- Email: [email protected]
Assessment of wall velocity gradient imaging using a test phantom
Copyrighr
ELSEVIER
l
Ultrasound m Med. & Biol., Vol. 22, No. 9. pp. 1255-1260, 1996 0 1996 Worid Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629196 $15.00 + .OO
PII: SO301-5629( 96)00159-7
Original Contribution ASSESSMENT
OF WALL
VELOCITY GRADIENT TEST PHANTOM
IMAGING
USING
A
A. NOWICKI, R. OLSZEWSKI, J. ETIENNE, P. KARLOWICZ and J. ADAMUS Institute of Fundamental Technological Research, Polish Academy of Sciences, and Department of Cardiology, Main Military Medical Academy, Warsaw, Poland (Received
11 March
1996; in jinal form
1 August 1996)
Abstract-A new phantom has been designedto gain a better understanding of tissueDoppler imaging (TDI). Specifically, the phantom can easily be used to determine myocardial velocity gradients. The phantom mimics the left ventricle and is made of fine-grade sponge material whose ultrasound image closely resemblesthe gray scaleimage obtained from heart walls. Theoretical analysis of phantom wall movements offers a plausible explanation for the velocity gradients developing across the heart walls, The results of computer analysis were found to be in very good agreement with TDI M-mode recordings of phantom wall displacement. Copyright 0 1996 World Federation for Ultrasound in Medicine & Biology. Key Words: TissueDoppler imaging, Velocity gradients, Echocardiography, Ultrasound.
additional information on heart tissue dynamics, which may be used as an early indicator of heart disease prior to visual ultrasound detection of cardiomyopathic conditions (Palka et al. 1995 ) . To properly evaluate the potential of TDI to detect cardiomyopathy, a well-designed phantom is needed. Several velocity resolutions phantoms have been re-
INTRODUCTION
In recent years, a number of studies have evaluated a new tissue Doppler imaging (TDI) technique for myocardial tissue motion imaging applications. Of particular interest was the technique’s validity in instantaneously estimating myocardial velocity gradients (Fleming et al. 1994a; Groundstroem et al. 1993; McDicken et al. 1992; Miyatake et al. 199.5; Moran et al. 1993; Sutherland et al. 1994). With normal physiological contraction, the velocity of the endocardium is higher than that of the epicardium, and estimation of the resulting velocity gradient can be of great diagnostic value, especially in differentiating active from passive heart wall regions. TDI may be well suited for diagnostic examination of patients with coronary artery diseases in whom changes of myocardial velocity gradient are expected at rest and during stress tests. It is expected that the velocity gradient between the endocardium and epicardium in systole may be used as an indicator of regional myocardial contraction. In current clinical practice, the progress of the disease is characterized by indicators that describe the overall function of the ventricular cavity only and do not contain information on the spatial distribution of heart tissue activity. Knowledge of myocardial velocity gradients brings
ported in the literature.
Fleming et al. (1994b) reported the results of velocity resolution, spatial resolution and accuracy of Doppler imaging performed on a specially designed rotating sponge test phantom and a phantom fabricated from two blocks of moulded gel sliding against each other and immersed in water. The authors found that the spatial resolution was better than 3 mm x 3 mm. They showed that velocity resolution depended on the intensity of backscattered signal from the tissue-mimicking target and its absolute velocity. They also observed an increase in velocity deviation with backscattered signal strength, which they ascribed to saturation of the Doppler signals and possible generation of their harmonic content. This indicates that the appropriately designed Doppler phantom should minimize backscattering of the imaging signal. Uematsu et al. ( 1995) assessed the value of TDI in studying the left ventricular wall. The authors pointed out that the Doppler angle of incidence and parallel motion of the whole heart can influence velocity gradient measurement. They were able to differentiate the degree of regional left
Address correspondence to: Andrzej Nowicki, Institute of Fundamental Technological Research, Polish Academy of Sciences, Swiqtokrzyska 2 I, 00-049 Warsaw, Poland. 1255
1256
Ultrasound in Medicine and Biology
Volume 22, Number 9, 1996
ventricular contraction abnormalities in the anteroseptal wall and posterior wall. However, interpretation of some of their results was not completely clear because the movement of the whole heart was superimposed onto the wall movement, and this superposition produced a complicated function of time and space. The goal of this work was to develop a realistic left ventricular phantom allowing testing of TDI and, among other things, verification of the critical correction of the angle between the acoustic axis of the ukrasound imaging transducer and the oblique angle of incidence. The phantom developed is described, and the measurement arrangement is detailed. Experimental results are compared with the computer simulation, and it is shown that the phantom offers a potential for quantitative estimation of myocardial velocity gradients by TDI.
(a)
METHODS Materials and phantom description The left ventricular phantom developed was shaped like a cylinder, 100 mm long and fabricated from a fine-grade, lo-mm-thick sponge. The sponge material produced the backscattered echoes with a structure and grey scale closely resembling that obtained from the heart wall. The internal diameter of the sponge cylinder was 33 mm, and the internal surface of the sponge was covered with the fine and almost ultrasonically transparent rubber. The sponge cylinder was filled with distilled water, connected to a water pump and then immersed in a plastic container, which was also filled with distilled water (Fig. 1) . Two bases of the sponge cylinder were attached to opposite walls of the container. Pumping of the water in and out resulted in radial displacement of the phantom walls. The sponge material was made of polyurethane (Polopren, Poland; or equivalent Moltopren, Bayer, Germany), which has an open cell architecture. The density of the cells (or pores) was about 30/mm3. Prior to measurements, the sponge was immersed in water and squeezed several times under water to remove air voids trapped in the pores. Such a prepared sponge was then left for 24 h, fully immersed in water, before the measurements were conducted. A few hours after the phantom was immersed, no discernible changes in the image were detected. This gave additional assurance that the air was effectively removed from the sponge phantom. The acoustic parameters of the sponge, including sound velocity, reflection coefficient and relative backscattering, were determined using a ~-MHZ defectoscope (INCO, Poland). The measurements were performed using 4 x 4 x 2 cm sponge material prepared as described above. The measured
2
03 Fig. 1. Left ventricular spongephantomusedfor TDI model experiments.(a) Generalview; (b) diagramof the phantom cross-section.1, ultrasonic scanninghead; 2, water container; 3, cross-sectionof the test phantom.
sound velocity was 1523 m/s, and the absorption coefficient was measured as 0.6 dB/cm. The echoes re-
ceived from the front sponge wall were 32 dB down in comparison with the echoes obtained from a perfect reflector. Similarly, the echoes received from the sponge volume were 44 dB down. This value was considered to be one of relative backscattering. This differs from the relative scattering definition introduced by Fleming et al. ( 1994b), who determined the relative scattering by adjusting Doppler signal intensity ampli-
Assessment of wall velocity gradient imaging 0 A.
fication to be 30% of the maximum achievable value. This approach required the use of a B-mode image digitizer, which allowed comparison and equalization of the image brightness obtained from the sponge phantom and normal myocardial tissue. We did not have access to that kind of equipment. However, similar image intensities of normal myocardium and the sponge phantom were obtained at the minimum and mid-range settings of depth gain control, respectively. The sponge cylinder was manufactured by cutting from a solid cylinder. The inside surface of the cylinder was lined with latex rubber in the following manner: a condom was filled with distilled water and carefully inserted into the sponge cylinder in such a way as to minimize rubber wrinkles. The excellent adhesion of the latex rubber to the sponge was confirmed by the observed ultrasound image. A diaphragm pump (3 GPM Foot Operated Galley Pump, Sea-Dog Line, Everett, WA, USA) was connected to the prepared phantom. The pump valves were slightly modified so they could be controlled by a 50-W DC source (ZEM, Warsaw, Poland). The pump yield was calibrated for several source signals by measuring the volume of water removed by the pump into a calibrated chemical glass. The synchronized “peak systole” signal was fed into the synchronizing EKG input of the imaging scanner, which facilitated a direct comparison of the TDI phantom image sequence associated with a given pump cycle. The pump sinusoidal cycle was set to f = 1 Hz. For the fixed volume of water filling the phantom, the minimum and maximum internal and external diameters of the phantom were measured using an Acuson XPlO scanner with a TDI program.
Mathematical modelling Model experiments were preceded by approximate mathematical analysis of the phantom wall movements. Since both B- and M-mode displays indicated symmetrical wall displacement, the assumption was made that radial displacement of the phantom was the same along the whole phantom length. Minimum and maximum inside (rimin and rimax) and outside (r,,, and r,,, ) radii of the phantom cylinder were determined from the phantom’s B- and Mimages. For a given pump output “stroke volume” V,,, the volume of the water pumped into the cylinder changes according to the formula:
V,,(t)=
$[l
- cos(27rft)l.
(1)
NOWICKI
1257
et al.
Time-dependent internal ri (t ) and external re(t) radii can be expressed as:
I/? 1
ri(t) =
&Vsv[l
- cos(27dt)l + (rIJnin12
[
(2)
and l/2
r,(t)
=
[
&Vesv[l
- cos(2rft)l+
1
(Lcn>2
(3)
In the next step, endocardial and epicardial velocities were derived as the time derivatives of ri(t) and r,(t):
vi(t) = $ vsv f sin(27rft)l
X
l/2
&
V,,[l
-
COS(2Tft)]
+ (rimin)*
[
1
(4)
and
v,(t) = $ vewf sin( 27rft)]
X
l/2
[
&
V,dl - cos(2nft)l
+ (remid
. (5)
1
.’
RESULTS The data acquired were as follows: minimum internal radius rImin = 1.65 cm, maximum internal radius riman = 2.4 cm, minimum external radius r,,,, = 2.65 cm and maximum external radius r,,, = 2.98 cm. For the given cylinder length of 100 mm, the approximated (equal radial displacement along the cylinder) minimum and maximum volumes bounded by the inner and outer wall surfaces were Vimin = 85 cm3, Vimax = 181 cm3, Vetin = 220 cm3 and V,,,, = 280 cm3, respectively. The resulting ‘ ‘stroke volume” V,, calculated as the difference between Vimax and Vlmin was close to 96 cm3. The difference between V,,, and V UIU” (“external stroke volume,” V,,,) was 60 cm3. As can be seen, these two stroke volumes are different because the sponge used for the phantom was of an open cell design, and water was partly squeezed out when the phantom diameter was increasing. For these data, the values of internal ri( t) and external re(t) cyl-
1258
Ultrasound in Medicine and Biology
inder radii as a function of time were calculated and plotted in Fig. 2. As predicted, the thickness of the wall decreases with extension of the cylinder diameter. Figure 3 shows the calculated instantaneous velocities of inner Vi(t) and outer v,(t) surfaces of the phantom wall. The difference between vi(t) and v,(t) was defined as the velocity gradient Av (t) across the phantom wall and plotted in Fig. 4 (curve a). The TDI images acquired from the pulsating model phantom were stored in scanner memory and replayed for additional measurements in both 2D (Fig. 5a) and M-mode (Fig. 5b). The local tissue velocities were measured about 1 mm inside the wall rather than on its outer boundaries (marked as ROI in Fig. 5). For approximately the same phantom wall coordinates, the velocities within the wall were calculated, and the resulting “internal” velocity gradient was computed and plotted in Fig. 4 (curve b). The measurements were repeated 3-5 times in each ROI, and the average velocity values were calculated. The set of data for averaging was taken from slightly different pixels within the ROI. The velocity image often has a mosaiclike color pattern, and using the different data from the chosen ROI (e.g., 3 x 3 color-coded velocity pixels matrix, which corresponds roughly to 1 X 1 mm) smoothes the value of the measured velocity considerably. Figure 4b was calculated from eqns (4) and (5) for modified values of the inside radius (increased by 1 mm) and outside radius (decreased by 1 mm). Therefore, the radii used to plot Fig. 4 (curve b) were rid” = 1.75 cm, ri, = 2.5 cm, reti” = 2.55 cm and r,,, = 2.88 cm, respectively. For these values, a new value of “internal stroke volume” = 80 cm3 was determined, and the differential velocity within the phantom’s wall was calculated. Initial experimental evaluation of the phantom indicates that it can be used to determine tissue movement velocity. The experimentally measured velocity gradient is shown in Fig. 4 (curve c). Both gradients, theoretically computed and derived from the recorded TDI images of the phantom, are in good agreement, proving the validity of the mathemati-
Volume 22, Number 9, 1996
[cm/s1
-31”““““““““’ 0
0.1
0.2
0.3
0.4
0.5
0.6
0 7
0.e
0.9
time
1s
Fig. 3. Calculated velocities of the inner vi(t) and outer v,(t) surfaces of the phantom wall.
cal model developed for the sinusoidally phantom.
pulsating
CONCLUSIONS A new phantom specially designed to determine myocar-dial velocity gradient using TDI was described. This phantom closely mimics left ventricular movements. Knowledge of the frequency of movement and displacement amplitude of the phantom’s wall velocity gradient within the phantom cross-section can be determined. This makes the phantom well suited to determine both qualitatively and quantitatively the velocity of the wall. The phantom can also be used as a teaching tool to demonstrate and analyze the relationship between the radial velocity of the phantom walls and their color coding. In comparison with the rotational phantom (McDicken et al. 1992) and the sliding phantom developed by Fleming et al. ( 1994b), the pulsating cylinder phantom better mimics the spatial movements of the left heart. The “stroke volume” and cross-section of the phantom were carefully selected to be simi-
Xace: .I 0.2
0.3
0.4
time
Fig. 2. Calculated displacement of the inner and outer walls of the phantom.
0.5
0.6
0.7
0.8
0.9
1
[sl
Fig. 4. Velocity gradients across the wall. (a) Corresponds to the velocity gradient between the external and internal surfaces of the phantom wall; (b) represents the calculation taken between two points lying within the wall, each 1 mm from the corresponding wall surface. The differential velocity (c) was measured between approximately the same sites. Error bars represent the variation of the individual measurements in the ROT.
Assessment of wall velocity gradient imaging
0 A. NOWICKI
et al.
1259
(b) Fig. 5. (a) TDI-2D sectorscansof the phantomwall in four different time sequences. Squareswithin the wall showthe site (ROI) of the velocity measurement.(b) The 2D sector and M-mode image (recorded along me dotted line) of the pulsatingwall showinga distinct changein thicknesssimilarto that predictedby the mathematical calculation(seeFig. 3 )
lar to the physiological ones. As already described, the phantom’s wall movement was produced by the sinusoidal change of the water volume injected by the pump into the phantom. This resulted in the changes in the phantom’s wall velocity and the wall’s thickness. While very good agreement between the theoretical prediction and experiments was achieved, it should
be noted that the assumptionabout uniform wall movement along the whole length of the phantom is not completely correct. Specifically, the sponge phantom is mechanically attached at both ends to the water container, which naturally modifies the displacement of the phantom wall adjacent to the container wall. For this reason, all measurementswere done in the center
1260
Ultrasound in Medicine and Biology
part of the phantom, where the distortions of the wall’s movement from those predicted theoretically were small. However, they may not be small enough to enable the calibration of tissue velocity measurements. In this sense, the rotational phantom described by Fleming et al. ( 1994b) is better suited for calibration of TDI systems. The strength of our phantom is that its relative backscattering is low enough to prevent the system from becoming saturated. The physiological movement of the heart wall’s displacement can be modelled by choosing the preprogrammed function of the voltage driving the DC motor pump. The local properties of the wall can also be changed by replacing part of the cylinder sponge with other sponge material having higher stiffness, thus imitating the stiffer postinfarct heart wall. There are no specific limits regarding phantom diameter and length. The size was chosen so as to obtain wall displacements similar to the real ones for realistic “stroke volumes.” Also, instead of water, we used a mixture of water and glycerin and a small amount of starch particles (4 g/L) with overall viscosity = 4 cP. The change of fluid did not affect TDI measurements. When air bubbles were not fully removed from the fluid, their flow/movements inside the phantom were clearly displayed in TDI mode but did not modify wall velocity.
Volume 22, Number 9, 1996
REFERENCES Fleming AD, Xia X, McDicken WN, Sutherland GR, Fenn I. Myocardial velocity gradients detected by Doppler imaging. Br J Radio1 1994a;67:679-688. Fleming AD, McDicken WN, Sutherland GR, Hoskings PR. Assessment of colour Doppler tissue imaging using test-phantoms. Ultrasound Med Biol 1994b;20:937-951. Groundstroem KWE, Sutherland GR, Moran CM, McDicken WN. Myocardial imaging by color Doppler coded velocity mappingFrom regional contraction to tissue characterization? In: Nanda N, S&&f R, eds. Advances in echo imaging using contrast enhancement. The Netherlands: Kluwer. 1993:375-399. McDicken WN, Sutherland GR, Moran CM, Gordon LR. Colour Doppler velocity imaging of the myocardium. Ultrasound Med Biol 1992; 18:651-654. Miyatake K, Yamagishi M, Tanaka N, et al. A new method for the evaluation of left ventricular wall motion by color-coded tissue Doppler imaging: In vitro and in viva studies. J Am Co11Cardiol 1995;25:717-724. Moran CM, McDicken WN, Groundstroem KWE, Sutherland GR. Potential applications of color-Doppler imaging of the myocardium in assessing contractility and perfusion. In: Nanda N, Schlief R, eds. Advances in echo imaging using contrast enhancement. The Netherlands: KIuwer. 1993:359-374. Palka P, Lange A, Fleming AD, et al.’ Doppler tissue imaging: Assessment of systolic and diastolic transmural mean velocity and velocity gradient in cardiomyopatbies-New diagnostic index of left ventricular function. Eur Heart J 1995; 16(Suppl): 105. Sutherland GR, Stewart MJ, Groundstroem KWE, et al. Color Doppler myocardial imaging: A new technique for the assessment of myocardial function. J Am Sot Echocardigr 1994;7:44-458. Uematsu M, Miyatake K, Tanaka N, et al. Myocardial velocity gradient as a new indicator of regional left ventricular contraction: Detection by a two-dimensional tissue Doppler imaging technique. J Am Co11Cardiol 1995;26:217-223.
ELSEVIER
l
Ultrasound m Med. & Biol., Vol. 22, No. 9. pp. 1255-1260, 1996 0 1996 Worid Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629196 $15.00 + .OO
PII: SO301-5629( 96)00159-7
Original Contribution ASSESSMENT
OF WALL
VELOCITY GRADIENT TEST PHANTOM
IMAGING
USING
A
A. NOWICKI, R. OLSZEWSKI, J. ETIENNE, P. KARLOWICZ and J. ADAMUS Institute of Fundamental Technological Research, Polish Academy of Sciences, and Department of Cardiology, Main Military Medical Academy, Warsaw, Poland (Received
11 March
1996; in jinal form
1 August 1996)
Abstract-A new phantom has been designedto gain a better understanding of tissueDoppler imaging (TDI). Specifically, the phantom can easily be used to determine myocardial velocity gradients. The phantom mimics the left ventricle and is made of fine-grade sponge material whose ultrasound image closely resemblesthe gray scaleimage obtained from heart walls. Theoretical analysis of phantom wall movements offers a plausible explanation for the velocity gradients developing across the heart walls, The results of computer analysis were found to be in very good agreement with TDI M-mode recordings of phantom wall displacement. Copyright 0 1996 World Federation for Ultrasound in Medicine & Biology. Key Words: TissueDoppler imaging, Velocity gradients, Echocardiography, Ultrasound.
additional information on heart tissue dynamics, which may be used as an early indicator of heart disease prior to visual ultrasound detection of cardiomyopathic conditions (Palka et al. 1995 ) . To properly evaluate the potential of TDI to detect cardiomyopathy, a well-designed phantom is needed. Several velocity resolutions phantoms have been re-
INTRODUCTION
In recent years, a number of studies have evaluated a new tissue Doppler imaging (TDI) technique for myocardial tissue motion imaging applications. Of particular interest was the technique’s validity in instantaneously estimating myocardial velocity gradients (Fleming et al. 1994a; Groundstroem et al. 1993; McDicken et al. 1992; Miyatake et al. 199.5; Moran et al. 1993; Sutherland et al. 1994). With normal physiological contraction, the velocity of the endocardium is higher than that of the epicardium, and estimation of the resulting velocity gradient can be of great diagnostic value, especially in differentiating active from passive heart wall regions. TDI may be well suited for diagnostic examination of patients with coronary artery diseases in whom changes of myocardial velocity gradient are expected at rest and during stress tests. It is expected that the velocity gradient between the endocardium and epicardium in systole may be used as an indicator of regional myocardial contraction. In current clinical practice, the progress of the disease is characterized by indicators that describe the overall function of the ventricular cavity only and do not contain information on the spatial distribution of heart tissue activity. Knowledge of myocardial velocity gradients brings
ported in the literature.
Fleming et al. (1994b) reported the results of velocity resolution, spatial resolution and accuracy of Doppler imaging performed on a specially designed rotating sponge test phantom and a phantom fabricated from two blocks of moulded gel sliding against each other and immersed in water. The authors found that the spatial resolution was better than 3 mm x 3 mm. They showed that velocity resolution depended on the intensity of backscattered signal from the tissue-mimicking target and its absolute velocity. They also observed an increase in velocity deviation with backscattered signal strength, which they ascribed to saturation of the Doppler signals and possible generation of their harmonic content. This indicates that the appropriately designed Doppler phantom should minimize backscattering of the imaging signal. Uematsu et al. ( 1995) assessed the value of TDI in studying the left ventricular wall. The authors pointed out that the Doppler angle of incidence and parallel motion of the whole heart can influence velocity gradient measurement. They were able to differentiate the degree of regional left
Address correspondence to: Andrzej Nowicki, Institute of Fundamental Technological Research, Polish Academy of Sciences, Swiqtokrzyska 2 I, 00-049 Warsaw, Poland. 1255
1256
Ultrasound in Medicine and Biology
Volume 22, Number 9, 1996
ventricular contraction abnormalities in the anteroseptal wall and posterior wall. However, interpretation of some of their results was not completely clear because the movement of the whole heart was superimposed onto the wall movement, and this superposition produced a complicated function of time and space. The goal of this work was to develop a realistic left ventricular phantom allowing testing of TDI and, among other things, verification of the critical correction of the angle between the acoustic axis of the ukrasound imaging transducer and the oblique angle of incidence. The phantom developed is described, and the measurement arrangement is detailed. Experimental results are compared with the computer simulation, and it is shown that the phantom offers a potential for quantitative estimation of myocardial velocity gradients by TDI.
(a)
METHODS Materials and phantom description The left ventricular phantom developed was shaped like a cylinder, 100 mm long and fabricated from a fine-grade, lo-mm-thick sponge. The sponge material produced the backscattered echoes with a structure and grey scale closely resembling that obtained from the heart wall. The internal diameter of the sponge cylinder was 33 mm, and the internal surface of the sponge was covered with the fine and almost ultrasonically transparent rubber. The sponge cylinder was filled with distilled water, connected to a water pump and then immersed in a plastic container, which was also filled with distilled water (Fig. 1) . Two bases of the sponge cylinder were attached to opposite walls of the container. Pumping of the water in and out resulted in radial displacement of the phantom walls. The sponge material was made of polyurethane (Polopren, Poland; or equivalent Moltopren, Bayer, Germany), which has an open cell architecture. The density of the cells (or pores) was about 30/mm3. Prior to measurements, the sponge was immersed in water and squeezed several times under water to remove air voids trapped in the pores. Such a prepared sponge was then left for 24 h, fully immersed in water, before the measurements were conducted. A few hours after the phantom was immersed, no discernible changes in the image were detected. This gave additional assurance that the air was effectively removed from the sponge phantom. The acoustic parameters of the sponge, including sound velocity, reflection coefficient and relative backscattering, were determined using a ~-MHZ defectoscope (INCO, Poland). The measurements were performed using 4 x 4 x 2 cm sponge material prepared as described above. The measured
2
03 Fig. 1. Left ventricular spongephantomusedfor TDI model experiments.(a) Generalview; (b) diagramof the phantom cross-section.1, ultrasonic scanninghead; 2, water container; 3, cross-sectionof the test phantom.
sound velocity was 1523 m/s, and the absorption coefficient was measured as 0.6 dB/cm. The echoes re-
ceived from the front sponge wall were 32 dB down in comparison with the echoes obtained from a perfect reflector. Similarly, the echoes received from the sponge volume were 44 dB down. This value was considered to be one of relative backscattering. This differs from the relative scattering definition introduced by Fleming et al. ( 1994b), who determined the relative scattering by adjusting Doppler signal intensity ampli-
Assessment of wall velocity gradient imaging 0 A.
fication to be 30% of the maximum achievable value. This approach required the use of a B-mode image digitizer, which allowed comparison and equalization of the image brightness obtained from the sponge phantom and normal myocardial tissue. We did not have access to that kind of equipment. However, similar image intensities of normal myocardium and the sponge phantom were obtained at the minimum and mid-range settings of depth gain control, respectively. The sponge cylinder was manufactured by cutting from a solid cylinder. The inside surface of the cylinder was lined with latex rubber in the following manner: a condom was filled with distilled water and carefully inserted into the sponge cylinder in such a way as to minimize rubber wrinkles. The excellent adhesion of the latex rubber to the sponge was confirmed by the observed ultrasound image. A diaphragm pump (3 GPM Foot Operated Galley Pump, Sea-Dog Line, Everett, WA, USA) was connected to the prepared phantom. The pump valves were slightly modified so they could be controlled by a 50-W DC source (ZEM, Warsaw, Poland). The pump yield was calibrated for several source signals by measuring the volume of water removed by the pump into a calibrated chemical glass. The synchronized “peak systole” signal was fed into the synchronizing EKG input of the imaging scanner, which facilitated a direct comparison of the TDI phantom image sequence associated with a given pump cycle. The pump sinusoidal cycle was set to f = 1 Hz. For the fixed volume of water filling the phantom, the minimum and maximum internal and external diameters of the phantom were measured using an Acuson XPlO scanner with a TDI program.
Mathematical modelling Model experiments were preceded by approximate mathematical analysis of the phantom wall movements. Since both B- and M-mode displays indicated symmetrical wall displacement, the assumption was made that radial displacement of the phantom was the same along the whole phantom length. Minimum and maximum inside (rimin and rimax) and outside (r,,, and r,,, ) radii of the phantom cylinder were determined from the phantom’s B- and Mimages. For a given pump output “stroke volume” V,,, the volume of the water pumped into the cylinder changes according to the formula:
V,,(t)=
$[l
- cos(27rft)l.
(1)
NOWICKI
1257
et al.
Time-dependent internal ri (t ) and external re(t) radii can be expressed as:
I/? 1
ri(t) =
&Vsv[l
- cos(27dt)l + (rIJnin12
[
(2)
and l/2
r,(t)
=
[
&Vesv[l
- cos(2rft)l+
1
(Lcn>2
(3)
In the next step, endocardial and epicardial velocities were derived as the time derivatives of ri(t) and r,(t):
vi(t) = $ vsv f sin(27rft)l
X
l/2
&
V,,[l
-
COS(2Tft)]
+ (rimin)*
[
1
(4)
and
v,(t) = $ vewf sin( 27rft)]
X
l/2
[
&
V,dl - cos(2nft)l
+ (remid
. (5)
1
.’
RESULTS The data acquired were as follows: minimum internal radius rImin = 1.65 cm, maximum internal radius riman = 2.4 cm, minimum external radius r,,,, = 2.65 cm and maximum external radius r,,, = 2.98 cm. For the given cylinder length of 100 mm, the approximated (equal radial displacement along the cylinder) minimum and maximum volumes bounded by the inner and outer wall surfaces were Vimin = 85 cm3, Vimax = 181 cm3, Vetin = 220 cm3 and V,,,, = 280 cm3, respectively. The resulting ‘ ‘stroke volume” V,, calculated as the difference between Vimax and Vlmin was close to 96 cm3. The difference between V,,, and V UIU” (“external stroke volume,” V,,,) was 60 cm3. As can be seen, these two stroke volumes are different because the sponge used for the phantom was of an open cell design, and water was partly squeezed out when the phantom diameter was increasing. For these data, the values of internal ri( t) and external re(t) cyl-
1258
Ultrasound in Medicine and Biology
inder radii as a function of time were calculated and plotted in Fig. 2. As predicted, the thickness of the wall decreases with extension of the cylinder diameter. Figure 3 shows the calculated instantaneous velocities of inner Vi(t) and outer v,(t) surfaces of the phantom wall. The difference between vi(t) and v,(t) was defined as the velocity gradient Av (t) across the phantom wall and plotted in Fig. 4 (curve a). The TDI images acquired from the pulsating model phantom were stored in scanner memory and replayed for additional measurements in both 2D (Fig. 5a) and M-mode (Fig. 5b). The local tissue velocities were measured about 1 mm inside the wall rather than on its outer boundaries (marked as ROI in Fig. 5). For approximately the same phantom wall coordinates, the velocities within the wall were calculated, and the resulting “internal” velocity gradient was computed and plotted in Fig. 4 (curve b). The measurements were repeated 3-5 times in each ROI, and the average velocity values were calculated. The set of data for averaging was taken from slightly different pixels within the ROI. The velocity image often has a mosaiclike color pattern, and using the different data from the chosen ROI (e.g., 3 x 3 color-coded velocity pixels matrix, which corresponds roughly to 1 X 1 mm) smoothes the value of the measured velocity considerably. Figure 4b was calculated from eqns (4) and (5) for modified values of the inside radius (increased by 1 mm) and outside radius (decreased by 1 mm). Therefore, the radii used to plot Fig. 4 (curve b) were rid” = 1.75 cm, ri, = 2.5 cm, reti” = 2.55 cm and r,,, = 2.88 cm, respectively. For these values, a new value of “internal stroke volume” = 80 cm3 was determined, and the differential velocity within the phantom’s wall was calculated. Initial experimental evaluation of the phantom indicates that it can be used to determine tissue movement velocity. The experimentally measured velocity gradient is shown in Fig. 4 (curve c). Both gradients, theoretically computed and derived from the recorded TDI images of the phantom, are in good agreement, proving the validity of the mathemati-
Volume 22, Number 9, 1996
[cm/s1
-31”““““““““’ 0
0.1
0.2
0.3
0.4
0.5
0.6
0 7
0.e
0.9
time
1s
Fig. 3. Calculated velocities of the inner vi(t) and outer v,(t) surfaces of the phantom wall.
cal model developed for the sinusoidally phantom.
pulsating
CONCLUSIONS A new phantom specially designed to determine myocar-dial velocity gradient using TDI was described. This phantom closely mimics left ventricular movements. Knowledge of the frequency of movement and displacement amplitude of the phantom’s wall velocity gradient within the phantom cross-section can be determined. This makes the phantom well suited to determine both qualitatively and quantitatively the velocity of the wall. The phantom can also be used as a teaching tool to demonstrate and analyze the relationship between the radial velocity of the phantom walls and their color coding. In comparison with the rotational phantom (McDicken et al. 1992) and the sliding phantom developed by Fleming et al. ( 1994b), the pulsating cylinder phantom better mimics the spatial movements of the left heart. The “stroke volume” and cross-section of the phantom were carefully selected to be simi-
Xace: .I 0.2
0.3
0.4
time
Fig. 2. Calculated displacement of the inner and outer walls of the phantom.
0.5
0.6
0.7
0.8
0.9
1
[sl
Fig. 4. Velocity gradients across the wall. (a) Corresponds to the velocity gradient between the external and internal surfaces of the phantom wall; (b) represents the calculation taken between two points lying within the wall, each 1 mm from the corresponding wall surface. The differential velocity (c) was measured between approximately the same sites. Error bars represent the variation of the individual measurements in the ROT.
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(b) Fig. 5. (a) TDI-2D sectorscansof the phantomwall in four different time sequences. Squareswithin the wall showthe site (ROI) of the velocity measurement.(b) The 2D sector and M-mode image (recorded along me dotted line) of the pulsatingwall showinga distinct changein thicknesssimilarto that predictedby the mathematical calculation(seeFig. 3 )
lar to the physiological ones. As already described, the phantom’s wall movement was produced by the sinusoidal change of the water volume injected by the pump into the phantom. This resulted in the changes in the phantom’s wall velocity and the wall’s thickness. While very good agreement between the theoretical prediction and experiments was achieved, it should
be noted that the assumptionabout uniform wall movement along the whole length of the phantom is not completely correct. Specifically, the sponge phantom is mechanically attached at both ends to the water container, which naturally modifies the displacement of the phantom wall adjacent to the container wall. For this reason, all measurementswere done in the center
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part of the phantom, where the distortions of the wall’s movement from those predicted theoretically were small. However, they may not be small enough to enable the calibration of tissue velocity measurements. In this sense, the rotational phantom described by Fleming et al. ( 1994b) is better suited for calibration of TDI systems. The strength of our phantom is that its relative backscattering is low enough to prevent the system from becoming saturated. The physiological movement of the heart wall’s displacement can be modelled by choosing the preprogrammed function of the voltage driving the DC motor pump. The local properties of the wall can also be changed by replacing part of the cylinder sponge with other sponge material having higher stiffness, thus imitating the stiffer postinfarct heart wall. There are no specific limits regarding phantom diameter and length. The size was chosen so as to obtain wall displacements similar to the real ones for realistic “stroke volumes.” Also, instead of water, we used a mixture of water and glycerin and a small amount of starch particles (4 g/L) with overall viscosity = 4 cP. The change of fluid did not affect TDI measurements. When air bubbles were not fully removed from the fluid, their flow/movements inside the phantom were clearly displayed in TDI mode but did not modify wall velocity.
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REFERENCES Fleming AD, Xia X, McDicken WN, Sutherland GR, Fenn I. Myocardial velocity gradients detected by Doppler imaging. Br J Radio1 1994a;67:679-688. Fleming AD, McDicken WN, Sutherland GR, Hoskings PR. Assessment of colour Doppler tissue imaging using test-phantoms. Ultrasound Med Biol 1994b;20:937-951. Groundstroem KWE, Sutherland GR, Moran CM, McDicken WN. Myocardial imaging by color Doppler coded velocity mappingFrom regional contraction to tissue characterization? In: Nanda N, S&&f R, eds. Advances in echo imaging using contrast enhancement. The Netherlands: Kluwer. 1993:375-399. McDicken WN, Sutherland GR, Moran CM, Gordon LR. Colour Doppler velocity imaging of the myocardium. Ultrasound Med Biol 1992; 18:651-654. Miyatake K, Yamagishi M, Tanaka N, et al. A new method for the evaluation of left ventricular wall motion by color-coded tissue Doppler imaging: In vitro and in viva studies. J Am Co11Cardiol 1995;25:717-724. Moran CM, McDicken WN, Groundstroem KWE, Sutherland GR. Potential applications of color-Doppler imaging of the myocardium in assessing contractility and perfusion. In: Nanda N, Schlief R, eds. Advances in echo imaging using contrast enhancement. The Netherlands: KIuwer. 1993:359-374. Palka P, Lange A, Fleming AD, et al.’ Doppler tissue imaging: Assessment of systolic and diastolic transmural mean velocity and velocity gradient in cardiomyopatbies-New diagnostic index of left ventricular function. Eur Heart J 1995; 16(Suppl): 105. Sutherland GR, Stewart MJ, Groundstroem KWE, et al. Color Doppler myocardial imaging: A new technique for the assessment of myocardial function. J Am Sot Echocardigr 1994;7:44-458. Uematsu M, Miyatake K, Tanaka N, et al. Myocardial velocity gradient as a new indicator of regional left ventricular contraction: Detection by a two-dimensional tissue Doppler imaging technique. J Am Co11Cardiol 1995;26:217-223.