Breaking the acoustic diffraction limit via nonlinear effect and thermal
confinement for potential deep-tissue high-resolution imaging
Mechanisms of the temperature-threshold-based method in ultrasound-switchable fluorescence
(USF) imaging 6:
In this method, a fluorescent polymer, which was extremely sensitive to temperature, was used
as an imaging contrast agent. This polymer showed a switch-like relationship of both its fluorescence
quantum yield and fluorescence lifetime in response to its temperature. Thus, a temperature threshold
was found. When the temperature was below the threshold, the polymer fluoresced weakly with a
short fluorescence lifetime. When the temperature was above the threshold, the polymer fluoresced
strongly with a long lifetime. A high intensity focused ultrasound (HIFU) transducer was used to heat
the fluorophores in the focal volume by only a few Celsius degrees. Only those fluorophores that
located in the volume where the temperature was above the threshold could be switched on, while
other fluorophroes remained off. Thus, the spatial resolution of this USF-based imaging method was
eventually determined by the size of the thermal field where the temperature was above the threshold.
This size is usually smaller than the actual thermal focal size and the acoustic intensity focal size if the
temperature threshold is above the sample background temperature and the HIFU exposure time is so
short that the thermal diffusion and conduction can be ignored. Thus, unlike pure ultrasound and other
ultrasound-combined optical imaging techniques, the USF-based imaging technique is less limited by
acoustic diffraction. See the details in Ref.6.
Simulation parameters 9:
(1) Khokhlov–Zabolotskaya–Kuznetsov (KZK) parameters: All the KZK parameters used
in this study were the same as the default values listed in the manual of the HIFU simulator 9, which
were typical parameters for human tissues, except the following ones. The transition distance in the
1
material 1 (z_) was 2 mm. The outer radius (a), inner radius (b) and focusing depth (d) of the
transducer are 4.37, 0 and 12 mm, respectively. The transducer frequency (f) and power (P) were
variable. The number of harmonics (K) maintained as 1 for linear calculations and 128 for nonlinear
calculations. Note that the accuracy of the calculated results might be slightly improved when using a
higher number for harmonics (K). However, the calculation time would be dramatically increased. To
balance the speed and accuracy, we maintained K as 128 for nonlinear calculations.
(2) Bioheat transfer (BHT) parameters: All the BHT parameters used in this study were the
same as the default values listed in the manual of the HIFU simulator 9, which were typical parameters
for human tissues, except the following ones. The initial sonication duration (ti) was equivalent to the
exposure time named in this study, which was variable. The number of additional pulse cycles (nc),
duty factor (D) and pulse cycle period (tp) were zeros because there was no periodic sonication. The
cool-off duration (tc) were maintained 5 times longer than the initial sonication duration (ti). Both the
reduction factors in r-direction (rskip) and z-direction (zskip) were changed into 1 because we were
interested in temperature distribution size and the temperature smoothing should be avoided (so more
pixels should be used in the temperature calculation).
(3) Data processing: The simulator required the f-number of the HIFU transducer >1.37 to
maintain the validity of the KZK equation. Therefore, we used an f-number of 1.373 in the
calculations. However, in our experiment, the HIFU transducer had an f-number of 0.85. Therefore,
we artificially scaled the calculated lateral and axial full width at half maximum (FWHMs) down by
multiplying the lateral FWHM by a conversion factor (0.85/1.373) and the axial FWHM by a
conversion factor of the square of (0.85/1.373). 11 Because this conversion is based on linear acoustic
theory, the absolute FWHMs may be underestimated.
11
However, because both the linear and
nonlinear calculations were converted by following the same rule, they should be comparable. Also,
2
the conclusions about the relative changes of the FWHMs as a function of HIFU exposure power and
exposure time would not be affected by this conversion.
Discussion about the disagreement between the experimental results in Fig.4(b) and the
simulation results in Fig.5(b):
The experimental data in Fig.4(b) indicate that when the exposure power is 13.75 W the axial
FWHM initially maintains a value that slightly reduces when increasing the exposure time. When the
exposure time is increased above 100 ms, the axial FWHM quickly reduces. The above results are not
in agreement with the simulated data in Fig.5(b) where the axial FWHM maintains almost constant
when the exposure time is short enough. A similar situation can also be found for the lateral FWHM in
Fig.4(a) and Fig.5(b) when the power is 13.75 W (but the dependence of the lateral FWHM on the
exposure time is relatively weaker compared with that of the axial FWHM). Generally, it is unclear
what may cause the disagreement. Some potential reasons are discussed as follows:
1) Comparing Fig.3 and Fig.5(a), one can find that the silicone phantom requires much lower
power to stimulate nonlinear effect compared with the power used in the simulation.
Therefore, we speculate that either the silicone sample may have additional or unique
acoustic nonlinearity, which are not considered in the simulation model, or the nonlinear
parameter used in simulation (beta1 in KZK_parameters of the simulator) is
underestimated.
2) Although the acoustic properties of silicone phantoms have been well studied in literature,
the thermal properties are not well investigated under the conditions mentioned in current
study. Therefore, we speculate whether the disagreement is generated by some unknown
thermal nonlinearities in the silicone phantom.
3
HIFU-induced peak temperature (TP):
(1) Simulated results: Fig.S1(a) displays the TP as a function of the exposure power with an
exposure time of 0.5 ms. The linear model shows a linear relationship between the TP and the power.
The nonlinear model indicates that TP significantly deviates from the linear model result and
increases quickly when the power is relatively high. For example, when the power is 150 W, the linear
and nonlinear models show TP are 0.47 and 5.29 0C, respectively. For imaging purposes, TP may be
controlled within a few degrees (such as 5 0C) to avoid potential tissue damage. While maintaining a
relatively high power for generating nonlinear effect (such as 150 W), Fig.S1(b) indicates that
reducing the exposure time is an efficient way to reduce TP and avoid tissue overheating.
(2) Experimental results: Fig.S2 (a) and (b) display the measured TP as a function of the
exposure power and exposure time, respectively. Fig.S2(a) shows that TP deviates from the linear
relationship when the power increases. This indicates the occurrence of the nonlinear acoustic effect.
Fig.S2(b) shows that when the power is low (0.38 W) TP initially increases linearly and eventually
reach a saturated value (note that the axis is in logarithmic scale). The nonlinear effect in this example
is weak because of the relatively low HIFU exposure power. When the HIFU exposure power
1
Nonlinear Model
Linear Model
10
HIFU-induced
Peak Temperature ( 0C)
Temperature Increase ( 0C)
increases to 13.75 W, TP increases much more quickly and nonlinear acoustics occurs.
Nonlinear
Linear
2
10
0
10
-1
10
-2
10
Frequency=2.5 MHz
Exposure time=0.5 ms
-3
10
0
10
0
10
1
2
10
10
Power (W)
(a)
Frequency=2.5 MHz
Power=150 W
-2
10
-2
10
0
2
10
10
4
10
Exposure Time (ms)
(b)
4
FIG.S1: Calculated peak temperature increase (TP) as a function of (a) the HIFU exposure power
and (b) the HIFU exposure time.
Peak Temperature ( 0C)
Peak Temperature ( 0C)
1
10
0.1s Exposure time
0.2 s Exposure time
0
10
1
10
HIFU Power (W)
(a)
0
10
HIFU Power=0.38 W
HIFU Power=13.75 W
-1
10
0
10
1
10
Exposure Time (Seconds)
(b)
FIG.S2: Measured peak temperature increase (TP) as a function of (a) HIFU exposure power and (b)
HIFU exposure time.
5