SALINE AND THERMAL DILUTION FLOW MEASUREMENTS: EVALUATION BY MEANS OF AN OPEN HYDRAULIC MODEL

Eduardo Valdez and Max E. Valentinuzzi

ABSTRACT

A simple open hydraulic model was constructed with the main objective of making comparative evaluations of flow rate measurements, with saline and thermal dilution. In the range of 0.5 to 3.5 I/min, it was found that saline indicator

ave t ermal indicator showed a minor overestimation of - 1%. 9,

a slight underestimation fin the order of 2%1 while the

These values were taken from the regression equations

F Isaline) = 0.945 F Ireall + 0.0351 and F (therm01 = 1.020 F (real) - 0.0144, both in Umin. Correlations were higher than 0.99 in the two cases. Considering the overall error range, thermodilution produced a value approximately twice that ot saline l-21 to 25% versus -12 to +ll%l. However, this is not necessarily extendable to living organisms. The model was found useful for test and calibration of detecting cells and for teaching purposes.

INTRODUCTION

Hydraulic models have been used in the past to assess various aspects of flow measurements by means of the classic indicator-dilution method (Emanuel and Norman, 1963; Emanuel et al., 1966 Valentinuzzi et al., 1969; Bate and Sirs, 1974; Pate1 and Sirs, 1977). Saline conductivity (Allen and Taylor, 1924; Smith et al., 1967; Geddes et al., 1972, 1974; Bourdillon et al., 1979) and thermo- dilution (Fegler, 1954; Goodyer et al., 1959; Evonuk et al., 1961; Sanmarco et al., 1971; Bredgaard et al., 1975; Roselli et al., 1975; Mathur et al., 1976; Moodie et al., 1978; Stawicki et al., 1979) are somewhat more recent variations which still call for development and further assessment.

The simple model herein described was constructed having in mind the following objectives:

1. To permit comparative evaluation of measure- ments made with saline and thermal indicators under different dynamic flow conditions.

2. To test and calibrate detecting cells for the two types of the above mentioned indicators.

3. To offer demonstrations for teaching purposes.

These objectives, in turn, would serve as a frame- work to further expand the studies in the model itself or, more desirable, in the experimental animal.

MATERIALS AND METHODS

Physical model

It is an open system (Figure 1) fed from the waterline via an elevated constant level tank to ensure a regu- lated head pressure. Different glass modules of several sizes and shapes allow the arrangement of a great variety of configurations, including the possibility

Laboratorio de Bioingenieria, Instituto de Ingenierika ElCctrica, Facultad de Ciencias Exactas y Tecnologia, Universidad National de Tucunh, 4000 San Miguel de Tucumrln, Argentina.

0141-5425/81/010053-04 $02.00 0 1981 IPC Business Press

of adding known leaks and elastic tubes with adjus- table clamps to vary the hydraulic resistance.

Conductivity cell It is a short lucite tube (ID = 10 mm) (Figure 2a) with two stainless steel plates parallel to the longi- tudinal axis to be connected to an impedance meter (Clavin and Valentinuzzi, 1977). The cell offers an average impedance of 825 ohms at 12 kHz when filled with Tucuman tap water at 27°C. A control calibration obtained with NaCl dissolved in distilled water, at 17.4’C, produced a set of 48 pairs of values yielding the following regression equation (Mandel, 1967):

Z=p+mC?SEE [kohms] (1)

in which p = 1.454 kohms, m = -1389 kohms.ml/g, C = concentration in (g/ml) and SEE = Standard Error of the Estimate = 16.6 ohms, with 0.99 as correlation coefficient r. The range of concentra- tion went from 0.4X10m3 up to O.65X1O-3 g/ml. This means that when, for example, C = 0.45X 10’s g/ml, 2 = (829 rt 16.6) ohms, as it can be easily veri- fied by application of equation (1). The negative sign of m indicates that the impedance of the cell decreases as concentration increases. Distilled water alone, as expected, gave a very high impedance (much beyond the range of the meter) due to its extremely low ionization.

Thermometric cell

Two silicon diodes (BA 127) placed in lucite tubes are the adjacent branches of a bridge configuration. One acts as the detecting cell while the other is a reference unit distally located in the model (Figure 16). In this way, changes in temperature due to self-heating or to other causes, common to all the system, are compensated for.

A p-n junction shows a thermic sensitivity of about -2 mV/‘C. Using an amplifier with a gain of ten and considering that the recorder (Berger, PN111,

J. Biomed. Engng. 1981, Vol. 3, January 53

Flow measurements: E. Voidez and MI. Valenthuzzi

Figure 1. Physical Model (a) Simple configuration employed in the experiments. The outlet of the con- stant level tank was connected as inflow to the system. (A) Ref erence thermometric cell. (B) Injec- tion site. (C) Conductivity cell. (0) Detecting ther- mometric cell. The outflow was connected to a sink. Several modules are also shown on the board. On the right side: electronic circuitry and controls asso- ciated with the model. (b) Detail of th e section where the cells and injection site were installed.

Buenos Aires, Argentina) provides a maximum amplification of 0.5 mVfcm, leads to an overaIl sensitivity of O.O25’C/cm of pen deflection.

Three cells (Figure 2b) wer constructed with care- fully chosen diodes varying experimentally an aver- age time constant of 0.55 s when a step change in temperature was applied (Zajic et al., 1975). Some other technical considerations using thermistor probes have been discussed by Neame et al., (1977).

Theoretical background The basis for flow rate determinations is the well- known Steward-Hamilton formula (Valentinuzzi et al., 1969) with the appropriate modifications for each indicator (Geddes et al., 1972, 1974; Evonuk et al., 1961; Sanmarco et al., 1971). In any case, the area under the recorded dihttion curve and the amount of injectate are required, both expressed in the corresponding units. Areas were measured in these experiments with a polar planimeter (Keuffel & Esser Co., USA).

Figure 2. Detecting cells (a) Conductivity cell (b) Thermometric cell

Calibration of the conductivity cell

When a bolus of saline is injected, the conductivity cell shows a change 62 in impedance described by:

where 6C (g/l) is the concentration variation of NaCl in the fluid (tap water in this model), A (cm2) is the electrode area, L (cm) is the distance between electrodes and 6p ( h o m.cm) represents the decrease in fluid resistivity. At constant temperature, the impedance change 62 due to a concentration change 6C between the electrode terminals does not depend on the impedance of the electrodes or the resistance of the intervening column (Geddes et al., 1972, 1974).

Saline solutions were prepared at different concen- trations obtaining values of resistivity from:

P= i) ; R

in which R (taken as equal to 2) is the resistance of the cell measured with the impedance meter (Clavin and Valentinuzzi, 1977). Resistivity was plotted as a function of concentration keeping constant the temperature T. A linear regression (Mandel, 1967)

54 .I. Biomed. Enana. 1981. Vol. 3. January

Flow measurements: E. Valdez and MI. Valentinuzzi

Table 1. Linear regression values, corresponding to the equation Fd = aF, + b (l/min) in which r = correlation coefficient and n = number of data points for the range 0.5 to 3.5 l/min.

of 2 1 data points produced a slope Sp/SC = -1609 kohms.cm.ml/g at 27’C with 0.9997 as correlation coefficient r. Therefore, from equation (2), a 62 = 56 ohms resulted equivalent to 6C = 34.79 pg/ml. Since the dimensions of the cell are 1x1~1 cm, the slope is also numerically equal to the aforesaid value when expressed in (kohms.ml/g).

Calibration of the thermometric cell

Voltages I’ were measured at the output of the detecting circuit with a digital voltmeter (HP 3430A) when tap water at known temperatures was intro- duced in the cell. A plot of I’ versus T was drawn calculating the linear regression slope 6 V/6T = 18.54 mV/“C, correlation of 0.9989, n = 29, for one cell, and 18.74 mV/‘C, correlation of 0.9975, n = 18, for another cell. The third unit was the reference. The calibrating pulse was produced by shortcircuiting a 6 ohm resistor in series with the detecting diode. For maximum gain, a pulse of 4.2 mV appeared at the output corresponding, for one cell, to 0.226”C and, for the second unit, to 0.224”C.

RESULTS

With several modules connected in series (Figure 1) up to about a length of 3.5 m, a total of 195 flow measurements were made employing saline and thermal indicators. The actual value was deter- mined by collecting fluid in a calibrated bottle for a given time checked with chronometer, The range covered went from 0.5 to 3.5 l/min.

Injecting small volumes of 1% saline (0.2 - 1 ml), 100 determinations were performed. In the case of thermodilution, volumes of 0.5 to 2 ml of hot (or cold) water at different temperatures were suddenly introduced in the stream. The sample size n was 95. In both cases, linear regressions were calculated according to the equation:

Fd =aF, +b (l/m4 (4)

where Fd is the value found by the dilution method (either saline or thermo), F, is the real flow, a is the slope and b is the independent term. Correlation coefficients r were also computed for both cases.

Table 1 summarizes the regression values just des- cribed. An analysis of the errors showed the distri- bution indicated in Table 2. For example, for saline, 5 1% of the measurements fell within an error of +5% while, for thermodilution, 62% of the population was contained in the same bracket. On the average, saline dilution underestimated by -2.37% (SD = 5.92), while the thermal indicator overesti- mated by 1.35% (SD = 7.64).0bserve that the total error range for thermodilution was about twice as much as for saline (-21 to +25% versus -12 to +ll%), instead up to an error of tlO% the distributions were almost the same in both cases.

DISCUSSION

Firstly, the model has been used repeatedly fulfilling the objectives for which it was designed, and secondly the saline method showed a minor underestimation while thermodilution gave a slight overestimation. This is clearly illustrated by the slopes of the regres- sion equations (smaller and greater than one, respec- tively). Errorwise, the saline method appeared to be slightly better than the thermodilution. However, this is not necessarily extendable to the living organism.

ACKNOWLEDGEMENTS

The errors obtained are comparable with those repor- This project has been supported by SECYT (Grants ted by Emanuel and Norman (1963), however, an N05565/76 and N”8145/77-8), by CONICET (Grant electromechanical injecting system (instead of the N”7589/76), and by the Consejo de Investigaciones

a b r n

Saline 0.9450 0.0351 0.9919 100

Therm0 1.0205 -0.0144 0.9876 95

Table 2. Distribution of errors

Saline

Therm0

%ofn Error(%)

51 -5 to +5 88 -10 to +10

100 -12 to+11

62 -5 to +5r 87 -10 to +10

100 -21 to +25

Average error (%)

-2.37 (SD = 5.92)

+1.35 (SD = 7.64)

The average errors were computed over the whole population for each type of indicator.

manual syringe used here) and a better determination of the dilution curve area (say, by electronic means) might improve these values. For example, Stawicki et al., in 1979, found that the reproducibility of measurements was within 1.9% with an automatic injection thermodilution method and 5.9% with a manual one, both tested in human patients.

The minor overestimation and greater error range of the thermal indicator might be related to heat loss through the tube walls. On the other hand, the slight underestimation of the saline indicator could call for a better calibration procedure. It must be remembered that electrolyte resistivity is strongly dependent on temperature. In animal experiments, however, this should not be a problem being necessary, instead, to consider the haematocrit (Geddes et al., 1972, 1974; Bourdillon et al., 1979).

Since the tubes are transparent, injecting a dye shows very well how the bolus is formed and how it elon- gates as it displaces downstream, giving also an idea of its length. A pump can be added to obtain a closed system with recirculation.

CONCLUSIONS

de la Universidad National de Tucuman (CIUNT, output using an electrically calibrated flow-through con-

Program N”57). Eduardo Valdez is Research Assis- ductivity cell’. J. App. Physiol., 37,972-977.

tant in the Laboratorio de Bioingenieri’a supported Goodyer, A.V.N., HUVOS, A., Eckhardt, W.F. and Ostberg,

by CIUNT and ME Valentinuzzi is Career Investigator R.H. (1959). ‘Thermal dilution curves in the intact

of the Conseio National de Investigaciones Cientificas animal’. Circ. Res., 7, 432-441.

Mandel..l. (1967). ‘The statistical Analvsis of Exnerimental y TCcnicas 01 Argentina (CONICE?).

REFERENCES

Allen, C.M. and Taylor, E.A. (1924). ‘The salt velocity method of water measurement’. Mech. Eng. 46, 13-l 6 and 51.

Bate, H. and Sirs, J.A. (1974). ‘Comparison of direct and indicator-dilution measurements of flow rate and mean circulation time’. Med. Biol. Eng., 12, 328-334.

Bredgaard Sorensen, M., Bille-Brahe, N.E. and Engell, H.C. ( 197 6). ‘Cardiac output measurement by thermal dllu- tion’. Ann. Surg., 183, 67-22.

Bourdillon, P J., Becket, J.M. and Duffin, P. (1979). ‘Saline conductivity method for measuring cardiac output simplified.‘Med. Biol. Eng. & Comput., 17,323-329.

Clavin, O.E. and Valentinuzzi, M.E. (1977). ‘Impedanci- metro biologic0 de alta linealidad.' Acta physiol. lutinoam., 27,215-230.

Data’: I&science Publishers, New York, 416~~. Mathur, M., Harris, E.A., Yarrow, S. and Barrat-Boyes, B.C.

(1976). ‘Measurement of cardiac output by thermodilu- tion in infants and children after open-heart operations’. J. Thor. Cardiovasc. Surg., 72,221-225.

Moodie, D.S. Feldt, R.H., Kaye, M.P., Strelow, D.A. and Van der Hagen, L J. (1978). ‘Measurement of cardiac output by thermodilution: development of accurate measurements at flows applicable to the pediatric patient’. J. Surg. Res., 25, 305-311.

Emanuel, R., Hamer, J., Chiang, B., Norman, J. and Manders, J. (1966). ‘A dynamic method for the calibration of dye dilution curves in a physiological system’. Br. Heart J., 27,143-146.

Emanuel, R. and Norman, J. (1963). ‘Evaluation of a dyna- mic method for calibration of dye dilution curves’. Br. Heart J., 25, 308-312.

Evonuk, E., Imig, C J., Greenfield, W. and Eckstein, J.W. (1961). ‘Cardiac output measured by thermal dilution of room temperature injectate.‘J. App. Physiol., 16, 271- 275.

Neame, R.L.B., Powis, D.A. and Imms, F J. (1977). ‘Con- struction of thermistor probes suitable for the estimation of cardiac output by the thermodilution method in small animals’. Med. Biol. Eng. & Comput., 15, 43-48.

Patel, I.C. and Sirs, J.A. (1977). ‘Indicator dilution measure- ments of flow parameters in curved tubes and branching networks’. Phys. Med. Biol., 22, 714-730.

Roselli, R J., and Talbot, L. (1975). ‘Evaluation of the ther- mal dilution technique for the measurement of steady and pulsatile flows’. J. Biomech., 8, 157-166.

Sanmarco, M.E. Philips, C.M., Marquez, L.A., Hall, C. and Davila, J.C. (1971). ‘Measurement of cardiac output by thermal dilution’. Am. J. Cardiol., 28, 54-58.

Smith, M., Geddes, L.A. and Hoff, H.E. (1967). ‘Cardiac output determined by the saline conductivity method using an extra-arterial conductivity cell’. Cardiovasc. Res. Cen. Bull., 5, 123-134.

Fegler, G. (1954). ‘Measurement of cardiac output in anaes- thetized animals by thermodilution method’. Q. J. Exp. Physiol., 39, 153-164.

Stawicki, J J., Holford, F.D., Michelson, E.L. and Josephson, M.E. (1979). ‘Multiple cardiac output measurements in man’. Chest, 76, 193-197.

Geddes, L.A., Da Costa, C.P. and Baker, L.E. (1972). ‘Electrical calibration of the saline-conductivity method for cardiac output’. Cardiovasc. Res. Cent. Bull., 10, 91-106.

Geddes, L.A., Peery, E. and Steinberg, R. (1974). ‘Cardiac

Valentinuzzi, M.E., Geddes, L.A. and Baker, L.E. (1969). ‘A simple mathematical derivation of the Stewart- Hamilton formula for the determination of cardiac out- put’. Med. Biol. Eng., 7, 277-282.

Zajic, F., Brun, Z. and Novotny, M. (1975). ‘Time constant of thermistors and its role in thermodilution methods. Cor pusa, 17.204-211.

Flow measurements: E. Valdez and MI. Volentinuzzi