10
A new method of measuring arterial dilation and its application* A. Leblanc Laboratoire de recherche en genie medical, Universite du Quebec a Trois-Rivieres, Canada Abstract--An instrument has been designed and constructed for the in-vivo measurement of instantaneous (phasic) diameter changes of arteries. The continuous record of this blood- vessel dimension, when recorded simultaneously with blood pressure, may be used to estimate the viscoelastic properties of the arterial wall. Keywords--Dilation, arteries, viscoelasticity, plethysrnograph Introduction THE TRANSDUCERconsists of a water-filled chamber surrounding a short segment of blood vessel, and serves as a volume meter (plethysmograph). The volume of fluid displaced by the periodically expanding artery is sensed as a change in water level in a fine tube connected to the larger chamber. The level in this fine tube is converted into an electrical signal, which is exactly proportional to the cross- sectional area of the artery under the probe. The instrument can be made very sensitive, since small volume changes of the vessel create, in the level sensing tube, larger level changes for a narrower tube. RUSHMER (1955), PETERSON et al. (1960) and MALLOS (1962) have described instruments for measuring the radius (or cross-sectional area) of blood vessels. Rushmer's and Mallos's transducers cannot very well be applied to small vessels with a diameter less than 1 mm. Peterson's and Patel's instruments require suturing to the vessel's wall, which is unphysiological and may have undesirable side effects. The loading of the vessel wall due to these instruments is probably minimal, but, none- theless, it may be rather unpredictable. On the other hand, it seems that only Rushmer's instrument is suitable for chronic implantation, although it is likely that electrochemical contact problems will arise. In the design of the instrument described, we have tried to avoid some of these disadvantages. The transducer can be usedon avesselas small as 0.5 mm in outside diameter and it can be implanted, with the vessel remaining intact. The loading due to the fluid mass within the plethysmograph has been minimised. It is not claimed, however, that the instrument can measure the vessel's mean diameter as accurately as it can measure phasic changes. * First received 17th April and in final form lOth July 1972 Design The blood vessel is inserted through the slot S to lie in the middle of the water-filled plethysmograph chamber C. The inside cylindrical wall isformed by a L S C W d R AV ~ ! -i Fig. 1 Principle of design operation 326 Medical and Biological Engineering May 1973

A new method of measuring arterial dilation and its application

Embed Size (px)

Citation preview

Page 1: A new method of measuring arterial dilation and its application

A new method of measuring arterial dilation and its application* A. Leblanc

Laboratoire de recherche en gen ie medical, Universite du Quebec a Trois-Rivieres, Canada

Abstract--An instrument has been designed and constructed for the in-vivo measurement of instantaneous (phasic) diameter changes of arteries. The continuous record of this blood- vessel dimension, when recorded simultaneously with blood pressure, may be used to estimate the viscoelastic properties of the arterial wall.

Keywords--Dilation, arteries, viscoelasticity, plethysrnograph

Introduction THE TRANSDUCER consists of a water-filled chamber surrounding a short segment of blood vessel, and serves as a volume meter (plethysmograph). The volume of fluid displaced by the periodically expanding artery is sensed as a change in water level in a fine tube connected to the larger chamber. The level in this fine tube is converted into an electrical signal, which is exactly proportional to the cross- sectional area of the artery under the probe. The instrument can be made very sensitive, since small volume changes of the vessel create, in the level sensing tube, larger level changes for a narrower tube.

RUSHMER (1955), PETERSON et al. (1960) and MALLOS (1962) have described instruments for measuring the radius (or cross-sectional area) of blood vessels. Rushmer's and Mallos's transducers cannot very well be applied to small vessels with a diameter less than 1 mm. Peterson's and Patel's instruments require suturing to the vessel's wall, which is unphysiological and may have undesirable side effects. The loading of the vessel wall due to these instruments is probably minimal, but, none- theless, it may be rather unpredictable. On the other hand, it seems that only Rushmer's instrument is suitable for chronic implantation, although it is likely that electrochemical contact problems will arise.

In the design of the instrument described, we have tried to avoid some of these disadvantages. The transducer can be usedon avesselas small as 0.5 mm in outside diameter and it can be implanted, with the vessel remaining intact. The loading due to the fluid mass within the plethysmograph has been minimised. It is not claimed, however, that the instrument can measure the vessel's mean diameter as accurately as it can measure phasic changes.

* First received 17th Apri l and in final form lOth July 1972

Design The blood vessel is inserted through the slot S to

lie in the middle of the water-filled plethysmograph chamber C. The inside cylindrical wall isformed by a

L

S

C W

d R AV ~ !

- i

Fig. 1 Principle of design operation

326 Medical and Biological Engineering May 1973

Page 2: A new method of measuring arterial dilation and its application

very thin rubber membrane R which is mounted unstressed at the ends E and which surrounds the blood vessel snugly (Fig. 1). A wet film between blood vessel and rubber prevents separation of the mem- branes. The motion of the blood vessel is constrained only at the ends E where the instrument diameter is equal to or slightly smaller than the artery. This necessitates the fabrication of a series of transducers so that the one of ideal size can be selected quickly as soon as the artery to be studied is exposed. A length of 20ram for the chamber l was chosen for the transducers used on vessels comparable in size to the femoral artery of 15 kg dogs; its outside diameter d was about 7 mm.

The chamber's walls are made of polystyrene. An expansion of the encased volume of the artery

by AV changes the water level in the indicating tube I by AV/zca 2. When used on the femoral artery, the inside diameter of the tube L was 1 ram; this

radius a is chosen to provide optimum sensitivity. A vessel of 1.5mm diameter expanding only 1 ~ in radius causes a rise in tube L of 3:5 mm.

There is no reason, in principle, for mounting tube L perpendicular to chamber C, as shown in Fig. 1. Although this design has proved to be convenient for acute experiments, it might be altered when the instrument is implanted.

Screw M is used for adjusting the mean water level in L and for calibration.

The fluid level in the narrow tube L is detected by measuring the capacitance of a thin insulated wire W placed in the middle of tube L. The enamel coat I acts as the dielectric of the capacitor whose one electrode is the copper wire itself and whose other electrode is the water saline solution. A sensitive capacitance meter (Fig. 3) with a fast response gives an output signal proportional to the fluid level.

I I II .I II

glass capillory

�9 Perspex

Fig. 2 Mounting of~eve~- sensing tube

centering hole (three holes for fluid path)

wall of chamberj C

Medical and Biological Engineering May 1973 327

Page 3: A new method of measuring arterial dilation and its application

9

8~ o.

u_ b_

~ OIL o.,-~ 6

F ~ o I-

6

I I

I,. . . . . . J

J 0 ~u =~ I~

I 1 1 I

0 "

11 J

r

E

328 Medical and Biological Engineering May 1973

Page 4: A new method of measuring arterial dilation and its application

Table 1, Pressure and dilation in the femoral artery o f dog no, 1

Frequency Pressure Dilation of harmonics amplitude phase* amplitude phase*

Phase lag k, kv of dilation

Hz mm H20 rad mm rad

2"78 199 6"56 0"0148 6"34 5" 56 207 5" 67 O' 0156 5" 40 8"33 67"2 4"96 0"0043 4"70

11 �9 11 38' 8 4' 66 O' 0031 4" 65 13"89 22 '4 4 '18 0"0019 3"96 16' 67 7" 1 3" 70 O' 00066 3" 74 19" 44 3"7 4' 26 0"001 O0 3' 90

P = 1550 mm H20 r = 1.75 mm

*phase reference is arbitrary, Le. roughly the "foot" of the pulse observed at the site

Details

Mechanical design: (In the following, some additional information on the transducer is given.) The slot S (Fig. 1) is designed so that the compressed blood vessel can be inserted without difficulty. The narrowest width of the slot should be about four times the wall thickness of the artery. Thus, assuming the wall thickness is about 10~o of the vessel radius, the opening S should have an angle of 25 ~ After the vessel is in place the opening is closed with an appropriately shaped wedge.

To obtain good accuracy, the level-indicator tube L must have a uniform diameter. We used glass capillary tubing and coated its inside with Siliclad (Clay-Adams Inc.), a nonwetting agent, prior to installation. The glass tube is connected to the plethysmographic chamber by a special fitting and holder (Fig. 2). This fitting is screwed into the chamber's wall and has two functions; it connects the glass capillary tube and positions the capacitor wire centrally in the base of this tube.

At the other end of the capillary tube, a cap ensures the exact central placement of the wire. In an acute experiment, this cap is provided with vent

degrees mm H20 10 .2 mm m/s 13-7 129 3"2 10"6 15"5 126 3"5 10 '5

5"9 151 4 10 '5 0"006 125 - - 10-5

12"6 115 2"6 10 --2"3 107 0"4 9 '7 20"6 34"7 1 "3 5"5

holes; for chronic implantation, it serves as a seal and provides an air pocket for expansion

An enamel coated wire, no. 40 (AWG), was used as the level detector. Its diameter is 0.08 mm; the thickness of the enamel coat is about 0.005 mm and the measured relative permittivity of the enamel was 4. Thus, the capacitor formed by the wire and the surrounding water has 1.8 • 10-~2 F /mm length of wire immersed in the fluid.

Electronics: The "circuit used to measure the change of capacitance (i.e. capacitance due to the section of wire immersed in the saline solution) is shown in Fig. 3. It contains an oscillator producing a 455 kHz signal, clipped at + 6 V, and applied across the unknown capacity. Since the voltage V is constant, the current flowing into the circuit is directly proportional to the total capacity. This current measurement is made by inserting the primary winding of a tuned transformer T2 in series with the probe. On the probe side of the transformer, the effective current-sensing impedance is about 150 f~, small compared with the mean value of the capacitor reactance (about 7 kf~). The voltage across this current-sensing impedance is stepped up and filtered

Table 2. Pressure and dilation on the femoral artery of dogs 2, 3 and 4

Frequency ~hase lag ke of harmonics of dilation

kv c

Femoral a dog no. 2.18 12-8 86"2 1.96 p ---- 1630 mm H20 4.36 10.4 79 1.45 re = 1 .95mm 6.54 17-6 101 3.2

dog no. p = 1630 mm H20 2.39 16.5 117 3-5

4.78 15-1 109 2.95 ro = 1 ' 7 4 m m 7.17 4.7 185 1.5

Carotid a p = 1730 mm H20 1-4 5.7 128 1.28

2.81 7.6 134 1.8 re = 1 "74mm 5-61 12.4 144 3

9.1 8.8 9"9

10 9.7

12.7

10.6 10 '8 11.2

Medical and Biological Engineering May 1973 329

Page 5: A new method of measuring arterial dilation and its application

by the transformer. Thus, the voltage across the output appears as a sinusoidal signal at 455 kHz, with an amplitude proportional to

oR C /~/ {1 + (coRC) 2} coR C

assuming perfect tuning where o = 2n x 4.55 x l0 s Hz, R is effective current- sensing resistance and C is total capacitance of probe.

c

"O

L

Fig. 4

[ i i

x(t) $1 1 , l . !

�9

time

ogRC = 0.01 for the values of R and C used in practice.

The signal is therefore closely proportional to the capacitance of the wire immersed in the fluid. This signal is subsequently rectified into the voltage quadrupler circuit (Fig. 3).

Performance

Theoretical: The static response of the transducer is very accurate. Whatever amount of fluid is displaced by the expanding artery must appear in the level-sensing tube. The only possible deviation from ideal response is caused by the end effect; the artery cannot expand freely close to the ends of the chamber E (Fig. 1). This effect cannot be detected, provided that the length of the chamber is chosen to be at least seven times the diameter of the blood vessel.

The dynamic response of the instrument can be discussed and evaluated with respect to the following phenomena: the forces necessary to accelerate the fluid from the main chamber into the fine tube; the frictional forces in the small level-sensing tube; and the pressures occurring due to convective forces within the liquid flowing from the large cross- section of chamber C to the fine tube. The magnitude of these three terms can be estimated by formulating the equation of motion of a liquid

within a simpler boundary exhibiting the same essential features (Fig. 4). After integrating the differential equation over the cross-sectional area, one obtains the following expression (containing the dominant forces only):

a + b + c = pH~+Slzlr { h + (Sc/S,)x2 ! j

i Sc 2 +�89 [ s , 2

where: x is displacement of arterial wall; p is density of fluid in plethysmograph; Sc is effective area through which the fluid flows in chamber C; $1 is cross-sectional area of level-sensing tube; H is effective thickness of chamber C; h is mean fluid level in fine tube; and / t is viscosity of fluid.

We have not taken into account the fine details of flow profiles within the instrument; further, it is clear that several simplifying assumptions have been ~sed in the above expression, such as Poiseuille flow in the small tube and no frictional losses in chamber C.

The sum of pressures shown in the above formula equals the pressure necessary to move the fluid by x(t). In our case x(t) is given essentially by the expansion of the artery (so long as a + b + c is small) and the pressure calculated represents the load on the

20

15

4o "6

i 2 pF I m

ine / 31.2 mV/ pg

0 / , , 2'5 3 3"5 4

V

Fig. 5 Calibration of wire @40 (water saturated with NaCI)

330 Medical and Biological Engineering May 1973

Page 6: A new method of measuring arterial dilation and its application

vessel. Therefore, we considered it sufficient to assume a rather extreme x(t) and compute the magnitudes of the various loading terms given a particular geometry of the instrument. If the loading pressure is found to be very much smaller than the driving arterial pressure, the instrument can be considered free of constraining effects. On the other hand, if some of the terms turn out to be compara- tively large, the design of the instrument would have to be modified. It is also clear that the simple hydrodynamic model would have to be refined if tests indicated a large load effect.

The motion of a blood vessel of 3 mm diameter expanding by 5 % in about 0.05 s during the beginning of systole, is approximated by a sinusoidal function. The amplitude of this oscillation then is 2.5 x 10 -2mm and its frequency is 10Hz. (Although a vessel may expand in a shorter time, we consider 10 Hz a reasonable frequency at which the velocity and acceleration of the vessel wall can be calculated.)

Using these figures in the differential equation, it is found that the maximum accelerative pressure at the fundamental frequency is 0.05 m m H 2 0 , and the maximum pressure due to convective force c is 10 mm H20 (effective Sc/Sz is assumed to be 300). These numbers indicate that the dynamic loading effect of the instrument is indeed minimal.

A limiting factor not yet mentioned is that a very

s 0

(3.

"6

E

0

13 r .o c r~ ~x

1.111[ o OxOxxqxxO x x x x x x x x ~ X 0

0.9[ ~ , , , / o

0.8 loss of liquid

small pressure might develop in the fine level- sensing tube when the vessel decreases in size and the fluid is 'sucked' into the main chamber. This pressure could be low enough to allow the formation of small vapour bubbles. The approximate formula of the pressure considered here (using the same notations as above) is:

S c .~ p(h+ xSc/S,) S~z x

This term assumes a value of about 50 mm H20, if x(t) is assumed to be changing equally rapidly during the latter part of systole (which certainly is a pessimistic assumption). Even lowering the pressure within the fluid by such an amount, however, would not cause local evaporation, and so it does not seem necessary to work with degassed fluid.

It must also be considered to what extent the rubber membrane forming the inner lining of the plethysmographic chamber represents a ' load ' for the arterial wall. The thinnest rubber sheet available available was 0.15 mm thick. Its modulus of elasticity was measured on strips out of these sheets and was found to be 2 x 104 N/m 2. Note that this is a value which is about 5 % of the Young's modulus of small arteries (BEaGEL, 1961). On the other hand, it is more instructive to calculate how large a pressure

X xX x X

X X

0

"o + 5

~ 0

v

<3

o - 5 r- r-1

X

. . . . . . . . . . . . ~ l 1 ~ . . . . . . . . ~ - - 1 - - x . . . . .

0 X 0 X

% x

I I "

5 !0

frequency, Hz

Fig. 6 Frequency response of the diamometer

x exponential no. 2 o exponential no. 4

Medical and Biological Engineering May 1973 331

Page 7: A new method of measuring arterial dilation and its application

it would take to change the radius of a hose, made of this same material, by 1 ~ :

Ap = 2 (A r/r) Eh/1 .5 r

where: r is radius of vessel; h is wall thickness of vessel; and E is Young's modulus of elasticity.

This formula is often used in the study of the elasticity of blood vessels; its derivation is given by HOREMAN and NOORDZRCRAAr (1958). F rom this expression, it is found that the rubber membrane discussed creates a loading pressure of about 1.5 mm H20 for a 1 7oo change in the radius of the blood vessel underneath it. I t therefore seems justified to assume that there is no significant constraint applied to the blood vessel by the transducer.

The continuous linear relation between the water level in the tube and the output of the capacitance meter was tested not only by connecting a variable calibrated capacitor to the detecting circuit instead of the probe, but also by changing the fluid contents by known amounts in a test tube with a wire mounted in place. The results of the latter run are shown in Fig. 5. The former experiments showed that the

.response of the circuit becomes nonlinear below 30 pF, and, depending on the damping resistor on the secondary side of the tuned i.f. transformer (T2) (Fig. 3), also at high capacitances of the probe. Appropriate values of resistor and fixed padding capacitors, however, ensure operation in the linear range.

The dynamic performance of the electric circuit can be easily predicted. I f the tuned transformer (T2)

(Fig. 3), has a relatively low Q factor, as is the case for the commercially available i.f. transformer used, the only limiting factor is the filter employed to eliminate the ripple left after the signal has been rectified. In our case we have used three stages of simple R C low-pass filters with a cutoff frequency of 3 kHz. Such an arrangement introduces a phase shift of 1.5 ~ at 60Hz, less below this frequency, about - 1 dB at 900 Hz and less below this latter frequency. This frequency response is very satisfactory.

Exper imenta l : The dynamic response of the instru- ment was tested in the following manner. The transducer was placed around a soft water-filled rubber tube, which was, in turn, connected to a specially designed pump producing sinusoidal flow. The pump consists of a crank-driven piston, the length of the piston being about 500 times that of the crank. The frequency of the pump could be varied continuously from 0 to 15 Hz. A steady large pressure was maintained within the system, partly to expand the rubber hose to the desired size and partly to avoid a decrease of total volume in the system due to leakage between piston and cylinder. The instrument was installed close to the end of the rubber hose, which was connected by a rigid tube to the pump in order to eliminate time delays between the displace- ment of the pump (monitored with a Sanborn pressure tranducer) and the signal from the instru- ment. The results of a frequency run are shown in Fig. 6.

It can be seen that the tendency of the amplitude response to 'fall off ' at the higher frequencies is not

11

10

9

~ E E

~ 5

• ,4

f . . -, 3

1:

femora l Qr tery pressure

/ _

, , , I , ' I I

0 0.2 0 .4 0.6

time> s

11

10

9

2

1

I

0 .8 1

8

7 E E

' o 5 •

~JO

4 ~ "(3

3 L

Fig. 7 Recorded pressure diameter variation in the femora~artery for dog no. 4 (the upper brace is an e,c,g.)

332 Medical and Biological Enaineering May 1973

Page 8: A new method of measuring arterial dilation and its application

significant, and the phase differences are not larger than those which could be attributed to the difficulty of measuring phase differences between two noisy signals. It is concluded that the dynamic response of the instrument is satisfactory to at least 15 Hz.

Calibration The absolute calibration of a particular instrument

was performed each time before and after the trans- ducer was applied to a blood vessel. The outside of the level-sensing tube was marked with fine lines 1 mm apart. By tightening screw M (Fig. 1), the fluid level within the fine tube was advanced, in steps, from one mark to the next. The corresponding electrical signals were recorded, and the output could be calibrated in terms of level changes in the level- sensing tube. Since the diameter of this tube is known it is possible to relate the signals at the output with volume changes within the plethysmograph chamber. The accuracy of this procedure depends mostly on the accuracy with which these millimetre marks can be applied and with which the level in the small tube can be adjusted to a particular desired height. The error involved is probably about 0.1 mm, and can be improved somewhat because the final calibration line is a least-squared error match to many points expected to lie on a straight line. Since the maximum excursion in the level-sensing tube is about 20 ram, the accuracy of this calibration procedure is about 0.5%, In absolute terms, the 'resolution' of this plethysmograph is about 0.08 mm 3.

Application Phasic diameters of femoral arteries of three dogs

and of the carotid artery of one dog were measured. The animals (each weighing about 15 kg) were kept under light anaesthesia (about 6.4 mg/h of pentobar- bital sodium) after premedication with morphine (0.015 g). A section of the records obtained is shown in Fig. 7. In addition to the signal from the transducer, the pressures in the arteries were measured through a fine polythene catheter inserted into the next (upstream) side vessel, which usually was not more than 2.5 cm away from the centre of the transducer. The small catheter was connected to a Statham P23D strain-gauge manometer. The frequency response of the manometer was determined after the experiments by recording the response to an applied pressure step and by using standard procedures as described by MACDONALD (1960). The third trace (seen in Fig. 7) is the e.c.g.

From these records, the peak dilation of the arteries can be obtained. We chose to analyse both radius and pressure curves in more detail by decom- posing the pulses into their sinusoidal components after a Fourier analysis. This was done by reading ordinates off the recorded pulses at 0-01 s intervals using a Datascaler (Datascaler Inc., Westfield, Mass.,

USA) and subsequently letting a digital computer find the Fourier components and correct for the frequency response of the pressure-measuring apparatus. * In this way, one can not only compute the distensibility of the vessel as a function of frequency, but also estimate the viscosity of the vessel wall material (BERcER, 1961; PATEL, 1963).

The data on the vessel's viscoelastic properties are represented in the following form for each of the Fourier components:

(i) Phase difference between pressure signal and dilation (if) (ii) Elastic part of the radius distensibility in terms of observables:

Ap k, = ~ c o s (~)

(iii) Viscous part of the radius distensibility (in quadrature with k,)

k~ = ~ - sin (~b)

(iv) Phase (Bramwell and Hill) velocity

where ro = radius.

As is seen under (iv), the mean (inside) radius of the vessel has also to be determined, since it is useful to obtain the phase velocity c; c can independently be estimated, for the purpose of comparison, from the foot-to-foot velocity of blood-pressure pulses. In these first experiments, we determined the mean outside radius of the blood vessel in situ with a micrometer. The internal radius was computed from this by assuming that the wall-thickness/radius ratio was 0.16. This procedure is obviously not very accurate. However, the phase velocity computed still does pot deviate much from its true value, since the square-root operation halves any errors involved.

Table 1 shows the complete results obtained with one of the animals. The results obtained for the vessels of the three other animals are given, in a shorter form, in Table 2. Elasticities of two other samples of femoral arteries (dog no. 2 and dog no. 3) and of one carotid artery (dog no. 4) are shown only at the first three harmonics in each case. These are frequencies at which we can be sure to deal with large signal/noise ratios.

These first few results obtained appear to be 'reasonable' in that the computed phase velocities compare very well with those obtained by other

*All computations were done in the Computing Centre of The Johns Hopkins Medical Institutions

Medical and Biological Engineering May 1973 333

Page 9: A new method of measuring arterial dilation and its application

means, such as the foot-to-foot velocity of the pulse in the femoral artery of the dog (found to be 8-10 m/s). BERGEL (1961) predicted phase velocities (on the basis of viscoelastic constants obtained in vitro) of 8.5-9.5m/s. However, PATEL et al. (1963) measured dilations at the level of the iliac artery of the dog which were much smaller. (ke = 350_+ 100ram H20/(10 -z rnm). The fact that PATEL et al. only considered peak-to-peak values does not seem to account for the discrepancy, since we have found the value of ke at the first harmonic to be very close to a ke derived from their peak-to-peak values. We cannot offer any explanation for these differences.

PETERSON et al. (1960) reported values of elastic moduli of the femoral artery which are only slightly higher than ours: ke = 165 _+ 70 mm H20/(10 -2 ram) (where ke is calculated from Peterson's E; from k e = Ep ro = p/dr). It has to be noted, however, that PETERSON et al. determined these values by comparing the pressure waveforms with the dilation signals processed by an analogue computer programmed to a first-order differential equation. Hence the criterion used in the choice as to which adjustment of the controls produced a 'perfect' match of the two curves influences the numerical values obtained. Peterson's results for the elasticity of the carotid artery yield a ke of 101_+ 32mm H20/(10-2mm). (Vessels of extremely small size have been omitted in the forming of these averages.) Though we have investigated only one case, our results (Table 2) do fall into the same range.

Discussion

Time spent on the careful machining necessary in the construction of the transducer in combination with the simple reliable electronic circuitry proved to be well invested; the possibility of error in the calibration of the instrument corresponds to a volume change (of the blood vessel) of only 8 • 3. If the plethysmograph's length is 20 mm, diameter changes as small as 5/zm can be resolved (about 1% of the physiological change). The electrical signal corresponding to this error is 0-01 V; i.e. the 'resolution' of the instrument is limited by the mechanical part. Thus it is possible to accept as reliable the calculated strains up to the sixth or seventh harmonic of a pulse recorded in a small vessel such as the femoral artery. It is particularly noteworthy that this transducer performs equally well when applied to arteries of elliptical cross- section. (It is doubtful that the large and variable ellipticity of veins would be compatible with this instrument.)

In this present study no attempt was made to determine the mean radius of the blood vessel to the

same accuracy as that of phasic changes. In the mean radius measurement we estimate our error to be 3-5 %. This error enters the calculation of the phase velocity, as does the possible computation of volume elasticity.

Limitations pertaining to the measurement of the dilatation of extremely small arteries have to be considered. The finer the blood vessel, the shorter becomes the length that can be placed within the plethysmograph. Therefore the volume changes to be measured also become progressively smaller than those of the central vessels. However, the sensitivity of the instrument described here can be kept constant by providing a corresponding decrease of the lumen of the level-sensing tube. There are, however, certain limitations owing to the fact that the frictional forces in this fine tube will load the vessel wall in these extreme cases. A simple method of estimating the loading pressure is given above. It also should be noted that mounting of the rubber membrane within the plethysmograph becomes increasingly difficult as the vessel size is reduced. We have found that it is possible, without much difficulty, to construct transducers of 0.75 mm in diameter.

The dynamic response shown to be 'flat' up to 15Hz appears to be satisfactory, since, at this frquency and above, the Fourier components of both pressure and dilatation are very small (Table 1). PATEL and FRY (1963) have found the same in the larger central arteries.

In the discussion of the first results obtained on the fermoral artery of a few dogs, we found the radial distensibility (Ap/Ar) to vary slightly with frequency about a value of about l l 0 m m H 2 0 ( 1 0 - 2 m m ) . This corresponds to a volume elasticity Ap/(2Ar/r) of about 104 mm H20 (i.e. 105 N/m 2) which agrees with values in the literature. We have avoided calculating values for Ey, the Young's modulus of elasticity, since it cannot be directly verified.

References BERGEL, D. H. (1961) The dynamic elastic properties of

the arterial wall. J. Physiol. 156, 458~469. HOREMAN and NOORDERGRAAF, A. (1958) Numerical

evaluation of volume pulsations in man. Phys. Med. Biol. 3, 51.

MALLOS, A. J. (1962) An electric caliper for continuous measurement of relative displacement. J. Appl. Physiol. 17, 131-134.

MACDONALD, D. A. (1960) Blood flow in arteries. Williams and Wilkins.

PATEL, D. J. (1963)Relationsbip of radius to pressure along the aorta in living dogs. J. Appl. Physiol. 18.

PETERSON, L. H., JENSON, R. E. and PARNELL, J. (1960) Mechanical properties of arteries in vivo. Circ. Res. VII, 662.

RUSnMER, R- F. (1955) Pressure-circumference relation in the aorta. Amer. J. Physiol. 183, 545-549.

334 Medical and Biological Engineering May 1973

Page 10: A new method of measuring arterial dilation and its application

Une nouvelle m6thode pour rnesurer la di lat ion art6r ie l le et son appl icat ion

Sommaire--Un instrument a 6t6 congu et fabriqu6 pour le mesurage in vivo des" changements instantan6s (de phase) au diam~tre des art~res. L'enregistrement continu de cette dimension des vaisseaux sanguins, quand il est relev6 en m~me temps que la tension art6rielle, peut ~tre utilis6 pour 6valuer ]es propri&6s visco-61astiques de la paroi art6rielle.

Eine neue M e t h o d e der Arter iendi latat ionsrnessung und ihre Anwendun- gen

Zusammeafassung--Entwurf und Konstruktion eines Instrumentes ftir die in-vivo Messung augenblicklicher (phasischer) Arteriendurchmesseriinderungen werden beschrieben. Die fortlaufende Aufzeichnung dieser Blutgef~issabmessung kann, wenn sie gleichzeitig mit dem Blutdruck registriertwird, zur Abschiitzung der viskoelastischen Eigenschaften der Arterienwand benutzt werden.

Medical and Biological Engineering May 1973 335