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Non-invasive cardiac output measurement using a fast mixing box to measure carbon dioxide elimination.

SUMMARY

This study investigated the accuracy of a new technique for measuring cardiac output using the derivative Fick principle based on the ratio of change in the partial pressures of end-tidal and mixed expired carbon dioxide produced by short periods of partial rebreathing.

A prospective clinical study involving 24 patients following cardiopulmonary bypass for coronary artery bypass grafting or valvular surgery was undertaken in the intensive care unit of a university-affiliated hospital.

Haemodynamic measurements were performed after admission to the intensive care unit. Cardiac output was measured simultaneously by bolus pulmonary artery thermodilution and by a non- invasive carbon dioxide partial rebreathing technique.

Cardiac output measurement using the new technique demonstrated a significant but consistent underestimate, with a bias of -0.60[+ or -]0.87 l/min.

This new adaptation of the partial rebreathing technique is reliable in measuring cardiac output in postoperative patients. Reasons for the consistent discrepancy between thermodilution and partial rebreathing techniques are discussed.

Key Words: cardiac output, carbon dioxide, partial rebreathing, haemodynamics, thermodilution

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Cardiac output (CO) monitoring is an important component in the haemodynamic management of critically ill patients. The pulmonary artery catheter (PAC) has been the mainstay of flow monitoring since it was introduced in the 1970s. Potential life-threatening complications, an error rate of up to 10% particularly in low-flow states and evidence that the use of PAC fails to decrease and indeed may even increase mortality rates, have led to concerns about its use (1). With the current emphasis on goal-directed therapy there is heightened interest in the various techniques that have been described for accurate, continuous but less invasive monitoring of the cardiac output (2,3).

Continuous cardiac output monitoring by pulse-contour analysis is now a well established technique which uses algorithms based on analysis of the arterial waveform to measure the stroke volume. These algorithms incorporate elements of resistance, capacitance and characteristic impedance estimated from patient gender, height, weight and age. The signal is further refined by calibration of mean cardiac output using an indicator dilution technique; transpulmonary lithium dilution in the case of PulseCo (LiDCO Ltd, Cambridge, UK) or transpulmonary thermodilution in the PiCCO monitor (Pulsion Medical Systems, Munich, Germany). However, both these systems require central venous and arterial catheters, and are problematic in patients with arrhythmias and poorly defined arterial waveforms.

A non-invasive technique for measuring cardiac output has been proposed using a modified Fick principle applied to carbon dioxide (Appendix A) (4). In brief, carbon dioxide (C[O.sub.2]) elimination from the body equals the delivery of C[O.sub.2] to the lung minus the C[O.sub.2] carried away from the lung:

VC[O.sub.2]=Qp.([C.sub.v]C[O.sub.2]-[C.sub.a]C[O.sub.2])

where VC[O.sub.2]=carbon dioxide elimination in ml/min, Qp=pulmonary capillary blood flow (l/min), [C.sub.v]C[O.sub.2] and [C.sub.a]C[O.sub.2]=venous and arterial content of carbon dioxide (ml/l). Briefly decreasing C[O.sub.2] elimination, by a period of rebreathing, leads to changes in [C.sub.a]C[O.sub.2], while [C.sub.v]C[O.sub.2] remains stable.

We can estimate [DELTA][C.sub.a]C[O.sub.2] from the [DELTA][P.sub.a]C[O.sub.2] using the local slope (S) of the C[O.sub.2] dissociation curve (5), and by equating [DELTA][P.sub.a]C[O.sub.2] with the more easily measured change in partial pressure of end-tidal C[O.sub.2] (PetC[O.sub.2])

Qp = [DELTA]VC[O.sub.2]/S x [DELTA]PetC[O.sub.2]

as described in detail in Appendix A.

To estimate cardiac output we therefore need to measure VC[O.sub.2] and PetC[O.sub.2] during two steady state periods, before and after the application of deadspace. These changes in VC[O.sub.2] and PetC[O.sub.2] only reflect blood flow that participates in gas exchange, and this will lead to an underestimate of cardiac output if a significant intrapulmonary shunt exists. Estimates of shunt fraction can be made non-invasively from iso-shunt plots using pulse oximetry and inspired oxygen fraction (Fi[O.sub.2]) readings (6), or by using the shunt formula (Qs/Qt=([C.sub.c][O.sub.2]-[C.sub.a][O.sub.2])/ ([C.sub.c][O.sub.2]-[C.sub.v][O.sub.2])%), but the requirement for mixed venous oxygen content measurements requires invasive access.

The rebreathing technique has been developed commercially in the NIC[O.sub.2] monitor (Novametrix Medical Systems Inc, Wallingford, CT, USA), which includes a non-invasively derived shunt correction, and the DAVID monitor (MedServ, Leipzig, Germany). The NIC[O.sub.2] device consists of an integrated infra-red C[O.sub.2] sensor and flow sensor allowing cross-multiplication of instantaneous airway flow and PC[O.sub.2] to calculate [DELTA]VC[O.sub.2]. A disposable loop is introduced into the ventilator circuit to add additional deadspace for rebreathing. Continuous pulse oximeter saturation readings are used to estimate shunt fraction by an undisclosed algorithm (7). Several studies have been published comparing these monitors with standard cardiac output measurements by pulmonary artery thermodilution techniques with varying results (8-10).

Our project aims to assess an adaptation of the technique for measuring cardiac output using the derivative Fick principle. In this new technique, C[O.sub.2] elimination is calculated from the partial pressure of mixed expired C[O.sub.2] (PmxC[O.sub.2]) multiplied by the minute volume (MV) recorded from the ventilator. The PmxC[O.sub.2] was measured using a fast mixing box and side-stream capnography, avoiding the complex cross-multiplication and integration of in-line flow and PetC[O.sub.2] measurements required in other software. The technique has the advantage of using more widely available side-stream capnography, while avoiding the difficulties associated with the varying phase lag between the flow and pC[O.sub.2] measurements. By alternating the sampling site, using a solenoid valve, we could use a single capnograph to measure both PmxC[O.sub.2] and PetC[O.sub.2], reducing the impact of errors in measurement. Additional deadspace for rebreathing is applied by redirecting the inspiratory flow down a portion of the expiratory circuit rather than introducing an additional loop into the circuit.

PATIENTS AND METHODS

After approval by the institutional review board and written informed consent, 24 patients who had undergone cardiac surgery for coronary artery bypass or valvular surgery were included. Patients in whom minor elevations of [P.sub.a]C[O.sub.2] were undesirable due to pulmonary hypertension, or with significant lung disease in whom PetC[O.sub.2] may not represent [P.sub.a]C[O.sub.2] were excluded.

All patients had 7.5-F flow-directed thermistor-tipped pulmonary artery catheters (Edward Lifesciences Irvine Ca USA) in situ. Arterial pressure monitoring was standard in all patients from either radial or femoral catheters. All patients were endotracheally intubated and mechanically ventilated in a volume controlled mode on a Drager Evita 4 ventilator (Drager Medical AG & Co KGaA, Lubeck, Germany). Patients received morphine infusions for analgesia and were sedated with propofol infusions (1 to 3 mg/kg/h).

A fast mixing box was connected to the expiratory flow port of the ventilator and attached to a side-stream capnograph (Datex Normocap 200, Helsinki, Finland). Both the end-tidal and mixed expired partial pressure of carbon dioxide were measured using a single capnograph with a software controlled solenoid valve alternating sampling flow between the two sites. A locally constructed electromagnetic rebreathing valve was introduced into the inspiratory limb of the ventilator circuit allowing inspiratory flow to be diverted down a segment of the expiratory limb (Figure 1). The length of this segment was adjusted to give an estimated rise in PetC[O.sub.2] of 5 to 6 mmHg during rebreathing (Appendix C). If the predicted rebreathing volume led to a smaller or larger rise than desired, the volume of the rebreathing segment was adjusted.

Using a one-litre capacity mixing box allowed the PmxC[O.sub.2] to reach the new equilibrium within the period of time allowed for rebreathing as long as the minute volume exceeded 5 l/min, and has been shown to provide efficient gas mixing and be accurate in the measurement of mixed expired gases in ventilated patients (12).

[FIGURE 1 OMITTED]

Cardiac output measurement by thermodilution using a PAC (COtd)

Standard pulmonary artery thermodilution cardiac output measurements were carried out using three 10 ml bolus injections of 5% glucose solution at room temperature. The averaged values for the three injections were used to determine each cardiac output.

Each time a COtd measurement was taken the most recent cardiac output measured by the rebreathing technique was documented. Paired recordings were ceased when the end-tidal C[O.sub.2] was no longer stable due to spontaneous breathing.

Cardiac output measured by partial rebreathing technique (Coc[o.sub.2])

After a period of stabilisation, carbon dioxide evolution was calculated, by recording the PmxC[O.sub.2] and minute volume. The sampling valve was cycled to the proximal airway and PetC[O.sub.2] recorded. The rebreathing valve was activated to allow rebreathing of deadspace gas and PetC[O.sub.2] monitored until a new steady state was reached, as defined by a constant PetC[O.sub.2] for three breaths (Standard Deviation <0.6 mmHg). The time taken to reach the new steady state varied slightly between patients, usually being 30 to 40 seconds. Patients with a lower cardiac output will take longer to achieve a new steady state. This value was recorded and the sampling valve switched to the mixing box to record the new PmxC[O.sub.2] at equilibrium. The rebreathing valve was then returned to the original non-rebreathing position. Readings were taken at intervals of not less than five minutes.

Haemoglobin (Hb) concentration and arterial oxygen and carbon dioxide partial pressure ([P.sub.a][O.sub.2] and [P.sub.a][CO.sub.2]) were measured by a calibrated blood gas analyser (ABL 700 series, Radiometer, Copenhagen, Denmark). Fi[O.sub.2] and minute volume measurements were recorded from the ventilator. The slope of the C[O.sub.2] dissociation curve was determined at a PC[O.sub.2] midway between the PetC[O.sub.2] measured during the non-rebreathing and rebreathing states with a correction factor of 4 mmHg for the [P.sub.a]C[O.sub.2]-PetC[O.sub.2] difference.

Shunted blood flow was calculated, as in Appendix B, and addition of shunt fraction (Qs/Qt) to pulmonary capillary blood flow was used to calculate cardiac output.

Statistical analyses

Correlation between methods was assessed by linear regression. A Bland-Altman analysis was used to assess the bias (mean difference) and precision (standard deviation (SD) of mean difference) of the technique (12). Limits of agreement were calculated as bias [+ or -] 2 SD.

RESULTS

Twenty-four patients who had undergone cardiac surgery were studied. Patient characteristics are given in Table 1. All patients tolerated the rebreathing period.

A total of 113 sets of paired cardiac output measurements were available for comparison. Cardiac outputs ranged from 1.98 to 6.99 l/min using Coc[o.sub.2] and from 2.5 to 9.4 l/min using the thermodilution technique. Figure 2 shows the correlation between cardiac output measured by thermodilution and rebreathing techniques. Correlation coefficient R=0.752, R2=0.565. Concordance analysis showed the bias between paired values (Coc[o.sub.2]-Cotd) was -0.60 l/min with a precision of 0.86 l/min. The limits of agreement were 1.11 and -2.32 l/min (Figure 3).

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

In the subset of patients with a cardiac output in the low to moderate range (less than 6.5 l/min) the bias and precision were -0.52[+ or -]0.75 l/min.

DISCUSSION

The results of this study show a consistent underestimation of cardiac output by the partial rebreathing technique when compared with values obtained by pulmonary artery thermodilution. Other investigators have found similar results in patients post cardiopulmonary bypass (CPB). Using the NIC[O.sub.2] monitor Nilsson et al recorded a bias and precision of -0.16 and 0.9 l/min. In common with other studies, our results show a tendency for greater underestimation of the cardiac output by the rebreathing technique as the output increases (8-10,13).

Although COtd remains the most widely used method for cardiac output measurement in intensive care units, results can be affected by injection technique, respiratory variation in pulmonary artery blood temperature and changes in injectate temperature, particularly in catheters floated via the femoral vein. Concerns about its accuracy have led to studies comparing it with other more accurate techniques which showed a tendency to over-estimate CO when compared with ultrasound transit-time flowmetry of the ascending aorta using an ultrasonic flow probe (14) and dye dilution with indocyanine green (15). Some of the apparent error in our results may be explained by the overestimate of flow by thermodilution.

When two methods are compared, if each technique has a poor coefficient of repeatability, the likelihood of agreement between methods is limited. Assessing the repeatability of measurements made by thermodilution and rebreathing methods, Nilsson found that both techniques showed acceptable results with coefficients of repeatability of 0.35 l/min for thermodilution and 0.6 l/min for the partial rebreathing technique (9).

Three main areas for error are inherent in measurement of PCBF from carbon dioxide changes. Using the modified Fick principle we assume that 1) cardiac output is not altered by the process of rebreathing, 2) no recirculation occurs during the rebreathing period and hence mixed venous C[O.sub.2] content remains constant and 3) pulmonary deadspace remains constant allowing us to substitute PetC[O.sub.2] for [P.sub.a]C[O.sub.2].

A study looking at changes in haemodynamics showed that during the period of rebreathing, which leads to a small rise (in the order of 5 to 6 mmHg) in [P.sub.a]C[O.sub.2], there was no significant change in cardiac output, heart rate, systemic and pulmonary artery pressures (16).

An important concept in the differential modification of the Fick principle is that [C.sub.v]C[O.sub.2] remains constant. Early studies showed a rise in [P.sub.v]C[O.sub.2] of less than 1.5 mmHg when the duration of rebreathing was shorter than 30 seconds (17). However, the NIC[O.sub.2] device has a 50 second rebreathing period and increases of 2.5% in [P.sub.v]C[O.sub.2] have been measured while [P.sub.a]C[O.sub.2] rose by 9.8% (9). Even this small rise with its associated increase in [C.sub.v]C[O.sub.2] may contribute to the rise in arterial C[O.sub.2] content and lead to underestimate in CO. Nilsson in a similar study showed a rise of only 1.2% (0.5 mmHg) with negligible effect on CO estimation (9). As the cardiac output increases, there is a reduction in recirculation time, which may explain the greater underestimate of cardiac output by rebreathing methods at higher flow rates, as has been documented in nearly all studies using NIC[O.sub.2] (8,18). During rebreathing, a new steady state for PetC[O.sub.2] is achieved more rapidly in patients with a higher cardiac output, so by reducing the period of rebreathing it is possible to decrease the effect of recirculation.

The original application of the Fick principle for non-invasive CO measurement substitutes changes in PetC[O.sub.2] for [P.sub.a]C[O.sub.2] in estimating the change in [C.sub.a]C[O.sub.2]. Due to the slight upward convexity of the C[O.sub.2] dissociation curve, the change in C[O.sub.2] content will be less for a given change in PC[O.sub.2] at higher initial PC[O.sub.2] values (Figure 4). Due to the effect of deadspace, PetC[O.sub.2] is less than [P.sub.a]C[O.sub.2] leading to an overestimate in the change in [C.sub.a]C[O.sub.2]. This causes cardiac output measurement to be underestimated, an effect which becomes more significant as the degree of deadspace, and PetC[O.sub.2] to [P.sub.a]C[O.sub.2] difference increases. The use of low tidal volume ventilation with a higher deadspace/tidal volume ratio increases the tendency to underestimate cardiac output (19). Modification of the technique using a measured [P.sub.a]C[O.sub.2] rather than PetC[O.sub.2] will compensate for increased deadspace, but requires more invasive monitoring. NIC[O.sub.2] measurements using both measured and fixed differences between PetC[O.sub.2] and [P.sub.a]C[O.sub.2] have been compared. A standard difference of 0.53 kPa (4 mmHg) between [P.sub.a]C[O.sub.2] and PetC[O.sub.2] has been suggested, although the measured differences in patients post CPB in a recent study was higher at 6.5 mmHg (19). Using the measured difference a bias and precision of 0.12 and 0.57 l/min was found comparing NIC[O.sub.2] to COtd readings, while a fixed difference of 4 mmHg produced similar results with a bias of -0.18 and 0.57 l/min (20). In our study the mean [P.sub.a]C[O.sub.2] to PetC[O.sub.2] difference was 3.8 mmHg and we used a fixed value of 4 mmHg as a correction factor in the calculation of our results to compensate for this.

[FIGURE 4 OMITTED]

The algorithm also assumes that the difference between [P.sub.a]C[O.sub.2] to PetC[O.sub.2] remains constant throughout non-rebreathing and rebreathing periods. However, Gama et al showed that the difference decreases proportionally with VC[O.sub.2] (18). The change in PetC[O.sub.2] is therefore greater than the change in [P.sub.a]C[O.sub.2] leading to an inaccuracy in the estimated change in C[O.sub.2] content and a further source for the underestimation of cardiac output.

In addition, calculation of total cardiac output depends upon an estimate of shunt fraction. This can be made non-invasively from iso-shunt diagrams using Sp[O.sub.2] and Fi[O.sub.2]. This requires the assumption of a standard arterio-venous oxygen content difference, usually taken to be 50 ml/l and haemoglobin concentration (10 to 14 g/dl), both of which may be inaccurate in critically ill patients. Other factors that alter the P50 of the haemoglobin dissociation curve, such as temperature and acid-base status, will also effect [C.sub.a][O.sub.2] estimation if Pa[O.sub.2] is used in place of Sa[O.sub.2]. Odenstadt et al measured the shunt fraction from arterial and mixed venous gas analysis using the standard shunt equation (Qs/Qt=([C.sub.c][O.sub.2]-[C.sub.a][O.sub.2])/ ([C.sub.c][O.sub.2]-[C.sub.v][O.sub.2]), and compared their results with the non-invasive estimates from an iso-shunt diagram. The non-invasive results tended to give a lower shunt fraction (1 to 34%, mean 11%) than those calculated using the shunt equation (10 to 53%, mean 22%). The discrepancy appeared to be largely due to the error in the standard arterio-venous [O.sub.2] difference with a mean of 29 ml/l (10 to 64 ml/l) measured in this set of patients (8). We used the measured VC[O.sub.2] (PmxC[O.sub.2]x MV) to calculate V[O.sub.2] for the estimate of shunt fraction in our trial in an attempt to circumvent this source of error. In this calculation we assumed a respiratory quotient (RQ) of 0.8. Variation in RQ may occur during periods of catabolism and with dietary composition, usually ranging from 0.7 to 1.0. This may lead to small errors in the calculation of shunt fraction. In a small series of patients post cardiotomy RQ ranged from 0.75 to 0.79 (21). In patients with no significant shunt a change in RQ from 0.8 to 1 would change the calculated cardiac output by <1%. We also used the pulmonary capillary blood flow as our best estimate of cardiac output in the calculation of [C.sub.v][O.sub.2]. This will lead to an increasing error in the final estimate of cardiac output as the degree of shunt increases. Rocco et al studied the reliability of the NIC[O.sub.2] monitor in two sets of six patients with low (<20%) and high (>35%) shunt fractions as measured by the shunt equation. In patients with large intrapulmonary shunts there was a greater underestimation of CO using the non-invasive technique. In general, these patients exhibited a hyperdynamic state and loss of hypoxic pulmonary vasodilatation may be the cause of the increased shunt (13). This may partly explain the underestimation commonly seen in patients with high cardiac outputs.

The early postoperative period following CPB is associated with marked haemodynamic and respiratory changes. A large increase in pulmonary deadspace ventilation and intrapulmonary shunts is frequently seen, due to intraoperative lung collapse and the use of glyceryl trinitrate infusion which inhibits pulmonary hypoxic vasoconstriction. Significant changes in haemoglobin concentration due to volume shifts, bleeding and transfusion of pump blood will also affect cardiac output measurement using the derivative Fick principle as the haemoglobin concentration is incorporated into both the calculation of carbon dioxide content and of shunt blood flow. A change in haemoglobin concentration of 3 g/dl will give a 10% change in cardiac output calculation necessitating frequent measurement of haemoglobin to adjust for changes. In keeping with the non-invasive nature of the monitor most software packages assume a standard haemoglobin concentration of 14 g/dl. Since most unstable intensive care patients have blood gas analysis performed on a regular basis, and most analysers measure haemoglobin concentration, we inserted the measured value into our algorithm.

In summary, this new adaptation of the technique for measuring cardiac output produced reliable results using a partial rebreathing manoeuvre. The values obtained underestimate cardiac output measured by thermodilution and possible reasons for this have been discussed. The limitations of the technique are the requirement for stable tidal volumes to permit C[O.sub.2] elimination measurement, although other investigators have reported good results in patients sedated on pressure-support modes. The reliance on measurements from different sources, all with percentages of errors, leads to potential miscalculations. The accuracy of the capnograph we used is quoted by the manufacturers as having an accuracy of [+ or -] 1.5 mmHg and the minute volume measurement by the ventilator software has an error margin of [+ or -] 8%. Added to this, the need for a stable haemoglobin concentration, or failing this frequent analysis of blood gases which detracts from the non-invasive nature of the device, may limit the use of the device as a continuous monitor. Unstable patients are likely to have invasive arterial pressure monitoring, and the addition of blood gas analysis data is helpful in improving the accuracy of this technique.

APPENDIX A

Application of the modified Fick principle (4,10)

The Fick principle applied to carbon dioxide states that C[O.sub.2] elimination will equal the difference between C[O.sub.2] delivered to the lung and C[O.sub.2] carried away from the lung:

VC[O.sub.2]=Qp.([C.sub.v]C[O.sub.2]-[C.sub.a]C[O.sub.2]) [1]

And Qp= VC[O.sub.2]/[C.sub.v]C[O.sub.2]-[C.sub.a]C[O.sub.2]

where VC[O.sub.2]=carbon dioxide elimination in l/min, Qp=pulmonary capillary blood flow (l/min), [C.sub.v]C[O.sub.2] and [C.sub.a]C[O.sub.2]=venous and arterial content of carbon dioxide(ml/l).

Changes in C[O.sub.2] elimination rate will induce changes in [C.sub.v]C[O.sub.2] and [C.sub.a]C[O.sub.2]. Assuming cardiac output remains stable a new steady state will be reached such that:

Qp= VC[O.sub.2]'/[C.sub.v]C[O.sub.2]'-[C.sub.a]C[O.sub.2]' [3]

Differentiating equation [2] with respect to time, assuming Qp constant:

Qp= [DELTA]VC[O.sub.2]'/[DELTA][C.sub.v]C[O.sub.2]'-[DELTA][C.sub.a]C[O.sub.2]' [4]

A brief period of rebreathing reduces C[O.sub.2] elimination causing the [C.sub.a]C[O.sub.2] to rise to a new steady state and, as long as this period is short and recirculation does not occur, [C.sub.v]C[O.sub.2] will not change ([DELTA][C.sub.v]C[O.sub.2]=0). Hence:

Qp= -[DELTA]VC[O.sub.2]/-[DELTA][C.sub.a]C[O.sub.2] [5]

Using the local slope of the C[O.sub.2] dissociation curve (S) (5), relating the partial pressure of C[O.sub.2] (PC[O.sub.2]) to C[O.sub.2] content, [C.sub.a]C[O.sub.2] can be estimated from the more easily measured partial pressure of end-tidal C[O.sub.2] (PetC[O.sub.2]) hence:

Qp= [DELTA]VC[O.sub.2]/S x PetC[O.sub.2] [6]

where S=slope of the C[O.sub.2] dissociation curve ([delta][C.sub.a]C[O.sub.2]/[DELTA][P.sub.a]C[O.sub.2]) = (1.34[Hb] + 18.34)/(1 + 0.193 [P.sub.a]C[O.sub.2]) mlC[O.sub.2]/l.blood/mmHg, and [Hb]= haemoglobin in g/dl.

When substituting PetC[O.sub.2] for [P.sub.a]C[O.sub.2] in the equation for S, a correction factor for the end-tidal to arterial C[O.sub.2] difference due to deadspace is required. We used a set value of 4 mmHg as discussed in the paper.

VC[O.sub.2] can be estimated by measuring the partial pressure of mixed expired C[O.sub.2] (PmxC[O.sub.2]) in mmHg and minute volume (MV) in l/min:

VC[O.sub.2]= PmxC[O.sub.2]/Patm x MV x 1000 ml/min [7]

where Patm is the atmospheric pressure in mmHg. Combining equation 6 and 7:

Qp= [DELTA]PmxC[O.sub.2] x MV x 1000/S x Patm x [DELTA]PetC[O.sub.2] [8]

APPENDIX B

Shunt calculation

The standard shunt equation states that:

Qt.[C.sub.a][O.sub.2]=Qs.[C.sub.v][O.sub.2]+Qp.[C.sub.c][O.sub.2] [9]

where Qt=cardiac output, Qs=shunt blood flow both in l/min. [C.sub.a][O.sub.2], [C.sub.v][O.sub.2], [C.sub.c][O.sub.2]=arterial, mixed venous and pulmonary capillary oxygen content in ml/l respectively.

This can be rearranged to give the shunt fraction:

Qs/Qt= [C.sub.c][O.sub.2]-[C.sub.a][O.sub.2]/[C.sub.c][O.sub.2]- [C.sub.v][O.sub.2] [10]

Using the alveolar gas equation we can estimate the PC[O.sub.2], SC[O.sub.2] and [C.sub.c][O.sub.2]:

Pc[O.sub.2]= Palv [O.sub.2]= ((Patm-P[H.sub.2]O) x Fi[O.sub.2])- ([P.sub.a]C[O.sub.2]/RQ) [11]

Palv=partial pressure of alveolar oxygen, Patm=atmospheric pressure, P[H.sub.2]O=water vapour pressure.

Using the oxyhaemoglobin dissociation curve we can equate Pc[O.sub.2] with Sc[O.sub.2] (22), and calculate [C.sub.c][O.sub.2] from the equation:

Cc[O.sub.2]=((1.34[Hb] x SC[O.sub.2]) [12] +(0.003 x PC[O.sub.2])) x 10 ml/l blood

where 1.34 equals the oxygen combining capacity of haemoglobin in ml/g (22).

Similarly if we measure [P.sub.a][O.sub.2] and [S.sub.a][O.sub.2] by arterial blood gas analysis we can calculate the arterial oxygen content:

[C.sub.a][O.sub.2]=((1.34[Hb] x [S.sub.a][O.sub.2]) [13] +(0.003 x [P.sub.a][O.sub.2])) x 10 ml/l blood

Assuming oxygen consumption (V[O.sub.2])=VC[O.sub.2]/RQ, where VC[O.sub.2]=PmxC[O.sub.2]/Patm x MV x 1000 ml/min as in [6] and RQ, the respiratory quotient =0.8, then we can use the reversed Fick technique:

V[O.sub.2]=Qt([C.sub.a][O.sub.2] -[C.sub.v][O.sub.2]) to calculate Cv[O.sub.2] [C.sub.v][O.sub.2]=[C.sub.a][O.sub.2]-V[O.sub.2]/Qt, [14]

By substituting Qp as measured above in [8] as our closest estimate of Qt, a small underestimation of shunt fraction is made, with little effect on final cardiac output values.

Finally substituting the calculated oxygen contents into equation [10] we can derive the shunt fraction.

APPENDIX C

Volume of deadspace required to raise PetC[O.sub.2] by 5 to 6 mmHg CO= [DELTA]VC[O.sub.2]/(S.[Delta]PetC[O.sub.2desired]) from equation [6] [DELTA]VC[O.sub.2]=Deadspace volume (DS) x (PetC[O.sub.2]/Patm) x respiratory rate(RR)

DS (ml)= COest x S x Patm x [DELTA]PetC[O.sub.2]/PetC[O.sub.2] x RR

COest is the estimated cardiac output (l/min) based on age, weight and height.

Using standard formulae:

COest=CIest x BSA, BSA=0.007184 x [Ht.sup.0.725] x [Wt.sup.0.425] CIest=4.5 x [0.99.sup.Age-15]

where Ht=height in cm, Wt=weight in kg, BSA= body surface area in [m.sup.2] and CIest=estimated cardiac index.

APPENDIX D

Normal values in a resting adult

V[O.sub.2] 250 ml/min VC[O.sub.2] 200 ml/min PmxC[O.sub.2] 28 mmHg

ACKNOWLEDGEMENTS

The authors thank all the staff on the Intensive Care Unit, particularly the research nurses, Pauline Galt, Bec Rutzou and Sue Burton for their help.

Accepted for publication on June 4, 2008.

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C. J. KILLICK *, W. G. PARKIN ([dagger])

Intensive Care Unit, Monash Medical Centre, Clayton, Victoria, Australia

* M.B., B.S., M.R.C.P., M.R.C.P.C.H., Consultant in Intensive Care and Paediatrics. ([dagger]) M.B., B.S., F.A.N.Z.C.A., F.J.F.I.C.M., Associate Professor.

Address for reprints: Dr C. J. Killick, Intensive Care Unit, Monash Medical Centre, Clayton Road, Clayton, Vic 3168.
TABLE 1
Patient characteristics

 Mean Range

Patient characteristics

Age, years 0:00 20-87
Height, cm 0:00 144-180
Weight, kg 78 53-107
Gender 16 M/8 F

 Number

CABG 18
Valve 5
CABG + valve 1

Haemodynamic results Mean (SD) Range

COtd 4.79 (1.28) l/min 2.5-9.4 l/min
CO[co.sub.2] 4.19 (1.12) l/min 2.0-7.0 l/min
Shunt fraction 11 (4)% 5-20%

CABG=coronary artery bypass graft.
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Author:Killick, C.J.; Parkin, W.G.
Publication:Anaesthesia and Intensive Care
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Date:Sep 1, 2008
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