Comparison of intensity modulated radiotherapy plan optimisation methods for a 1.5 T MR‐Linac

Abstract Purpose For the 1.5 T Elekta MR‐Linac it is essential that the optimisation of a treatment plan accounts for the electron return effect on the planned dose distribution. The ability of two algorithms for the first stage fluence optimisation, pencil beam (PB) and Monte Carlo (MC), to produce acceptable plan quality was investigated. Optimisation time for each algorithm was also compared. Methods Ten head and neck patients, ten lung patients and five prostate patients were selected from the clinical archive. These were retrospectively planned using a research version of Monaco with both the PB and MC algorithms for the fluence optimisation stage. After full optimisation DVH parameters, optimisation time and the number of Monitor Units (MU) as a measure of plan complexity were extracted. Results There were no clinically significant differences between any of the DVH parameters studied or the total number of MUs between using PB or MC for stage 1 optimisation across the three patient groups. However, planning time increased by a factor of ten using MC algorithms for stage 1. Conclusion The use of MC calculations compared to PB, for stage 1 fluence optimisation, results in increased planning time without clinical improvement in plan quality or reduction in complexity and is therefore not necessary.

example at the patient's skin or internal air cavities. Which can result in increases of up to 56% for a single beam at highly oblique surfaces. 4 The B-field also influences the path of the electrons in tissue with differences seen in the percentage depth dose curves and field profiles. 3 However, despite these effects, when the planning system accounts for the ERE clinically acceptable plans can be created. This is possible as the Monte Carlo (MC) algorithm accurately models the dose caused by the ERE, which can then be accounted for and removed by the modulation of the fields when IMRT is utilized. [4][5][6] Planning studies have been conducted for rectum 7 and lung SBRT 5 leading to clinically acceptable plans, this has also been shown for pancreatic, head and neck, breast, and lung cases, 6 where optimising including the B-field was shown to remove the effects of the ERE.
Plan creation for the MR-Linac will utilize the Monaco treatment planning system (Elekta AB, Stockholm, Sweden), which uses a two-stage method to optimize the dose. 8 The first stage is fluence optimisation and the second is segment shape optimisation. The dose calculation in the second stage is always MC which includes the effect of the 1.5 T B-field in the dose calculation using the GPUMCD algorithm 9 and has been shown to produce acceptable results when compared against GEANT4. 10 However, for the first stage of the optimisation the user has the option to use either a Pencil Beam (PB) or the MC algorithm. The PB algorithm does not account for the B-field, but has the benefit of being very fast, whereas the MC algorithm will account for the B-field but is much slower.
It is unknown whether using MC in the first stage (i.e., accounting for the B-field) improves the final plan quality or if we can use the PB algorithm in stage 1 and recover the plan, accounting for the B-field, in stage 2 only. The latter option could save a significant amount of time in plan creation. Therefore, it is the purpose of this paper to compare plan quality for plans optimized in stage 1 with PB with those optimized with the MC algorithm. Additionally, a comparison of the MUs required for each plan as a surrogate for plan complexity 11,12 and the total time taken to optimize using each method will be compared.

2.A | Patient selection
Ten head and neck, ten lung and five prostate patients, all treated curatively at the authors institution, were randomly selected from the clinical archive. All target volumes and organs at risk (OAR) had been delineated at the time of planning by a radiation oncologist specialising in the relevant treatment site.

2.B | Choice of segmentation parameters
To investigate whether the choice of segmentation parameters could significantly affect the results, a range of segmentation parameters were investigated for a representative lung plan. A lung plan was chosen as this treatment site would, potentially, show a larger effect from the ERE due to the greater number of air-tissue interfaces. The following parameters were varied: minimum segment area, minimum segment width, minimum MU per segment and maximum number of segments per plan. Three combinations were tested, aiming to cover the range of likely optimisation parameters used clinically. One allowed small segments and 180 segments per plan, one only allowed large segments and only 60 segments per plan, whilst the final test had intermediate parameters (Table 1). For each patient, the first plan was fully optimized using the PB algorithm for the fluence optimisation (stage 1). The second plan was optimized using the same objective functions and the GPUMCD algorithm for the fluence optimisation stage. Both optimisation arms performed a GPUMCD optimisation as standard in stage 2. This process was automated utilising Elekta's research automation toolkit which is an API allowing the software to communicate with the Monaco user interface. All calculation and segmentation parameters were kept constant between plans; details of these are shown in Table 2. This ensures that the plan comparison is between the stage 1 dose calculation and is not influenced by the objective functions or optimisation parameters.

2.D | Analysis of results
The relevant dose statistics to the PTVs and the OARs important for each site were recorded, as documented in Table 3. For each of the sites the maximum dose to 2 cc of the skin, defined here as a 5 mm contraction from the external contour, was extracted. Due to the potential increase in dose at the lung-tissue interface the maximum 2 cc dose to the lung surface was extracted, defined as a 5 mm thick layer around the inside of the lung contour. A planning risk volume T A B L E 1 For a representative lung patient showing the segment parameters used to test the sensitivity to these for the results obtained. The parameters in bold are the ones selected for plan optimisation of the lung plans.

Segment test Complex Intermediate Simple
Minimum segment area (cm 2 ) 3. The time taken to optimize each plan was measured, from initiating stage 1 optimisation to the end of the dose calculation, to assess the usability of each method. Additionally, the total number of MUs was also recorded to provide an estimate of deliverability. 11

| RESULTS
Different segmentation parameters were tested for a representative lung plan. Table 4 shows that the number of MUs was much greater for plans that allowed more segments but the MUs were not significantly (P < 0.01) different between PB and MC for any choice of segmentation parameters. Additionally, regardless of choice of segmentation parameters the time taken using the MC algorithm was always much larger but decreases from being 20 times larger to 6 times larger going from complex to more simple segments. The variation in the DVH parameters for the target and OARs can be seen in Table 5. The differences between using the PB and MC algorithms for the three different segmentation parameters are all below 2% and mostly below 1%, highlighting that segmentation parameters have a small effect on the outcome of this comparison.
The average MUs and optimisation time over the number of patients planned for each treatment group are shown in Table 6.
This shows the average time taken to optimize using the PB and MC algorithms, as well as the average number of MUs. The standard deviation is shown in parentheses. T A B L E 5 DVH parameters for the PTV IMRTs, both lungs, heart, skin and lung surface for the three different segmentation parameter choices used (see Table 1) for a representative lung plan. Differences above 1% are highlighted in red/italics. F I G . 3. DVH parameters for five prostate patients optimized with a PB algorithm (thin black lines) and MC algorithm (thick red lines) for fluence optimisation. The boxes mark the 5 th and 95 th percentiles, the band marks the median, stars mark the mean and the whiskers mark the maximum and minimum values.

CONF LICT OF I NTEREST
The Christie is a member of the Elekta MR-Linac consortium from which we have received financial and technical support under a research agreement with Elekta AB. However, Elekta had no part in the design or execution of the study.