Signal Processing - May 2017 - 94

life sciences
Jørgen Arendt Jensen, Carlos Armando Villagómez Hoyos,
Simon Holbek, and Kristoffer Lindskov Hansen

Velocity Estimation in Medical Ultrasound

his article describes the application
of signal processing in medical ultrasound velocity estimation. Special
emphasis is on the relation among
acquisition methods, signal processing,
and estimators employed. The description spans from current clinical systems
for one- and two-dimensional (1-D and
2-D) velocity estimation to the experimental systems for three-dimensional
(3-D) estimation and advanced imaging
sequences, which can yield thousands
of images or volumes per second with
fully quantitative flow estimates. Here,
spherical and plane wave emissions are
employed to insonify the whole region
of interest, and full images are reconstructed after each pulse emission for
use in velocity estimation.
Ultrasound velocity estimation is
widely used for diagnosing circulatory
and cardiac problems in the human body.
The investigations are conducted in real
time and can directly reveal quantitative
data about blood velocity, turbulence,
volume flow, resistive index, and other
haemodynamic quantities. Ultrasound
velocity estimation can provide instantaneous images of the spatial velocity distribution as well as single site measurements
of velocity distribution and its evolution
over time. Conventional ultrasound velocity estimation is widely used due to the
widespread ability, its inexpensive nature,
no preparation of the patients, and safety,
since nonionizing radiation is used. The

Digital Object Identifier 10.1109/MSP.2017.2665719
Date of publication: 26 April 2017

underlying estimation schemes involve a
combination of ultrasound physics, image
acquisition, and velocity estimation. This
article touches on all three aspects and
spans from the currently available commercial systems using sequential data
acquisition to the latest research techniques using parallel acquisition yielding
thousand of images per second. They are
capable of showing complex pulsating
flow with vortices in two and three dimensions. The signal processing is tightly
integrated with the underlying physics.

Physics of velocity estimation
Conventional ultrasound systems are
often called Doppler systems, indicating that the instantaneous frequency
shift of the emitted spectrum is estimated. This would indicate that a single
pulse-echo measurement is sufficient
to find the velocity. However, this is not
done in practice as scattering and attenuation contribute to significant shifts in
the received signal's mean frequency.
Unless the unknown factors from attenuation and scattering are compensated
for, a frequency estimation would be
highly inaccurate. Thus, a more precise
understanding is needed.
In basic blood ultrasound imaging, a single blood scatterer traverses
the ultrasound beam. The position is
denoted as rv1 at the first measurement
and rv2 for the second measurement
acquired Tprf s after. The interpulse
motion and, thereby positional shift,
gives rise to a delay t s in the second received signal corresponding to
IEEE Signal Processing Magazine

May 2017

v v
t s = 2 | r1 - r2 | cos i
c
v
2 | | Tprf cos i
2v
=
= z Tprf ,
c
c

(1)

where i is the angle between the ultrasound beam and the blood motion
direction, and c is the speed of sound,
usually 1,540 m/s. The axial velocity
component is v z = | v | cos i. Motion
away from the transducer gives rise
to a signal arriving with an increasing
delay, while a scatterer moving toward
the transducer will decrease the time from
pulse emission to reception.
The emitted pulse p ( t) in ultrasound
is sinusoidal, and for velocity estimation
often consists of four to eight cycles. The
received signal can be written as
x i (t) = ba sin ` 2r f0 ` t - 2d - i·t s jj,
c
(2)
where a is the pulse amplitude, f0 is
the emitted frequency, d is the depth
of the scatterer, and b is its amplitude.
Making a measurement at one fixed
time instance t d = n d fs for sample
index n d, corresponding to a fixed depth,
then gives a sampled signal as
x s (n d, i) = - ba sin c 2r

2v z
c

# f0 Tprf i - H d m,

H d = 2rf0 c n d /fs - 2d m,
c

(3)

Table of Contents for the Digital Edition of Signal Processing - May 2017