Sensitivity analysis for lexicographic ordering in radiation therapy treatment planning

Influence of optimisation parameters on directly deliverable Pareto fronts explored for prostate cancer

PURPOSE

In inverse radiotherapy treatment planning, the Pareto front is the set of optimal solutions to the multi-criteria problem of adequately irradiating the planning target volume (PTV) while reducing dose to organs at risk (OAR). The Pareto front depends on the chosen optimisation parameters whose influence (clinically relevant versus not clinically relevant) is investigated in this paper.

METHODS

Thirty-one prostate cancer patients treated at our clinic were randomly selected. We developed an in-house Python script that controlled the commercial treatment planning system RayStation to calculate directly deliverable Pareto fronts. We calculated reference Pareto fronts for a given set of objective functions, varying the PTV coverage and the mean dose of the primary OAR (rectum) and fixing the mean doses of the secondary OARs (bladder and femoral heads). We calculated the fronts for different sets of objective functions and different mean doses to secondary OARs. We compared all fronts using a specific metric (clinical distance measure).

RESULTS

The in-house script was validated for directly deliverable Pareto front calculations in two and three dimensions. The Pareto fronts depended on the choice of objective functions and fixed mean doses to secondary OARs, whereas the parameters most influencing the front and leading to clinically relevant differences were the dose gradient around the PTV, the weight of the PTV objective function, and the bladder mean dose.

CONCLUSIONS

Our study suggests that for multi-criteria optimisation of prostate treatments using external therapy, dose gradient around the PTV and bladder mean dose are the most influencial parameters.

Fast and exact Hessian computation for a class of nonlinear functions used in radiation therapy treatment planning

In nonlinear optimisation, using exact Hessian computations (full-Newton) hold superior convergence properties over quasi-Newton methods or gradient-based methods. However, for medium-scale problems, computing the Hessian can be computationally expensive and thus time-consuming. For solvers dedicated to a specific problem type, it can be advantageous to hard-code optimised implementations to keep the computation time to a minimum. In this paper we derive a computationally efficient canonical form for a class of additively and multiplicatively separable functions. The major computational cost is reduced to a single multiplication of the data matrix with itself, allowing simple parallellisation on modern-day multi-core processors. We present the approach in the practical application of radiation therapy treatment planning, where this form appears for many common functions. In this case, the data matrices are the dose-influence matrices. The method is compared against automatic differentiation.

Automated 4π radiotherapy treatment planning with evolving knowledge-base

PURPOSE

Non-coplanar 4π radiotherapy generalizes intensity modulated radiation therapy (IMRT) to automate beam geometry selection but requires complicated hyperparameter tuning to attain superior plan quality, which can be tedious and inconsistent. In this study, a fully automated 4π treatment planning was developed using evolving knowledge-base (EKB) planning guided by dose prediction.

METHODS

Twenty 4π lung and twenty 4π head and neck (HN) cases were included. A statistical voxel dose learning model was initially trained on low-quality plans created using generic hyperparameter templates without manual tuning. To improve the automated plan quality without being limited by the training data quality, a new 4π optimization problem was formulated to include a one-sided penalty on the organ-at-risk (OAR) dose deviation from the predicted dose. This directional OAR penalty encourages superior OAR sparing. The fast iterative shrinkage-thresholding algorithm (FISTA) was used to solve the large-scale beam orientation optimization problem. With the improved plans, new predictions were created to guide the next loop of EKB planning for a total of 10 loops. Plan quality was evaluated using a plan quality metric (PQM) points system based on clinical dose constraints and compared with automated planning approaches guided by manual high-quality plans using all non-coplanar beams, automated plans using individually evolved targeted dose, and manually created 4π plans.

RESULTS

For the lung cases, the final EKB plans had significantly higher PQM than manually created 4π (+2.60%). The improvements plateaued after the third loop. The final HN EKB plans and manually created 4π plans had comparable PQMs, but had lower PQM compared to automated plans using a high-quality training set (-3.00% and -4.44%, respectively). The PQM consistently increased up to the sixth loop. Individually evolved plans were able to improve the plan quality from initial condition due to the one-sided cost function but the 60% of them were trapped in undesired local minima that were substantially worse than their corresponding EKB plans.

CONCLUSION

Evolving knowledge-base planning is a novel automated planning technique guided by the predicted three-dimensional dose distribution, which can evolve from low-quality plans. EKB allows new beams to be used in the automated planning workflow for superior plan quality.

Automatically configuring the reference point method for automated multi-objective treatment planning

Automated treatment planning algorithms have demonstrated capability in generating consistent and high-quality treatment plans. Their configuration (i.e. determining the algorithm's parameters), however, can be a labour-intensive and time-consuming trial-and-error procedure. Previously, we introduced the reference point method (RPM) for fast automated multi-objective treatment planning. The RPM generates a single Pareto optimal plan for each patient. When the RPM is configured appropriately, this plan has clinically favourable trade-offs between all plan objectives. This paper proposes a new procedure to automatically generate a single configuration of the RPM per tumour site. The procedure was tested for prostate cancer. Planning CT scans of 287 previously treated patients were included in a database, together with corresponding Pareto optimal plans generated using our clinically applied two-phase [Formula: see text]-constraint method (part of Erasmus-iCycle) for automated multi-objective treatment planning. The procedure developed acquires plan characteristics observed in a training set. Based on these, an RPM configuration is automatically generated according to user preferences which specify acceptable differences between training set plans and corresponding RPM generated plans. For example, compared to the training set plans, the RPM generated plans need to have similar PTV coverage, and preferably reduced high rectum dose while slight deteriorations in other objectives are allowed. Training sets of different sizes were tested, and the quality of the resulting RPM configurations was evaluated on the test set (subset of the database not used for training). Using the new procedure, an RPM configuration was generated for each training set. The quality of RPM generated plans was similar or slightly better than that of the corresponding test set plans. The proposed automated configuration procedure greatly reduces the manual configuration workload, and thereby improves the efficiency and effectiveness of an automated clinical treatment planning workflow.

Fast and fuzzy multi-objective radiotherapy treatment plan generation for head and neck cancer patients with the lexicographic reference point method (LRPM)

Previously, we have proposed Erasmus-iCycle, an algorithm for fully automated IMRT plan generation based on prioritised (lexicographic) multi-objective optimisation with the 2-phase ϵ-constraint (2pϵc) method. For each patient, the output of Erasmus-iCycle is a clinically favourable, Pareto optimal plan. The 2pϵc method uses a list of objective functions that are consecutively optimised, following a strict, user-defined prioritisation. The novel lexicographic reference point method (LRPM) is capable of solving multi-objective problems in a single optimisation, using a fuzzy prioritisation of the objectives. Trade-offs are made globally, aiming for large favourable gains for lower prioritised objectives at the cost of only slight degradations for higher prioritised objectives, or vice versa. In this study, the LRPM is validated for 15 head and neck cancer patients receiving bilateral neck irradiation. The generated plans using the LRPM are compared with the plans resulting from the 2pϵc method. Both methods were capable of automatically generating clinically relevant treatment plans for all patients. For some patients, the LRPM allowed large favourable gains in some treatment plan objectives at the cost of only small degradations for the others. Moreover, because of the applied single optimisation instead of multiple optimisations, the LRPM reduced the average computation time from 209.2 to 9.5 min, a speed-up factor of 22 relative to the 2pϵc method.

Optimization of rotational arc station parameter optimized radiation therapy

PURPOSE

To develop a fast optimization method for station parameter optimized radiation therapy (SPORT) and show that SPORT is capable of matching VMAT in both plan quality and delivery efficiency by using three clinical cases of different disease sites.

METHODS

The angular space from 0° to 360° was divided into 180 station points (SPs). A candidate aperture was assigned to each of the SPs based on the calculation results using a column generation algorithm. The weights of the apertures were then obtained by optimizing the objective function using a state-of-the-art GPU based proximal operator graph solver. To avoid being trapped in a local minimum in beamlet-based aperture selection using the gradient descent algorithm, a stochastic gradient descent was employed here. Apertures with zero or low weight were thrown out. To find out whether there was room to further improve the plan by adding more apertures or SPs, the authors repeated the above procedure with consideration of the existing dose distribution from the last iteration. At the end of the second iteration, the weights of all the apertures were reoptimized, including those of the first iteration. The above procedure was repeated until the plan could not be improved any further. The optimization technique was assessed by using three clinical cases (prostate, head and neck, and brain) with the results compared to that obtained using conventional VMAT in terms of dosimetric properties, treatment time, and total MU.

RESULTS

Marked dosimetric quality improvement was demonstrated in the SPORT plans for all three studied cases. For the prostate case, the volume of the 50% prescription dose was decreased by 22% for the rectum and 6% for the bladder. For the head and neck case, SPORT improved the mean dose for the left and right parotids by 15% each. The maximum dose was lowered from 72.7 to 71.7 Gy for the mandible, and from 30.7 to 27.3 Gy for the spinal cord. The mean dose for the pharynx and larynx was reduced by 8% and 6%, respectively. For the brain case, the doses to the eyes, chiasm, and inner ears were all improved. SPORT shortened the treatment time by ∼1 min for the prostate case, ∼0.5 min for brain case, and ∼0.2 min for the head and neck case.

CONCLUSIONS

The dosimetric quality and delivery efficiency presented here indicate that SPORT is an intriguing alternative treatment modality. With the widespread adoption of digital linac, SPORT should lead to improved patient care in the future.

Intensity modulated proton therapy

Intensity modulated proton therapy (IMPT) implies the electromagnetic spatial control of well-circumscribed "pencil beams" of protons of variable energy and intensity. Proton pencil beams take advantage of the charged-particle Bragg peak-the characteristic peak of dose at the end of range-combined with the modulation of pencil beam variables to create target-local modulations in dose that achieves the dose objectives. IMPT improves on X-ray intensity modulated beams (intensity modulated radiotherapy or volumetric modulated arc therapy) with dose modulation along the beam axis as well as lateral, in-field, dose modulation. The clinical practice of IMPT further improves the healthy tissue vs target dose differential in comparison with X-rays and thus allows increased target dose with dose reduction elsewhere. In addition, heavy-charged-particle beams allow for the modulation of biological effects, which is of active interest in combination with dose "painting" within a target. The clinical utilization of IMPT is actively pursued but technical, physical and clinical questions remain. Technical questions pertain to control processes for manipulating pencil beams from the creation of the proton beam to delivery within the patient within the accuracy requirement. Physical questions pertain to the interplay between the proton penetration and variations between planned and actual patient anatomical representation and the intrinsic uncertainty in tissue stopping powers (the measure of energy loss per unit distance). Clinical questions remain concerning the impact and management of the technical and physical questions within the context of the daily treatment delivery, the clinical benefit of IMPT and the biological response differential compared with X-rays against which clinical benefit will be judged. It is expected that IMPT will replace other modes of proton field delivery. Proton radiotherapy, since its first practice 50 years ago, always required the highest level of accuracy and pioneered volumetric treatment planning and imaging at a level of quality now standard in X-ray therapy. IMPT requires not only the highest precision tools but also the highest level of system integration of the services required to deliver high-precision radiotherapy.

A multicriteria framework with voxel-dependent parameters for radiotherapy treatment plan optimization

PURPOSE

To establish a new mathematical framework for radiotherapy treatment optimization with voxel-dependent optimization parameters.

METHODS

In the treatment plan optimization problem for radiotherapy, a clinically acceptable plan is usually generated by an optimization process with weighting factors or reference doses adjusted for a set of the objective functions associated to the organs. Recent discoveries indicate that adjusting parameters associated with each voxel may lead to better plan quality. However, it is still unclear regarding the mathematical reasons behind it. Furthermore, questions about the objective function selection and parameter adjustment to assure Pareto optimality as well as the relationship between the optimal solutions obtained from the organ-based and voxel-based models remain unanswered. To answer these questions, the authors establish in this work a new mathematical framework equipped with two theorems.

RESULTS

The new framework clarifies the different consequences of adjusting organ-dependent and voxel-dependent parameters for the treatment plan optimization of radiation therapy, as well as the impact of using different objective functions on plan qualities and Pareto surfaces. The main discoveries are threefold: (1) While in the organ-based model the selection of the objective function has an impact on the quality of the optimized plans, this is no longer an issue for the voxel-based model since the Pareto surface is independent of the objective function selection and the entire Pareto surface could be generated as long as the objective function satisfies certain mathematical conditions; (2) All Pareto solutions generated by the organ-based model with different objective functions are parts of a unique Pareto surface generated by the voxel-based model with any appropriate objective function; (3) A much larger Pareto surface is explored by adjusting voxel-dependent parameters than by adjusting organ-dependent parameters, possibly allowing for the generation of plans with better trade-offs among different clinical objectives.

CONCLUSIONS

The authors have developed a mathematical framework for radiotherapy treatment optimization using voxel-based parameters. The authors can improve the plan quality by adjusting voxel-based weighting factors and exploring the unique and large Pareto surface which include all the Pareto surfaces that can be generated by organ-based model using different objective functions.

A column-generation-based method for multi-criteria direct aperture optimization

Navigation-based multi-criteria optimization has been introduced to radiotherapy planning in order to allow the interactive exploration of trade-offs between conflicting clinical goals. However, this has been mainly applied to fluence map optimization. The subsequent leaf sequencing step may cause dose discrepancy, leading to human iteration loops in the treatment planning process that multi-criteria methods were meant to avoid. To circumvent this issue, this paper investigates the application of direct aperture optimization methods in the context of multi-criteria optimization. We develop a solution method to directly obtain a collection of apertures that can adequately span the entire Pareto surface. To that end, we extend the column generation method for direct aperture optimization to a multi-criteria setting in which apertures that can improve the entire Pareto surface are sequentially identified and added to the treatment plan. Our proposed solution method can be embedded in a navigation-based multi-criteria optimization framework, in which the treatment planner explores the trade-off between treatment objectives directly in the space of deliverable apertures. Our solution method is demonstrated for a paraspinal case where the trade-off between target coverage and spinal-cord sparing is studied. The computational results validate that our proposed method obtains a balanced approximation of the Pareto surface over a wide range of clinically relevant plans.