CARDIAC OUTPUT, INDICATOR DILUTION MEASUREMENT OF

by this method will be 80% of the total cardiac output. The shunting fraction is calculated using the arterial oxygen saturation (SaO2, from a pulse oximeter), the fraction of inspired oxygen (FiO2), arterial oxygen tension (PaO2) and standard isoshunt tables. The requirement of an arterial blood gas sample for PaO2 means that this method is not truly noninvasive.

As mentioned previously, this noninvasive method involves a number of assumptions. In summary, these assumptions are the CO2 exchange at the alveolar–arterial membrane reaches equilibrium. Therefore, ETCO2 is equal to PaCO2; cardiac output remains constant during rebreathing; venous CO2 content does not change during a brief period of rebreathing; and there is little or no intrapulmonary shunting.

SUMMARY

The Fick method remains the gold standard of cardiac output measurement. While technically challenging, it relies on direct measurement of oxygen consumption and uptake to determine the rate of blood flow through the lungs and around the body. Accurate measurement of cardiac output is necessary for the estimation of several important parameters and assessment of complex congenital cardiac conditions. Variations of the classical Fick principle allow estimation of cardiac output in patients who might otherwise be unsuitable.

BIBLIOGRAPHY

1.Vandam LD, Fox JA, Fick A. (1829–1901), Physiologist: A heritage for anaesthesiology and critical care medicine. Anaesthesiology 1998;88(2):514–518.

2.Kendrick AH, West J, Papouchado M, Rozkovec A. Direct Fick cardiac output: Are assumed values for oxygen consumption acceptable? Eur Heart J 1988;9(3):337–342.

3.Wolf A, et al. Use of assumed versus measured oxygen consumption for the determination of cardiac output using the Fick principle. Catheterization Cardiovascular Diagnosis 1998;43(4): 372–380.

4.Hagen PT, Scholz DG, Edwards WD. Incidence and size of patent foramen ovale during the first 10 decades of life: An autopsy study of 965 normal hearts. Mayo Clinic Proc 1984; 59(1):17–20.

5.Tachibana K, et al. Effect of ventilatory settings on accuracy of cardiac output measurement using partial CO(2) rebreathing. Anesthesiology 2002;96(1):96–102.

Reading List

Grossman W. Blood flow measurement: The cardiac output. In: Baim DS, Grossman W. Cardiac Catheterization, Angiography and Intervention. 5th ed. Baltimore: Williams and Wilkins; 1996: pp 109–120.

Davidson CJ, Fishman RF, Bonow RO. Cardiac Catheterization (Ch 6). In: Braunwald E, editor. Heart Disease: A textbook of cardiovascular medicine. 5th ed. Philadelphia: WB Saunders; 1997: pp 177–203.

Grossman W. Shunt detection and measurement. In: Baim DS, Grossman W. Cardiac Catheterization, Angiography and Intervention. 5th ed. Baltimore: Williams and Wilkins; 1996: pp 167–180.

Feneley MP. Measurement of cardiac output and shunts. In: Boland J, Muller DWM, editors. Cardiology and cardiac catheterisation: The essential guide. Amsterdam: Harwood Academic Publishers; 2001: pp 197–205.

See also BLOOD GAS MEASUREMENTS; CARDIAC OUTPUT, INDICATOR DILUTION MEASUREMENT OF; CARDIAC OUTPUT, THERMODILUTION MEASUREMENT OF; PERIPHERAL VASCULAR NONINVASIVE MEASUREMENTS; RESPIRATORY MECHANICS AND GAS EXCHANGE.

CARDIAC OUTPUT, INDICATOR DILUTION MEASUREMENT OF

F. M. DONOVAN

University of South Alabama

B. C. TAYLOR

The University of Akron

Akron, Ohio

INTRODUCTION

Cardiac output is defined as the volume of blood pumped by the left or right ventricle per unit of time and is normally expressed in L min 1 (1). For the average 70 kg adult male, the cardiac output is 5 L min 1, however, exercise can cause this figure to increase as much as six times the resting value in well-trained athletes (2). Knowledge of cardiac function is an important tool for determining the hemodynamic status of an individual whether he/she is a trained athlete or a patient in a critical care setting. Accurate direct measurement of cardiac output is a rather difficult task since to obtain a direct measurement would require collecting and measuring all of the blood pumped from the heart into the aortic outflow tract. It is necessary, therefore, to develop indirect methods for the measurement of cardiac output that would provide equivalent accuracies. The Fick (2) and other indicator dilution methods (3) are two of the invasive procedures that provide good reasonable results. More recently, echo cardiography and other noninvasive techniques have been gaining in popularity, yet the Fick and Indicator Dilution methods remain the ‘‘Gold Standards’’ against which all other methods are compared because of their accuracy, safety, reproducibility, and relative simplicity (1).

The Fick principle (4) is based on the fact that the amount of an indicator taken up (or released) by an organ is the product of its blood flow and the difference in concentration of the substance between the organ’s arterial and venous blood. Cardiac output can be determined by dividing the amount of oxygen consumed by the arterialvenous oxygen difference (AVO2 difference). The theory behind this procedure is explained more fully below.

The indicator dilution method became widely accepted after Hamilton, in 1948, demonstrated that this technique agreed with the Fick method. In the indicator dilution method (5) an indicator(dye, thermal, saline) is injected into the venous blood and its concentration is measured continuously in the arterial blood as it passes through the circulatory system The cardiac output is determined by analyzing the resulting time-dependent concentration curve.

INDICATOR DILUTION METHOD FUNDAMENTAL EQUATIONS

Figure 1. Simple mixing chamber.

Consider the simple mixing chamber shown in Fig. 1, where Q is the constant volumetric flow rate into and out of the chamber, mi is the mass of indicator injected into the inflow stream, C(t) is the concentration of indictor in the chamber at any instant, and mL is the mass of indicator that leaves the chamber due to diffusion to the wall and/or metabolism. The differential mass of indicator that leaves the chamber at point 2 per differential time is given by

dm2 ¼ CðtÞQdt

where C(t) at point 2 is the same as the concentration of indictor in the mixing chamber assuming complete mixing in the chamber. The total mass of indicator that leaves the chamber is determined by integrating the above equation with the result shown below.

Z 1

m2 ¼ Q CðtÞdt

0

The differential mass of indicator that leaves the chamber due to diffusion to the chamber wall and/or metabolism is proportional to the concentration of indicator, C(t), and the surface area of the chamber, A.

dmL ¼ CðtÞADdt

where D is the proportionality constant for diffusion and/or metabolism.

The total mass of indicator leaving the chamber due to diffusion is

Z 1

mL ¼ AD CðtÞdt

0

The total mass of indicator leaving the chamber is equal to the mass of indicator entering the chamber minus the mass loss of indicator due to diffusion

m2 ¼ mi mL

which leads to

Z 1 Z 1

Q CðtÞdt ¼ mi AD CðtÞdt

0 0

and subsequently to the equation for volumetric flow rate

CðtÞdt

0

The integral of C(t)dt is determined from the area under the indicator dilution curve. Note that if the area of the

chamber wall is large and/or the diffusion coefficient is large, then the flow rate will be overestimated unless the diffusion is taken into account. In practice, the effect of diffusion is taken into account by a multiplying calibration factor (K) as shown in equation 1.

CðtÞdt

0

This is the familiar Stewart–Hamilton equation for calculating cardiac output from the indicator dilution curve (6).

INDICTOR DILUTION CURVE FUNDAMENTAL EQUATIONS

The equations for the indicator dilution curve are determined by the indicator mass flow rate conservation, which states that the mass flow rate of indicator into the mixing chamber must equal the mass flow rate of indicator out of the mixing chamber plus the mass rate of removal by diffusion plus the rate of change of indictor stored in the chamber.

The parameter V is the volume of the chamber and complete mixing is assumed so that the concentration of indicator leaving the container at point 2 is equal to the concentration of indicator in the chamber at any instant.

Rearranging this equation results in the first-order

which has a time constant of

t ¼

V

Q þ AD

After the injection of the indicator is complete, the concentration of indicator flowing into the chamber becomes zero resulting in the following equation during the washout phase.

t dCdtðtÞ þ CðtÞ ¼ 0

The solution to this equation is

CðtÞ ¼ Cðt1Þe ½ðt t1Þ=t&

where C(t1) is the indicator concentration at time t1 on the washout part of the indicator dilution curve.

Taking the natural log of this equation results in

ln CðtÞ ¼ ln Cðt1Þ ½ðt t1Þ=t&

This shows that if the indicator dilution curve is plotted as natural log of C versus t, then the curve will become a straight line during the washout phase and the slope of the curve is the negative reciprocal of the system time constant.

Rearranging this equation yields

This equation can be rearranged to the following:

APPLICATION OF THE INDICATOR DILUTION EQUATIONS AND RECIRCULATION

The following results are from a computer simulation in which 6 mg of indicator are injected into the right atrium of an average male with indicator concentrations being read from the radial artery. The volumes used by the simulation for the chambers involved are shown in Figure 2.

Figure 3. Indicator dilution curve.

The area under the indicator dilution curve can not be determined directly from the dilution curve. The dilution curve is plotted on a semilog graph in Fig. 4.

During the washout phase, the concentration curve approaches a straight line (dashed line) before the recirculation distorts the plot (solid line). This indicates that the system is behaving as a first-order decay, and we can use equation 2 to determine the area under the curve from any chosen time on the straight-line portion of the curve to infinity.

In this simulation, the area under the indicator dilution curve that would occur if there were no recirculation from 0 to 40 s is found to be 59.8 mg s L 1, which results in a calculated cardiac output of 6.02 L min 1.

With recirculation we determine the area under the curve from 0 to 15 s to be 47.387 mg s L 1 and use equation 2 to calculate the area from 15 s to infinity.

For example, use the concentrations at 15 and 20 s that are in the straight-line portion of the semilog plot.

Figure 2. Schematic of simulation system.

Q is cardiac output (6 L min 1)

1is the right atrium (V1 ¼ 100 mL)

2is the right ventricle (V2 ¼ 100 mL)

3is the pulmonary circulatory system (V3 ¼ 600 mL)

4is the left atrium (V4 ¼ 100 mL)

5is the left ventricle (V5 ¼ 100 mL)

6is the systemic artery volume from the left ventricle to the radial artery (V6 ¼ 100 mL)

The total circulatory system volume is taken to be 6 L.

The diffusion coefficient D is taken to be zero in the simulation. The resulting indicator dilution curve as measured in the radial artery is shown in Fig. 3.

The dashed line beginning at 22 s shows what the curve would do if there were no recirculation of the indicator through the circulatory system back to the right atrium. The solid line shows the actual curve with recirculation.

Time (s)

Figure 4. Semilog plot of indicator dilution curve.

Solving for Q yields the equation on which the Fick method is based.

Q ¼ mfi

C2 C1

In practice, the indicator used in the measurement of cardiac output by the Fick method is oxygen so that mfi is the consumption rate of oxygen in the lungs, C1 is the concentration of oxygen in the venous blood, and C2 is the concentration of oxygen in the arterial blood.

Z 1

E ¼ rCPQ TðtÞdt

0

The total thermal energy that enters the system is a combination of energy carried into the system by blood flow and the thermal energy carried into the system by the injectate, where the subscript b refers to blood and subscript i refers to injectate.

Z 1

Ei ¼ rbQCPb Tbdt þ riCPi ViTi

0

THERMAL DILUTION METHOD FUNDAMENTAL EQUATIONS

For thermal dilution measurement of cardiac output, a warm or cold injectate is injected into the right atrium and the temperature of blood in the pulmonary artery is measured by a thermistor as shown in Fig. 5. A warm injectate would need to be considerably warmer than the blood that might be hot enough to denature proteins (608C). If it were not very warm, the poor signal/noise ratio would render the method unusable. Therefore cold injectate is the only practical thermal indicator (7,8).

A bolus of cold fluid is injected into the right atrium and the resulting temperature is recorded from the pulmonary artery. Conservation of energy requires that the total thermal energy entering the system during the procedure must be equal to the total thermal energy that leaves the system as the system returns to normal temperatures.

The thermal energy carried across a boundary by a differential volume of fluid is given by

dE ¼ rCPTðtÞQdt

where r is the density of the fluid, CP is the specific heat of the fluid, T(t) is the temperature of the fluid at any instant, Q is the volumetric flow rate of fluid crossing the boundary, and dt is the differential time.

The total thermal energy that leaves the system is a combination of the energy carried out of the system by blood flow and thermal energy loss to the walls of the atrium and ventricle.

Z 1 Z 1

Eo ¼ rbQCPb TðtÞdt þ riCPi ViTb þ hA ðT TbÞdt

0 0

where T(t) is the temperaturerecordedbythe thermistor at any instant, h is the thermal convection coefficient, and A is the internal surface area of the right atrium and right ventricle.

Using these equations in the thermal energy conservation equation

Ei ¼ Eo

and rearranging gives

Z 1

rbCPb Q ðTðtÞ TbÞdt ¼ riCVi ViðTi TbÞ

hA ðTðtÞ TbÞdt

0

Solving for Q yields the thermal dilution equation for volumetric flow rate.