1

Robust Optimization for Intensity Modulated Proton Therapy Plans with 1

Multi-Isocenter Large Fields 2

3

Li Liao, MS,3 Gino J. Lim, PhD,3 Yupeng Li, MS,4 Juan Yu, PhD,1,5 Narayan Sahoo, 4

PhD,1 Heng Li, PhD,1 Michael Gillin, PhD,1 X. Ronald Zhu, PhD,1 Anita Mahajan, MD,2 5

Steven J. Frank, MD,2 David R. Grosshans, MD, PhD,2 Quynh-Nhu Nguyen, MD, 2 6

Daniel Gomez, MD,2 and Xiaodong Zhang, PhD,1 7

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Departments of 1Radiation Physics and 2Radiation Oncology, The University of Texas 9

MD Anderson Cancer Center, Houston, Texas; 3 Department of Industrial Engineering, 10

The University of Houston, Houston, Texas; 4 Applied Research, Varian Medical 11

Systems, Palo Alto, California; 5Maryland Proton Treatment Center, Department of 12

Radiation Oncology, University of Maryland School of Medicine, Baltimore, MD 13 14

15 Corresponding author: 16

Xiaodong Zhang 17

Dept. Radiation Physics, The University of Texas, MD Anderson Cancer Center, Houston, Texas, 18

77030 19

Email: xizhang@mdanderson.org 20

Tel: (713) 563-2533 21

Fax: (713) 563-254 22

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Keywords: CSI, mesothelioma, optimization, IMPT 24

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Abstract 25

We have developed a robust optimization approach for intensity modulated proton 26

therapy treatment plans with multi-isocenter large fields. The method creates a low-27

gradient field dose in the junction regions to mitigate the impact caused by misalignment 28

errors and is more efficient than the conventional junction shifting technique. 29

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1. Introduction 31

Proton therapy is being used for an increasing range of disease sites as a result 32

of the development of patient-specific planning and delivery techniques that improve the 33

therapeutic ratio by taking advantage of finite proton ranges in patients [1-6]. For large 34

and irregular-shape tumors, such as craniospinal irradiation (CSI) [4, 5, 7] and 35

mesothelioma irradiation [3], techniques are being developed at our center. In those 36

cases, the size of the target volume normally exceeds the mechanical limitations of the 37

treatment field size, and multiple fields with different isocenters are required to be 38

matched together to cover the target [8, 9]. Normally, the field dose in the junction area 39

has a steep gradient, which makes the treatment plan sensitive to misalignment errors, 40

and even small uncertainties can significantly affect dose uniformity. Traditionally, 41

preventing the risk of dose deviation in junction regions usually requires a manual shift of 42

the field junctions, which can be technically challenging. 43

In conjunction with the development of applying intensity modulated proton 44

therapy (IMPT) to more disease sites, there is a major progress in the robust 45

optimization techniques [10-13]. Robust optimization methods have been developed for 46

mitigating the effects of proton range, setup and anatomical motion uncertainties on 47

dose delivered to a patient. However, none of the robust optimization methods reported 48

in literature are dealing with the junction mismatch which is special for the large and 49

irregular targets. 50

Here, we introduce a general robust optimization approach for IMPT plans with 51

multi-isocenter large fields. This approach incorporates field misalignment uncertainties 52

during the optimization process and generates a low-gradient field dose in junction 53

regions. 54

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2. Materials and methods 55

We selected one CSI case and one mesothelioma case to demonstrate the use 56

of the proposed approach. Both patients underwent the simulation in the supine position. 57

Images were obtained from patients in the treatment position with a multi-slice CT 58

scanner at a 2.5-mm slice thickness. Target structures and organs at risk were outlined 59

by experienced dosimetrists or radiation oncologists. The clinical target volume (CTV) in 60

the CSI patient comprised the brain and spinal canal and was extended caudally to just 61

beyond the thecal sac. In the mesothelioma patient, the gross tumor volume (GTV) 62

encompassed gross disease on the postsurgical positron emission CT scan, the CTV 63

was contoured by radiation oncologist, and the planning target volume (PTV) was 64

consist with a 0.5-cm margin expansion around the GTV plus a 6-mm internal margin 65

and a 1-cm external margin expansion on CTV. 66

For the CSI patient, a radiobiological equivalent dose of 36 Gy in 1.8-Gy fractions 67

was prescribed for CTV. For the mesothelioma patient, the prescription dose was 45 Gy 68

in 1.8-Gy fractions to PTV. For contouring, spot arrangement and dose we used the 69

Eclipse version 13.0 system (Varian Medical Systems, Palo Alto, CA). The robust 70

optimization was performed using an in-house proton treatment planning system [10]. All 71

plans were normalized to 95% of target volume (i.e. CTV for CSI case, PTV for 72

mesothelioma case) received 100% prescribed dose. The homogeneity index (HI = 73

D5/D95) was used to evaluate the target dose uniformity. The beam has a spot size with a 74

diameter of approximately 1.6-2.2 cm (full width half maximum). 75

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2.1 Field setup and spot arrangement 76

Fig 1A-C show representative axial, sagittal and coronal views with marked field 77

projections for the CSI patient. Two brain fields with the same isocenter are typically 78

angled 15° posteriorly from the horizontal plane to reduce the dose to the lens (Fig 1A). 79

For each field, the corresponding CTV included the brain contour and a portion of the 80

upper spine contour that extended approximately 1 to 2 cm superior to the shoulders 81

(Fig 1D). The spinal fields were equally spaced along the spine axis, and the isocenters 82

were designed to minimize the total number of spinal fields and maximize the field 83

overlap region for junctions (Fig 1B, C). The target covered by the spinal field 84

immediately inferior to the brain fields may include the upper spine as well as portions of 85

the brain target (Fig 1E). The maximum field size of our system is 30 cm × 30 cm; to 86

maximize junction size, we applied a 45° couch rotation for spinal fields (Fig 1C, E and 87

F). 88

Fig 1G and H show representative axial and sagittal views with marked field 89

projections for the mesothelioma patient. The PTV was covered by four fields (Fig 1G): 90

two upper fields with one isocenter matched with two lower fields with another isocenter 91

(Fig 1H). The corresponding targets for the upper and lower fields are shown in Fig 1I 92

and J. 93

For both patients, the spot arrangement volume of each field was expanded by 8 94

mm uniformly in all directions from the corresponding target contour. 95

2.2 Robust optimization and uncertainty setup 96

In our in-house proton treatment planning system, the worst-case dose algorithm 97

is adopted for robust optimization. In this algorithm, the dose distributions from different 98

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scenarios, including the nominal dose (i.e., without uncertainties) and different 99

uncertainty setups, are computed. The worst-case dose distribution is represented by 100

the maximum (for overdosage) or minimum (for underdosage) dose from all computed 101

dose distributions in each voxel corresponding to specific structures. The formulation 102

can be described as: 103

2,min ,min ,

2,max ,max ,

2,max ,

( )

( )

( )

Robust T i p Ti T

T i p Ti T

OAR i p OARi OAR

Min F w D D

w D D

w D D +

∈

∈

∈

= −

+ −

+ −

∑

∑

∑

104

where iD is the worst-case dose at voxel i , pD is the prescription dose for the target or 105

OAR, w is the penalty weight of the specific structure , the step function 106

,max ,( )i p OARD D +− equals ,max ,( )i p OARD D− if ,max ,i p OARD D> but zero if ,max ,i p OARD D≤ . 107

We designed two uncertainty scenarios for robust optimization to simulate 108

misalignment errors that may occur at all field junctions. In these scenarios, field 109

isocenters shift ±3 mm in the superior–inferior direction alternately. For example, for CSI 110

patient, two brain fields are shifted by -3 mm, and the first and second spinal fields are 111

shifted by +3 and −3 mm in scenario I, respectively. In scenario II, the fields are shifted 112

by 3 mm in the opposite direction with respect to scenario I. 113

2.3 Plan robustness evaluation 114

Robust optimized and conventional, nonrobust IMPT plans were generated for 115

both patients. Alternating isocenter shifts of 3 mm per field (6-mm total error) were 116

performed to simulate the longitudinal mismatching error for robustness analysis. The 117

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dose profiles in the junction regions were used to demonstrate the deviation caused by 118

misalignment uncertainty. For the CSI patient, robust IMPT plans with different junction 119

sizes (8, 12, 16 and 26 cm) were generated to illustrate the relationship between junction 120

size and dose deviation, and the robustness of a robust optimized IMPT plan with a 121

large junction size was compared with that of a robust optimized treatment plan with a 122

small junction and conventional junction shifting. 123

3. Results 124

First, we evaluated the robustness of the dose distribution in field junctions for 125

the robust and conventional IMPT plans for the CSI case. As shown in Fig 2A, the field 126

dose in the junction region has a low smooth gradient in the robust IMPT plan but is 127

irregular (non-smooth) in the conventional IMPT plan (Fig 2B).The hot and cold doses 128

were evenly distributed in the junction region in the robust plan, and the deviation for the 129

simulated error was around 5% (Fig 2A), which is significantly smaller than the 20% 130

deviation in the conventional plan (Fig 2B). Similar results were observed for the 131

mesothelioma patient (Fig 2C and D). 132

Fig 2E shows the dose profiles in robust IMPT plans for the CSI case with 133

different junction sizes (8, 12, 16 and 26 cm) and a 3-mm misalignment error. And the 134

uncertainty yield 9.9%, 5.4%, 4.5% and 2.6% dose deviation in the junction region for 135

the IMPT plans with 8, 12, 16 and 26 cm junction size respectively. For a given 136

uncertainty level, the dose deviation decreased as junction size increased. This result is 137

also consistent with the results reported in previous study. [4, 5] The relationship 138

between dose deviation, uncertainty and junction size can be rough simplified as: 139

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𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑑𝑑𝐷𝐷𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝐷𝐷𝑑𝑑 (%) = 𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝐽𝐽𝐽𝐽𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑖𝑖𝑈𝑈 𝑠𝑠𝑈𝑈𝑠𝑠𝑈𝑈

× 100%. 140

Fig 2F demonstrates two strategies to increase the robustness of the 141

misalignment errors: a robust IMPT plan with an 18-cm dose junction and a robust IMPT 142

plan with a 7-cm dose junction and junction shifting. The second plan includes three 143

subplans, each delivering 1/3 of the total dose. The total lateral dose profiles for the two 144

plans are quite similar. Each subplan in the second plan has large dose deviations, but 145

shifting the junction helps to spread the uncertainty. Thus, in general, the dose 146

deviations of the two plans are similar. This result suggests that if the overlapping region 147

is sufficiently enlarged, the shifting of junctions will not be necessary for the robust IMPT 148

plan. 149

The dose volume histograms (DVHs) of robust and non-robust IMPT plans were 150

illustrated in Fig 3. The tradeoff between target uniformity and robustness between 151

robust and non-robust IMPT plans was within 1.5% for two patient cases. For CSI 152

patient, the HI of spinal cord, brain and cribriform plan were 1.041, 1.051 and 1.030 in 153

robust IMPT plan compare to 1.036, 1.045 and 1.025 in non-robust IMPT plan. And the 154

mean doses of left lens and right lens were increased from 8.9 Gy and 8.7 Gy to 10.3 Gy 155

to 10.1 Gy from non-robust plan to robust plan. For the mesothelioma case, robust IMPT 156

plan achieved similar plan quality of non-robust plan in nominal scenario. 157

158

4. Discussion 159

Robust optimization is aimed at reducing uncertainty in IMPT. Whereas previous 160

studies only investigated setup errors in single-isocenter treatment plans [10], the 161

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current study provides, to our knowledge, the first demonstration of efficient integration 162

of intrafractional setup errors for multi-isocenter fields into a general robust planning 163

algorithm. Such robust optimization is especially important for treatment planning for 164

large, complex and irregular-shape targets. 165

Many strategies have been proposed to handle field misalignment errors during 166

treatment. For CSI treatment planning, a volumetric gradient dose optimization (GDO) 167

methodology [14] was recently introduced for IMPT technology [4, 5]. The GDO method, 168

which was initially introduced for volume modulated arc therapy (VMAT) planning [14], is 169

a two-step manual planning approach. In this method, gradient volumes are generated in 170

the overlap regions as four equally spaced sections. The first step is to optimize the first 171

volume field so that the four gradient volumes receive 80%, 60%, 40% and 20% of the 172

prescribed volume. The second step is to optimize the second field separately so that 173

the four gradient volumes receive 20%, 40%, 60% and 80% of the prescribed volume. 174

This method, which produces a tapered dose distribution in the junction regions, has 175

several limitations. (i) In both VMAT and IMPT planning, the GDO method increases the 176

optimization time significantly, since the manual GDO requires delineation of structures 177

for optimizing the dose in the junction and running extra optimizations. So, an automatic 178

process is desired. (ii) In GDO method, the assigned field dose in gradient volumes was 179

not continuous, so it is hard to produce a more general tapered dose distribution for 180

large junction sizes. (iii) The GDO method applies single field optimization. This process 181

cannot be used for mesothelioma cases since it often requires at least two fields for 182

each isocenter. A non-optimal GDO solution for a large overlap region has been 183

described for a VMAT optimization [14]. 184

An important finding of the current study is that dose gradients that are low and 185

tapered in field junctions can be achieved through a robust optimization that is much 186

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more general and simple than manual single-field optimization [4, 5]. Our approach 187

overcomes the limitations of the GDO method in that it (i) is automated, (ii) can be used 188

for any junction size and (iii) use multi-field optimization and can be used for large and 189

complex targets. In addition, as the use of scanning beam proton therapy is increasing, 190

the robust optimization planning method is being implemented in commercially available 191

treatment planning systems, such as Eclipse V13.7 system (Varian Medical Systems, 192

Palo Alto, CA). So, our general robust optimization method for multi-isocenter large field 193

treatment plan can be easily applied in other proton therapy center. Our work is the first 194

time to report the utilization of this automatic process for two distinct disease sites. 195

As shown above, robust IMPT greatly improves the efficiency of treatment over 196

conventional IMPT. For the CSI treatment, one of the important results is that junction 197

shifting was not necessary. For the mesothelioma treatment, the second isocenter was 198

setup simply by shifting the couch during the treatment, since the plan is robust to 199

intrafractional junction shifting. Currently, our center uses the robust optimization 200

planning approach for complex-target treatments and can perform CSI or mesothelioma 201

IMPT in 45-min sessions. 202

Although the robust optimization tools have been well developed, planners are 203

still lack of experience in clinical application. The setup of uncertainty scenarios is crucial 204

for the use of robust optimization in clinical practice. The inclusion of too many scenarios 205

will increase the computation burden and thereby prevent optimization in an acceptable 206

time frame, whereas the inclusion of too few scenarios may not guarantee robustness. 207

How to balance the plan robustness and quality in nominal scenarios also need more 208

experience. For example, in CSI case to increase the dose conformality in brain target 209

and keep taped dose in junction. The uncertainty scenarios can change to two brain 210

fields are kept still and the first and second spinal fields are shifted by ±3 mm. The DVHs 211

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of this uncertainty setting are demonstrated in Fig 4. It shows that in brain target robust 212

IMPT plan achieved the same plan quality of non-robust IMPT plan in nominal case. The 213

selective robust optimization strategies [15] also can apply to increase the dose 214

uniformity in nominal case. In this study, we only discussed uncertainty scenarios to 215

generate a robust field junction. The conventional interfractional patient setup 216

uncertainties and system range uncertainties can also be integrated into treatment plan 217

optimization. 218

219

Acknowledgement 220

This work was supported in part by NIH NCI Cancer Center Support (Core) Grant 221

CA016672 to The University of Texas MD Anderson Cancer Center 222

We would also like to show our gratitude to Arthur Gelmis and Christine F Wogan for 223

their comments and editing of the manuscript. 224

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Conflict of interest statement 227

There are no conflicts of interest. 228

229

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Figure legends 275

Figure 1. Field arrangement for the craniospinal irradiation patient (A-F) and 276

mesothelioma irradiation patient (G-J). (A) Two brain fields; (B) upper spine field; (C) 277

lower spine field; (D-F) corresponding target volumes. (G) Axial view; (H) sagittal view; (I, 278

J) target volumes corresponding to the two upper and two lower fields, respectively. 279

Field isocenters are indicated (blue cross). 280

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Figure 2. Dose color wash and corresponding dose profiles of the robust and 282

conventional IMPT plans for the craniospinal irradiation patient (A, B) and the 283

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mesothelioma patient (C, D). The dose color wash and dashed lines represent the 284

dosimetric deviations resulting from a 3-mm alternating misalignment error (brain fields, -285

3 mm; upper spine field, +3 mm; lower spine field, -3 mm). (E) Dose profiles in junctions 286

for the CSI IMPT plans with junction sizes of 8, 12, 16 and 26 cm and a longitudinal 287

misalignment error of 3 mm per field (total, 6 mm). (F) Robustness comparison between 288

a robust IMPT plan with a large dose junction (18 cm) and a robust IMPT plan with a 289

small dose junction (7 cm) and junction shifting for the CSI patient. 290

291

Figure 3. Dose volume histograms of robust and non-robust IMPT plans for craniospinal 292

irradiation patient (A) and mesothelioma patient (B). Solid lines: robust IMPT plan; 293

Dashed lines: non-robust IMPT plan. 294

295

Figure 4. Dose volume histograms of robust IMPT plan with fixed brain fields uncertainty 296

setup and non-robust IMPT plan for craniospinal irradiation patient. Solid lines: robust 297

IMPT plan; Dashed lines: non-robust IMPT plan. 298

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Figure 1.

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Figure 2.

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Figure 3.

Figure 4.