Improved modeling of multiple scattering in the Voxel Monte Carlo model

A fast GPU-accelerated Monte Carlo engine for calculation of MLC-collimated electron fields

BACKGROUND

Although intensity-modulated radiation therapy and volumetric arc therapy have revolutionized photon external beam therapies, the technological advances associated with electron beam therapy have fallen behind. Modern linear accelerators contain technologies that would allow for more advanced forms of electron treatments, such as beam collimation, using the conventional photon multi-leaf collimator (MLC); however, no commercial solutions exist that calculate dose from such beam delivery modes. Additionally, for clinical adoption to occur, dose calculation times would need to be on par with that of modern dose calculation algorithms.

PURPOSE

This work developed a graphics processing unit (GPU)-accelerated Monte Carlo (MC) engine incorporating the Varian TrueBeam linac head geometry for a rapid calculation of electron beams collimated using the conventional photon MLC.

METHODS

A compute unified device architecture framework was created for the following: (1) transport of electrons and photons through the linac head geometry, considering multiple scattering, Bremsstrahlung, Møller, Compton, and pair production interactions; (2) electron and photon propagation through the CT geometry, considering all interactions plus the photoelectric effect; and (3) secondary particle cascades through the linac head and within the CT geometry. The linac head collimating geometry was modeled according to the specifications provided by the vendor, who also provided phase-space files. The MC was benchmarked against EGSnrc/DOSXYZnrc/GEANT by simulating individual interactions with simple geometries, pencil, and square beam dose calculations in various phantoms. MC-calculated dose distributions for MLC and jaw-collimated electron fields were compared to measurements in a water phantom and with radiochromic film.

RESULTS

Pencil and square beam dose distributions are in good agreement with DOSXYZnrc. Angular and spatial distributions for multiple scattering and secondary particle production in thin slab geometries are in good agreement with EGSnrc and GEANT. Dose profiles for MLC and jaw-collimated 6-20-MeV electron beams showed an average absolute difference of 1.1 and 1.9 mm for the FWHM and 80%-20% penumbra from measured profiles. Percent depth doses showed differences of <5% for as compared to measurement. The computation time on an NVIDIA Tesla V100 card was 2.5 min to achieve a dose uncertainty of <1%, which is ∼300 times faster than published results in a similar geometry using a single-CPU core.

CONCLUSIONS

The GPU-based MC can quickly calculate dose for electron fields collimated using the conventional photon MLC. The fast calculation times will allow for a rapid calculation of electron fields for mixed photon and electron particle therapy.

Correlation between the γ passing rates of IMRT plans and the volumes of air cavities and bony structures in head and neck cancer

Background

Both patient-specific dose recalculation and γ passing rate analysis are important for the quality assurance (QA) of intensity modulated radiotherapy (IMRT) plans. The aim of this study was to analyse the correlation between the γ passing rates and the volumes of air cavities (V_air) and bony structures (V_bone) in target volume of head and neck cancer.

Methods

Twenty nasopharyngeal carcinoma and twenty nasal natural killer T-cell lymphoma patients were enrolled in this study. Nine-field sliding window IMRT plans were produced and the dose distributions were calculated by anisotropic analytical algorithm (AAA), Acuros XB algorithm (AXB) and SciMoCa based on the Monte Carlo (MC) technique. The dose distributions and γ passing rates of the targets, organs at risk, air cavities and bony structures were compared among the different algorithms.

Results

The γ values obtained with AAA and AXB were 95.6 ± 1.9% and 96.2 ± 1.7%, respectively, with 3%/2 mm criteria (p > 0.05). There were significant differences (p < 0.05) in the γ values between AAA and AXB in the air cavities (86.6 ± 9.4% vs. 98.0 ± 1.7%) and bony structures (82.7 ± 13.5% vs. 99.0 ± 1.7%). Using AAA, the γ values were proportional to the natural logarithm of V_air (R² = 0.674) and inversely proportional to the natural logarithm of V_bone (R² = 0.816). When the V_air in the targets was smaller than approximately 80 cc or the V_bone in the targets was larger than approximately 6 cc, the γ values of AAA were below 95%. Using AXB, no significant relationship was found between the γ values and V_air or V_bone.

Conclusion

In clinical head and neck IMRT QA, greater attention should be paid to the effect of V_air and V_bone in the targets on the γ passing rates when using different dose calculation algorithms.

Validation of the Acuros XB dose calculation algorithm versus Monte Carlo for clinical treatment plans

PURPOSE

The two distinct dose computation paradigms of Boltzmann equation solvers and Monte Carlo simulation both promise in principle maximum accuracy. In practice, clinically acceptable calculation times demand approximations and numerical short-cuts on one hand, and modeling the beam characteristics of a real linear accelerator to the required accuracy on the other. A thorough benchmark of both algorithm types therefore needs to start with beam modeling, and needs to include a number of clinically challenging treatment plans.

METHODS

The Acuros XB (v 13.7, Varian Medical Systems) and SciMoCa (v 1.0, Scientific RT) algorithms were commissioned for the same Varian Clinac accelerator for beam qualities 6 and 15 MV. Beam models were established with water phantom measurements and MLC calibration protocols. In total, 25 patients of five case classes (lung/three-dimensional (3D) conformal, lung/IMRT, head and neck/VMAT, cervix/IMRT, and rectum/VMAT) were randomly selected from the clinical database and computed with both algorithms. Statistics of 3D gamma analysis for various dose/distance-to-agreement (DTA) criteria and differences in selected DVH parameters were analyzed.

RESULTS

The percentage of points fulfilling a gamma evaluation was scored as the gamma agreement index (GAI), denoted as G(ΔD, DTA). G(3,3), G(2,2), and G(1,1) were evaluated for the full body, PTV, and selected organs at risk (OARs). For all patients, G(3,3) ≥ 99.9% and G(2,2) > 97% for the body. G(1,1) varied among the patients. However, for all patients, G(1,1) > 70% and G(1,1) > 80% for 68% of the patients. For each patient, the mean dose deviation was ΔD < 1% for the body, PTV, and all evaluated OARs, respectively. In dense bone and at off-axis distance > 10 cm, the Acuros algorithm yielded slightly higher doses. In the first layer of voxels of the patient surface, the calculated doses deviated between the algorithms. However, at the second voxel, good agreement was observed. The differences in D(98%PTV) were <1.9% between the two algorithms and for 76% of the patients, deviations were below 1%.

CONCLUSIONS

Overall, an outstanding agreement was found between the Boltzmann equation solver and Monte Carlo. High-accuracy dose computation algorithms have matured to a level that their differences are below common experimental detection thresholds for clinical treatment plans. Aside from residual differences which could be traced back to implementation details and fundamental cross-section data, both algorithms arrive at identical dose distributions.

Beam’s-eye-view dosimetrics (BEVD) guided rotational station parameter optimized radiation therapy (SPORT) planning based on reweighted total-variation minimization

Conventional VMAT optimizes aperture shapes and weights at uniformly sampled stations, which is a generalization of the concept of a control point. Recently, rotational station parameter optimized radiation therapy (SPORT) has been proposed to improve the plan quality by inserting beams to the regions that demand additional intensity modulations, thus formulating nonuniform beam sampling. This work presents a new rotational SPORT planning strategy based on reweighted total-variation (TV) minimization (min.), using beam’s-eye-view dosimetrics (BEVD) guided beam selection. The convex programming based reweighted TV min. assures the simplified fluence-map, which facilitates single-aperture selection at each station for single-arc delivery. For the rotational arc treatment planning and non-uniform beam angle setting, the mathematical model needs to be modified by additional penalty term describing the fluence-map similarity and by determination of appropriate angular weighting factors. The proposed algorithm with additional penalty term is capable of achieving more efficient and deliverable plans adaptive to the conventional VMAT and SPORT planning schemes by reducing the dose delivery time about 5 to 10 s in three clinical cases (one prostate and two head-and-neck (HN) cases with a single and multiple targets). The BEVD guided beam selection provides effective and yet easy calculating methodology to select angles for denser, non-uniform angular sampling in SPORT planning. Our BEVD guided SPORT treatment schemes improve the dose sparing to femoral heads in the prostate and brainstem, parotid glands and oral cavity in the two HN cases, where the mean dose reduction of those organs ranges from 0.5 to 2.5 Gy. Also, it increases the conformation number assessing the dose conformity to the target from 0.84, 0.75 and 0.74 to 0.86, 0.79 and 0.80 in the prostate and two HN cases, while preserving the delivery efficiency, relative to conventional single-arc VMAT plans.

Total-variation regularization based inverse planning for intensity modulated arc therapy

Intensity modulated arc therapy (IMAT) delivers conformal dose distributions through continuous gantry rotation with constant or variable speed while modulating the field aperture shape and weight. The enlarged angular space and machine delivery constraints make inverse planning of IMAT more intractable as compared to its counterpart of fixed gantry IMRT. Currently, IMAT inverse planning is being done using two extreme methods: the first one computes in beamlet domain with a subsequent arc leaf sequencing, and the second proceeds in machine parameter domain with entire emphasis placed on a pre-determined delivery method without exploring potentially better alternative delivery schemes. Towards truly optimizing the IMAT treatment on a patient specific basis, in this work we propose a total-variation based inverse planning framework for IMAT, which takes advantage of the useful features of the above two existing approaches while avoiding their shortcomings. A quadratic optimization algorithm has been implemented to demonstrate the performance and advantage of the proposed approach. Applications of the technique to a prostate case and a head and neck case indicate that the algorithm is capable of generating IMAT plans with patient specific numbers of arcs efficiently. Superior dose distributions and delivery time are achieved with a maximum number of apertures of three for each field. As compared to conventional beamlet-based algorithms, our method regularizes the field modulation complexity during optimization, and permits us to obtain the best possible plan with a pre-set modulation complexity of fluences. As illustrated in both prostate and head-and-neck case studies, the proposed method produces more favorable dose distributions than the segment-based algorithms, by optimally accommodating the clinical need of intensity modulation levels for each individual field. On a more fundamental level, our formulation preserves the convexity of optimization and makes the search of the global optimal solution possible with a deterministic method.

Toward a planning scheme for emission guided radiation therapy (EGRT): FDG based tumor tracking in a metastatic breast cancer patient

PURPOSE

Emission guided radiation therapy (EGRT) is a new modality that uses PET emissions in real-time for direct tumor tracking during radiation delivery. Radiation beamlets are delivered along positron emission tomography (PET) lines of response (LORs) by a fast rotating ring therapy unit consisting of a linear accelerator (Linac) and PET detectors. The feasibility of tumor tracking and a primitive modulation method to compensate for attenuation have been demonstrated using a 4D digital phantom in our prior work. However, the essential capability of achieving dose modulation as in conventional intensity modulated radiation therapy (IMRT) treatments remains absent. In this work, the authors develop a planning scheme for EGRT to accomplish sophisticated intensity modulation based on an IMRT plan while preserving tumor tracking.

METHODS

The planning scheme utilizes a precomputed LOR response probability distribution to achieve desired IMRT planning modulation with effects of inhomogeneous attenuation and nonuniform background activity distribution accounted for. Evaluation studies are performed on a 4D digital patient with a simulated lung tumor and a clinical patient who has a moving breast cancer metastasis in the lung. The Linac dose delivery is simulated using a voxel-based Monte Carlo algorithm. The IMRT plan is optimized for a planning target volume (PTV) that encompasses the tumor motion using the MOSEK package and a Pinnacle3™ workstation (Philips Healthcare, Fitchburg, WI) for digital and clinical patients, respectively. To obtain the emission data for both patients, the Geant4 application for tomographic emission (GATE) package and a commercial PET scanner are used. As a comparison, 3D and helical IMRT treatments covering the same PTV based on the same IMRT plan are simulated.

RESULTS

3D and helical IMRT treatments show similar dose distribution. In the digital patient case, compared with the 3D IMRT treatment, EGRT achieves a 15.1% relative increase in dose to 95% of the gross tumor volume (GTV) and a 31.8% increase to 50% of the GTV. In the patient case, EGRT yields a 15.2% relative increase in dose to 95% of the GTV and a 20.7% increase to 50% of the GTV. The organs at risk (OARs) doses are kept similar or lower for EGRT in both cases. Tumor tracking is observed in the presence of planning modulation in all EGRT treatments.

CONCLUSIONS

As compared to conventional IMRT treatments, the proposed EGRT planning scheme allows an escalated target dose while keeping dose to the OARs within the same planning limits. With the capabilities of incorporating planning modulation and accurate tumor tracking, EGRT has the potential to greatly improve targeting in radiation therapy and enable a practical and effective implementation of 4D radiation therapy for planning and delivery.

Improving IMRT delivery efficiency with reweighted L1-minimization for inverse planning

PURPOSE

This study presents an improved technique to further simplify the fluence-map in intensity modulated radiation therapy (IMRT) inverse planning, thereby reducing plan complexity and improving delivery efficiency, while maintaining the plan quality.

METHODS

First-order total-variation (TV) minimization (min.) based on L1-norm has been proposed to reduce the complexity of fluence-map in IMRT by generating sparse fluence-map variations. However, with stronger dose sparing to the critical structures, the inevitable increase in the fluence-map complexity can lead to inefficient dose delivery. Theoretically, L0-min. is the ideal solution for the sparse signal recovery problem, yet practically intractable due to its nonconvexity of the objective function. As an alternative, the authors use the iteratively reweighted L1-min. technique to incorporate the benefits of the L0-norm into the tractability of L1-min. The weight multiplied to each element is inversely related to the magnitude of the corresponding element, which is iteratively updated by the reweighting process. The proposed penalizing process combined with TV min. further improves sparsity in the fluence-map variations, hence ultimately enhancing the delivery efficiency. To validate the proposed method, this work compares three treatment plans obtained from quadratic min. (generally used in clinic IMRT), conventional TV min., and our proposed reweighted TV min. techniques, implemented by a large-scale L1-solver (template for first-order conic solver), for five patient clinical data. Criteria such as conformation number (CN), modulation index (MI), and estimated treatment time are employed to assess the relationship between the plan quality and delivery efficiency.

RESULTS

The proposed method yields simpler fluence-maps than the quadratic and conventional TV based techniques. To attain a given CN and dose sparing to the critical organs for 5 clinical cases, the proposed method reduces the number of segments by 10-15 and 30-35, relative to TV min. and quadratic min. based plans, while MIs decreases by about 20%-30% and 40%-60% over the plans by two existing techniques, respectively. With such conditions, the total treatment time of the plans obtained from our proposed method can be reduced by 12-30 s and 30-80 s mainly due to greatly shorter multileaf collimator (MLC) traveling time in IMRT step-and-shoot delivery.

CONCLUSIONS

The reweighted L1-minimization technique provides a promising solution to simplify the fluence-map variations in IMRT inverse planning. It improves the delivery efficiency by reducing the entire segments and treatment time, while maintaining the plan quality in terms of target conformity and critical structure sparing.

Emission guided radiation therapy for lung and prostate cancers: a feasibility study on a digital patient

PURPOSE

Accurate tumor tracking remains a challenge in current radiation therapy. Many strategies including image guided radiation therapy alleviate the problem to certain extents. The authors propose a new modality called emission guided radiation therapy (EGRT) to accurately and directly track the tumor based on its biological signature. This work is to demonstrate the feasibility of EGRT under two clinical scenarios using a 4D digital patient model.

METHODS

EGRT uses lines of response (LOR's) from positron emission events to direct beamlets of therapeutic radiation through the emission sites inside a tumor. This is accomplished by a radiation delivery system consisting of a Linac and positron emission tomography (PET) detectors on a fast rotating closed-ring gantry. During the treatment of radiotracer-administrated cancer patients, PET detectors collect LOR's from tumor uptake sites and the Linac responds in nearly real-time with beamlets of radiation along the same LOR paths. Moving tumors are therefore treated with a high targeting accuracy. Based on the EGRT concept, the authors design a treatment method with additional modulation algorithms including attenuation correction and an integrated boost scheme. Performance is evaluated using simulations of a lung tumor case with 3D motion and a prostate tumor case with setup errors. The emission process is simulated by Geant4 Application for Tomographic Emission package (GATE) and Linac dose delivery is simulated using a voxel-based Monte Carlo algorithm (VMC++).

RESULTS

In the lung case with attenuation correction, compared to a conventional helical treatment, EGRT achieves a 41% relative increase in dose to 95% of the gross tumor volume (GTV) and a 55% increase to 50% of the GTV. All dose distributions are normalized for the same dose to the lung. In the prostate case with the integrated boost and no setup error, EGRT yields a 19% and 55% relative dose increase to 95% and 50% of the GTV, respectively, when all methods are normalized for the same dose to the rectum. In the prostate case with integrated boost where setup error is present, EGRT contributes a 21% and 52% relative dose increase to 95% and 50% of the GTV, respectively.

CONCLUSIONS

As a new radiation therapy modality with inherent tumor tracking, EGRT has the potential to substantially improve targeting in radiation therapy in the presence of intrafractional and interfractional motion.

Dose optimization with first-order total-variation minimization for dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT)

PURPOSE

A new treatment scheme coined as dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT) has recently been proposed to bridge the gap between IMRT and VMAT. By increasing the angular sampling of radiation beams while eliminating dispensable segments of the incident fields, DASSIM-RT is capable of providing improved conformity in dose distributions while maintaining high delivery efficiency. The fact that DASSIM-RT utilizes a large number of incident beams represents a major computational challenge for the clinical applications of this powerful treatment scheme. The purpose of this work is to provide a practical solution to the DASSIM-RT inverse planning problem.

METHODS

The inverse planning problem is formulated as a fluence-map optimization problem with total-variation (TV) minimization. A newly released L1-solver, template for first-order conic solver (TFOCS), was adopted in this work. TFOCS achieves faster convergence with less memory usage as compared with conventional quadratic programming (QP) for the TV form through the effective use of conic forms, dual-variable updates, and optimal first-order approaches. As such, it is tailored to specifically address the computational challenges of large-scale optimization in DASSIM-RT inverse planning. Two clinical cases (a prostate and a head and neck case) are used to evaluate the effectiveness and efficiency of the proposed planning technique. DASSIM-RT plans with 15 and 30 beams are compared with conventional IMRT plans with 7 beams in terms of plan quality and delivery efficiency, which are quantified by conformation number (CN), the total number of segments and modulation index, respectively. For optimization efficiency, the QP-based approach was compared with the proposed algorithm for the DASSIM-RT plans with 15 beams for both cases.

RESULTS

Plan quality improves with an increasing number of incident beams, while the total number of segments is maintained to be about the same in both cases. For the prostate patient, the conformation number to the target was 0.7509, 0.7565, and 0.7611 with 80 segments for IMRT with 7 beams, and DASSIM-RT with 15 and 30 beams, respectively. For the head and neck (HN) patient with a complicated target shape, conformation numbers of the three treatment plans were 0.7554, 0.7758, and 0.7819 with 75 segments for all beam configurations. With respect to the dose sparing to the critical structures, the organs such as the femoral heads in the prostate case and the brainstem and spinal cord in the HN case were better protected with DASSIM-RT. For both cases, the delivery efficiency has been greatly improved as the beam angular sampling increases with the similar or better conformal dose distribution. Compared with conventional quadratic programming approaches, first-order TFOCS-based optimization achieves far faster convergence and smaller memory requirements in DASSIM-RT.

CONCLUSIONS

The new optimization algorithm TFOCS provides a practical and timely solution to the DASSIM-RT or other inverse planning problem requiring large memory space. The new treatment scheme is shown to outperform conventional IMRT in terms of dose conformity to both the targetand the critical structures, while maintaining high delivery efficiency.

Inverse planning for IMRT with nonuniform beam profiles using total-variation regularization (TVR)

PURPOSE

Radiation therapy with high dose rate and flattening filter-free (FFF) beams has the potential advantage of greatly reduced treatment time and out-of-field dose. Current inverse planning algorithms are, however, not customized for beams with nonuniform incident profiles and the resultant IMRT plans are often inefficient in delivery. The authors propose a total-variation regularization (TVR)-based formalism by taking the inherent shapes of incident beam profiles into account.

METHODS

A novel TVR-based inverse planning formalism is established for IMRT with nonuniform beam profiles. The authors introduce a TVR term into the objective function, which encourages piecewise constant fluence in the nonuniform FFF fluence domain. The proposed algorithm is applied to lung and prostate and head and neck cases and its performance is evaluated by comparing the resulting plans to those obtained using a conventional beamlet-based optimization (BBO).

RESULTS

For the prostate case, the authors' algorithm produces acceptable dose distributions with only 21 segments, while the conventional BBO requires 114 segments. For the lung case and the head and neck case, the proposed method generates similar coverage of target volume and sparing of the organs-at-risk as compared to BBO, but with a markedly reduced segment number.

CONCLUSIONS

TVR-based optimization in nonflat beam domain provides an effective way to maximally leverage the technical capacity of radiation therapy with FFF fields. The technique can generate effective IMRT plans with improved dose delivery efficiency without significant deterioration of the dose distribution.

A unified framework for 3D radiation therapy and IMRT planning: plan optimization in the beamlet domain by constraining or regularizing the fluence map variations

The purpose of this work is to demonstrate that physical constraints on fluence gradients in 3D radiation therapy (RT) planning can be incorporated into beamlet optimization explicitly by direct constraint on the spatial variation of the fluence maps or implicitly by using total-variation regularization (TVR). The former method forces the fluence to vary in accordance with the known form of a wedged field and latter encourages the fluence to take the known form of the wedged field by requiring the derivatives of the fluence maps to be piece-wise constant. The performances of the proposed methods are evaluated by using a brain cancer case and a head and neck case. It is found that both approaches are capable of providing clinically sensible 3D RT solutions with monotonically varying fluence maps. For currently available 3D RT delivery schemes based on the use of customized physical or dynamic wedges, constrained optimization seems to be more useful because the optimized fields are directly deliverable. Working in the beamlet domain provides a natural way to model the spatial variation of the beam fluence. The proposed methods take advantage of the fact that 3D RT is a special form of intensity-modulated radiation therapy (IMRT) and finds the optimal plan by searching for fields with a certain type of spatial variation. The approach provides a unified framework for 3D CRT and IMRT plan optimization.

Recommendations for clinical electron beam dosimetry: supplement to the recommendations of Task Group 25

The goal of Task Group 25 (TG-25) of the Radiation Therapy Committee of the American Association of.Physicists in Medicine (AAPM) was to provide a methodology and set of procedures for a medical physicist performing clinical electron beam dosimetry in the nominal energy range of 5-25 MeV. Specifically, the task group recommended procedures for acquiring basic information required for acceptance testing and treatment planning of new accelerators with therapeutic electron beams. Since the publication of the TG-25 report, significant advances have taken place in the field of electron beam dosimetry, the most significant being that primary standards laboratories around the world have shifted from calibration standards based on exposure or air kerma to standards based on absorbed dose to water. The AAPM has published a new calibration protocol, TG-51, for the calibration of high-energy photon and electron beams. The formalism and dosimetry procedures recommended in this protocol are based on the absorbed dose to water calibration coefficient of an ionization chamber at 60Co energy, N60Co(D,w), together with the theoretical beam quality conversion coefficient k(Q) for the determination of absorbed dose to water in high-energy photon and electron beams. Task Group 70 was charged to reassess and update the recommendations in TG-25 to bring them into alignment with report TG-51 and to recommend new methodologies and procedures that would allow the practicing medical physicist to initiate and continue a high quality program in clinical electron beam dosimetry. This TG-70 report is a supplement to the TG-25 report and enhances the TG-25 report by including new topics and topics that were not covered in depth in the TG-25 report. These topics include procedures for obtaining data to commission a treatment planning computer, determining dose in irregularly shaped electron fields, and commissioning of sophisticated special procedures using high-energy electron beams. The use of radiochromic film for electrons is addressed, and radiographic film that is no longer available has been replaced by film that is available. Realistic stopping-power data are incorporated when appropriate along with enhanced tables of electron fluence data. A larger list of clinical applications of electron beams is included in the full TG-70 report available at http://www.aapm.org/pubs/reports. Descriptions of the techniques in the clinical sections are not exhaustive but do describe key elements of the procedures and how to initiate these programs in the clinic. There have been no major changes since the TG-25 report relating to flatness and symmetry, surface dose, use of thermoluminescent dosimeters or diodes, virtual source position designation, air gap corrections, oblique incidence, or corrections for inhomogeneities. Thus these topics are not addressed in the TG-70 report.

Search for IMRT inverse plans with piecewise constant fluence maps using compressed sensing techniques

An intensity-modulated radiation therapy (IMRT) field is composed of a series of segmented beams. It is practically important to reduce the number of segments while maintaining the conformality of the final dose distribution. In this article, the authors quantify the complexity of an IMRT fluence map by introducing the concept of sparsity of fluence maps and formulate the inverse planning problem into a framework of compressing sensing. In this approach, the treatment planning is modeled as a multiobjective optimization problem, with one objective on the dose performance and the other on the sparsity of the resultant fluence maps. A Pareto frontier is calculated, and the achieved dose distributions associated with the Pareto efficient points are evaluated using clinical acceptance criteria. The clinically acceptable dose distribution with the smallest number of segments is chosen as the final solution. The method is demonstrated in the application of fixed-gantry IMRT on a prostate patient. The result shows that the total number of segments is greatly reduced while a satisfactory dose distribution is still achieved. With the focus on the sparsity of the optimal solution, the proposed method is distinct from the existing beamlet- or segment-based optimization algorithms.

Using total-variation regularization for intensity modulated radiation therapy inverse planning with field-specific numbers of segments

Currently, there are two types of treatment planning algorithms for intensity modulated radiation therapy (IMRT). The beamlet-based algorithm generates beamlet intensity maps with high complexity, resulting in large numbers of segments in the delivery after a leaf-sequencing algorithm is applied. The segment-based direct aperture optimization (DAO) algorithm includes the physical constraints of the deliverable apertures in the calculation, and achieves a conformal dose distribution using a small number of segments. However, the number of segments is pre-fixed in most of the DAO approaches, and the typical random search scheme in the optimization is computationally intensive. A regularization-based algorithm is proposed to overcome the drawbacks of the DAO method. Instead of smoothing the beamlet intensity maps as in many existing methods, we include a total-variation term in the optimization objective function to reduce the number of signal levels of the beam intensity maps. An aperture rectification algorithm is then applied to generate a significantly reduced number of deliverable apertures. As compared to the DAO algorithm, our method has an efficient form of quadratic optimization, with an additional advantage of optimizing field-specific numbers of segments based on the modulation complexity. The proposed approach is evaluated using two clinical cases. Under the condition that the clinical acceptance criteria of the treatment plan are satisfied, for the prostate patient, the total number of segments for five fields is reduced from 61 using the Eclipse planning system to 35 using the proposed algorithm; for the head and neck patient, the total number of segments for seven fields is reduced from 107 to 28. The head and neck result is also compared to that using an equal number of four segments for each field. The comparison shows that using field-specific numbers of segments achieves a much improved dose distribution.

Evaluation of dose prediction errors and optimization convergence errors of deliverable-based head-and-neck IMRT plans computed with a superposition/convolution dose algorithm

The purpose of this study is to evaluate dose prediction errors (DPEs) and optimization convergence errors (OCEs) resulting from use of a superposition/convolution dose calculation algorithm in deliverable intensity-modulated radiation therapy (IMRT) optimization for head-and-neck (HN) patients. Thirteen HN IMRT patient plans were retrospectively reoptimized. The IMRT optimization was performed in three sequential steps: (1) fast optimization in which an initial nondeliverable IMRT solution was achieved and then converted to multileaf collimator (MLC) leaf sequences; (2) mixed deliverable optimization that used a Monte Carlo (MC) algorithm to account for the incident photon fluence modulation by the MLC, whereas a superposition/convolution (SC) dose calculation algorithm was utilized for the patient dose calculations; and (3) MC deliverable-based optimization in which both fluence and patient dose calculations were performed with a MC algorithm. DPEs of the mixed method were quantified by evaluating the differences between the mixed optimization SC dose result and a MC dose recalculation of the mixed optimization solution. OCEs of the mixed method were quantified by evaluating the differences between the MC recalculation of the mixed optimization solution and the final MC optimization solution. The results were analyzed through dose volume indices derived from the cumulative dose-volume histograms for selected anatomic structures. Statistical equivalence tests were used to determine the significance of the DPEs and the OCEs. Furthermore, a correlation analysis between DPEs and OCEs was performed. The evaluated DPEs were within +/- 2.8% while the OCEs were within 5.5%, indicating that OCEs can be clinically significant even when DPEs are clinically insignificant. The full MC-dose-based optimization reduced normal tissue dose by as much as 8.5% compared with the mixed-method optimization results. The DPEs and the OCEs in the targets had correlation coefficients greater than 0.71, and there was no correlation for the organs at risk. Because full MC-based optimization results in lower normal tissue doses, this method proves advantageous for HN IMRT optimization.

A "HOWFARLESS" option to increase efficiency of homogeneous phantom calculations with DOSXYZnrc

This paper describes a "HOWFARLESS" transport option, which has been added to DOSXYZnrc to increase the efficiency of beam commissioning calculations in homogeneous phantoms. The algorithm speeds up charged particle transport by only considering the distance to the extreme outer boundaries of the phantom, thus eliminating the need to stop at voxel boundaries. Dose is deposited by approximating the total curved charged particle steps by two straight-line steps joined at a hinge point. Good agreement with normal simulations is achieved at all beam energies and for all practical maximum step lengths with a 1:1 mixture of approximations based on the initial position/ direction of the particle and on its final position/direction. Use of the "HOWFARLESS" option in phantom calculations for 6 and 18 MV photon beams (10 x 10 cm2 and 40 x 40 cm2 fields) from BEAMnrc-simulated accelerators increases the efficiency at the optimum photon splitting number by a factor of 2.9-5.4 when the exact EGSnrc boundary crossing algorithm (BCA) is used and by 51%-89% when the faster PRESTA-I BCA is employed. The efficiency gain due to the "HOWFARLESS" transport option increases with increasing beam energy and decreases with increasing field/dose voxel size. Efficiency improvement is greater when the efficiency of the particle source itself is not a factor, and in such cases the "HOWFARLESS" option improves the DOSXYZnrc efficiency by up to a factor of 13.1 (exact BCA) or 3.5 (PRESTA-I BCA) for photon beams, and up to a factor of 17.2 (exact BCA) or 5.2 (PRESTA-I BCA) for electron beams.

Dose calculation validation of VMC++ for photon beams

The radiation therapy specific Voxel Monte Carlo (VMC+ +) dose calculation algorithm achieves a dramatic improvement in MC dose calculation efficiency for radiation therapy treatment planning dose evaluation compared with other MC algorithms. This work aims to validate VMC+ + for radiation therapy photon beam planning. VMC++ was validated with respect to the well-benchmarked EGS-based DOSXYZnrc by comparing depth dose and lateral profiles for field sizes ranging from 1 X 1 to 40 x 40 cm(2) for 6 and 18 MV beams in a homogeneous water phantom and in a simulated bone-lung-bone phantom. Patient treatment plan dose distributions were compared for five prostate plans and five head-and-neck (H/N) plans, all using intensity-modulated radiotherapy beams. For all tests, the same incident particles were used in both codes to isolate differences due to modeling of the radiation source. Voxel-by-voxel observed differences were analyzed to distinguish between systematic and purely statistical differences. Dose-volume-histogram-derived dose indices were compared for the patient plans. For the homogeneous water phantom and the bone-lung-bone phantom, the depth dose curve predicted by VMC+ + agreed with that predicted by DOSXYZnrc within expected statistical uncertainty in all voxels except the surface voxel of the water phantom, where VMC+ + predicted a lower dose. When the electron cutoff parameter was decreased for both codes, the surface voxel agreed within expected statistical uncertainty. For prostate plans, the most severe difference between the codes resulted in 55% of the voxels showing a systematic difference of 0.32% of maximum dose. For H/N plans, the largest difference observed resulted in 2% of the voxels showing a systematic difference of 0.98% of maximum dose. For the prostate plans, the most severe difference in the planning target volume D95 was 0.4%, the rectum D35 was 0.2%, the rectum DI7 was 0.2%, the bladder D50 was 0.3% and the bladder D25 was 0.3%. For the H/N plans, the most severe difference in the gross tumor volume D98 was 0.4%, the clinical target volume D90 was 0.2%, the nodes D90 was 0.2%, the parotids D95 was 0.8%, and the cord D2 was 0.8%. All of these differences are clinically insignificant. VMC++ showed an average efficiency gain over DOSXYZnrc of at least an order of magnitude without introducing significant systematic bias. VMC + + can be used for photon beam MC patient dose computations without a clinically significant loss in accuracy.

Beamlet dose distribution compression and reconstruction using wavelets for intensity modulated treatment planning

Intensity modulated radiation therapy (IMRT) treatment planning is often formulated as the optimization of weights of fixed-geometry subfields (beamlets). Efficient optimization techniques can be based on direct storage of the influence matrix relating beamlet weights to dose values. However, direct storage of beamlet dose distributions for IMRT treatment planning can easily exceed several gigabytes, and is therefore often not feasible. We present a method for rapidly calculating full three-dimensional IMRT dose distributions, based on a vector of beamlet weights. The method is based on compressed beamlet dose distributions using fast digital wavelet transforms and so-called hard thresholding. We studied the method with a rectangular beamlet of 0.5 cm x 0.5 cm cross section from a monoenergetic 6 MeV photon point source simulated in homogeneous (water) and heterogeneous (CT-data) phantoms. Dose was calculated using the accurate VMC+ + Monte Carlo engine. The beamlet dose distributions were wavelet transformed and compressed by dropping wavelet coefficients below a given threshold value. Dose is then computed using the remaining wavelets. Selection of the wavelet basis function, decomposition level, and threshold values, for different slice orientations (transverse or parallel to the beam) and varying angles of beamlet incidence are studied. A typical in-slice compression ratio for a plane containing a beamlet was 32:1 using the sym2 wavelet and a threshold of 0.01, with a typical root-mean-square error, for voxels above 50% of the maximum dose, of about 0.04%. The overall compression performance, which includes many planes with little information content, is on the order of 100:1 or greater compared to full matrix storage. Although other methods are available to make the use of stored influence matrix values more feasible in IMRT treatment planning (such as using coarse grids or restricting values to defined volumes of interest) we conclude that wavelet compression facilitates the storage and use of full pencil dose deposition (influence matrix) data in IMRT treatment planning.

Comparison of dose calculation algorithms with Monte Carlo methods for photon arcs

The objective of this study is to seek an accurate and efficient method to calculate the dose distribution of a photon arc. The algorithms tested include Monte Carlo, pencil beam kernel (PK), and collapsed cone convolution (CCC). For the Monte Carlo dose calculation, EGS4/DOSXYZ was used. The SRCXYZ source code associated with the DOSXYZ was modified so that the gantry angle of a photon beam would be sampled uniformly within the arc range about an isocenter to simulate a photon arc. Specifically, photon beams (6/18 MV, 4 x 4 and 10 x 10 cm2) described by a phase space file generated by BEAM (MCPHS), or by two point sources with different photon energy spectra (MCDIV) were used. These methods were used to calculate three-dimensional (3-D) distributions in a PMMA phantom, a cylindrical water phantom, and a phantom with lung inhomogeneity. A commercial treatment planning system was also used to calculate dose distributions in these phantoms using equivalent tissue air ratio (ETAR), PK and CCC algorithms for inhomogeneity corrections. Dose distributions for a photon arc in these phantoms were measured using a RK ion chamber and radiographic films. For homogeneous phantoms, the measured results agreed well (approximately 2% error) with predictions by the Monte Carlo simulations (MCPHS and MCDIV) and the treatment planning system for the 180 degrees and 360 degrees photon arcs. For the dose distribution in the phantom with lung inhomogeneity with a 90 degrees photon arc, the Monte Carlo calculations agreed with the measurements within 2%, while the treatment planning system using ETAR, PK and CCC underestimated or overestimated the dose inside the lung inhomogeneity from 6% to 12%.

[Verification of a fast Monte Carlo dose calculation algorithm by EGSnrc using the statistical separation method]

The recently developed XVMC code, a fast Monte Carlo (MC) algorithm to calculate the dose of photon and electron beams in treatment planning, was compared to EGSnrc, an enhanced version of the well-known EGS4 system. Because of the numerous and accurate verification measurements, this system can be considered as golden standard. The comparison was performed using phantoms consisting of water, lung tissue and bone. Dose profile and difference distributions showed good agreement within the accuracy requirements. Because deviations between the results of two MC algorithms are caused by systematic errors and statistical fluctuations, a separation method was used to quantify the systematic discrepancies. Using this method, it could be shown that there was good agreement between the three dimensional dose distributions, calculated with XVMC and EGSnrc, if maximum systematic deviation of 2% are accepted.

[Foundations of the Monte Carlo method for dose calculation in radiotherapy]

Monte Carlo (MC) methods applied in dose calculation are based on fundamental principles of radiation interaction with matter. In contrast to other methods, the accuracy of dose calculation achievable with MC depends only on the determination of the beam quality and the interaction coefficients. Using MC techniques it is possible to predict the dose for clinical photon and electron beams with an accuracy of > +/- 2%. Especially for inhomogeneous regions like head, neck, and lung, the MC technique can significantly improve the accuracy compared to conventional algorithms. Therefore, in the present paper the basic features of the MC method are reviewed in the context of treatment planning in radiation therapy. The main shortcoming in the past, i.e., that MC algorithms are too slow to be acceptable for clinical purposes, could be solved by using faster computers and by introducing new variance reduction (VR) techniques. These techniques decrease the statistical fluctuations without increasing the number of particle histories. Therefore, MC calculation times in the order of a few minutes are possible. A brief overview of VR methods is provided.

Fast Monte Carlo dose calculation for photon beams based on the VMC electron algorithm

A new Monte Carlo algorithm for 3D photon dose calculation in radiation therapy is presented, which is based on the previously developed Voxel Monte Carlo (VMC) for electron beams. The main result is that this new version of VMC (now called XVMC) is more efficient than EGS4/PRESTA photon dose calculation by a factor of 15-20. Therefore, a standard treatment plan for photons can be calculated by Monte Carlo in about 20 min. on a "normal" personal computer. The improvement is caused mainly by the fast electron transport algorithm and ray tracing technique, and an initial ray tracing method to calculate the number of electrons created in each voxel by the primary photon beam. The model was tested in comparison to calculations by EGS4 using several fictive phantoms. In most cases a good coincidence has been found between both codes. Only within lung substitute dose differences have been observed.

Relevance of accurate Monte Carlo modeling in nuclear medical imaging

Monte Carlo techniques have become popular in different areas of medical physics with advantage of powerful computing systems. In particular, they have been extensively applied to simulate processes involving random behavior and to quantify physical parameters that are difficult or even impossible to calculate by experimental measurements. Recent nuclear medical imaging innovations such as single-photon emission computed tomography (SPECT), positron emission tomography (PET), and multiple emission tomography (MET) are ideal for Monte Carlo modeling techniques because of the stochastic nature of radiation emission, transport and detection processes. Factors which have contributed to the wider use include improved models of radiation transport processes, the practicality of application with the development of acceleration schemes and the improved speed of computers. In this paper we present a derivation and methodological basis for this approach and critically review their areas of application in nuclear imaging. An overview of existing simulation programs is provided and illustrated with examples of some useful features of such sophisticated tools in connection with common computing facilities and more powerful multiple-processor parallel processing systems. Current and future trends in the field are also discussed.

Monte Carlo study of fluence perturbation effects on cavity dose response in clinical proton beams

Current protocols for clinical proton beam dosimetry have not implemented any chamber-dependent correction factors for absorbed dose determination. The present work initiates a Monte Carlo study of these factors with emphasis on proton fluence perturbation effects and preliminary calculations of perturbation effects from secondary electrons. The proton Monte Carlo code PTRAN was modified to allow simulation of proton transport in non-homogeneous geometries of both unmodulated and modulated beams. The dose to water derived from the dose calculated in an air cavity agrees well with results from analytical calculations assuming a displacement of the point of measurement. For unmodulated beams small differences, limited to 0.8%, could be partially attributed to proton multiple scattering. Effects of replacing water around the cavity with wall material are explained by the introduction of a water-equivalent wall thickness. For modulated beams no significant perturbation effects arise. Secondary electron spectra are calculated analytically. Preliminary electron transport calculations with EGS4 show that wall perturbations of the order of 1% could result. Perturbation effects caused by the energy transport of secondary particles from inelastic nuclear interactions have not been studied here. Inclusion of inelastic nuclear energy transfers in the cavity dose, assuming total local absorption, indicate that separate scaling of this contribution with the ratio of total inelastic nuclear cross sections could be important.