Signal Processing - March 2016 - 113

0.6

0.15 0.3 0.45 0.6
t (microseconds)

Power Spectra

2

r+
r-
rPI

0.15 0.3 0.45 0.6
t (microseconds)

0.15 0.3 0.45 0.6
t (microseconds)

(d) PI Transmissions

(e) MB Echoes Before
and After PI Cancellation

1 cm

4
6
8
10
Frequency (MHz)

PI
Single Echo

0
-10
-20
-30
2

4
6
8
10
Frequency (MHz)
(f) PI Spectra Before
and After Cancellation

1 cm

(g) Conventional B-Mode Image

12

(c) Transmission
and MB Echo Spectra

Scattereded
Pressure

b1p0(t )
b2p0(t )

Transmitted
Received

0
-10
-20
-30

(b) MB echo

(a) Transmitted US Pulse and MB
Behavior
Emitted Pressure

Power Spectrum [dB]

0.3

t (microseconds)

Power Spectrum [dB]

0

Reception
Scattereded
Pressure

Emitted Pressure

Transmission

12

1 cm

(h) SH Filtered

(i) PI

figure 2. Principles of MB detection. (a) MB oscillation in response to an external US pressure field, (b) the scattered US wave, and (c) the frequency
response. (d)-(f) illustrates the principle of PI detection: (d) depicts positive and negative transmitted pulses and (e) shows the MB responses to them;
the sum of the two responses is shown by the solid line and the frequency spectrum in (f). (i) The PI image has better specificity in imaging MBs than (g)
B-mode and (h) SH-filtered images.

There are a number of multipulse
techniques related to PI that employ varying pulse phase or amplitude. These can
be summarized through a mathematical
generalization [4]. If the transmitted US
wave is given by
b k p (t) = b k P0 e j~ 0 t + {0
b k = b k e j{k,
{ k ! 60, 2r@, k = 1, 2, ..., K,

(2)

where p ^ t h represents the basic pulse,
P0 the amplitude of the wave, ~ 0 the
US angular frequency, and { 0 the phase.
The changes in amplitude and phase
applied to the kth transmitted pulse are
indicated by b k . The kth received wave
can then be modeled as a Taylor series
rk (t) =

/ a n 6b k p^ t h@n,
N

n=1

(3)

where a n is the weight of the nth nonlinear component and N is the model
order. Given a sinusoidal p ^ t h, the nth
nonlinear component contains the nth
harmonic. After consecutive transmission and reception of K pulses in the
medium, the postprocessing to generate contrast specific signals can be
done by a weighted sum of the
received pulses
rsum ^ t h =
=

K

/ m k rk (t)

k=1
N

K

/ c / m k b nk ma n p n (t) ,

(4)

n=1 k=1

where m k is a reception coefficient that
must be appropriately chosen depending on b k to cancel linear components.
The transmission and reception parameters of PI, amplitude modulation (AM),
IEEE Signal Processing Magazine

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March 2016

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and contrast pulse sequence (CPS) are
given in Table 1 [4].
While multipulse transmission
reduces the imaging frame rate, this can
be compensated by the emerging ultrafast imaging techniques with up to tens
of thousands of frames/second [5].

Encoded pulses
Even at moderate US amplitudes (tens to
hundreds of kilo-Pascals), MBs can be
disrupted. This occurs, for example, due
to the negative pressure portion in the
US pulse can cause the shell to expand
until it ruptures. To mitigate this effect,
the transmit amplitude needs to be kept
low, with a consequent reduction in the
SNR. Transmitting longer pulses can
increase the signal energy and consequently the SNR, without increasing the
peak pressures and the associated risk of
113
Table of Contents for the Digital Edition of Signal Processing - March 2016
