Cardiovascular

Monitoring Cardiac Output: Science and Challenges

Pekka Meriläinen, PhD Chief Scientist of Datex-Ohmeda Email: pekka.merilainen@datex-ohmeda.com

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Introduction

When facing the technical challenge of measuring basic physiological processes like circulation and ventilation for the first time, bright young biomedical engineers, physicists and mathematicians usually start by modeling the systems. They take the equivalent circuits used in electronics textbooks, replacing voltage with pressure, current with flow, capacitance with compliance, and so on.

But after some experience intellectual frustration will inevitably set in. Applying basic models using linear elements may sometimes work in a healthy body – where monitoring is seldom needed – but not in the critically ill where it would be most beneficial.

In this column my purpose is to illuminate some issues related to this dilemma in the field of noninvasive cardiac output (NICO) monitoring. I’ll also make a brief digression into the wonderland of statistics used to compare the performance of different methods.

Pressure or flow, or just plain power?

Stubborn engineers sometimes irritate clinicians with silly questions like "Do you know if the heart is a flow or a pressure generator?" In electronics, or course, it makes quite a difference if the power supply is specified as a voltage or a current generator. This question might be witty but it is largely irrelevant. Why not just see the heart as a generator of power, which is the product of pressure and flow?

From one perspective the flow is only needed to maintain pressure in the organs to enable autoregulation of blood flow distribution. But another obvious task for blood flow (generated by pressure) is to transport O2 from the lungs to the organs and take the waste CO2 back to be removed by exhalation. Thinking the other way round, the CO2 transfer from the pulmonary artery capillaries to the alveolar space can be used to calculate the blood flow through the lungs.

What does measuring NICO actually measure?

The concept of measuring NICO by disturbing the CO2 transfer to the lungs in a controlled fashion has been around for more than 20 years (1). The alveolar CO2 can be changed during a single breath, e.g. by manipulating the ventilation or using valves to make the subject rebreath some of the CO2 exhaled during the previous breath.

Crunching the Fick equation for the mass balance of CO2 into a differential form reveals that pulmonary capillary blood flow (PCBF) is proportional to the ratio of the change of CO2 flux from the mixed venous blood to the alveoli (VCO2) and the change of CO2 content of the alveolar gas (CaCO2):

The difference () refers to the values measured from the breaths just before and after the perturbation. Since these parameters cannot be measured directly inside the lungs, it is necessary to use as surrogates the changes in the CO2 elimination and end-tidal CO2 (et CO2) concentration as measured at the airway. These are valid only if the lungs are healthy and homogenous so that et CO2 represents mixed alveolar gas and the CO2 removal from the lungs is in a steady state, i.e. not affected by changes in the store of CO2 in the body.

The equation reveals that the measurement errors in the CO2 concentration tend to get cancelled, but the error in the instantaneous flow measurement, which is needed for V CO2, affects the result. The ratio of numbers obtained by subtracting large and almost equal numbers from one another is mathematically problematical. Any small errors like notches in the CO2 curve due to cardiogenic oscillations tend to get substantially amplified in the final result.

Obviously, this method does not measure the true CO nor, precisely speaking, even the PCBF, but only the PCBF perfusing the ventilated alveoli as defined in the basic three-compartment model consisting of alveolar dead space and shunt (2). In a real and sick lung with substantial abnormalities in the ventilation-perfusion ratio the correlation of the results with CO certainly gets fuzzier.

How about the radial arterial pressure wave?

Another old indirect method that has enjoyed a kind of renaissance is the pulse contour method which makes use of the radial arterial pressure wave (3).

The basic idea is to calculate flow from the area under the curve of the systolic portion of the arterial pressure wave. This has been further developed by employing sophisticated nonlinear multi-element models for the aortic and arterial system (4). Thoughtful modeling also takes into account all the physical phenomena related to the flow-pressure couplings as well as the reflections of pressure wave in the vascular circuitry.

The problem remains, however, of how to set the values for the model’s key parameters. It would help a lot if at least the true measured values of the diameter and elastance of the aorta were available.

A suggested solution seems to recommend a one-point calibration of the system against bolus thermodilution. It is not wholly clear how the calibration factor is actually embedded in the model parameters. I leave it up to the reader to imagine what sarcastic comments might be stimulated in the simple mind of an engineer by the need to insert a highly invasive PA catheter to calibrate a noninvasive method.

Measuring the Doppler shift of blood velocity

One of the few, if not the only, direct NICO methods is to use back scattering of ultrasound to measure the Doppler shift generated the blood moving through the arteries. What actually gets measured, though, is the average velocity of blood flow inside the space that the sound beam crosses.

The basic form of the Doppler equation is:

where f0 is the frequency of the transmitted ultrasonic signal, f is the received signal, vB the velocity of blood flow, c the velocity of sound in the blood (about 1500 m/s) and the angle between the ultrasonic beam and the axis of the blood vessel.

The measurement can be performed either externally or internally. In the first case, a probe is placed at the suprasternal notch allowing alignment of the beam parallel to the blood flow in the ascending aorta; in the internal method, the probe is placed in the esophagus with the beam at an oblique angle to the descending aorta. The esophageal option is more attractive because signal quality is better and the probe is easier to position. To calculate the blood flow in l/min the aortic diameter has to be known. This can be measured accurately using modern double-beam devices.

Engineers still not satisfied

But the problem bothering the engineers developing ultrasonic gas flow sensors remains: how does the beam actually average over the flow profile, which varies over the phases of the cardiac cycle depending on the presence of turbulences. Moreover, the esophageal probe does not reach the part of the CO going to the head and other upper extremities. There are also concerns about holding the probe continuously in a fixed position with best signal quality and constant angle in longer-term routine use.

If you ask for my personal view on these three methods, I would probably vote for the soundest one, i.e. ultrasound. It directly measures the real thing and, as a bonus, the information on the dynamic flow signal can be used to calculate other interesting cardiac parameters like contractility of the left ventricle.

But still a key concern remains: how do we guess the portion of the CO going "upstairs" and how does it vary over time?

And now for the statistics

These were my more or less subjective opinions about some NICO methods, but how have my fellow scientists been doing in comparing them objectively?

Everybody has seen lot of papers with scattergrams of NICOs measured by method X against thermodilution, the golden standard. Regression lines and correlation coefficients were gradually replaced by Bland-Altman plots (5) (difference vs. average) from 1986 on. Many of the papers end by concluding that method X measures with a small bias and within acceptable limits of agreement compared to the reference.

Despite this, the naked eye often reveals a pattern of data points like pellets fired from a shotgun from a long distance. Let’s take a typical example (6): cardiac output was measured in a range from 4 to 10 l/min, with a bias of close to zero and standard error (SD) of about 1 l/min. The percentage error is defined as ± 2SD/mean, which in this case makes ± 28%. Since the accuracy of thermodilution is reportedly ± 10% in the best case and ± 20% in routine use, it has been proposed that an error of ± 30% can be accepted for the difference between the new method and thermodilution (7).

However, the scattergram revealed that at the low end the new method in some cases gave 5 l/min vs. 3 l/min from the reference, which is a 67% error – and in the wrong direction if the goal is to warn about too low a cardiac output. Extrapolating this analysis down to 2 l/min of CO level would in the worst case mean a 200% error (3l/min vs. 1 l/min). I leave it to the reader to consider if such a not-so-uncommon use of the respectable science of statistics raises the blood pressure or the blood flow of the writer.

Disclaimer: My wife has hung a plaque on the wall of our living room which says, carved in solid brass: "The opinions expressed by the man of this house… are not necessarily those of the management". Please understand this statement, when appropriately modified, when reading this column as well.

References:

1. Gedeon A, Forslund L, Hedenstierna G, Romano E. A new method for noninvasive bedside determination of pulmonary blood flow. Med Biol Eng Comput 1980; 18: 411-418
2. Nunn JF. Applied Respiratory Physiology, 4th Edition, Oxford, Butterworth Ltd, 1993
3. Wesselingh KH, De Wit B, Weber JAP, Smith NT, A simple device for the continuous measurement of cardiac output. Adv Cardiovasc Phys 1983; 5: 16-52
4. Jansen JRC, Schreuder JJ, Mulier JP, Smith TN, Settels JJ, Wesseligh KH. A comparison of cardiac output derived from the arterial pressure wave against thermodilution in cardiac surgery patients. Br J Anaesth 2001; 87: 212-222
5. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986; 1: 307-310
6. Botero M, Lobato EB. Advances in noninvasive cardiac output monitoring: an update. J Cardiothorac Vasc Anesth 2001; 5: 631-640
7. Critchley LAH, Critchley JAJH. A meta-analysis of studies using bias and precision statistics to compare cardiac output measurement techniques. J Clin Monit 1999; 15: 85-91

Last updated: 1 December 2002Created
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