Dawn Williams
MCEN 5208: 533581555
11/15/2004
Echo-Particle Image Velocimetry (or Echo-PIV) is a very new technique for measuring
velocity fields in opaque flows. Therefore it does not have a rich literary tradition from
which to draw technical expertise. However, optical Digital Particle Image Velocimetry
(DPIV), on which the algorithms for Echo-PIV are based, has been around for more than
10 years and is well developed in peer-reviewed literature. This review is intended to
carefully examine previous work, as well as the technical concepts on which Echo-PIV is
based.
PIV and Echo-PIV
Particle Image Velocimetry is a velocity field mapping technique typically used with
optical imaging. In one application, a laser is used to scatter light off of fluorescent tags,
which are then photographed at high shutter speed. The DPIV algorithm is applied to
correlate the two digital images, determining a 2-D field map. However, because of the
opacity of many medical and micro-fluidics applications, optical imaging is not possible.
Echo-PIV applies PIV algorithms to ultrasound Brightness-mode imaging of opaque
flows. Gas-lipid microbubbles, because of their nonlinear response and high
echogenicity, are ideal as contrast agents. Echo-PIV is cheaper and has better resolution
than Magnetic Resonance Imaging or Nuclear Magnetic Resonance. It requires less
contrast agent than Speckle-tracking Ultrasound, and therefore is potentially less toxic.
Echo-PIV Development and Validation
In 2000, a Diagnostic Sonar Sonarscan Prisma system was used to image a kaolin/saltwater suspension laminar flows (straight, gap-constrained, and obstructed) seeded with
conifer pollen as a contrast agent [1]. The results were validated with video camera PIV
to agree within ±15%. This early work made it clear that ultrasound B-mode imaging
with PIV was a potential alternative for visualizing flow fields of opaque flows (estuarine
mud in this instance.)
A paper was presented at the 12th International Conference on Solid State Sensors,
Actuators and Microsystems in 2003 reporting on an ultrasound based particle image
velocimetry system for opaque flows [2]. It demonstrated through figures of filling in the
left ventricle of the heart (including vortex formation) in a canine model that ultrasound
based PIV was capable of measuring multiple velocity components in complex flows.
In 2004, the first paper was published (in the journal Experiments in Fluids) with intent to
validate this new technique [3]. It described the use of a commercial ultrasound system
(Vivid Five by GE/VingMed) in conjunction with Optison contrast agent to image two
test flows: fully developed laminar pipe flow and stirred reservoir flow. The laminar
pipe flow results were validated with an optical DPIV system with good agreement
(within 7.7%).
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Dawn Williams
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Resolution and Cross-Correlation
The cornerstone of particle image velocimetry is the cross-correlation technique used to
determine the velocity field map. Before the advent of digital technologies, the fringe
pattern that directly correlated to the velocity field was analyzed opto-mechanically on a
double exposure [6]. Now a Fast Fourier Transform cross correlation is applied to two
digital images.
F (u , v)  S (u , v)  D(u , v)  G (u, v)
F (u , v)  {image1}
G (u , v)  {image2}
S (u , v)  {spatialshift}
D(u, v)  {noise}
Figure 1 Equations of correlation with Fourier Transforms
A concern in 1991 was that the low image acquisition rate of video systems (30 Hz)
limited the maximum measurable velocity in digital particle image velocimetry. This is
also a concern for Echo-PIV. For example, in 2000 in Scotland, the dynamic range of
both the ultrasound and optical PIV techniques were limited by the frame rates of the
image acquisition [1]. The maximum measurable speed was 0.06m/s.
Frame rate in Echo-PIV is determined by the ultrasound system. It can be increased by
limiting the depth of the image to decrease time of flight, or decreasing the sector angle
(in a curvilinear array transducer) of a beam sweep. In 2004, the maximum measurable
velocity was 0.6m/s with the GE/VingMed system [3].
Spatial resolution is also fixed by the transducer specifications. Axial resolution depends
on the wavelength and number of cycles in the excitation pulse, and lateral resolution
depends on aperture size (or the beam diameter at the focus). Advanced PIV processing
techniques were used in 2004 to improve spatial resolution by, iteration of the
interrogation window size (versus the previously used double exposure), and, including a
50% interrogation window overlap to decrease the effect of noise [3],[7]. The signals
from the microbubbles were maximized through second harmonic imaging (utilizing the
contrast agent’s nonlinear response to ultrasound interrogation). The optimum contrast
agent concentration for accurate Echo-PIV was found to be 3 particle pairs per
interrogation window (compared to 10 for conventional optical PIV).
Optimization of Contrast Agent
The difference between the acoustic impedances of two materials at an interface
determines the amount of sound that is transmitted or reflected (please see Figure 2).
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 Z  Z1 
R 2

 Z 2  Z1 
11/15/2004
2
T  1 R
Figure 2 Equations for Percent Reflected and Percent Transmitted Sound
Many gases have much lower acoustic impedances than solids or liquids – a difference in
magnitude between 104 and 106 (please see Figure 3 below). Therefore standard
ultrasound contrast agents such as Optison® or Definity® typically consist of
microbubbles (radius 1-10µm) with air or per-fluorocarbon encased by an outer shell
made of lipid or protein (thickness 100-500nm).
Material
Water
Human Tissue
Air
Other Gas
Fat
Density
Velocity
3
kg/m
m/s
1000.000
1482
1025.000
1540
1.225
332
0.00193
600
920.000
1450
Impedance
rayls
1.482E+06
1.579E+06
4.067E+02
1.158E+00
1.334E+06
Figure 3 Acoustic Impedance Comparison Chart
In one of the first Echo-PIV papers, a conifer pollen contrast agent was chosen because it
can be used for both optical and ultrasound imaging, being a good reflector of both light
and sound, and neutrally buoyant (after absorbing water). Contrast agents should be
neutrally buoyant so their motion represents the flow field, and is not altered by inertial
or gravitational effects [1].
There are other physical characteristics of ultrasound contrast agents that should be
considered to maximize their use in Echo-PIV. Through numerical analysis, it was
pressure
determined that with an intermediate mechanical index, MI 
, the
frequency1/ 2
microbubbles have the greatest non-linear response while remaining intact [2] . This
paper was the first to report use of second harmonic imaging in Echo-PIV to maximize
the signal response from the insonified microbubbles.
Another paper emphasized the importance of careful selection of microbubbles tailored to
the Echo-PIV application. A modified Rayleigh-Plesset equation was used to
numerically model ultrasound backscatter from microbubbles of varying sizes and shell
thicknesses, under varying conditions of insonification [5]. It was found that the
microbubble shell acts as a damper, decreasing the intensity of the pulse echo. Thin
shells have better non-linear response than thick, however, they tend to be less stable over
time.
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Lower frequencies should be used to insonify larger diameter microbubbles, (above two
micron) and are optimized with the mechanical index (0.2<MI<0.6) to maximize the
second harmonic signal strength. Lower excitation frequencies are also preferred for
imaging deep in the body for better penetration depth. These factors should be
considered also with the opposing factors that govern spatial and axial resolution in
ultrasound imaging.
Applications of Echo-PIV
The applications for Echo-PIV have mostly been considered from a medical perspective.
The University of Colorado research group has already simulated blood flow through
arteries during the cardiac cycle in vitro, with both steady and pulsatile flow of water
through an acrylic pipe [4]. Echo-PIV results for the velocity profile were compared to
DPIV and theoretical values. For steady flow, the error of Echo-PIV derived shear rates
was 8% compared to theoretical values. This was in agreement with DPIV derived shear
rates, which had an error of 6.5%. However, because of poor spatial resolution (as a
function of distance from the transducer surface) high shear rates that occured near the
pipe walls were not accurately calculated with Echo-PIV.
Other medical applications (besides shear stress in arteries) include the: vortex dynamics
of cardiac filling, fluid dynamics and modeling of mechanics of pulmonary vasculature in
children, and, use of targeted microbubbles for early cancer identification and treatment.
However, though medical applications are currently of most interest, Echo-PIV can
potentially be used in any non-destructive evaluation of opaque flows, including oil or
gas pipelines, chemical batch production processes, local sewer systems or estuarine mud
flow. Of particular interest at the University of Edinbergh, Scotland, analysis of 2-D
velocity field maps in sediment-laden flow would allow scientists a better understanding
of the processes behind erosion, settlement and transport of mud, allowing for better
environmental management of estuaries and coastlines [1].
Conclusions
The body of work on Echo-PIV is in its infancy. In four years, results have been
published showing that it is a very promising technique for measurement of velocity
fields in opaque flows, with potential applications in medicine, micro fluidics, and marine
engineering.
2-D flow fields in steady and pulsatile flow have been validated with DPIV. 2-D Flow
fields for vortices have been presented, but not validated with an alternative standard
method.
Numerical modeling of microbubble echogenicity has been performed in order to
determine which physical parameters of the microbubble to optimize for greatest second
harmonic response. Echo-PIV requires a minimum concentration of three particle pairs
per interrogation window for accurate measurement.
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Spatial resolution needs to be improved to decrease error in echo-PIV. This is especially
important when measuring fluid velocities near the arterial wall (in order to determine
shear rate). However, it is ultimately limited by the physical characteristics of the
transducer. Temporal resolution is quite good. However, it can be increased to improve
the dynamic range of the measurable velocity profile.
REFERENCES
Papers
[1] Crapper, M., Bruce, T., Gouble, C, 2000, “Flow field visualization of sedimentladen flow using ultrasonic imaging,” Dynamics of Atmospheres and Oceans 31,
pp. 233-245
[2] Shandas, R., Kim, H.B., Hertzberg, J.R., Mukdadi, O., 2003, “An Ultrasound
based method for measuring multiple component velocity components in opaque
macro and micro flows.” Transducers ’03, pp. 919-922
[3] Kim, H.B., Hertzberg, J.R., Shandas, R., 2004, “Development and Validation of
Echo-PIV,” Exp. Fluids. 36, pp. 455-462
[4] Kim, H.B., Hertzberg, J., Lanning, C., Shandas, R., 2004, “Noninvasive
Measurement of Steady and Pulsating Velocity Profiles and Shear Rates in
Arteries using Echo-PIV: In Vitro Validation Studies,” Ann. Biomed. Eng. 32,
pp. 1067-1076
[5] Mukdadi, O., Kim, H.B., Hertzberg, J., Shandas, R., 2004, “Numerical modeling
of microbubble backscatter to optimize ultrasound particle image velocimetry
imaging: initial studies,” Ultrasonics 42, pp. 1111-1121
[6] Willert C.E., Gharib M., 1991, “Digital particle image velocimetry.” Exp.
Fluids 10, pp. 181–193
[7] Westerweel J., Dabiri D., Gharib M., 1997, “The effect of a discrete
window offset on the accuracy of cross-correlation analysis of
digital PIV recordings.” Exp. Fluids 23, pp. 20–28
[8] Zheng, H., Mukdadi, O., Hertzberg, J., Shandas, R., 2004, “Advantages in using
multi-frequency driving ultrasound for optimizing echo particle image
velocimetry techniques,” Biomed. Sci. Instrument., pp. 371-376
[9] Kim, H.B., Hertzberg, J.R., Shandas, R., 2004 “Echo PIV for Flow field
Measurements in vivo,” Biomed. Sci. Instrument., pp. 357-363
[10] Mukdad, O., Shandas, R., 2004, “Ultrasound wave propagation in tissue and
scattering from microbubbles for echo particle image Velocimetry technique,”
Biomed. Sci. Instrument., pp. 364-370
Textbooks
[11] Raffel, M., Willert, C., Kompenhans, J., Particle Image Velocimetry A Practical
Guide. Springer-Verlag. Berlin, 1998
[12] Kremkau, F. W., Diagnostic Ultrasound Principles and Instruments. 6th ed.
W.B. Saunders Company. Philadelphia, 2002.
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