Ultrasound rn Med. & Em/ Printed in the U.S.A.

Vol. 17, No. 5, pp. 433-444,

0301-5629/91 $3.CKl+ .oO 0 1991 Pergamon Press plc

1991

*Original Contribution MEASUREMENT OF BLOOD PERFUSION IN TISSUE USING DOPPLER ULTRASOUND STEPHANO.DYMLING,HANSW.PERSSON~~~

C. HELLMUTHHERTZ

Department of Electrical Measurements, Lund Institute of Technology, P.O. Box 118, S-22 1 00 Lund, Sweden Abstract-A diagnostic tool for noninvasive evaluation of microcirculatory blood flow using continuous-wave CW Doppler ultrasound is presented. In this study, the properties of this method are investigated both theoretically and experimentally. The method utilizes a nondirectional CW Doppler flowmeter. Blood perfusion in tissue is shown to be proportional to the integral sfS(f)df where S(f) is the Doppler power spectrum and f is the Doppler frequency. The instrumentation needed to implement the method is described. Using an experimental flow model it is demonstrated that the above integral is proportional to the product between the number of scatterers in the sample volume of the Doppler probe and the mean speed of these scatterers. This is true even for low flow velocities (down to 1 mm/s). The results from in-viva measurements on tissues in the finger, and the calf demonstrate that the method can monitor changes in the blood perfusion. It also shows the present limitations of the method due to movement artefacts. Key Words: Ultrasonics, Diagnostic ultrasound, Blood perfusion, Doppler, Continuous-wave, Artefacts.

flow in muscle (cJ Lassen et al. 1964) uses a radioactive tracer which is injected into the muscle. Blood flow in then deduced from the clearance rate of this tracer. Other methods, such as electrical impedance techniques and plethysmography, measure the volume of blood flowing into a tissue segment (e.g., a segment of the limb). These methods are based on the occlusion principle, and can only make noncontinuous measurements (cf: Rowan 198 1) . A method for measuring microcirculatory flow of the skin using a laser Doppler technique has been developed by a number of researchers (Stem et al. 1975; Holloway 1977; Nilsson et al. 1980). This technique can make continuous noninvasive measurements of skin blood flow. However, the effective penetration depth of light in human skin is only 0.5 mm, which makes deeper lying tissues inaccessible. The Doppler flowmeter has made transcutaneous measurements of blood flow in larger vessels possible ( cf Strandness et al. 1966). In this report, a technique that uses continuous-wave (CW) Doppler ultrasound to overcome the poor penetration depth of the laser Doppler flowmeter will be presented. Instead of the traditional use of the CW Doppler flowmeter for investigating a single larger vessel, the attention will be on the collection of vessels that perfuse tissues. This technique for measuring tissue blood flow was first pointed out by Hertz ( 198 1) and Dymling et al.

INTRODUCTION

The fundamental role of the systematic circulation is to convey blood to and from body tissues. The exchange of nutrients and cell products between blood and tissue takes place in the capillaries. Therefore, it is of great clinical value to measure the blood flow in tissue to assess the efficiency of this transport mechanism. The ultimate goal of such a measurement would be to noninvasively measure the nutritive blood flow of a certain volume of tissue. When investigating tissue blood flow, it is desirable to determine the efficiency of the exchange of nutrients and cell products between blood and tissue. This can be achieved by measuring the amount of blood supplied to the tissue, e.g., muscle, tumors, placenta or brain. This so-called blood perfusion of tissue is defined as the blood volume which flows through a unit volume of tissue per second, i.e., ml/(cms. s) . Anatomically, this corresponds to the total blood flow through the microvascular exchange vessels, i.e., the capillaries. Currently, there are a number of techniques to evaluate microcirculatory blood flow-perfusion. Different tracer techniques (cf: Rowan 198 1) which measure the circulation of a tracer in the vascular system (nondiffusible tracers) or the exchange of a tracer between tissue and blood (diffusible tracers) are widely used. For instance, the measurement of blood 433

434

Ultrasound in Medicine and Biology

( 1982 ) . Millner et al. ( 1982 ) have also reported early clinical results using a similar technique. Measurements with ultrasound frequencies above 20 MHz have been reported by Ash et al. ( 1985) and Chmiel and Mauser ( 1982). To measure the blood perfusion of a part of a tissue, information about the volume of blood in that part of the tissue as well as the velocity of the blood is needed. The Doppler spectrum contains this information, which is intuitively clear from Fig. 1. In Fig. 1a, a transmitter (T) emits a beam of ultrasound into the tissue. This ultrasound is backscattered by the moving blood cells and detected by the receiver (R). The backscattered radiation from the blood cells will exhibit a frequency shift proportional to their velocity relative to the transmitter and the receiver. The frequency, f,, of the emitted ultrasonic wave will be shifted by an amountfd by the moving particles. This Doppler shift is determined by (cf: Reid 1978)

h=

Volume 17, Number 5, 1991

transmitted ultrasonic frequency, c is the speed of sound in the medium, and 0 is the angle between the particles velocity vector and the transducer orientation angle. As different cells move with different velocities, a spectrum of Doppler frequencies at the receiver will be observed (cf: Fig. 1b). The backscattered power into any frequency band is proportional to the number of blood cells generating a specific Doppler frequency. For instance, the shaded area shown in Fig. 1b is proportional to the number of cells which shifts the backscattered radiation by the amountf, . It will be demonstrated that if certain criteria are met, the blood perfusion P is proportional to the first moment of the Doppler spectrum. The theoretical background for this method will be presented as well as in-vitro and in-vivo investigations. THEORY

The concept of blood perfusion

2VfCOSB c

where v is the speed of the scattering particle,& is the

MICRO “ASC”LAR BED

::..:-::.

In order to evaluate the use of CW Doppler for the measuring of tissue blood flow, or blood perfusion, this quantity must first be defined. A mathematical definition of blood perfusion is given by Dymling ( 1984). Intuitively, the concept of blood perfusion can be described in the following way. Consider an arbitrary volume of tissue (cf: Fig. 2). The blood perfusion is obtained as the difference between the arterial inflow and the arterial outflow from the considered volume. This is also the part of the arterial flow which passes a capillary and becomes venous flow in the volume. Using this definition of blood perfusion Dymling ( 1984) has shown that the blood perfusion P can be obtained from

\

(a)

P=+--n,E{U,} s

/ / / / / /

n fl

+

lb)

Fig. 1. The transmitter (T) emits an ultrasound beam into the investigated tissue shown in (a). This ultrasound is backscattered by the moving blood cells and detected by the receiver (R). In (b), the spectrum of Doppler shifted frequencies of the detected signal is shown.

(2)

where Q, is the total capillary flow, V, is the sample volume of tissue, n, is the number of capillaries per volume of tissue, and E { V, } is the average blood velocity in the capillaries. A review of the structure and proportions of the vasculature clearly shows that a typical sample volume of a CW Doppler transducer does not contain only capillaries (cjYSchmid-Schbnbein 1976). In fact, of the total volume in the vascular system, only 5% is found in the capillaries. Apart from capillaries a sample volume also contains vessels carrying blood to and from the capillaries. Also, some vessels may simply traverse the sample volume. The method presented in this study for measuring blood perfusion is based on the assumption that these flows are all proportional to

Measurement of blood perfusion 0 S. 0. DYMLING et al.

P = blood perfusion Fig. 2. Definition

= - V=va

of blood perfusion of a volume of tissue.

the capillary flow. Therefore, if the sum of these flows can be measured, then the blood perfusion of the tissue is obtained. A model of the functional behavior of the part of the microcirculation that is present inside the sample volume of the CW Doppler probe has been reported by Dymling ( 1984). The computer simulations performed using this model have demonstrated the validity of the expression P - N,E{

v}

(3)

where N,, is the number of moving red cells in the sample volume and E { 2,} is the mean speed of these cells. This is the fundamental equation that will be investigated in this study. It will be shown how it can be measured utilizing a CW Doppler flowmeter. Measurement of tissue perfusion by CW ultrasound Doppler methods In the first part of this section, the results obtained by Brody ( 1974) will be reviewed. He has calculated the autocorrelation function of the received signal in a CW Doppler system. In the latter part of this section, the emphasis will be on application where the receiver signal is generated from blood cells in the microvasculature, as shown in Fig. 1. The microvasculature represents a network with an irregular geometrical structure. The analysis of the Doppler signal from such a network will be extremely cumbersome if based on a detailed geometrical description of the network. Instead, the blood flow will be described by making assumptions regarding the spatial distribution of red cells and their velocities. Since the scattering of ultrasound by blood is a

435

random phenomenon, it is necessary to describe the scattering process on a statistical basis. Therefore, the signals found in a Doppler flowmeter will be described in a statistical manner. The steps will be outlined here, but the complete calculations can be found in Brody ( 1974) or Dymling ( 1984). The receiver signal Y(t) is assumed to be a sample function from a random process { Y(t) } (cf: Fig. 3 ) . By making basic assumptions regarding the scattering process, the properties of this random process can be determined. Specifically, the power spectrum of the signal Y(t) will be calculated. When this spectrum is known, the spectrum of the signal, Z(t) , after the demodulator part in Fig. 3, can easily be determined. The spectrum of the signal Z(t) will referred to as the Doppler spectrum. Before going into the details of this calculation the assumptions made will be discussed. These are stated as follows: 1) The red blood cells are the primary source of ultrasonic scattering in blood. 2) The interaction between red blood cells and ultrasound in a volume of tissue can be described by the Rayleigh scattering theory. The red cells are independent and act as isotropic scatterers, i.e., scattering a small fraction of the incident ultrasonic power equally in all directions. 3) The “strength” of each scatterer is described by the scattering cross section ui. This constant gives the fraction of incident ultrasonic power scattered by a red cell. 4) The position and velocity of each red cell are random variables described by the joint probability density function ~(?,a). Reid ( 1969) has presented experimental evidence for assumption 1. It has been shown experimentally by Shung ( 1976) that the scattering from red blood cells obeys Rayleigh scattering theory for small particles. Also the assumption of independent red cell scattering indicates that the scattered power from a sample of blood is a linear function of the concentration of red cells in the sample. The extensive work by Shung ( 1976) shows that such a relation exists only for sparse concentrations of red cells below lo%, where the concentration of red cells is expressed as:

P=

Volume of red cells total volume of red cells and plasma

In medical literature, p is often referred to as the hematocritfactor, or simply hematocrit. For low hematocrits, single scattering is the dominant interaction between the incident sound wave and the red cells. The

Ultrasound in Medicine and Biology

436

Volume 17, Number 5, 199I

2cos2nfot

XW’COS 2+fot I

I r

TRPNSMIT-IING ELECTRUJICS AND TRANSDUCER

SCATTERING '

l

PROCESS

RECEIVING TRANSDUCER AND ELECTRONICS

‘A

Fig. 3. Basic configuration of a nondirectional CW Doppler. X(t), Y(t) and Z(I) are the transmitted, and demodulated signal, respectively. The subsystem Z, represents a low-pass filter.

red cells then scatter independently of each other, and multiple scattering does not occur. In whole blood the hematocrit is of the order of 45% (cf: Rowan 198 1)) and the red cells are not independent. In the microvasculature, the situation is somewhat different because the number of red cells in moderately perfused tissue is 0.5-4’31 by volume of tissue (cf: Bonner et al. 198 1). Locally, inside the blood vessels, the hematocrit factor is of the order of 45% but we will nevertheless treat the red cells as independent scatterers. Since all the red cells are identical and independent it is sufficient to have a statistical description of a single red cell. For a single red cell the following probability function is defined: ~(7, S)d%?fd’T = the probability that a red cell has a velocity in the range 3 and 3 + d if and is located between 7 and 7 + d7.

This density function has a somewhat different meaning than that given by Brody ( 1974). Here, it represents the blood cell that is found in the microvasculature instead of only inside one large vessel as was the case in Brody’s analysis. This fact does not alter the mathematical analysis, but other properties of this function will be investigated. To simplify the mathematics, it will be assumed that the blood flow is steady (time independent). This means that the density function ~(7, ?i) will not be a function of time. After using the above-discussed assumptions, the Doppler power spectra can be calculated by calculating the autocorrelation function of the receiver signal, and from it, the Doppler power spectra. These calculations will be omitted here as they can be found in Brody ( 1974) and Dymling ( 1984)) where it is shown that the Doppler power spectra, S,(f), can be obtained from eqns (4) and ( 5): S,(f) %0-)

= rZ&at

= frs”,(f) ss

+ Q-f)1

(4)

~(7, QG2V) x 6(27rj-+ i;. 3)d’Td’if

(5)

b

z(t)

received

where I, is the transmitted intensity, G(T) is the dissipation function, and R is the net wave vector resulting from the beams incident and reflected from a red blood cell located in T. The dissipation function G(T) describes the effects ofthe transmitting and receiving transducer apertures; the overlap of these apertures is shown in Fig. 1. G(7) also includes the different attenuation mechanisms of the wave that travels from the transmitter to the red cell and then back again to the receiver. Random flow directions In this section, the previous results will be ap plied to a specific flow situation. When the sample volume of the CW Doppler is located in the microvasculature, blood flows in all directions. This can be described by the proper choice of distribution function ~$7, a). It will be shown that information concerning tissue blood perfusion can be obtained if we calculate the first moment of the Doppler spectrum. This moment is related to the spectral density j,(f) in the following way:

Assume that the tissue blood flow is completely isotropic in the investigated volume, i.e., independent of the position in space. The distribution function ~(7, 3) can then be written as:

Substituting this in eqn (5) yields

s,(f) = dolo&

[j-G2(r)d3?] X

p(?3)6(2?rf+ R- a)d%

1

(7)

Let the integral over space be called T. Then the first moment of the Doppler power spectrum becomes

437

Measurement of blood perfusion 0 S. 0. DYMLING et al.

INSTRUMENTATION

where the relations

and IX.

2xf,luzl 2

$1 =

COS

cyo

C

(10)

have been used. Here, o, is the velocity component along the z-axis shown in Fig. 1, and 6 ( ) is Diracs delta function. The term cos a0 is discussed in more detail in Dymling ( 1984). This leads to the following proportionality

which shows that the first moment of the Doppler spectrum is proportional to the mean number of red cells in the sample volume and the mean speed of these cells along the z-axis (cf: Fig. 1). To show that the blood perfusion is proportional to the first moment of the Doppler spectrum, the mean speed along the z-axis must be related to the overall mean speed, E { D} . This is due to the fact that the CW Doppler flowmeter gives information concerning the velocity component along the z-axis, i.e., (v,) when a nondirectional Doppler is used. Dymling ( 1984) has shown that when all velocity directions are equally probable, then the overall mean speed is related to the mean speed along the z-axis in the following way

W~,lI

= +W4

The different functions needed to measure the Doppler shift of eqn ( 1) are shown in Fig. 4. The oscillator produces a sinusoidal waveform which is amplified and used to drive the transmitting transducer. This transducer will generate an acoustic wave with a frequency equal to the oscillator frequency. This wave is scattered by the moving particle and some of the scattered energy returns to the receiving transducer. Here, the acoustic energy is converted into an electric signal which is amplified by the preamplifier. Because of the low-level signals involved it is of great importance that this pre-amplifier has optimum noise performance (cf: Dymling 1985). The mixer now makes a frequency transformation with an amount determined by the reference signal coming from the oscillator. In this way it is possible to eliminate the constant frequency term& so that the Doppler difference signal is found at the output of the mixer, i.e., the Doppler shift is obtained. After further amplification in a low-frequency (LF) amplifier, the output signal from the mixer is analyzed by an FFT analyzer which can rapidly measure the spectral distribution of a low-frequency signal. Finally the FIT analyzer is connected to a computer which can access the Doppler spectrum in the FFT analyzer and perform the calculations of eqn ( 14).

Velocity resolution Of basic interest when designing a CW Doppler flowmeter are the flow velocities that the flowmeter should be able to detect, and the resolution necessary to distinguish different flow velocities. Eqn 1 relates

fo

Oscillata

/

(12)

Combining eqns ( 11) and ( 12) gives the relation

smf&(fWf-

NoEW

(13)

0

Using eqn ( 3 ) this finally shows that under the abovediscussed assumptions the blood perfusion can be obtained from

P-

L

s 0mf&mf

(14)

I

L

I

Fig. 4. Basic block diagram of the CW Doppler flowmeter.

438

Ultrasound in Medicine and Biology

the expected Doppler shift associated with a given flow velocity. For a given velocity component along the dotted line in Fig. 4, we obtain a Doppler shift proportional to the velocity and the ultrasound frequency being used. When investigating the small vessels that perfuse tissue, the expected flow velocities can be as low as 1 mm/s in these applications (cf: Dymling 1984). If an ultrasound frequency of 10 MHz is used, and the angle between the flow velocity vector and symmetry axis of the transmitter and receiver is 45”, this corresponds to a Doppler shift of about 10 Hz, if the speed of sound is 1500 m/s. Thus, the Doppler shift is 1OP6 of the emitted frequency, which demands a shortterm stable oscillator in order to detect these very small Doppler shifts. This small Doppler shift will also place a lower limit on the measurement time. For instance, if a velocity resolution of 0.1 mm/s is needed, in a IO-MHz system, a frequency resolution of approximately 1 Hz must be used. To obtain a frequency resolution of Af the FFT analyzer must observe the Doppler signal for a minimum time T given by

T=L_ Al Thus, in the IO-MHz system mentioned above, the measuring time is in the order of 1 s. In practice it is often also necessary to average a number of frequency spectra to obtain a good estimate of the Doppler spectrum. This will further increase the measuring time. A way to decrease the measuring time is, of course, by increasing the ultrasound frequency which will make the Doppler shift larger for a given velocity. It is desirable to make the measuring time as small as possible. In respect to velocity resolution the ultrasound frequency should be made as high as possible.

Frequency choice As the ultrasonic energy scattered by the red blood cells is very weak, the ultrasound frequency in a CW Doppler flowmeter is chosen to make the signalto-noise ratio as large as possible. To find the optimum frequency choice, an analysis of how this choice effects the signal strength and the noise level at the receiving transducer must be performed. Two different effects oppose each other. First, the scattered intensity is proportional to the fourth power of the ultrasound frequency. Second, the attenuation of the scattered wave increases with the frequency and the depth of the investigated tissue. Baker et al. ( 1978) has shown that the following expression gives the optimum frequency for a Doppler flowmeter

Volume 17, Number 5, 1991

h=

15 log(e) rR

where y is the soft tissue attenuation

coefficient, and

R is the depth of the sampling volume of the CW Doppler flowmeter probe. According to Baker et al. ( 1978) the soft tissue attentuation coefficient, y, can range from 0.2 dB/ MHz/cm to more than 2 dB/MHz/cm in different types of tissue. Thus, the optimal ultrasound frequency for a given investigation depth will depend on the intervening tissue. For an investigation depth of 1 cm, the optimal frequency choice may be as high as 30 MHz, while for a depth of 5 cm this frequency lies somewhere between 1 and 7 MHz. EXPERIMENTAL

STUDY IN FLOW MODEL

The measurement of blood perfusion in tissue with a CW Doppler is an application of the Doppler technique which is quite different from the clinical use of CW Doppler today. Technically, the main difference lies in the flow velocities encountered in this application. As noted before, it is desirable to detect frequency shifts of 10m6times the emitted frequency which corresponds to flow velocities in the order of 1 mm/s. Before making clinical measurements under these conditions, it is important to investigate the suggested technique under controlled conditions. The basic relation to study was given in eqn ( 14 ). In order to examine this relation in practice, a special flow model was designed. As it is inconvenient to use blood in these model studies, other particles were used as scatterers of ultrasound. In the previous sections of this study, the product N,E { D} has been referred to as the blood perfusion of tissue. Here, the same quantity for the particles in the flow model will be measured. Instead of referring to blood perfusion in this case, the product between N, and E { o } will be referred to as the particle flux inside the sample volume.

Materials and methods To investigate the relation in eqn ( 13)) a special flow model was designed where it is possible to vary N, and E { II} independently of each other. The principle of this model is shown in Fig. 5. It consists of a container with glycerol through which a small tube transports a moving liquid past the probe of a CW Doppler flowmeter. The angle between the Doppler probe and the tube is 45”. This liquid, a mixture of glycerol and Sephadex, is pumped around in the tube by a roller pump.

439

Measurement of blood perfusion 0 S. 0. DYMLING et al. cw

Probe

Doppler

Fig. 5. Flow model used to study the Doppler spectrum in a CW Doppler system when the flow velocity and the concentration of scatterers are changed.

Sephadex is a trade name (Pharmacia) for spherical dextran gel particles. The Sephadex used in this investigation had a diameter between 10 and 40 pm (Sephadex G- 10). These particles scatter ultrasound and, hence, simulate red blood cells. The magnetic stirrer is used to keep the Sephadex particles suspended and, in this way, maintain a uniform concentration of Sephadex througout the liquid mixture. Finally, with the roller pump, the flow velocity in the tube can be changed. In this flow model it is simple to vary the flow velocity of the scatterers by changing the speed of the roller pump. A variation of the second parameter, NO, in eqn ( 13) could be achieved in two ways: 1) By a variation of the liquid volume inside the sample volume of the Doppler probe. 2) By a variation of the concentration of scatterers inside the sample volume. As was discussed in Dymling ( 1984)) a variation according to # 1 is expected in tissue when the diameters of various vessels is changed in order to regulate the blood flow in the tissue. However, in this investigation, a variation according to #2 was chosen since it was simpler to implement. Thus, liquids with differ-

Table 1. Liquid number

Concentration of Sephadex G- 10 (g/80 cm’)

:

0.5 0.0

3 4 5 6 7

1.0 3.0 5.0 10.0 15.0

ent concentrations of Sephadex were used to study the effect of varying N, . Glycerol was used in the container, as a coupling medium between the Doppler probe and the tube, because it has a high viscosity ( 1490 X low3 Ns/m’). By using such a liquid, acoustic streaming in the liquid is kept low. The material in the container was chosen to avoid reflections of ultrasound at the boundary between glycerol and the walls of the container. This guarantees that the emitted ultrasound from the transmitter traverses the scatterers in the tube only once. To this end, the acoustic impedance of the walls in the container were made equal to that of glycerol (acoustic impedance of 2.44 X lo3 kg/cm3/s). The material used in the walls was Eccogel 1365-90 by Frace N. V. In Table 1, six different liquids of Sephadex in glycerol are listed which were used in these investigations. A seventh liquid of pure glycerol was also included in the investigation as a reference. The total volume of each sample liquid was 80 ml. These liquids were prepared 4 days before they were investigated in the flow model. During these days, they were stirred carefully to eliminate air bubbles in the liquid. In Fig. 4, the principle of the system used to analyze the flow in the model is also shown. It consists of a CW Doppler using a frequency of 9.6 MHz. To measure the Doppler spectrum, an FFT analyzer was used (HP3582A). Finally, the Doppler spectrum was transferred to a computer where further calculations were performed. The speed of the roller pump can be varied with the help of a potentiometer on the pump. This potentiometer can be changed between values of 0- 1000. For each of the seven liquids, the speed of the roller pump was varied between settings of 20 and 200 in increments of 20, giving a total of 10 spectra for each investigated liquid. These spectra were stored on disc and studied in detail as well as compared to each other. The inner diameter of the tube (Silastic by Dow Corning) was 2 mm. Further, the average speed of flow was 0.56 mm/s at the 20 setting, and 5.6 mm/s at the 200 setting of the roller pump. These values were obtained by a calibration of the pump flow using a Mettler balance. The flow generated by the pump was proportional to the potentiometer setting. From each of these spectra, both the particle flux and the mean speed were calculated from the expressions: 256

440

Ultrasound in Medicine and Biology

where h = (i - 1) 0.4 Hz and S(J) is the power spectrum measured by the FFT analyzer. The FFT analyzer primarily measures the RMS spectrum of the Doppler signal. Therefore, the spectrum from the FFT analyzer is squared to obtain the power spectrum. The quantities of eqns ( 19) and (20) are thus obtained as a function of the speed of the roller pump as well as the concentration of Sephadex in the liquid used. To investigate if the presented method is sensitive to variations in the Sephadex concentration, a relative value for N, can be estimated from eqns ( 15 ) and ( 16) for each setting on the roller pump. To get a better estimate for N,,, a linear regression method was used to deduce No from all the measurements made with different pump velocities. Therefore, we made a linear regression between the measured values for N,, E { v } and E { v } where each observation used in the regression corresponds to a specific speed of the roller pump. The regression coefficient will then give an estimate of the number of scatterers inside the sample volume of the Doppler probe.

Volume 17, Number 5, 199 1 60

-80

-100

T

_B w

s

-140 20

-60

+z

-g

-100

-140

0

50

In Fig. 6a, selected Doppler spectra are shown when liquid number 4 (cf: Table 1) was investigated in the flow model. Similar spectra were obtained from each of the seven different sample liquids shown in Table 1. Using eqns ( 15) and ( 16)) the particle flux and mean frequency was calculated as a function of the velocity used on the roller pump. In Fig. 7, the result of such a calculation is shown for liquid number 4. For each of the seven liquids, these measurements of particle flux and mean frequency were used to estimate the number of scatterers in the sample volume of the Doppler probe. This estimate of N, is shown in Fig. 8 as a function of the true concentration of Sephadex in the investigated liquid. To evaluate to what extent the streaming generated by the ultrasound itself will influence the results in the flow model the Doppler spectrum when the roller pump was turned off was registered. Such a spectrum is shown in Fig. 6b. As can be seen, the generated Doppler frequencies are below 2 Hz. Thus, in these model studies, this acoustic streaming has a small influence on the results. BLOOD PERFUSION MEASUREMENTS IN A FINGER

Instrumentation The ultrasound CW Doppler technique was used to measure the blood perfusion of the index finger when

60

100

Frequency (Hz) (a)

Pump vel:O -60

-100

-140 0

Results ofjlow model studies

100 0

5

10

Frequency (Hz) (b)

Fig. 6. Spectra obtained when a liquid mixture of Sephadex and glycerol were measured in the flow model. In (a), se-

lected spectra are shown when pump velocities 200, 120,80 and 20 were used. In (b), the spectrum obtained in the flow model when the roller pump is turned off, and there is no flow in the tube containing the Sephadex and glycerol mixture is shown. Observe that the frequency resolution has been increased in this spectrum as compared to (a).

the blood flow to the finger was varied in different manners. As the tissues in the finger are very close to the skin surface, the ultrasound frequency should be high. The ultrasound frequency of the Doppler probe used was 8.5 MHz, and the probe was designed to give a sample volume with a depth between 1.2 mm and 5.9 mm from the bottom of the Doppler probe. The ceramic material used in the transmitter and receiver transducer is Pz27 by Ferroperm, Denmark. The CW Doppler instrumentation used for these measurements has already been described in the instrumentation section above. The FFI’ analyzer used to measure the Doppler spectrum, and the computer for analyzing them, made the time between two successive measurements of blood perfusion 5 seconds. The total dynamic range of the m analyzer is 80 dB. This dynamic range was insufficient to handle the dynamic range of the detected Doppler signal in this experimental set-up. To overcome this limitation we introduced a high-pass filter at the input of the FFr

Measurement

of

blood perfusion0

20

441

etal

Method 0

0

S. 0. DYMLING

I 0

I 50

I

I

I

I

I

150 100 Pump velocity

I, 200

(4

,

With the flowmeter described above, the blood perfusion P was measured in the index finger of a healthy male subject. The probe was located on the radial side of the distal phalange, between the joint and the nail root. Before the start of the measurements the subject rested in a supine position for a period of 20 min. During the measurements, the investigated hand was held at a level slightly below heart level. Because of the already mentioned high-pass filter at the input of the FFT analyzer, the blood perfusion, P, was calculated as the first moment of the Doppler spectrum between 10 and 255 Hz. The acoustic coupling between the Doppler probe and the skin was achieved by using transmission gel. The Doppler probe was fixed to the finger with adhesive tape. Two different series of measurements were performed. In the first, a reactive hyperemia was induced following a complete arterial occlusion of the blood flow to the finger. This occlusion was achieved by a blood pressure cuff placed around the proximal phalange of the finger. The occlusion lasted for a period of 3 min, and the cuff was inflated to a pressure above 220 mm Hg during this period. In the second measurement series, the effect of smoking on the blood perfusion in the finger was investigated. The subject, therefore, restrained himself from smoking for more than 12 h before the investigation was performed.

Results The results of the measurement on the index finger following arterial occlusion are shown in Fig. 9. A 0

I

0

I

50

I

I

I

100

I 150

I

I. 200

.

c

10

Pump velocity @I

Fig. 7. The particle flux (a), and mean frequency (b), of the spectra in Fig. 6 were calculated from Eqns. ( 13) and ( 14).

analyzer. This high-pass filter removed the high-amplitude parts of the Doppler spectrum which were located at the low-frequency part of the spectrum. However, as pointed out earlier, it is essential to detect the low velocities of the cells in the smaller vessels that perfuse tissue. Consequently, the cutoff frequency of this high-pass filter was made as small as possible. The excitation voltage of the transmitting Doppler probe was 2 V,,. The total investigation time was 20 min. The frequencies measured by the FFT analyzer lie between 0 and 255 Hz.

0

1

0

I

,

5 Concentration

I

I

10 (g/80

I

15 ml)

Fig. 8. The number of scatterers inside the Doppler probe was estimated from the measurements of particle flux and mean frequency performed on the different mixtures of Sephadex and glycerol.

442

Ultrasound in Medicine and

I I I I I I I 10

15

I

II

Biology

I

20

Time (minutes)

Fig. 9. The blood perfusion in the index finger was measured when a reactive hyperemia was induced following a complete arterial occlusion. The occlusion was applied between 5 and 8 min after the start of the measurements.

relative value for the blood perfusion during the measurement was calculated with the maximum value set as a reference value of 100%. During resting conditions, the blood perfusion varied between 20% and 50% of the maximum value. In Fig. 10, the effect of smoking on the blood perfusion of the index finger is shown. Five minutes after the start of the investigation the subject smoked one cigarette. Smoking lasted for a period of 3 min. Immediately after the start of smoking there was a slight increase in the blood perfusion, followed by a slow decrease until the blood perfusion increased again 5 min after the start, and 2 min after the end of the smoking.

Volume 17, Number 5,

1991

tained. This is natural since random flow directions of the blood in the sample volume was assumed. The CW Doppler method does not measure blood perfusion directly as it cannot distinguish between capillary blood flow and other flow. However, the product N,E { II } is related to the capillary flow in the investigated tissue. It was shown, theoretically, that by measuring NJ { 21), the blood perfusion can be monitored (an indirect measure can be obtained). To achieve this, the investigated volume should contain the exchange vessels and a minimum of vessels that simply traverses the tissue without being connected to the exchange vessels. The model studies were made in order to show that the Doppler technique is useful even for measuring very low flow velocities. In Fig. 6a, it can be seen that it is possible to detect Doppler shifts of 15 Hz and lower ( CJ the spectrum corresponding to a pump velocity setting of 20 in Fig. 6a). Since the ultrasound frequency was 9.6 MHz, and the speed of sound in glycerol is 1923 m/s, this corresponds to a flow velocity of 2 mm/s as the fastest velocity component in this spectrum. It was also shown that for low concentrations of scatterers, a linear relation exists between the flow velocity in the tube of the flow model and both the mean Doppler frequency (cf: Fig. 7a) and the particle flux (cf: Fig. 7b) calculated from the Doppler spectrum according to eqn ( 14). This linear relation was also valid when the concentration ofscatterers in the examined liquid was varied.

DISCUSSION

In this report, it has been shown that the CW Doppler flowmeter can be used for measuring tissue blood flow. It was shown that the first moment of the Doppler power spectrum is an estimate of the product N,,E { v } ; i.e., the mean number of red cells in the sample volume and the mean speed of these cells. To arrive at this result, assumptions concerning the interaction between ultrasound and blood was made. Further we assumed that the investigated tissue had isotropic blood flow, i.e., independent of the position in space. Finally, note that an estimate of the overall mean speed of the red cells and not only the mean speed along the axis of the Doppler probe can be ob-

5

10

15

20

Time (minutes)

Fig. 10. The effect of smoking on blood perfusion in the index finger was measured. Five minutes after the start of the investigation, the subject smoked one cigarette. Smoking lasted for a period of 3 min.

Measurement of blood perfusion 0 S. 0. DYMLINGet al.

In Fig. 7b, the mean Doppler frequency is expected to be zero when extrapolated to a no-flow situation in the tube. However, the mean frequency is approximately 2-3 Hz for zero flow in the tube. This is due to the acoustic streaming generated by the emitted ultrasound. The Doppler spectrum when there is no flow in the tube of the flow model is shown in Fig. 6b. Here, Doppler frequencies up to 2 Hz were obtained which explains why the mean Doppler frequency is nonzero when there is no flow in the tube of the flow model. The flow model was also used to show that the proposed technique can monitor a change of blood perfusion due to a change of the blood volume inside the sample volume of the Doppler flowmeter. In the model studies, the volume of liquid in the sample volume could not be changed directly. Instead, the number of scatterers inside the sample volume was varied. This was done by changing the concentration of Sephadex particles in the liquid examined in the flow model. In Fig. 8, the number of scatterers in the sample volume of the Doppler flowmeter was estimated. This curve shows that: 1) a linear relation exists for low concentrations of Sephadex ( CJ concentrations below 5 g/ 80 cm3). 2) at high concentrations, the curve decreases instead of increases. 3) the estimated concentration of scatterers is nonzero when a liquid of pure glycerol was used in the model. The estimate of N, shows that it is possible to measure the number of scatterers inside the sample volume, at least for low concentrations. This estimate is based on the measurements of the particle flux according to eqn ( 15 ), which shows the validity of this equation. The reason for the decrease according to #2 has been described both in theoretical work concerning scattering of ultrasound ( cJ: Twersky 1962, and 1964) and experimental work (cf: Shung et al. 1975). At very high concentrations of Sephadex, the liquid resembles a perfect crystalline solid. There would be no wave scattering if all the Sephadex particles were regularly spaced at a very small distance from each other (smaller than the wavelength of the ultrasound). Although the cells can be considered scattering centers, the wave scattered from them will interfere destructively at any point of observation. The reason for this is that cells can be paired so that the waves from each pair travelling in a particular direction are exactly out of phase. The explanation for the observed effect (#3) is that even the pure glycerol liquid is contaminated with other scatterers of ultrasound. The main source of

443

these scatterers is believed to be a residue of air bubbles in the liquid. The linear relation at low concentrations indicates that these additional scatterers of ultrasound occur with approximately the same concentration in the different liquids that were examined. To summarize, these model studies show that it is possible to measure particle flux in the sample volume of the Doppler flowmeter, and this can be done at the very low flow velocities expected when applying this technique to real tissue. However, acoustic streaming generated by the emitted ultrasound will be a possible source of error when using this technique for measurement of blood perfusion in tissue. The measurement on a finger has demonstrated that blood perfusion in tissue can be monitored transcutaneously with the CW Doppler method. Due to the preliminary nature of these investigations, the clinical value of the method is yet unproven. Further in-vivo measurements were also performed on deeper lying tissue with a different probe geometry. These experiments show that the artefacts produced by movements are even greater in this case. However, an understanding of the artefacts produced by movements in the tissue has been obtained (cJ: Dymling 1985). The simplest way to overcome this problem has already been implemented in the measurements on the finger. Here, the transducer configuration results in a small sample volume. The number of tissue boundaries in such a sample volume is then reduced as compared to the configuration where the transmitter and receiver crystals are parallel to each other. The probability of a moving tissue boundary inside the sample volume is then reduced. For the measurements on more deeply located tissues, the first way to suppress movement artefacts is, therefore, to design a Doppler probe with these characteristics. In order to obtain a clinically useful technique, the future development will be concentrated on the removal of these artefacts. Acknowledgement-We thank Professor Sven-Eric Lindell and Professor Kjell Lindstrom for their generous support in the clinical phase of this study. The financial support given by the Swedish National Board of Technical Development is greatly appreciated.

REFERENCES Ash, E.; Giblin, R.; Frew, S. Ultrasonic measurement ofblood flow. Electronic Eng. 23; August; 1985. Baker, D. W.; Forster, F. K.; Daigle, R. E. Doppler principles and techniques. In: Frv, F. J.. ed. Ultrasound. itsaonlication in medicine and biology; Amsterdam: Else&r Scientific Publishing Company; 1978. Bonner, R. F.; Nossal, R. Models for laser Doppler measurements of blood flow in tissue. Appl. Optics 20( 12):2097-2107; 1981. Brody, W. R. Theoretical analysis ofthe ultrasonic blood flowmeter TR No. 4958-1, Stanford Electronics Laboratories, Stanford University, Stanford, CA; 197 1.

444

Ultrasound in Medicine and Biology

Brody, W. R. Theoretical analysis of the CW Doppler Flowmeter. IEEE Trans. Bio-Med. Eng. BME-21(3):183-192; 1974. Chmiel, H.; Mauser, R. Noninvasive measurement of blood flow rate utilizing ultrasound. US patent 4327739, 4 May 1982. Dymling, S. 0. Measurement of blood perfusion in tissue using Doppler ultrasound-A theoretical study. Report I/ 1984, Department of Electrical Measurements, Lund Institute of Technology, LUTEDX/(TEEM-1022) (1984). Dymling, S. 0. Measurement of blood perfusion in tissue using Doppler ultrasound-Experimental implementation and clinical results. Report 3/ 1985, Department of Electrical Measurements, Lund Institute of Technology. -_ LUTEDX/(TEEM1026) (1985). Dymling, S. 0.; Persson, H. W.; Hertz, C. H. The measurement of blood perfusion in tissue. Fifth World Conaress of Ultrasound in Medicine and Biology, Brighton, UK, 26-30 July, 1982. Hertz, C. H. Fourth European Congress on Ultrasound in Medicine, Dubrovnik, 17-24 May, 198 1. Holloway, Cl. A. Jr.; Watkins, D. W. Laser Doppier measurement of cutaneous blood flow. J. Invest. Dermatol. 69:306-309; 1977. Lassen, N. A.; Lindbergh, I. F.; Munck, 0. Measurement of bloodflow through skeletal muscle by intramuscular injection of Xenon-l 33. Lancet 686-689; 1964. Nilsson, G. E.; Tenland, T.; obetg, P. A. A new instrument for continuous measurement of tissue blood flow by light beating spectroscopy. IEEE Trans. Bio-Med. Eng. BME-27( 1) : 12- 19; 1980.

Volume 17, Number 5, 1991 Millner, R.; Cobet, U.; Klemens, A.; Blumenstein, G. Meglichkeiten der Ultraschali-Donder-Untersuchunaen bei hoheren Frequenzen. Therapiewoche 32:5082-5088;\982. Reid, J. M. Principles of doppler ultrasound. In: de Vlieger, M., ed. Handbook of clinical ultrasound, New York: Wiley, 1978. Reid, J. M.; Siegelmann, R. A.; Nasser, M. G.; Baker, D. W. The scattering of ultrasound by human blood. Proc. 8th ICMBE, Chicago, IL, 1969. Rowan, J. 0. Physics and the circulation-Medical physics handbooks 9, Bristol: Adam Hilger Ltd; 198 1. Schmid-Schonbein, H. Microrheology of erythrocytes, blood, viscosity, and the distribution of blood flow in the microcirculation. In: Guyton, A. C.; Cowley, A. W., eds. Cardiovascular physiology II (vol. 9). International review ofphysiology. Baltimore: University Park Press; 1976. Shung, K. K.; Siegelmann, R. A.; Reid, J. M. Scattering of ultrasound by blood. IEEE Trans. Bio-Med. Eng. BME-23( 6); 1976. Stem, M. D. In vivo evaluation of microcirculation by coherent light scattering. Nature 254:56-58; 1975. Strandness, D. E. Jr.; McCutcheon, E. P.; Rushmer, R. F. Applications of a transcutaneous Doppler flowmeter in evaluation of occlusive arterial disease. Surg. Gynecol. Obstet., May:l0391045; 1966. Twersky, V. Acoustic bulk parameters of random volume distribution of small scatterers. J. Acoust. Sot. Am. 36: 13 14; 1964. Twersky, V. On scatterings of waves by random distribution. J. Math. Phys. 3:700; 1962.