The first direct method of spot sparsity optimization for proton arc therapy

Abstract

Notations and outlineWe describe the notation that we will use throughout the paper. We use regular lowercase letters for scalars, bold lowercase letters for vectors, BOLD CAPITAL LETTERS for matrices, and normal CAPITAL LETTERS for sets. We use subscript i for i-th element. Superscript represents iteration steps (k for outer iteration and j for inner loop). For a vector v, ∥v∥ l0 , ∥v∥ l2 , and ∥v∥ l∞ denote l 0 -, l 2 -, and l ∞ -norms, respectively. supp(v) represents the nonzero elements of v. For a vector v ∈ R n , u = max{v, 0} denotesFor a matrix Φ ∈ R m×n and an index set A ⊆ {1, 2, • • • , n}, Φ A stands for the submatrix of Φ obtained by keeping only the columns indexed by A. Also, v A denotes the vector obtained by keeping only the components of a vector v ∈ R n indexed by A.

The first investigation of spot-scanning proton arc (SPArc) delivery time and accuracy with different delivery tolerance window settings

“…Unfortunately, as of today, all the existing and published optimization and planning strategies are still based on static control point optimization (Gu et al 2020, Liu et al 2020, Wuyckens et al 2022, Zhang et al 2022. For example, the direct optimization approaches (DOA) are proposed to search the spot (Zhao et al 2022a(Zhao et al , 2023, and energy layers' sparsity solution in balancing the plan quality and treatment delivery time using the number of spot and energy layers as a surrogate. Although the DOA approach is beautiful in a mathematical form and capable of searching for the global minimum, it is difficult to translate the complicated gantry mechanical constraint and various delivery sequence models into a solvable optimization problem.…”

“…Although the DOA approach is beautiful in a mathematical form and capable of searching for the global minimum, it is difficult to translate the complicated gantry mechanical constraint and various delivery sequence models into a solvable optimization problem. Thus, the assumption and simplification of the delivery sequence were adopted in all the DOA publications at this moment which might not be a true treatment delivery time and delivery sequence of the SPArc therapy (Zhao et al 2022a(Zhao et al , 2023. On the other hand, the iterative optimization approaches (IOA) are first proposed to select the spot and energy layers by applying different selection and optimization in each step.…”

“…As our particle therapy community eagerly explores the opportunity to implement such a novel technique in future clinical settings (ESTRO-Particle Arc Therapy: from concept to clinical reality), one of the main research directions at this stage is to develop a treatment planning framework for SPArc therapy. In the last few years, different planning strategies have been proposed, such as the iterative approach (Ding et al 2016, Liu et al 2020, Zhao et al 2022a and direct sparsity optimization approach (Gu et al 2020, Wuyckens et al 2022, Zhao et al 2023. These optimization frameworks aim to search for the optimal energy layer number, sequencing, and spot number in a SPArc plan to deliver the treatment efficiently while ensuring the plan quality.…”

FLASH instead of proton arc therapy is a more promising advancement for the next generation proton radiotherapy

“…The proton system manufacturers such as IBA are taking the key steps to such development, while the Treatment Planning System (TPS) providers such as RaySearch and Elekta are also providing the proton arc module in support of future clinical implementations 68,69 . Additionally, many ideas have been formed to optimize particle arc therapy in a more efficient way 70–75 . In recent years, we saw exponentially increased publications on the topic of particle arc therapy.…”

“…68,69 Additionally, many ideas have been formed to optimize particle arc therapy in a more efficient way. [70][71][72][73][74][75] In recent years, we saw exponentially increased publications on the topic of particle arc therapy.These encouraging trends and global efforts might suggest that the proton RT is at an important turning point, similar to the invention of VMAT in the 2000s in the photon world. 30 Besides the potential clinical benefits, one driving factor that pushes particle arc therapy to dominate the future market is simplifying the clinical workflow and shortening the treatment delivery time.…”