Re‐irradiation volumetric modulated arc therapy optimization based on cumulative biologically effective dose objectives

Abstract The objective of this note is to introduce a clinical tool that generates ideal base plan dose distributions to enable re‐irradiation volumetric modulated arc therapy (VMAT) optimization based on cumulative biological effective dose objectives for specific organs at risk (OARs). The tool is demonstrated with a lung cancer case that required re‐irradiation at our clinic. First, previous treatment dose is deformed onto the retreatment computed tomography (CT) using commercial software. Then, the in‐house Matlab tool alters the deformed previous dose using radiobiological concepts on a voxel‐by‐voxel manner to generate an ideal base plan dose distribution. Ideal base plans that were generated using the in‐house Matlab tool were compatible with the Varian Eclipse™ treatment planning system. The tool enabled optimization of VMAT re‐irradiation plans using cumulative dose limits for OARs and all OAR cumulative dose objectives were met on the first optimization for the recurrent lung cancer case tested.


| INTRODUCTION
High-dose re-irradiation has emerged as a feasible treatment option in lung cancer patients with locoregional relapse and few other treatment options. Re-irradiation of locoregional relapse is becoming more common as lung cancer patients continue to live longer. Modern radiotherapy inverse plan optimization and delivery technologies such as intensity modulated radiotherapy (IMRT) and volumetric modulated arc therapy (VMAT) improve sparing of organs at risk (OARs) and make high-dose re-irradiation more feasible. Still, re-irradiation introduces several complexities and plan optimization is cumbersome. For example, patient anatomy changes and dose accumulation to OARs must be accounted for. The challenge of changing patient anatomy has largely been met through rigid and deformable image registration (IR) algorithms that enable IR-guided dose transfer between planning computed tomography (CT) scans. 1 In addition, computer software capable of converting voxel doses using the linear-quadratic model (LQM) 2 to calculate biologically effective dose (BED) distributions is now commercially available. 3,4 Converting previously delivered physical dose to BED allows differing dose-per-fraction. 4 Moreover, BED distributions are theoretically additive according to the LQMmeaning distributions from separate courses of treatment can be summed to quantify cumulative BED for each voxel. [3][4][5][6] The mechanistic LQM is often considered to be over simplistic 7 ; however, it is almost universally used to adjust for fraction size because it is practical, biologically based and acceptably accurate for dose-per-fractions below 15 Gy. 2,8 Based on recent reports, a growing number of radiation oncologists are using cumulative BED distributions to guide their re-irradiation plan evaluation. 3,6 Several institutions have reported OAR toxicity along with cumulative BED metrics in lung cancer patients receiving re-irradiation, 9,10 with some instances of severe toxicities after delivering high cumulative dose to the aorta, 11,12 esophagus, 9,13 and lungs. [14][15][16] This clinical evidence has motivated radiation oncologists to prescribe cumulative BED limits for specific OARs. 3 17 For initial irradiation plans, the evolving DVHs display total physical dose delivered over all planned fractions. For re-irradiation optimization, TPSs allow for VMAT optimization using previously delivered dose as a base plan. Throughout optimization with a base plan, displayed DVHs result from the sum of base plan and optimizing plan dose distributions and are henceforth referred to as sum DVHs. Re-irradiation plan optimization using previously delivered physical dose as a base plan may be useful when initial and re-irradiation plans deliver the same dose-per-fraction. However, when significantly different dose-per-fractions are used, sum DVHs become nonsense since nonlinear radiobiological effects are not accounted for. Thus, plan optimization is cumbersome because dosimetrists lose the ability to adjust objectives based on evolving DVHs. Furthermore, after each optimization cycle, dosimetrists or physicists must convert dose to BED to determine whether cumulative BED objectives are satisfied. 3,6 Application of base plan dose is further limited in re-irradiation scenarios because optimization of uniform target dose is impossible due to the presence of heterogenous base plan dose within the new PTV, which is henceforth referred to as PTV 2 .
In this technical note, we introduce a clinical tool that enables direct VMAT optimization of cumulative dose objectives using an ideal base plan dose that is compatible with a commercial TPS. Our proposed tool manipulates previously delivered dose to circumvent conventional base plan limitations and help guide VMAT optimization of re-irradiation. Specifically, ideal base plans restore the ability to monitor whether cumulative dose objectives are achieved using the evolving sum DVHs throughout optimization. The tool is demonstrated retrospectively for a lung cancer case where re-irradiation was prescribed.

2.A | Patient data
A patient with recurrent lung cancer previously treated and retreated at our clinic was used in this study. An initial course of VMAT was used to deliver a prescription of 60 Gy in 30 fractions to a primary lung PTV (PTV 1 ). Approximately 3 yr later, a second primary lesion was discovered and a course of stereotactic ablative radiotherapy (SABR) was prescribed to deliver 48 Gy in four fractions to the PTV 2 . The clinically delivered initial course dose, referred to as D 1 , was used in this study along with the initial and retreatment CTs, referred to as CT 1 and CT 2 , respectively. To guide the optimization of the re-irradiation dose distribution (D 2 ), a radiation oncologist retrospectively provided a list of OAR-specific α/β ratios and prioritized cumulative dose limits which are listed in both physical dose (Gy per 4 fractions) and BED (Gy α/β ) in

2.B | CT 1 -to-CT 2 deformable image registration
An overview of the re-irradiation planning workflow that incorporates the proposed tool is shown in Fig. 1. First, CT 1 -to-CT 2 deformable IR was performed and D 1 was warped onto CT 2 to generate D 1_onCT2 using a commercial intensity-based IR algorithm (MIM Software Inc., Cleveland, OH, USA). As per clinical protocol, deformable IR was performed by a medical physicist and verified independently by a second medical physicist and a radiation oncologist. Deformable IR errors are not explicitly quantified or accounted for in this workflow.

2.C | Generation of base plan
The tool is an in-house Matlab (The Mathworks Inc., Natick, MA, USA) program that manipulates D 1_onCT2 to generate an ideal base plan dose for re-irradiation optimization, referred to as D 1_baseplan . The tool requires user-specified initial course prescription (R x1 ) in Gy, the number of fractions for initial (n 1 ) and re-irradiation (n 2 ) courses, and OARspecific priorities and α/β ratios. In addition, the tool requires a cumulative dose limit (D L ) specified in Gy per n 2 fractions (D L = d L × n 2 ) for each OAR. The tool allows for one D L per OAR and D L must represent a maximum point dose limit (e.g ., D max < D L ) or a maximum dose to a specified volume limit (e.g., V DL ≤ % OAR volume).
The tool requires the digital imaging and communications in medicine (DICOM) structure file associated with CT 2 to label each voxel in D 1_onCT2 as a specific OAR or PTV 2 . In cases of overlapping contours, voxels are labeled as the highest priority structure. Since TPSs display the sum DVH (D 1_baseplan + optimizing D 2 ) throughout optimization in Gy per n 2 fractions, D 1_baseplan voxel dose is also specified in Gy per n 2 fractions.

2.C.1 | OAR base plan dose
For each OAR, D 1_onCT2 is converted voxel-by-voxel to a physical dose in Gy per n 2 fractions equal to the radiobiological fraction of D L previously delivered by initial treatment. To do this, D L is converted to BED (BED L ) using the LQM formalism 2,19 : Similarly, D 1_onCT2 is converted to BED (BED 1 ) for all voxels.
Then, for each voxel with BED 1 < BED L , the allowed re-irradiation voxel dose is defined as D allowed = d allowed × n 2 , with d allowed calculated using the equality: and then, D 1_baseplan voxel dose is set to D L − D allowed .
Here, we highlight two important points regarding voxels with BED 1 < BED L that receive exactly D allowed during re-irradiation: (a) D 1_baseplan + D allowed = D L and therefore, these voxels are easily monitored on the sum DVH throughout optimization and (b) BED 1 + BED allowed = BED L ; hence, the sum DVH value at D L accurately portrays whether D L is satisfied or not. Furthermore, voxels with BED 1 < BED L that receive under D allowed will appropriately appear below D L on the sum DVH throughout optimization, whereas voxels with BED 1 < BED L that receive over D allowed appear above For OARs where D L represents a maximum dose to a specified volume, some voxels will have BED 1 ≥ BED L . For these voxels, D 1_baseplan voxel dose is set to the isoeffective dose delivered in n 2 fractions, referred to as D 1_n2 where D 1_n2 = d 1_n2 × n 2 , with d 1_n2 calculated using the equality: The isoeffective dose conversion essentially scales D 1_onCT2 dose to the re-irradiation fractionation such that it will correctly appear above D L on the sum DVH throughout the entire optimization. It must be recognized that none of the OAR sum DVH values represent true physical or biological dose when D 1_baseplan is used. However, each sum DVH may be regarded as a LQM-scaled approximation that accurately reports whether D L is satisfied.

2.C.2 | PTV 2 base plan dose
All voxels labeled as PTV 2 are set to an arbitrary uniform dose in

2.D | Re-irradiation VMAT optimization
The re-irradiation plan consisted of two full coplanar arcs placed at the center of PTV 2 . For the recurrent lung case, D 1_baseplan was generated using tool inputs: R x1 /n 1 = 60/30, n 2 = 4 along with all OARspecific priorities, α/β, and D L listed in Table 1. Optimization dose objectives were set according to prioritized cumulative dose limits in Gy per n 2 fractions listed in Table 1. Since PTV 2 voxel dose is 0 Gy in D 1_baseplan , PTV 2 lower dose objective is set to R x2 (48 Gy).

2.E. | Re-irradiation plan evaluation
After optimization, D 2 and D 1_onCT2 were converted to BED using MIM software and the cumulative BED was calculated. Cumulative dose limits were satisfied and OAR-specific sum BED metrics are reported in Table 1. For the re-irradiation plan only, the percent volume of PTV 2 that received ≥100% of the R x2 (V 100% ) was 99.9% and the D max was 128% (61.6 Gy), which is acceptable for SABR treatment at our clinic.

| DISCUSSION
To our knowledge, this is the first strategy to use the previously delivered dose and radiobiological concepts to generate an ideal threedimensional base plan for re-irradiation optimization. The impact of the ideal base plan on the final optimized dose distribution is outlined further here. In serial OARs where D L represents a maximum point dose limit, voxels that previously received higher doses will be preferentially spared compared to voxels that received lower doses in order to achieve cumulative D max < D L in each voxel. This effect is in agree- In this work, a tool was shown to facilitate optimization of VMAT re-irradiation plans using cumulative dose limits for OARs. Ideal base plans generated using our tool were compatible with the Varian Eclipse ™ TPS and similar tools could be developed for other TPSs that accommodate base plans. The presented tool may also be used for inverse-planning of IMRT plans as long as base plans can be used during optimization. Although the underlying algorithm used to create the ideal base plan is complex, the tool is clinically practical because it only requires simple OAR-specific inputs to generate an ideal base plan for each patient. Furthermore, use of the ideal base plan eliminates timeconsuming iterations of plan optimization, dose conversion to BED and BED accumulation to verify whether cumulative dose objectives are achieved or not. Future work will aim to incorporate representation of dosimetric uncertainties associated with deformable IR errors during cumulative dose evaluation. 22 Furthermore, a script will be developed using Eclipse scripting Application Programming Interface to streamline clinical use of this tool. Finally, we will investigate potential improvements in planning time required and overall plan quality introduced by the proposed planning approach.

CONF LICT OF I NTEREST
The authors declare no conflict of interest.