12 CARDIAC OUTPUT, FICK TECHNIQUE FOR

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See also BIOELECTRODES; INTEGRATED CIRCUIT TEMPERATURE SENSOR.

CARBON. See BIOMATERIALS: CARBON.

CARDIAC CATHETERIZATION. See CORONARY

ANGIOPLASTY AND GUIDEWIRE DIAGNOSTICS.

CARDIAC LIFE SUPPORT. See CARDIOPULMONARY

RESUSCITATION.

CARDIAC OUTPUT, FICK TECHNIQUE FOR

STEVEN C. FADDY

University of Sydney

Darlinghurst, Australia

INTRODUCTION

Cardiac output (CO) is an important measurement in many medical investigations. It is the amount of blood pumped by the ventricles of the heart and can be defined as the product of stroke volume (SV) and heart rate (HR), where stroke volume is the amount of blood expelled by the ventricle with each contraction and the HR is the number of contractions per minute:

CO ¼ SV HR

Cardiac output gives an indication of ventricular function and is also used in the calculation of a number of flowdependent parameters, such as cardiac index, systemic vascular resistance, pulmonary vascular resistance, valve areas, and intracardiac shunt ratios.

The Fick technique is the gold standard in CO measurement. It relies on direct measurement of oxygen consumption and expenditure to derive the rate of blood flow throughout the individual.

HISTORY

In 1870, the German physiologist, Adolf Fick (1829–1901), described a novel method of determining cardiac output based on diffusion of respiratory gases in the lungs. This came after almost 30 years of work by Fick and numerous others, who reasoned that diffusion was one of the most essential events within the living organism. In 1855, Fick had published his findings relating to diffusion of gas across a fluid membrane. These became known as Fick’s law of diffusion and stated that the rate of diffusion of a gas is proportional to the partial pressures of the gas on either side of the membrane, the area across which diffusion is taking place and the distance over which diffusion must take place. As an aside, Fick also invented contact lenses in 1887.

The 1870 publication by Adolf Fick stated: ‘‘It is astonishing that no one has arrived at the following obvious method by which [the amount of blood ejected by the ventricle of the heart with each systole] may be determined directly, at least in animals. One measures how much oxygen an animal absorbs from the air in a given time, and how much carbon dioxide it gives off. During the experiment one obtains a sample of arterial and venous blood; in both the oxygen and carbon dioxide content are measured. The

difference in oxygen content tells how much oxygen each cubic centimeter of blood takes up in its passage through the lungs. As one knows the total quantity of oxygen absorbed in a given time one can calculate how many cubic centimeters of blood passed through the lungs in this time. Or if one divides by the number of heart beats during this time one can calculate how many cubic centimeters of blood are ejected with each beat of heart. The corresponding calculation with the quantities of carbon dioxide gives a determination of the same value, which controls the first (1).’’

In simplest terms, cardiac output can be calculated as a ratio of the amount of oxygen consumed through breathing and the rate in which oxygen is taken up by the tissues.

Cardiac Output

¼ Oxygen consumption=Arteriovenous oxygen dierence

It was not until the 1930s that quantitative measurement of the components allowed confirmation of the Fick equation as a means of calculating cardiac output.

PHYSIOLOGY OF THE FICK TECHNIQUE

Oxygen Consumption (VO2)

The first step in calculating CO by the Fick technique is to determine the amount of oxygen consumed by the individual over a period of time. This is best done in the resting state so that there is constant oxygen consumption over the collection period. The traditional method is collection of expired gases in a Douglas bag over a period of 3 min. Then, from the volume of expired gas, the oxygen content of the expired gas and the oxygen content of the inspired room air, it is possible to calculate the amount of oxygen taken up by the individual.

Subtracting the oxygen content of expired gas from that of the inspired room air (%v/v or mL of O2 100 mL 1 of the gas) gives the oxygen difference between the inspired and expired gases, expressed in mL of O2 100 mL 1 of expired gas. Applying a factor of 10 gives this figure as milliliters of O2 per liter of expired gas, which are the units used later in the calculation. Dividing the total volume of expired gas by the collection time gives the minute ventilatory rate, expressed in liters per minute L min 1.

The product of the O2 difference (mL L 1) and the minute volume (L min 1) is the oxygen consumption (VO2) expressed in milliliters of oxygen absorbed per minute.

VO2 ¼ ðO2 Room air O2 expiredÞ ðvolume=timeÞ

Example : InspiredO2 ¼ 21:0mL 100mL 1 room air ExpiredO2 ¼ 16:7mL 100mL 1 expired gas O2 difference ¼ 21:0 16:7 ¼ 4:3mL 100mL 1

Total volume expired ¼ 26:1L

Collection time ¼ 3min

Minute volume ¼ 26:1L 3min 1 ¼ 8:7L min 1

Therefore;

O2consumption ¼ ð4:3 10ÞmL L 1

8:7L min 1 ¼ 374mL min 1

An alternative to the Douglas bag method is the use of a metabolic rate meter with a hood or facemask, a variablespeed blower and a servocontrol loop with an oxygen sensor. This method employs essentially the same principle as the Douglas bag method, but gives a real-time measurement of VO2. The variable-speed blower maintains a flow of room air through the hood or facemask past the patient into a polarographic oxygen sensor (gold and silver–silver chloride electrode), varying the flow in order to keep the oxygen concentration at the measuring electrode constant. By keeping the oxygen concentration at the measuring electrode constant, the only variable is the flow rate through the system. Under steady-state conditions, this is the only variable determining the oxygen consumption (VO2).

Although this method provides a real-time measurement of VO2, thus excluding the need for collection of a Douglas bag, it is still rather time and labor intensive. In addition, it has been suggested that it is difficult to obtain reproducible results and the method gives consistently lower results then the Douglas bag technique.

Arteriovenous Difference

As with oxygen consumption, measurement of oxygen uptake by the body involves measuring blood oxygen content before and after entering the lungs. The arteriovenous oxygen difference (AVdiff) is the difference between the content of oxygen (ctO2) in the oxygenated arterial blood leaving the lungs and the deoxygenated venous blood returning to the lungs (mL O2 per 100 mL of blood). The AVdiff represents the volume of oxygen delivered to meet the body’s metabolic demands. Again, this figure is multiplied by 10 to give the AVdiff in units of mL O2 per liter of blood.

AVdiff ¼ ctO2ðArterialÞ ctO2ðVenousÞ

Example : ArterialO2 content ¼ 19:5mL dL 1 blood

VenousO2 content ¼ 13:2mL dL 1 blood

AVdiff ¼ 19:5 13:2 ¼ 6:3mL dL 1 ¼ 63mL L 1

Typically, a sample from the main pulmonary artery is used for venous blood and a sample from the left ventricle or aorta is used for arterial blood oxygen content measurements.

Cardiac Output

The rate at which oxygen is taken up by the lungs and the rate at which it is taken up by the body is now known from the above calculations. The ratio of these two figures gives the cardiac output. The examples above show that the lungs take up 374 mL of oxygen each minute and that the blood takes up 63 mL of oxygen for each liter that passes through the lungs. How many lots of 63 mL (1 L aliquots of blood) must pass through the lungs to take up 374 mL of oxygen each minute? The answer is 5.9 L of blood must pass through the lungs each minute in order to absorb this amount of inspired oxygen.

Example : VO2 ¼ 374 mL min 1

AVdiff ¼ 63 mL L 1

CO ¼ 374=63 ¼ 5:9 L min

14 CARDIAC OUTPUT, FICK TECHNIQUE FOR

PRACTICAL CONSIDERATIONS FOR USING THE FICK TECHNIQUE

Oxygen Consumption

The measured volume of a gas is affected in part by the ambient temperature and atmospheric pressure in which it is collected. Obviously, these will vary from day to day, leading to a potential source of variation in the calculation of oxygen consumption, and ultimately, cardiac output. The combined gas law (a combination of Boyle’s and Charles’ law) describes the relationship of pressure, temperature, and volume in a gas. This law can be used to correct measured gas volumes to standard temperature and pressure (STP). This means that the measured volume of gas is standardised to 273 K and 760 mmHg (101.32 kPa).

As well as correcting for variations in atmospheric pressure, it is also necessary to correct for water vapor pressure. Dalton’s law tells us that the pressure of a gas mixture is equal to the partial pressures of all of the components of the mixture. Water vapor is present in the atmosphere and in exhaled gas and its partial pressure contributes to the total atmospheric pressure. Water vapor exerts a constant pressure at a given temperature, regardless of the atmospheric pressure. Water vapor pressure is 47 mmHg (6.26 kPa) at normal body temperature and 17.5 mmHg at (2.33 kPa) 20 8C. Before correcting for STP it is necessary to subtract the water vapor pressure from the total atmospheric pressure to obtain the dry gas pressure at the ambient temperature. This is known as ‘standard temperature and pressure, dry’ (STPD), which is used for the correction.

Example : Atmospheric pressure ¼ 762 mmHg ð6:26 kPaÞ Ambient temperature ¼ 23 C

Water vapor pressure at 23 C ¼ 21 mmHg ð2:79 kPaÞ

Dry gas pressure ¼ 762 21 mmHg

¼ 741 mmHg ð98:79 kPaÞ

STPD correction factor for 741 mmHg and 23 C ¼ 0:8991ffrom standard tablesg

Volume of expired gas ¼ 9:68 L min 1

STPD corrected volume ¼ 9:68 0:8991 ¼ 8:7 L min 1

By standardizing to STPD, we have removed the effect of water vapor pressure, ambient pressure, and temperature on the volume measurement and, hence, potential sources of day to day variation in measurement of the cardiac output.

Arteriovenous Oxygen Difference

Although many current generation analyzers can calculate oxygen content (ctO2), earlier models did not. It may be necessary to manually calculate oxygen content from the hemoglobin level (Hb) and oxygen saturation of a sample. Hemoglobin is able to carry 1.36 mL of oxygen per gram of hemoglobin. Therefore, by multiplying the hemoglobin

level by 1.36 it is possible to calculate the oxygen carrying capacity of the individual. Simply stated, this is the maximum amount of oxygen that can be carried by 100 mL of the individual’s blood and is dependent on the hemoglobin level. Some textbooks have quoted the constant as 1.34 and others add a value of 0.03 to account for oxygen dissolved in plasma, but 1.36 is the generally accepted constant for calculation of oxygen carrying capacity.

If the total amount of oxygen that the blood is capable of carrying and the saturation of the sample is known, it is possible to calculate the oxygen content of that sample.

ctO2 ¼ oxygen carrying capacity % saturation

The arteriovenous oxygen difference is the difference in oxygen content between arterial and venous blood.

Example : Hb ¼ 14:5 g dL 1

Oxygen carrying capacity ¼ 14:5 1:36

¼ 19:72 mL dL 1

Arterial saturation ¼ 98:9%

Arterial oxygen content ¼ 19:72 98:9% ¼ 19:5 mL dL 1

Venous saturation ¼ 66:9%

Venous oxygen content ¼ 19:72 66:9%

In this example, each liter of blood leaving the lungs delivers 63 mL of oxygen to the tissues.

Figure 1 shows a complete example of CO measurement using the Fick technique.

ASSUMPTIONS WHEN USING THE FICK TECHNIQUE FOR CARDIAC OUTPUT

Absence of Intracardiac Shunt

The method of calculating cardiac output described above uses the amount of oxygen absorbed by the blood as it travels through the lungs. We then assume that the amount of blood pumped by the right ventricle through the lungs is equal to the amount pumped by the left ventricle through the systemic vessels since the cardiovascular system is a closed system. This assumption does not always hold true and it is sometimes necessary to alter the calculation.

The term shunt describes the condition where a communication exists between the leftand right-sided chambers of the heart. If this condition results in shunting of blood between the venous and arterial circulation, the assumption becomes invalid because some blood is being recirculated through part of the circuit and the two ventricles are pumping unequal volumes. If an intracardiac shunt is known or suspected, it is necessary to collect blood samples at different points than the standard arterial and pulmonary artery sites. Calculation of cardiac output and

A. Standard Temperature and Pressure

Atmospheric pressure = 762 mmHg

Ambient temperature = 23 ºC

Water vapor pressure at 23 ºC = 21 mmHg

Dry gas pressure = 762 – 21 mmHg = 741 mmHg

STPD correction factor for

741 mmHg and 23 ºC = 0.8991

B. Volume measurement

Total volume expired = 28.14 L

Collection time = 3 min

Minute volume = 28.14 L 3 min–1 = 9.68 L min–1

STP corrected volume

0.8991 × 9.68 L min–1 = 8.7 L min–1

shunt ratios in the presence of an intracardiac shunt is discussed later in this article.

Collection of True Arterial Sample

In a normal heart, it is not easy to gain access to the pulmonary veins to collect an arterial sample as the blood leaves the lungs. As a result, left ventricular or aortic blood is used to measure arterial oxygen content. This method ignores the small amount of venous admixture from bronchial and thebesian venous drainage into the left atrium.

Direct Measurement of Oxygen Consumption

temptation to use an estimate of oxygen consumption rather than direct measurement. Standard formulas and nomograms are used to estimate VO2 from height, weight, age, and sex. The body surface area (BSA) is calculated from height and weight and expressed in units of square meters (m2).

BSA ¼ 0:007184 weight0:425 height0:725

Age, sex, and basal metabolic rate are used to determine heat production from standard nomograms. Finally, heat production and BSA are used to estimate the oxygen consumption.

VO2 ¼ ½BSA Heat Production&=291:72

Owing to the timeand labor-intensive methods of measurement of oxygen consumption (VO2), there is often a

This method estimates the basal oxygen consumption at rest. It does not make allowances for any pathological

16 CARDIAC OUTPUT, FICK TECHNIQUE FOR

conditions, including those being investigated, that may affect the resting oxygen consumption. Studies comparing measured and estimated VO2 have shown that estimating VO2 from the various available formulas can lead to large and unpredictable errors in both VO2 and cardiac output values (2,3). The practice of estimating VO2 is strongly discouraged.

DETECTION AND ASSESSMENT OF INTRACARDIAC SHUNTS

Earlier in this article it was seen how the oxygen content of blood entering and leaving the lungs was used to calculate the cardiac output. It was assumed that blood flowing through the lungs is equal to blood flowing through the systemic circulation (since the cardiovascular system is a closed circuit). Several conditions may result in blood being recirculated between the left and right sides of the heart, leading to unequal flow in the pulmonary and systemic circulation. These conditions include atrial septal defects, patent foramen ovale, ventricular septal defects, and patent ductus arteriosus. Patent foramen ovale has been estimated to be present in 27.3% of the population (4), but the presence of a defect does not necessarily result in intracardiac shunting.

A communication between the leftand right-sided chambers of the heart can result in blood being shunted from right to left (venous blood being mixed into the arterial circulation), left to right (arterial blood being mixed into the pulmonary circulation), or as a bidirectional shunt (blood moves back and forth across the communication at different stages of the cardiac cycle). Although the method of calculating cardiac output remains essentially the same, the sites of blood collection are different in cases where intracardiac shunting exists. The following passages describe the methods for calculating systemic and pulmonary flow in the presence of different intracardiac shunts.

Left-to-Right Shunt

In a left-to-right shunt, arterial blood is pushed across the defect into the pulmonary circulation. This will artificially elevate the oxygen saturation and oxygen content in the pulmonary artery. To avoid error in the calculation of systemic cardiac output in the presence of a left-to-right shunt, it is necessary to collect the venous blood sample in the chamber immediately proximal to the shunt. In the case of atrial defects, blood is collected from both the inferior and superior vena cavae. Oxygen content (ctO2) from these sites is used in the calculation of mixed venous oxygen content (MVO2). The individual values are weighted and averaged according to the relatively higher flow from the superior vena cava and the absence of coronary sinus blood in the measurements. The generally accepted formula used for estimation of mixed venous oxygen content is

MVO2 ¼ ½3 ctO2ðSVCÞ þ ctO2ðIVCÞ&=4

MVO2 becomes the venous component of the arteriovenous difference calculation and cardiac output (systemic flow, Qs) is calculated as described earlier.

It is also possible to calculate pulmonary flow (Qp) by using the pulmonary artery oxygen content as the venous component (blood entering the lungs) and left ventricular or aortic oxygen content as the arterial component (blood leaving the lungs). The pulmonary flow is equal to the systemic flow returning to the heart plus the volume being recirculated from the left-sided chambers via the shunt. This is reflected in the CO calculation. Because of the recirculated arterial blood, the venous oxygen content in the pulmonary artery will be elevated, leading to a decrease in the arteriovenous difference and, hence, a higher pulmonary flow.

Right-to-Left Shunt

The opposite occurs in a right-to-left shunt. Venous blood is mixed into the arterial circulation leading to a decrease in systemic arterial oxygen saturation. The calculation of systemic flow (Qs) uses the arterial and venous (pulmonary artery) samples as usual. The calculation of pulmonary flow (Qp) requires a sample to be taken after the blood leaves the lungs, but proximal to the shunt. In a right-to- left shunt it is necessary to sample blood from the pulmonary veins. In practical terms, this requires the catheter to pass from the right atrium across the defect to the left atrium and then into a pulmonary vein. Pulmonary vein oxygen content becomes the arterial component of the arteriovenous difference and pulmonary flow is calculated as usual.

In the presence of a right-to-left shunt, systemic flow is equal to the pulmonary flow leaving the lungs plus the amount that passes across the shunt directly from the right-sided chambers. Sampling in the left ventricle or aorta distal to the shunt will therefore give a lower arterial oxygen content than would be measured in the pulmonary veins, leading to an decrease in the arteriovenous difference and, hence, a higher systemic flow compared to the pulmonary flow.

A right-to-left shunt should be suspected in any patient who has an arterial oxygen saturation less than 95%. Investigation of these patients should include assessment for the presence of a bidirectional shunt.

Bidirectional Shunt

The presence of a bidirectional shunt complicates the calculation of pulmonary and systemic flow. Neither of the methods described above is suitable since both assume shunting in only one direction. The systemic blood flow (SBF) is calculated using oxygen contents sampled at the sites where blood enters and leaves the systemic circulation (arterial and mixed venous sites, respectively). Pulmonary blood flow (PBF) is calculated using sampling sites where blood enters and leaves the lungs (pulmonary artery and pulmonary vein, respectively). Finally, effective blood flow (EBF) is calculated using samples taken where the blood enters the heart and leaves the lungs (mixed venous and pulmonary vein oxygen contents). The mixed venous oxygen values should be the same as the pulmonary artery sample if no shunts are present. Similarly, the pulmonary vein should be the same as the left ventricular or aortic

Figure 2. Bidirectional shunt calculation in a 55 year old woman with Eisenmenger’s syndrome secondary to an atrial septal defect (ASD). Note the predominantly right-to-left shunt due to increased pulmonary vascular resistance. These results show little deterioration compared to measurements taken six

sample in the absence of any shunts. Therefore, by sampling at these sites, the pulmonary (and hence, systemic) flow that would normally occur if no shunts were present is being calculated

Since the systemic flow (SBF), pulmonary flow (PBF), and the flow that would occur in the absence of any shunts (EBF) is known, the size of the shunts can also be calculated

Figure 2 shows calculations for a bidirectional shunt based on the principles discussed above. Note the changes in oxygen saturation and content as blood passes the atrial defect. In the left heart, oxygen saturation decreases as blood passes from pulmonary veins to the left ventricle due to mixing of deoxygenated blood being shunted across the defect. Conversely, oxygen saturation in the right heart increases as blood passes from the vena cavae (mixed venous) to pulmonary artery due to oxygenated blood being shunted across the defect from the left atrium.

Pulmonary–Systemic Flow Ratio

An alternative to calculating flow across a defect is to calculate the pulmonary/systemic flow ratio (P/S ratio). This value is a ratio of the pulmonary flow relative to

18 CARDIAC OUTPUT, FICK TECHNIQUE FOR

the systemic flow. Calculation of the P/S ratio does not involve calculation of actual flows, so it is not necessary to collect expired gases to calculate the VO2. The P/S ratio is calculated using only the oxygen content (or saturation) from arterial, pulmonary artery, mixed venous, and pulmonary vein samples.

The AVdiff for the pulmonary component is calculated by subtracting mixed venous oxygen content from systemic

arterial oxygen content. The systemic AVdiff is calculated by subtracting the pulmonary artery oxygen content from the pulmonary vein oxygen content. If a pulmonary vein sample is not possible, use an estimate of 98% unless the arterial saturation is higher. Using arterial oxygen content to estimate the pulmonary vein content will assume that there is no right-to-left shunt. The P/S ratio (or P:S ratio) is the calculated by dividing the pulmonary component by the systemic component.

The P/S ratio is the proportion of flow through the pulmonary circulation relative to the systemic circulation. Therefore, a value > 1.0 indicates left-to-right shunting. An arbitrary value of between 1.5 and 2.0 is often used to determine the need for definitive treatment to correct the defect, in order to avoid late sequelas from prolonged pulmonary vascular overload. A P/S flow ratio < 1 indicates right-to-left shunting and may be a sign of irreversible pulmonary vascular disease.

Arterial oxygen content ¼ 98:9% ctO2ðArtÞ ¼ 19:5 mL dL 1

Pulmonary artery oxygen content ¼ 66:9% ctO2ðPAÞ ¼ 13:2 mL dL 1

Mixed venous oxygen content ¼ 63:1% ctO2ðMVÞ ¼ 12:4 mL dL 1

¼ 6:3 mL dL 1

P=S ratio : 7:1=6:3 ¼ 1:13

FLOW-DEPENDENT PARAMETERS

A number of frequently used parameters in cardiovascular medicine are dependent on knowing systemic or pulmonary flow. Calculation of these parameters, and the effect that the cardiac output has on each, is discussed. Table 1 lists expected normal ranges for a number of common flowdependent parameters.

Cardiac Index

Cardiac output is often corrected for patient’s size, based on body surface area (BSA). Cardiac index (CI) is calculated by dividing the cardiac output by the body surface area.

CI ¼ CO=BSA L min 1 m 2

Table 1. Expected Ranges for Common

Flow-Dependent Parameters

Oxygen consumption Cardiac Output ¼ Arteriovenous oxygen difference

VO2 ¼ BSA Heat Production

291:72

MVO2 ¼

3 ctO2ðSVCÞ þ ctO2ðIVCÞ

4

SBF ¼ VO2 ctO2ðArtÞ ctO2ðMVÞ

PBF ¼ VO2

ctO2ðP veinÞ ctO2ðP artÞ

EBF ¼ VO2

ctO2ðP veinÞ ctO2ðMVÞ

CO ¼ VCO2 ctCO2ðVenÞ ctCO2ðArtÞ

CO ¼ DVCO2

DctCO2ðArtÞ

CO ¼ DVCO2

S DETCO2

Some believe cardiac index is a more useful parameter than cardiac index because it accounts for the patient’s size. A large person (as approximated by BSA) would be expected to have a higher cardiac output while a low cardiac output in a smaller person may not necessarily be indicative of a poorly functioning ventricle. Many authors only express cardiac output in terms of cardiac index for this reason.

Valve Areas

Basic fluid dynamic principles state that a fluid exerts pressure equally in all directions. Therefore, when the valves of the heart are open they should allow equalisation of pressure in the two chambers that they separate. Sometimes the valves of the heart become stiff, thickened or do not open properly, inhibiting flow through the valve. This is referred to as valve stenosis. A result of this process is a pressure gradient, a difference in pressure on either side of the valve. Take an example of aortic valve stenosis. When

the left ventricle contracts, it is pushing against an obstruction. The systolic pressure will be higher in the ventricle that in the aorta. The difference in pressure is referred to as a pressure gradient (expressed in mmHg) and can be measured during cardiac catheterisation. The pressure gradient across a valve is often used to determine the severity of a valve stenosis. However, the main parameter that should be considered is the cross-sectional area of the valve. A pressure gradient of 20 mmHg (2.66 kPa) is often considered an indication of mild aortic stenosis. However, in the presence of low cardiac output, it is necessary to have quite a narrow valve orifice to achieve this gradient. Conversely, a less severe stenosis could achieve a gradient of 50 mmHg (6.66 kPa) in a patient with a high cardiac output.

Both the cardiac output and mean pressure gradient are used in the calculation of valve area. The Gorlin formula is used for calculating valve area of the aortic or pulmonary valve:

p

Area ¼ ½fCO=ðSEP HRÞg=ð44:3 gradientÞ&

where HR is the heart rate and SEP is the systolic ejection period (since gradients in these valves are measured during systole). However, a shorter formula is often used as an

approximation:

p

Area ¼ Cardiac output= Gradient

Taking the example of aortic stenosis, a mean gradient of

gradient. Similarly, our patient with a mean gradient of 50 mmHg (6.66 kPa) would not have such a severe narrow-

where DFP is the diastolic filling period (since gradients in these valves are measured during diastole).

Vascular Resistance

Measurements of vascular resistance are based on principles of fluid dynamics where resistance is defined as the decrease in pressure between two points in a vascular segment divided by the flow through that segment. While this simplification does not account for pulsatile flow, calculation of vascular resistance in this way is useful in a number of clinical settings.

In the past, Wood units (mmHg L min 1) were used to express vascular resistance. Today, vascular resistance is more commonly expressed in absolute resistance units (dyn.s.cm 5), which are derived from the mean pressure gradient (dyn cm 2) divided by the mean flow (cm3 s 1). A constant of 80 is used to convert values from traditional units (mmHg and L min 1) to absolute resistance units.

Systemic vascular resistance (SVR) is therefore defined as the difference in pressure between blood entering the systemic circulation (mean aortic pressure) and blood leav-

ing the systemic circulation (mean right atrial pressure) divided by the systemic blood flow:

SVR ¼ ½80 ðAOm RAmÞ=Qs&

Similarly, pulmonary vascular resistance (PVR) is defined as the difference between mean pulmonary artery pressure and mean left atrial pressure divided by the pulmonary flow:

PVR ¼ ½80 ðPAm LAmÞ=Qp&

In the absence of intracardiac shunting both SVR and PVR can be calculated using the standard cardiac output measurement. If intrapulmonary shunting is present, systemic and pulmonary flow must be individually calculated for use in the SVR and PVR calculations, respectively.

There are a number of causes of increased systemic or pulmonary vascular resistance, some reversible and some permanent. The use of serial cardiac output and pressure measurements during drug challenges can assist in identifying management strategies that may be helpful in reducing vascular resistance.

VARIATIONS OF THE FICK METHOD

The Fick principle can be applied to any gas involved in diffusion, including carbon dioxide. Such variations to the classic Fick formula are often referred to as the indirect Fick principle.

By measuring the difference between inspired and expired CO2 and the minute ventilation volume we can calculate CO2 production (VCO2). Arteriovenous CO2 difference is calculated from the measured values of arterial and venous carbon dioxide content (ctCO2). The ratio of VCO2 and the arteriovenous CO2 difference gives the cardiac output.

Earlier in this article it was seen how the oxygen content (ctO2) of blood is calculated from the amount of hemoglobin and oxygen saturation of the sample, since nearly all of the oxygen is bound to hemoglobin. A relatively smaller proportion of CO2 is bound to hemoglobin. About 70% is transported in the blood as bicarbonate. Only 23% is bound to hemoglobin and 7% is transported as dissolved CO2. Therefore, the calculation of CO2 content is not dependent on hemoglobin level.

Carbon dioxide content (ctCO2) is calculated from the formula:

ctCO2 ¼ 11:02 PCO20:396

Thus, if we have partial CO2 pressure of arterial (PaCO2) and venous (PvCO2) samples, we can calculate the arteriovenous carbon dioxide difference as

ctCO2ðVenÞ ctCO2ðArtÞ ¼ 11:02ðPvCO02:396 PaCO02:396Þ

Then cardiac output is calculated with the formula:

CO ¼ VCO2=ðctCO2ðVenÞ ctCO2ðArtÞÞ

There are some advantages to using the carbon dioxide method. When a patient is receiving high concentrations of supplemental oxygen, analysis of inspired and expired

20 CARDIAC OUTPUT, FICK TECHNIQUE FOR

oxygen will give a small difference between two relatively large values. Even a small error in the estimation of either value will yield an inaccurate VO2. Additionally, some oxygen analysers (e.g., paramagnetic analyzers) have poor accuracy at high oxygen concentrations. Measurement of cardiac output in patients receiving high concentrations of supplemental oxygen may be erroneous and the Fick principle using carbon dioxide may prove more accurate.

Applying the Fick principle to carbon dioxide involves the same steps as using oxygen for the calculation. There is still the requirement for analysis of expired gases, as well as collection and analysis of arterial and mixed venous blood samples. However, there are a number of ways of estimating, rather than directly measuring, the various parameters necessary to calculate cardiac output using the Fick CO2 technique.

Infrared (IR) light absorption sensors in the breathing circuit can measure inspired and expired CO2 content. Alternatively, an assumption can be made about the content of CO2 in the inhaled gas (especially if the patient is being ventilated with 100% oxygen) and only expired CO2 needs to be measured. Along with an airflow sensor (e.g., as a differential pressure pneumotachometer), these measurements can provide real-time estimation of VCO2.

There is a logarithmic relationship between cardiac output and end-tidal CO2 (ETCO2). At normal or high cardiac output the respiratory rate determines the amount of CO2 that is eliminated by the lungs with each breath. If it is assumed that CO2 exchange at the alveolar–arterial membrane reaches equilibrium, then ETCO2 can be used to estimate PaCO2. In this way, it is possible to estimate cardiac output without subjecting the patient to unnecessarily invasive procedures.

The critically ill patient presents a number of challenges. These patients are usually intubated and manually ventilated with high concentrations of inspired oxygen. While many will have arterial lines for blood pressure monitoring, those that do not are exposed to added risk of morbidity if arterial access is necessary to determine cardiac output. In addition, placement of a pulmonary artery catheter for the measurement of mixed venous gas tension exposes the patient to significant risk of sepsis, pneumothorax, thrombosis, or pulmonary artery rupture. However, cardiac output is often vital in determining endorgan perfusion.

Recently, a system for noninvasive measurement of cardiac output using the Fick principle and carbon dioxide was developed for use with ventilated patients in the intensive care unit, based on the estimations described above. A number of assumptions allow this system to be used without the need for arterial or mixed venous blood samples. The technique involves measuring changes in carbon dioxide production and arterial CO2 content between normal breathing conditions and under rebreathing conditions with 10–15% CO2 and a reservoir with a volume 1.5 times the tidal volume. Carbon dioxide production (VCO2) is calculated from the minute ventilation and expired CO2 content under normal breathing conditions. Arterial CO2 content

[ctCO2(Art)] is estimated from the end-tidal CO2 (ETCO2) with adjustments for the slope of the CO2 dissociation curve

and degree of dead space ventilation.

During partial rebreathing, carbon dioxide elimination from the blood is reduced, but ETCO2 increases and reaches a plateau within a few breaths. Studies conducted in anaesthetised dogs have showed that during a brief period of CO2 rebreathing there is a change in PaCO2 and in calculated VCO2, but little or no change in venous carbon dioxide

content (ctCO2(Ven)) (5). It is believed that this finding is due to the quantity of CO2 stores in the body being large

and new equilibrium levels not being attained for 20–30 min. This finding becomes highly important in the noninvasive estimation of cardiac output. Any change in the arteriovenous CO2 difference during the brief rebreathing period can be attributed to changes in the arterial CO2 component alone.

If it is assumed that the cardiac output and

ctCO2(Ven) remain constant during normal breathing

(N) rebreathing (R):

CO ¼ VCO2ðNÞ=ðctCO2ðVenÞðNÞ ctCO2ðArtÞðNÞÞ

¼ VCO2ðRÞ=ðctCO2ðVenÞðRÞ ctCO2ðArtÞðRÞÞ

From basic algebra it is known that

X ¼ A=B ¼ C=D ¼ ðA CÞ=ðB DÞ

Then,

CO ¼ ðVCO2ðNÞ VCO2ðRÞÞ=½ðctCO2ðVenÞðNÞ ctCO2ðArtÞðNÞÞ

ðctCO2ðVenÞðRÞ ctCO2ðArtÞðRÞÞ&

Rearranging this equation:

CO ¼ ðVCO2ðNÞ VCO2ðRÞÞ=½ðctCO2ðVenÞðNÞ ctCO2ðVenÞðRÞÞ

ðctCO2ðArtÞðNÞ ctCO2ðArtÞðRÞÞ&

Since it has been assumed that ctCO2(Ven) does not change during rebreathing (ctCO2(Ven)(N) is equal to ctCO2(Ven)(R)), these values cancel each other out and the equation becomes:

CO ¼ ðVCO2ðNÞ VCO2ðRÞÞ=ðctCO2ðArtÞðRÞ ctCO2ðArtÞðNÞÞ

In other words, cardiac output is equal to the change in VO2 divided by the change in arterial CO2 content between the normal and rebreathing states:

CO ¼ DVCO2=DctCO2ðArtÞ

As ctCO2(Art) is estimated from ETCO2 and the slope (S) of the CO2 dissociation curve:

CO ¼ DVCO2=S DETCO2

This method of cardiac output estimation gives a measure of

the pulmonary capillary blood flow (QPCBF). Changes in VCO2 and ETCO2 only reflect the blood flow that participates in gas

exchange. An intrapulmonary shunt occurs when venous blood passes through unventilated areas of the lungs and moves into the arterial circulation without taking up oxygen or releasing carbon dioxide. A large intrapulmonary shunt will not be reflected in the changes seen in VCO2 and ETCO2. Therefore, it is necessary to estimate the degree of shunting and correct the cardiac output estimation accordingly. For example, if only 80% of pulmonary blood flow is participating in gas exchange, the QPCBF estimated