Acoustic Time-of-Flight for Proton Range Verification in Water
Kevin C. Jones1, François Vander Stappen2, Chandra M. Sehgal3, Stephen Avery1,a)
1
Department of Radiation Oncology, University of Pennsylvania, Philadelphia, Pennsylvania
Ion Beam Applications SA, Louvain-la-Neuve, Belgium
3
Department of Radiology, University of Pennsylvania, Philadelphia, Pennsylvania
2
a)
Author to whom correspondence should be addressed. Electronic mail:
[email protected]; Telephone: 215-615-5631; Fax: 215-746-1727.
SUPPLEMENTAL INFORMATION
Experiment
The electronic pulse used to modulate the cyclotron proton source was created by a
function generator (HP8116A) that has a faster rise time (7 ns) and larger pulse-width range (10
ns - 999 ms) than the home-built chopper used previously1 (rise time 5-6 µs, FWHM 30 µs). For
the pulse generation method used here, the achievable rise times are limited by the cyclotron:
shorter pulses can be created at greatly reduced instantaneous currents (a decrease in rise time
from 11 to 8 µs came at the expense of a ~4x drop in proton current).
The protons per pulse were calculated by subtracting the dark ionization chamber current,
Idark (in the absence of the modulating electronic pulses), from the average ionization chamber
current, I (electronic pulse on), dividing by the pulse repetition frequency (PRF [Hz]), and
converting the ionization chamber current to proton current:
protons  I  I dark  1


pulse
 PRF  qe K
(S1)
where qe is the charge of an electron and K is the number of ionization chamber electrons
produced per irradiating proton. K is calculated as 25.8 e-/p+ for 230 MeV protons, and it was
measured as 24 e-/p+ for 226 MeV protons for the ionization chamber used here.
1
The instantaneous proton current was calculated based on the protons per pulse and the
scintillator/PMT-measured shape of the proton spill.
To maximize the proton current reaching the treatment room, the energy selection slit
width openings were maximized (the energy spread was 0.2% of the average energy), and no
energy degrader was inserted into the 230 MeV beam emitted from the cyclotron.
Pulse Repetition Frequency
Figure S1: The protoacoustic pressure measured
with varying PRF by a detector at (s,z) = (9.6, 300
mm). The data is presented as a waterfall plot
(incrementing offsets of 30 mPa were added to
each data set). The dashed line indicates the 20 µs
electronic function generator pulse used to
modulate the proton ion source.
To determine the proper proton pulse repetition frequency (PRF) for the experiments, the
protoacoustic signal was collected at various function generator (and, thus, proton pulse)
repetition rates. The collected traces are shown in Fig. S1. In these averaged protoacoustic traces,
additional acoustic peaks at negative and positive times (preceding and following the proton
pulse) were observed at proton pulse repetition frequencies ≥ 200 Hz (see asterisk for negative
2
time peak appearing at PRF = 200 Hz). The pressure traces measured at proton pulse repetition
frequencies ≤ 100 Hz were consistent, and did not display these additional peaks.
The appearance of these additional acoustic peaks in averaged pressure traces collected
with proton pulse repetition frequencies greater than or equal to 200 Hz indicates that nonnegligible reflected protoacoustic waves persist within the experimental setup for > 5 ms. Due to
the large number of reflecting surfaces (5 tank walls and 1 water surface) and the interference
between reflections, assigning reflection peaks after the first pass of reflections (which arrive at
< ~400 µs) is complex. Increasing the delay between repeated proton pulses to 10 ms (100 Hz
pulse repetition frequency), however, allowed a sufficient period for decay of these reflections.
Experiments were performed at ≤ 100 Hz to prevent this pile-up of echoes from persisting to the
next proton pulse irradiation, a phenomenon that may have influenced the arrival time accuracy
and shape of previous results1. Given the low attenuation of water at these frequencies (water
attenuates ~2 dB/km at these temperatures2, in 10 ms the protoacoustic waves travel 15 m), the
observed decay in echo intensity is most likely due to destructive interference created by
reflections from the air/tank wall and tank wall/water surfaces.
Following the leading and trailing edge, the function generator pulse appears to induce
electronic noise in the protoacoustic traces via proximal BNC cables at the oscilloscope. This
noise is of small amplitude, and it is delayed relative to arrival of the protoacoustic signal.
Random Noise
The random noise, N, was calculated as the standard deviation of the pressure trace, p,
over the time range 0.205 - 10 ms following the proton pulse irradiation. The noise was
calculated as N = 27 mPa when high-pass and low-pass frequency filters of 0.5 and 100 kHz
were applied to p during data processing. As the number of averages was increased, the standard
3
deviation of p decreased with the square root of the number of averages, n1/2, as is shown in
Figure S2.
Figure S2: The standard deviation of p decreases
with increasing averages.
Additional Arrival Times
In addition to the three arrival time metrics analyzed in the main text (  comp ,  comp,p ,
 max(P ) ) three additional metrics were also assessed:  rare , the arrival time of the rarefaction peak
from p; (  comp +  rare )/2, the mean of the compression and rarefaction peak arrival times from p,
which was previously proposed3; and  rare,p , the analgous rarefaction peak from pδ. In addition,
for the infrequent case where detectors were placed at z < RBP and the α and γ wave were


separably distinguishable, the  rare
and  rare,p
arrival times were also extracted (in addition to the

higher amplitude α wave features), but the associated positive compression peaks were too weak
4


to consistently measure  comp
and  comp,p
. In theory, the measurement of α and γ arrival times

allows for measurement of both s and l. The arrival time metrics are indicated in Figure S3.
Figure S3 (a) The experimentally measured proton pulse, simulated protoacoustic wave ( p sim
), and experimentally measured protoacoustic wave ( p exp ) collected after 1024 averages for a
hydrophone positioned at (s,z) = (45, 62 mm). Metrics corresponding to the arrival time of the



experimental compression (  comp
) and rarefaction (  rare
,  rare
) peaks are labeled. The same
metrics (not shown) are also measured from the simulated trace. t = 0 is set to the midpoint
between the 50% rise and fall times of the proton pulse. (b) From the data shown in (a),
deconvolution of p exp with the excitation proton pulse results in pdecon . The corresponding
simulated pressure trace calculated for an impulsive proton pulse, psim , is also plotted.



Metrics corresponding to the deconvoluted arrival times are labeled (  comp,p
,  rare,p
,  rare,p
). (c)



Cumulative integration of the traces shown in (c) results in Pdecon and Psim , from which the
metric  max(P ) is measured.
5
Arrival Time Analysis: cΔτ
To compare simulation to experiment, the differences in observed and simulated arrival
times (cΔτ = cτexp- cτsim) extracted from all data traces (excluding data with proton pulse
repetition frequency >100 Hz and averages < 512) were calculated and plotted in Fig. S4. The
six described arrival time metrics are plotted (from p:  comp ,  rare , (  comp +  rare )/2; from pδ:  comp,p ,
 rare,p ; from Pδ:  max(P ) ). The data is partitioned into three non-overlapping subsets: variable
proton width (function generator ≠ 20 µs), α wave (from detectors with z < RBP), and γ wave
(from detectors with z > RBP). For the infrequent case where detectors were placed at z < RBP
Figure S4: Histograms of the difference between simulated and experimentally determined
protoacoustic arrival times, cΔτ = cτexp- cτsim, are plotted for the considered arrival time metrics
(see horizontal axis labels). The top row (a-c) metrics are drawn directly from the measured
pressure trace, while the bottom row (d-f) displays metrics that are extracted after deconvolution
of the proton pulse. The data is partitioned into 4 subsets: the arrival times of the α wave (teal), γ
wave (blue, z > RBP), variable pulse width (vpw, red; γ wave at [s,z] = [10,300] ), and γ wave
(black, z < RBP). The mean and standard deviation is given for each data subset and the union of
the α and γ wave data.
6


and the α and γ wave were separably distinguishable, the  rare
and  rare,p
arrival times were also

extracted (and plotted in Fig. S4b+e).
Consistent with the analysis in the main text, measurement of the arrival time based on
the compression peak (  comp and  comp,p ) is more robust (lower standard deviation) compared to
measurement from the rarefaction peak or cumulatively integrated pressure trace (  rare , rare,p ,
 max(P ) ). This can be explained by the fact that the compression peak is the first arriving and most
intense feature of the pressure wave.
The rarefaction peak is generally broader, skewed towards later times, and has a lower
magnitude amplitude than the compression peak, which may shift the distribution of measured


(3.5 mm) and c rare
 rare to higher values, which may explain the differences between c comp
(6.7 mm).
As a sum of  comp and  rare , Δ(  comp +  rare )/2 reflects a mean and standard deviation
intermediate between Δ  comp and Δ  rare .
For pressure traces emitted in response to variable proton pulse-shapes, deconvolution (
 comp,p ,  rare,p ,  max(P ) ) provided a lower variation compared to the original data (  comp ,  rare ).
For detectors placed at the appropriate pre-Bragg peak position (z < RBP, s ≠ l), the α and
γ wave can be simultaneously measured to provide information on s and l. The γ wave has
weaker amplitude than the α wave in these cases (the Bragg peak is further away, s < l), and the γ
wave baseline is generally lowered by the persisting α wave negative rarefaction peak (see Fig.


S3a). Therefore, it is difficult to measure  comp
for these detector positions. The  rare
was
measured, although the decreased amplitude and interference from the α wave result in a broad
7
distribution (Fig. S4b). Therefore, given the proton pulses used here, calculation of the Bragg

peak position based on this  rare
(detectors z < RBP, s ≠ l) is not tenable. Use of sharper proton
pulses (faster rise times) will generate narrower protoacoustic peaks which would allow for these
calculations4. Deconvolution results in oscillations that can obscure the simultaneous
measurement of this γ wave (see Fig. S3b).
Arrival Time Analysis: εTOF
To assess the range verification measurement, the difference between experimental
protoacoustic arrival time and relevant distance, εTOF = τexpc - (l or s) are plotted in Fig. S5.
The standard deviations observed in εTOF reflect the variations observed in cΔτ.
Deconvolution resulted in smaller standard deviations, particularly for the variable pulse width
data. The compression peak metrics also exhibited smaller standard deviations than the
rarefaction or intermediate metrics ((  comp +  rare )/2 +  comp,p ).
Figure S5: Histograms of the difference between experimental protoacoustic arrival time and
relevant distance, εTOF = τexpc - (l or s), are plotted for the considered arrival time metrics (see
horizontal labels). The data is partitioned as described in Fig. S4.
8
None of the analyzed εTOF had distributions (means) centered at 0, which would be ideal.
TOF
TOF
Because the compression peak precedes the rarefaction peak, the means of  comp
and  comp,
p are
TOF
TOF
less than  rare
and  rare,
p , while the other metrics based on (  comp +  rare )/2 and  max(P ) are
intermediate. Although simulations and/or intuition predict that (  comp +  rare )/2 and  max(P ) should
provide lower average, absolute error in the case of impulsive proton pulses3, the experimental
TOF
TOF
data indicate otherwise for the case of longer proton pulses: the mean of  comp
and  comp,
p are
closer to zero than those displayed in Fig. S5c+f. None of the considered metrics have a εTOF = 0.
But, for eventual use, we propose that the standard deviation is a more important measure for
assessing the usefulness of a particular metric: simulations and/or experimental calibration can
Figure S6: The arrival times measured from a 5
cm radius circle of detector positions at fixed depth
were used to calculate the x and y position of the
beam axis. xoff, yoff, and S were fit to minimize the
error in observed and calculated τcomp with
2
2 

calc.
The
 comp
   x  xoff    y  yoff   c  S .


 comp calculated with this equation are shown for
the acoustic data best fit (xoff,yoff) = (-2.0, 0.5 mm)
and the film-measured beam propagation axis
positions (xoff,yoff) = (0,0). A systematic error of S =
-2.9 µs was used in both cases.
9
measure the systematic offset mean of εTOF to correct experimental results. Even if one of the
metrics had displayed a low absolute mean εTOF (close to 0), this correlation would not have
justified universal adoption of the metric as the ideal because the mean εTOF is expected to be
specific to the detector (due to Sdet) and other experimental variables (represented by Sinher).
Lateral Beam Position Measurement
As described in the main text, the lateral position of the proton beam was measured based
on the arrival time of the protoacoustic pressure collected at 8 positions forming a circle at fixed
depth surrounding the beam. The angle-dependent arrival times and the results of the fitting are
plotted in Figure S6.
Amplitude Dependence on Proton Pulse Rise Time
As the pulse-width of the function generator rectangular pulse increased, the resulting
emitted proton pulse rise time increased. To understand how the pressure amplitude scales with
proton pulse rise time, the maximum observed pressure scaled by the maximum of the proton
pulse (E(t)) is plotted in Fig. S7. The protoacoustic signal amplitude depends on the shape of the
proton pulse, and it scales linearly with proton current (or dose). By normalizing the pressure
amplitude by the maximum instantaneous proton current, the dependence on proton pulse shape
(ie proton pulse rise time) can be identified. Consistent with previous3 and presented simulation,
the protoacoustic amplitude per maximum proton current decreases with lengthening rise time,
which indicates that sharper, faster rising proton pulses will increase the protoacoustic signal
generated per deposited dose. The non-monotonic, increased ratio observed in Fig. S7 at 33-34
µs may be due to saturation of the PMT detector and/or increased recombination of the
ionization chamber at longer proton pulse lengths.
10
Figure S7: The maximum protoacoustic pressure
divided by the maximum of the instantaneous
proton pulse power plotted as a function of proton
pulse rise time. The variable proton pulse width
data presented here was collected at a hydrophone
position of (s,z) = (10,300) mm.
Projected Total Dose versus σ'noise
BP
The total dose at the Bragg peak ( Dtotal
) and the standard deviation of the arrival time
measurement (σ'noise) can both be related to the signal-to-noise-ratio (SNR). The SNR is given by
the noise, N (measured to be 27 mPa), the number of averages, n, and the maximum
protoacoustic pressure, pmax (measured to be 5.2 mPa / 1 x 107 protons at 5 cm) :
SNR  n
pmax
N
(S2)
The total dose at the Bragg peak is related to the number of averages and the dose from a single
BP
proton pulse, Dsingle
(measured to be 6.1 mGy / 1 x 107 protons) by:
BP
BP
Dtotal
 nDsingle
(S3)
The relation between SNR and σ'noise was empirically fit to an exponential function in
Figure 3 as:
11

 'noise  A exp SNR B

(S4)
Combining eqs. (S2), (S3), and (S4) gives:

 'noise  A exp  


BP
Dtotal
pmax
BP
Dsingle NB




(S5)
BP
where both pmax and Dsingle
scale linearly with the protons / pulse.
BP
Eq. (S5) was used to project σ'noise as a function of Dtotal
in Figure 4 in the main text.
References
1.
2.
3.
4.
K. C. Jones, F. Vander Stappen, C. R. Bawiec, G. Janssens, P. A. Lewin, D. Prieels, T. D.
Solberg, C. M. Sehgal and S. Avery, "Experimental Observation of Acoustic Emissions
Generated by a Pulsed Proton Beam from a Hospital-Based Clinical Cyclotron," Medical
Physics 42, 7090-7097 (2015).
R. J. Urick, Principles of Underwater Sound, 3rd Edition, 3rd ed. (McGraw-Hill, New
York, 1983).
K. C. Jones, C. M. Sehgal and S. Avery, "How proton pulse characteristics influence
protoacoustic determination of proton-beam range: Simulation studies " Phys. Med. Biol.
61, 2213-2242 (2016).
K. C. Jones, A. Witztum, C. M. Sehgal and S. Avery, "Proton beam characterization by
proton-induced acoustic emission: simulation studies," Physics in Medicine and Biology
59, 6549 (2014).
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