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- Abstract
- ERRORS IN ESTIMATING CARDIAC OUTPUT BY SLUG-INJECTION DYE DILUTION TECHNIQUE
- ROENTGEN VIDEODENSITOMETRY
- References

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Mayo Clin Proc. Author manuscript; available in PMC 2010 November 12.

Published in final edited form as:

Mayo Clin Proc. 1970 August; 45(8): 563–572.

PMCID: PMC2980553

NIHMSID: NIHMS233518

James B. Bassingthwaighte, Department of Physiology and Biophysics^{†};

A short review of some of the newer indicator dilution techniques is presented to illustrate their potential usefulness in the study of acute illness. The advantage of these methods lies in the increased ease of obtaining fundamental data from the patient. In particular, roentgen videodensitometry and videotape recording show great promise for the near future.

Indicator dilution techniques are now widely used in circulatory studies and in general are well understood. Nevertheless, new applications and approaches continue to appear in the literature. Because of our familiarity with these techniques it is easy to forget the fundamental assumptions on which they are based and to apply them in inappropriate situations.

The first purpose of this review is to point out some sources of serious error in the estimation of cardiac output by dye dilution techniques and to point out remedies. The second is to suggest and to illustrate new techniques, some of which are applicable to studies in ill patients and will allow greater precision in the assessment of their status.

The top panel of Figure 1 shows a dye curve recorded by one of us (E. H. Wood) in 1951 from a normal human. The problem is to estimate cardiac output from curves such as those shown in the middle and bottom panels, recorded from patients with congestive heart failure. There is no obvious recirculation peak; semilogarithmic extrapolation of the downslope does not exclude recirculated indicator which has merged with the primary curve. The area is always overestimated and the flow is always underestimated very significantly.

Effect of cardiac failure on shape of dye dilution curves (concentration increases downward). In contrast to normal curve *(Top),* in which concentration minimum was reached about 10 seconds after peak, curves obtained from patients with cardiac failure, **...**

The technique to be used to avoid such a problem is simple theoretically—move the injection and sampling points temporally closer together so that the volume of circulation traversed between these sites is smaller. Theye and Kirklin^{1} used this approach in postoperative studies on patients after repair of intracardiac defects. At operation, a small catheter was left in the left atrium rather than in the right atrium, and its end was brought out through the chest wall. After injection of dye into the left atrium through this catheter, intra-arterial sampling produced crisp, clean dye curves whose area could be measured easily^{2} (Fig. 2). Sampling from the femoral artery is better than sampling from the radial artery because brachial artery flow is often low and transit times are long. Small dye injections can be used to avoid exceeding the range of calibration of the densitometers.

Dye dilution curve recorded from radial artery of patient, after left atrial injection, 1 day after repair of ventricular septal defect. (From Theye RA.^{2} By permission of W. B. Saunders Company.)

Use of short, low-volume sampling systems with high sampling flow rates (>20 ml/min) or catheter-tip detectors should theoretically allow an increase in accuracy. However, accurate calibrations and correction for flow artifacts in the recorded curves are difficult to achieve with these assemblies. Similarly, one can use right atrial injection and pulmonary artery sampling to obtain sharp dilution curves. However, in many ill patients with depressed cardiac output, satisfactory curves can be obtained with pulmonary artery injection and rapid sampling via a 1-mm (outside diameter) nylon cannula advanced to the bifurcation of the aorta through a thin-walled 19-gauge needle inserted percutaneously into the femoral artery. The densitometer should be attached directly to the cannula with no intervening tubing, so that the total sampling system volume from cannula tip to densitometer lumen is much less than 1 ml. The importance of keeping the volume small becomes obvious when one considers that, when sampling at 30 ml/min, a 1-ml system has a mean transit time of 2 seconds. A pure delay would introduce no problem, but in actual practice the accompanying dispersion is disturbing because significant fractions of the flow take up to 20 seconds to traverse even this small sampling system. This results in some slurring of the arterial curve and decreases the separation between the primary and recirculated curves.

The bolus-injection technique is based on the assumption that flow is steady while the dye curve is recorded. Variation in flow at respiratory and cardiac frequencies with sampling at a constant rate introduces potentially large errors^{3} because the bloodstream is being sampled steadily with respect to time instead of in proportion to flow as theory requires.^{4} The magnitude of the problem can be demonstrated by using a mathematical model which describes dilution curves in the presence of variable, unsteady flow. For simplicity, sinusoidally varying flow will be assumed for the analogy.

Figure 3 shows four computer-generated curves. An “injection,” or pulse input, was made at a phase, Φ, when the flow equalled the mean flow (40 ml/sec) and was increasing (Φ = 0). The system volume was constant at 250 ml. In the right lower panel the frequency was 180/min, and the flow ranged from zero to twice its mean, an amplitude of 1.0. Despite this, the dilution curve is very nearly smooth and has the correct area, mean transit time, and dispersion (the square root of the variance). In the left lower panel, simulating a heart rate of 60/min, the fluctuations are more apparent, but the area and mean transit time are essentially correct. It is the fluctuations at low frequencies that produce remarkable deformities and errors. The curves in the upper panels show mild deformities, the amplitude of fluctuation in flow being but 30% which is approximately the magnitude of respiratory variation in cardiac output. The curve in the left upper panel is diminished 20% in area and in mean transit time because the maximal flow occurred about 6 seconds after injection and the bolus moved past the sampling point rapidly.

Dilution curves recorded during sinusoidally varying flow, after an ideal injection: mean flow = 40 ml/sec; volume = 250 ml; Φ = 0; injection = 4 mg. High frequencies of flow variation *(Lower Panels)* cause obvious deformities in dye curve but **...**

To consider the problem from the theoretic viewpoint, flow is calculated from the equation:

$$\text{I}\phantom{\rule{0.16667em}{0ex}}(\text{mg})=\underset{0}{\overset{\infty}{\int}}\text{C}(\text{t})\xb7\text{F}(\text{t})\phantom{\rule{0.16667em}{0ex}}\text{dt}$$

(equation 1)

in which I = amount injected and C (t) = indicator concentration. F(t), the flow, can be correctly removed from under the integral only when it is constant. The mean flow, , which ordinarily is what we want, is given by:

$$\overline{\text{F}}=\frac{\text{I}\xb7\overline{\text{F}}}{\underset{0}{\overset{\infty}{\int}}\text{C}(\text{t})\xb7\text{F}(\text{t})\text{dt}}=\frac{\text{I}}{\underset{0}{\overset{\infty}{\int}}\text{C}(\text{t})\xb7\frac{\text{F}(\text{t})}{\overline{\text{F}}}\text{dt}}.$$

(equation 2)

With a catheter-tip transducer that will provide C(t) and relative flow, F(t)/, simultaneously, an accurate estimate of can be obtained at once along with an accurate calibration factor for the flow transducer. For instance, the ratio of the instantaneous pressure gradient to mean gradient, Δp(t)/Δ, could be used for relative flow. Gabe and associates^{5} used an electromagnetic catheter-tip velocity probe to record the fluctuations in flow but have not used its signal to correct the dye curves. It is likely that fiber-optic catheters or thermo-sensitive devices will be improved to provide the two signals simultaneously and therefore will provide hitherto unattainable accuracy as long as the effects of localized variations of blood flow and other nonspecific factors of the light transmission and reflectance characteristics or heat dissipation of the blood in proximity to the catheter-tip transducer can be avoided. The validity of this approach (equation 2) is based on the observations^{6}^{,}^{7} that the shapes (relative time spread and skewness) of dye dilution curves and of the distribution of transit times through particular segments of the circulation are unaffected by changes in flow.

In the meantime, we must put up with significant inaccuracy. Figure 4 shows the effect of variation in flow on the areas of recorded dye curves. The ordinate is area as a percentage of the area obtained at steady flow. The abscissa is relative frequency of sinusoidal 30% fluctuation in flow and applies to the same 250-ml segment as defined above with = 40 ml/sec or to any system of larger or smaller volume but having roughly similar mixing characteristics. Putting this plot in terms of dye dilution curves sampled in the aorta after dye injection into the pulmonary artery, normal respiratory frequencies are at about ω/ω_{c} = 0.1 to 0.3 and cardiac frequencies are above 1.0; to the left are lower frequencies representing slow physiologic variations in flow that occur spontaneously. The phase, Φ, of the fluctuation in flow at which injection was made is indicated on each line. It is apparent that cardiac frequencies cause no error in dilution curve area, the relative areas all being close to 100%, but frequencies in the respiratory range cause up to 20% error. The dilution technique measures the flow during the passage time of the dye curve quite well at frequencies less than 1 cycle/200 sec but, in order to estimate the mean flow at such low frequencies, several dye curves would have to be recorded. To obtain a reasonable estimate of mean flow, first one must recognize the source and frequency of the flow variation and then do a sequence of curves at different phases. Since the important disturbing function is usually respiration, this is not too difficult, and manual injection methods suffice.

Flow estimate relative to actual mean flow (area) plotted against relative frequency of cyclic variation in flow. Major errors in flow estimate occur at frequencies near to or less than respiratory frequencies and are dependent on phase at which injection **...**

Very often a shift in injection or sampling site or a change in the patient’s respiration rate may be helpful in avoiding errors. For example, when using pulmonary artery injection and left atrial sampling, any variation in pulmonary blood flow with phase of respiration will result in erroneous estimates of cardiac output. The error can be lessened greatly by asking the patient to breathe quietly during the recording of the curve or to suspend ventilation (but not to do a Valsalva maneuver) for 30 seconds. A most effective means of decreasing the error is to increase the rate of breathing and decrease the tidal volume. This can be done by an awake patient or can be done for an anesthetized patient. In this same situation, improvement can be achieved by increasing the distance between injection and sampling sites, so that the interfering respiratory frequency is increased relative to the dilution curve, which becomes broader and therefore encompasses more respiratory cycles.^{3}

Roentgen video methods currently being developed^{8}^{–}^{10} appear very promising for application to acutely ill patients. Roentgen videodensitometry provides: (1) indicator dilution curves undistorted by a hydraulic sampling system, (2) choice of observation site in the circulation in prospect or retrospect, (3) calibration without drawing blood, (4) low dosage requirements for contrast medium so that peripheral vasodilatation is insignificant, (5) low radiation levels, thereby allowing several injections, and (6) anatomic detail similar to that provided by good cinefluoroscopic methods.^{10}

If one compares concentration-time curves obtained by roentgen videodensitometry and by conventional catheter sampling at the same site after the injection upstream of indocyanine green and Renovist simultaneously, the difference in dynamic response becomes obvious, the video curve being earlier and having sharper contours even when the catheter volume is small and the sampling flow rate is as high as is practicable^{8} (Fig. 5).

Comparison of contours of roentgen videodensitometric dilution curve (upper tracing) and conventional (spectrophotometric) dye dilution curve (lower tracing) recorded simultaneously from left ventricle. Sharp spikes in the video curve during the main **...**

The videodensitometry curves are a measure of the x-ray absorption by tissue plus iodinated indicator in a chosen small area of the roentgen field, and, given constancy of depth of absorbing tissue and either constant or cyclicly varying depth of the blood-indicator mixture, the concentration can be estimated—that is, the x-ray transmission, which is 1.0 minus the absorption, is given by the equation:

$$\text{T}\cong {\text{e}}^{-{\text{E}}_{\text{w}}{\text{c}}_{\text{w}}{\text{d}}_{\text{w}}}\xb7{\text{e}}^{-{\text{E}}_{\text{R}}{\text{c}}_{\text{R}}{\text{d}}_{\text{R}}}$$

(equation 3)

in which T is relative transmission, E is extinction coefficient, c is concentration, and d is depth of solution, and the subscripts w and R refer to water (or tissue) and Renovist, respectively. Since this equation theoretically requires monochromatic radiation, it is more accurate when copper filters are used in the x-ray beam. Since c_{w} changes insignificantly when small amounts of Renovist are used, when the depth of tissue (d_{w}) is constant, equation 3 can be simplified to:

$$\text{T}\cong {\text{k}}_{1}\phantom{\rule{0.16667em}{0ex}}{\text{e}}^{-{\text{E}}_{\text{R}}{\text{c}}_{\text{R}}{\text{d}}_{\text{R}}}\phantom{\rule{0.16667em}{0ex}}\text{or}$$

(equation 4a)

$$\text{D}\cong {\text{E}}_{\text{R}}{\text{c}}_{\text{R}}{\text{d}}_{\text{R}}$$

(equation 4b)

in which k_{1} = e^{−Ewcwdw} and the relative optical density, D = −log_{e} (T/k_{1}).

This is the form used in the assessment of mitral incompetence by videodensitometry.^{11} The video method is much simpler than the classic upstream-sampling technique, which requires left atrial catheterization. Only a left ventricular catheter need be introduced. Because relatively small amounts of contrast medium are needed, a small catheter will do, and it is not necessary to use a high-velocity injection which might irritate or damage the myocardium. With videodensitometry we are concerned more with the relative quantity of indicator being ejected into the atrium rather than with the concentration of it. Quantity of Renovist, q, is the product of concentration times volume, c_{R}d_{R}, such that the regurgitant fraction, RF, is given by:

$$\frac{\text{area}\phantom{\rule{0.16667em}{0ex}}\text{of}\phantom{\rule{0.16667em}{0ex}}\text{left}\phantom{\rule{0.16667em}{0ex}}\text{atrial}\phantom{\rule{0.16667em}{0ex}}\text{curve}}{\text{area}\phantom{\rule{0.16667em}{0ex}}\text{of}\phantom{\rule{0.16667em}{0ex}}\text{left}\phantom{\rule{0.16667em}{0ex}}\text{ventricular}\phantom{\rule{0.16667em}{0ex}}\text{curve}}=\underset{0}{\overset{\infty}{\int}}{\text{q}}_{\text{LA}}(\text{t})\phantom{\rule{0.16667em}{0ex}}\text{dt}/\underset{0}{\overset{\infty}{\int}}{\text{q}}_{\text{LV}}(\text{t})\phantom{\rule{0.16667em}{0ex}}\text{dt}.$$

(equation 5)

From equation 4b, q(t) =D(t)/E_{R}. Substitution of this into equation 5 gives us the readily applied formula:

$$\text{RF}=\underset{0}{\overset{\infty}{\int}}{\text{D}}_{\text{LA}}(\text{t})\phantom{\rule{0.16667em}{0ex}}\text{dt}/\underset{0}{\overset{\infty}{\int}}{\text{D}}_{\text{LV}}(\text{t})\phantom{\rule{0.16667em}{0ex}}\text{dt}$$

(equation 6)

which is the ratio of the areas of the density curves. The secret of success in applying this formula is to obtain a reading of zero x-ray transmission at each location by inserting a 0.5-cm-thick piece of lead into the field over the locations of interest while continuing the video tape recording. Because there is no sampling system to slur the curves, they usually return to the base line and obviate the need to use any method of extrapolation of the downslope.

In circumstances in which d_{R} is relatively constant, the conversion to optical density facilitates the estimation of concentration:

$${\text{c}}_{\text{R}}(\text{t})=\text{D}(\text{t})/{\text{k}}_{2}$$

(equation 7)

in which k_{2} = E_{R}d_{R}. For a cylindric vessel, d_{R} may be taken as the observed diameter in the plane perpendicular to the x-ray beam. E_{R} for Renovist is 25 times E_{w}. From concentration-time curves in a vessel, it is possible to estimate flow. After a bolus of Renovist solution is injected into the central circulation, curves of c_{R}(t) may be recorded from any or several chosen vessels within the field of the image intensifier. When a pair of concentration-time curves are recorded at two points, 1 and 2, a short distance, L, apart along a cylindric vessel, the mean transit time, , for the bolus to pass each site may be estimated. The mean velocity along the vessel is L/(_{2}−_{1}) and the flow, , is:

$$\pi {\text{r}}^{2}\phantom{\rule{0.16667em}{0ex}}\text{L}/({\overline{\text{t}}}_{2}-{\overline{\text{t}}}_{1})$$

(equation 8)

in which r is the radius of the vessel. This method has been used for measuring flow in large arteries in the dog and is most accurate when the injections are made distal to the lung capillary bed.^{12}^{,}^{13} Velocity of flow also may be estimated from the advancing bolus front. Because of geometric difficulties in measuring the length, L, or the radius, r, when the vessels are short, small, and crooked, it will be difficult to apply this method to the measurement of flow in important arteries such as the middle cerebral or the circumflex coronary. But, it may be possible to obtain some data on the redistribution of cardiac output or the changes in regional flows in patients with shock or other acute illnesses while causing a minimum of discomfort.

^{*}This investigation was supported in part by Research Grants HE-9719, HE-4664, and FR-7 from the National Institutes of Health, Public Health Service.

James B. Bassingthwaighte, Department of Physiology and Biophysics^{†}.

Ralph E. Sturm, Bioelectronic Consultant, Department of Physiology and Biophysics.

Earl H. Wood, Department of Physiology and Biophysics^{‡}.

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12. Bassingthwaighte JB, Reed JH, Sturm RE, et al. Unpublished data.

13. Rutishauser W, Simon H, Stucky JP, et al. Evaluation of roentgen cinedensitometry for flow measurement in models and in the intact circulation. Circulation. 1967;36:951–963. [PubMed]

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