Biomedical Engineering Reference
In-Depth Information
CBE with various SNR. µ ± σ of 25 Trials.
CBE at SNR = 17dB. µ ± σ of 25 Trials.
4
4
3
3
2
2
1
SNR:17dB
SNR:23dB
SNR:29dB
1
CBE without noise
CBE with noise
CBE from pdf
0
0
−1
−1
−2
−2
−3
−3
36
38
40
42
44
46
36
38
40
42
44
46
Temperature (°C)
Temperature (°C)
FIGURE 13.10
(Left) Mean ± standard deviation of positive (PCBE) and negative (NCBE) CBE from simulated images over the range of signal-
to-noise ratios (SNRs) seen in our experiments. CBE was calculated from the means of the image ratios. Both the initial value of CBE (at 37°C) and
the slope with temperature are affected by SNR.
57
(Right) Mean ± standard deviation of positive (PCBE) and negative (NCBE) CBE from simulated
images with SNRs of 17 dB computed from the means of the image ratios. These curves are compared to CBE from images with infinite SNR and
CBE computed using pdfs from the 17 dB SNR images. CBE from the pdfs in each case is close to CBE found without noise (infinite SNR). (From
Guo, Y.,
A Framework for Temperature Imaging using the Change in Backscattered Ultrasonic Signals,
PhD thesis, Washington University, St. Louis,
MO, 2009. With permission.)
motion on CBE, limitations of motion-compensation techniques,
and accuracy of temperature estimation, including tradeoffs
between temperature accuracy and available spatial resolution.
Signal-to-noise ratio (SNR) in images from a given region
size, with a particular scatterer type and population, affects the
accuracy of the CBE temperature image from that tissue region.
Figure 13.10 shows CBE from simulated images with various
SNRs, typical of those seen in experiments. The initial (37°C)
value of CBE and the slope with temperature are a function of SNR.
Figure 13.10 also shows the effect on CBE of using the framework
described in the previous section that allows for reduction of the
noise effect by using the probability density function (pdf) from
the low (17 dB) SNR images. Reduction of the noise effects on CBE
improves temperature accuracy for a given spatial resolution.
Noise effects can also be reduced by image averaging. Averaging
20 images results in about the same improvement in CBE shown
in Figure 13.10 by using the pdfs from the images.
We studied effects of noise level on temperature imaging using
Pennes's bioheat equation, which has had widespread application
in the reconstruction of temperature fields in biological tissue.
117
For the
in vitro
case, in which perfusion and metabolism can be
neglected, the heat flow equation at temperature
T
becomes
Thermal parameters were taken from values for muscle given in
the literature.
119
Temperature images with time are shown in the
upper panel of Figure 13.11 for an initial temperature surround-
ing the medium of 37°C. At time zero, temperature on the inner
surface (location of a heating tube in experiments) was raised to
65°C to match subsequent experiments.
102
CBE with nonuniform heating was computed from simu-
lated B-mode images with additive Gaussian random noise
using the FEM temperature images. Figure 13.11 also shows
temperature maps based on the computed CBE for an SNR
of 24 dB, typical of that seen in an experiment. For noise-
less B-mode images, the CBE temperature images followed
the FEM simulated temperature maps closely. The error in
estimation for the noiseless condition was 0.01 ± 0.2°C. The
mean estimation error for 24 dB SNR was 0.4 ± 0.2°C. Note
that the CBE temperature image was less affected by noise
where the change in temperature was largest, that is, where
CBE value was larger than the noise.
Another aspect of noise effects is seen in Figure 13.12, which
shows CBE increasing to 60°C. This behavior may make CBE
temperature imaging useful in high-temperature ablation bor-
der zones. The initial jump in CBE near 37°C indicates B-mode
images that were noisier than usual for our imaging system.
On the right in Figure 13.12, however, the jump at 37°C is small.
The noise levels were reduced by synthetic-aperture imaging. In
this case the completed dataset (64
2
signals) from a 64-element
array was used to generate each pixel in each B-mode image,
resulting in noise reduction due to spatial averaging compared
to conventional phased-array imaging. Note too that the array
operated at 2.25 Mhz, which shows that CBE can be effective for
temperature imaging at both 2.25 and 7.5 MHz.
∂
∂
T
t
ρ
C
=
(
kT Q
)
+
,
(13.12)
p
where
ρ
is density,
C
p
is specific heat,
k
is heat conductivity, and
Q is the heat delivered to the specimen.
The bioheat equation (Equation 13.12) was implemented using
finite-element software to simulate temperature distributions
expected in the experimental fixture shown in Figure 13.5
102, 118
