Reduced order constrained optimization (ROCO): clinical application to lung IMRT

On the optimal number of dose-limiting shells in the SBRT auto-planning design for peripheral lung cancer

PURPOSE

The number of dose-limiting shells in the optimization process is one of the key factors determining the quality of stereotactic body radiotherapy (SBRT) auto-planning in the Pinnacle treatment planning system (TPS). This study attempted to derive the optimal number of shells by evaluating the auto-plans designed with different number of shells for peripheral lung cancer patients treated with SBRT.

METHODS

Identical treatment technique, optimization process, constraints, and dose calculation algorithm in the Pinnacle TPS were retrospectively applied to 50 peripheral lung cancer patients who underwent SBRT in our center. For each of the patients, auto-plans were optimized based on two shells, three shells, four shells, five shells, six shells, seven shells, eight shells, respectively. The optimal number of shells for the SBRT auto-planning was derived through the evaluations and comparisons of various dosimetric parameters of planning target volume (PTV) and organs at risk (OARs), monitor units (MU), and optimization time of the plans.

RESULTS

The conformity index (CI) and the gradient index (GI) of PTV, the maximum dose outside the 2 cm of PTV (D2cm ), Dmax of spinal cord (SCmax ), the percentage of volume of total lung excluding ITV receiving 20 Gy (V20) and 10 Gy (V10), and the mean lung dose (MLD) were improved when the number of shell increased, but the improvement became not significant as the number of shell reached six. The monitor units (MUs) varied little among different plans where no statistical differences were found. However, as the number of shell increased, the auto-plan optimization time increased significantly.

CONCLUSIONS

It appears that for peripheral lung SBRT plan using six shells can yield satisfactory plan quality with acceptable beam MUs and optimization time in the Pinnacle TPS.

Multiobjective, Multidelivery Optimization for Radiation Therapy Treatment Planning

Purpose

To introduce multiobjective, multidelivery optimization (MODO), which generates alternative patient-specific plans emphasizing dosimetric trade-offs and conformance to quasi-constrained (QC) conditions for multiple delivery techniques.

Methods and Materials

For M delivery techniques and N organs at risk (OARs), MODO generates M (N + 1) alternative treatment plans per patient. For 30 locally advanced lung cancer cases, the algorithm was investigated based on dosimetric trade-offs to 4 OARs: each lung, heart, and esophagus (N = 4) and 4 delivery techniques (4-field coplanar intensity modulated radiation therapy [IMRT], 9-field coplanar IMRT, 27-field noncoplanar IMRT, and noncoplanar arc IMRT) and conformance to QC conditions, including dose to 95% (D95) of the planning target volume (PTV), maximum dose (Dmax) to PTV (PTV-Dmax), and spinal cord Dmax. The MODO plan set was evaluated for conformance to QC conditions while simultaneously revealing dosimetric trade-offs. Statistically significant dosimetric trade-offs were defined such that the coefficient of determination was >0.8 with dosimetric indices that varied by at least 5 Gy.

Results

Plans varied mean dose by >5 Gy to ipsilateral lung for 24 of 30 patients, contralateral lung for 29 of 30 patients, esophagus for 29 of 30 patients, and heart for 19 of 30 patients. In the 600 plans, average PTV-D95 = 67.6 ± 2.1 Gy, PTV-Dmax = 79.8 ± 5.2 Gy, and spinal cord Dmax among all plans was 51.4 Gy. Statistically significant dosimetric trade-offs reducing OAR mean dose by >5 Gy were evident in 19 of 30 patients, including multiple OAR trade-offs of at least 5 Gy in 7 of 30 cases. The most common statistically significant trade-off was increasing PTV-Dmax to reduce dose to OARs (15 of 30). The average 4-field plan reduced total lung V20 by 10.4% ± 8.3% compared with 9-field plans, 7.7% ± 7.9% compared with 27-field noncoplanar plans, and 11.7% ± 10.3% compared with 2-arc noncoplanar plans, with corresponding increases in PTV-Dmax of 5.3 ± 5.9 Gy, 4.6 ± 5.6 Gy, and 9.3 ± 7.3 Gy.

Conclusions

The proposed optimization method produces clinically relevant treatment plans that meet QC conditions and demonstrate variations in OAR doses.

Automated inverse optimization facilitates lower doses to normal tissue in pancreatic stereotactic body radiotherapy

Purpose

Inverse planning is trial-and-error iterative process. This work introduces a fully automated inverse optimization approach, where the treatment plan is closely tailored to the unique patient anatomy. The auto-optimization is applied to pancreatic stereotactic body radiotherapy (SBRT).

Materials and methods

The automation is based on stepwise reduction of dose-volume histograms (DVHs). Five uniformly spaced points, from 1% to 70% of the organ at risk (OAR) volumes, are used. Doses to those DVH points are iteratively decreased through multiple optimization runs. With each optimization run the doses to the OARs are decreased, while the dose homogeneity over the target is increased. The iterative process is terminated when a pre-specified dose heterogeneity over the target is reached. Twelve pancreatic cases were retrospectively studied. Doses to the target, maximum doses to duodenum, bowel, stomach, and spinal cord were evaluated. In addition, mean doses to liver and kidneys were tallied. The auto-optimized plans were compared to the actual treatment plans, which are based on national protocols.

Results

The prescription dose to 95% of the planning target volume (PTV) is the same for the treatment and the auto-optimized plans. The average difference for maximum doses to duodenum, bowel, stomach, and spinal cord are -4.6 Gy, -1.8 Gy, -1.6 Gy, and -2.4 Gy respectively. The negative sign indicates lower doses with the auto-optimization. The average differences in the mean doses to liver and kidneys are -0.6 Gy, and -1.1 Gy to -1.5 Gy respectively.

Conclusions

Automated inverse optimization holds great potential for personalization and tailoring of radiotherapy to particular patient anatomies. It can be utilized for normal tissue sparing or for an isotoxic dose escalation.

A singular value decomposition linear programming (SVDLP) optimization technique for circular cone based robotic radiotherapy

With robot-controlled linac positioning, robotic radiotherapy systems such as CyberKnife significantly increase freedom of radiation beam placement, but also impose more challenges on treatment plan optimization. The resampling mechanism in the vendor-supplied treatment planning system (MultiPlan) cannot fully explore the increased beam direction search space. Besides, a sparse treatment plan (using fewer beams) is desired to improve treatment efficiency. This study proposes a singular value decomposition linear programming (SVDLP) optimization technique for circular collimator based robotic radiotherapy. The SVDLP approach initializes the input beams by simulating the process of covering the entire target volume with equivalent beam tapers. The requirements on dosimetry distribution are modeled as hard and soft constraints, and the sparsity of the treatment plan is achieved by compressive sensing. The proposed linear programming (LP) model optimizes beam weights by minimizing the deviation of soft constraints subject to hard constraints, with a constraint on the l 1 norm of the beam weight. A singular value decomposition (SVD) based acceleration technique was developed for the LP model. Based on the degeneracy of the influence matrix, the model is first compressed into lower dimension for optimization, and then back-projected to reconstruct the beam weight. After beam weight optimization, the number of beams is reduced by removing the beams with low weight, and optimizing the weights of the remaining beams using the same model. This beam reduction technique is further validated by a mixed integer programming (MIP) model. The SVDLP approach was tested on a lung case. The results demonstrate that the SVD acceleration technique speeds up the optimization by a factor of 4.8. Furthermore, the beam reduction achieves a similar plan quality to the globally optimal plan obtained by the MIP model, but is one to two orders of magnitude faster. Furthermore, the SVDLP approach is tested and compared with MultiPlan on three clinical cases of varying complexities. In general, the plans generated by the SVDLP achieve steeper dose gradient, better conformity and less damage to normal tissues. In conclusion, the SVDLP approach effectively improves the quality of treatment plan due to the use of the complete beam search space. This challenging optimization problem with the complete beam search space is effectively handled by the proposed SVD acceleration.

Esophagus and Contralateral Lung-Sparing IMRT for Locally Advanced Lung Cancer in the Community Hospital Setting

BACKGROUND

The optimal technique for performing lung IMRT remains poorly defined. We hypothesize that improved dose distributions associated with normal tissue-sparing IMRT can allow safe dose escalation resulting in decreased acute and late toxicity.

METHODS

We performed a retrospective analysis of 82 consecutive lung cancer patients treated with curative intent from 1/10 to 9/14. From 1/10 to 4/12, 44 patients were treated with the community standard of three-dimensional conformal radiotherapy or IMRT without specific esophagus or contralateral lung constraints (standard RT). From 5/12 to 9/14, 38 patients were treated with normal tissue-sparing IMRT with selective sparing of contralateral lung and esophagus. The study endpoints were dosimetry, toxicity, and overall survival.

RESULTS

Despite higher mean prescribed radiation doses in the normal tissue-sparing IMRT cohort (64.5 vs. 60.8 Gy, p = 0.04), patients treated with normal tissue-sparing IMRT had significantly lower lung V20, V10, V5, mean lung, esophageal V60, and mean esophagus doses compared to patients treated with standard RT (p ≤ 0.001). Patients in the normal tissue-sparing IMRT group had reduced acute grade ≥3 esophagitis (0 vs. 11%, p < 0.001), acute grade ≥2 weight loss (2 vs. 16%, p = 0.04), and late grade ≥2 pneumonitis (7 vs. 21%, p = 0.02). The 2-year overall survival was 52% with normal tissue-sparing IMRT arm compared to 28% for standard RT (p = 0.015).

CONCLUSION

These data provide proof of principle that suboptimal radiation dose distributions are associated with significant acute and late lung and esophageal toxicity that may result in hospitalization or even premature mortality. Strict attention to contralateral lung and esophageal dose-volume constraints are feasible in the community hospital setting without sacrificing disease control.

A novel reduced-order prioritized optimization method for radiation therapy treatment planning

In this study, a novel reduced order prioritized algorithm is presented for optimization in radiation therapy treatment planning. The proposed method consists of three stages. In the first stage, the intensity space was sampled by solving a series of unconstrained optimization problems. The objective function of the first stage is expressed as a scalarized weighted sum of partial objectives for the target and organ at risk. Latin hypercube sampling was utilized to define the weights for each run of the unconstrained optimizations. In the second stage, principal component analysis is applied to the solutions determined in the first stage to identify the major eigen modes in the intensities space, significantly reducing the number of independent variables. In the third stage, treatment planning goals/objectives are prioritized, and the problem is solved in the reduced order space. After each objective is optimized, that objective function is converted into a constraint for the lower-priority objectives. In the current formulation, a slip factor is used to relax the hard constraints for planning target volume (PTV) coverage. The applicability of the proposed method is demonstrated for one prostate and one lung intensity-modulated radiation therapy treatment plan. Upon completion of the sequential prioritized optimization, the mean dose at the rectum and bladder was reduced by 21.3% and 22.4%, respectively. Additionally, we investigated the effect of the slip factor 's' on PTV coverage and we found minimal degradation of the tumor dose (∼4%). Finally, the speed up factors upon the dimensionality reduction were as high as 49.9 without compromising the quality of the results.

Reduced-order constrained optimization (ROCO): clinical application to head-and-neck IMRT

PURPOSE

The authors present the application of the reduced order constrained optimization (ROCO) method, previously successfully applied to the prostate and lung sites, to the head-and-neck (H&N) site, demonstrating that it can quickly and automatically generate clinically competitive IMRT plans. We provide guidelines for applying ROCO to larynx, oropharynx, and nasopharynx cases, and report the results of a live experiment that demonstrates how an expert planner can save several hours of trial-and-error interaction using the proposed approach.

METHODS

The ROCO method used for H&N IMRT planning consists of three major steps. First, the intensity space of treatment plans is sampled by solving a series of unconstrained optimization problems with a parameter range based on previously treated patient data. Second, the dominant modes in the intensity space are estimated by dimensionality reduction using principal component analysis (PCA). Third, a constrained optimization problem over this basis is quickly solved to find an IMRT plan that meets organ-at-risk (OAR) and target coverage constraints. The quality of the plan is assessed using evaluation tools within Memorial Sloan-Kettering Cancer Center (MSKCC)'s treatment planning system (TPS).

RESULTS

The authors generated ten H&N IMRT plans for previously treated patients using the ROCO method and processed them for deliverability by a dynamic multileaf collimator (DMLC). The authors quantitatively compared the ROCO plans to the previously achieved clinical plans using the TPS tools used at MSKCC, including DVH and isodose contour analysis, and concluded that the ROCO plans would be clinically acceptable. In our current implementation, ROCO H&N plans can be generated using about 1.6 h of offline computation followed by 5-15 min of semiautomatic planning time. Additionally, the authors conducted a live session for a plan designated by MSKCC performed together with an expert H&N planner. A technical assistant set up the first two steps, which were performed without further human interaction, and then collaborated in a virtual meeting with the expert planner to perform the third (constrained optimization) step. The expert planner performed in-depth analysis of the resulting ROCO plan and deemed it to be clinically acceptable and in some aspects superior to the clinical plan. This entire process took 135 min including two constrained optimization runs, in comparison to the estimated 4 h that would have been required using traditional clinical planning tools.

CONCLUSIONS

The H&N site is very challenging for IMRT planning, due to several levels of prescription and a large, variable number (6-20) of OARs that depend on the location of the tumor. ROCO for H&N shows promise in generating clinically acceptable plans both more quickly and with substantially less human interaction.