Equivalent Uniform Dose Constraints Research Articles

A comparative study of volumetric modulated arc therapy plans based on the equivalent uniform dose optimization for left-sided breast cancer

PurposeTo investigate the effect of equivalent uniform dose (EUD)-based optimization on radiotherapy planning for left-sided breast cancer after mastectomy. MethodsTwelve patients treated with left-sided breast cancer using volumetric modulated arc therapy (VMAT) were retrospectively enrolled in this study. Four plans were generated for each patient. Plan A was optimized based on only physical parameters. EUD with α > 0 to organ at risk (OARs) was added in Plan B on the basis of Plan A; EUD with α < 0 to planning tumor volume (PTV) was added in Plan C on the basis of Plan A; EUD constraints were added for both OARs and PTV in Plan D. The quality of plans was evaluated in terms of Vx (volume percent of PTV or OARs received xGy dose), Dx (dose received by volume above x% of PTV or OARs), conformity index (CI), mean dose (Dmean), maximum dose (Dmax) and minimum dose (Dmin). ResultsFor PTV: Plan A vs. Plan B, the difference of D2 and CI was statistically significant (P < 0.05); Plan A vs. Plan C, the differences in D98, Dmean and HI were statistically significant (P < 0.05); Plan A vs. Plan D, differences in D2, Dmean and HI were statistically significant (P < 0.05). For OARs: Plan A vs. Plan B, and Plan A vs. Plan D, the differences in V5, V10, V20, V30, Dmean of the left lung and V10, V20, V30, Dmean of the heart were statistically significant (P < 0.05), the differences in Dmean of the thyroid and contralateral breast and the D2 and Dmax of spinal cord and spinal cord planning risk volume (PRV) were statistically significant (P < 0.05); Plan A vs. Plan C, only the difference in Dmax of spinal cord was statistically significant (P < 0.05). ConclusionCompared with DV condition, the dosimetric data with EUD-based optimization for OARs and PTV confer advantages in terms of the mean dose region of the left lung, heart, thyroid and contralateral (right) breast and the maximum dose of the spinal cord, and the improvement of the conformity and homogeneity of the target.

Image-guided adaptive brachytherapy dose escalation for cervix cancer via fractionation compensation

PurposeIn image-guided adaptive brachytherapy (IGABT), dose distributions are optimized for each fraction. Optimum fractional dose can be constant or adapted to previous fractions and a conjecture about the future ones. We evaluate the efficacy of different fraction size schemes, derived from total IGABT dose constraints, against constant per-fraction constraints. Methods and MaterialsThis retrospective planning study included 20 IGABT patients where four different fractionation schedules were compared based on modern planning recommendations. A total high-risk–clinical target volume D90 (minimum dose in 90% of the volume) dose aim of 90.0 Gy with constant per-fraction organs at risk (OARs) dose constraint planning (CONST) was compared with conservative and aggressive fractionation compensation (COMP) techniques. COMP allows variations in the per-fraction dose constraints. Dose accumulation was performed through dose summation at a given volume and equivalent uniform dose (EUD) worst-case dose estimates. ResultsNo significant differences were identifiable between dose metrics of CONST and COMP in the total patient population. However, a subgroup of patients with alternating dose-limiting OARs had significant benefit from COMP. Median high-risk–clinical target volume dose escalation ranged from 5% to 12%, whereas OAR dose increases were lower and ranged from 3% to 8%. EUD-based planning delivered similar tumor doses, although slightly lower OAR doses. By distributing the treatment aim over an increased number of treatment fractions, median tumor dose could be increased by a further 8% per additional treatment fraction at the same OAR dose levels for both CONST and COMP. ConclusionsCOMP is effective in patients with alternating dose-limiting OARs and is enhanced using more treatment fractions and EUD constraints.

The benefit of using bladder sub-volume equivalent uniform dose constraints in prostate intensity-modulated radiotherapy planning.

BackgroundTo assess the benefits of bladder wall sub-volume equivalent uniform dose (EUD) constraints in prostate cancer intensity-modulated radiotherapy (IMRT) planning.MethodsTwo IMRT plans, with and without EUD constraints on the bladder wall, were generated using beams that deliver 80 Gy to the prostate and 46 Gy to the seminal vesicles and were compared in 53 prostate cancer patients. The bladder wall was defined as the volume between the external manually delineated wall and a contraction of 7 mm apart from it. The bladder wall was then separated into two parts: the internal-bladder wall (bla-in) represented by the portion of the bladder wall that intersected with the planning target volume (PTV) plus 5 mm extension; the external-bladder wall (bla-ex) represented by the remaining part of the bladder wall. In the IMRT plan with EUD constraints, the values of “a” parameter for the EUD models were 10.0 for bla-in and 2.3 for bla-ex. The plans with and without EUD constraints were compared in terms of dose–volume histograms, 5-year bladder and rectum normal tissue complication probability values, as well as tumor control probability (TCP) values.ResultsThe use of bladder sub-volume EUD constraints decreased both the doses to the bladder wall (V70: 22.76% vs 19.65%, Dmean: 39.82 Gy vs 35.45 Gy) and the 5-year bladder complication probabilities (≥LENT/SOMA Grade 2: 20.35% vs 17.96%; bladder bleeding: 10.63% vs 8.64%). The doses to the rectum wall and the rectum complication probabilities were also slightly decreased by the EUD constraints compared to physical constraints only. The minimal dose and the V76Gy of PTVprostate were, however, slightly decreased by EUD optimization, nevertheless without significant difference in TCP values between the two plans, and the PTV parameters finally respected the Groupe d’Etude des Tumeurs Uro-Génitales recommendations.ConclusionSeparating the bladder wall into two parts with appropriate EUD optimization may reduce bladder toxicity in prostate IMRT. Combining biological constraints with physical constraints in the organs at risk at the inverse planning step of IMRT may improve the dose distribution.

EUD-based biological optimization for carbon ion therapy.

Treatment planning for carbon ion therapy requires an accurate modeling of the biological response of each tissue to estimate the clinical outcome of a treatment. The relative biological effectiveness (RBE) accounts for this biological response on a cellular level but does not refer to the actual impact on the organ as a whole. For photon therapy, the concept of equivalent uniform dose (EUD) represents a simple model to take the organ response into account, yet so far no formulation of EUD has been reported that is suitable to carbon ion therapy. The authors introduce the concept of an equivalent uniform effect (EUE) that is directly applicable to both ion and photon therapies and exemplarily implemented it as a basis for biological treatment plan optimization for carbon ion therapy. In addition to a classical EUD concept, which calculates a generalized mean over the RBE-weighted dose distribution, the authors propose the EUE to simplify the optimization process of carbon ion therapy plans. The EUE is defined as the biologically equivalent uniform effect that yields the same probability of injury as the inhomogeneous effect distribution in an organ. Its mathematical formulation is based on the generalized mean effect using an effect-volume parameter to account for different organ architectures and is thus independent of a reference radiation. For both EUD concepts, quadratic and logistic objective functions are implemented into a research treatment planning system. A flexible implementation allows choosing for each structure between biological effect constraints per voxel and EUD constraints per structure. Exemplary treatment plans are calculated for a head-and-neck patient for multiple combinations of objective functions and optimization parameters. Treatment plans optimized using an EUE-based objective function were comparable to those optimized with an RBE-weighted EUD-based approach. In agreement with previous results from photon therapy, the optimization by biological objective functions resulted in slightly superior treatment plans in terms of final EUD for the organs at risk (OARs) compared to voxel-based optimization approaches. This observation was made independent of the underlying objective function metric. An absolute gain in OAR sparing was observed for quadratic objective functions, whereas intersecting DVHs were found for logistic approaches. Even for considerable under- or overestimations of the used effect- or dose-volume parameters during the optimization, treatment plans were obtained that were of similar quality as the results of a voxel-based optimization. EUD-based optimization with either of the presented concepts can successfully be applied to treatment plan optimization. This makes EUE-based optimization for carbon ion therapy a useful tool to optimize more specifically in the sense of biological outcome while voxel-to-voxel variations of the biological effectiveness are still properly accounted for. This may be advantageous in terms of computational cost during treatment plan optimization but also enables a straight forward comparison of different fractionation schemes or treatment modalities.

SU‐E‐P‐42: Benefit of Equivalent Uniform Dose in Prostate IMRT Planning to Reduce Bladder Toxicity

Purpose:To assess the benefit of bladder wall sub‐volume equivalent uniform dose (EUD) constrains in prostate cancer IMRT planningMethods:The bladder wall was defined by the volume between the external manually delineated wall and a contraction of 7 mm from this external wall. This bladder wall was then separated into two parts: the internal‐bladder wall (bla‐in) represented by the portion of the bladder wall that intersected with the planning target volume (PTV) plus 5 mm extension; the external‐bladder wall (bla‐ex) represented by the remaining part of the bladder wall. Two IMRT plans, with and without using EUD constraints, were generated and compared for 53 prostate cancer patients, to deliver 80Gy to the prostate PTV (V95&gt;95%). In the plan with EUD constraints, the values of the “a” parameter of the EUD models were: 10.0 for bla‐in and 2.3 for bla‐ex., and 5 for the rectum.Results:The use of bladder EUD objectives increased significantly the conformal index (0.73±0.04 vs. 0.93±0.02) and decreased both the doses in the bladder wall (V70: 22.66% vs. 18.88%, Dmean: 39.40Gy vs. 35.04Gy) and the bladder wall NTCP values (NTCP at 3 years bladder toxicity &gt;= LENT/SOMA Grade2: 16.68% vs. 14.48%, NTCP at 3 years bladder bleeding: 7.16% vs. 5.88%, NTCP at 5 years bladder toxicity &gt;= LENT/SOMA Grade2: 20.15% vs. 17.75%, NTCP at 5 years bladder bleeding: 10.38% vs. 8.36%). The use of bladder EUD objectives, although slightly decreasing the dose to the rectum wall (Dmax: 75.19Gy vs. 75.05Gy, V72: 12.95Gy vs. 12.72Gy) as well, increased however the dose in the femoral heads (V55‐femoral head left: 0.06% vs. 0.30%, V55‐femoral head right: 0.04% vs. 0.21%).Conclusion:Separating bladder wall into two parts with appropriate bladder EUD objectives may reduce bladder toxicity, while keeping high dose to the prostate.

SU-GG-T-500: Controlling and Refining 3D Dose Distribution at an Individual Voxel Level in Biological IMRT Treatment Planning

Purpose: Biological treatment planning based on the equivalent uniform dose (EUD) demonstrates reduced treatment toxicity and better tumor control. However, EUD based approaches are lacking tools for controlling and refining resultant dose distributions on a voxel level. Here we introduce a method enabling regional dose distribution manipulations for biological IMRT treatment planning. Method and Materials: Two dose distributions with the same EUD are EUD equivalent. However, one might be more clinically acceptable than the other. Embedding tools that find clinically more acceptable solutions and allow dose refining into biologic optimization is thus very important. We propose to use a hybrid biologic/physical dose optimization approach. We first identify region(s) where dose refinement is desired. For them a quadratic dose-volume objective function with a homogeneous prescription is formulated. The remaining structures are included into the planning via EUD dose constraints. If the resultant optimal dose distribution does not fulfill planner's clinical dose-volume criteria then the prescription is adjusted and the problem is re-optimized. The adjustment mechanism accounts for the intrinsic dosimetric inequality between voxels which is ignored by the EUD and the objective function. Results: A clinical prostate case was used to test our method. The PTV was selected as a primary target for dose refinement. The rectum and the bladder were incorporated into the optimization via EUD constraints. By adjusting voxel prescriptions in the PTV iteratively, a dose improvement was obtained for the PTV and dose reduction was achieved in the critical structures comparing to a conventional dose-volume based objective plan with the same PTV coverage. For instance, we demonstrate up to 25% reduction in the mean dose to the rectum. Conclusions: We show that regional dose distribution control and refinement can be achieved for biological optimization. It is relevant in the context of 3D dose sculpting based on the EUD.

Real-time fast inverse dose optimization for image guided adaptive radiation therapy–Enhancements to fast inverse dose optimization (FIDO)

A fast, accurate and stable optimization algorithm is very important for inverse planning of intensity-modulated radiation therapy (IMRT), and for implementing dose-adaptive radiotherapy in the future. Conventional numerical search algorithms with positive beam weight constraints generally require numerous iterations and may produce suboptimal dose results due to trapping in local minima regions of the objective function landscape. A direct solution of the inverse problem using conventional quadratic objective functions without positive beam constraints is more efficient but it will result in unrealistic negative beam weights. We review here a direct solution of the inverse problem that is efficient and does not yield unphysical negative beam weights. In fast inverse dose optimization (FIDO) method the objective function for the optimization of a large number of beamlets is reformulated such that the optimization problem is reducible to a linear set of equations. The optimal set of intensities is then found through a matrix inversion, and negative beamlet intensities are avoided without the need for externally imposed ad hoc conditions. In its original version [S. P. Goldman, J. Z. Chen, and J. J. Battista, in Proceedings of the XIVth International Conference on the Use of Computers in Radiation Therapy, 2004, pp. 112–115; S. P. Goldman, J. Z. Chen, and J. J. Battista, Med. Phys. 32, 3007 (2005)], FIDO was tested on single two-dimensional computed tomography (CT) slices with sharp KERMA beams without scatter, in order to establish a proof of concept which demonstrated that FIDO could be a viable method for the optimization of cancer treatment plans. In this paper we introduce the latest advancements in FIDO that now include not only its application to three-dimensional volumes irradiated by beams with full scatter but include as well a complete implementation of clinical dose-volume constraints including maximum and minimum dose as well as equivalent uniform dose constraints. The method has been integrated into a commercial treatment planning system (Pinnacle, Philips Medical Systems) for beta testing using clinical radiotherapy cases and standard dose constraints set by radiation oncologists. Our FIDO method consistently delivered excellent treatment plans comparable and often better than those obtained using standard optimization techniques that are considerably slower. By design, FIDO is guaranteed to find a global minimum and will achieve highly conformal and homogeneous dose distributions without the need for artificial internal contours that must be created in conventional IMRT optimization systems to help the search engines better control some beam entry directions and in this way avoid the creation of hot and cold spots. This method provides a fast, intuitive and robust technique that yields excellent results for the inverse planning of IMRT. FIDO’s ability to efficiently optimize very large numbers of beamlet weights also makes it an ideal tool for the optimization of helical tomotherapy. Future gains in speed will make it possible to use FIDO for instant treatment plan reoptimization using CT images produced at the radiotherapy machine, just prior to daily treatments of the patient.

A unified approach for inversion problems in intensity-modulated radiation therapy

We propose and study a unified model for handling dose constraints (physical dose, equivalent uniform dose (EUD), etc) and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function. The optimization algorithm minimizes a weighted proximity function that measures the sum of the squares of the distances to the constraint sets. This guarantees convergence to a feasible solution point if the split feasibility problem is consistent (i.e., has a solution), or, otherwise, convergence to a solution that minimally violates the physical dose constraints and EUD constraints. We present computational results that demonstrate the validity of the model and the power of the proposed algorithmic scheme.

Temporo-spatial IMRT optimization: concepts, implementation and initial results

With the recent availability of 4D-CT, the accuracy of information on internal organ motion during respiration has improved significantly. We investigate the utility of organ motion information in IMRT treatment planning, using an in-house prototype optimization system. Four approaches are compared: (1) planning with optimized margins, based on motion information; (2) the ‘motion kernel’ approach, in which a more accurate description of the dose deposit from a pencil beam to a moving target is achieved either through time-weighted averaging of influence matrices, calculated for different instances of anatomy (subsets of 4D-CT data, corresponding to various phases of motion) or through convolution of the pencil beam kernel with the probability density function describing the target motion; (3) optimal gating, or tracking with beam intensity maps optimized independently for each instance of anatomy; and (4) optimal tracking with beam intensity maps optimized simultaneously for all instances of anatomy. The optimization is based on a gradient technique and can handle both physical (dose–volume) and equivalent uniform dose constraints. Optimization requires voxel mapping from phase to phase in order to score the dose in individual voxels as they move. The results show that, compared to the other approaches, margin expansion has a significant disadvantage by substantially increasing the integral dose to patient. While gating or tracking result in the best dose conformation to the target, the former elongates treatment time, and the latter significantly complicates the delivery procedure. The ‘motion kernel’ approach does not provide a dosimetric advantage, compared to optimal tracking or gating, but might lead to more efficient delivery. A combination of gating with the ‘motion kernel’ or margin expansion approach will increase the duty cycle and may provide one with the most efficient solution, in terms of complexity of the delivery procedure and dose conformality to the target.

From physical dose constraints to equivalent uniform dose constraints in inverse radiotherapy planning.

Optimization algorithms in inverse radiotherapy planning need information about the desired dose distribution. Usually the planner defines physical dose constraints for each structure of the treatment plan, either in form of minimum and maximum doses or as dose-volume constraints. The concept of equivalent uniform dose (EUD) was designed to describe dose distributions with a higher clinical relevance. In this paper, we present a method to consider the EUD as an optimization constraint by using the method of projections onto convex sets (POCS). In each iteration of the optimization loop, for the actual dose distribution of an organ that violates an EUD constraint a new dose distribution is calculated that satisfies the EUD constraint, leading to voxel-based physical dose constraints. The new dose distribution is found by projecting the current one onto the convex set of all dose distributions fulfilling the EUD constraint. The algorithm is easy to integrate into existing inverse planning systems, and it allows the planner to choose between physical and EUD constraints separately for each structure. A clinical case of a head and neck tumor is optimized using three different sets of constraints: physical constraints for all structures, physical constraints for the target and EUD constraints for the organs at risk, and EUD constraints for all structures. The results show that the POCS method converges stable and given EUD constraints are reached closely.