Dynamic calibration of manometer systems* B. H6k Department of Electromedicine, Siemens-Elema AB, S-171 95 Solna, Sweden~
A b s t r a c t - - T w o simple and inexpensive methods for dynamic calibration of manometer systems for the clinical environment are described. One is a modification of a well known step-function technique, the other is a sinusoidal pressure generator using magnetic fluids. The practical use of both methods is described in detail, and a test of the accuracy of the methods is made. In particular, it is found that both methods are useful in the frequency range of at least 0 to 100 Hz, and that resonance frequencies could be determined with an error of about +. 5%, whereas the error in damping factor is greater, of the order of + 50%. The step-function technique is quicker and easier to apply under sterile conditions and is therefore recommended for wider use. Keywords--Pressure generator, Manometer calibration
Introduction THE limited dynamic response of manometers and catheter-manometer systems should imply that all measurements be preceded by a dynamic calibration. The requirements of such a calibration technique would be to detect resonance frequencies and damping below 100 Hz, a frequency limit which is
believed to be sufficient for most, if not all, pressure measurements of clinical value (McDoNALD, 1974; KROVETZ and GOLDBLOOM, 1974). Once the dynamic response has been determined with reasonable accuracy, experience with the system at hand should decide if improvements could be expected from flushing with CO2, addition of
Step function
Frequency response
j~ Output
!, Amplitude Amax I
e2
Ao
I
]/fd I
Time ~ = A(4 2 + ^2)-1/2
f
max
Amax/Ao = I/2 ~-I(1-C2)-I/2
A = 2(In61 - lne2)
fo = fmax(1 - 2~2)-I/2
fo = fd (I - K2) -I/2
'
~ 3dB
.... ?.--% 10% N
I I fu
r
fu
I n9 = ~
O' 35 =
tr
* First received 14th March and in final form 26th March 1975 The work was carried out at the Electronics Department, Institute of Technology, University of Uppsala
Medical and Biological Engineering
March 1976
Fig. I Summary of the formulas needed for the interpretation o f dynamic response records
193
detergent, impedance matching or whatever the preferred technique may be. Dynamic calibration is, however, seldom performed in routine clinical work, probably due to difficulties in maintaining the sterility of the system during the calibration procedure. Another contributing factor is believed to be the degree of complexity introduced by some of the designers o f pressure generators. In general, these pumps require well equipped workshops for their construction as well as great care in performing the calibration to give correct results. The purpose of this paper is to show that it is possible to devise simple and inexpensive means for the dynamic calibration of manometer systems under sterile conditions. The first approach is a modification of a well known technique to generate pressurestep functions, and the second is a simple method of generating sinusoidal pressure waveforms using a magnetic fluid. t~
90
-r
E LU Cc
w rr n
-15
10 % -ill
I
0 I
5
~, ~ RISE TIME
I 10
15
=
TIME (msec)
Fig. 2 Step response rise time recorded with a directly connectedfastpressure transducer. This recording, like Fig. 3, was made with a Datalab DL 905 Transient Recorder and displayed with a Watanabe WX 431 XY-recorder
In Fig. 1, a summary is given of the formulae needed for the interpretation of results obtained with the two methods. A 2nd-order model is used, with a damping factor ( a n d an undamped resonance frequency fo. The correspondence at low damping between the two methods is obvious from Fig. 1. With increased damping, it becomes increasingly difficult to determinefo and ~ independently, and, for the overdamped case, it is more relevant to measure the rise time of the step response which corresponds to a certain upper frequency limit. The system approaches a lst-order model in the interesting frequency range, and, for this model, the upper frequency limit f= is related to the rise time tr by f , = ln9/2ntr. F o r systems close to critical damping (( = 1), step-response recordings deviate from an exponential rise, a difference which is difficult to see directly on the recording. Therefore, in this case, frequency-response recordings are easier to interpret; for high frequencies, the output falls by 12 dB per octave in contrast to a I st-order system which gives a 6 dB per octave fall. 194
Pressure-step generation The originator of the proposed pressure-step technique appears to be HANSEN (1949). He drilled a hole through the piston and stem of an ordinary glass syringe. The manometer system was connected with a needle to the syringe, which was mounted vertically and contained both water and air. If the piston was withdrawn with one finger covering the drilled hole, a negative pressure developed inside the syringe, and when the finger was released the pressure returned to ambient pressure with a rise time of less than l0 ms (as estimated from Hansen's recordings). It is interesting to note, however, that Hansen obviously made the whole sequence, that is, withdrawal of the syringe and removal of the finger, in rapid succession so that the excitation would be an impulse rather than a step function. The duration of the entire transient was about 30-50 ms, which cannot be regarded as short compared with the period lengths of catheter resonances. According to McDoNALD (1974), it is also difficult to avoid vibration artefacts with this technique. To make use of the fast step when the finger is released, a stable base line prior to the step is required, so that resonances are excited by the step alone. The same argument also applies to another version of the technique, where the piston is simply drawn out of the syringe giving a sharp transient when the piston leaves it; in this case, it is inherently impossible to obtain a stable base line immediately prior to the step. In the present modified technique, ordinary plastic 1 ml tuberculin syringes are used with a 2 mm hole drilled in the wall close to the outlet, which is connected to the manometer system via a needle (18G or thicker). The syringe is air filled, and the pressure step is performed as did Hansen with the exception that the negative pressure is allowed to persist for a few seconds, while the vibrations from piston movement die out. The piston generally stops owing to static friction at pressures of more than 30 mmHg. It is then a simple matter to rapidly lift the finger without causing vibrations that are visible on the records. Fig. 2 shows a recording of the system rise time. The pressure transducer used in this and all following experiments was an improved version of an electrolytic microtransducer described earlier (H6K, 1975). The calculated resonance frequency of the transducer used was 600 Hz, but a low-pass filter in the amplifier with a time constant of 0.5 ms set a somewhat lower limit to the system. Thirty consecutive measurements of the rise time with a transducer directly connected gave a mean value of 2-1 ms and a standard deviation of 0.5 ms. The highest measured value was 3.2ms. This experiment shows that the technique is reproducible and capable of exciting resonance frequencies in the range 0-100 Hz. Longer sweep times than that used in Fig. 2 show a stable base line, which is to be expected since the
Medical and Biological Engineering
March 1976
first, represented by YANOF et al. (1963) and by BALL and GABE(1963), uses an electric motor as the driving element connected via a cam to a pressure chamber which is compressible either by the compressibility of water or by allowing the chamber to be partly filled with air. The problem with this type of generator, as pointed out by VIERHOUT and VENDRIK (1964), is the fact that it is basically a volume generator shunted by the compliance of the chamber. According to Thgvenin's theorem, this is equivalent to a pressure generator with the same compliance connected in series. The compliance must then be large and frequency independent so that compliant loading of the system does not influence the pressure output. This is difficult to achieve in a single system with either air or fluid-filled chambers. The second approach has been represented by authors such as NOBLE (1959), VIERHOUT and VENDRIK (1961), STEGALL (1967), HENRY et al. (1967) and SHELTON and WATSON (1968). The difference from the first approach is that the connection between the actuating element and the pressure chamber is not stiff but provides for much of the compliance needed according to the discussion above. In practice, the actuator may be a loudspeaker coil which acts on a piece of magnetic material. This, in turn, is fixed to a membrane, and the forces on this membrane causes the pressure to vary in an adjacent fluid-filled chamber. In this case, the compliance of the membrane limits the allowed degree of loading. The present sinusoidal pump, shown in Fig. 4, comes under the second category of generators. The only new feature is the use of a drop of a magnetic fluid (commercially available from Ferrofluidics Corp., 144 Middlesex Turnpike, Burlington, Massachusetts 01803, USA) instead of a diaphragm. This has the advantage that the pressure-chamber part can be manufactured from a few pieces of tubing and an O ring, and that this part does not need to be permanently fixed to the actuator, which, in this case, is a small electromagnet with a soft-iron core having a d.c. resistance of 8fl and an inductance of 10 mH.
syringe has free communication with ambient air. Fig. 3 demonstrates the excitation of resonance frequencies by using a polyethylene catheter (PE 90, inner diameter 0- 87 mm, outer diameter 1-27 ram) between the syringe and the transducer. 50 cm and 10cm lengths of the catheter gave undamped resonance frequencies of 42 and 108 Hz, respectively. The damping factor was about 0" 15 in both cases.
Sinusoidai-pressure generator The problem of generating sinusoidal-pressure signals has been mainly tackled in two ways. The +5 -1E E
0
it3 UJ
(~ -10
-15
I 0
I
I
t
50 a
100
150 TIME (ms)
b v
*5 I E
E
0
LD LU Or" ~-
-I0
-15
I 50
I 100
b
I 150 v TIME [ms~
Fig. 3 Catheter resonance excited by a step function. (a) Polyethylene PE 90 catheter, 0.5 m length, (b) Same catheter cut down to O" I m length Electromagnet
Polyethylene tube
O-ring
Transducer or
\ Current generator
Magnetic fluid
\ Water
Medical and Biological Engineering
M a r c h 1976
Fig. 4 Schematic of the new sinusoidal pressure generator
195
The magnetic fluid is a colloidal suspension of small ferrite particles with linear dimensions of the order of 10 nm. According to the manufacturer, the particles are prevented from sticking together by a 2"5 nm coating. A wide spectrum of liquids, including water, can be used as carrier fluids. The presence of the magnetic particles has the effect that a force will act on the fluid as a whole when it is influenced by an inhomogeffeous magnetic field. Other properties, such as viscosity, are virtually unaffected by the relatively low concentration of ferrite particles. The relaxation time of the ferrite dipoles is of the order of microseconds. Fig. 5 shows the static characteristics of the generator. A t low current levels, the transfer function is superlinear owing to incomplete orientation o f the ferrite particles in a weak magnetic field. When saturation occurs, at 0"02 T ( = 200 gauss, manufacturer's figure), the force acting on the fluid is approximately linearly related to the field strength which, in turn, is linearly related to the coil current. The force develops a negative pressure which may be sensed by a transducer (Fig. 4). The linearity of the sensor in this pressure region was established in an independent experiment. F r o m Fig. 5, it should be clear that, if a sinusoidal component is superimposed on a direct current in the linear part of the characteristics, a sinusoidal pressure variation will be generated. To achieve this, the circuit in Fig. 6 has been used. It is a common emitter transistor stage which serves mainly as a current amplifier. It can be driven by any sine-wave oscillator capable of delivering a few volts across slightly less than 100 ~ . The power supply must be able to supply at least 2A, and the power loss in I
i
CURRENT IA}
1 I I
~..
,x... -0.5
12
3
II
i
I
I
.t
I E E
-I'0 to -1"5
5o_ S (D -2"0
Fig. 5 Static characteristics of the pressure generator
196
the transistor calls for proper cooling; all the components can easily be mounted directly on the heat sink holding the transistor. Fig. 7 shows recordings of the relative pressure amplitude and phase as a function of frequency. The phase was measured relative to the voltage across the 1 fl resistor; this was believed to be an adequate monitor of the coil current. The drop in output of the direct recording at high frequencies is attributed to the detector-amplifier low-pass filter. A more thorough test of the limitations of the generator was not performed, since the frequency range of biomedical signals was shown to be covered. Catheter resonance is also demonstrated in Fig. 7 with a 0"5 m PE 90 polyethylene catheter. The transducer used for this experiment was stiffer than that used in Fig. 3, which accounts for the higher resonance frequency. A
~7~ 1N5050~__~
250 uF15V
.,
II-
"
II
* 24 - 30V i II
Electro magnet
10 mH 8,0.
2N 3055/8
SINE WAVE iNPUT 100 1/"2W
J
Ill
i
2W
&
/ov
Fig. 6 Transistorised power stage for delivering a constant sinusoidal current to the electromagnet over the desired frequency range Accuracy
test
To test the correlation between the two methods, a series of parallel determinations of resonance frequency and damping was performed. The result is shown in Fig. 8, and it can be seen that a high correlation for resonance frequencies is obtained, whereas the damping-factor estimations are less reliable. The resonance-frequency determinations have an error of less than + 5~o in about 7 5 ~ of the determinations. The correlation coefficient is 0.989, and the equation for the regression line is y = (0.93 + 0 . 0 4 ) x + ( 4 + 2 ) x and y stand for the step-function and frequencyresponse resonance frequencies, and the errors are standard deviations. It was not determined whether the deviation from the identityy = x is a result of the small statistical population or of a systematic deviation from the 2nd-order model of the system. Damping-factor determinations have a low correlation factor of 0.11, and 7 5 ~ of the measurements are within an error of + 50~/~. Frequencyresponse determinations show a tendency to be somewhat higher than the corresponding stepfunction determinations. Medical and Biological Engineering
March 1976
/ 0
9
c
Fig. 7 Amplitude and phase charac>= o
ox
\ 1
lO --
teristics of two recordings made with the pressure generator. The solid line is a recording made with a directly connected pressure transducer and the dashed line was made with a 0.5 m polyethylene PE 90 catheter
\
I
20
I
i
30
I
5O
1
I
1
\
I I
Q~
100
270
p/
f
I
J
200
300 Frequency (Hz)
200
300 Frequency t HZ)
fo
/
~L~180
/
2
F
90 n
JT~ ~
y I
2-0
:30
50
100
Discussion
I001
From Fig. 8, the potential applicabilities of the two methods should be dear. The accuracy of about + 5% in resonance frequency and _+50% in damping factor is probably sufficient for most routine calibrations. The error in damping factor will be excessive only in very special investigations, e.g. tests of manometer-system models. The step-function technique is quicker and easier to apply under sterile conditions than the frequencyresponse method. Faults, such as leaking syringes or improper handling are directly visible on the records, and a new recording can be made immediately in contrast to some other step-response techniques, e.g. balloon explosion. On the other hand, the frequency-response method has the advantages of a somewhat greater bandwidth and the possibility of applying bias pressure, a technique which can be used for the detection of air bubbles (HENRY et al., 1967). Moreover, for systems close to critical damping, frequency-response records may be somewhat easier to interpret, In most cases, however, these advantages are less important than the advantages of the step-function technique, which therefore can be recommended for more general use than is current practice.
5O
BALL, G. and G~d3E,I. (1963) Sinusoidal pressure generator for testing differential manometers. Med. Electron. Biol. Eng. 1,237-241. Medical and Biological Engineering
f
~
a
50
1oo
SF Resonance frequency (Hz)
0.8 t
o *50 Yo
|
Acknowledgments I wish to thank Kenth Nilsson of Siemens-Elema AB, for valuable suggestions. The work is supported by STU, the Swedish Board of Technical Development under grant 74-3205. References
~ -5% 0
@2
0%
0.z. 0"5 0.6 SF Damping factor
Fig. 8 Correlation between measurements with the step response technique (SF) and frequency response technique (FR) of (a) resonance frequency and (b) damping factor
March 1976
197
HANSEN,A. T. (1949) Pressure measurement in the human
SHELTON,C. D. and WATSON,B. W. (1968) A pressure
organism. Acta Physiol. Scand. 19, Suppl. 68, 7-230. HENRY, W. L., WIENER, B. and HARRISON, D. C. (1967)A calibrator for detecting bubbles in cardiac cathetermanometer systems. J. ,4ppl. Physiol. 23, 1007-1009. H6K, B. (1975) New microtransducer for physiological pressure recordings. Med. and Biol. Eng. 13, 279-284. KROVETZ, L. J. and GOLDBLOOM, S. D. (1974) Frequency content of intravascular and intracardiac pressures and their time derivatives. IEEE Trans. Biomed. Eng. BME-21, 498-501. MCDONALD, D. A. (1974) Bloodflow in arteries, 2nd ed. Edward Arnold, London. NOBLE, F. W. (1959) A hydraulic pressure generator for testing the dynamic characteristics of blood pressure manometers. J. Lab. & Clin. Med. 54, 897-902.
generator for testing the frequency response of cathetertransducer systems used for physiological pressure measurements. Phys. Med. Biol. 13, 523-528. STEGALL,H. F. (1967) A simple, inexpensive, sinusoidal pressure generator. J. Appl. Physiol. 22, 591-592. VIERHOUT,R. R. and VENDRIK,A. J. H. (1961) A hydraulic pressure generator for testing the dynamic characteris/ tics of catheters and manometers. J. Lab. Clin. Med. 58, 330-333. VIERHOUT, R. R. and VENDRIK, A. J. H. (1964) On pressure generators for testing catheter manometer systems. Phys. Med. Biol. 10, 403-406. YANOF, H. M., ROSEN,A. L., McDONALD,N. M. and McDONALD,D. A. (1963) A critical study of the response of manometers to forced oscillations. Phys. Med. Biol. 8, 407-422.
Calibration dynamique des syst~mes manomdtriques Sommaire--L'article d~crit deux m~thodes simples et non cofiteuses de calibration dynamique des syst~mes manom6triques, applicables dans les milieux cliniques. La premi6re est une modification d'une technique de fonction en 6chelon bien connue et la seconde est un g6n6rateur de pression sinusoidale 5. partir de fluides magn6tiques. L'usage pratique des deux m6thodes est d6crit en d6tail et des essais sur leur pr6cisions sont effectu6s. On trouve en particulier que les deux m6thodes sont pratiques dans la zone allant de 0 5. 100 Hz au moins et que les fr6quences de r~sonance peuvent ~tre d6termin6es avec une erreur d'environ + 5~o alors que l'erreur du facteur d'att6nuation est plus 61ev6e, de l'ordre de + 5 0 ~ . La technique de la fonction en 6chelon est plus rapide et plus simple 5. utiliser sous milieu ambiant st6rile, son usage est donc recommand6 dans un plus grand nombre de cas.
Dynamische Eichung yon Manometersystemen Zusammenfassung--Zwei einfache, biUige Verfahren zur dynamischen Eichung von Manometersystemen ffir den klinischen Gebrauch werden beschrieben. Das eine ist eine ANinderung eines wohlbekannten Stufenfunktionsverfahrens, das andere ist ein sinus~ihnlicher Druckgenerator mit Magnetfliissigkeiten. Die praktische Anwendung beider Verfahren wird genau beschrieben, und die Genauigkeit der Verfahren wird geprtift. Insbesondere wird festgestellt, dal] beide Verfahren im Frequenzbereich von wenigstens 0 bis 100 Hz nfitxlich sind und dab Resonanzfrequenzen mit einer Regelabweichung von etwa + 5~o bestimmt werden k6nnten, wogegen die Regelabweichung im Schwachungsfaktor gr613er ist, d.h. bei _ 5 0 ~ liegt. Das Stufenfunktionsverfahren ist schneller und leichter unter sterilen Bedingungen anzuwenden und wird daher ftir einen Gebrauch in gr6Berem Umfang emfohlen.
198
Medical and Biological Engineering
March 1976
A b s t r a c t - - T w o simple and inexpensive methods for dynamic calibration of manometer systems for the clinical environment are described. One is a modification of a well known step-function technique, the other is a sinusoidal pressure generator using magnetic fluids. The practical use of both methods is described in detail, and a test of the accuracy of the methods is made. In particular, it is found that both methods are useful in the frequency range of at least 0 to 100 Hz, and that resonance frequencies could be determined with an error of about +. 5%, whereas the error in damping factor is greater, of the order of + 50%. The step-function technique is quicker and easier to apply under sterile conditions and is therefore recommended for wider use. Keywords--Pressure generator, Manometer calibration
Introduction THE limited dynamic response of manometers and catheter-manometer systems should imply that all measurements be preceded by a dynamic calibration. The requirements of such a calibration technique would be to detect resonance frequencies and damping below 100 Hz, a frequency limit which is
believed to be sufficient for most, if not all, pressure measurements of clinical value (McDoNALD, 1974; KROVETZ and GOLDBLOOM, 1974). Once the dynamic response has been determined with reasonable accuracy, experience with the system at hand should decide if improvements could be expected from flushing with CO2, addition of
Step function
Frequency response
j~ Output
!, Amplitude Amax I
e2
Ao
I
]/fd I
Time ~ = A(4 2 + ^2)-1/2
f
max
Amax/Ao = I/2 ~-I(1-C2)-I/2
A = 2(In61 - lne2)
fo = fmax(1 - 2~2)-I/2
fo = fd (I - K2) -I/2
'
~ 3dB
.... ?.--% 10% N
I I fu
r
fu
I n9 = ~
O' 35 =
tr
* First received 14th March and in final form 26th March 1975 The work was carried out at the Electronics Department, Institute of Technology, University of Uppsala
Medical and Biological Engineering
March 1976
Fig. I Summary of the formulas needed for the interpretation o f dynamic response records
193
detergent, impedance matching or whatever the preferred technique may be. Dynamic calibration is, however, seldom performed in routine clinical work, probably due to difficulties in maintaining the sterility of the system during the calibration procedure. Another contributing factor is believed to be the degree of complexity introduced by some of the designers o f pressure generators. In general, these pumps require well equipped workshops for their construction as well as great care in performing the calibration to give correct results. The purpose of this paper is to show that it is possible to devise simple and inexpensive means for the dynamic calibration of manometer systems under sterile conditions. The first approach is a modification of a well known technique to generate pressurestep functions, and the second is a simple method of generating sinusoidal pressure waveforms using a magnetic fluid. t~
90
-r
E LU Cc
w rr n
-15
10 % -ill
I
0 I
5
~, ~ RISE TIME
I 10
15
=
TIME (msec)
Fig. 2 Step response rise time recorded with a directly connectedfastpressure transducer. This recording, like Fig. 3, was made with a Datalab DL 905 Transient Recorder and displayed with a Watanabe WX 431 XY-recorder
In Fig. 1, a summary is given of the formulae needed for the interpretation of results obtained with the two methods. A 2nd-order model is used, with a damping factor ( a n d an undamped resonance frequency fo. The correspondence at low damping between the two methods is obvious from Fig. 1. With increased damping, it becomes increasingly difficult to determinefo and ~ independently, and, for the overdamped case, it is more relevant to measure the rise time of the step response which corresponds to a certain upper frequency limit. The system approaches a lst-order model in the interesting frequency range, and, for this model, the upper frequency limit f= is related to the rise time tr by f , = ln9/2ntr. F o r systems close to critical damping (( = 1), step-response recordings deviate from an exponential rise, a difference which is difficult to see directly on the recording. Therefore, in this case, frequency-response recordings are easier to interpret; for high frequencies, the output falls by 12 dB per octave in contrast to a I st-order system which gives a 6 dB per octave fall. 194
Pressure-step generation The originator of the proposed pressure-step technique appears to be HANSEN (1949). He drilled a hole through the piston and stem of an ordinary glass syringe. The manometer system was connected with a needle to the syringe, which was mounted vertically and contained both water and air. If the piston was withdrawn with one finger covering the drilled hole, a negative pressure developed inside the syringe, and when the finger was released the pressure returned to ambient pressure with a rise time of less than l0 ms (as estimated from Hansen's recordings). It is interesting to note, however, that Hansen obviously made the whole sequence, that is, withdrawal of the syringe and removal of the finger, in rapid succession so that the excitation would be an impulse rather than a step function. The duration of the entire transient was about 30-50 ms, which cannot be regarded as short compared with the period lengths of catheter resonances. According to McDoNALD (1974), it is also difficult to avoid vibration artefacts with this technique. To make use of the fast step when the finger is released, a stable base line prior to the step is required, so that resonances are excited by the step alone. The same argument also applies to another version of the technique, where the piston is simply drawn out of the syringe giving a sharp transient when the piston leaves it; in this case, it is inherently impossible to obtain a stable base line immediately prior to the step. In the present modified technique, ordinary plastic 1 ml tuberculin syringes are used with a 2 mm hole drilled in the wall close to the outlet, which is connected to the manometer system via a needle (18G or thicker). The syringe is air filled, and the pressure step is performed as did Hansen with the exception that the negative pressure is allowed to persist for a few seconds, while the vibrations from piston movement die out. The piston generally stops owing to static friction at pressures of more than 30 mmHg. It is then a simple matter to rapidly lift the finger without causing vibrations that are visible on the records. Fig. 2 shows a recording of the system rise time. The pressure transducer used in this and all following experiments was an improved version of an electrolytic microtransducer described earlier (H6K, 1975). The calculated resonance frequency of the transducer used was 600 Hz, but a low-pass filter in the amplifier with a time constant of 0.5 ms set a somewhat lower limit to the system. Thirty consecutive measurements of the rise time with a transducer directly connected gave a mean value of 2-1 ms and a standard deviation of 0.5 ms. The highest measured value was 3.2ms. This experiment shows that the technique is reproducible and capable of exciting resonance frequencies in the range 0-100 Hz. Longer sweep times than that used in Fig. 2 show a stable base line, which is to be expected since the
Medical and Biological Engineering
March 1976
first, represented by YANOF et al. (1963) and by BALL and GABE(1963), uses an electric motor as the driving element connected via a cam to a pressure chamber which is compressible either by the compressibility of water or by allowing the chamber to be partly filled with air. The problem with this type of generator, as pointed out by VIERHOUT and VENDRIK (1964), is the fact that it is basically a volume generator shunted by the compliance of the chamber. According to Thgvenin's theorem, this is equivalent to a pressure generator with the same compliance connected in series. The compliance must then be large and frequency independent so that compliant loading of the system does not influence the pressure output. This is difficult to achieve in a single system with either air or fluid-filled chambers. The second approach has been represented by authors such as NOBLE (1959), VIERHOUT and VENDRIK (1961), STEGALL (1967), HENRY et al. (1967) and SHELTON and WATSON (1968). The difference from the first approach is that the connection between the actuating element and the pressure chamber is not stiff but provides for much of the compliance needed according to the discussion above. In practice, the actuator may be a loudspeaker coil which acts on a piece of magnetic material. This, in turn, is fixed to a membrane, and the forces on this membrane causes the pressure to vary in an adjacent fluid-filled chamber. In this case, the compliance of the membrane limits the allowed degree of loading. The present sinusoidal pump, shown in Fig. 4, comes under the second category of generators. The only new feature is the use of a drop of a magnetic fluid (commercially available from Ferrofluidics Corp., 144 Middlesex Turnpike, Burlington, Massachusetts 01803, USA) instead of a diaphragm. This has the advantage that the pressure-chamber part can be manufactured from a few pieces of tubing and an O ring, and that this part does not need to be permanently fixed to the actuator, which, in this case, is a small electromagnet with a soft-iron core having a d.c. resistance of 8fl and an inductance of 10 mH.
syringe has free communication with ambient air. Fig. 3 demonstrates the excitation of resonance frequencies by using a polyethylene catheter (PE 90, inner diameter 0- 87 mm, outer diameter 1-27 ram) between the syringe and the transducer. 50 cm and 10cm lengths of the catheter gave undamped resonance frequencies of 42 and 108 Hz, respectively. The damping factor was about 0" 15 in both cases.
Sinusoidai-pressure generator The problem of generating sinusoidal-pressure signals has been mainly tackled in two ways. The +5 -1E E
0
it3 UJ
(~ -10
-15
I 0
I
I
t
50 a
100
150 TIME (ms)
b v
*5 I E
E
0
LD LU Or" ~-
-I0
-15
I 50
I 100
b
I 150 v TIME [ms~
Fig. 3 Catheter resonance excited by a step function. (a) Polyethylene PE 90 catheter, 0.5 m length, (b) Same catheter cut down to O" I m length Electromagnet
Polyethylene tube
O-ring
Transducer or
\ Current generator
Magnetic fluid
\ Water
Medical and Biological Engineering
M a r c h 1976
Fig. 4 Schematic of the new sinusoidal pressure generator
195
The magnetic fluid is a colloidal suspension of small ferrite particles with linear dimensions of the order of 10 nm. According to the manufacturer, the particles are prevented from sticking together by a 2"5 nm coating. A wide spectrum of liquids, including water, can be used as carrier fluids. The presence of the magnetic particles has the effect that a force will act on the fluid as a whole when it is influenced by an inhomogeffeous magnetic field. Other properties, such as viscosity, are virtually unaffected by the relatively low concentration of ferrite particles. The relaxation time of the ferrite dipoles is of the order of microseconds. Fig. 5 shows the static characteristics of the generator. A t low current levels, the transfer function is superlinear owing to incomplete orientation o f the ferrite particles in a weak magnetic field. When saturation occurs, at 0"02 T ( = 200 gauss, manufacturer's figure), the force acting on the fluid is approximately linearly related to the field strength which, in turn, is linearly related to the coil current. The force develops a negative pressure which may be sensed by a transducer (Fig. 4). The linearity of the sensor in this pressure region was established in an independent experiment. F r o m Fig. 5, it should be clear that, if a sinusoidal component is superimposed on a direct current in the linear part of the characteristics, a sinusoidal pressure variation will be generated. To achieve this, the circuit in Fig. 6 has been used. It is a common emitter transistor stage which serves mainly as a current amplifier. It can be driven by any sine-wave oscillator capable of delivering a few volts across slightly less than 100 ~ . The power supply must be able to supply at least 2A, and the power loss in I
i
CURRENT IA}
1 I I
~..
,x... -0.5
12
3
II
i
I
I
.t
I E E
-I'0 to -1"5
5o_ S (D -2"0
Fig. 5 Static characteristics of the pressure generator
196
the transistor calls for proper cooling; all the components can easily be mounted directly on the heat sink holding the transistor. Fig. 7 shows recordings of the relative pressure amplitude and phase as a function of frequency. The phase was measured relative to the voltage across the 1 fl resistor; this was believed to be an adequate monitor of the coil current. The drop in output of the direct recording at high frequencies is attributed to the detector-amplifier low-pass filter. A more thorough test of the limitations of the generator was not performed, since the frequency range of biomedical signals was shown to be covered. Catheter resonance is also demonstrated in Fig. 7 with a 0"5 m PE 90 polyethylene catheter. The transducer used for this experiment was stiffer than that used in Fig. 3, which accounts for the higher resonance frequency. A
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To test the correlation between the two methods, a series of parallel determinations of resonance frequency and damping was performed. The result is shown in Fig. 8, and it can be seen that a high correlation for resonance frequencies is obtained, whereas the damping-factor estimations are less reliable. The resonance-frequency determinations have an error of less than + 5~o in about 7 5 ~ of the determinations. The correlation coefficient is 0.989, and the equation for the regression line is y = (0.93 + 0 . 0 4 ) x + ( 4 + 2 ) x and y stand for the step-function and frequencyresponse resonance frequencies, and the errors are standard deviations. It was not determined whether the deviation from the identityy = x is a result of the small statistical population or of a systematic deviation from the 2nd-order model of the system. Damping-factor determinations have a low correlation factor of 0.11, and 7 5 ~ of the measurements are within an error of + 50~/~. Frequencyresponse determinations show a tendency to be somewhat higher than the corresponding stepfunction determinations. Medical and Biological Engineering
March 1976
/ 0
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Fig. 7 Amplitude and phase charac>= o
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teristics of two recordings made with the pressure generator. The solid line is a recording made with a directly connected pressure transducer and the dashed line was made with a 0.5 m polyethylene PE 90 catheter
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From Fig. 8, the potential applicabilities of the two methods should be dear. The accuracy of about + 5% in resonance frequency and _+50% in damping factor is probably sufficient for most routine calibrations. The error in damping factor will be excessive only in very special investigations, e.g. tests of manometer-system models. The step-function technique is quicker and easier to apply under sterile conditions than the frequencyresponse method. Faults, such as leaking syringes or improper handling are directly visible on the records, and a new recording can be made immediately in contrast to some other step-response techniques, e.g. balloon explosion. On the other hand, the frequency-response method has the advantages of a somewhat greater bandwidth and the possibility of applying bias pressure, a technique which can be used for the detection of air bubbles (HENRY et al., 1967). Moreover, for systems close to critical damping, frequency-response records may be somewhat easier to interpret, In most cases, however, these advantages are less important than the advantages of the step-function technique, which therefore can be recommended for more general use than is current practice.
5O
BALL, G. and G~d3E,I. (1963) Sinusoidal pressure generator for testing differential manometers. Med. Electron. Biol. Eng. 1,237-241. Medical and Biological Engineering
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Acknowledgments I wish to thank Kenth Nilsson of Siemens-Elema AB, for valuable suggestions. The work is supported by STU, the Swedish Board of Technical Development under grant 74-3205. References
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Fig. 8 Correlation between measurements with the step response technique (SF) and frequency response technique (FR) of (a) resonance frequency and (b) damping factor
March 1976
197
HANSEN,A. T. (1949) Pressure measurement in the human
SHELTON,C. D. and WATSON,B. W. (1968) A pressure
organism. Acta Physiol. Scand. 19, Suppl. 68, 7-230. HENRY, W. L., WIENER, B. and HARRISON, D. C. (1967)A calibrator for detecting bubbles in cardiac cathetermanometer systems. J. ,4ppl. Physiol. 23, 1007-1009. H6K, B. (1975) New microtransducer for physiological pressure recordings. Med. and Biol. Eng. 13, 279-284. KROVETZ, L. J. and GOLDBLOOM, S. D. (1974) Frequency content of intravascular and intracardiac pressures and their time derivatives. IEEE Trans. Biomed. Eng. BME-21, 498-501. MCDONALD, D. A. (1974) Bloodflow in arteries, 2nd ed. Edward Arnold, London. NOBLE, F. W. (1959) A hydraulic pressure generator for testing the dynamic characteristics of blood pressure manometers. J. Lab. & Clin. Med. 54, 897-902.
generator for testing the frequency response of cathetertransducer systems used for physiological pressure measurements. Phys. Med. Biol. 13, 523-528. STEGALL,H. F. (1967) A simple, inexpensive, sinusoidal pressure generator. J. Appl. Physiol. 22, 591-592. VIERHOUT,R. R. and VENDRIK,A. J. H. (1961) A hydraulic pressure generator for testing the dynamic characteris/ tics of catheters and manometers. J. Lab. Clin. Med. 58, 330-333. VIERHOUT, R. R. and VENDRIK, A. J. H. (1964) On pressure generators for testing catheter manometer systems. Phys. Med. Biol. 10, 403-406. YANOF, H. M., ROSEN,A. L., McDONALD,N. M. and McDONALD,D. A. (1963) A critical study of the response of manometers to forced oscillations. Phys. Med. Biol. 8, 407-422.
Calibration dynamique des syst~mes manomdtriques Sommaire--L'article d~crit deux m~thodes simples et non cofiteuses de calibration dynamique des syst~mes manom6triques, applicables dans les milieux cliniques. La premi6re est une modification d'une technique de fonction en 6chelon bien connue et la seconde est un g6n6rateur de pression sinusoidale 5. partir de fluides magn6tiques. L'usage pratique des deux m6thodes est d6crit en d6tail et des essais sur leur pr6cisions sont effectu6s. On trouve en particulier que les deux m6thodes sont pratiques dans la zone allant de 0 5. 100 Hz au moins et que les fr6quences de r~sonance peuvent ~tre d6termin6es avec une erreur d'environ + 5~o alors que l'erreur du facteur d'att6nuation est plus 61ev6e, de l'ordre de + 5 0 ~ . La technique de la fonction en 6chelon est plus rapide et plus simple 5. utiliser sous milieu ambiant st6rile, son usage est donc recommand6 dans un plus grand nombre de cas.
Dynamische Eichung yon Manometersystemen Zusammenfassung--Zwei einfache, biUige Verfahren zur dynamischen Eichung von Manometersystemen ffir den klinischen Gebrauch werden beschrieben. Das eine ist eine ANinderung eines wohlbekannten Stufenfunktionsverfahrens, das andere ist ein sinus~ihnlicher Druckgenerator mit Magnetfliissigkeiten. Die praktische Anwendung beider Verfahren wird genau beschrieben, und die Genauigkeit der Verfahren wird geprtift. Insbesondere wird festgestellt, dal] beide Verfahren im Frequenzbereich von wenigstens 0 bis 100 Hz nfitxlich sind und dab Resonanzfrequenzen mit einer Regelabweichung von etwa + 5~o bestimmt werden k6nnten, wogegen die Regelabweichung im Schwachungsfaktor gr613er ist, d.h. bei _ 5 0 ~ liegt. Das Stufenfunktionsverfahren ist schneller und leichter unter sterilen Bedingungen anzuwenden und wird daher ftir einen Gebrauch in gr6Berem Umfang emfohlen.
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Medical and Biological Engineering
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