Full Utilization of Lignocellulose with Ionic Liquid Polyoxometalates in a One-Pot Three-Step Conversion

Article abstract of DOI:10.1002/cssc.201902503

The lignin-first concept is a new innovation for full utilization of lignocellulose into value-added chemicals. Ionic liquid (IL) polyoxometalates [MIMPS]₂H₄P₂Mo₁₈O₆₂ [MIMPS=1-(3-sulfonic group) propyl-3-methyl imidazolium] are reported to be active in the cleavage of β-O-4, α-O-4, and 4-O-5 bonds in three kinds of lignin models and also efficient for converting native lignocellulose. The three components in soft or hard lignocellulose were depolymerized in a one-pot three-step treatment. For soft lignocellulose (pine), lignin was first decomposed into guaiacol and phenol with yields of 15.3 and 12.9 % at 98.6 % delignification efficiency at 130 °C for 14 h. Meanwhile, hemicellulose and cellulose were intact during the delignifying process and were subsequently hydrolyzed to 3.5 % xylose at 100 % hemicellulose conversion efficiency at 150 °C for 14 h and 36.4 % glucose at 100 % cellulose conversion efficiency at 170 °C for 12 h, respectively. For hard lignocellulose (poplar), the yields of guaiacol and phenol were 10.1 and 8.7 % at 91.9 % delignification efficiency at 130 °C for 14 h, whereas 12.9 % xylose at 90.4 % hemicellulose conversion efficiency at 150 °C for 12 h and 32.9 % glucose at 100 % cellulose conversion efficiency at 170 °C for 12 h were obtained. [MIMPS]₂H₄P₂Mo₁₈O₆₂ achieved the full utilization of lignocellulose with total conversion in the lignin-first strategy and also showed the easy separation as a result of temperature-reversibility with ten recycling runs.

Full text of DOI:10.1002/cssc.201902503

An analytical model for the upper bound estimation of respiratory
motion–induced dose uncertainty in spot-scanning proton beam therapy
Heng Lia), Xiaodong Zhang, Yupeng Li, and Ronald X. Zhu
Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, Houston, TX, USA
(Received 18 December 2018; revised 13 August 2019; accepted for publication 14 August 2019;
published xx xxxx xxxx)
Purpose: We developed an analytical model of a spot-scanning beam delivery system to estimate the
upper bound of respiratory motion–induced dose uncertainty for a given treatment plan.
Methods: The effective delivery time for each spot position in the treatment plan was calculated on
the basis of the parameters of the delivery system. The upper bound of the dose uncertainty was then
calculated as a function of the effective delivery time. Two-dimensional (2D) measurements with a
detector array on a one-dimensional moving platform were obtained to validate the model.
Results: We performed 351 two-dimensional measurements on a moving platform for different deliv-
ery sequences of a single-layer uniform pattern and patient treatment field. The measured dose uncer-
tainty was a strong function of the effective delivery time: The shortest effective delivery time resulted
in a maximum absolute dose error of >90%, while the longest ones resulted in a maximum absolute
dose error of 4.9% for a single layer and 9.7% for a patient field with heterogeneity. The relationship of
the effective delivery time and the measured dose uncertainty followed the analytical formula.
Conclusions: With our analytical model, the upper bound of the dose uncertainty due to motion can
be estimated in spot-scanning proton therapy without four-dimensional dynamic dose calculation.
© 2019 American Association of Physicists in Medicine [https://doi.org/10.1002/mp.13811]
Key words: motion, proton therapy, spot scanning
1. INTRODUCTION
patient anatomy under the influence of motion, has often been
used to evaluate the interplay effect.13 In essence, the spots in
the treatment plan were first distributed to individual 4D com-
puted tomography (4DCT) phases according to the timing of
the delivery of each spot, which was calculated on the basis of
spot delivery sequence and machine delivery parameters. The
doses on different phases were then calculated using individ-
ual phase CTs and the assigned spot distribution. Finally, the
individual phase doses were mapped to a reference phase
using deformable image registration and accumulated as the
4D dynamic dose for a single delivery.8,9,12,14–16 However,
each pass of the 4D dynamic dose calculation is only the sim-
ulation of a single fraction of proton beam delivery, and even
with repeated calculations to simulate the fractionated deliv-
ery, the sample size of the simulation is very limited given the
size of all possible scenarios where tens of thousands of spots
are assigned to ten breathing phases. Therefore, it is difficult
to rely on 4D dynamic dose calculation to make clinical deci-
sions, and a method to determine patient-specific dose uncer-
tainty is needed for safe treatment of lung cancer patients
using scanning beam proton therapy.
Intensity-modulated proton therapy (IMPT) can result in a
lower dose to normal tissue than does intensity-modulated
photon radiotherapy (IMRT)1 and has been implemented clin-
ically for selected patients with lung cancer at the University
of Texas MD Anderson Cancer Center Proton Therapy Center
(Houston, Texas) (PTC-H).2 However, dose uncertainty due to
respiratory motion remains a major concern in treating lung
and liver cancer patients.3–5 Respiratory motion–induced dose
uncertainty, often referred to as the interplay effect, could lead
to large dose error within the target. Lambert et al. demon-
strated that for patients treated with scanning proton beams,
respiratory motion could introduce a maximum error of
>60%, resulting in 100% of the target receiving a dose error
of >5%, and that using margins around the tumor cannot com-
pensate for the effect.6 Bert et al. found in a planning study on
five lung tumor patients that, due to interplay, the target vol-
ume receiving at least 95% of the prescribed dose was on
average (standard deviation) 71.0% (14.2%), and concluded
that interplay of scanned particle beams and moving targets
has severe impact on the resulting dose distributions.7 Owing
to the potentially large dose error, the interplay effect has been
studied extensively. The magnitude of motion-induced dose
uncertainty was found to be delivery system dependent and
patient specific, and could vary as a function of parameters
including spot size,4,8,9 fractionation,4,8,10 rescanning,4,11,12
delivery time,8 scanning direction,4,6 and patient breathing
magnitude.9 Four-dimensional (4D) dynamic dose, in which
the delivered dose is calculated with consideration of time-de-
pendent delivery sequence or radiation fluence along with
In this study, we developed and validated an analytical
model to calculate the upper bound of respiratory motion–in-
duced dose uncertainty.
2. MATERIALS AND METHODS
2.A. Spot-scanning delivery system
The Probeat spot-scanning delivery system (Hitachi Amer-
ica, Ltd., Tarrytown, NY) used at PTC-H was described in
1
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Li et al.: Dose uncertainty for SSPT of moving tumors
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detail by Gillin et al.17 and Li et al.16 The Probeat system gen-
erates a proton beam using a synchrotron with 94 discrete
energies ranging from 72.5 to 221.8 MeV (4.0–30.6 cm in
water). Each spill of proton particles by the synchrotron
lasted a maximum of 4.4, and 2.1 s was required between
spills for the deceleration and acceleration of protons. The
proton beam was then diverted by the scanning magnets in
the delivery nozzle to create spots that deliver a certain pro-
ton fluence to the desired depth and location in the patient. In
this study, proton spots were modeled using a single two-di-
mensional (2D) Gaussian distribution18,19 and characterized
by the standard deviation (r) of the Gaussian distribution.
The spot size increases with decreasing initial particle energy,
and r ranges between 5.57 and 14.91 mm in air (for 221.8
and 72.5 MeV, respectively). The proton fluence delivered
by each spot was characterized using the spot monitor unit
(MU), which ranges from 0.005 to 0.04 MU17; the delivery
time for each spot was 1–10 ms depending on the spot MU,
and an interval of 3 ms between consecutive spots was used
for internal checks by the delivery system. Therefore, each
spot in a patient treatment plan is defined by the proton
energy (which in turn defines both the depth dose and spot
size), spot position at the isocenter plane (u*), and spot MU.
In cases where the required spot dose exceeded 0.04 MU, the
treatment planning system (Eclipse, Varian Medical Systems,
Palo Alto, CA) generated the final DICOM treatment plan
using a post-processing method that included splitting each
spot into multiple spots that satisfied the MU limits and
arranging the spots in a raster scanning fashion [Fig. 1(c)].20
K
ZZ
ꢀ ꢀ
ꢁ
ꢀ ꢁꢁ
X
*
*
D3D
¼
M F u; e; k ; V x
:
(2)
*
u
k¼1
With knowledge of the delivery system,16 the delivery time
FðkÞ
needed for spot k can be calculated as tk ¼
ꢂ 0:01 s; the
0:04
total delivery time (s) to deliver spots 1 through k can be writ-
ten as
k
ꢀ
ꢁ
X
X
Tk ¼
ðtj þ 0:003Þ þ 2:1 ꢀ
j tj=4:4 þ ek
;
(3)
j¼1
where the second part is the acceleration and deceleration
time (2.1 s) needed between the spills ( tj=4:4, each spill
P
j
could last up to 4.4 s) and the energy change(ek, each energy
change also takes 2.1 s). Therefore, the fluence map for spot
ꢀ
ꢁ
ꢀ
ꢁ
*
*
k, F u; e; k can also be written as F u; e; Tk , with the
delivery time under consideration. Assuming the delivery
starts at time t0, the delivered dose to the patient can be writ-
ten as
ZZ
K
ꢀ ꢀ
ꢁ
ꢀ
ꢁꢁ
X
*
*
D ¼
M F u; eL; t0 þ Tk ; V x; t0 þ Tk
;
*
u
k¼1
(4)
ꢀ
ꢁ
*
where V x; t is the patient volume information at time t,
which is usually unknown. The 4D dose is the expectation of
the delivered dose, regardless of the delivery modality (e.g.,
photon or proton), given the beam delivery and patient
breathing are independent to each other21; thus, the 4D dose
of the treatment plan described above can be written as
2.B. Modeling the spot-scanning proton treatment
plan and delivery
A detailed dose model of the spot-scanning proton beam
in a commercial system was described by Zhu et al.19; a sim-
plified model was used in this study.
ZZ
K
N
X X
1
D4D
¼
MðFðkÞ; VðnÞÞ;
(5)
*
u
n¼1 N
k¼1
ꢀ
ꢁ
The proton fluence of each spot could be described using
a 2D fluence map, and each treatment field is a collection of
spots, and thus, the summation of proton fluence maps. Con-
sidering spot delivery sequence, for a given spot-scanning
proton treatment plan, the fluence map for each spot can be
*
where V x; n is the patient data (i.e., 4DCT) for phase n
and N is the total number of phases. Delivery time is not a
factor in the 4D dose calculation. The motion-induced dose
uncertainty for a certain delivery can then be quantified by
comparing the delivered dose and the 4D dose:
ꢀ
ꢁ
*
denoted as F u; e; k , where F is the pencil beam fluence
*
map for spot number k on 2D space u that is perpendicular to
DD¼DꢁD4D
¼
the beam axis with energy e, and the fluence map has the unit
"
!#
Z Z
K
N
X
X
1
MU.
M
Fðt0 þTkÞ;Vðt0 þTkÞꢁ
MðFðkÞ;VðnÞÞ
:
*
*
u
n¼1 N
Assuming the center of the spot at uk has fluence MUk,
modeling the spot as a single Gaussian with re will result in a
k¼1
(6)
spot fluence map that can be written as
0
1
ꢀ
ꢁ
Therefore, as demonstrated by Eq. (6), (a) dose uncertainty
is a function of the delivery sequence (i.e., which spot was
2
*
*
ꢀ
ꢁ
u ꢁ uk
2r2e
*
F u; e; k ¼ MU ꢀ exp
B
@
C
A
ꢁ
:
(1)
k
delivered at what time), and (b) the effect of dose uncertainty
*
can be evaluated on surface u; if the dose uncertainties for all
locations on the surface are minimized, the total dose uncer-
tainty will be minimized as well. As shown in previous stud-
ies16,21,22 and as illustrated above, the motion-induced dose
uncertainty decreases with a decreasing effective dose rate.
Given the proton dose calculation algorithm M and three-
*
dimensional (3D) patient data V x but without considering
ꢀ ꢁ
motion, the 3D patient dose can be written as
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Li et al.: Dose uncertainty for SSPT of moving tumors
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FIG. 1. Examples of different delivery sequences. (a) Spot pattern to be delivered. There were 1764 spots delivered to 441 spot positions (4 spots at each position),
and the total delivery time was 15.5 s for all delivery sequences. Spots delivered within the first 0.5 s with the (b) worst delivery sequence, (c) raster scanning
(with rescanning) deliver sequence, and (d) optimized delivery sequence are shown. Delivered spots are represented by a circle with a diameter of 5 mm for illus-
tration purposes; spot spacing was 5 mm. Forty-one spots were delivered in 0.5 s. Color bar represents the number of rescanning, ranging from one to four.
a fixed MD0max, dose uncertainty decreases with increasing v.
2.C. Poisson model of motion-induced dose
uncertainty for pulsed pencil beams
In other words, dose uncertainty decreases when reducing the
patient breathing period Tb, or increasing Tk0 , the total effec-
0
For a single pencil beam delivered in pulsed mode, the
time difference between consecutive pencil beams can be
modeled as a Poisson distribution, and the dose uncertainty
becomes a function of the delivery time and breathing
cycle21:
tive delivery time (T ) for spots 1 through k that contribute
dose to the pencil beam location, as shown in the following
equation:
ꢀ ꢁ
ꢀ ꢁ
*
T0k u ¼ T0kꢁ1
*
u
ꢀ
ꢁ
*
F u; e; k
ꢂ
ꢃ
ꢀ ꢁ
N
Tb
N
*
þ min Tk ꢁ T u ;
MD ¼ MD0
v
ꢁ1MADPoissonðvÞ;
(7)
ꢀ ꢀ
ꢁꢁ
:
max 2ðN ꢁ 1Þ
*
max F u; e; k
k
where MD0max is the maximum possible dose error with 0
(9)
ꢀ ꢁ
delivery time.
*
*
T u denotes when the dose is delivered to position u.
min Tk ꢁ T u ; T reflects that the time difference of suc-
ꢀ
ꢀ ꢁ
ꢁ
*
b
N
2eꢁv ꢀ vbvcþ1
MADPoissonðvÞ ¼
(8)
bvc!
cessive delivery to the same spot could reduce the motion
uncertainty, only up to Tb/N or the time length of a breathing
phase, which is also the main difference between the delivery
time and effective delivery time. For example, with a patient
breathing period of 5 s, successive deliveries to the same spot
position close to 0.5 s will be the most effective and efficient
is the mean absolute deviation (MAD) of a Poisson distribu-
0
tion with parameter (mean) v; and v ¼ N TT is the effective
K
b
number of deliveries per breathing phase (Tb/N, where Tb is
the breathing period). Here, one could observe that assuming
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Li et al.: Dose uncertainty for SSPT of moving tumors
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in terms of reducing motion uncertainties, when considering
motion mitigation techniques such as rescanning. This princi-
ple is also adopted in techniques such as phase-controlled
scanning (PCR),23–25 or breath sampling repainting.11 Also
note that T0 is scaled by the spot fluence F.
corresponding pencil beam doses and timings delivered to
(0 mm, 0 mm) were (0.04 MU, 13 ms), (0.003 MU, 26 ms),
and (2 9 10ꢁ6
MU, 39 ms).
2.E. Maximum dose error as a function of motion
range and spot size
2.D. Delivery time vs effective delivery time
T0 differs from the delivery time because increasing the
time between consecutive pencil beams is effective at reduc-
ing the dose uncertainty (up to Tb/N, after which there is no
further benefit from increasing the time interval), as shown in
our previous study.21
In the formula for motion-induced dose uncertainty [Eq.
(7)], the maximum possible dose error for a single delivery
(MD0max) was used to normalize the dose uncertainty. There-
fore, we quantitatively studied the factors that affect MDm0 ax
.
There is a lack of studies of this topic specifically, but tumor
motion is often modeled as powers of a sinusoidal function,27,28
with motion amplitude A and period Tb. Using a single 2D
Gaussian model of spot r, we performed simple simulations to
determine the relationship between MD0max, and A and r.
A uniform field was generated (Fig. 2) by placement of
spots with a size of r = 6.75 mm at a spacing of d mm (d
ranged from 1 to r mm). With a one-dimensional motion
range of 0–4 cm, the lower half of the spots was shifted
upward, resulting in a dose error. The maximum dose error in
this case could be derived as
Figure 1(a) shows an example of a 10 9 10 cm uniform
field of a single energy (173.7 MeV with a 20-cm range and
r = 6.75 mm). There were 441 spot positions with a spot
spacing of 5 mm. We delivered 0.16 MU to each position in
four spots of 0.04 MU each, and resulting in 1764 spots for
the field. The total MU was 70.56, and the required time to
deliver this field was 15.5 s. Figures 1(b) to 1(d) shows the
first 0.5 s of delivery for three delivery schemes with the
same overall delivery time (15.5 s) but very different effec-
tive delivery times for different spot positions: the worst spot
delivery sequence with no rescanning (WS), where all MU to
the same spot was delivered as quickly as possible, resulting
in the minimized effective delivery time; the spot sequence
with raster rescanning (RS), which has been adopted by com-
mercial planning systems (e.g., Eclipse), where the spots
were split according to the maximum MU constraint and
delivered in a raster scanning fashion; and the optimized
delivery sequence with spot repainting (OS) detailed in our
previous study,26 where the effective delivery time was maxi-
mized. Figure 1(c) shows the first 0.5 s of the RS plan as
generated by the treatment planning system (Eclipse). The
dose at any given spot position also contributes to nearby spot
positions, depending on the spot size and spot spacing, as
shown in Eq. (1). The spot delivery sequence in this case can
ꢂ
ꢃ
A
MD0max ¼ erf
;
(10)
pffiffi
2 2r
where erf(x) is the error function. Simulations were per-
formed as described below to confirm the result and
showed that the maximum dose error increased with
increasing motion range and decreasing spot size but not as
a function of spot spacing, and the maximum dose error
ꢀ
ꢁ
*
be written as u; Tk , and the first three spots can be written
as (0 mm, 0 mm, 13 ms), (5 mm, 0 mm, 26 ms), and
(10 mm, 0 mm, 39 ms). The corresponding pencil beam
doses and timings delivered to (0 mm, 0 mm) can be written
as ðF; TkÞ: (0.04 MU, 13 ms), (0.03 MU, 26 ms), and
(0.013 MU, 39 ms), where 0.03 and 0.013 MU are the flu-
ences contributed by the second and third spots to location
(0 mm, 0 mm), respectively. Figure 1(b) shows the WS plan,
where the spot delivery sequence for the first three spots was
(0 mm, 0 mm, 13 ms), (0 mm, 0 mm, 26 ms), and (0 mm,
0 mm, 39 ms), and the corresponding pencil beam doses and
timings delivered to (0 mm, 0 mm) were (0.04 MU, 13 ms),
(0.04 MU, 26 ms), and (0.04 MU, 39 ms). On the contrary,
for the OS plan, with minimized dose uncertainty, the spots
are placed far apart from each other so that the minimum
dose is delivered to the same pencil beam location in any Tb/
N interval [Fig. 1(d)]. The spot delivery sequence for the first
three spots in this case was (0 mm, 0 mm, 13 ms), (15 mm,
0 mm, 26 ms), and (30 mm, 0 mm, 39 ms), and the
FIG. 2. The simulated proton fluence map of a uniform pattern with motion.
The proton fluence map was generated using a single Gaussian model of spot
size 6.75 mm and spot spacing of 2 mm. The upper half was stationary; the
arrows indicate the motion of the lower half. Motion amplitude is 0 in the
shown figure, and the color bar represents the percentage intensity of the pro-
ton fluence.
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Li et al.: Dose uncertainty for SSPT of moving tumors
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with this model was up to 100%. Measurement results were
also compared with Eq. (10) to validate the calculation and
simulation.
2. for each energy, and
3. for each spot in this energy and all higher energies, cal-
*
culate the fluence at location u.
A similar relationship can also be established between
D0max and water equivalent thickness change in the depth
direction (MWET), with a known depth dose curve. However,
since the dose falloff of the mono-energy proton beam Bragg
peak in the depth direction is much steeper than the spot fal-
loff in the lateral direction, we used D0max = 1, that is, the
maximum dose error of 100%, in this study for simplicity
unless otherwise specified.
4. Calculate the total effective delivery time using Eq. (9).
5. Calculate the upper bound of the dose error from the
4D dose using Eq. (7).
2.H. Measurement setup
The measurement setup (Fig. 3) was described previ-
ously.26
A MatriXX multi-ion chamber detector (IBA Dosimetry,
Schwarzenbruck, Germany) was placed on a 1D moving
platform29 and used to acquire the 2D dose distribution
with and without motion. The MatriXX consists of 1020
vented pixel ionization chambers with 4.5 mm in diameter
and 7.62 mm center to center spacing. While there could
be dose averaging effect due to the finite size of the detec-
tor, we considered the ion chambers to be sufficiently
small compared to the proton spot size (e.g., 173.7 MeV
with a 20-cm range and r = 6.75 mm). The 1D moving
platform was driven by a VXM stepper motor controller
attached to a BSlide assembly (Velmex, Inc., Bloomfield,
NY). The motor controller can be programmed to move
with different amplitudes and periods and can simulate
most types of respiratory motion, including actual patient
respiration.
2.F. Dose error and energy layers
IMPT is usually delivered in a layer-by-layer fashion
(i.e., all spots in a certain energy are delivered before the
next proton energy starts). In the PTC-H system, the proton
energies are delivered in a monotonically decreasing man-
ner. As with the finite size of the proton spots, the proton
spot dose is deposited not only to a certain depth but also
along the beam path up to the depth determined by the
proton energy. Therefore, for a certain beam angle, the
higher energy layers contribute dose to voxels that are cov-
ered by lower energies and effectively reduce the dose rate
to those voxels; the lower energies, on the other hand, do
not contribute to deeper depth. As a result, qualitatively,
the higher energy layers require more dose to each pencil
beam location to deliver the same total dose to each voxel.
That, along with a large spot size in the lower energy lay-
ers, indicates that spots and layers with lower energies
require less splitting than do higher energies to achieve the
same level of motion-induced dose uncertainty. A conserva-
tive estimate of the fluence contributed by a spot in a
2.I. Single-layer uniform pattern measurements
A single-layer, 10 9 10 cm uniform field [Fig. 1(a)]
was delivered and measured using the setup shown in
Fig. 3. We obtained 310 2D measurements using
MatriXX, delivering the same total MU to each spot
position under various motion conditions and spot
higher energy layer (eH) to a lower energy layer (eL) at
*
pencil beam location u can be written as
ꢀ
ꢁ
ꢀ
ꢁ
IDDe ðdmaxðeLÞÞ
*
*
H
F u; eL; k ¼ F u; eH; k
;
(11)
IDDe ðdmaxðeLÞÞ
L
where IDD is the integrated depth dose; eH and eL are the
high and low energies, respectively; and dmax is the depth of
the maximum dose (Bragg peak). Equation (11) is only exact
at dmax(eL); it underestimates the contribution from the high
energy and is thus conservative.
2.G. Upper bound of dose error as a function of
maximum dose error and effective delivery time
With the fluence map and delivery sequence for all energy
layers established for a given treatment plan, the upper bound
of the dose error of the treatment plan at all pencil beam posi-
tions can be estimated using Eqs. (7) to (9) and the following
procedure:
FIG. 3. Measurement setup using a 1D moving phantom with heterogeneity
using a wedge with maximum MWET of 4.8 cm on a 5-cm-thick solid water
slab
*
1. Calculate the fluence at location u for pencil beam
location *u,
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Li et al.: Dose uncertainty for SSPT of moving tumors
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FIG. 4. (a) Nominal three-dimensional dose distribution for a single-layer uniform plan with r = 6.75 mm and spot spacing of 5 mm. (b) Four-dimensional (4D)
calculated dose distribution with 4-cm motion. (c) Single-fraction measured dose with the worst delivery sequence (maximum dose error up to 90%). (d) Raster
scanning delivery sequence (maximum dose error up to 35%). (e) Optimized delivery sequence (maximum dose error 4.9%). (f) Plot of the y-axis with x = 0 for
the nominal dose, 4D dose, and measured doses with worst (WS), optimized (OS), and raster (RS) scanning sequences. Color bar represents relative dose. Note
that color scales are different for panels c and d to show the full range of dose.
delivery sequences. The following motion conditions were
investigated:
perpendicular to the scanning direction yields the maximum
dose error (data now shown), and that longer motion period
results in larger dose error (When compare 3s period to 5s
and 10s period, all with 1 cm range, the maximum dose error
were 21%, 27% and 35%, respectively). Because of limited
space, the results for these conditions were not presented sep-
arately. All results presented were measured under a motion
direction perpendicular to the scanning direction with one
1. Motion range (A): 0 to 4 cm
2. Motion period (Tb): 3 to 10 s
À
Á
3. Motion pattern: A cos2n
ꢀ t , patient RPM pattern
2p
normalized to a given amplTitbude
4. Motion direction: parallel or perpendicular to scanning
direction
motion pattern (A cos4 (2Tp t)) unless otherwise specified.
b
For all motion conditions, the same spot pattern was deliv-
ered, with a spot size (r) of 6.75 and 14.91 mm (173.7 MeV
and 72.5 MeV).
First, we found that the motion pattern affects only the 4D
dose calculation, not the maximum dose error between the
measured dose and the 4D dose, that the motion direction
We used the following delivery sequence:
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Li et al.: Dose uncertainty for SSPT of moving tumors
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FIG. 5. (a) Nominal three-dimensional dose distribution for a single-layer uniform plan with r = 15 mm and spot spacing of 5 mm. (b) Four-dimensional (4D)
calculated dose distribution with 4-cm motion. (c) Single-fraction measured dose with worst delivery sequence (maximum dose error up to 65%), (d) for raster
scanning delivery sequence (maximum dose error up to 50%), and (e) for optimized delivery sequence (maximum dose error 4.1%). (f) Plot of y-axis with x = 0
for nominal dose, 4D dose, and measured dose with worst (WS), optimized (OS), and raster (RS) scanning sequences. Color bar represents relative dose. Color
scales are different for panels c and d.
1. Given 1, 2, 4, and 8 rescans, corresponding to delivery
times of 16, 31, 42, and 84 s, respectively, the corre-
sponding spot MUs were 0.04, 0.02, 0.01, and 0.005
per spot, respectively.
All spot sequences delivered the same amount of total
MU; the central axis doses at the measurement plane were
138 cGy for spot size r = 6.75 mm and 87 cGy for spot size
r = 14.91 mm.
2. Given an optimized spot delivery sequence that corre-
sponded to a delivery time of 55 s, the corresponding
spot MUs varied with constraints of a maximum MU
of 0.04 and a minimum MU of 0.005.
2.J. Patient treatment plan measurements
A treatment plan for a patient with hepatic cancer was
used for patient plan measurements. The treatment plan con-
sisted of three fields for delivering 360 cGy (RBE) to CTV
with single field optimization. For measurement purposes,
one of the fields was renormalized to deliver all 360 cGy
(RBE). The field size was about 12 9 12 cm, with 45 energy
layers ranging from 155.3 to 86.4 MeV (proton range of 16.4
(1) and (2) resulted in five spot patterns with different
numbers of spots and delivery times of 16, 31, 42, 84,
and 55 s; the spot patterns were then formed into WS,
RS, and OS delivery sequences for spot numbers in (1)
and (2).
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FIG. 6. Maximum dose error as a function of motion range and spot size. MDmax as a function of motion range (a) in mm for a spot size of r = 6.75 mm, (b) in
mm for spot size of r = 15 mm, and (c) in multiplication of r for different delivery modes. In (c), different spot sizes are shown in different colors.
to 5.6 cm). The total delivery time for the original plan was
238 s. We developed an OS using the method described in
the previous session; we considered all the delivery con-
straints and used criteria Tk ≥ 30 s, with a total delivery time
of 357 s. WS, RS, and OS plans for each spot number (deliv-
ery time) were developed and delivered.
Thirty-six measurements were obtained with a 4-cm
range, 10-s period, and 1D motion perpendicular to the
scanning direction. To measure the dose error with hetero-
geneity, we placed an acrylic wedge on a 5-cm-thick solid
water slab (Fig. 3). The cross section of the wedge was a
right-angle triangle with a hypotenuse length of 13 cm.
Therefore, the 4-cm motion range resulted in a maximum
MWET of 4.8 cm.
3. RESULTS
3.A. Single-layer uniform pattern measurements
0
Figure 4 shows the results of measurement with 4 cm of
motion for a single delivery of a single-layer 10 9 10 cm
uniform field with r = 6.75 mm. Figure 4(a) shows the mea-
surement results with no motion. Figure 4(b) shows the cal-
culated 4D dose based on the motion pattern, and Figs. 4(c)
to 4(e) shows the measurement results for the RS, WS, and
OS plans, respectively. Figure 4(f) shows the plot of the y-
axis at x = 0 for the nominal, 4D, WS, OS, and RS plans in a
single fraction. The maximum dose error between the deliv-
ered dose and the 4D dose was >90% for WS, >60% for RS,
and 4.9% for OS.
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FIG. 7. Maximum and mean dose error as a function of the effective delivery time of the treatment plan (Poisson model estimation assumed MDmax = 100%).
(a) Maximum and mean dose errors of each measurement plot against the calculated minimum and mean effective delivery time for the corresponding treatment
plan with a given delivery pattern. (b) Mean and standard deviations of the measured maximum and mean dose errors for a given effective delivery time.
Figure 5 shows the same measurements as in Fig. 4 but
with a spot size of r = 14.91 mm. The maximum dose error
between the delivered dose and the 4D dose was >60% for
WS, >50% for RS, and 4.1% for OS.
Figure 6 shows the relationship between the maximum
dose error and the spot size. The simulation and calculation
results of Eq. (10) matched perfectly (therefore only one line
is visible), and both bounded the measurement results using
WS, RS, or OS. Therefore, MD0max could be calculated with
known A and r. However, in this study, we used a conserva-
tive number, MD0max = 1, to avoid confusion. Also note that
all measurements with OS, represented by the connected
nabla symbol, are well below measurement for other two
delivery sequences.
Figure 7 shows all 310 measurement results as a function
of T0. For each delivery, T0 of the center of each spot position
was calculated, and the Tm0 in was plotted against the measured
maximum absolute dose error between the measurement and
the 4D dose MDmax. Similarly, the T0
was plotted against
mean
the mean absolute dose error between the measurement and
the 4D dose MDmean. The theoretical upper bound of the dose
error using the Poisson model in Eqs. (7) to (9) for a given T0
was also plotted. Figure 7(a) shows individual measurement
results, and Fig. 7(b) shows the mean and two standard
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FIG. 8. Measurements of a patient field with heterogeneity using a wedge. (a) Nominal three-dimensional dose distribution. (b) Four-dimensional (4D) calculated
dose distribution with 4-cm motion. (c) Single-fraction measured dose with worst delivery sequence (maximum dose error up to 25%). (d) Measurement for ras-
ter scanning delivery sequence (maximum dose error up to 15%). (e) Measurement for optimized delivery sequence (maximum dose error 8.6%). (f) Plot of y-
axis with x = 0 for the nominal dose, 4D dose and measured doses with worst (WS), optimized (OS), and raster (RS) scanning sequences. Color bar represents
relative dose.
deviations for each T0. Even under extreme motion conditions
(e.g., 4-cm motion range and 10-s breathing cycle), the Pois-
son model predicted and bound the dose error. While the ini-
tial gain from increasing T0 was quite drastic, the gain from
increasing T0 for each pencil beam diminished after
T0 > 30 s. Increasing T0 from 30 to 50 s reduced the maxi-
mum dose error by only ~2.5%, as predicted by the Poisson
model.
dose at the center of each phase, derived from the motion
pattern; in other words, 10 measurements without motion
were obtained to calculate the 4D dose. Figures 8(c) to
8(e) shows the measurement results with WS, RS, and
OS, respectively. Figure 8(f) shows the plot of the y axis
at x = 0 for the measurement results for the nominal, 4D,
WS, OS, and RS sequences in a single fraction. The max-
imum dose error between the delivered dose and the 4D
dose could be >50% for WS, >40% for RS, and ~10% for
OS.
Figure 9 compares WS, RS, and OS for a patient treat-
ment plan. Figure 9(a) shows Tm0 ean for each layer, with
the WS, RS, and OS, from the highest energy to the low-
est (155.3 to 86.4 MeV, total of 45). The WS, RS, and
OS plans had a total delivery time of 238 s. Specifically,
3.B. Patient treatment plan measurement results
Figure 8 shows the results for a patient plan measure-
ment with a wedge and 4 cm of motion (maximum
MWET of 4.8 cm) in a 10-s breathing period. The 4D
dose was calculated by taking the average of the measured
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Li et al.: Dose uncertainty for SSPT of moving tumors
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FIG. 9. Comparison of WS, RS, and OS in a patient plan. (a) Mean effective delivery time as a function of the energy layer for different spot sequence. The solid
red (WS), blue (RS), and green (OS) lines have the same number of spots and a total delivery time of 238 s. Specifically, RS is the plan exported from the treat-
ment planning system. The dashed red (WS), blue (RS), and green (OS) lines have the same number of spots and a total delivery time of 357 s. The black line
does not satisfy delivery constraints, cannot be delivered by the PTC-H delivery system, and has a total delivery time of 1038 s. (b) The measured mean and max-
imum dose errors from the four-dimensional dose for patient treatment plan, with and without a wedge, as well as the theoretical upper bound with a Poisson
model using Eq. (6).
RS is the plan exported from the treatment planning sys-
tem. The delivery sequence was optimized using the meth-
ods presented above, with all delivery constraints
considered, and resulted in an OS plan. The corresponding
WS and RS plans were generated using the same number
of spots and spot MUs. Therefore, the WS, RS, and OS
plans had the same number of spots and a total delivery
time of 357 s. An “ideal” plan without considering the
delivery constraints was also generated and plotted; it did
not satisfy the delivery constraints, cannot be delivered by
the PTC-H delivery system, and had a total delivery time
of 1038 s.
The 36 measurements of the deliverable plans are shown
in Fig. 9(b). Again, the measured mean and maximum abso-
lute dose errors from the 4D dose were plotted against the
mean and minimum calculated effective delivery times,
respectively. The Poisson upper bound based on Eq. (6) esti-
mated the measurement results of a patient treatment plan,
even with the most extreme motion condition: a 4-cm motion
range, 10-s breathing cycle, and a 4.8-cm maximum MWET.
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Li et al.: Dose uncertainty for SSPT of moving tumors
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With the OS plan, the measured maximum absolute dose
error was 9.7%, and the mean absolute dose error was 3.3%
in a single fraction.
The current study used the delivery parameters for PTC-
H, but the principle of the model remains the same for all
spot-scanning proton delivery machines and could be easily
customized for different delivery systems. In particular, in this
study we assumed a monotonically decreasing energy during
delivery owing to current system constraints. However, with
advanced energy switching techniques such as multiple
energy extraction,34 the order of energy delivery could be
optimized in addition to the spot delivery sequence, which
possibly lead to a deliverable plan for patient treatment even
with large tumor motion [Fig. 9(a)]. We also only modeled
the proton spot using a single Gaussian model. However,
since the second Gaussian used in the double Gaussian model
of the proton spots35 has a large r and low weighting, it con-
tributes little to the motion-induced uncertainty, as estab-
lished in this study.
Our study assumed the scanning beam proton delivery and
patient breathing are completely independent, and that patient
breathing was not monitored or regulated during treatment.
However, if patient breathing pattern were monitored and pro-
ton beam delivery could be correlated to patient breathing,
motion mitigation could be achieved more efficiently, in that
one could now “assign” the spots to be delivered to a certain
phase, instead of counting on the spots to “arrive” at those
phases. Investigation on fast beam delivery with patient
motion monitor has been conducted by several groups36–38
but is outside the scope of the current study. Another limita-
tion of the study is that we assumed the patient0s position and
breathing pattern remained the same as that of the 4DCT
throughout treatment. This assumption was inherited from the
treatment planning process and may not be valid in practice.
Therefore, clinically, it is important to monitor patients0 posi-
tion and breathing during treatment and provide training as
needed. The dose deviation from the 4D dose with breathing
pattern irregularity would be a function of the fractional time
of patient breathing amplitude of the 4DCT range; while con-
ceptually, the optimized dose delivery sequence would mini-
mize this dose deviation as well,39 quantitative evaluation in a
patient setting is necessary. For patient positioning and range
uncertainties, the incorporation of robust optimization might
mitigate the problem but further evaluation is necessary.
4. DISCUSSION
Spot-scanning proton therapy can be highly sensitive to
motion; we found that the motion-induced dose error was
up to 100% in a single fraction if the delivery was not
handled properly. The current study achieved its aim of
quantifying dose uncertainty in a single fraction by devel-
oping an analytical model for the scanning beam delivery
and patient breathing pattern. We found that the analytical
model effectively estimated the upper bound of the dose
error for a given treatment plan, even under extreme
motion conditions. This method does not require repeated
dose calculations and can easily incorporate techniques
such as rescanning and spot delivery sequence optimiza-
tion.13,26
A complete analytical model of patient breathing and
the delivery system was built to calculate the upper bound
of the motion-induced dose error from the 4D dose. It was
established that the upper bound of the dose error is a
function of the maximum dose error with MD0max and T0.
The MD0max is, in turn, a function of motion amplitude (A),
spot size (r), and change in water equivalent thickness
(MWET); and T0 is dependent on the spot delivery
sequence, the timing parameters of the delivery system,
and the breathing period (Tb). MD0max is patient specific
and can be conservatively set at 100%. Tb is patient speci-
fic and usually not a variable, and the timing parameters of
the delivery system are fixed; therefore, the controlling fac-
tor of motion-induced dose uncertainty is the spot delivery
sequence. Our study established that instead of actual deliv-
ery time,8 the effective delivery time is associated with
motion-induced dose uncertainties. The Poisson model–es-
timated dose error not only was validated by our extensive
measurement, but also was consistent with previous studies
at varies institutes on the relationship between dose error
and delivery time/number of rescanning, even though the
effective delivery time was not used in those studies.11,30–33
Based on the analytical model of the PTC-H system, and
4D dynamic dose calculation evaluating the interplay
effect,15 we concluded that delivery sequence could have a
great impact on the delivered dose to the patient when
there were respiratory motion presented. We then proposed
and studied a technique to optimize the delivery sequence
in order to reduce the motion induce dose uncertainty. The
delivery sequence optimization technique was applied to
ten lung patients, and we showed that the optimized deliv-
ery sequence developed based on the analytical model
reduces the mean of fractional maximum absolute dose
error compared with the regular delivery sequence by 3.3%
to 10.6% (32.5%–68.0% relative reduction) for different
patients.26 While the patient number was limited, these
results further validated the analytical model for lung
patients.
5. CONCLUSIONS
After extensive validation, we conclude that our analytical
model effectively estimates the upper bound of dose uncer-
tainty for spot-scanning proton therapy.
ACKNOWLEDGMENTS
The authors would like to thank Sarah Bronson of MD
Anderson’s Scientific Publications Department for her sug-
gestions for and careful review of this manuscript.
a)Author to whom correspondence should be addressed. Electronic mail: hen-
gli@jhu.edu.
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monitor unit constraints on plan quality. Med Phys. 2010;37:1210–
1219.
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