Thermal method for continuous blood-velocity measurements in large blood vessels, and U C l l ' U l C l t J ' U U l , l J t l l , I L I I ~ I L I ~ I - I I I I I I I I , I, I U I I t

A. L. Delaunois J. F. & C. Heymans Institute, Rijksuniversiteit, Ghent, Belgium

Abs t rac t - - -A catheter-type flowmeter for continuous blood-velocity measurements is described, The new device is based on the thermal method: a constant amount of electrically produced heat is partly dissipated by convection into the bloodstream. The resulting equilibrium for each value of blood velocity determines the temperature of the heat-dissipating body. This temperature is accurately measured by means of thermistors. Linearisation of the hyperbolic blood-velocity thermistor-resistance relationship is performed by means of an appropriate antilogarithmic amplifier.

Keywords--blood-veloci ty measurement, cardiac output, flowmeters

Introduction

THE DETERMINATION of the cardiac output adds an important haemodynamic parameter to the results obtained from experimental or clinical cardio- vascular measurements.

In pharmacological research, a knowledge of the cardiac-output values before and after the admini- stration of drugs can produce important information about the therapeutic value of the administered substance when combined with other cardiovascular data.

Cardiac-output measurements are nowadays mainly performed by means of the dye- or thermo- dilution methods, or in experiments on animals with the electromagnetic flowmeter. The dye- or thermo- dilution methods are single-point determinations, and often produce doubtful results. Electromagnetic measurements are accurate, and give beat-by-beat information. This latter method has the disadvan- tage of surgical intervention for probe placement, which may modify physiological parameters.

Most of the electrical cardiac-output measuring devices are in fact blood-velocity meters. The lumen of the blood vessel in which the measurement is made is kept constant (electromagnetic probes), or assumed to be constant. The flow is then given by:

F = S v

in which S represents the surface of the lumen, and v the blood velocity.

As there is a blunt velocity profile (FRY e t al . ,

1958) in the large vessels, flowmeters of the catheter type can be considered as reliable instruments for cardiac-output measurements in the pulmonary artery and in the ascending aorta. They measure the blood velocity in the vessel, and this parameter is directly proportional to the cardiac output as shown.

Further, if information is needed from conscious animals and telemetry is used, the equipment has to be of low power consumption, light weight and easily introduced in the animal. A thermal method will fulfil the telemetering requirements.

Stycost I

" Th I c o n s t a n t a n w i r e O . 0 5 m m dia. Th2

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output .

*First received 28th March and in final form 5th April 1972 tThis paper was presented at the IEEE Eurocon 71 meeting, Lausanne, Switzerland. October 1971

Fig. 1 Construction of flowmeter, showing catheter and thermistors. The arrows show heat loss by convection from the silver tube

Medical and Biological Engineering March 1973 201

Thermal flowmetering devices of the needle or catheter type have been described previously by GraBs (1933), HENSEL (1954, 1956), DELAUNOIS (1956, 1958, 1961), CASELLA and DECARO (1960), and MELLANDER and RUSHMeR (1960). In these methods, thermocouples or thermistors were used as thermosensitive elements.

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Fig. 2 Water-bath system for calibration o f the f lowmeter. The water temperature is regulated by a thermostat at 38~

Methods

In the new device, electrically generated heat is dissipated by thermal convection into the blood stream through the mediation of a small silver tube, which is electrically heated on one side, and is in thermal contact with the blood on the other side. Continuous measurement of the temperature of this silver body provides the information on the blood velocity. By choosing the proper convecting surface for a given amount of heat, equilibrium can be obtained within the limits of the expected flowrates.

The higher sensitivity to temperature variations of thermistors makes them particularly suited for use in velocity meters. Their advantage over thermo- couples is that thermistors can be mounted in a bridge configuration, and that the bridge can be fed by sine or square waves. Unfortunately, there are some disadvantages in the use of thermistors which have to be elimina d before stable and reliable measuring instruments can be produced.

A heated body having an exposed surface and a temperature th, placed in a blood stream with velocity v and temperature tb, will dissipate, mainly by convection, in a time ff a quantity of heat H, given by

H = Cpvs(t~- t~)~

in which C and p are, respectively, the specific heat and the specific mass of the blood.

e q u a l , a n d

The heat produced electrically in the body is given by:

n = VIE~

with V the voltage, I the current of the heating element, and E the mechanical equivalent of heat.

At equilibrium, the two quantities of heat are

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rotameter

t I

I i,.,.~ I,.,,~ needle stopcock for flow regulation

Cpvs( th- t~) = V I E

As C, p, s, I1, I and E are constants, the equation can be simplified to:

vAt = constant

This is the equation of a rectangular hyperbola. At very low blood velocities, there is a deviation

from this simple formula owing to the change in relative importance of conduction and convection.

2mm length ..x-! -~5"4) / / exposed ~,y~X~x-(-~4"7 ) / /

4 3~/.-x ~4 m m (..P5.1) / / - - 4 V l r ~ r ~ I X / >

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s / o O ~' .__

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Fig. 3 Calibration curves for the silver tubes

202 Medical and Biological Engineering March 1973

In practice At for zero flow has a finite, instead of an infinite, value. The expression then becomes:

(v + a)At = constant

a being a constant of the catheter. The results observed in an experimental model

using water as the fluid, as well as in the living animal, are summarised by this equation. From this formula, two important conclusions can be drawn: (i) The amount of heat available has to be larger

than the quantity lost by convection. Since the heat production is limited by the size of the heating element and the allowed heating voltage, the only way to reach the required condition is to reduce the convecting surface.

(ii) I f the flow measurements must be computerised, it is necessary to have a linear relationship between v and At. This can be realised by using an appropriate amplifier (described elsewhere).

The flowmeter consists of a small heat-convecting element fixed at the tip of a No. 6 French catheter, and two thermistors (Thl and Th2), one inside the convector, the other about 25 mm from the first.

The heat-convecting element is a silver tube, 2 m m in diameter, and I 0 m m long, on which a heating coil is wound (insulated Constantan wire of 0.05 mm diameter). An electrically insulating but thermally conducting coating (Stycast*) lies between the heating wire and the silver body. The tube has a bore of 1 ram, which is filled with Stycast compound, and the first thermistor bead (Thl; 10 kW at 25 ~ C) is introduced into this filling. A second matched thermistor bead (Th2) is placed

about 25 mm from the silver tube. This last thermi- stor is the second branch of a Wheatstone bridge circuit, and compensates for slow body-temperature variations. The heating coil has a resistance of 150El, and is fed by a 6 V d.c. source. The dis- sipation in the coil is only 240 roW.

The Wheatstone bridge* of which the thermistors form two branches is completed by a potentiometric circuit. The bridge current is kept as low as possible to reduce heat generation in the thermistors. There is indeed a compromise: using the thermistors as pure thermometers requires a very low current through them to avoid heating. But, on the other hand, to keep the signal/noise ratio at the bridge output at a reasonable level, a maximum output voltage of about 50 mV seems to be necessary. The bridge is therefore fed by a square-wave voltage source at a frequency of 400 Hz and an amplitude of 1 V, the pulses having a duration of 0.25 ms. The pulse current through the thermistors (each of resistance 5 k~2 at 37 ~ C) is then about 100 #A, and the resulting total power dissipation in both thermi- stors is only 9 pW.

Calibration

For calibration purposes, the following procedure is used: with the catheter in the calibration fluid at zero velocity, and with the heating on, the bridge is balanced. The heating then is switched off with the result that both thermistors attain the same tempera- ture, causing imbalance of the bridge, which produces, after amplication and linearisation, an

*Available from the Emerson & Cuming Co.

"1"

E 250 E

200

L 1 5 0 EL

"0

o 100 o J~

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~_ 50

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Fig. 4 Typical blood-velocity and blood-pressure recordship before, during and after Isuprel injection

Medical and Biological Engineering March 1973 203

output of about 4-5 V. This voltage theoretically represents the output at infinite velocity; it is easily reproducible, and can always be reached by switching off heating, even with the catheter in the animal.

Calibration is therefore started by setting the bridge without the heating to this output. The process is then completed by placing the catheter in a tube through which flows the calibration fluid at known velocities, and applying the heating.

The calibration of the flowmeter is possible with water, glucose solution or blood. The only difference between these fluids is the product Cp (for water, 0.99; for blood, 0.918). Calibration can, for example, be carried out with water, and the resulting difference may be corrected for by calculation.

A waterbath with a heart and aorta simulator, a rotameter and a circulating pump is used for this purpose (Fig. 2). Measurements at different temperatures prove the efficiency of the compen- sating thermistor, as curves obtained from calibra- tions at 20, 25, 30, 35 and 40 ~ C coincide completely.

Fig. 3 shows calibration curves for different values of the exposed convecting surface(s) of the silver tube. There seems to be an optimum value for s, and, with our flowmeters, this surface is 6.28 mm 2 in area, which corresponds to a silver tube length of 2 mm. One set of curves is recorded without linearisation, and these curves are, of course, hyperbolic. The other curve is obtained after linearisation with the optimum value of s.

The time constant of the flowmeter is 1 s, and the velocity measurements taken are averaged auto- matically by the instrument.

Application and results

The instrument allows continuous velocity measurements in intact animals. The catheter is introduced through the carotid and the brachio- cephalic arteries into the aorta. This can be done without X ray fluoroscopy simply by observing the recording. Indeed, in the ligatured carotid artery, there is no flow, and reaching the brachiocephalic artery produces a slight deflection in the recording. It is only in the aorta that maximal values are obtained. Pushing the catheter further generally produces a decrease in deflection which is due to the fact that the silver convector is pushed against the aortic wall and less heat is removed. When it is desired to keep the carotid arteries intact, the catheter can be introduced into the femoral artery,

but in that case fluoroscopy will be necessary to localise the convecting tip in the ascending aorta.

During the many experiments which were per- formed on dogs, it has been proved that the instru- ment is reliable and gives reproducible results. At any moment the zero-velocity value can be obtained by pulling the catheter back into the carotid artery, while maximum-velocity values are easily obtained by switching off the heating.

Pulling the catheter back and replacing it into the aorta always produces the same values.

Fig. 4 shows a typical recording of aortic blood velocity before, during and after an injection of Isuprel in a dog,

References CASELLA, C. and DECARO, L. G. (1960) Description of

a thermo-fluximetric device attached to an intra- vascular catheter. Arch. Sci. BioL 44, 194.

DELAUNOIS, A. L. (1956) A new method for intravascular flow and cardiac output measurements by means of thermistors. Abstracts Comm. XXth International Physiological Congress, 228.

DELAUNOIS, A. L. (1961) Continuous measurement of blood flow and cardiac output by means of a calibrated catheter equipped with thermistors. Abstracts Inter- national Biophysics Congress, Stockholm, 127.

DELAUNOIS, A. L. (1961) Continuous measurement of blood flow and cardiac output by means of a Cournand catheter equipped with thermistors. Arch. lnt. Pharmacodyn. 134, 245.

DELAUNOIS, A. L. and ROVATI, L. A. (1958) A new method for continuous measurements of cardiac output. Arch. lnt. Pharmacodyn. 116, 228.

DELAUNOIS, A. L. and BERNARO, P. J. (1966) Cardiac output measurements by means of thermosensible catheters. Arch. Int. Pharmacodyn. 160, 474.

FRY, D. L., MALLOS, A. J. and CASPER, A. G. T. (1958) A catheter tip method for measurement of the instantaneous aortic blood velocity. Circ. Res. 4, 627.

GIBBS, F. A. (1933) A thermoelectric blood flow recorder in the form of a needle. Proc. Soc. Exp. BioL Med. 31, 141.

HENSEr-, H. and RuEF, J. (1954) Fortlaufende Registrie- rung der Muskeldurchblutung am Menschen mit einer Calorimetersonde. Pftugers Arch. Ges. PhysioL 259, 267.

HENSEL, H. and BENDER, F. (1956) Fortlaufende Bestim- mung der Hautdurchblutung am Menschen mit einen electrischen Warmeleitmesser. Pflugers Arch. Ges. Physiol. 263, 603.

MELLANDER, ST. and RUSHMER, R. F. (1960) Venous blood flow recorded with an isothermal flowmeter. Acta. Physiol. Scand. 48, 13.

M d t h o d e t h e r m i q u e pour la mesure cont inue de la vitesse du sang dans les gros vaisseaux d6bi t et la dd te rmina t ion du card iaque

Sommaire---On d6crit un d6bitm~tre du type cath6ter pour les mesures continues de vitesses sanguines. Le nouvel instrument est bas6 sur la m6thode thermique: une quantit6 constante de chaleur produite 61ectriquement est dissip6e partiellement par convection dans le r6seau sanguin. L'6quilibre r6sultant pour chaque valeur de vitesse sanguine d6termine la temp6rature du corps dissipateur de chaleur. Cette temp6rature est d6termin6e avec prfcision ~t l'aide de thermistances. La lin6arisation de la relation hyperbolique vitesse sanguine/r6sistance de la thermistance est accomplie par un amplificateur antilogarithmique appropri6.

204 Medical and Biological Engineering ~ March 1973

Thermische Methode fur kontinuierliche Blutflussmessungen in grossen Blutgef&ssen und Herzleistungsbestimmung

Zusammenfassung--Ein katheterhhnlicher Durchflussmesser fi.ir kontinuierliche Blutflussmessungen wird beschrieben. Das neue Ger~tt arbeitet auf thermischem Prinzip: ein konstanter Betrag von elektrisch erzeugter Wiirme wird teilweise dutch Konvektion in den Blutstrom abgegeben. Das sich einstellende Gleichgewicht fi.ir jeden Betrag von Blutflussgeschwindigkeit bestimmt die Temperatur des w~irme- gebenden K6rpers. Diese Temperatur wird mittels eines Thermistors genau gemessen. Die hyper- bolische Abhhngikeit der Blutgeschwindigkeit und des Thermistorwiderstandes wird mittels eines ~ l l t ~ ; p l i ~ i J l i ~ l l U i:l_llLllO~:~i:l,l ILIIIIIISL:II~I1 y r ~,LI::tEK~I'~ lli~l.~i:ll ' l~il~l L.

Medical and Biological Engineering March 1973 205