Improving the efficiency of small animal 3D printed compensator IMRT with
beamlet intensity total variation regularization
Xinmin Liu, PhD1, Alexander L. Van Slyke, PhD1, Erik Pearson, PhD2,
Khayrullo Shoniyozov, PhD1, Gage Redler, PhD3, Rodney D. Wiersma, PhD1
1 Department of Radiation Oncology, University of Pennsylvania, Philadelphia,
PA
2 Department of Radiation and Cellular Oncology, University of Chicago,
Chicago, IL
3 Moffitt Cancer Center, Department of Radiation Oncology, Tampa, FL

Email: Xinmin.Liu1<EMAIL_ADDRESS>

###### Abstract

Purpose: There is growing interest in the use of modern 3D printing technology
to implement intensity-modulated radiation therapy (IMRT) on the preclinical
scale which is analogous to clinical IMRT. However, current 3D-printed IMRT
methods suffer from complex modulation patterns leading to long delivery
times, excess filament usage, and inaccurate compensator fabrication. In this
work, we have developed a total variation regularization (TVR) approach to
address these issues.
Methods: TVR-IMRT, a technique designed to minimize the intensity difference
between neighboring beamlets, was used to optimize the beamlet intensity map,
which was then converted to corresponding compensator thicknesses in copper-
doped PLA filament. IMRT and TVR-IMRT plans using five beams were generated to
treat a mouse heart while sparing lung tissue. The individual field doses and
composite dose were delivered to film and compared to the corresponding
planned doses using gamma analysis.
Results: TVR-IMRT reduced the total variation of both the beamlet intensities
and compensator thicknesses by around 50% when compared to standard 3D printed
compensator IMRT. The total mass of compensator material consumed and
radiation beam-on time were reduced by 20-30%, while DVHs remained comparable.
Gamma analysis passing rate with 3%/0.3mm criterion was 89.07% for IMRT and
95.37% for TVR-IMRT.
Conclusions: TVR can be applied to small animal IMRT beamlet intensities in
order to produce fluence maps and subsequent 3D-printed compensator patterns
with less total variation, simplifying 3D printing and reducing the amount of
filament required. The TVR-IMRT plan required less beam-on time while
maintaining the dose conformity when compared to a traditional IMRT plan.

###### Contents

  1. I. Introduction
  2. II. Methods and materials
    1. II.A. TVR-based inverse planning
    2. II.B. Development and 3D Printing of Compensators
    3. II.C. IMRT plan for a mouse heart with lung OARs
  3. III. Results
    1. III.A. Experimental setup and copper filament transmission
    2. III.B. Plan delivery statistics and compensator dimensions
    3. III.C. Gamma analysis
  4. IV. Discussion and Conclusions
  5. References

##  I. Introduction

Intensity-modulated radiation therapy (IMRT) has become one of the predominant
forms of radiation therapy (RT) currently utilized in clinical treatments.
This prevalence is the result of ongoing research efforts that continue to
improve the conformity and accuracy with which IMRT plans can be delivered. As
the precision of equipment and accuracy of treatment planning algorithms
improves, understanding the radiobiology involved becomes increasingly
important 1, 2, 3, 4. As such, preclinical studies are essential for fully
investigating novel RT treatment techniques and technologies before they can
be implemented in the clinic 3. Accurate delivery of radiation to the site of
disease in humans is a critical part of achieving a favorable outcome, so it
would reasonably follow that the analogously accurate delivery of radiation to
small animals desireable in order to facilitate translation of preclinical
findings to clinical improvements. Given the small scales involved in mice,
the tolerance of spatial deviation is on the submillimeter scale, rather than
the multiple millimeter tolerance acceptable in humans 5. For these reasons,
the need for IMRT and image guided RT in preclinical studies at this
submillimeter scale is important for enhancing the clinical relevance of
associated results.

Currently, small animal IMRT methods include the use of millimeter scale
secondary collimators with standard geometric shapes, and 3D-printed
compensators to create a specific fluence map. Secondary collimators has been
implemented in two forms, the first of which utilizes a series of motorized
jaw positions to create small rectangular segments delivered in a serial
fashion and the second uses a Sparse Orthogonal Collimator (SOC), which
consists of 4 sets of orthogonally positioned leaves 6, 7, 8, 9, 10. Aperture-
based methods are limited by a minimum size of the apertures, as well as
potentially long treatment times requiring numerous exposures through
different jaw/leaf positions. Another approch is through compensator-based
methods which utilize 3D printed patterns through which the beam is delivered
at specified angles. In order to achieve their attenuation, a shaped
polylactic acid (PLA) compensator can either be packed with sodium iodide
powder, or the compensator itself can be printed out of PLA impregnated with
copper or tungsten 11, 12. Some advantages of the compensator method are the
submillimeter resolution achievable by modern 3D printers, a reduction in the
number of segments that need to be delivered in order to achieve a conformal
dose, and the absence of additional mechanical parts which require maintenance
and quality control 6, 12. However, 3D-printed compensators are specific to
each plan and beam angle, thus a new set needs to be made for each plan,
consuming additional material and printing time. The printing process, while
capable of the aforementioned submillimeter accuracy, is more prone to error
in abutting regions of greatly differing attenuation (and therefore
thickness). Furthermore, adjacent regions with a large difference in intensity
will lose lateral electronic equilibrium, as electrons scatter out of the
copper in the highly attenuated area into the column of air above low-
attenuation segments.

Total variation regularization (TVR) is most often used in digital image
processing for noise removal. Total variation refers to the integral of the
absolute gradient of the signal. TVR is based on the principle that noisy
signals have high total variation 13.TVR has been adopted in the field of
radiation oncology in the form of compressed sensing used during inverse
treatment planning14. Compressed sensing facilitates planning by reducing the
complexity of the optimized fluence map, reducing the number of multi-leaf
collimator segments for a given treatment plan without sacrificing plan
quality. A TVR term can be added to the cost function in order to minimize the
complexity of fluence patterns for IMRT segments, or in this case, modulation
between adjacent beamlets.

In this work we develop a TVR-based inverse planning method for IMRT in small
animals based on a novel micrometer-scale dose deposition kernel designed for
accurate treatment planning at the sub-millimeter scale. This approach is
designed to reduce the complexity of the modulation pattern, overall beam-on
time, and the amount of material used to create 3D printed compensators, while
maintaining or improving the DVH that can been achieved with previous
compensator-based IMRT methods.

##  II. Methods and materials

###  II.A. TVR-based inverse planning

In TVR based inverse planning for small animal, a gradient operator is defined
as

$\nabla
x(u,v)=\bigl{|}x_{u,v}-x_{u-1,v}\bigl{|}\;+\;\bigl{|}x_{u,v}-x_{u,v-1}\bigl{|},$
(1)

where $x$ is beamlet intensity, and $u$ and $v$ are its row and column
indices, respectively. The total variation (TV) of intensity is defined as the
summation of the gradients in beam view of all fields as the following
$\ell_{1}$ norm term,

$\phi=\sum_{u,v}\nabla x(u,v)=\|Gx\|_{1}.$ (2)

The complexity of the fluence map can be evaluated by TV of intensity. The TVR
based IMRT includes this extra gradient term, and so it is given by

$\begin{array}[]{rl}\mbox{minimize}&h(y)+\beta\|Gx\|_{1}\\\ \mbox{subject
to}&y=Dx,\;\;0\preceq x\preceq u_{x},\end{array}$ (3)

where $D$ is the dose matrix, $y$ is the dose to the voxels, and $u_{x}$ is
the upper bounds of beamlet intensity, $\beta$ is the weight of variation. The
function $h(y)$ is the cost function for conventional IMRT, and it can be a
linear, quadratic or other nonlinear functions of the voxel doses of the
targets and organs at risk (OAR). Due to the $\ell_{1}$ norm term, the TVR-
IMRT cost function in (3) is now convex but not differentiable. To apply the
efficient Limited-memory Broyden–Fletcher–Goldfarb–Shanno optimization
algorithm (LBFGS), in which the derivative of the objective function is used,
it is therefore necessary to approximate $|x|$ by a smooth function. The
function $|x|$ can be approximated by $\sqrt{x^{2}+\nu^{2}}$ as in 15, or by
parabolic functions at the neigherhood of $x=0$. The differentials involved in
optimization can be derived accordingly.

###  II.B. Development and 3D Printing of Compensators

A photon beam passing through a sample of thickness $z$ is attenuated via
numerous types of interactions with the surrounding medium. The photons are
transmitted according to Beer–Lambert’s law 16. The parameters of
polychromatic transmission through both copper- and tungsten-PLA filaments
were calculated by measuring the radiation transmitted through material
thicknesses ranging from 0 to 20 mm with an ionization chamber. See Figure 1
in the next section for the copper-PLA transmission. The radiation attenuation
of tungsten-PLA is about four times larger than copper-PLA. The copper-PLA was
used to shape the fluence map inside the beams-eye-view region containing the
target, while the tungsten-PLA was used to print the trimmers to block the
radiation outside the desired field (analogous to portions of beam collimated
by MLCs and jaws, respectively, with cinical treatment machines). In the case
of our copper filament compensators, a thin base layer of 0.4mm is first
printed in the modulation area, and the maximum thickness of the compensators
was assumed to be 20mm. Therefore, the bound of beamlet intensity $x$ in (3)
should be replaced by $l_{x}\preceq x\preceq u_{x},$, and the ratio of minimum
intensity $l_{x}$ to maximum intensity $u_{x}$ for the optimization was set to

$l_{x}/u_{x}=T_{\tiny\mbox{Cu}}(20)/T_{\tiny\mbox{Cu}}(0.4),$ (4)

where $T_{\tiny\mbox{Cu}}(z)$ is the transmission through Copper-PLA filament
of thickness $z$. The optimization was first run without constraint on fluence
intensity, then $u_{x}$ was set to an appropriate value accordingly. Once
obtaining the optimized bixel intensity $x$, the compensator thickness can be
computed accordingly. Denote $x=\mbox{col}(x_{1},\cdots,x_{m})$, where $m$ is
number of gantry angles. For the $i$-th each gantry angle, the expose time
$t_{i}=\mbox{max}(x_{i}/T_{\tiny\mbox{Cu}}(0.4))$. The dose in a single time
interval is $x_{i}/t_{i}$, and thus the thickness $z_{i}$ is given by

$z_{i}=T_{\tiny\mbox{Cu}}^{-1}(x_{i}/t_{i}),$

The total variation (TV) of thickness is defined in the similar way as in (1)
and (2),

$\varphi=\sum_{u,v}\nabla z(u,v)=\|Gz\|_{1},$ (5)

which can be used to evaluate the complexity of 3D printing surface inside
beamview.

The compensators used in this study were printed using a Raise3D Pro2 Plus
(Raise3D Technologies Inc, Irvine, CA). The current version of these
3D-printed compensators have a tab and outer ring for mounting and alignment.
The associated tungsten trimmer is positioned downstream, in contact with the
compensator, in order to remove any scatter from outside the desired region.
See Figure 1.

###  II.C. IMRT plan for a mouse heart with lung OARs

A comprehensive practical implementation of IMRT using 3D-printed beam
compensators on the Xstrahl Small Animal Radiation Research Platform (Xstrahl
Inc, Suwanee, GA) (SARRP) was used to illustrate the TVR method. The Source-
Axis-Distance (SAD) of the SARRP is 350mm, and, for the customized collimator,
the source-to-compensator distance is 290mm. The bixel width was set to 1.0mm
at SAD for all treatment planning, thus the bixel width of the 3D-printed
compensators was 290/350=0.8286mm.

Plans were generated from a CT taken for use in a study on heart toxicity,
using the built-in imaging system on the SARRP 17. Hounsfield unit (HU) values
were discretized to 5 categories: air, lung, fat, muscle, and bone, which were
assigned an electron density by Muriplan (xStrahl) which are based on
ICRU-4418. The CT dimensions used for optimization were $126\times 126\times
134$ voxels with a voxel width of 0.254mm. The lengths of target in $xyz$
direction are 8.9, 5.6, and 8.6mm. Relative dosimetry measurements and
subsequent dose calculation using the 3D printed compensators was verified as
in the previous work 19.

The heart was designated as the planning target volume (PTV) and the lungs
were the only organ at risk (OAR) contoured and given dose constraints. The
plan generated by each optimization method was evaluated by comparing the
$D95_{\tiny\mbox{PTV}}$[%], $V95_{\tiny\mbox{PTV}}$[%],
$D95_{\tiny\mbox{lung}}$[%], $V95_{\tiny\mbox{lung}}$[%], and
$V110_{\tiny\mbox{lung}}$[%], as well as the total variation (TV) of both the
fluence and compensator thicknesses, and total beam-on time.

In order to evaluate the accuracy of the delivered plan, each of the five
beams, as well as the composite dose was delivered to EBT2 film placed in a
$32\times 32$ mm high-density polyethylene (HDPE) phantom with the center of
the film placed at isocenter. The accuracy of the dose calculation algorithm
and resultant compensator was assessed both on a per-field and composite dose
planar gamma analysis by using previously published software 20 21.

##  III. Results

###  III.A. Experimental setup and copper filament transmission

Figure 1: Left panel: Irradiation and measurement setup. Right upper panel:
Radiation transmission of copper-PLA. Right lower panel: 3D-printed tungsten-
PLA trimmer (black) and corresponding copper-PLA IMRT and TVR-IMRT
compensators.

For this study, a custom brass collimator and compensator-holder was machined
to fit the Xstrahl SARRP. This collimator held a series of notches and
alignment pins to ensure that the compensator for each beam was held at the
same source to compensator distance, without allowing rotation around the beam
axis. The $32\times 32$ mm HDPE phantom can be seen with the film inside
placed at isocenter (Figure 1, left panel).

Transmission through a range of Cu-PLA thicknesses was measured in order to
translate desired bixel intensity into a physical compensator (Figure 1, right
upper panel). Cu-PLA compensators for each beam angle were designed with and
without TVR. A tungsten-PLA trimmer was designed to reduce out of field
scatter and aligned to the compensators with three tongue-and-groove points
(Figure 1, right lower panel).

###  III.B. Plan delivery statistics and compensator dimensions

Figure 2: Dose distribution and DVH comparison for IMRT (solid) and TVR-IMRT
(dashed)

The dose heat maps shown on an axial slice of the mouse CT (Figure 2)
containing the heart and lungs and the corresponding DVH were similar between
both planning methods, with the TVR-IMRT having slightly more homogenity
(lower hotspot). This is also shown by the data in Table 1.

Table 1: DVH statistics comparison of optimization results

PTV $D_{95}$ [%] $V_{95}$ [%] $V_{110}$ [%] Lung $D_{95}$ [%] $V_{50}$ [%]
$V_{95}$ [%] IMRT 94.5% 94.2% 0.9% 0.0% 21.9% 0.1% TVR-IMRT 94.4% 93.9% 0.0%
0.1% 23.1% 0.1%

All dose objectives were met by both plans and were within 0.5% for all but
the PTV $V_{110}$ and the Lung $V_{50}$ (Table 1). The TVR-IMRT plan did not
deliver 110% of the dose to any portion of the PTV, while the IMRT plan
delivered it to 0.9%. The Lung $V_{50}$ was 1.2% lower for the IMRT plan than
the TVR-IMRT plan (Table 1).

Figure 3: Bixel intensity comparison of the compensators designed for each
gantry angle. Top: IMRT. Bottom: TVR-IMRT

Figure 4: Compensator thicknesses for each gantry angle. Top: IMRT. Bottom: TVR-IMRT Table 2: IMRT vs TVR-IMRT | Intensity TV | Thickness TV (mm) | Total thickness (mm) | Exposure time (s)
---|---|---|---|---
IMRT | 997 ( 0%) | 1620 ( 0%) | 1771 ( 0%) | 280 ( 0%)
TVR-IMRT | 517 ( -48%) | 728 ( -54%) | 902 ( -28%) | 218 ( -22%)

The TV of the delivered dose and physical thickness for the TVR-IMRT
compensator was reduced by 48% and 54% respectively, when compared to the IMRT
compensator as shown in Table 2. TVR reduced the sum of the thicknesses of
each discrete region in the beam path (corresponding to the filament used
during printing) by 28%. The time to deliver the plan was similarly decreased
by 22% for TVR-IMRT.

###  III.C. Gamma analysis

The planar dose profile (perpendicular to beam-axis) of each individual
compensator for each of 5 gantry angles (0∘, 72∘, 144∘, 216∘, 288∘), were all
delivered from gantry angle 0∘ to a HDPE phantom for ease of comparison and to
facilitate gamma analysis for both IMRT and TVR-IMRT (Figure 5). Composite
dose delivery with the film horizontally placed for each plan was also
performed (Figure 6).

The films were calibrated by net-OD with actual dose delivered to the films,
and fitted by a polynomial with degree of two. The measured dose distribution
was compared with calculated dose distribution by dose profiles and gamma
analysis.

For single field dose delivery (Figure 5), the measured and calculated dose
distributions match each other very well, which indicated that all dose
calculation algorithm, measurement of radiation transmission, 3D printing,
experimental dose delivery and film calibration worked appropriately. Compared
to IMRT, the TVR-IMRT plan appears more blurred, which is evidence of the
reduction in fluence TV. Gamma analysis indicated that TVR-IMRT has a slightly
better fidelity than IMRT.

Figure 5: Gamma analysis of single field dose delivery. a: films. b and c:
measured and calculated dose heat maps. d and e: profiles for measured dose
(dotted line) and calculated dose (solid line). Green line denotes difference
between measured and calculated. f: Gamma analysis of 3%/0.3mm heat maps (Top:
IMRT. Bottom: TVR-IMRT)

Figure 6: Gamma analysis of composite dose delivery. Each column is the same
as that in Figure 5. (Top: IMRT. Bottom: TVR-IMRT)

The gamma analysis for each plan composite dose delivery with 3%/0.3mm
criterion achieved a passing rate of 89.07% and 95.37% for IMRT and TVR-IMRT
respectively, but the IMRT plan showed more distinct regions with significant
deviation around the edges of the field (Figure 6).

The gamma analysis of the composite dose meets the 90% clinical passing
threshold at 3%/0.5mm for the IMRT plan, while TVR-IMRT passes at the more
strict 3%/0.2mm criteria (Table 3).

Table 3: Gamma analysis results for IMRT and TVR-IMRT | beam1 | beam2 | beam3 | beam4 | beam5 | composite
---|---|---|---|---|---|---
3%/0.5mm:  IMRT | 99.60 | 99.15 | 99.69 | 97.88 | 96.59 | 94.35
TVR-IMRT | 99.53 | 98.81 | 99.79 | 99.52 | 97.84 | 97.51
3%/0.3mm:  IMRT | 99.23 | 97.36 | 98.33 | 93.62 | 94.05 | 89.07
TVR-IMRT | 99.09 | 97.76 | 99.04 | 96.63 | 95.28 | 95.37
3%/0.2mm:  IMRT | 97.51 | 94.03 | 93.80 | 86.23 | 87.76 | 84.11
TVR-IMRT | 98.09 | 93.47 | 96.79 | 88.78 | 88.96 | 91.42

##  IV. Discussion and Conclusions

Preclinical research is essential to the continued development of RT
technologies, fractionation schema, and knowledge of the underlying
radiobiology which have all contributed to the improvement of clinical
outcomes. The growing interest in small animal IMRT stems, in part, from the
high degree of conformality and precision that is demanded in the clinic. In
order to best predict the biological effects and outcomes of a procedure prior
to use in the clinic, preclinical studies must be performed which can adhere
to those same standards.

Dose painting and the associated sparing of neighboring healthy tissues has
been proven to improve patient outcomes, so certain preclinical studies could
benefit from these clinical-quality plans even though it would result in a
smaller sample size.

We have shown that this method of planning is capable of producing the high
fidelity dose distributions which make 3D-printed compensators an attractive
method of small animal IMRT, with the plan generated by both IMRT and TVR-IMRT
meeting all dose constraints and remaining within 1.2% of one another for all
of the plan evaluation metrics that we used. This was achieved while limiting
the total variation, resulting in compensator modulation patterns that have
shallow physical gradients relative to previous design methods12, 11.

The reduction in steep gradients and variation produces a compensator design
which enables higher fidelity printing, as shown by both the individual field
dose heat maps and improved gamma passing rate for the TVR-IMRT plan (Figures
5-6 and Table 3). Furthermore, complex modulation patterns present in each
beam angle may also result in a plan which is less robust with respect to
small (sub degree, sub millimeter) variations in compensator positioning
between dose deliveries, resulting in several areas of dose deviation in the
composite dose films for the IMRT plan which were not present for the TVR-IMRT
plan (Figure 6). Both plans exhibited some deviation around the periphery, but
it was more pronounced in the IMRT plan. The composite dose delivery of the
TVR-IMRT plan passing the gamma analysis with 3%/0.2mm criteria, compared with
the IMRT plan only passing the 3%/0.5mm criteria is further evidence that TVR-
IMRT produces a compensator which is both more likely to print accurately and
more robust to small positioning errors.

The TVR-IMRT method of 3D-printed compensator design was shown to provide an
advantage over previous methods by reducing the sum of thicknesses used in the
fluence map modulation region, resulting in lower cost and shorter print
times, as well as reducing the total beam- on time for each exposure, while
preserving or improving the dose distribution in the target as confirmed by
DVH and gamma analysis.

In conclustion, here we have presented a technique utilizing total variation
regularization (TVR) which improves upon the current design method for
3D-printed compensators for small animal IMRT. This is a subject which is
garnering increasing interest due to the need to produce clinically analogous
results in preclinical studies. TVR-IMRT limits the total variation across the
modulated intensity pattern to be produced by the variable thickness
compensator, resulting in more shallow gradients that facilitate high fidelity
printing and can produce plans with improved gamma analysis passing rates.
Furthermore, there is a significant reduction in total beam-on time to deliver
a plan, total compensator thickness, 3D printer filament consumed, and print
time when compared to previous methods.

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