Empirical modeling of the percent depth dose for megavoltage photon beams

Introduction This study presents an empirical method to model the high-energy photon beam percent depth dose (PDD) curve by using the home-generated buildup function and tail function (buildup-tail function) in radiation therapy. The modeling parameters n and μ of buildup-tail function can be used to characterize the Collimator Scatter Factor (Sc) either in a square field or in the different individual upper jaw and lower jaw setting separately for individual monitor unit check. Methods and materials The PDD curves for four high-energy photon beams were modeled by the buildup and tail function in this study. The buildup function was a quadratic function in the form of dd2+n with the main parameter of d (depth in water) and n, while the tail function was in the form of e−μd and was composed by an exponential function with the main parameter of d and μ. The PDD was the product of buildup and tail function, PDD = dd2+n·e−μd. The PDD of four-photon energies was characterized by the buildup-tail function by adjusting the parameters n and μ. The Sc of 6 MV and 10 MV can then be expressed simply by the modeling parameters n and μ. Results The main parameters n increases in buildup-tail function when photon energy increased. The physical meaning of the parameter n expresses the beam hardening of photon energy in PDD. The fitting results of parameters n in the buildup function are 0.17, 0.208, 0.495, 1.2 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The parameter μ can be treated as attenuation coefficient in tail function and decreases when photon energy increased. The fitting results of parameters μ in the tail function are 0.065, 0.0515, 0.0458, 0.0422 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The values of n and μ obtained from the fitted buildup-tail function were applied into an analytical formula of Sc = nE(S)0.63μE to get the collimator to scatter factor Sc for 6 and 10 MV photon beam, while nE, μE, S denotes n, μ at photon energy E of field size S, respectively. The calculated Sc were compared with the measured data and showed agreement at different field sizes to within ±1.5%. Conclusions We proposed a model incorporating a two-parameter formula which can improve the fitting accuracy to be better than 1.5% maximum error for describing the PDD in different photon energies used in clinical setting. This model can be used to parameterize the Sc factors for some clinical requirements. The modeling parameters n and μ can be used to predict the Sc in either square field or individual jaws opening asymmetrically for treatment monitor unit double-check in dose calculation. The technique developed in this study can also be used for systematic or random errors in the QA program, thus improves the clinical dose computation accuracy for patient treatment.

Minimum-monitor-unit optimization via a stochastic coordinate descent method

Objective: Deliverable proton spots are subject to the minimum monitor-unit (MMU) constraint. The MMU optimization problem with relatively large MMU threshold remains mathematically challenging due to its strong nonconvexity. However, the MMU optimization is fundamental to proton radiotherapy (RT), including efficient IMPT, proton arc delivery (ARC), and FLASH-RT. This work aims to develop a new optimization algorithm that is effective in solving the MMU problem. Approach: Our new algorithm is primarily based on stochastic coordinate decent (SCD) method. It involves three major steps: first to decouple the determination of active sets for dose-volume-histogram (DVH) planning constraints from the MMU problem via iterative convex relaxation method; second to handle the nonconvexity of the MMU constraint via SCD to localize the index set of nonzero spots; third to solve convex subproblems projected to this convex set of nonzero spots via projected gradient descent method. Main results: Our new method SCD is validated and compared with alternating direction method of multipliers (ADMM) for IMPT and ARC. The results suggest SCD had better plan quality than ADMM, e.g., the improvement of conformal index (CI) from 0.51 to 0.71 during IMPT, and from 0.22 to 0.86 during ARC for the lung case. Moreover, SCD successfully handled the nonconvexity from large MMU threshold that ADMM failed to handle, in the sense that (1) the plan quality from ARC was worse than IMPT (e.g., CI was 0.51 with IMPT and 0.22 with ARC for the lung case), when ADMM was used; (2) in contrast, with SCD, ARC achieved better plan quality than IMPT (e.g., CI was 0.71 with IMPT and 0.86 with ARC for the lung case), which is compatible with more optimization degrees of freedom from ARC compared to IMPT. Significance: To the best of our knowledge, our new MMU optimization method via SCD can effectively handle the nonconvexity from large MMU threshold that none of the current methods can solve. Therefore, we have developed a unique MMU optimization algorithm via SCD that can be used for efficient IMPT, proton arc delivery (ARC), FLASH-RT, and other particle RT applications where large MMU threshold is desirable (e.g., for the delivery of high dose rates or/and a large number of spots).

A comparative study of the dosimetric impact on IMRT planning with VMAT plans using a varying number of arcs in prostate cancer

A study has been carried out to explore the impact by varying the number of arcs and beam arrangement on dose distributions. For this volumetric modulated arc therapy and 7-field, intensity-modulated radiation therapy plans have use for prostate cancer cases. The eclipse treatment planning system version 13.6 (Varian California, USA) was used to assess dosimetry data for 20 patients. All patients received intensity-modulated radiation therapy and volumetric modulated arc therapy plans with a varying number of arcs. 6MV X-Ray photon beam energy uses for each patient. Statistical plan assessments have been carried out for various dosimetric parameters to evaluate execution efficiency. There were no statistically significant changes (p>0.05) observed in D98% dose coverage while D2%, conformity index, homogeneity index, monitor unit, and treatment delivery time were showing statistically significant changes (p<0.05). In contrast to six arc volumetric modulated arc therapy and 7 field-intensity-modulated radiation therapy plans, Single arc volumetric modulated arc therapy plans showed 23.28 % and 25.96 % less monitor unit, 97.52 % and 137.53 % less treatment delivery time. It concluded that using a higher number of arcs in volumetric modulated arc therapy plans for prostate cancer improves plan efficiency. The four arc volumetric modulated arc therapy plans appeared to provide a reasonable trade-off between enhanced treatment delivery time and high treatment plan quality.

Beam complexity and monitor unit efficiency comparison in two different volumetric modulated arc therapy delivery systems using automated planning

Background To investigate the beam complexity and monitor unit (MU) efficiency issues for two different volumetric modulated arc therapy (VMAT) delivery technologies for patients with left-sided breast cancer (BC) and nasopharyngeal carcinoma (NPC). Methods Twelve left-sided BC and seven NPC cases were enrolled in this study. Each delivered treatment plan was optimized in the Pinnacle3 treatment planning system with the Auto-Planning module for the Trilogy and Synergy systems. Similar planning dose objectives and beam configurations were used for each site in the two different delivery systems to produce clinically acceptable plans. The beam complexity was evaluated in terms of the segment area (SA), segment width (SW), leaf sequence variability (LSV), aperture area variability (AAV), and modulation complexity score (MCS) based on the multileaf collimator sequence and MU. Plan delivery and a gamma evaluation were performed using a helical diode array. Results With similar plan quality, the average SAs for the Trilogy plans were smaller than those for the Synergy plans: 55.5 ± 21.3 cm2 vs. 66.3 ± 17.9 cm2 (p < 0.05) for the NPC cases and 100.7 ± 49.2 cm2 vs. 108.5 ± 42.7 cm2 (p < 0.05) for the BC cases, respectively. The SW was statistically significant for the two delivery systems (NPC: 6.87 ± 1.95 cm vs. 6.72 ± 2.71 cm, p < 0.05; BC: 8.84 ± 2.56 cm vs. 8.09 ± 2.63 cm, p < 0.05). The LSV was significantly smaller for Trilogy (NPC: 0.84 ± 0.033 vs. 0.86 ± 0.033, p < 0.05; BC: 0.89 ± 0.026 vs. 0.90 ± 0.26, p < 0.05). The mean AAV was significantly larger for Trilogy than for Synergy (NPC: 0.18 ± 0.064 vs. 0.14 ± 0.037, p < 0.05; BC: 0.46 ± 0.15 vs. 0.33 ± 0.13, p < 0.05). The MCS values for Trilogy were higher than those for Synergy: 0.14 ± 0.016 vs. 0.12 ± 0.017 (p < 0.05) for the NPC cases and 0.42 ± 0.106 vs. 0.30 ± 0.087 (p < 0.05) for the BC cases. Compared with the Synergy plans, the average MUs for the Trilogy plans were larger: 828.6 ± 74.1 MU and 782.9 ± 85.2 MU (p > 0.05) for the NPC cases and 444.8 ± 61.3 MU and 393.8 ± 75.3 MU (p > 0.05) for the BC cases. The gamma index agreement scores were never below 91% using 3 mm/3% (global) distance to agreement and dose difference criteria and a 10% lower dose exclusion threshold. Conclusions The Pinnacle3 Auto-Planning system can optimize BC and NPC plans to achieve the same plan quality using both the Trilogy and Synergy systems. We found that these two systems resulted in different SAs, SWs, LSVs, AAVs and MCSs. As a result, we suggested that the beam complexity should be considered in the development of further methodologies while optimizing VMAT autoplanning.

Beam complexity and monitor unit efficiency comparison in two different volumetric modulated arc therapy delivery using automated planning

Background: To investigate the beam complexity and monitor unit（MU）efficiency issues for two different volumetric modulated arc therapy (VMAT) delivery technologies for patients with left-sided breast cancer (BC) and nasopharyngeal carcinoma (NPC). Methods: Twelve left-sided BC and seven NPC cases were enrolled in this study. Each delivered treatment plan was optimized in Pinnacle 3 treatment planning system with Auto-Planning module for Trilogy and Synergy systems. Similar planning dose objectives and beam configuration were used for each site in two different delivery systems to produce clinically acceptable plans. Beam complexity was evaluated in terms of segment area(SA), segment width(SW), leaf sequence variability(LSV), aperture area variability(AAV), modulation complexity score(MCS) based on MLC sequence and MU. Results: With similar plan quality, the average SAs for Trilogy plans were smaller than those for Synergy plans: 55.5 ± 21.3 cm 2 vs. 66.3 ± 17.9 cm 2 (p<0.05) for the NPC cases, and 100.7 ± 49.2 cm 2 vs. 108.5 ± 42.7 cm 2 (p<0.05) for BC cases, respectively. The SW was statistically significant for two delivery systems (NPC: 6.87±1.95cm vs.6.72±2.71cm, p < 0.05; BC: 8.84±2.56cm vs.8.09±2.63cm, p < 0.05). LSV was statistically significant smaller for Trilogy (NPC: 0.84±0.033 vs.0.86±0.033, p < 0.05; BC: 0.89±0.026 vs.0.90±0.26, p < 0.05). The mean AAV was statistically significant larger for Trilogy than Synergy (NPC: 0.18±0.064 vs.0.14±0.037, p < 0.05; BC: 0.46±0.15 vs.0.33±0.13, p < 0.05). The MCS values for the Trilogy were higher than those for the Synergy: 0.14 ± 0.016vs. 0.12 ± 0.017 (p<0.05) for the NPC cases, and 0.42 ± 0.106 vs. 0.30 ± 0.087(p<0.05) for the BC cases. Compared with Synergy plans, the average MU for Trilogy plans were larger: 828.6±74.1MU and 782.9±85.2MU (p>0.05) for the NPC cases, and 444.8±61.3MU and 393.8±75.3MU (p>0.05) for the BC cases. Conclusions: The pinnacle 3 Auto planning system can optimize BC and NPC plans to obtain the same plan quality using Trilogy and Synergy systems. We found that this two systems resulted in different SA, SW, LSV, AAV and MCS. As a result, we suggested that beam complexity should be considered in providing further methodologies while optimizing VMAT auto planning.