A convex optimization approach to radiation treatment planning with dose constraints

Efficient radiation treatment planning based on voxel importance

Objective.Radiation treatment planning (RTP) involves optimization over a large number of voxels, many of which carry limited information about the clinical problem. We propose an approach to reduce the large optimization problem by only using a representative subset of informative voxels. This way, we drastically improve planning efficiency while maintaining the plan quality.Approach.Within an initial probing step, we pre-solve an easier optimization problem involving a simplified objective from which we derive an importance score per voxel. This importance score is then turned into a sampling distribution, which allows us to subsample a small set of informative voxels using importance sampling. By solving a-now reduced-version of the original optimization problem using this subset, we effectively reduce the problem's size and computational demands while accounting for regions where satisfactory dose deliveries are challenging.Main results.In contrast to other stochastic (sub-)sampling methods, our technique only requires a single probing and sampling step to define a reduced optimization problem. This problem can be efficiently solved using established solvers without the need of modifying or adapting them. Empirical experiments on open benchmark data highlight substantially reduced optimization times, up to 50 times faster than the original ones, for intensity-modulated radiation therapy, all while upholding plan quality comparable to traditional methods.Significance.Our novel approach has the potential to significantly accelerate RTP by addressing its inherent computational challenges. We reduce the treatment planning time by reducing the size of the optimization problem rather than modifying and improving the optimization method. Our efforts are thus complementary to many previous developments.

Simultaneous reduction of number of spots and energy layers in intensity modulated proton therapy for rapid spot scanning delivery

BACKGROUND

Reducing proton treatment time improves patient comfort and decreases the risk of error from intrafractional motion, but must be balanced against clinical goals and treatment plan quality.

PURPOSE

To improve the delivery efficiency of spot scanning proton therapy by simultaneously reducing the number of spots and energy layers using the reweightedl 1 $l_1$ regularization method.

METHODS

We formulated the proton treatment planning problem as a convex optimization problem with a cost function consisting of a dosimetric plan quality term plus a weightedl 1 $l_1$ regularization term. We iteratively solved this problem and adaptively updated the regularization weights to promote the sparsity of both the spots and energy layers. The proposed algorithm was tested on four head-and-neck cancer patients, and its performance, in terms of reducing the number of spots and energy layers, was compared with existing standardl 1 $l_1$ and groupl 2 $l_2$ regularization methods. We also compared the effectiveness of the three methods (l 1 $l_1$ , groupl 2 $l_2$ , and reweightedl 1 $l_1$ ) at improving plan delivery efficiency without compromising dosimetric plan quality by constructing each of their Pareto surfaces charting the trade-off between plan delivery and plan quality.

RESULTS

The reweightedl 1 $l_1$ regularization method reduced the number of spots and energy layers by an average over all patients of40 % $40\%$ and35 % $35\%$ , respectively, with an insignificant cost to dosimetric plan quality. From the Pareto surfaces, it is clear that reweightedl 1 $l_1$ provided a better trade-off between plan delivery efficiency and dosimetric plan quality than standardl 1 $l_1$ or groupl 2 $l_2$ regularization, requiring the lowest cost to quality to achieve any given level of delivery efficiency.

CONCLUSIONS

Reweightedl 1 $l_1$ regularization is a powerful method for simultaneously promoting the sparsity of spots and energy layers at a small cost to dosimetric plan quality. This sparsity reduces the time required for spot scanning and energy layer switching, thereby improving the delivery efficiency of proton plans.

Effective optimization strategy for large optimization volume object, remaining volume at risk (RVR):α-value selection and usage from generalized equivalent uniform dose (gEUD) curve deviation perspective

Objective.A large optimization volume for intensity-modulated radiation therapy (IMRT), such as the remaining volume at risk (RVR), is traditionally unsuitable for dose-volume constraint control and requires planner-specific empirical considerations owing to the patient-specific shape. To enable less empirical optimization, the generalized equivalent uniform dose (gEUD) optimization is effective; however, the utilization of parametera-values remains elusive. Our study clarifies thea-value characteristics for optimization and to enable effectivea-value use.Approach.The gEUD can be obtained as a function of itsa-value, which is the weighted generalized mean; its curve has a continuous, differentiable, and sigmoid shape, deforming in its optimization state with retained curve characteristics. Using differential geometry, the gEUD curve changes in optimization is considered a geodesic deviation intervened by the forces between deforming and retaining the curve. The curvature and gradient of the curve are radically related to optimization. The vertex point (a=a_k) was set and thea-value roles were classified into the following three parts of the curve with respect to thea-value: (i) high gradient and middle curvature, (ii) middle gradient and high curvature, and (iii) low gradient and low curvature. Then, a strategy for multiplea-values was then identified using RVR optimization.Main results.Eleven head and neck patients who underwent static seven-field IMRT were used to verify thea-value characteristics and curvature effect for optimization. The lowera-value (i) (a= 1-3) optimization was effective for the whole dose-volume range; in contrast, the effect of highera-value (iii) (a= 12-20) optimization addressed strongly the high-dose range of the dose volume. The middlea-value (ii) (arounda=a_k) showed intermediate but effective high-to-low dose reduction. Thesea-value characteristics were observed as superimpositions in the optimization. Thus, multiple gEUD-based optimization was significantly superior to the exponential constraints normally applied to the RVR that surrounds the PTV, normal tissue objective (NTO), resulting in up to 25.9% and 8.1% improvement in dose-volume indices D2% and V10Gy, respectively.Significance.This study revealed an appropriatea-value for gEUD optimization, leading to favorable dose-volume optimization for the RVR region using fixed multiplea-value conditions, despite the very large and patient-specific shape of the region.

Conic formulation of fluence map optimization problems

The convexity of objectives and constraints in fluence map optimization (FMO) for radiation therapy has been extensively studied. Next to convexity, there is another important characteristic of optimization functions and problems, which has thus far not been considered in FMO literature: conic representation. Optimization problems that are conically representable using quadratic, exponential and power cones are solvable with advanced primal-dual interior-point algorithms. These algorithms guarantee an optimal solution in polynomial time and have good performance in practice. In this paper, we construct conic representations for most FMO objectives and constraints. This paper is the first that shows that FMO problems containing multiple biological evaluation criteria can be solved in polynomial time. For fractionation-corrected functions for which no exact conic reformulation is found, we provide an accurate approximation that is conically representable. We present numerical results on the TROTS data set, which demonstrate very stable numerical performance for solving FMO problems in conic form. With ongoing research in the optimization community, improvements in speed can be expected, which makes conic optimization a promising alternative for solving FMO problems.

Pareto Optimal Projection Search (POPS): Automated Radiation Therapy Treatment Planning by Direct Search of the Pareto Surface

OBJECTIVE

Radiation therapy treatment planning is a time-consuming, iterative process with potentially high inter-planner variability. Fully automated treatment planning processes could reduce a planner's active treatment planning time and remove inter-planner variability, with the potential to tremendously improve patient turnover and quality of care. In developing fully automated algorithms for treatment planning, we have two main objectives: to produce plans that are 1) Pareto optimal and 2) clinically acceptable. Here, we propose the Pareto optimal projection search (POPS) algorithm, which provides a general framework for directly searching the Pareto front.

METHODS

Our POPS algorithm is a novel automated planning method that combines two main search processes: 1) gradient-free search in the decision variable space and 2) projection of decision variables to the Pareto front using the bisection method. We demonstrate the performance of POPS by comparing with clinical treatment plans. As one possible quantitative measure of treatment plan quality, we construct a clinical acceptability scoring function (SF) modified from the previously developed general evaluation metric (GEM).

RESULTS

On a dataset of 21 prostate cases collected as part of clinical workflow, our proposed POPS algorithm produces Pareto optimal plans that are clinically acceptable in regards to dose conformity, dose homogeneity, and sparing of organs-at-risk.

CONCLUSION

Our proposed POPS algorithm provides a general framework for fully automated treatment planning that achieves clinically acceptable dosimetric quality without requiring active planning from human planners.

SIGNIFICANCE

Our fully automated POPS algorithm addresses many key limitations of other automated planning approaches, and we anticipate that it will substantially improve treatment planning workflow.

Fully automated noncoplanar radiation therapy treatment planning

PURPOSE

To perform fully automated noncoplanar (NC) treatment planning, we propose a method called NC-POPS to produce NC plans using the Pareto optimal projection search (POPS) algorithm.

METHODS

NC radiation therapy treatment planning has the potential to improve dosimetric quality as compared to traditional coplanar techniques. Likewise, automated treatment planning algorithms can reduce a planner's active treatment planning time and remove inter-planner variability. Our NC-POPS algorithm extends the original POPS algorithm to the NC setting with potential applications to both intensity-modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT). The proposed algorithm consists of two main parts: (1) NC beam angle optimization (BAO) and (2) fully automated inverse planning using the POPS algorithm.

RESULTS

We evaluate the performance of NC-POPS by comparing between various NC and coplanar configurations. To evaluate plan quality, we compute the homogeneity index (HI), conformity index (CI), and dose-volume histogram statistics for various organs-at-risk (OARs). As compared to the evaluated coplanar baseline methods, the proposed NC-POPS method achieves significantly better OAR sparing, comparable or better dose conformity, and similar dose homogeneity.

CONCLUSIONS

Our proposed NC-POPS algorithm provides a modular approach for fully automated treatment planning of NC IMRT cases with the potential to substantially improve treatment planning workflow and plan quality.

Direct optimization of dose-volume histogram metrics in radiation therapy treatment planning

We present a method of directly optimizing on deviations in clinical goal values in radiation therapy treatment planning. Using a new mathematical framework in which metrics derived from the dose-volume histogram are regarded as functionals of an auxiliary random variable, we are able to obtain volume-at-dose and dose-at-volume as infinitely differentiable functions of the dose distribution with easily evaluable function values and gradients. Motivated by the connection to risk measures in finance, which is formalized in this framework, we also derive closed-form formulas for mean-tail-dose and demonstrate its capability of reducing extreme dose values in tail distributions. Numerical experiments performed on a prostate and a head-and-neck patient case show that the direct optimization of dose-volume histogram metrics produced marginally better results than or outperformed conventional planning objectives in terms of clinical goal fulfilment, control of low- and high-dose tails of target distributions and general plan quality defined by a pre-specified evaluation measure. The proposed framework eliminates the disconnect between optimization functions and evaluation metrics and may thus reduce the need for repetitive user interaction associated with conventional treatment planning. The method also has the potential of enhancing plan optimization in other settings such as multicriteria optimization and automated treatment planning.