1Division of Peri-operative Care, Anaesthesia and Pain Medicine, University Medical Centre Utrecht (UMCU), Utrecht, The Netherlands. 2Department of Anesthesiology, St Maartenskliniek, Nijmegen, The Netherlands. 3Julius Centre for General Practice and Patient Oriented Research, (UMCU), Utrecht, The Netherlands. 4Department of Medical Statistics, N.V. Organon, Oss, The Netherlands*Corresponding author: University Medical Centre Utrecht (UMCU), DPAP E03.511, Heidelberglaan 100, Postbus 85500, NL-3508 GA Utrecht, The Netherlands
Accepted for publication: September 12, 2001 ;
![]() |
Abstract |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Methods. We have recalibrated a previously validated physiological model for enflurane closed-circuit inhalation anaesthesia, using individual continuous cardiac output measurements as well as age-related enflurane solubility coefficients as inputs to the model. Two model versions using calculated (Brodys formula) or measured (thoracic electrical bioimpedance) cardiac output values, and two versions with standard (fixed) or age-related solubility coefficients were formulated.
Results. Data from 62 ophthalmic surgical patients were used to validate the predictive performance of the four model versions. The root mean squared errors (total error) and scatters (error variation) were similar with the extended model versions, but the group biases (systematic error component) were significantly less with the model versions that included age-related solubility compared with the versions using standard solubility coefficients (bias 0.76/0.78% vs 3.44/3.60%).
Conclusion. The inclusion of age-related solubility coefficients but not of continuous cardiac output measurements improves the predictive performance of the physiological model for closed-circuit inhalation anaesthetic conditions in routine clinical practice.
Br J Anaesth 2002; 88: 3845
Keywords: anaesthetics volatile, enflurane; equipment, breathing systems, closed-circuit; measurement techniques, mass spectrometry; heart, cardiac output; model, physiological; pharmacokinetics, uptake; pharmacokinetics, solubility
![]() |
Introduction |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
We investigated whether the use of real-time continuously measured cardiac output values and age-related solubility coefficients, that is two variables from the Fick formula (Uptake=dQ/dtxx(PinPout)), would improve the prediction of end-expired anaesthetic concentrations in the clinical conditions of closed-circuit inhalation anaesthesia. Therefore, four extended versions of the physiological model were formulated: two model versions using calculated or measured cardiac output values (referred to as version C or version E, respectively, with standard solubility coefficients), and two corresponding versions with age-related solubility coefficients (referred to as version C or E, respectively). The predictive performance of these various model versions was experimentally validated during routine clinical practice.
![]() |
Methods |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Patients and anaesthetic procedure
After approval of the Institutional Ethical and Research Committee and informed consent, we studied 62 adult patients (ASA I or II) undergoing elective ophthalmic procedures. The patients were pre-medicated with diazepam (510 mg orally) and droperidol (2.55 mg orally) 1 h before surgery. Before induction of anaesthesia, pure oxygen was administered at a flow rate of 10 litre min1 via a tight fitting mask for 3 min. Then anaesthesia was induced with fentanyl 0.10.2 mg i.v. and a dose of thiopentone sufficient to abolish the eyelash reflex, followed by vecuronium 0.1 mg kg1 i.v. After spraying the vocal cords with 4.3% lignocaine, a cuffed tracheal tube was placed. The lungs of the patient were artificially ventilated with a high fresh gas flow of oxygen and nitrous oxide (1:2 ratio) for a maximum of 5 min or until the end-expired nitrogen concentration was less than 1 vol%. Next, the anaesthetic system was closed and closed-circuit anaesthesia started. The anaesthetic equipment was an Ohmeda Modulus CD anaesthesia system (Madison, WI, USA) with a standing bellows ventilator (Ohmeda 7850). The fresh gas flow of oxygen and nitrous oxide was adjusted manually to maintain the inspired oxygen concentration at 3540 vol%. Tidal volume was adjusted to maintain the end-expired carbon dioxide concentration at 4.05.0 vol%. As the delivered tidal volume depends on the rate of fresh gas flow into the standing bellows ventilator, adapting the fresh gas flow to obtain the prescribed closed-circuit conditions necessitated frequent adjustments of the tidal volume and the gas flows at the start of closed-circuit anaesthesia.8 Therefore, 5 min were allowed until we were confident that the tidal volume and gas flows were stable. Only data acquired after this initial non-steady state period were analysed.
Liquid enflurane was injected into the expiratory limb of the circuit: an initial volume of 0.02 ml kg1 (loading dose) at the start of closed-circuit inhalation anaesthesia and repeated volumes of 0.01 ml kg1 (maintenance doses) during anaesthesia. All anaesthetic procedures were performed by the same anaesthetist (P.M.V.). The time for start of ophthalmic surgery was within a maximum of 5 min after the start of enflurane administration. We did not use a rigid time schedule and did not aim to maintain a predetermined end-expired anaesthetic concentration, but modified the enflurane administration according to the patients anaesthetic needs as in good clinical practice. Therefore, the non-invasive blood pressure, heart rate, heart rate variability (judged by ear with the aid of pulse oximetry), transcutaneous arterial oxygen saturation, and the end-expired enflurane concentrations (i.e. the best possible approach to the alveolar concentrations measured during routine circumstances), were carefully and continuously monitored.9 If necessary in response to surgical stimuli, analgesia was supplemented with additional increments of fentanyl 0.050.1 mg i.v. A respiratory mass spectrometer (Centronic 200 MGA or QP9000; CaSE, Gillingham, UK) continuously sampled gas (40 ml min1) at the Y-piece of the anaesthetic circuit via a side-stream sampling port (the sample flow is part of the model). Before using the mass spectrometer we verified its calibration for enflurane with a certified calibration gas mixture (1% enflurane in 30% oxygen, 30% nitrous oxide and balance gas nitrogen; AGA Gas, Amsterdam, The Netherlands). The coefficient of variation of the mass spectrometer readings was 2%. The times and volumes of each liquid enflurane administration were noted.
Cardiac output was estimated and recorded continuously by a thoracic electrical bioimpedance monitor (BoMed NCCOM-3, software version 6; BoMed Medical Manufacturing Ltd Instruments, Irvine, CA, USA). This method gave the possibility of including direct non-invasive cardiac output measurements as a continuous non-linear and subject-specific input to the model. This device derives the cardiac output by measuring changes in electrical bioimpedance of the thorax.10 11 Four pairs of surface electrodes were placed mid-circumferential on each side of the neck and on each side of the chest (equidistant from the xiphoid processus), and connected to the BoMed monitor. Cardiac output values were calculated and recorded from the average thoracic electrical bioimpedance for 12 successive acceptable heartbeats. The real-time cardiac output recordings, starting from immediately before the first injection of enflurane into the closed system, were processed in the appropriate model versions.
A personal computer with a 12-bit analogue-to-digital board (Keithley Metrabyte, Taunton, MA, USA) processed the signals from the mass spectrometer, the cardiac output monitor, and the anaesthesia system. On-line display of the respiratory waveforms allowed constant monitoring of the actual inspired and end-expired concentrations of nitrogen, oxygen, carbon dioxide, nitrous oxide, argon, and enflurane. The trends of the enflurane and oxygen concentrations in the last 20 min were also displayed continuously to provide a visual impression on the quality of the measurements. End-expired enflurane concentration and non-invasive cardiac output values were saved to disc every 10-s period for further off-line data processing.
Model and its versions
Initially a theoretical physiological 14-compartment model (the basic model version A), based on data from the literature for a standard human, was formulated to predict the end-expired concentrations of inhalation anaesthetics under closed-circuit conditions.12 13 In the present study, four extended versions derived from the basic model were evaluated (Fig. 017F1). The formerly validated model version C uses a fixed, calculated cardiac output value. It was extended with real-time cardiac output measurements from each patient (version E). Versions C and E both used fixed solubility coefficients for a standard human, whereas two corresponding versions were created, versions C and E respectively, that incorporated age-related enflurane solubility coefficients (Table 1). For every patient each of the four model versions predicted the end-expired anaesthetic concentrations (i.e. four simulation runs per patient). After compiling the predicted and measured anaesthetic concentrations, the predictive performance measures were calculated by comparing the measured end-expired enflurane concentrations with those predicted by the four different model versions. The sequence of the data processing is depicted in Figure 017F2.
|
|
|
|
![]() |
Results |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
|
|
|
|
|
![]() |
Discussion |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Cardiac output
Measured cardiac output values did not improve predictions, but some aspects need to be discussed. Brodys equation is used for a standard human under basic, resting conditions and is derived from a large normal sample population. It does not necessarily predict an output for the individual patient (e.g. during surgery) and might under- or over-predict the measured cardiac output values in the clinical situation. A more reliable approach for dealing with variability is to gain subject-specific knowledge through the incorporation of individual measurements. In this study, electrical bioimpedance monitoring provided us with a simple continuous non-invasive measurement of cardiac output.11
Our patients underwent routine ophthalmic procedures and this type of surgery is usually not associated with large haemodynamic alterations. Because cardiac output remained stable we cannot be sure that extreme changes in cardiac output, for example during major surgical procedures, might influence the model predictions. In many models of inhalation anaesthesia, cardiac output should theoretically influence the disposition of inhalation anaesthetics. Nonetheless, in the absence of actual data, most authors had to build their models using approximate estimates for a standard human because more detailed information was not available.1517 Lockwood and co-workers performed computer simulations and argued that the initial uptake of volatile anaesthetics in closed-system anaesthesia, with a steady end-expired anaesthetic concentration, would not be affected by changes in cardiac output.18 Several mechanisms could compensate for changes in uptake caused by changes in cardiac output. Using a continuous infusion of enflurane in a closed breathing system during cardiac bypass surgery, the same research group did not find a quantitative relationship between anaesthetic uptake and cardiac output.19 Hendrickx and co-workers showed that cardiac output had no major impact on the prediction of sevoflurane kinetics during feedback-controlled closed-circuit conditions.20 21 Our experimental findings confirm the theoretical calculations of Lockwood and Lerou and co-workers, and suggest that earlier work overestimated the importance of cardiac output for the predictive performance of models concerning closed-circuit inhalation anaesthesia.18 22
Theoretically, oscillations in the enflurane concentrations caused by the intermittent bolus injection technique might cause changes in cardiac output and we were interested whether this would influence the quality of the model predictions. We found no effect of injections on continuous cardiac output measurements, and confirm the findings of a recent study by Couto da Silva and co-workers who noted no major fluctuations on the systolic arterial pressure when using the intermittent bolus injection technique during closed-circuit anaesthesia.23 Injection into the expiratory limb allows dilution in the ventilatory circuit and this attenuates the peak effects of the bolus injection technique. Also, the myocardium is saturated by more than 95% after three time constants, that is within only 10 min, so the peak loads of the anaesthetic injection method would not cause detectable variations of cardiac output.
The haemodynamic effects of inhalation anaesthetics are profoundly influenced by individual variability, and changes in cardiac output (body perfusion) do not cause proportional changes in blood flows to the different compartments (tissue perfusion).24 Both Ashman and Cowles suggested that the construction of realistic models would need the inclusion of more detailed circulatory effects of anaesthesia, but they also recognized that the fractional flow and blood volume of each organ or compartment is difficult to measure in humans.2527 They stated that the changes in cardiac output and its distribution influence the size of all compartments, and the assumption that the partitioning of cardiac output does not change clearly also is an oversimplification. As measurement of regional organ blood flow in humans is not feasible during routine surgery, inclusion of continuously measured rather than fixed relative organ flows in physiological models seems unwarranted at present.
Solubility
Tissue and blood solubility coefficients are important in the prediction of the kinetics of inhalation anaesthetics during closed-circuit anaesthesia. The tissue/gas solubility coefficients reported by early investigators showed large differences (>150%) and also the ranges reported in single studies may be very large. The older standard coefficients were about 30% higher than the values determined more recently.4 6 28--30 Table 1 shows that the age-related enflurane solubility coefficients for the compartments of the vessel rich group (especially brain, heart and liver) are considerably less than the older fixed solubility coefficients. Body composition changes with age and this will influence the pharmacological behaviour of inhalation anaesthetic agents. In the prediction of the pharmacokinetics of inhaled anaesthetics, solubility coefficients are particularly important during the first hour of anaesthesia. The model versions that used standard coefficients gave a small but systematic under-prediction, which could be corrected by the implementation of age-related solubility coefficients, suggesting that the age-related coefficients are better than the older standard coefficients.
The solubility of anaesthetic agents may vary between patients and between tissues. Solubility is also influenced by changes in body temperature, blood and tissue composition, genetic predisposition, and other unknown physiological influences.28 Even during the course of an anaesthetic, there may be rapid changes of the anaesthetic solubility caused by acute changes in blood (and tissue) composition. Steady-state clinical conditions suitable for accurate determinations of the anaesthetic solubility are often impossible to achieve in vivo.31 32 So, solubility data must be interpreted cautiously in the clinical setting. In addition, the present model does not account for a possible redistribution of anaesthetics within or from one tissue to another (inter-compartmental diffusion).
We found that this physiological 14-compartment model is robust, as the group-bias remained below 10% and the rmse was less than 30% for most (>90%) of the patients. These criteria were used in earlier validation studies for the model, as this does not result in systematic over- or under-prediction (bias) and 30% is a limit imposed by the biological variability.2 The true picture will be complex because detailed information on the cascade of kinetics of the volatile anaesthetics is not well known.21 33 During daily anaesthetic practice, fast and accurate gas monitoring systems are available, and anaesthetic equipment may now have adequate feedback control for anaesthetic agent delivery. This reduces the importance of on-line kinetic models for the routine clinical administration of inhalation anaesthesia. However, physiological models remain important to allow a more fundamental understanding of the process of inhalation anaesthesia, and can be valuable teaching tools when used in patient simulators.17 These models should be updated regularly with recent data obtained in new research and the performance of the models should be explored in real clinical circumstances.
In conclusion, we studied the effect of two factors that control anaesthetic uptake according to the Fick principle, continuous cardiac output measurements and age-related solubility coefficients, on the predictive performance of a physiological model for closed-circuit enflurane anaesthesia. Cardiac output measurements did not improve the model predictions, but recalibration with age-related solubility coefficients improved the predictive performance of the model.
![]() |
Acknowledgements |
---|
|
|
|
|
![]() |
References |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
2 Vermeulen PM, Lerou JGC, Dirksen R, Booij LHDJ, Borm GF. A system model for halothane closed-circuit anesthesia: structure considerations and performance evaluation. Anesthesiology 1995; 83: 51527[ISI][Medline]
3 Vermeulen PM, Lerou JGC, Dirksen R, Booij LHDJ, Borm GF. Repeated enflurane anaesthetics and model predictions: a study of the variability in the predictive performance measures. Br J Anaesth 1997; 79: 48896
4 Lowe HJ, Ernst EA. The Quantitative Practice of Anesthesia. Baltimore: Williams & Wilkins, 1981
5 Lerman J, Gregory GA, Willis MM, Eger EI, II. Age and solubility of volatile anesthetics in blood. Anesthesiology 1984; 61: 13943[ISI][Medline]
6 Lerman J, Schmitt-Bantel BI, Gregory GA, Willis MM, Eger EI, II. Effect of age on the solubility of volatile anesthetics in human tissues. Anesthesiology 1986; 65: 30711[ISI][Medline]
7 Malviya S, Lerman J. The blood/gas solubilities of sevoflurane, isoflurane, halothane, and serum constituent concentrations in neonates and adults. Anesthesiology 1990; 72: 7936[ISI][Medline]
8 Gravenstein N, Banner MJ, McLaughlin G. Tidal volume changes due to the interaction of anesthesia machine and anesthesia ventilator. J Clin Monit 1987; 3: 18790[ISI][Medline]
9 Landon MJ, Matson AM, Royston BD, Hewlett AM, White DC, Nunn JF. Components of the inspiratory-arterial isoflurane partial pressure difference. Br J Anaesth 1993; 70: 60511[Abstract]
10 Bernstein DP. A new stroke volume equation for thoracic electrical bioimpedance: theory and rationale. Crit Care Med 1986; 14: 9049[ISI][Medline]
11 Fuller HD. The validity of cardiac output measurement by thoracic impedance: a meta-analysis. Clin Invest Med 1992; 15: 10312[ISI][Medline]
12 Lerou JGC, Dirksen R, Beneken Kolmer HH, Booij LHDJ. A system model for closed-circuit inhalation anesthesia: I. Computer study. Anesthesiology 1991; 75: 34555[ISI][Medline]
13 Lerou JGC, Dirksen R, Beneken Kolmer HH, Booij LHDJ, Borm GF. A system model for closed-circuit inhalation anesthesia: II. Clinical validation. Anesthesiology 1991; 75: 2307[ISI][Medline]
14 Armitage P, Berry G. Distribution-free methods. In: Armitage P, ed. Statistical Methods in Medical Research. Oxford: Blackwell Science Ltd, 1994; 4613
15 Mapleson WW. Mathematical aspects of the uptake, distribution and elimination of inhaled gases and vapours. Br J Anaesth 1964; 36: 12939[ISI]
16 Davis NR, Mapleson WW. Structure and quantification of a physiological model of the distribution of injected agents and inhaled anaesthetics. Br J Anaesth 1981; 53: 399405[Abstract]
17 Sear JW. Why not model physiologically? Br J Anaesth 1993; 70: 2435[ISI][Medline]
18 Lockwood GG, White DC. Effect of ventilation and cardiac output on the uptake of anaesthetic agents from different breathing systems: a theoretical study. Br J Anaesth 1991; 66: 51926[Abstract]
19 Watt SJ, Cook LB, Ohri S, Lockwood GG. The relationship between anaesthetic uptake and cardiac output. Anaesthesia 1996; 51: 248[ISI][Medline]
20 Hendrickx JFA, Van Zundert AAJ, De Wolf AM. Sevoflurane pharmacokinetics: effect of cardiac output. Br J Anaesth 1998; 81: 495501
21 Eger EI, II. Complexities overlooked: things may not be what they seem. Anesth Analg 1997; 84: 23940[ISI][Medline]
22 Lerou JGC, Booij LHDJ. Model-based administration of inhalation anaesthesia: 2. Exploring the system model. Br J Anaesth 2001; 86: 2937
23 Couto da Silva JM, Mapleson WW, Vickers MD. Quantitative study of Lowes square-root-of-time method of closed-system anaesthesia. Br J Anaesth 1997; 79: 10312
24 Hoffman WD, Banks SM, Alling DW, et al. Factors that determine the hemodynamic response to inhalation anesthetics. J Appl Physiol 1991; 70: 215563
25 Ashman MN, Blesser WB, Epstein RM. A nonlinear model for the uptake and distribution of halothane in man. Anesthesiology 1970; 33: 41929[ISI][Medline]
26 Cowles AL, Borgstedt HH, Gillies AJ. The uptake and distribution of four inhalation anesthetics in dogs. Anesthesiology 1972; 36: 55870[ISI][Medline]
27 Cowles AL, Borgstedt HH, Gillies AJ. A simplified digital method for predicting anesthetic uptake and distribution. Comput Biol Med 1973; 3: 38595[Medline]
28 Eger EI, II. Respiratory and circulatory factors in uptake and distribution of volatile anaesthetic agents. Br J Anaesth 1964; 36: 15571[ISI]
29 Yasuda N, Targ AG, Eger EI, II. Solubility of I-653, sevoflurane, isoflurane, and halothane in human tissues. Anesth Analg 1989; 69: 3703[Abstract]
30 Lockwood GG, Sapsed-Byrne SM, Smith MA. Effect of temperature on the solubility of desflurane, sevoflurane, enflurane and halothane in blood. Br J Anaesth 1997; 79: 51720
31 Tarr TJ, Snowdon SL. Blood/gas solubility coefficient and blood concentration of enflurane during normothermic and hypothermic cardiopulmonary bypass. J Cardiothoracic Vasc Anesth 1991; 5: 1115[Medline]
32 Feingold A. Crystalloid hemodilution, hypothermia, and halothane blood solubility during cardiopulmonary bypass. Anesth Analg 1977; 56: 6226[Abstract]
33 Bouillon T, Shafer SL. Hot air or full steam ahead? An empirical pharmcacokinetic model of potent inhalational agents. Br J Anaesth 2000; 84: 42931