Predictive performance of a physiological model for enflurane closed-circuit anaesthesia: effects of continuous cardiac output measurements and age-related solubility data

P. M. Vermeulen*,1, C. J. Kalkman1, R. Dirksen2, J. T. A. Knape1, K. G. M. Moons1,3 and G. F. Borm4

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
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Background. The disposition of inhalation anaesthetics is governed by the factors described in the Fick principle.

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’ (Brody’s 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: 38–45

Keywords: anaesthetics volatile, enflurane; equipment, breathing systems, closed-circuit; measurement techniques, mass spectrometry; heart, cardiac output; model, physiological; pharmacokinetics, uptake; pharmacokinetics, solubility


    Introduction
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
The uptake and disposition of inhalation anaesthetic agents follows the Fick principle, and depends on the delivered anaesthetic concentration, on the patient’s cardiac output as well as regional organ blood flow, and on blood and tissue solubility. To predict the end-expired anaesthetic concentrations following bolus injections of liquid enflurane, we previously validated a 14-compartment physiological model for closed-circuit inhalation anaesthesia.13 This model, designated version C, incorporated a fixed estimate of the cardiac output calculated per patient (Brody’s formula: cardiac output = (0.2 kg0.75) litre min–1), as well as anaesthetic solubility coefficients of a standard human.4 Assuming a fixed value of the cardiac output during the entire course of anaesthesia is obviously an oversimplification and is inconsistent with the observations in clinical practice. In addition, Lerman and co-workers showed that the solubility of volatile anaesthetics varies with age.57

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/dtx{lambda}x(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
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
The structure of the model and modelling methodology has been described extensively elsewhere.13 The model and methods are summarized here along with the modifications and additions necessary for this particular study.

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 (5–10 mg orally) and droperidol (2.5–5 mg orally) 1 h before surgery. Before induction of anaesthesia, pure oxygen was administered at a flow rate of 10 litre min–1 via a tight fitting mask for 3 min. Then anaesthesia was induced with fentanyl 0.1–0.2 mg i.v. and a dose of thiopentone sufficient to abolish the eyelash reflex, followed by vecuronium 0.1 mg kg–1 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 35–40 vol%. Tidal volume was adjusted to maintain the end-expired carbon dioxide concentration at 4.0–5.0 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 kg–1 (loading dose) at the start of closed-circuit inhalation anaesthesia and repeated volumes of 0.01 ml kg–1 (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 patient’s 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 0.05–0.1 mg i.v. A respiratory mass spectrometer (Centronic 200 MGA or QP9000; CaSE, Gillingham, UK) continuously sampled gas (40 ml min–1) 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.



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Fig 1 Four extended model versions of the basic physiological model (model version A) were formulated. The formerly validated version C uses a fixed value of the cardiac output calculated per patient (Brody’s formula Q=0.2 BW0.75).1–3 In the present study the model version E, which uses the continuous cardiac output measurements tracked from the individual, was validated. Both versions C and E use the fixed solubility coefficients of a standard human.4 To evaluate the influence of the factor solubility, two extended versions (C’ and E’) which adopt age-related partition coefficients according to the studies of Lerman and Malviya (Table 1) were also tested.5–7 The four model versions tested all account for a constant fraction of non-pulmonary elimination (fNPE) for enflurane. The small difference between the fNPE for the versions C/E vs C’/E’ (that is 0.131 vs 0.126) was effected by the different solubility data (fixed vs age-related) used while determining the appropriate size of non-pulmonary elimination for enflurane (the procedure was described in a previous study).1

 

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Table 1 Enflurane solubility coefficients. *According to Lowe and Ernst.4 **According to Lerman and co-workers5 6 and Malviya and Lerman;7 in the present study we had to interpolate for the intervening ages of the individual patients as Lerman and co-workers reported values for only five different ages. Where no age-adjusted values were available, the data reported by Lowe and Ernst were used. (The studies were reported without reference to gender)
 


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Fig 2 For the data processing, the patient characteristics (age, gender, body weight, and height) were collected for each patient. The enflurane administration schedule (injection time and volume) was added as input to the model. The amount of liquid enflurane per injection was converted into millilitres of vapour, and supplied to the model as if added to the anaesthetic system over a 60-s interval (i.e. the average evaporation time). The continuous cardiac output measurements per patient were entered to the model as an independent variable. Next, the appropriate version of the model was selected and activated to generate the predicted time courses of the end-expired enflurane concentrations by running a special purpose simulation programme (TUTSIM®, Meerman Automation, Neede, The Netherlands).12 For each patient and anaesthetic procedure the end-expired concentrations were predicted by applying the appropriate version of the model. Finally the model’s predictive performance measures were calculated by comparing the predicted with the measured end-expired enflurane concentrations quantitatively.

 
Predictive performance measures and statistics
The following measures were used to determine the predictive performance of each model version (Table 2). The prediction error (pe) is the difference between the predicted and measured concentration, expressed as a percentage of the measured value. The pe and squared prediction error (pe2), calculated for each 10-s period, were used to provide three additional predictive performance measures. (1) The mean squared error (mse) is the average of the squared prediction errors per patient. The root-mean squared error (rmse) is a measure of the total error budget for an individual patient during one anaesthetic procedure: it is not influenced by the sign of the prediction errors and can be decomposed into two terms: bias and scatter. (2) The bias is the average of the prediction errors for an individual patient: it is a measure of the systematic error component and can be either positive or negative, indicating either over- or under-prediction. (3) The scatter is a measure of the variation of the prediction errors around their mean (bias) during one anaesthetic procedure. Finally, calculating the average of all the individual rmses, biases or scatters—one per patient—yields the group rmse, the group bias or the group scatter.


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Table 2 Predictive performance measures (pe is the prediction error in per cent, n is the number of measurements per patient, pei is the i-th prediction error and me is the mean prediction error; CA,p and CA,m are the predicted and the measured alveolar concentrations of enflurane)

 
Friedman’s analysis of variance was used to analyse the differences in the predictive performance measures across the four model versions. If the Friedman analysis revealed a difference for a particular performance measure, post hoc analysis using sign tests for paired data were done to further evaluate the differences between the model versions.14 Differences yielding P<0.05 were considered significant.


    Results
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
The characteristics of the 62 adult patients (45 males) are listed in Table 3. Details of the closed-circuit conditions (Table 4) show that a total of 438 ml of liquid enflurane (450 injections) was used to provide more than 63 h of anaesthesia, during which 23 000 values of end-expired enflurane concentrations were recorded. Figure 017F3 shows the average values of the measured and calculated cardiac output data per patient. Although the group means of the measured (5.28 (SD 1.25) litre min–1) and the calculated (5.17 (0.66) litre min–1) cardiac output values were very similar, the range was more dispersed for the measured (2.91–8.03 litre min–1) compared with the calculated (3.76–6.65 litre min–1) cardiac output data. The trend of the measured cardiac output values throughout the anaesthetic procedures can be appreciated from Figure 017F4.


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Table 3 Anthropometric patient characteristics (n=62)
 

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Table 4 Details of the closed-circuit conditions (n=62)
 


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Fig 3 Scattergram of the cardiac output values: that is the calculated vs the mean measured cardiac output (l min–1) per patient. The triangles and thick lines on the abscissas and ordinates, represent the group mean cardiac output and SD, respectively. The coefficient of variation was 13% for the calculated vs 24% for the measured cardiac output value. Both methods correlate moderately well (R2=0.064).

 


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Fig 4 The group means cardiac output values (litre min–1) are plotted over time (in blocks of 5 min). The mean calculated ({square}, SD dotted line) values of the cardiac output prove to be a good average of the mean measured (•, SD bars) cardiac output values throughout the different stages of routine surgical anaesthesia.

 
The results of the three predictive performance measures (the group rmse, bias and scatter) for the four model versions are summarized in Table 5. There were no statistically significant differences across the four group rmses. The total error budget (rmse) was mainly the result of variations of the prediction errors around their mean (the scatter) rather than the result of the systematic error component (the bias). There was a statistically significant difference across the group biases of the four versions (P<0.0001). This difference is mainly determined by the differences between the model versions that implemented age-related solubility coefficients (C’ and E’) vs the versions that used standard solubility coefficients (C and E). However, there was no significant difference for the biases of the versions that used calculated cardiac output values (C and C’) vs the versions that used measured cardiac output data (E and E’). The rank order for the magnitude of the group biases was E>C>E’>=C’. Similar results were found for the group scatters: the age-related versions (C’ and E’) performed significantly though only slightly better (i.e. a statistically smaller scatter) compared with their non-age-related counterparts (C and E).


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Table 5 Predictive performance measures of the different model versions (mean (SD)). *Friedman two-way analysis of variance; {dagger}statistically significant different vs non-accent counterparts (sign test for paired data); {ddagger}statistically significant different vs version C (sign test for paired data)
 

    Discussion
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
In this study, we assessed the effect of a further individualization and subject-specific stratification of the model input by identifying and using individual patient factors given in the Fick formula. The predictive performance of a physiological model for closed-circuit anaesthesia is improved by incorporating age-related solubility coefficients instead of the solubility coefficients reported for a standard human. In contrast, model-based predictions of end-expired enflurane concentrations were not better if fixed calculated cardiac output value was replaced with continuous measured cardiac output data. Our results suggest that version C’ (using a fixed cardiac output and age-related solubility data) is the most appropriate model to predict the end-expired anaesthetic concentration of enflurane during closed-circuit anaesthesia, while aiming at a constant level of the end-expired anaesthetic concentration and using the bolus injection technique in a routine clinical setting.

Cardiac output
Measured cardiac output values did not improve predictions, but some aspects need to be discussed. Brody’s 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
 
The data acquisition was performed while the first and third author worked in the Institute for Anaesthesiology at the University of Nijmegen, The Netherlands. We would like to thank Prof. Dr Ir. A. G. L. Burm (University of Leiden, The Netherlands) for his valuable comments.



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    References
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
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