[Show abstract][Hide abstract] ABSTRACT: 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.
Physics in Medicine and Biology 06/2015; 60(13):5179-5198. DOI:10.1088/0031-9155/60/13/5179 · 2.76 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Range and set-up uncertainties in intensity-modulated proton therapy cannot be addressed with margins. Instead, several robust optimization (RO) models have been developed that explicitly take uncertainty into account. RO optimizes the worst case at the cost of the treatment outcome in more likely scenarios. The goal is to provide insight in the trade-off between robustness and plan quality and the behavior of different trade-off methods.
We present four methods to trade-off robustness with plan quality that can be applied to any of the worst case methods found in literature. Each trade-off is a mixture between worst case, expected value, and non-robust planning, which effectively corresponds to assigning different importance weights to error scenarios. Each method is tested on several worst case methods for a sarcoma case, a paraspinal case and a benchmark case from literature.
Each trade-off method yields a unique dose distribution in the border region between target volume and adjacent normal tissues, corresponding to a specific trade-off between robustness and nominal plan quality. The fully robust solutions perform badly when the realized errors are smaller than the maximum projected errors. Compared to fully robust solutions, significant improvements are possible for non-extreme scenarios while only slightly deteriorating plan quality at an extreme scenario. It is further observed that trade-off methods cannot be mimicked by putting different weights on objectives for the tumor and the normal tissue.
The method to trade-off robustness with plan quality should be chosen carefully, as each method has a different impact on plan quality. Two of the methods can directly be implemented in any framework for multicriteria optimization, hopefully leading to their quick dissemination.
Medical Physics 06/2015; 42(6):3494. DOI:10.1118/1.4925047 · 2.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Cell survival experiments suggest that the relative biological effectiveness (RBE) of proton beams depends on linear energy transfer (LET), leading to higher RBE near the end of range. With intensity-modulated proton therapy (IMPT), multiple treatment plans that differ in the dose contribution per field may yield a similar physical dose distribution, but the RBE-weighted dose distribution may be disparate. RBE models currently do not have the required predictive power to be included in an optimization model due to the variations in experimental data. We propose an LET-based planning method that guides IMPT optimization models towards plans with reduced RBE-weighted dose in surrounding organs at risk (OARs) compared to inverse planning based on physical dose alone.
Optimization models for physical dose are extended with a term for dose times LET (doseLET). Monte Carlo code is used to generate the physical dose and doseLET distribution of each individual pencil beam. The method is demonstrated for an atypical meningioma patient where the target volume abuts the brainstem and partially overlaps with the optic nerve.
A reference plan optimized based on physical dose alone yields high doseLET values in parts of the brainstem and optic nerve. Minimizing doseLET in these critical structures as an additional planning goal reduces the risk of high RBE-weighted dose. The resulting treatment plan avoids the distal fall-off of the Bragg peaks for shaping the dose distribution in front of critical stuctures. The maximum dose in the OARs evaluated with RBE models from literature is reduced by 8-14\% with our method compared to conventional planning.
LET-based inverse planning for IMPT offers the ability to reduce the RBE-weighted dose in OARs without sacrificing target dose. This project was in part supported by NCI - U19 CA 21239.
Medical Physics 06/2015; 42(6):3616. DOI:10.1118/1.4925663 · 2.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Fractionation decisions in radiotherapy face the tradeoff between increasing the number of fractions to spare normal tissues, and increasing the total dose to achieve the same effect in the target volume. In that regard, the ideal treatment would fractionate in normal tissues while simultaneously hypo-fractionating in the target. Interestingly, this is possible to a limited degree by delivering distinct dose distributions in different fractions. The dose distributions have to be designed such that similar doses are delivered to normal tissues while delivering high single fraction doses to parts of the target. We demonstrate that this concept may lead to an improved therapeutic ratio for rotation therapy treatments using conventional photon beams.
Fractionation effects are modeled via the biologically equivalent dose (BED) model. Treatment plan optimization is performed using objective functions evaluated for the cumulative BED delivered at the end of treatment. This allows for simultaneously optimizing multiple distinct treatment plans for different fractions.
The concept is demonstrated for large cerebral arteriovenous malformations (AVM) treated in two fractions. It is shown that the optimal treatment delivers a large dose to the center of the AVM in the first fraction. The second fraction delivers the missing dose to the rim of the target volume. The target is divided into center and rim in such a way that the dose received by normal brain adjacent to the AVM is approximately equal in both fractions.
The BED in the target can be increased by hypo-fractionating the central core. Since the fractionation effect is exploited in the normal tissue, this leads to an improved therapeutic ratio overall. The approach may potentially be beneficial for large AVMs or tumors embedded in a dose-limiting normal tissue treated with stereotactic regimens.
Medical Physics 06/2015; 42(6):3741. DOI:10.1118/1.4926297 · 2.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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 the DICOM structure file, are provided for each case.
Here we present an open dataset - the first of its kind - to the radiation oncology community, which will allow researchers to compare methods for optimizing radiation dose delivery.
[Show abstract][Hide abstract] ABSTRACT: 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.
Medical Physics 05/2015; 42(5):2234-2241. DOI:10.1118/1.4916684 · 2.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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 improvements are discussed.
Medical Physics 03/2015; 42(3):1367. DOI:10.1118/1.4908224 · 2.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
Medical Physics 06/2014; 41(6):354-354. DOI:10.1118/1.4888884 · 2.64 Impact Factor
[Show abstract][Hide abstract] 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.
Medical Physics 06/2014; 41(6):569-569. DOI:10.1118/1.4889665 · 2.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Glioblastoma are known to infiltrate the brain parenchyma instead of forming
a solid tumor mass with a defined boundary. Only the part of the tumor with
high tumor cell density can be localized through imaging directly. In contrast,
brain tissue infiltrated by tumor cells at low density appears normal on
current imaging modalities. In clinical practice, a uniform margin is applied
to account for microscopic spread of disease.
The current treatment planning procedure can potentially be improved by
accounting for the anisotropy of tumor growth: Anatomical barriers such as the
falx cerebri represent boundaries for migrating tumor cells. In addition, tumor
cells primarily spread in white matter and infiltrate gray matter at lower
rate. We investigate the use of a phenomenological tumor growth model for
treatment planning. The model is based on the Fisher-Kolmogorov equation, which
formalizes these growth characteristics and estimates the spatial distribution
of tumor cells in normal appearing regions of the brain. The target volume for
radiotherapy planning can be defined as an isoline of the simulated tumor cell
A retrospective study involving 10 glioblastoma patients has been performed.
To illustrate the main findings of the study, a detailed case study is
presented for a glioblastoma located close to the falx. In this situation, the
falx represents a boundary for migrating tumor cells, whereas the corpus
callosum provides a route for the tumor to spread to the contralateral
hemisphere. We further discuss the sensitivity of the model with respect to the
input parameters. Correct segmentation of the brain appears to be the most
crucial model input.
We conclude that the tumor growth model provides a method to account for
anisotropic growth patterns of glioblastoma, and may therefore provide a tool
to make target delineation more objective and automated.
Physics in Medicine and Biology 02/2014; 59(3):747-70. DOI:10.1088/0031-9155/59/3/747 · 2.76 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Gliomas differ from many other tumors as they grow infiltratively into the brain parenchyma rather than forming a solid tumor mass with a well-defined boundary. Tumor cells can be found several centimeters away from the central tumor mass that is visible using current imaging techniques. The infiltrative growth characteristics of gliomas question the concept of a radiotherapy target volume that is irradiated to a homogeneous dose-the standard in current clinical practice. We discuss the use of the Fisher-Kolmogorov glioma growth model in radiotherapy treatment planning. The phenomenological tumor growth model assumes that tumor cells proliferate locally and migrate into neighboring brain tissue, which is mathematically described via a partial differential equation for the spatio-temporal evolution of the tumor cell density. In this model, the tumor cell density drops approximately exponentially with distance from the visible gross tumor volume, which is quantified by the infiltration length, a parameter describing the distance at which the tumor cell density drops by a factor of e. This paper discusses the implications for the prescribed dose distribution in the periphery of the tumor. In the context of the exponential cell kill model, an exponential fall-off of the cell density suggests a linear fall-off of the prescription dose with distance. We introduce the dose fall-off rate, which quantifies the steepness of the prescription dose fall-off in units of Gy mm(-1). It is shown that the dose fall-off rate is given by the inverse of the product of radiosensitivity and infiltration length. For an infiltration length of 3 mm and a surviving fraction of 50% at 2 Gy, this suggests a dose fall-off of approximately 1 Gy mm(-1). The concept is illustrated for two glioblastoma patients by optimizing intensity-modulated radiotherapy plans. The dose fall-off rate concept reflects the idea that infiltrating gliomas lack a defined boundary and are characterized by a continuous fall-off of the density of infiltrating tumor cells. The approach can potentially be used to individualize the prescribed dose distribution if better methods to estimate radiosensitivity and infiltration length on a patient by patient basis become available.
Physics in Medicine and Biology 02/2014; 59(3):771-89. DOI:10.1088/0031-9155/59/3/771 · 2.76 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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 02/2014; 41(2):021709. DOI:10.1118/1.4859295 · 2.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In concurrent chemoradiotherapy, chemotherapeutic agents are administered
during the course of radiotherapy to enhance the primary tumor control.
However, that often comes at the expense of increased risk of normal-tissue
complications. The additional biological damage is mainly attributed to two
mechanisms of action, which are the independent cytotoxic activity of
chemotherapeutic agents and their interactive cooperation with radiation. The
goal of this study is to develop a mathematical framework to obtain drug and
radiation administration schedules that maximize the therapeutic gain for
concurrent chemoradiotherapy. In particular, we analyze the impact of
incorporating these two mechanisms into the radiation fractionation problem.
Considering each mechanism individually, we first derive closed-form
expressions for the optimal radiation fractionation regimen and the
corresponding drug administration schedule. We next study the case in which
both mechanisms are simultaneously present and develop a dynamic programming
framework to determine optimal treatment regimens. Results show that those
chemotherapeutic agents that interact with radiation may change optimal
radiation fractionation regimens. Moreover, administration of chemotherapeutic
agents possessing both mechanisms may give rise to non-stationary radiation
[Show abstract][Hide abstract] ABSTRACT: We analyze the effect of tumor repopulation on optimal dose delivery in
radiation therapy. We are primarily motivated by accelerated tumor repopulation
towards the end of radiation treatment, which is believed to play a role in
treatment failure for some tumor sites. A dynamic programming framework is
developed to determine an optimal fractionation scheme based on a model of cell
kill due to radiation and tumor growth in between treatment days. We find that
faster tumor growth suggests shorter overall treatment duration. In addition,
the presence of accelerated repopulation suggests larger dose fractions later
in the treatment to compensate for the increased tumor proliferation. We prove
that the optimal dose fractions are increasing over time. Numerical simulations
indicate potential for improvement in treatment effectiveness.
[Show abstract][Hide abstract] ABSTRACT: 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.
We introduce a dynamic tumor model that incorporates three factors: radiation
induced cell kill, tumor shrinkage, and tumor cell repopulation. The design of
multi-stage radiotherapy is formulated as a mathematical optimization problem
in which the total dose to the liver is minimized, subject to delivering the
prescribed dose to the tumor. Based on the model, we gain insight into the
optimal administration of radiation over time, i.e. the optimal treatment gaps
and dose levels.
We analyze treatments consisting of two stages in detail. The analysis
confirms the intuition that the second stage should be delivered just before
the tumor size reaches a minimum and repopulation overcompensates shrinking.
Furthermore, it was found that, for a large range of model parameters,
approximately one third of the dose should be delivered in the first stage. The
projected benefit of multi-stage treatments depends on model assumptions.
However, the model predicts large liver dose reductions by more than a factor
of two for plausible model parameters.
The analysis of the tumor model suggests that substantial reduction in normal
tissue dose can be achieved by exploiting tumor shrinkage via an optimal design
of multi-stage treatments. This suggests taking a fresh look at multi-stage
radiotherapy for selected disease sites where substantial tumor regression
translates into reduced target volumes.
Physics in Medicine and Biology 11/2013; 59(12). DOI:10.1088/0031-9155/59/12/3059 · 2.76 Impact Factor