Ultrasound Doppler vector tomography measurements of directional blood flow

Ultrasound in Med. & Biol., Vol. 23, No. 1, pp. 47-57, 1997 Copyright 6 1997 World Federation for Ultrasound in Medicine & Biology

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@Original Contribution

ULTRASOUND DOPPLER VECTOR TOMOGRAPHY MEASUREMENTS OF DIRECTIONAL BLOOD FLOW

TOMAS JANSSON,* MONICA ALMQVIST,* KENT STRAHLBN,~ ROGER ERIKSSON,* GUNNAR SPARR,+ HANS W. PERSSON* and KJELL LINDSTR~M*

Departments of *Electrical Measurements and +Mathematics, Lund Institute of Technology, Lund, Sweden

(Received 6 December 1995; in jnal form 3 September 1996)

Abstract-An experimental system has been developed to verify the possibility of detecting f#ow activity using a technique called ultrasound Doppler vector tomography. A tomography algorithm is used to reconstruct blood flow vector fields using data from computer-controlled ultrasound continuous-wave Doppler scanning equipment. The result is a picture in which the brightness variations represent the reconstructed values of the curl of the velocity field (V x v). Continuous ultrasound is transmitted into a region with flow activity and the Doppler-shifted signals are received. To obtain measurement data suited for fan beam tomography, the scanning is performed in a plane from points encircling the region. Recoustructions have been achieved using measurement data from two different flow phantoms. A comparison between the experimental results and simulations shows good conformity. Copyright 0 1997 World Federation for Ultra- sound in Medicine & Biology.

Key Words: Ultrasound, Doppler, Tomography, Blood flow, Vector fields, Continuous wave, Vorticity, Curl.

INTRODUCTION

The quality of modern ultrasound scanners facilitates very good diagnostic results in the hands of an experienced and scrupulously careful ultrasound operator. However, a general disadvantage of diagnostic ultrasound methods is the need for an individualised scan- ner parameter setting and scanning procedure to ensure optimum diagnostic results. This makes the method vulnerable to less experienced operators, a factor that may give this diagnostic procedure an undeserved bad reputation. A solution to this problem could be the development of fully automated ultrasound scanning systems that can present standardised organ images and flow maps for further diagnosis by any radiologist.

An especially interesting part of ultrasound diagnostics concerns blood flow measurements using different forms of Doppler methodology. One future application for blood flow measurements may be for ultrasound mammography screening, Many clinical studies have shown that the prognosis of breast cancer

Address correspondence to: Dr. Monica Almqvist, Department of Electrical Measurements, Lund Institute of T&hnolo&, Lund University, P.O. Box 118, S-221 00 Lund, Sweden. E-mail: Monica. [email protected]

is related to the stage of the disease at diagnosis and treatment. X-ray mammography is a sensitive method for detecting breast cancer at an early stage, some- times even at an in situ stage; hence, mortality from breast cancer should be reduced by mammographic screening ( Andersson et al. 1988). Concern about the radiation doses emitted to the patients (Otto 1996) has recently stimulated the development of alternative diagnostic methods for breast cancer, e.g., laser light and ultrasound. Such systems should include some kind of specific breast cancer markers to enhance diagnostic accuracy.

For ultrasound, one such marker could be regional blood flow in the breast. In a fascinating article, Wells et aI. (1977) described how they could detect ultrasonic Doppler blood flow signals that seemed to be associated with malignant tumours in the female breast. For a number of patients, the signals from tumours were distinguishable from those from the normal breast. The tumour signals seemed to originate from the neovascular bed and give rise to Doppler signals. Using ~-MHZ ultrasound, strong Doppler signals in the l- to 2-kHz range were recorded from tumours, contrary to nonmalignant lesions, such as cysts,

47

48 Ultrasound in Medicine and Biology Volume 23, Number 1, 1997

from which no or only weak Doppler signals could be detected. However, clinical use of this interesting method is time consuming and must be performed by a very competent sonographer, which makes its direct use in a breast cancer screening programme difficult.

Almost 40 years ago, Satomura ( 1956) introduced the Doppler effect in ultrasound diagnostics. Whereas some of Satomura’s first medical attempts focused on recording of movements of cardiac walls and leaflets, later use of Doppler technique has focused more on noninvasive measurement of blood flow velocity. Sub- sequent evolution of the basic continuous-wave (CW) ultrasound Doppler technique has involved its supple- mentation with directional Doppler, Pulsed Doppler, and, most recently, different forms of Color Doppler to improve its diagnostic potential. Inherent limitations of the Doppler technique, such as its sensitivity to different forms of movement artifacts, grossly reduce the possibility for direct measurement of blood flow velocities below a few cm/s. However, a recent interest in measurements of low-velocity perfusion blood flow has resulted in a number of new “Doppler” methods, such as the ultrasound perfusion method (Eriksson et al. 1995a), power Doppler and harmonic Doppler (Meritt 1994). Careful use of these methods has ex- tended the applicable velocity range of the ultrasound Doppler method to normal blood flow velocities in soft tissue (mm/s).

All of these methods must be performed by an experienced operator. In search of possible techniques to enable fully automatic breast scanning and breast blood flow measurement, the use of some kind of tomographic scanning procedures came to our attention. Reconstruction of ultrasound images is relatively straightforward using this technique, like in normal computerised tomography (CT) images, whereas the reconstruction of Doppler images create much greater problems. The main difference between these two situ- ations is that the state at a certain point in the body is scalar and contributes equally to all beams going through it in the first case, but in the latter case, when the measurand is a vector field, the contribution also depends on the direction of the beam. As a result, standard tomographic reconstruction algorithms are not directly available. Several attempts have been made to recover a velocity field with ultrasound measurements and a tomographic procedure (Braun and Hauck 1991; Johnson et al. 1977a and 1977b; Winters and Rouseff 1990 and 1993). However, they are based on time of flight measurements and not Doppler-shifted ultrasound. Another method, pulse Doppler CT, com- bines flow images of a cross-sectional area obtained from different directions to complete a two-dimen-

sional flow image (Schmolke and Ermert 1988). An interesting method, Doppler tomography, was developed by Greenleaf and Ylitalo ( 1986). Using backscat- ter CW Doppler signals measured along 200 profiles taken at equispaced angles of view around the phantom, they report that directional flow can be measured. However, experimental results show only images where direction is ignored and the integral of the entire signal spectrum that is Doppler shifted for each point in the profile is used. The resulting reconstruction is an image in which brightness represents the total amount of scatterers that have created a Doppler shift within the window used for the integral. No attempt was made to obtain quantitative images of flow vectors.

Our aim is to develop techniques that combine CW Doppler ultrasound and tomographic reconstruction methodologies to enable automatic recording of directional flow in a scanning plane. We collaborate on the development of the new computational algorithms as well as experimental verification of the measurement method. Computerised tomography usually deals with the problem of recovering a scalar function when the values of (a set of) its line integrals are known. Motivated by the physics of the Doppler effect, we consider analogous problems for vector fields. This nonlinear inverse problem seems not to have been considered previously, and no reconstruction algorithm is known. A full three-dimensional (3D) reconstruction of a vector field from its Doppler-Radon transform is not possible without knowing its divergence and boundary values. However, by limiting the problem to two dimensions, i.e., to reconstruct the field in a slice, one needs only to know the divergence, i.e., the flow into and out of each point of the slice. Even if such information generally is not available, by invoking a priori information about the flow, more can be said. For example, in the blood flow application, one can use the fact that flow to a large extent appears in ves- sels, giving rise to “channels” in two dimensions. For this kind of flow, one thus can expect “N-shaped” regions in the grey-level landscape illustrating the magnitude of the curl (Juhlin 1992; Sparr et al. 1995). We have named this technique ultrasound Doppler vector tomography.

The specific objective of the present study is to verify experimentally the possibility of detecting directional flow using tomographic reconstruction of ultrasound CW Doppler measurements obtained from velocity fields of a moving fluid. To link this work with an eventual future clinical application of detecting pathological blood flow associated with malignant tumour neovascularisation in the female breast, phantom tests are performed using a blood-mimicking liquid as

Doppler vector tomography 0 T. JANSSON ct ai. 49

the experimental fluid and with flow velocities adjusted to the same magnitude as would be expected in the pathological breast.

MATERIALS AND METHODS

Doppler theor?, To obtain a Doppler shift from a flow, the medium

must contain particles that have an acoustic impedance different from that of the surrounding medium. Blood in tissue is a good example, since the acoustic impedance of red blood cells differs from that of surrounding tissue and blood plasma. In these experiments, a blood- mimicking fluid flowed through a tube with acoustic properties similar to those of the surrounding medium. As the speed of the particles was held much lower than the speed of sound in the medium, the Doppler shift can be written as:

(f-f)=kvwithk=ZfO. 0 (1) C

Here f denotes frequency of the reflected signal, f0 is the frequency of the transmitted ultrasound, v is the speed of the particles in the direction of the ultrasound beam and c is the speed of sound in the medium.

From a CW Doppler transducer, the received signal is also continuous but has a broadened frequency spectrum. This spectrum is a function of all velocity components parallel to the measurement direction in the ultrasound beam. From this spectrum, the integral:

v=$ s

z (f - f,)S(f)df (2)

0

is calculated, where S (f ) denotes the Doppler power spectrum (for definition, see Atkinson and Woodcock 1982) and k’ is a constant. This integral is also used in perfusion measurements. Dymling (1985) has shown that V is a measure of the net flow in the ultrasound beam direction, as f - f. corresponds to velocity and S(f) is proportional to the number of particles travelling at that velocity. It is assumed that all particles are the same size.

Tomography theory Consider continuous ultrasound transmitted into

a region with flow activity and the received Doppler- shifted ultrasound echoes. If a series of measurements is performed along different lines in a plane of that region, a picture of the flow distribution can be reconstructed in much the same manner as a CT picture (Juhlin 1992). In the present study, the component of

the curl perpendicular to the measurement plane was calculated and visualised.

In ordinary tomography, the energy absorption in tissue of a test beam of some sort is often measured. This process can be described by:

I = Ioexp(- ~L4xldl), (3)

where I is the intensity of the test beam, (u(x) is the absorption as a function of position x = (x, y, z) and L is the line defined by the beam. IO is the intensity when the absorption is zero. If all the lines of measurement are contained in a plane or a slice of the tissue, we obtain a problem in two dimensions.

By using the two-dimensional Radon transform:

/a(L) = s

dx)dl, (4) L

it is possible to calculate the value of (Y for every position in the measured slice of tissue. A number of algorithms for this calculation exist (Natterer 1986).

In the present study, there is another situation. If we introduce signed polar coordinates (r, 0)) where 19 is the angle from the x-axis with 0 5 19 < rr and r is the radius with sign so that --cc < r < ~0, then the measured quantity V from eqn (2) can be written in the form:

V(L) = s

i&-w x v(x)dl, (5) L

where 6, and w denote the unit vectors (0, 0, 1) and (cos 8, sin 0, 0), respectively, and v(x) is the velocity vector (Fig. 1) . Hence, V is the integral of all velocity components in the direction of the measurement beam along the line L.

The difference between this situation and the one in ordinary tomography is that the state at a certain point in the body does not contribute equally to all beams going through it, as it is dependent on the direction of the beam. Accessible experimental information is not sufficient for reconstruction of the vector field v(x) ; however, it is possible to reconstruct V X v, the curl of v (Juhlin 1992; Sparr et al. 1995). Their results have given us a usable formula:

i V(r, ti) = s

&.V x v(x)dl, (6) L

Ultrasound in Medicine and Biology Volume 23, Number 1, 1997

--

L

Fig. 1. Sketch of vectors defined in eqn (5).

where the left-hand side may be approximated with:

g V(r, w) = V(r + E, 0~) - V(r, w)

. (7) E

This means that in eqn (6)) the left-hand side can, in the experimental situation, be approximated by the difference of two close and parallel measurements and then division by the distance between the two measurement lines, E. This method, based on derivation, is sensitive to noise; therefore, special care has to be taken to reduce noise, e.g., averaging of the measured Doppler spectra.

Hence, if two close (distance E) and parallel measurements are performed and their values are sub- tracted and divided by 6, the result is an approximation of an ordinary scalar Radon transform of the z-component of the curl of v. Now the inverse Radon transform can be applied:

iZ;V Xv(x,y,O) = %-‘(gV(r,,)).

This can be performed for all other z-values. By rotat- ing the body, one can obtain the x- and the y-components in the same way. It follows that the curl of v can be fully recovered.

In the experimental situation, the measurement lines are arranged into fans emitting from source points equidistantly put on a circle with a radius r. around the flow phantom (Fig. 2). s source points and d detector angles in every source point have been used. Let (Y be the angle between a measurement line and the

tangent of the circle at the source point (positive orien- tation), and p be the angle along the circle to the source point from the initial. Thus, 0 5 p < 2n and 0 5 (Y < n. Then the source points pj can be written as pj = ro(:g,&r), with fij = jAp, A@ = ~T/s, j = 0,

s - 1 and the detector angles ok = kAcu, with A,‘= rrld and k = 0, . . . ,d- 1.

Now, consider a line emitting from source point pi. If d is chosen to be a multiple of s, we can find a line in the bundle of lines at source point pi+1 , which is parallel to the line of pi. The distance between the lines will depend on cr and is even zero for one line at each source point. The line corresponding to this case has been cancelled.

Now, when the subtractions are calculated, a reconstruction algorithm can be applied to the data to perform the inversion of the scalar Radon transform. For this, a filtered back projection algorithm based on fan-beam geometry has been used (Natterer 1986).

For flow in a pipe with a parabolic-shaped profile in the xy-plane, the z-component of the curl of v will be “N-shaped” over the flow profile. For a perfect parabolic flow along the y-axis, the velocity in the measurement plane can be written as:

v(x) = -A(x2 - R’)&,;

where R is the radius of the pipe (-R 5 x I R) and A is a constant. Then, the z-component of the curl of

i line ’

Flow 4 \\ ‘\ Phantom ,; \\ ‘i,,

,’

‘. ,,*”

‘b.- ,’ ,’

-----* _____-- -*=

Fig. 2. Explanatory sketch of an ultrasound Doppler vector tomography system. The CW ultrasound transducer is moved at a distance r0 around the flow phantom. Doppler spectrums are recorded at every source point (defined by angle p) for a limited number of detection angles (defined by angle (Y).

Doppler vector tomography 0 T. JANSSON et al. 51

Fig. 3. (a) Parabolic flow profile in the xy-plane with the resulting “N’ ‘-shaped z-component of the curl. The gray level in the “N” illustrates additionally how the magnitude of the curl vector varies with y position. (b) A deformed

“N”-shape occurs if the flow profile is not parabolic.

v(x) is 2Ax$, i.e., it will be linear (Fig. 3a), with positive maximum and negative minimum values at the edges (Juhlin 1992)) and the slope of N is proportional to the velocity of the flow. If the flow profile is not perfectly parabolic, then the “N-shape” will be deformed (Fig. 3b). As long as the profile does not change dramatically, the size of this deformed N will still vary with the flow velocity.

Simulations For the simulations, two different approaches

were used. For straight flow, the integral:

V(L) = s, &-cc, x v(x)dl (8)

was calculated using MAPLE (Waterloo Maple Soft-

ware, Canada, Waterloo, Ontario, Canada) on analytic expressions for the phantom flow. Therefore, these simulations are “exact” in some sense. For the other simulations, a somewhat cruder numerical model was used. The experimental situation was approximated by a matrix M (350 * 350) in which each matrix element was a two-dimensional vector. This vector was the value of the vector field in the centre of the pixel corresponding to the matrix element. To simulate the measurements, a matrix of weights was computed for each beam, the weight being the length of the beam within each pixel. For each pixel (i, j), these weights were multiplied by the value of M( i, j) projected onto the direction of the line. To compute integral (8), the sum over all pixels was calculated.

In this model, the test beam has a width that depends on the number of rows and columns in M. The test beam width can be decreased by increasing the size of M, but at the cost of an increased computation time.

Instrumentation To verify experimentally the concept of ultra-

sound Doppler vector tomography for measurement of blood flows, an experimental equipment set-up con- sisting of CW Doppler ultrasound transducers, elec- tronic instrumentation, a flow phantom and an associated scanning system was assembled. A block diagram of the experimental set-up is shown in Fig. 4.

The CW Doppler ultrasound transducer system was manufactured in-house and consisted of two 5- MHz ultrasound transducers, one working as a transmitter and the other as a receiver. The transducers were designed to have a radiating diameter of 6.35 mm, which results in a near-field length of 29 mm and a diffraction angle of 3.1” (calculated for the velocity of the liquid used in the experimental tank).

The selected resonant frequency and physical size

Fig. 4. Block diagram of the measurement set-up used in the ultrasound Doppler vector tomography experiments.

52 Ultrasound in Medicine and Biology Volume 23, Number I, 1997

Center of 2 4

c

rotation 1 I I 1 1

A cm

Fig. 5. The measurement volume of the CW ultrasound Doppler measurement system is determined by the intersection of the transmitter and receiver beams. The solid lines describe the calculated near and far fields for the transducers. r. is the radius of the scanning circle, and a is the measurement volume length, measured to be approximately 7 cm.

The figure is drawn to scale.

of the transducers, as well as their intervening angle, determine the active measurement volume (Fig. 5). This angle was adjusted in such a way that the measurement volume length (approximately 7 cm) ex- tended all through the flow phantom. This was con- firmed with a simple pulse-echo test. For the present experiments, an angle of 14” was used, which set the intersection of the centre lines of the transducers at the centre of the flow phantom. The radius of the transducer scanning circle was 70 mm.

A synthesiser/function generator (Hewlett Pack- ard [Andover, MA, USA] model 3325B) was used to drive the transmitter transducer with a 5.00-MHz sine wave. The amplitude of the excitation signal was set at 1 V RMS, which generates strong Doppler-shifted signals from the flow phantom without excessive heat- ing of the transducer.

The received Doppler signal was further amplified (maximum 53 dB ) before it was frequency shifted to a centre frequency of 10 kHz. Subsequent signal analysis was performed using a Hewlett Packard spectrum analyser model 3582A. The reason for shifting the Doppler spectra to a frequency separated from zero was the requirement to be able to determine the direction of the flow. This frequency shift of the Doppler signal was achieved by mixing the original ultrasound signal with a sine wave from a 5.01-MHz quartz oscillator and then bandpass filtering the mixer output.

To reduce noise in the measurements, the spectrum analyser averaged 16 measurements before sending a spectrum to the computer. For further noise reduction, an algorithm was implemented by the computer, which eliminated spurious signals outside the expected frequency range. This algorithm first searched for the peak

value of spectral amplitude (corresponding to signals from stationary structures, i.e., non-Doppler-shifted fie- quencies) and then examined the spectrum on both sides of the peak. At the frequency where the amplitude fell below a certain level, Doppler broadening of the reflected signal was considered to have ceased. For our experiments, this level was arbitrarily set to -60 dBV after some preliminary tests. Amplitude values for frequency components outside this frequency band were set to -70 dBV.

The Doppler transducer system was mounted in a test fixture controlled by four stepping motors (PH264- E1.5, Oriental Motor Co. Ltd., Torrance, CA, USA), which enabled arbitrary scanning movements. Move- ments of the transducer were thus possible along three orthogonal axes as well as rotation perpendicular to the measurement plane. To control the motors, commercial driver interfaces (GS-DC200S, SGS-Thomson, Lin- coln, MA, USA) were used.

A standard personal computer (Macintosh Quadra 700) was used for collection of the Doppler spectra, necessary calculations and control of the spectrum analyser as well as the stepping motors. The software was developed using LabVIEW (National Instruments, Inc., Austin, TX, USA). The spectrum analyser was connected to the computer via GPIB, and the stepping motor control cards were connected to the serial port. The derivatives were approximated using MATLAB (The Math Works, Inc., Natick, MA, USA), which is a software used for scientific calculations. The reconstruction algorithm was implemented in C-code.

Flow phantom An overview of the flow phantom system is shown

in Fig. 6. The flow phantom, manufactured using plas- tic tubing and containing a flow of blood-mimicking liquid, was placed in a liquid-filled experimental tank. The immersed ultrasound transducers were mounted on a rod connected to a scanning system on top of the tank.

Two different flow phantoms were used for these experiments, one with a straight flow and one with a circular flow in the measurement plane. The straight pipe (Fig. 7)) manufactured of polyethylene, had an outer diameter of 11 mm, an inner diameter of 8 mm and a length of 70 mm. At both ends, supply pipes of the same type were welded at a right angle to the 70- mm pipe. The circular flow phantom had a total outer diameter of 60 mm. It was manufactured of the same material with supply pipes in the same fashion, but the dimension of this pipe was slightly smaller (outer diameter 8 mm and inner diameter 5 mm) to facilitate


Glycerol / Magnetic Peristaltic SOlUtiOll stirrer pump

Fig. 6. Computer-controlled measurement system used to scan the flow phantom. The phantom is immersed in a tank containing impedance-matched liquid. A peristaltic pump circulates the blood-mimicking particle suspension through the phantom. The particles are prevented from sedimentation

by the magnetic stirrer.

shaping of the circular form. The right-angle connections were chosen to increase the Doppler signal at the ends of the phantom. This type of connection was used for this first study even though it is not ideal for min- imizing secondary flow components. The ends of each flow phantom were connected to soft silicone tubes, which could be connected to the pump outside the scanning tank.

Acoustic matching between the polyethylene flow phantom and the surrounding liquid was accomplished using a solution of 40% glycerol (by weight) in water (Eriksson et al. 1995b) as the liquid in the experimental tank. This results in an almost perfect match of the acoustic impedances for the two materials, ZslYc = 1864 x lo3 kg*m-2.s-1 andZ,,,,l = 1882 X lo3 kg-m-‘*s-l. However, due to some differences in the sound velocities ( 17 10 m * s -’ for the glycerol solution and 2050 m * S-I for the polyethylene pipe), a reflection occurs if the incident sound is not parallel to the normal of the pipe wall. The reflected pressure amplitude is theo- retically below 10% for angles up to 40”.

The blood-mimicking liquid used is a solution equal to the one used in the surrounding liquid, to minimise reflections, mixed with Sephadex@ G25 Su- perfine particles (Pharmacia, Uppsala, Sweden). Five grams of Sephadexe was dissolved in 100 g of the glycerol-water solution. The particles used in the suspension had a dry diameter of lo-40 ,um, but they increase slightly in solution. This particle size is somewhat larger than the diameter of red blood cells, which is normally about 7.5 pm. The density of the particle suspension was 1090 kg * me3. The viscosity was mea-

sured with a viscosimeter (Bohlin Visco 88, Bohlin Reologi AB, Lund, Sweden) to be approximately 0.01 Pascal seconds (Pa * s), or about ten times the viscosity of water.

The particle suspension was degassed by a vac- uum pump before use to prevent gas bubble formation in the pipe. During the measurements, the liquid was continuously stirred by a magnetic stirrer (Fig. 6) to prevent sedimentation of the Sephadex@ particles.

A peristaltic pump was used to produce controlled flow of the particle suspension. It was noted that the pulsations produced by the pump were reduced by let- ting the pump pull, and not push, the suspension through the phantom. However, the pulsations were still very pronounced, but they were reduced further by averaging spectra.

For the straight phantom, the mean velocity over the flow profile was 1 .O cm * s -’ . The circular phantom was measured for different flow velocities between 0.58 and 1.44 cm-s-’ . This ensured that the Reynold’s numbers for the different cases were well below what was required to obtain a parabolic velocity profile. Sec- ondary flow components due to the shape of the circular phantom should not be a major problem with the velocities involved. However, the right-angle connections may have caused problems, as discussed earlier.

The experimental tank was rectangular with dimensions of 250 x 700 X 300 mm. The walls and bottom of the tank were made of glass, and the inside of the walls was covered with a special ultrasound absorbing material (Ceram AB, Lund, Sweden) to prevent reflections and standing waves.

RESULTS AND DISCUSSION

Images of the curl component, or vorticity, perpendicular to the measurement plane have been reconstructed using experimental measurement data from a straight and a circular flow phantom and for corresponding simulated, ideal measurement values. In the images in Figs. 8, 9 and 10, the “N-shaped” effect can be recognised as black and white fields close to each other. All of these images are normalised to fully utilise the 256 grey-scale levels.

In Fig. 8a, a drawing of the straight flow phantom is shown. The image reconstructed from simulation of a straight flow with a parabolic flow profile is visualised in Fig. 8b, and a corresponding image for cases when experimental data were used is shown in Fig. 8c. Figure 8d shows a reconstructed image based on simulated data, with the exclusion of data from the source points close to the far ends of the pipe.

The conformity between the images in Figs. 8c

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Fig. 7. Close-up photo of the straight flow phantom showing the connected silicone feeding tubes 90” off the scanning

plane. The transducer can be seen to the right.

and 8d indicates that difficulties exist in receiving sufficient signal power at the ends of the straight pipe. One possible explanation is that Doppler-shifted ultrasound from these positions is more likely to be scattered and damped on the way back to the receiver than sound that has been reflected closer to the transducer. How- ever, the main reason more likely is the difference in acoustic velocity between the pipe and the solution, which would cause increased reflections in these positions where the incident angles are large. This problem is obviously related to the type of phantom used, and it is expected that blood flow in tissue will be easier to detect.

It is obvious that the number of source points is crucial when considering the resolution. The number of source points and detector angles used in the measurements were 45 X 90 for the straight phantom and 45 x 45 for the circular phantom, respectively. Corre- sponding numbers have been used in the simulations, except for Fig. 9c, where 130 X 130 measurements were performed.

Another important parameter is the beam width. Figure 9c shows that, if the ultrasound beam width was decreased to a size on the order of 0.3 nun and the number of source points and detector angles were increased, then the resolution should also increase re- markably. A comparison between Figs. lob and 9b shows that the large width of the flow depends on the low number of source points and detector angles, as the images are very similar in spite of the differences in beam width. The simulated beam width used was approximately 0.3 mm (depending on the matrix M), and the experimental beam had a width of about 7 mm.

To avoid this problem, a circular flow phantom The CW Doppler transducer arrangement used in- was studied. A grey-scale plot of a simulated parabolic cludes one transmitting and one receiving transducer flow and the reconstructed image are shown in Figs. (Fig. 5). The intersection of the transmission and re- 9a and 9b. The radius of curvature and the width of ception beams forms the measurement volume. The

Volume 23, Number 1, 1997

the flow profile in Fig. 9a both equal the dimensions of flow in the physical phantom. Another simulation of the same theoretical flow is shown in Fig. 9c, but with a higher number of source points and detector angles. The corresponding circular flow phantom used in our experiments is shown in Fig. 10a. Figure lob shows the reconstructed image based on data from measurements of the circular flow phantom with a mean flow velocity of 1.44 cm * s-l. A comparison between Figs. 9b and lob shows very good agreement. The circular flow is clearly shown, and some distortion caused by the flow connections can also be seen.

Fig. 8. (a) Outline of the straight flow phantom. Reconstructed images of straight flow using (b) simulated, (c) experimental and (d) simulated data with exclusion of data from the two source points at the ends of the pipe.

The outline in (a) is drawn to the same scale as the reconstructed images.

Doppler vector tomography 0 T. JANSSON et al.

0 a 0 c Fig. 9. (a) Picture of the theoretical circular flow. Reconstructed images using simulated data of (b) 45 source

points and 4.5 detector angles and (c) 130 source points and 130 detector angles.

size and shape of this volume is far from the ideal shape and may be a major cause for artifacts in the images. Furthermore, the overall sensitivity pattern of the transmitter/receiver configuration was approximated to be homogeneous in the measurement volume. Due to diffraction and wave interference, the sensitivity pattern will have a complicated shape, with high sensitivity in the centre where the central axes of the

transducers intersect. The effect of the size, shape and sensitivity pattern of measurement volume may be minimised if the tomography algorithm includes these parameters in the reconstruction calculation.

To study the variation of vorticity with velocity, four measurements were performed on the circular phantom at 0.58,0.89, 1.16 and 1.44 cm-s-‘. The amplitudes along the horizontal line through the centre of the reconstructed

( > a Fig. 10. (a) Outline of the circular flow phantom used. (b) Reconstructed pictures of circular flow using

experimental data.

56 Ultrasound in Medicine and Biology Volume 23, Number 1, 1997

- 1.45 cm/s - - -1.16cds -----0.87cm's . . . . . . . . . ,,58 cm/s

0 5 10 15 20 25 30

Position

Fig. 11. Graph of the variation of vorticity along the horizontal center line in reconstructed images, using the circular flow phantom for four different mean flow velocities. Forty-

five source points and 45 detector angles were used.

images are shown in Fig. 11, In the left half of the graph, the vorticity profile is seen as an inverted “N.” In the right half, the corresponding vorticity profile is shown for flow in the other direction. It can be observed that the size and slope of the “N” varies with velocity. The bias level in the middle of the graph is an artifact associated with the reconstruction algorithm.

To reconstruct absolute values of the vorticity, the system must be calibrated. This was not done, since the goal of this study was to determine the possibilities of detecting directional flow. It is therefore difficult to compare the experimental results with the simulations in any way other than a qualitative one. Furthermore, the question of how the vorticity exactly relates to velocity in these experiments has not been addressed.

To determine whether the present ultrasound Doppler vector tomograph is able to resolve appro- priate blood flow velocities, in vitro measurements have been performed using the circular flow phantom. Studies of blood flow in female breasts (Wells et al. 1977) show that characteristic ultrasonic Doppler blood flow velocities around 10 cm/s seem to be associated with malignant tumour neovascularisation. To create a certain margin, lower mean flow velocities (0.6-1.4 cm/s) were used through the flow phantom. The flow produced strong detected velocity signals with a satisfactory signal-to-noise ratio. This experi- ment confirms that the ultrasound Doppler vector tomograph can detect blood flow in a phantom, with velocities corresponding to or lower than the above- mentioned tumour blood flow.

The reconstructed images show a map of the z- component of the curl of the blood flow, a presentation that is very unfamiliar to most physicians. This type

of presentation may, in the future, give additional information on the state of blood flow inside the body. However, to simplify the ongoing evaluation of the method, efforts will be made to find other modalities to depict blood flow activity in the reconstructed pictures. Digital image processing will most likely solve some of these problems.

The measuring time for one slice is notably long in our first experiments, on the magnitude of hours. The exact time depends on the chosen number of measurement points and projection angles. If this method is to be used as a clinical examination method, the measuring time has to be shortened. This could be done in a number of ways, e.g., use of transducer arrays.

Ultrasonic Doppler vector tomography is an im- aging method in which tomographic lines of sight are used to measure vector fields. Specifically, in connection with blood flow velocity measurements, the method has been utilised to reconstruct images of the curl component perpendicular to the scanning plane from measurement data. Remaining problems concern attainable spatial resolution of the flow images, development of better tissue-mimicking flow phantoms, conversion of the curl images obtained into blood flow images and reduction of the present image generation time. Further studies are needed to clarify the value of this method in clinical practice.

Acknowledgements-The authors wish to thank Tomas Persson and Per Wendel, who designed the measurement equipment as their master’s theses. We also wish to thank Lennart Nilsson, who patiently manufactured numerous phantoms at our request. This work was supported by the Swedish National Board for Industrial and Technical Development (NUTEK grant no. 8524-93-07422) and the Swedish Research Council for Engineering Sciences (TFR, DNR 94-388).

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Ultrasound Doppler vector tomography measurements of directional blood flow