Biomedical Engineering Reference
In-Depth Information
Figure 13.1. Motion-compensated RF images can then be enve-
lope detected to yield the motion-compensated conventional
B-mode images of Figure 13.2.
Potential pitfalls with motion tracking and compensation
techniques involve (1) propagation of errors in displacement
estimation over the temperature range and (2) nonrigid image
motion (i.e., apparent motion over temperatures that cannot be
compensated by a simple shift of the images). Errors in displace-
ment estimation depend on multiple factors, including: quanti-
zation errors that depend on the image sampling rate (or pixel
size); decorrelation of the RF signals due to small changes in the
underlying scattering structure;
56
signal-to-noise ratio and size
of the region;
46, 57
and artifacts or features that appear in only one
of the images.
There are two primary objectives for motion tracking in
ultrasonic temperature imaging. For methods based on echo
shifts, tracking is local and most effective in 1D. For methods
that use signal strength changes, tracking is global, that is over
a tissue volume and in 2D or 3D, where motion is likely to be
nonrigid.
direction, because shifts in this direction are less influenced by
noise, using the time-shift relation,
t
δ
(
z
), in Equation 13.1 given
before. Its application is illustrated in the section on thermal
strain imaging following.
13.3.2 tracking and Compensating for
real and apparent Motion
Estimation of tissue motion is a key step in many applications
associated with ultrasonic imaging, such as elasticity imag-
ing,
49,63-65
estimation of the velocity of blood flow,66-68
66-68
and
noninvasive temperature estimation, including our work.
43,69-71
These approaches have focused on 2D motion in ultrasound
images.
13.3.2.1 rigid Motion
Apparent tissue motion from rigid-motion, cross-correlation
algorithms in both axial and lateral directions from eight over-
lapping regions in 10 by 40 mm images of four specimens of
bovine liver, two of turkey breast, and one of pork-rib muscle
had mean values within ±0.5 mm over the 37 to 50°C tempera-
ture range.
43
Tissue features appeared to move closer to the
transducer in the turkey, pork, and two of the liver specimens,
which is consistent with the increase in the SOS in the water path
between the tissue and transducer. In the other two liver speci-
mens, presumably nonuniform thermal effects in tissue were
larger than the changes due to SOS changes in the water bath.
A nonuniform component of tissue motion in the seven speci-
mens cited herein was indicated by the lateral motion. This tis-
sue-dependent component also contributed to the axial motion,
particularly at temperatures above 47°C. There were also dif-
ferences in the apparent lateral motion in the two specimens of
turkey breast. One exhibited nearly constant lateral motion. Its
tissue fibers were parallel to the array of transducer elements.
The other one showed a change of several tenths of a millimeter
near 47°C. Its striations were perpendicular to the array.
13.3.1 tracking Echo Shifts
Of the ultrasonic thermometry methods explored to date, the use
of echo shifts has received the most attention in the last decade.
Most of these efforts have been geared toward RF ablation and
high intensity focused ultrasound (HIFU) therapy, which typi-
cally heats small volumes of tissue to above 60°C.
Apparent and actual displacements of scattering regions are
produced by changes in SOS and thermal expansion, respec-
tively. Temperature estimation using these effects is based on
measuring displacements in the direction of propagation
z
,
which can be related to changes in SOS and to thermal expan-
sion.
44, 58-61
The echo shift
t
δ
(
z
):
z
ζ
[1
−αζ∂θζ ζ
ζθζ
()] ()
[, ()]
d
1
[, ()]
∫
tz tz
()
=−=
()
tz
() 2
−
d
,
(13.1)
δ
0
c
c
ζθζ
13.3.2.2 Nonrigid Motion
Differences in apparent motion from varying fixed regions sug-
gest that apparent motion during heating may not be rigid. If a
rigid-motion assumption does not hold, the size of the tissue
region over which rigid motion compensation will be success-
ful is limited. To overcome this limitation and to compensate
for motion over the whole tissue region of interest in a single
operation, we developed nonrigid motion-compensation algo-
rithms that can operate in 1D, 2D, or 3D. They are based on opti-
mization of a function of the cross correlation of an image at a
particular temperature with a reference image.
46, 73
The cost function for our motion-compensation algorithms
is the normalized cross-correlation function of two RF datasets.
Let
I
r
(
x
) and
I
t
(
x
) be the image at the reference temperature
r
and
a shifted image at temperature
t
, respectively, where
where
t
(
z
) is the propagation and return time for an echo from
depth
z
after heating,
t
0
(
z
) is the time before heating, and
c
is
the SOS, which is a function of depth ζ and the temperature
θ(ζ) at that depth. The linear coefficient of thermal expansion,
α
, depends on the medium and is also a function of depth.
52
In
this approach, variation in SOS with temperature is assumed to
be linear up to about 45°C, but the method has proven useful in
assessing high-temperature ablation.
62
The echo shift occurring between two successive RF images is
estimated using the speckle tracking technique described before
has been most successful in the axial dimension, that is, along
the propagation axis. Repeating this process along adjacent
beams can generate a 2D or 3D map of the shifts in a region of
interest.
60
Shifts in the lateral and elevation are usually smaller
than those in the axial direction, and their assessment tends to
more subject to noise. Temperature maps are typically generated
in 1D, based on differentiation of shifts along the propagation
(13. 2)
I
()
x
t
=+
I
(
x
x
)
r
