The effect of cardiac output changes on endâexpired volatile ...

Anaesthesia, 2001, 56, pages 1034±1040 ................................................................................................................................................................................................................................................

The effect of cardiac output changes on end-expired volatile anaesthetic concentrations ± a theoretical study R. R. Kennedy1 and A. B. Baker2 1 Clinical Senior Lecturer & Consultant Anaesthetist, Department of Anaesthesia, The Christchurch School of Medicine, Christchurch, New Zealand 2 Nuffield Professor of Anaesthetics, University of Sydney, New South Wales, Australia Summary

Cardiac output is one of the major determinants of the rate of uptake, and therefore the end-expired concentration (FE 0 ) of volatile anaesthetic agents. The purpose of this theoretical study was to explore the effect of cardiac output changes on FE 0 for a range of volatile anaesthetics. A multicompartment model of anaesthetic uptake and distribution which produces constant values of FE 0 was used. The minimum detectable change in cardiac output was determined for a variety of anaesthetic agents for four patterns of cardiac output change. The effect of a step change in cardiac output from 5 to 10 l.min21 was also recorded. The smallest cardiac output changes (average 33%) were detected with isoflurane. As blood solubility increased or decreased, larger cardiac output changes were needed before they could be detected. With a large step change in cardiac output and with increasing solubility, the final change in FE 0 increased but the initial rate of change of FE 0 is decreased. A significant cardiac output change will produce a change in volatile anaesthetic uptake. An unexpected change in FE 0 should be considered as a possible signal of a sudden cardiac output change. The difference between agents may represent a balance between the amount of agent taken up and the size of the tissue `sink' for that agent. Keywords

Anaesthetics, volatile. Heart: cardiac output. Pharmacokinetics.

................................................................................................. Correspondence to: Dr R. R. Kennedy E-mail: [email protected] Accepted: 18 May 2001

Cardiac output is one of the major determinants of the rate of anaesthetic uptake. Recent work [1] has demonstrated that there are detectable changes in expired enflurane concentrations with changes in cardiac output but these changes could not be quantified. Modelling work [2] also suggests that quantitative estimates of cardiac output changes based on simple models are unlikely to be of value without other measurements, for example of helium or argon concentrations, which may not be practical during routine anaesthesia. The aim of this paper is to establish, in a theoretical model, the smallest cardiac output change that produces a detectable change in expired concentration of anaesthetic agents (FE 0 ) and to look at the effect of different anaesthetic agents on this relationship. A model of anaesthetic uptake and distribution is combined with a trend-detection algorithm to explore the ability of this algorithm to 1034

detect changes in cardiac output by observing changes in FE 0 . This model is used to investigate the size and type of change in cardiac output that can be detected. Method

This paper combines two models described previously. Anaesthetic uptake and distribution was modelled using a multiple-compartment model based on that described by Heffernan et al. [3]. In Heffernan et al.'s Model 1, cardiac output and ventilation remain constant at their initial values. In addition to several corrections and extensions to the model [4], including incorporation of the concentration effect, the model was modified to allow input of the following parameters: fresh gas flow rate into the circuit (constant for each run); initial and final cardiac output; time and type of cardiac output change (no change, an q 2001 Blackwell Science Ltd

Anaesthesia, 2001, 56, pages 1034±1040 R. R. Kennedy and A. B. Baker Volatile anaesthetics and cardiac output ................................................................................................................................................................................................................................................

Table 1 Values used for the distribution of tissue volume and cardiac output between the compartments of the model used, together

with blood/gas and tissue/blood partition coefficients for the anaesthetic agents studied Anaesthetic agent

Arterial blood Heart Brain Liver Kidney Muscle Fat Vessel-poor group Lung

Compartment volume; l

Compartment flow; %

0.28 1.43 3.91 0.32 30.25 12.84 7.14

3.7 12.3 24.5 21.4 10.5 4.7 6.9

Desflurane

Nitrous oxide

Sevoflurane

Isoflurane

Enflurane

Halothane

Methoxyflurane

0.42 1.29 1.3 1.4 1.0 2.0 27 1.5 1.5

0.47 0.87 1.13 1.06 0.93 0.86 3.0 1.4 1.0

0.69 1.78 1.7 0.8 1.2 3.1 48 1.5 1.5

1.5 1.3 1.5 2.4 2.3 1.5 63 2.0 1.9

1.9 1.2 1.6 1.6 2.0 1.6 37 1.4 1.3

2.4 2.9 2.7 2.5 1.45 2.5 65 2.3 2.0

11 1.2 2.0 2.5 2.3 1.6 76 1.2 2.3

abrupt step or a linear ramp change over 5 min); agent to be modelled; and rate at which the agent was to be added to the circuit. Other parameters of the model including the size of tissue compartments and relative blood flows were as described by Heffernan et al. [3]. In particular, functional residual capacity was set at 2.5 l, while total minute ventilation was 5 l.min21 with dead space ventilation 30% of the total. The breathing system volume was 6 l. Constant (controlled) ventilation was assumed. Table 1 lists the size of each compartment and the relative blood flow to each compartment. Heffernan et al.'s model [3] does not include blood pools or allow for transit time of blood. Instead, the total blood volume is distributed amongst the tissue compartments. The agents studied and the partition coefficients used are listed in Table 1. Partition coefficients for halothane, isoflurane, enflurane, methoxyflurane and nitrous oxide are those we have used previously [2]. Values for desflurane and sevoflurane are those used by Yasuda et al. [5] except for the heart [6], the vessel-poor group and lung values. Data were not found for the vessel-poor group/blood and lung tissue/blood partition coefficients for desflurane and sevoflurane. However, with both agents there is no discernible difference in the FE 0 when values for these `missing' partition coefficients are changed from 1 to 2, which are reasonable limits for these parameters. A value of 1.5 was therefore used for these two missing partition coefficients for both desflurane and sevoflurane. Heffernan et al. [3] used a value of 6.45 l for effective lung volume with halothane. In the present version, effective lung volume was calculated as: V eff FRC 1 0:5V t 1 V lt :ll/b 1 CBV:lb/g

1

where Veff effective lung volume; FRC functional residual capacity 2.5 l; Vt tidal volume 0.5 l; Vlt lung tissue volume 0.5 l; CBV central blood q 2001 Blackwell Science Ltd

volume 1.03 l; ll/b and lb/g lung/blood and blood/ gas partition coefficients, respectively, The primary output from this model was FE 0 . A small amount of random noise was added to FE 0 to simulate inaccuracy in measurement devices, using an algorithm for generating a normally distributed random variable [7]. The SD of the noise was set at 0.006% atm for all agents. The value for FE 0 at each iteration (0.1 min) was used as input for the trend-detection algorithm. A multiple cycle version of the Triggs Tracking Variable [8] was used to detect changes. Calculation of the Triggs Tracking Variable [9] involves a simple predictive model indicating when actual data deviate from the prediction. Values for the Triggs Tracking Variable are between 2 1 and 1 1 where 1 1 represents a 100% probability that the parameter being studied is increasing in value, 0 represents no change and 2 1 represents 100% certainty that the value is falling. A change was considered to be occurring when the absolute value of the Triggs Tracking Variable exceeded 0.93 on four consecutive cycles [8]. Values for the rate of delivery of anaesthetic vapour to the circuit followed the form suggested by Beatty et al. [10] which is a generalisation of the `square root of time model' used by Severinghaus [11] to describe the rate of nitrous oxide uptake and applied by Lowe and Ernst [12] to many other anaesthetics: Rate of delivery of vapour prime 1 unit t 2 b ml:min 2 1

2

where prime volume of vapour (ml) delivered at a constant rate over the first minute; unit unit dose (ml vapour) as described by Lowe and Ernst [12]; b negative exponent (in a closed circuit, b 0.5); t time (min). The amount to be added to the system was calculated for each 0.1-min cycle. The volatile agents were studied with a target FE 0 of 1%. Nitrous oxide was studied at 1035

R. R. Kennedy and A. B. Baker Volatile anaesthetics and cardiac output Anaesthesia, 2001, 56, pages 1034±1040 ................................................................................................................................................................................................................................................

Table 2 Parameters for the power-law equation describing the

rate at which anaesthetic agent was added to the circuit to maintain the desired target concentration from t 7 to t 45 min. As discussed in the text, vapour was administered at a rate of ùnit' t2exponent ml.min21 plus `prime' ml vapour administered in the first minute. The target concentration was 1% except for nitrous oxide, for which target concentrations of 1, 10 and 50% were studied. Fresh gas flow and initial cardiac output were 5 l.min21 in all simulations

Anaesthetic agent

Prime; ml vapour

Unit; ml vapour

Exponent

Desflurane Nitrous oxide (1%) Nitrous oxide (10%) Nitrous oxide (50%) Sevoflurane Isoflurane Enflurane Halothane Methoxyflurane

0 30 30 0 80 60 400 550 2800

72 70 680 3100 75 125 93 115 600

0.08 0.07 0.06 0.04 0.08 0.20 0.10 0.14 0.43

target concentrations of 1, 10 and 50%. Values for the prime, unit dose and exponent were found by trial and error to give FE 0 within 5% of the target from t 7 to t 45 min and with no change detected by Triggs Tracking Variable. Table 2 lists the parameters for delivery of agent to the circuit for each agent with a fresh gas flow of 5 l.min21 and an initial cardiac output of 5 l.min21. Each agent was then studied with all eight combinations of the following types of change: a rise or fall in cardiac output; a change occurring at 10 min or 30 min; and a step change or a linear-ramp change over 5 min. For each set of conditions the model was run for 45 min with the change in cardiac output increased in 0.5-l.min21 steps between runs to determine the minimum change that could be detected. In addition, isoflurane was studied for a range of initial cardiac outputs and fresh gas flow for all eight types of cardiac output change. Table 3 lists the initial conditions and the model parameters for each combination for isoflurane. To explore further the effect of a change in cardiac output, FE 0 was recorded for 40 min for each agent with the cardiac output constant at 5 l.min21 and then the simulation was repeated with a step change in cardiac output from 5 to 10 l.min21 made at 10 min. The difference in FE 0 at each time point and the maximum difference were recorded. All models were written in C and run on an Apple PowerMacintosh 7100 computer. Results

Table 4 lists the means of the smallest detectable cardiac output for each of the eight types of cardiac output 1036

Table 3 Parameters for the power-law equation to maintain a

constant end-expired concentration of 1 ^ 0.05% isoflurane from 7 to 40 min in the model for a range of initial cardiac outputs and fresh gas flows. Values for `prime', ùnit' and èxponent' were found by trial and error as described in the text Fresh gas flow; Cardiac output; Prime; Unit; l.min21 l.min21 ml vapour ml vapour Exponent 0.3 0.3 0.3 2 2 2 5 5 5 15 15 15

3 5 10 3 5 10 3 5 10 3 5 10

45 55 70 170 210 310 50 60 145 300 600 1200

55 65 80 58 65 75 100 125 145 260 280 315

0.45 0.43 0.40 0.20 0.20 0.20 0.15 0.20 0.22 0.10 0.11 0.12

change with the agents studied. With a ramp decrease at 30 min using desflurane or nitrous oxide, decreases in cardiac output to a negative value were required to produce a detectable change in this model. For ramp increases of nitrous oxide with a target concentration of 50%, a change from 5 to 20 l.min21 was not detectable in this model. Above a cardiac output of 20 l.min21 unstable oscillations were seen in the output values of the uptake model [4]. In these cases, the magnitude of the detectable change was taken as 15 l.min21. These values were included in the calculations of the means for each agent since to omit them would have biased the results in favour of those agents. Table 4 also lists the ratios of the various pairs of changes. These results suggest that step changes are easier to detect than ramp changes, changes at 30 min are harder to detect than those at 10 min and falls are easier to detect than rises. Based on these results, the ability to detect cardiac output changes in this model can be ranked as isoflurane . enflurane . halothane . methoxyflurane . sevoflurane . desflurane . nitrous oxide (10%) nitrous oxide (1%) . nitrous oxide (50%). Table 5 shows the effect of initial conditions on the magnitude of the cardiac output changes that can be detected using isoflurane. These results suggest that the size of change that can be detected is relatively unaffected by the initial fresh gas flow. As initial cardiac output increases, the size of cardiac output change needed before detection increases from approximately 1 l.min21 when the initial cardiac output was 3 l.min21 (33%) to 2.5 l.min21 when the initial cardiac output was 10 l.min21 (25%). The ratios between the various pairs of cardiac output changes with a range of initial conditions are similar to those in Table 4. q 2001 Blackwell Science Ltd


Table 4 Smallest detectable changes in cardiac output for each agent with fresh gas flow and initial cardiac output of 5 min

21

Mean of all eight cardiac output changes;

Mean of ratios of four pairs of cardiac output changes

Anaesthetic agent

l.min21

%

rise/fall

ramp/step

30 min/10 min

Desflurane Nitrous oxide (1%) Nitrous oxide (10%) Nitrous oxide (50%) Sevoflurane Isoflurane Enflurane Halothane Methoxyflurane Mean (SD)*

3.69 4.31 4.06 7.31 2.81 1.69 1.75 1.87 2.69 2.86 (1.06)

73.7 86.2 81.2 146 56.2 33.7 35.0 37.5 53.7 57.2 (21.2)

1.27 1.46 1.50 2.55 1.25 1.08 1.55 1.31 1.53 1.37 (0.17)

1.95 1.56 1.83 2.12 1.31 1.45 1.33 1.31 1.33 1.52 (0.24)

1.36 1.38 1.32 1.29 1.14 1.08 1.33 1.14 1.33 1.25 (0.12)

*Excluding nitrous oxide (50%).

Figure 1 shows the effect of a change in cardiac output from 5 to 10 l.min21 at 10 min. Agents with a higher solubility in blood show an increase in both the magnitude of the change in FE 0 and the time until this maximum occurs. The amount of change in FE 0 /target FE 0 one minute after the step change in cardiac output from 5 l.min21 to 10 l.min21 was taken as an index of the early rate of change. Figure 2 shows the change in the ratio FE 0 /target FE 0 (where target FE 0 is the expected FE 0 at a cardiac output of 5 l.min21) 1 min after the cardiac output change and also the maximum value for this ratio. Figure 2 demonstrates that the maximum change in FE 0 /target FE 0 increases as solubility in blood increases. The change seen at 1 min can be ranked as isoflurane

. halothane . enflurane . sevoflurane . desflurane . N2O (1%) . N2O (10%) . methoxyflurane . N2O (50%). This ranking is similar to the ranking in ability to detect cardiac output changes seen with this model. Discussion

Continuous or regular measurement of cardiac output would be a very useful monitor during routine anaesthesia. Invasive methods of measuring cardiac output have significant risks and unfortunately results with noninvasive methods have been variable. Recent observations [1] suggest that changes in enflurane concentration are at least as useful as changes in FE 0 co2 at detecting changes in cardiac output. A previous model also suggested that

Table 5 Smallest detectable changes in cardiac output for isoflurane only, with various values for fresh gas flow and initial cardiac

output

Fresh gas flow; l.min21

Initial cardiac output; l.min21

0.3 0.3 0.3 2 2 2 5 5 5 15 15 15 Mean (SD)

3 5 10 3 5 10 3 5 10 3 5 10

q 2001 Blackwell Science Ltd

Mean of all eight cardiac output changes

Mean of ratios of four pairs of cardiac output changes

l.min21

%

rise/fall

ramp/step

30 min/10 min

1.0 1.37 2.19 1.12 1.50 2.37 0.94 1.69 2.62 1.06 1.62 2.56 1.67 (0.62)

33.3 27.5 21.9 37.5 30.0 23.7 31.2 33.7 26.2 35.4 32.5 25.6 29.9 (4.89)

1.29 1.44 1.06 1.25 1.40 1.24 0.88 1.08 1.47 1.12 1.36 1.33 1.24 (0.18)

1.67 1.20 1.33 1.57 1.67 1.38 2.00 1.45 1.62 1.43 1.36 1.47 1.51 (0.21)

1.29 1.00 1.33 1.25 1.00 1.24 1.50 1.08 1.47 1.43 1.36 1.47 1.28 (0.18)

1037


21 to 10 l.min21 for a variety of agents with a fresh gas flow of 5 l.min21. Target FE 0 is the expected FE 0 at a cardiac output of 5 l.min21. Where the target value was 1%, values equate to volume percentage change in FE 0 . Isoflurane A; enflurane S; halothane W; methoxyflurane K; sevoflurane outline crosses; desflurane linear cross; N2O (1%) B; N2O (10%) X; N2O (50%) O.

Figure 1 Change in the FE 0 /target FE 0 ratio resulting from a step change in cardiac output from 5 l.min

changes in enflurane concentration may be more sensitive to changes in cardiac output than other gases [2]. The aim of this study was to determine the magnitude of cardiac output change that produces a detectable change in FE 0 . Table 4 shows that cardiac output changes of 30±40% produce a detectable change with isoflurane, enflurane or halothane. Sensitivity to cardiac output increases with a progression from low (nitrous oxide) to moderate

(isoflurane) solubility in blood. As solubility increases (from isoflurane to methoxyflurane), the ability to detect cardiac output changes deteriorates. Figure 2 shows that following an increase in cardiac output, the largest 1-min change is seen with isoflurane. The largest eventual change is seen with methoxyflurane, the most soluble agent studied, but this does not occur until more than 40 min after the change in cardiac output. These results suggest that the ability of an agent to detect a cardiac

Figure 2 Change in the FE 0 /target FE 0

ratio at 1 min (solid) and the maximum change (clear) produced by a step change in cardiac output from 5 to 10 l.min21 for several agents (Des desflurane; Sev sevoflurane; Iso isoflurane; Enf enflurane; Hal halothane; Meth methoxyflurane). The target FE 0 (the expected FE 0 at a cardiac output of 5 l.min21) was 1% for volatile agents while nitrous oxide was studied at a target of 1, 10 or 50% as shown in brackets. Where the target value was 1%, values equate to volume percentage change in FE 0 . 1038



output change with this model is a balance between the absolute magnitude of the change in FE', which increases with increasing lb/g, and the proportion of change in FE 0 completed early (say in 1 min) which decreases as lb/g increases, as shown in Fig. 2. The Triggs Tracking Variable detects the rate of change rather than the magnitude of the change. Smaller cardiac output changes will be detected with an agent that produces large early changes in FE 0 than with an agent producing a lower initial rate of change regardless of the size of the final change in FE 0 . In a clinical setting, the existence of a change is more important and useful than the eventual size of the change. Information on changes occurring in the last few minutes is much more useful than data on changes 30±40 min previously. In addition, many other factors may affect the relationship between cardiac output and expired anaesthetic concentration, making data more than a few minutes old less useful. To be detected, a larger cardiac output change is needed at 30 min than at 10 min (Tables 4 and 5). With increasing time the better perfused tissues become saturated. A change in cardiac output, and hence the rate of delivery to the tissues, has less effect on well-perfused tissues and on the concentration in the venous blood draining these tissues. Because well-perfused tissues receive the bulk of cardiac output, these tissues will have a shorter time constant and the effect of a given cardiac output change on expired gas concentration will decrease with increasing time. In Table 4 and Figs 1 and 2, the results for nitrous oxide with target concentrations of 1 and 10% are similar, while a target concentration of 50% is much less sensitive to cardiac output changes. It may be that with a high target concentration of a poorly soluble agent the body will be much nearer to saturation with the agent at the time the cardiac output change occurs. Therefore although the mass of agent being carried to the various compartments will change, the effect on tissue concentration, mixed venous concentration and alveolar concentration will be reduced. This is a similar mechanism to that suggested above to explain the difference between a change at 30 min and a change at 10 min. The concentration effect [13], which has been included in the gas uptake model used in this paper, will also accelerate uptake in the early stages. Results in Table 5 demonstrate that in this model, the effect of cardiac output changes of 20±40% are detectable with isoflurane. Smaller changes in cardiac output can be detected when the change occurs as a step rather than as a 5-min ramp (Tables 4 and 5). This is not surprising as the more rapid cardiac output change will produce a faster change in uptake and hence in FE 0 . The more rapid rate of change of FE 0 will be detected more readily with the Triggs Tracking Variable than a slower change. q 2001 Blackwell Science Ltd

In our previous model [2], enflurane detected smaller cardiac output changes than isoflurane. This result is in contrast to that seen with the current model. In our previous model, only blood and lung tissues and the time period before recirculation (15 s) were considered, while the present model is more comprehensive, being affected by uptake into multiple compartments over a much longer time period. The lung tissue/gas partition coefficient for enflurane is less than that for isoflurane but the total body uptake of isoflurane is less than that of enflurane. This difference between the agents, combined with the effect of the changes in the model, probably explains the difference in the results seen between the models. The difference between isoflurane and enflurane in the ability to detect cardiac output changes is small in both models, with enflurane slightly more sensitive to a decrease, and isoflurane more sensitive to an increase in cardiac output. Both isoflurane and enflurane are better at detecting these changes than any other agent tested in either model. Clinical studies [1, 14] have also failed to demonstrate a qualitative relationship between cardiac output and the uptake of volatile anaesthetics. However, these studies do suggest that changing trends in uptake or end-expired values for an individual patient may give an indication of changes in cardiac output. This approach supports the results of both our previous study [2] and the current study. Our results suggest that if a change in FE 0 of a volatile anaesthetic agent occurs, one possible cause may be an abrupt change in cardiac output. Of the agents studied, isoflurane is the most sensitive, but there are only small differences between isoflurane, enflurane and halothane. These results confirm our previous finding [2] that the best volatile respiratory agents to detect changes in cardiac output would have blood/gas solubilities around 1.5±2.5. The ability of an agent to detect these changes is primarily determined by blood solubility. A low solubility produces a rapid rate of rise which can be detected by the Triggs Tracking Variable while a high solubility increases the magnitude of the change in FE 0 . The optimum point represents a balance between these effects. References 1 Watt SJ, Cook LB, Ohri S, Lockwood GG. The relationship between anaesthetic uptake and cardiac output. Anaesthesia 1996; 51: 24±8. 2 Kennedy RR, Baker AB. Solubility characteristics of the ideal agent for measurement of cardiac output by soluble gas uptake methods. British Journal of Anaesthesia 1993; 71: 398±402. 3 Heffernan PB, Gibbs JM, McKinnon AE. Teaching halothane uptake and distribution. A computer simulation program. Anaesthesia 1982; 37: 9±17. 1039


4 Kennedy RR. Modelling Change in Anaesthesia. PhD Thesis, University of Otago, 1996. 5 Yasuda N, Targ AG, Eger EI 2nd. Solubility of I-653, sevoflurane, isoflurane and halothane in human tissues. Anesthesia and Analgesia 1989; 69: 370±3. 6 Jones RM. Desflurane and sevoflurane: inhalational anaesthetics for this decade. British Journal of Anaesthesia 1990; 65: 527±36. 7 Kennedy RR, Baker AB. Analysis of uncertainty in theoretical methods of cardiac output measurement using the `Monte Carlo' technique. British Journal of Anaesthesia 1993; 71: 403±9. 8 Kennedy RR. A modified `Triggs Tracking Variable' as an advisory alarm during anaesthesia. International Journal of Clinical Monitoring and Computing, 1995; 12: 197±204. 9 Lewis CD. Statistical monitoring techniques. Medical and Biological Engineering 1971; 9: 315±23.

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10 Beatty PCW, Kay B, Healy TEJ. Measurement of the rates of nitrous oxide uptake and nitrogen excretion in man. British Journal of Anaesthesia 1984; 56: 223±32. 11 Severinghaus JW. The rate of uptake of nitrous oxide in man. Journal of Clinical Investigation 1954; 33: 1183±9. 12 Lowe HJ, Ernst EA. The Qualitative Practice of Anaesthesia: Use of Closed Circuit. London: Williams & Wilkins Baltimore, 1981. 13 Epstein RM, Rackow H, Salinitre E, Wolf GL. Influence of the concentration effect on the uptake of anesthetic mixtures: the second gas effect. Anesthesiology 1964; 25: 364±71. 14 Myles PS, Storer R, Millar C. Haemodynamic Effects and uptake of enflurane in patients undergoing cardiac surgery. Good versus poor myocardial function. Anaesthesia and Intensive Care 1992; 20: 21±7.


The effect of cardiac output changes on endâexpired volatile ...

The effect of cardiac output changes on endâexpired volatile ...

The effect of cardiac output changes on endâexpired volatile ...

The effect of cardiac output changes on endâexpired volatile ...