Dávid Papp - Academia.edu (original) (raw)

Papers by Dávid Papp

Medical Physics

Purpose: Non-uniform fractionation, i.e. delivering distinct dose distributions in two subsequent... more Purpose: Non-uniform fractionation, i.e. delivering distinct dose distributions in two subsequent fractions, can potentially improve outcomes by increasing biological dose to the target without increasing dose to healthy tissues. This is possible if both fractions deliver a similar dose to normal tissues (exploit the fractionation effect) but high single fraction doses to subvolumes of the target (hypofractionation). Optimization of such treatment plans can be formulated using biological equivalent dose (BED), but leads to intractable nonconvex optimization problems. We introduce a novel optimization approach to address this challenge.

The main approach to smooth Pareto surface navigation for radiation therapy multi-criteria treatm... more The main approach to smooth Pareto surface navigation for radiation therapy multi-criteria treatment planning involves taking real-time averages of pre-computed treatment plans. In fluence-based treatment planning, fluence maps themselves can be averaged, which leads to the dose distributions being averaged due to the linear relationship between fluence and dose. This works for fluence-based photon plans and proton spot scanning plans. In this technical note, we show that two or more sliding window volumetric modulated arc therapy (VMAT) plans can be combined by averaging leaf positions in a certain way, and we demonstrate that the resulting dose distribution for the averaged plan is approximately the average of the dose distributions of the original plans. This leads to the ability to do Pareto surface navigation, i.e. interactive multi-criteria exploration of VMAT plan dosimetric tradeoffs.

Treating a realistic problem in any field of reaction kinetics raises a series of problems: we re... more Treating a realistic problem in any field of reaction kinetics raises a series of problems: we review these illustrated with examples using ReactionKinetics, a Mathematica based package.

Physics in Medicine and Biology, 2015

Utilizing noncoplanar beam angles in volumetric modulated arc therapy (VMAT) has the potential to... more Utilizing noncoplanar beam angles in volumetric modulated arc therapy (VMAT) has the potential to combine the benefits of arc therapy, such as short treatment times, with the benefits of noncoplanar intensity modulated radiotherapy (IMRT) plans, such as improved organ sparing. Recently, vendors introduced treatment machines that allow for simultaneous couch and gantry motion during beam delivery to make noncoplanar VMAT treatments possible. Our aim is to provide a reliable optimization method for noncoplanar isocentric arc therapy plan optimization. The proposed solution is modular in the sense that it can incorporate different existing beam angle selection and coplanar arc therapy optimization methods.Treatment planning is performed in three steps. First, a number of promising noncoplanar beam directions are selected using an iterative beam selection heuristic; these beams serve as anchor points of the arc therapy trajectory. In the second step, continuous gantry/couch angle trajectories are optimized using a simple combinatorial optimization model to define a beam trajectory that efficiently visits each of the anchor points. Treatment time is controlled by limiting the time the beam needs to trace the prescribed trajectory. In the third and final step, an optimal arc therapy plan is found along the prescribed beam trajectory. In principle any existing arc therapy optimization method could be incorporated into this step; for this work we use a sliding window VMAT algorithm.The approach is demonstrated using two particularly challenging cases. The first one is a lung SBRT patient whose planning goals could not be satisfied with fewer than nine noncoplanar IMRT fields when the patient was treated in the clinic. The second one is a brain tumor patient, where the target volume overlaps with the optic nerves and the chiasm and it is directly adjacent to the brainstem.Both cases illustrate that the large number of angles utilized by isocentric noncoplanar VMAT plans can help improve dose conformity, homogeneity, and organ sparing simultaneously using the same beam trajectory length and delivery time as a coplanar VMAT plan.

Medical Physics, 2014

ABSTRACT Purpose: To demonstrate a method for what-you-see-is-what-you-get multi-criteria Pareto ... more ABSTRACT Purpose: To demonstrate a method for what-you-see-is-what-you-get multi-criteria Pareto surface navigation for step and shoot IMRT treatment planning.

Medical Physics, 2015

Nonuniform spatiotemporal radiotherapy fractionation schemes, i.e., delivering distinct dose dist... more Nonuniform spatiotemporal radiotherapy fractionation schemes, i.e., delivering distinct dose distributions in different fractions can potentially improve the therapeutic ratio. This is possible if the dose distributions are designed such that similar doses are delivered to normal tissues (exploit the fractionation effect) while hypofractionating subregions of the tumor. In this paper, the authors develop methodology for treatment planning with nonuniform fractions and demonstrate this concept in the context of intensity-modulated proton therapy (IMPT). Treatment planning is performed by simultaneously optimizing (possibly distinct) IMPT dose distributions for multiple fractions. This is achieved using objective and constraint functions evaluated for the cumulative biologically equivalent dose (BED) delivered at the end of treatment. BED based treatment planning formulations lead to nonconvex optimization problems, such that local gradient based algorithms require adequate starting positions to find good local optima. To that end, the authors develop a combinatorial algorithm to initialize the pencil beam intensities. The concept of nonuniform spatiotemporal fractionation schemes is demonstrated for a spinal metastasis patient treated in two fractions using stereotactic body radiation therapy. The patient is treated with posterior oblique beams with the kidneys being located in the entrance region of the beam. It is shown that a nonuniform fractionation scheme that hypofractionates the central part of the tumor allows for a skin and kidney BED reduction of approximately 10%-20%. Nonuniform spatiotemporal fractionation schemes represent a novel approach to exploit fractionation effects that deserves further exploration for selected disease sites.

SIAM Journal on Optimization, 2014

Medical physics, 2015

Volumetric modulated arc therapy (VMAT) has found widespread clinical application in recent years... more Volumetric modulated arc therapy (VMAT) has found widespread clinical application in recent years. A large number of treatment planning studies have evaluated the potential for VMAT for different disease sites based on the currently available commercial implementations of VMAT planning. In contrast, literature on the underlying mathematical optimization methods used in treatment planning is scarce. VMAT planning represents a challenging large scale optimization problem. In contrast to fluence map optimization in intensity-modulated radiotherapy planning for static beams, VMAT planning represents a nonconvex optimization problem. In this paper, the authors review the state-of-the-art in VMAT planning from an algorithmic perspective. Different approaches to VMAT optimization, including arc sequencing methods, extensions of direct aperture optimization, and direct optimization of leaf trajectories are reviewed. Their advantages and limitations are outlined and recommendations for impro...

GigaScience, 2014

We provide common datasets (which we call the CORT dataset: common optimization for radiation the... more We provide common datasets (which we call the CORT dataset: common optimization for radiation therapy) that researchers can use when developing and contrasting radiation treatment planning optimization algorithms. The datasets allow researchers to make one-to-one comparisons of algorithms in order to solve various instances of the radiation therapy treatment planning problem in intensity modulated radiation therapy (IMRT), including beam angle optimization, volumetric modulated arc therapy and direct aperture optimization. We provide datasets for a prostate case, a liver case, a head and neck case, and a standard IMRT phantom. We provide the dose-influence matrix from a variety of beam/couch angle pairs for each dataset. The dose-influence matrix is the main entity needed to perform optimizations: it contains the dose to each patient voxel from each pencil beam. In addition, the original Digital Imaging and Communications in Medicine (DICOM) computed tomography (CT) scan, as well as...

Physics in Medicine and Biology, 2014

Purpose: In multi-stage radiotherapy, a patient is treated in several stages separated by weeks o... more Purpose: In multi-stage radiotherapy, a patient is treated in several stages separated by weeks or months. This regimen has been motivated mostly by radiobiological considerations, but also provides an approach to reduce normal tissue dose by exploiting tumor shrinkage. The paper considers the optimal design of multi-stage treatments, motivated by the clinical management of large liver tumors for which normal liver dose constraints prohibit the administration of an ablative radiation dose in a single treatment.

Medical Physics, 2014

ABSTRACT Purpose: In split-course radiotherapy, a patient is treated in several stages separated ... more ABSTRACT Purpose: In split-course radiotherapy, a patient is treated in several stages separated by weeks or months. This regimen has been motivated by radiobiological considerations. However, using modern image-guidance, it also provides an approach to reduce normal tissue dose by exploiting tumor shrinkage. In this work, we consider the optimal design of split-course treatments, motivated by the clinical management of large liver tumors for which normal liver dose constraints prohibit the administration of an ablative radiation dose in a single treatment.

Proceedings of the 2011 Winter Simulation Conference (WSC), 2011

An efficient method for the smooth estimation of the arrival rate of non-homogeneous, multi-dimen... more An efficient method for the smooth estimation of the arrival rate of non-homogeneous, multi-dimensional Poisson processes from inexact arrivals is presented. The method provides a piecewise polynomial spline estimator. It is easily parallelized, and it exploits the sparsity of the neighborhood structure of the underlying spline space; as a result, it is very efficient and scalable. Numerical illustration is included.

SIAM Journal on Optimization, 2013

We extend Nesterov's semidefinite programming characterization of squared functional systems, and... more We extend Nesterov's semidefinite programming characterization of squared functional systems, and Faybusovich's abstraction to bilinear symmetric maps, to cones of sum-of-squares elements in general abstract algebras. Using algebraic techniques such as isomorphism, linear isomorphism, tensor products, sums, and direct sums, we show that many concrete cones are in fact sum-of-squares cones with respect to some algebra and thus are representable by the cone of positive semidefinite matrices. We also consider nonnegativity with respect to a proper cone K and show that in some cases cones of K-nonnegative functions are either sum of squares or at least semidefinite representable. For example, we show that some well-known Chebyshev systems, when extended to Euclidean Jordan algebras, induce cones that are semidefinite representable. Finally we will discuss some concrete examples and applications, including minimum ellipsoid enclosing given space curves, minimization of eigenvalues of polynomial matrix pencils, approximation of functions by shapeconstrained functions, and approximation of combinatorial optimization problems by polynomial programming.

SIAM Journal on Optimization, 2013

ABSTRACT An optimization based method is proposed to generate moment matching scenarios for numer... more ABSTRACT An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming. The main advantage of the method is its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order, and the distribution can be defined over an arbitrary set. This allows for a reduction in the number of scenarios and allows the scenarios to be better tailored to the problem at hand. The method is based on a semi-infinite linear programming formulation of the problem that is shown to be solvable with polynomial iteration complexity. A practical column generation method is implemented. The column generation subproblems are polynomial optimization problems; however, they need not be solved to optimality. It is found that the columns in the column generation approach can be efficiently generated by random sampling. The number of scenarios generated matches a lower bound of Tchakaloff’s. The rate of convergence of the approximation error is established for continuous integrands, and an improved bound is given for smooth integrands. Extensive numerical experiments are presented in which variants of the proposed method are compared to Monte Carlo and quasi-Monte Carlo methods on both numerical integration problems and stochastic optimization problems. The benefits of being able to match any prescribed set of moments, rather than all moments up to a certain order, is also demonstrated using optimization problems with 100-dimensional random vectors. Empirical results show that the proposed approach outperforms Monte Carlo and quasi-Monte Carlo based approaches on the tested problems.

Medical Physics, 2014

The authors propose a novel optimization model for volumetric modulated arc therapy (VMAT) planni... more The authors propose a novel optimization model for volumetric modulated arc therapy (VMAT) planning that directly optimizes deliverable leaf trajectories in the treatment plan optimization problem, and eliminates the need for a separate arc-sequencing step. In this model, a 360° arc is divided into a given number of arc segments in which the leaves move unidirectionally. This facilitates an algorithm that determines the optimal piecewise linear leaf trajectories for each arc segment, which are deliverable in a given treatment time. Multileaf collimator constraints, including maximum leaf speed and interdigitation, are accounted for explicitly. The algorithm is customized to allow for VMAT delivery using constant gantry speed and dose rate, however, the algorithm generalizes to variable gantry speed if beneficial. The authors demonstrate the method for three different tumor sites: a head-and-neck case, a prostate case, and a paraspinal case. The authors first obtain a reference plan for intensity modulated radiotherapy (IMRT) using fluence map optimization and 20 intensity-modulated fields in equally spaced beam directions, which is beyond the standard of care. Modeling the typical clinical setup for the treatment sites considered, IMRT plans using seven or nine beams are also computed. Subsequently, VMAT plans are optimized by dividing the 360° arc into 20 corresponding arc segments. Assuming typical machine parameters (a dose rate of 600 MU/min, and a maximum leaf speed of 3 cm/s), it is demonstrated that the optimized VMAT plans with 2-3 min delivery time are of noticeably better quality than the 7-9 beam IMRT plans. The VMAT plan quality approaches the quality of the 20-beam IMRT benchmark plan for delivery times between 3 and 4 min. The results indicate that high quality treatments can be delivered in a single arc with 20 arc segments if sufficient time is allowed for modulation in each segment.

Medical Physics, 2014

To describe a method for combining sliding window plans [intensity modulated radiation therapy (I... more To describe a method for combining sliding window plans [intensity modulated radiation therapy (IMRT) or volumetric modulated arc therapy (VMAT)] for use in treatment plan averaging, which is needed for Pareto surface navigation based multicriteria treatment planning. The authors show that by taking an appropriately defined average of leaf trajectories of sliding window plans, the authors obtain a sliding window plan whose fluence map is the exact average of the fluence maps corresponding to the initial plans. In the case of static-beam IMRT, this also implies that the dose distribution of the averaged plan is the exact dosimetric average of the initial plans. In VMAT delivery, the dose distribution of the averaged plan is a close approximation of the dosimetric average of the initial plans. The authors demonstrate the method on three Pareto optimal VMAT plans created for a demanding paraspinal case, where the tumor surrounds the spinal cord. The results show that the leaf averaged plans yield dose distributions that approximate the dosimetric averages of the precomputed Pareto optimal plans well. The proposed method enables the navigation of deliverable Pareto optimal plans directly, i.e., interactive multicriteria exploration of deliverable sliding window IMRT and VMAT plans, eliminating the need for a sequencing step after navigation and hence the dose degradation that is caused by such a sequencing step.

Medical Physics

Purpose: Non-uniform fractionation, i.e. delivering distinct dose distributions in two subsequent... more Purpose: Non-uniform fractionation, i.e. delivering distinct dose distributions in two subsequent fractions, can potentially improve outcomes by increasing biological dose to the target without increasing dose to healthy tissues. This is possible if both fractions deliver a similar dose to normal tissues (exploit the fractionation effect) but high single fraction doses to subvolumes of the target (hypofractionation). Optimization of such treatment plans can be formulated using biological equivalent dose (BED), but leads to intractable nonconvex optimization problems. We introduce a novel optimization approach to address this challenge.

The main approach to smooth Pareto surface navigation for radiation therapy multi-criteria treatm... more The main approach to smooth Pareto surface navigation for radiation therapy multi-criteria treatment planning involves taking real-time averages of pre-computed treatment plans. In fluence-based treatment planning, fluence maps themselves can be averaged, which leads to the dose distributions being averaged due to the linear relationship between fluence and dose. This works for fluence-based photon plans and proton spot scanning plans. In this technical note, we show that two or more sliding window volumetric modulated arc therapy (VMAT) plans can be combined by averaging leaf positions in a certain way, and we demonstrate that the resulting dose distribution for the averaged plan is approximately the average of the dose distributions of the original plans. This leads to the ability to do Pareto surface navigation, i.e. interactive multi-criteria exploration of VMAT plan dosimetric tradeoffs.

Treating a realistic problem in any field of reaction kinetics raises a series of problems: we re... more Treating a realistic problem in any field of reaction kinetics raises a series of problems: we review these illustrated with examples using ReactionKinetics, a Mathematica based package.

Physics in Medicine and Biology, 2015

Utilizing noncoplanar beam angles in volumetric modulated arc therapy (VMAT) has the potential to... more Utilizing noncoplanar beam angles in volumetric modulated arc therapy (VMAT) has the potential to combine the benefits of arc therapy, such as short treatment times, with the benefits of noncoplanar intensity modulated radiotherapy (IMRT) plans, such as improved organ sparing. Recently, vendors introduced treatment machines that allow for simultaneous couch and gantry motion during beam delivery to make noncoplanar VMAT treatments possible. Our aim is to provide a reliable optimization method for noncoplanar isocentric arc therapy plan optimization. The proposed solution is modular in the sense that it can incorporate different existing beam angle selection and coplanar arc therapy optimization methods.Treatment planning is performed in three steps. First, a number of promising noncoplanar beam directions are selected using an iterative beam selection heuristic; these beams serve as anchor points of the arc therapy trajectory. In the second step, continuous gantry/couch angle trajectories are optimized using a simple combinatorial optimization model to define a beam trajectory that efficiently visits each of the anchor points. Treatment time is controlled by limiting the time the beam needs to trace the prescribed trajectory. In the third and final step, an optimal arc therapy plan is found along the prescribed beam trajectory. In principle any existing arc therapy optimization method could be incorporated into this step; for this work we use a sliding window VMAT algorithm.The approach is demonstrated using two particularly challenging cases. The first one is a lung SBRT patient whose planning goals could not be satisfied with fewer than nine noncoplanar IMRT fields when the patient was treated in the clinic. The second one is a brain tumor patient, where the target volume overlaps with the optic nerves and the chiasm and it is directly adjacent to the brainstem.Both cases illustrate that the large number of angles utilized by isocentric noncoplanar VMAT plans can help improve dose conformity, homogeneity, and organ sparing simultaneously using the same beam trajectory length and delivery time as a coplanar VMAT plan.

Medical Physics, 2014

ABSTRACT Purpose: To demonstrate a method for what-you-see-is-what-you-get multi-criteria Pareto ... more ABSTRACT Purpose: To demonstrate a method for what-you-see-is-what-you-get multi-criteria Pareto surface navigation for step and shoot IMRT treatment planning.

Medical Physics, 2015

Nonuniform spatiotemporal radiotherapy fractionation schemes, i.e., delivering distinct dose dist... more Nonuniform spatiotemporal radiotherapy fractionation schemes, i.e., delivering distinct dose distributions in different fractions can potentially improve the therapeutic ratio. This is possible if the dose distributions are designed such that similar doses are delivered to normal tissues (exploit the fractionation effect) while hypofractionating subregions of the tumor. In this paper, the authors develop methodology for treatment planning with nonuniform fractions and demonstrate this concept in the context of intensity-modulated proton therapy (IMPT). Treatment planning is performed by simultaneously optimizing (possibly distinct) IMPT dose distributions for multiple fractions. This is achieved using objective and constraint functions evaluated for the cumulative biologically equivalent dose (BED) delivered at the end of treatment. BED based treatment planning formulations lead to nonconvex optimization problems, such that local gradient based algorithms require adequate starting positions to find good local optima. To that end, the authors develop a combinatorial algorithm to initialize the pencil beam intensities. The concept of nonuniform spatiotemporal fractionation schemes is demonstrated for a spinal metastasis patient treated in two fractions using stereotactic body radiation therapy. The patient is treated with posterior oblique beams with the kidneys being located in the entrance region of the beam. It is shown that a nonuniform fractionation scheme that hypofractionates the central part of the tumor allows for a skin and kidney BED reduction of approximately 10%-20%. Nonuniform spatiotemporal fractionation schemes represent a novel approach to exploit fractionation effects that deserves further exploration for selected disease sites.

SIAM Journal on Optimization, 2014

Medical physics, 2015

Volumetric modulated arc therapy (VMAT) has found widespread clinical application in recent years... more Volumetric modulated arc therapy (VMAT) has found widespread clinical application in recent years. A large number of treatment planning studies have evaluated the potential for VMAT for different disease sites based on the currently available commercial implementations of VMAT planning. In contrast, literature on the underlying mathematical optimization methods used in treatment planning is scarce. VMAT planning represents a challenging large scale optimization problem. In contrast to fluence map optimization in intensity-modulated radiotherapy planning for static beams, VMAT planning represents a nonconvex optimization problem. In this paper, the authors review the state-of-the-art in VMAT planning from an algorithmic perspective. Different approaches to VMAT optimization, including arc sequencing methods, extensions of direct aperture optimization, and direct optimization of leaf trajectories are reviewed. Their advantages and limitations are outlined and recommendations for impro...

GigaScience, 2014

We provide common datasets (which we call the CORT dataset: common optimization for radiation the... more We provide common datasets (which we call the CORT dataset: common optimization for radiation therapy) that researchers can use when developing and contrasting radiation treatment planning optimization algorithms. The datasets allow researchers to make one-to-one comparisons of algorithms in order to solve various instances of the radiation therapy treatment planning problem in intensity modulated radiation therapy (IMRT), including beam angle optimization, volumetric modulated arc therapy and direct aperture optimization. We provide datasets for a prostate case, a liver case, a head and neck case, and a standard IMRT phantom. We provide the dose-influence matrix from a variety of beam/couch angle pairs for each dataset. The dose-influence matrix is the main entity needed to perform optimizations: it contains the dose to each patient voxel from each pencil beam. In addition, the original Digital Imaging and Communications in Medicine (DICOM) computed tomography (CT) scan, as well as...

Physics in Medicine and Biology, 2014

Purpose: In multi-stage radiotherapy, a patient is treated in several stages separated by weeks o... more Purpose: In multi-stage radiotherapy, a patient is treated in several stages separated by weeks or months. This regimen has been motivated mostly by radiobiological considerations, but also provides an approach to reduce normal tissue dose by exploiting tumor shrinkage. The paper considers the optimal design of multi-stage treatments, motivated by the clinical management of large liver tumors for which normal liver dose constraints prohibit the administration of an ablative radiation dose in a single treatment.

Medical Physics, 2014

ABSTRACT Purpose: In split-course radiotherapy, a patient is treated in several stages separated ... more ABSTRACT Purpose: In split-course radiotherapy, a patient is treated in several stages separated by weeks or months. This regimen has been motivated by radiobiological considerations. However, using modern image-guidance, it also provides an approach to reduce normal tissue dose by exploiting tumor shrinkage. In this work, we consider the optimal design of split-course treatments, motivated by the clinical management of large liver tumors for which normal liver dose constraints prohibit the administration of an ablative radiation dose in a single treatment.

Proceedings of the 2011 Winter Simulation Conference (WSC), 2011

An efficient method for the smooth estimation of the arrival rate of non-homogeneous, multi-dimen... more An efficient method for the smooth estimation of the arrival rate of non-homogeneous, multi-dimensional Poisson processes from inexact arrivals is presented. The method provides a piecewise polynomial spline estimator. It is easily parallelized, and it exploits the sparsity of the neighborhood structure of the underlying spline space; as a result, it is very efficient and scalable. Numerical illustration is included.

SIAM Journal on Optimization, 2013

We extend Nesterov's semidefinite programming characterization of squared functional systems, and... more We extend Nesterov's semidefinite programming characterization of squared functional systems, and Faybusovich's abstraction to bilinear symmetric maps, to cones of sum-of-squares elements in general abstract algebras. Using algebraic techniques such as isomorphism, linear isomorphism, tensor products, sums, and direct sums, we show that many concrete cones are in fact sum-of-squares cones with respect to some algebra and thus are representable by the cone of positive semidefinite matrices. We also consider nonnegativity with respect to a proper cone K and show that in some cases cones of K-nonnegative functions are either sum of squares or at least semidefinite representable. For example, we show that some well-known Chebyshev systems, when extended to Euclidean Jordan algebras, induce cones that are semidefinite representable. Finally we will discuss some concrete examples and applications, including minimum ellipsoid enclosing given space curves, minimization of eigenvalues of polynomial matrix pencils, approximation of functions by shapeconstrained functions, and approximation of combinatorial optimization problems by polynomial programming.

SIAM Journal on Optimization, 2013

ABSTRACT An optimization based method is proposed to generate moment matching scenarios for numer... more ABSTRACT An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming. The main advantage of the method is its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order, and the distribution can be defined over an arbitrary set. This allows for a reduction in the number of scenarios and allows the scenarios to be better tailored to the problem at hand. The method is based on a semi-infinite linear programming formulation of the problem that is shown to be solvable with polynomial iteration complexity. A practical column generation method is implemented. The column generation subproblems are polynomial optimization problems; however, they need not be solved to optimality. It is found that the columns in the column generation approach can be efficiently generated by random sampling. The number of scenarios generated matches a lower bound of Tchakaloff’s. The rate of convergence of the approximation error is established for continuous integrands, and an improved bound is given for smooth integrands. Extensive numerical experiments are presented in which variants of the proposed method are compared to Monte Carlo and quasi-Monte Carlo methods on both numerical integration problems and stochastic optimization problems. The benefits of being able to match any prescribed set of moments, rather than all moments up to a certain order, is also demonstrated using optimization problems with 100-dimensional random vectors. Empirical results show that the proposed approach outperforms Monte Carlo and quasi-Monte Carlo based approaches on the tested problems.

Medical Physics, 2014

The authors propose a novel optimization model for volumetric modulated arc therapy (VMAT) planni... more The authors propose a novel optimization model for volumetric modulated arc therapy (VMAT) planning that directly optimizes deliverable leaf trajectories in the treatment plan optimization problem, and eliminates the need for a separate arc-sequencing step. In this model, a 360° arc is divided into a given number of arc segments in which the leaves move unidirectionally. This facilitates an algorithm that determines the optimal piecewise linear leaf trajectories for each arc segment, which are deliverable in a given treatment time. Multileaf collimator constraints, including maximum leaf speed and interdigitation, are accounted for explicitly. The algorithm is customized to allow for VMAT delivery using constant gantry speed and dose rate, however, the algorithm generalizes to variable gantry speed if beneficial. The authors demonstrate the method for three different tumor sites: a head-and-neck case, a prostate case, and a paraspinal case. The authors first obtain a reference plan for intensity modulated radiotherapy (IMRT) using fluence map optimization and 20 intensity-modulated fields in equally spaced beam directions, which is beyond the standard of care. Modeling the typical clinical setup for the treatment sites considered, IMRT plans using seven or nine beams are also computed. Subsequently, VMAT plans are optimized by dividing the 360° arc into 20 corresponding arc segments. Assuming typical machine parameters (a dose rate of 600 MU/min, and a maximum leaf speed of 3 cm/s), it is demonstrated that the optimized VMAT plans with 2-3 min delivery time are of noticeably better quality than the 7-9 beam IMRT plans. The VMAT plan quality approaches the quality of the 20-beam IMRT benchmark plan for delivery times between 3 and 4 min. The results indicate that high quality treatments can be delivered in a single arc with 20 arc segments if sufficient time is allowed for modulation in each segment.

Medical Physics, 2014

To describe a method for combining sliding window plans [intensity modulated radiation therapy (I... more To describe a method for combining sliding window plans [intensity modulated radiation therapy (IMRT) or volumetric modulated arc therapy (VMAT)] for use in treatment plan averaging, which is needed for Pareto surface navigation based multicriteria treatment planning. The authors show that by taking an appropriately defined average of leaf trajectories of sliding window plans, the authors obtain a sliding window plan whose fluence map is the exact average of the fluence maps corresponding to the initial plans. In the case of static-beam IMRT, this also implies that the dose distribution of the averaged plan is the exact dosimetric average of the initial plans. In VMAT delivery, the dose distribution of the averaged plan is a close approximation of the dosimetric average of the initial plans. The authors demonstrate the method on three Pareto optimal VMAT plans created for a demanding paraspinal case, where the tumor surrounds the spinal cord. The results show that the leaf averaged plans yield dose distributions that approximate the dosimetric averages of the precomputed Pareto optimal plans well. The proposed method enables the navigation of deliverable Pareto optimal plans directly, i.e., interactive multicriteria exploration of deliverable sliding window IMRT and VMAT plans, eliminating the need for a sequencing step after navigation and hence the dose degradation that is caused by such a sequencing step.