilation differently affect [F.sub.VRG] when either [F.sub.A] or [F.sub.I] are kept constant and thus warrant a different interpretation of the [F.sub.A]/[F.sub.I] curve.


GasMan[R], a computer program, is a physiologically-based model of inhaled anaesthetic uptake and distribution. Agent solubility in blood and tissues, gas and blood flows, and compartment volumes (lungs, VRG, muscle group and fat group) determine the rate of agent transfer (5,6). The version used in this study does not correct for inter-tissue diffusion, anaesthetic metabolism, dead space or ventilation/perfusion abnormalities. The GasMan[R] program allows the user to manipulate the vaporiser setting ([F.sub.D]) of an agent of choice, FGF, circuit volume, ventilation and cardiac output, and to observe the resulting course of [F.sub.I] and [F.sub.A] and the partial pressure of the potent inhaled anaesthetic in several tissues (arterial and venous blood, VRG, muscle group and fat group). Three different scenarios were studied, with the following program settings kept constant for all simulations: a 70 kg patient, an anaesthesia breathing circuit volume of 8 l and a FGF of 8 l.[min.sup.-1]. High FGF was used to avoid rebreathing, so that the delivered concentration matched [F.sub.I].

First, the effect of using agents with different blood solubility was studied. While maintaining either [F.sub.A] or [F.sub.I] constant at 1 MAC, isoflurane or desflurane was administered to a patient with a cardiac output of 5 l.[min.sup.-1] and a minute ventilation of 4 l.[min.sup.-1]. Next, the effect of cardiac output was simulated by choosing a cardiac output of 5 or 10 l.[min.sup.-1] while maintaining either desflurane [F.sub.A] or [F.sub.I] constant at 1 MAC while also keeping minute ventilation at 4 l.[min.sup.-1]. Finally, the effect of ventilation was examined by using a minute ventilation of 4 or 8 l.[min.sup.-1] while maintaining desflurane [F.sub.A] or [F.sub.I] constant at 1 MAC while also keeping cardiac output at 5 l.[min.sup.-1]. When performing the simulation, it is easy to keep [F.sub.I] constant but, to keep [F.sub.A] constant, the [F.sub.D] setting has to be continuously adjusted, which causes small oscillations.

[F.sub.A]/[F.sub.I] values were calculated from [F.sub.I] and [F.sub.A] and [F.sub.A]/[F.sub.I] versus time curves were constructed. We then examined by visual inspection how differences in blood solubility, cardiac output and ventilation affect the [F.sub.A]/[F.sub.I] versus time curves and the [F.sub.VRG] under conditions of constant [F.sub.I] and constant [F.sub.A].


When [F.sub.I] is kept constant, [F.sub.A] is higher with the less soluble agent (desflurane) (Figure 1[L.sub.1]); [F.sub.A] is lower with a higher cardiac output (Figure 2[L.sub.1]) and [F.sub.A] is higher with a higher minute ventilation (Figure 3[L.sub.1]). When [F.sub.A] is kept constant, [F.sub.I] has to be higher by design but [F.sub.I] is relatively higher for isoflurane than for desflurane (Figure 1[R.sub.1]). The [F.sub.I] required to achieve the desired [F.sub.A] is higher when cardiac output is higher (Figure 2[R.sub.1]) and [F.sub.I] is lower when ventilation is higher (Figure 3[R.sub.1]). The effect of blood solubility (Figures 1[L.sub.2] and 1[R.sub.2]), cardiac output (Figures 2[L.sub.2] and 2[R.sub.2]) and ventilation (Figures 3[L.sub.2] and 3[R.sub.2]) on the [F.sub.A]/[F.sub.I] curves are qualitatively the same, regardless of whether [F.sub.I] or [F.sub.A] was kept constant: the [F.sub.A]/[F.sub.I] curves are shifted upwards when blood solubility decreases, cardiac output decreases or ventilation increases (Figures 1[L.sub.2] and 1[R.sub.2], 2[L.sub.2] and 2[R.sub.2], 3[L.sub.2] and 3[R.sub.2], respectively). However, the [F.sub.VRG] curves depend on the mode of administration. With [F.sub.I] control, a lower blood solubility or higher ventilation results in a higher [F.sub.VRG] (Figures 1[L.sub.3] and 3[L.sub.3], respectively). With a higher cardiac output, the [F.sub.VRG] is higher at two to six minutes, but ultimately results in a lower [F.sub.VRG] (Figure 2[L.sub.3]). Once [F.sub.A] is controlled, the difference in blood solubility between isoflurane and desflurane has only a minimal effect on [F.sub.VRG] (Figure 1[R.sub.3]); an increase in cardiac output hastens the rise of [F.sub.VRG] to the same plateau value (Figure 2[R.sub.3]) and a change in ventilation has minimal effect on [F.sub.VRG] (Figure 3[R.sub.3]).



Our GasMan[R] simulation illustrates how the mode of administration of potent inhaled anaesthetics differently affects the impact of blood solubility, cardiac output and ventilation on the rise and rate of rise of the [F.sub.VRG], even though their effect on the [F.sub.A]/[F.sub.I] curve is qualitatively the same.

With both the constant [F.sub.I] and constant [F.sub.A] techniques, the [F.sub.A]/[F.sub.I] versus time curve is lower for isoflurane (with the greater blood and tissue solubility) than for desflurane (Figures 1[L.sub.2] and 1[R.sub.2]). When keeping [F.sub.I] constant, the isoflurane [F.sub.A] rises more slowly than that of desflurane because uptake by the blood is higher (as a result of higher tissue uptake). Consequently, [F.sub.VRG] of isoflurane rises slower than that of desflurane, suggesting that induction would be slower with isoflurane (Figure 1[L.sub.3]). When using a constant [F.sub.A] technique, the difference between the course of [F.sub.VRG] of desflurane and isoflurane is minimal because a feedback system (e.g. an anaesthetist using the overpressure technique; an automated anaesthesia machine) 'automatically' supplies the relatively larger amounts taken up of the more soluble agent by increasing [F.sub.D] and therefore [F.sub.I] (Figure 1[R.sub.3]). As a result, with a constant [F.sub.A] technique, the rate of rise of [F.sub.VRG] becomes almost independent of blood solubility. Indeed, the rate of rise of [F.sub.VRG] is then determined by the capacity of the VRG tissues (determined by tissue solubility and volume of the VRG tissues) and by the transport function of the blood (determined by blood solubility and blood flow to the VRG tissues). A lower 'tissue capacity' (lower tissue solubility) will result in a faster rise of [F.sub.VRG] but a lower transport of the agent to the tissue (lower blood solubility) will slow the rise of [F.sub.VRG].


A higher cardiac output increases desflurane uptake by transferring more desflurane to unsaturated tissues and therefore decreases the rate of rise of [F.sub.A] towards [F.sub.I]: the [F.sub.A]/[F.sub.I] curves are shifted down with either a constant [F.sub.I] or constant [F.sub.A] technique (Figures 2[L.sub.2] and 2[R.sub.2]). With the constant [F.sub.I] technique, [F.sub.VRG] is initially higher with higher cardiac output because there is rapid transfer of agent from the alveoli to the VRG tissues despite the lower [F.sub.A]. However, after a few minutes, the effect of the lower [F.sub.A] comes into play and [F.sub.VRG] with high cardiac output becomes lower than the [F.sub.VRG] with low cardiac output. All this results in an ultimately slower induction with a higher cardiac output (Figure 2[L.sub.3]). While equilibration between the arterial blood and the VRG is faster with a high cardiac output, the arterial partial pressure and therefore [F.sub.VRG] is lower because the [F.sub.A] with which it equilibrates is lower. Consequently, induction is expected to be slower with a higher cardiac output (Figure 2[L.sub.3]). With the constant [F.sub.A] technique, the [F.sub.A]/[F.sub.I] is also decreased when cardiac output is high, but mainly because [F.sub.I] has to be increased in order to keep the [F.sub.A] constant. Thus, in this case, the cause for the lowered [F.sub.A]/[F.sub.I] is the increase in [F.sub.I] (Figure 2[R.sub.1]). Equilibration between the arterial blood and the VRG is also faster, but because a feedback system (anaesthetist or automated anaesthesia machine) 'automatically' supplies the larger amounts taken up in the hyperdynamic patient by increasing [F.sub.I] (and thus keeping [F.sub.A] constant), a higher cardiac output hastens desflurane wash-in of the VRG towards that constant [F.sub.A] (Figure 2[R.sub.3]). This suggests that induction would be faster with a higher cardiac output. This is somewhat analogous to what happens with intravenous agents.


An increase in ventilation raises the [F.sub.A]/[F.sub.I] curves with both techniques (Figures 3[L.sub.2] and 3[R.sub.2]). With the constant [F.sub.I] technique, an increase in ventilation results in a faster rise of [F.sub.A] and, therefore, [F.sub.VRG], suggesting that induction will be faster (Figure 3[L.sub.3]). With the constant [F.sub.A] technique however, an increase in ventilation will result in only a slightly faster rise of [F.sub.VRG], because higher ventilation will merely hasten lung wash-in (Figure 3[R.sub.3]). The simulation does not include the possible effects of hyperventilation on cerebral blood flow, which could influence the rate of rise of [F.sub.VRG].

Our GasMan[R] simulation illustrates that when [F.sub.A] is kept constant, 1) the difference in the rise of [F.sub.VRG] between agents with a different blood solubility becomes dependent on the relative values of tissue solubility and blood solubility, 2) a higher cardiac output accelerates the rise of [F.sub.VRG] and 3) a change in ventilation has minimal effect on the course of [F.sub.VRG].

This interpretation is different from the classical interpretation of the [F.sub.I]/[F.sub.A] curve, which suggests that the speed of induction (rise of [F.sub.VRG]) is slower with the use of an agent with higher blood solubility, higher cardiac output and lower ventilation. Besides being of theoretical interest, this difference is clinically relevant with anaesthesia machines that use closed-loop end-expired feedback administration of inhaled anaesthetics, where the equipment determines the [F.sub.D] required to obtain the desired [F.sub.A]. One only needs to consider the examples of a patient with a low cardiac output (e.g. shock) or a hyperdynamic state (e.g. sepsis, burns, liver failure) producing the opposite effect of cardiac output on the course of [F.sub.VRG] with the constant [F.sub.A] versus constant [F.sub.I] technique to realise the potential implications.

In clinical practice we often use a hybrid approach: we first allow [F.sub.A] to gradually rise towards [F.sub.I] (often while the effect of intravenous induction agents is waning) and, once the desired [F.sub.A] is reached, we adjust [F.sub.I] to maintain [F.sub.A] at the desired value. The difficulty comes in when FGF is lowered. Re-breathing causes a discrepancy between [F.sub.D] and [F.sub.I]. The lower the FGF, the larger the discrepancy between [F.sub.D] and [F.sub.I]. This may have potentially deterred many anaesthesiologists from using lower FGF and may have been the impetus for the development of modern closed-loop end-expired feedback anaesthesia machines. These machines take over this task, allowing better and more rapid control of [F.sub.A] under low-flow conditions. This shift of focus demands an interpretation of the [F.sub.A]/[F.sub.I] curve which is different to what has traditionally been used to describe kinetics of inhaled agents.


In summary, the mode of administration of potent inhaled anaesthetics alters the impact of changes in blood solubility, cardiac output and ventilation on the rate of rise of [F.sub.VRG]. When [F.sub.I] is kept constant, [F.sub.VRG] will rise faster and higher with an agent with a lower solubility, lower cardiac output and higher ventilation. This results in an ultimately slower induction with a higher cardiac output. However, when [F.sub.A] is kept constant, the course of [F.sub.VRG] is minimally affected by solubility and ventilation but [F.sub.VRG] will rise faster towards the same [F.sub.A] with a higher cardiac output. Thus, when [F.sub.A] is kept constant, induction of anaesthesia is faster with a higher cardiac output. Because the effects of changes in solubility, cardiac output and ventilation on [F.sub.A]/[F.sub.I] are similar when either [F.sub.I] or [F.sub.A] are kept constant yet have different effects on the [F.sub.VRG], care has to be taken when making inferences from the [F.sub.A]/[F.sub.I] curve regarding the effect of these parameters on depth of anaesthesia or speed of induction. It should not be overlooked, however, that the ultimate factor determining speed of induction depends mainly on the absolute [F.sub.A], which is not represented by the [F.sub.A]/[F.sub.I] curve.

Accepted for publication on June 20, 2009


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(4.) Struys MM, Kalmar AF, De Baerdemaeker LE, Mortier EP, Rolly G, Manigel J et al. Time course of inhaled anaesthetic drug delivery using a new multifunctional closed-circuit anaesthesia ventilator. In vitro comparison with a classical anaesthesia machine. Br J Anaesth 2005; 94:306-317.

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Address for correspondence: Dr J. Hendrickx, Department of Anaesthesiology, Onze Lieve Vrouw Hospital, Moorselbaan 164, 9300 Aalst, Belgium.

T. VAN ZUNDERT *, J. HENDRICKX ([dagger]), A. BREBELS ([double dagger]), S. DE COOMAN ([section]), S. GATT **, A. DE WOLF ([dagger dagger])

Department of Anaesthesiology, Intensive Care and Pain Therapy, Onze Lieve Vrouw Hospital, Aalst, Belgium and University of Maastricht, Maastricht, The Netherlands

* B.Sc., Research Fellow.

([dagger]) M.D., Ph.D., Consultant Anaesthesiologist, Department of Anaesthesiology, Intensive Care and Pain Therapy, Onze Lieve Vrouw Hospital and Consulting Assistant Professor, Stanford University, Stanford, USA.

([double dagger]) M.D., Resident Anaesthesiologist, Department of Anaesthesiology, Intensive Care and Pain Therapy.

([section]) M.D., Consultant Anaesthesiologist, Department of Anaesthesiology, Institut Jules Bordet, Universite Libre de Bruxelles, Brussels, Belgium.

** M.D., F.A.N.Z.C.A., F.J.F.I.C.M., Professor and Consultant Anaesthesiologist, Department of Anaesthesiology and Intensive Care, University of New South Wales, Prince of Wales and Sydney Children's Hospital, Sydney, New South Wales, Australia.

([dagger dagger]) M.D., Professor, Department of Anesthesiology, Feinberg School of Medicine, Northwestern University, Chicago, Illinois, USA.
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Article Details
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Author:van Zundert, T.; Hendrickx, J.; Brebels, A.; de Cooman, S.; Gatt, S.; de Wolf, A.
Publication:Anaesthesia and Intensive Care
Article Type:Report
Geographic Code:8AUST
Date:Jan 1, 2010
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