Inverse-planned deliverable 4D-IMRT for lung SBRT

Abstract

Purpose: We present a particle swarm optimization (PSO)-based technique to create deliverable four-dimensional (4D = 3D + time) intensity-modulated radiation therapy (IMRT) plans for lung stereotactic body radiotherapy (SBRT). The 4D planning concept uses respiratory motion as an additional degree of freedom to achieve further sparing of organs at risk (OARs). The 4D-IMRT plan involves the delivery of an order of magnitude more IMRT apertures (~15,000-20,000), with potentially large interaperture variations in the delivered fluence, compared to conventional (i.e., 3D) IMRT. In order to deliver the 4D plan in an efficient manner, we present an optimization-based aperture sequencing technique.

Method: A graphic processing unit (GPU)-enabled PSO-based inverse planning engine, developed and integrated with a research version of the Eclipse (Varian, Palo Alto, CA) treatment planning system (TPS), was employed to create 4D-IMRT plans as follows. Four-dimensional computed tomography scans (4DCTs) and beam configurations from clinical treatment plans of seven lung cancer patients were retrospectively collected, and in each case, the PSO engine iteratively adjusted aperture monitor unit (MU) weights for all beam apertures across all respiratory phases to optimize OAR dose sparing while maintaining planning target volume (PTV) coverage. We calculated the transition times from each aperture to all other apertures for each beam, taking into account the maximum leaf velocity of the multileaf collimator (MLC), and developed a mixed integer optimization technique for aperture sequencing. The goal of sequencing was to maximize delivery efficiency (i.e., minimize the time required to deliver the dose map) by accounting for leaf velocity, aperture MUs, and duration of each respiratory phase. The efficiency of the proposed delivery method was compared with that of a greedy algorithm which chose only from neighboring apertures for the subsequent steps in the sequence.

Results: 4D-IMRT-optimized plans achieved PTV coverage comparable to clinical plans while improving OAR sparing by an average of 39.7% for $D_{\max }$ heart, 20.5% for $D_{\max }$ esophagus, 25.6% for $D_{\max }$ spinal cord, and 2.1% for $V_{13}$ lung (with $D_{\max }$ standing for maximum dose and $V_{13}$ standing for volume receiving $\ge$ 13 Gy). Our mixed integer optimization-based aperture sequencing enabled the delivery to be performed in fewer cycles compared to the greedy method. This reduction was 89 ± 79 cycles corresponding to an improvement of 15.94 ± 8.01%, when considering respiratory cycle duration of 4 s, and 55 ± 33 cycles corresponding to an improvement of 15.14 ± 4.45%, when considering respiratory cycle duration of 6 s.

Conclusion: PSO-based 4D-IMRT represents an attractive technique to further improve OAR sparing in lung SBRT. Efficient delivery of a large number of sparse apertures (control points) introduces a challenge in 4D-IMRT treatment planning and delivery. Through judicious optimization of the aperture sequence across all phases, such delivery can be performed on a clinically feasible time scale.

Keywords: 4D-IMRT; aperture sequencing; lung SBRT; mixed integer programming; particle swarm optimization.

Figure 1

Overall workflow of our proposed 4D‐IMRT planning: We use three modules: Eclipse treatment planning system (TPS), PSO inverse planning, and aperture sequencing for deliverability (MIOBAS). [Color figure can be viewed at wileyonlinelibrary.com]

Figure 2

Coronal views with planning target volumes (PTVs) outlined in red (note yellow arrows) are shown for the seven patients of this study. Patient‐specific maximum respiration‐induced target motions and number of clinically assigned radiotherapy beams and fractions as well as prescribed PTV doses are also reported. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 3

Workflow of the aperture sequencing system (MIOBAS). In finding the optimized aperture sequence in respiratory cycle k, the greedy method chooses only from neighboring apertures whereas our proposed method uses an optimization‐based model which searches beyond neighboring apertures.

Figure 4

The schematic display of apertures of a beam along with a sequence for three phases highlighted in red. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 5

A typical solution proposed by greedy (red) and MIOBAS (green) methods. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 6

DVHs of the three following plans are compared: (1) Blue curves: 4D PSO‐Optimized plans, which are created by employing the in‐house PSO engine to optimize MU weights of the 3D IMRT plans created by the commercial TPS for the ten respiratory phases individually, (2) Red curves: 4D equal‐weight plans, which are created through an equally‐weighted summation of the individual‐phase 3D IMRT plans, and, (3) Black curves: the clinical ITV‐based IMRT plans, which are created by the commercial TPS. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 7

Box plots for percent improvement of doses deposited on OARs with 4D‐IMRT PSO‐optimized plans relative to ITV‐based plans. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 8

Total number of cycles for both the greedy and the MIOBAS approaches, and percent improvement of using the MIOBAS relative to the greedy for each patient with 4 and 6 s respiratory cycle time. [Color figure can be viewed at wileyonlinelibrary.com]

Figure A1

Two apertures in an 4D‐IMRT. [Color figure can be viewed at wileyonlinelibrary.com]

Figure A2

Distance of kth leaf pairs in Aperture 1 and Aperture 2. [Color figure can be viewed at wileyonlinelibrary.com]

Figure A3

Residual MU per beam for Patient 1 and Patient 7. [Color figure can be viewed at wileyonlinelibrary.com]