Monte Carlo-based inverse treatment planning

Prediction of dose deposition matrix using voxel features driven machine learning approach

OBJECTIVES

A dose deposition matrix (DDM) prediction method using several voxel features and a machine learning (ML) approach is proposed for plan optimization in radiation therapy.

METHODS

Head and lung cases with the inhomogeneous medium are used as training and testing data. The prediction model is a cascade forward backprop neural network where the input is the features of the voxel, including 1) voxel to body surface distance along the beamlet axis, 2) voxel to beamlet axis distance, 3) voxel density, 4) heterogeneity corrected voxel to body surface distance, 5) heterogeneity corrected voxel to beamlet axis, and (6) the dose of voxel obtained from the pencil beam (PB) algorithm. The output is the predicted voxel dose corresponding to a beamlet. The predicted DDM was used for plan optimization (ML method) and compared with the dose of MC-based plan optimization (MC method) and the dose of pencil beam-based plan optimization (PB method). The mean absolute error (MAE) value was calculated for full volume relative to the dose of the MC method to evaluate the overall dose performance of the final plan.

RESULTS

For patient with head tumor, the ML method achieves MAE value 0.49 × 10-4 and PB has MAE 1.86 × 10-4. For patient with lung tumor, the ML method has MAE 1.42 × 10-4 and PB has MAE 3.72 × 10-4. The maximum percentage difference in PTV dose coverage (D98) between ML and MC methods is no more than 1.2% for patient with head tumor, while the difference is larger than 10% using the PB method. For patient with lung tumor, the maximum percentage difference in PTV dose coverage (D98) between ML and MC methods is no more than 2.1%, while the difference is larger than 16% using the PB method.

CONCLUSIONS

In this work, a reliable DDM prediction method is established for plan optimization by applying several voxel features and the ML approach. The results show that the ML method based on voxel features can obtain plans comparable to the MC method and is better than the PB method in achieving accurate dose to the patient, which is helpful for rapid plan optimization and accurate dose calculation.

ADVANCES IN KNOWLEDGE

Establishment of a new machine learning method based on the relationship between the voxel and beamlet features for dose deposition matrix prediction in radiation therapy.

Hypofractionation and SABR: 25 years of evolution in medical physics and a glimpse of the future

As we were invited to write an article for celebrating the 50^th Anniversary of Medical Physics journal, on something historically significant, commemorative, and exciting happening in the past decades, the first idea came to our mind is the fascinating radiotherapy paradigm shift from conventional fractionation to hypofractionation and stereotactic ablative radiotherapy (SABR). It is historically and clinically significant since as we all know this RT treatment revolution not only reduces treatment duration for patients, but also improves tumor control and cancer treatment outcomes. It is also commemorative and exciting for us medical physicists since the technology development in medical physics has been the main driver for the success of this treatment regimen which requires high precision and accuracy throughout the entire treatment planning and delivery. This article provides an overview of the technological development and clinical trials evolvement in the past 25 years for hypofractionation and SABR, with an outlook to the future improvement.

EGSnrc application for IMRT planning

The aim of this study was to describe a detailed instruction of intensity modulated radiotherapy (IMRT) planning simulation using BEAMnrc-DOSXYZnrc code system (EGSnrc package) and present a new graphical user interface based on MATLAB code (The MathWorks) to combine more than one. 3ddose file which were obtained from the IMRT plan. This study was performed in four phases: the commissioning of Varian Clinac iX6 MV, the simulation of IMRT planning in EGSnrc, the creation of in-house VDOSE GUI, and the analysis of the isodose contour and dose volume histogram (DVH) curve from several beam angles. The plan paramaters in sequence and control point files were extracted from the planning data in Tan Tock Seng Hospital Singapore (multileaf collimator (MLC) leaf positions - bank A and bank B, gantry angles, coordinate of isocenters, and MU indexes). VDOSE GUI which was created in this study can display the distribution dose curve in each slice and beam angle. Dose distributions from various MLC settings and beam angles yield different dose distributions even though they used the same number of simulated particles. This was due to the differences in the MLC leaf openings in every field. The value of the relative dose error between the two dose ditributions for "body" was 51.23 %. The Monte Carlo (MC) data was normalized with the maximum dose but the analytical anisotropic algorithm (AAA) data was normalized by the dose in the isocenter. In this study, we have presented a Monte Carlo simulation framework for IMRT dose calculation using DOSXYZnrc source 21. Further studies are needed in conducting IMRT simulations using EGSnrc to minimize the different dose error and dose volume histogram deviation.

Development of a Geant4-based independent patient dose validation system with an elaborate multileaf collimator simulation model

Despite the improvements in the dose calculation models of the commercial treatment planning systems (TPS), their ability to accurately predict patient dose is still limited. One of the limitations is caused by the simplified model of the multileaf collimator (MLC). The aim of this study was to develop a Monte Carlo (MC) method‐based independent patient dose validation system with an elaborate MLC model for more accurate dose evaluation. Varian Clinac 2300 IX was simulated using Geant4 toolkits, after which MC commissioning with measurements was performed to validate the simulation model. A DICOM‐RT interface was developed to obtain the beam delivery conditions including the hundreds of MLC motions. Finally, the TPS dose distributions were compared with the MC dose distributions for water phantom cases and a patient case. Our results show that the TPS overestimated the absolute abutting leakage dose in the closed MLC field, with about 20% more of the maximum dose than that of the MC calculation. For water phantom cases, the dose distributions inside the target region were almost identical with the dose difference of less than 2%, while the dose near the edge of the target shows difference about 10% between Geant4 and TPS due to geometrical differences in MLC model. For the patient analysis, the Geant4 and TPS doses of all organs were matched well within 1.4% of the prescribed dose. However, for organs located in areas with high ratio of leaf pairs with distances less than 10 mm leaf pair (LP_(<10mm)), the maximum dose of TPS was overestimated by about 3% of the prescribed dose. These dose comparison results demonstrate that our system for calculating the patient dose is quite accurate. Furthermore, if the MLC sequences in treatment plan have a large ratio of LP_(short), more than 3% dose difference in normal tissue could be seen.

Clinical implementations of 4D pencil beam scanned particle therapy: Report on the 4D treatment planning workshop 2016 and 2017

In 2016 and 2017, the 8th and 9th 4D treatment planning workshop took place in Groningen (the Netherlands) and Vienna (Austria), respectively. This annual workshop brings together international experts to discuss research, advances in clinical implementation as well as problems and challenges in 4D treatment planning, mainly in spot scanned proton therapy. In the last two years several aspects like treatment planning, beam delivery, Monte Carlo simulations, motion modeling and monitoring, QA phantoms as well as 4D imaging were thoroughly discussed. This report provides an overview of discussed topics, recent findings and literature review from the last two years. Its main focus is to highlight translation of 4D research into clinical practice and to discuss remaining challenges and pitfalls that still need to be addressed and to be overcome.

Independent dose validation system for Gamma Knife radiosurgery, using a DICOM-RT interface and Geant4

Leksell GammaPlan was specifically designed for Gamma Knife (GK) radiosurgery planning, but it has limited accuracy for estimating the dose distribution in inhomogeneous areas, such as the embolization of arteriovenous malformations. We aimed to develop an independent patient dose validation system based on a patient-specific model, constructed using a DICOM-RT interface and the Geant4 toolkit. Leksell Gamma Knife Perfexion was designed in Geant4.10.00 and includes a DICOM-RT interface. Output factors for each collimator in a sector and dose distributions in a spherical water phantom calculated using a Monte Carlo (MC) algorithm were compared with the output factors calculated by the tissue maximum ratio (TMR) 10 algorithm and dose distributions measured using film, respectively. Studies using two types of water phantom and two patient simulation cases were evaluated by comparing the dose distributions calculated by the MC, the TMR and the convolution algorithms. The water phantom studies showed that if the beam size is small and the target is located in heterogeneous media, the dose difference could be up to 11%. In the two patient simulations, the TMR algorithm overestimated the dose by about 4% of the maximum dose if a complex and large bony structure was located on the beam path, whereas the convolution algorithm showed similar results to those of the MC algorithm. This study demonstrated that the in-house system could accurately verify the patient dose based on full MC simulation and so would be useful for patient cases where the dose differences are suspected.

Motion management strategies and technical issues associated with stereotactic body radiotherapy of thoracic and upper abdominal tumors: A review from NRG oncology

The efficacy of stereotactic body radiotherapy (SBRT) has been well demonstrated. However, it presents unique challenges for accurate planning and delivery especially in the lungs and upper abdomen where respiratory motion can be significantly confounding accurate targeting and avoidance of normal tissues. In this paper, we review the current literature on SBRT for lung and upper abdominal tumors with particular emphasis on addressing respiratory motion and its affects. We provide recommendations on strategies to manage motion for different, patient-specific situations. Some of the recommendations will potentially be adopted to guide clinical trial protocols.

Generation of a novel phase-space-based cylindrical dose kernel for IMRT optimization

PURPOSE

Improving dose calculation accuracy is crucial in intensity-modulated radiation therapy (IMRT). We have developed a method for generating a phase-space-based dose kernel for IMRT planning of lung cancer patients.

METHODS

Particle transport in the linear accelerator treatment head of a 21EX, 6 MV photon beam (Varian Medical Systems, Palo Alto, CA) was simulated using the EGSnrc/BEAMnrc code system. The phase space information was recorded under the secondary jaws. Each particle in the phase space file was associated with a beamlet whose index was calculated and saved in the particle's LATCH variable. The DOSXYZnrc code was modified to accumulate the energy deposited by each particle based on its beamlet index. Furthermore, the central axis of each beamlet was calculated from the orientation of all the particles in this beamlet. A cylinder was then defined around the central axis so that only the energy deposited within the cylinder was counted. A look-up table was established for each cylinder during the tallying process. The efficiency and accuracy of the cylindrical beamlet energy deposition approach was evaluated using a treatment plan developed on a simulated lung phantom.

RESULTS

Profile and percentage depth doses computed in a water phantom for an open, square field size were within 1.5% of measurements. Dose optimized with the cylindrical dose kernel was found to be within 0.6% of that computed with the nontruncated 3D kernel. The cylindrical truncation reduced optimization time by approximately 80%.

CONCLUSIONS

A method for generating a phase-space-based dose kernel, using a truncated cylinder for scoring dose, in beamlet-based optimization of lung treatment planning was developed and found to be in good agreement with the standard, nontruncated scoring approach. Compared to previous techniques, our method significantly reduces computational time and memory requirements, which may be useful for Monte-Carlo-based 4D IMRT or IMAT treatment planning.

First steps towards a fast-neutron therapy planning program

BACKGROUND

The Monte Carlo code GEANT4 was used to implement first steps towards a treatment planning program for fast-neutron therapy at the FRM II research reactor in Garching, Germany. Depth dose curves were calculated inside a water phantom using measured primary neutron and simulated primary photon spectra and compared with depth dose curves measured earlier. The calculations were performed with GEANT4 in two different ways, simulating a simple box geometry and splitting this box into millions of small voxels (this was done to validate the voxelisation procedure that was also used to voxelise the human body).

RESULTS

In both cases, the dose distributions were very similar to those measured in the water phantom, up to a depth of 30 cm. In order to model the situation of patients treated at the FRM II MEDAPP therapy beamline for salivary gland tumors, a human voxel phantom was implemented in GEANT4 and irradiated with the implemented MEDAPP neutron and photon spectra. The 3D dose distribution calculated inside the head of the phantom was similar to the depth dose curves in the water phantom, with some differences that are explained by differences in elementary composition. The lateral dose distribution was studied at various depths. The calculated cumulative dose volume histograms for the voxel phantom show the exposure of organs at risk surrounding the tumor.

CONCLUSIONS

In order to minimize the dose to healthy tissue, a conformal treatment is necessary. This can only be accomplished with the help of an advanced treatment planning system like the one developed here. Although all calculations were done for absorbed dose only, any biological dose weighting can be implemented easily, to take into account the increased radiobiological effectiveness of neutrons compared to photons.

Motion management with phase-adapted 4D-optimization

Cancer treatment with ionizing radiation is often compromised by organ motion, in particular for lung cases. Motion uncertainties can significantly degrade an otherwise optimized treatment plan. We present a spatiotemporal optimization method, which takes into account all phases of breathing via the corresponding 4D-CTs and provides a 4D-optimal plan that can be delivered throughout all breathing phases. Monte Carlo dose calculations are employed to warrant for highest dosimetric accuracy, as pertinent to study motion effects in lung. We demonstrate the performance of this optimization method with clinical lung cancer cases and compare the outcomes to conventional gating techniques. We report significant improvements in target coverage and in healthy tissue sparing at a comparable computational expense. Furthermore, we show that the phase-adapted 4D-optimized plans are robust against irregular breathing, as opposed to gating. This technique has the potential to yield a higher delivery efficiency and a decisively shorter delivery time.

The effect of statistical noise on IMRT plan quality and convergence for MC-based and MC-correction-based optimized treatment plans

Monte Carlo (MC) is rarely used for IMRT plan optimization outside of research centres due to the extensive computational resources or long computation times required to complete the process. Time can be reduced by degrading the statistical precision of the MC dose calculation used within the optimization loop. However, this eventually introduces optimization convergence errors (OCEs). This study determines the statistical noise levels tolerated during MC-IMRT optimization under the condition that the optimized plan has OCEs <100 cGy (1.5% of the prescription dose) for MC-optimized IMRT treatment plans.Seven-field prostate IMRT treatment plans for 10 prostate patients are used in this study. Pre-optimization is performed for deliverable beams with a pencil-beam (PB) dose algorithm. Further deliverable-based optimization proceeds using: (1) MC-based optimization, where dose is recomputed with MC after each intensity update or (2) a once-corrected (OC) MC-hybrid optimization, where a MC dose computation defines beam-by-beam dose correction matrices that are used during a PB-based optimization. Optimizations are performed with nominal per beam MC statistical precisions of 2, 5, 8, 10, 15, and 20%. Following optimizer convergence, beams are re-computed with MC using 2% per beam nominal statistical precision and the 2 PTV and 10 OAR dose indices used in the optimization objective function are tallied. For both the MC-optimization and OC-optimization methods, statistical equivalence tests found that OCEs are less than 1.5% of the prescription dose for plans optimized with nominal statistical uncertainties of up to 10% per beam. The achieved statistical uncertainty in the patient for the 10% per beam simulations from the combination of the 7 beams is ~3% with respect to maximum dose for voxels with D>0.5D(max). The MC dose computation time for the OC-optimization is only 6.2 minutes on a single 3 Ghz processor with results clinically equivalent to high precision MC computations.

Performance of a hybrid MC dose algorithm for IMRT optimization dose evaluation

This paper presents a hybrid intensity modulated radiation therapy (IMRT) optimization strategy which combines the speed of pencil beam (PB) and the accuracy of Monte Carlo (MC) dose calculations. After an initial deliverable-based optimization using a PB algorithm, doses are recomputed using the VMC++ MC code to determine dose correction factors, which are then utilized during further PB-based optimization. The hybrid method is benchmarked with respect to full MC deliverable-based optimization for ten prostate and ten head-and-neck IMRT plans. Final optimized plans are compared in terms of dose-volume indices used for the plan optimization. Dose prediction errors (DPEs) and optimization convergence errors (OCEs) at intermediate steps of the hybrid sequence are evaluated. The hybrid method is found to produce optimized plans that are clinically equivalent to full MC-based optimization, yet requires only 40% of the number of MC dose calculations. With the hybrid strategy presented here, MC-based optimization results are achieved in 35 min or less on a modest computing cluster. While the initial PB-deliverable-based optimization is found to have DPEs and OCEs of up to 3 Gy relative to the 65-73 Gy prescription doses, application of the first MC correction reduces the average DPEs to less than 0.3 Gy for the prostate plans and less than 0.06 Gy for the head and neck plans. The maximum observed DPE or OCE is 0.7 Gy after 1 MC dose correction, indicating that a single MC dose calculation correction might be sufficient for IMRT optimization.

Application of adjoint Monte Carlo to accelerate simulations of mono-directional beams in treatment planning for boron neutron capture therapy

This paper deals with the application of the adjoint transport theory in order to optimize Monte Carlo based radiotherapy treatment planning. The technique is applied to Boron Neutron Capture Therapy where most often mixed beams of neutrons and gammas are involved. In normal forward Monte Carlo simulations the particles start at a source and lose energy as they travel towards the region of interest, i.e., the designated point of detection. Conversely, with adjoint Monte Carlo simulations, the so-called adjoint particles start at the region of interest and gain energy as they travel towards the source where they are detected. In this respect, the particles travel backwards and the real source and real detector become the adjoint detector and adjoint source, respectively. At the adjoint detector, an adjoint function is obtained with which numerically the same result, e.g., dose or flux in the tumor, can be derived as with forward Monte Carlo. In many cases, the adjoint method is more efficient and by that is much quicker when, for example, the response in the tumor or organ at risk for many locations and orientations of the treatment beam around the patient is required. However, a problem occurs when the treatment beam is mono-directional as the probability of detecting adjoint Monte Carlo particles traversing the beam exit (detector plane in adjoint mode) in the negative direction of the incident beam is zero. This problem is addressed here and solved first with the use of next event estimators and second with the application of a Legendre expansion technique of the angular adjoint function. In the first approach, adjoint particles are tracked deterministically through a tube to a (adjoint) point detector far away from the geometric model. The adjoint particles will traverse the disk shaped entrance of this tube (the beam exit in the actual geometry) perpendicularly. This method is slow whenever many events are involved that are not contributing to the point detector, e.g., neutrons in a scattering medium. In the second approach, adjoint particles that traverse an adjoint shaped detector plane are used to estimate the Legendre coefficients for expansion of the angular adjoint function. This provides an estimate of the adjoint function for the direction normal to the detector plane. In a realistic head model, as described in this paper, which is surrounded by 1020 mono-directional neutron/gamma beams and from which the best ones are to be selected, the example calculates the neutron and gamma fluxes in ten tumors and ten organs at risk. For small diameter beams (5 cm), and with comparable relative errors, forward Monte Carlo is seen to be 1.5 times faster than the adjoint Monte Carlo techniques. For larger diameter neutron beams (10 and 15 cm), the Legendre technique is found to be 6 and 20 times faster, respectively. In the case of gammas alone, for the 10 and 15 cm diam beams, both adjoint Monte Carlo Legendre and point detector techniques are respectively 2 and 3 times faster than forward Monte Carlo.

A greedy heuristic using adjoint functions for the optimization of seed and needle configurations in prostate seed implant

We continue our work on the development of an efficient treatment-planning algorithm for prostate seed implants by incorporation of an automated seed and needle configuration routine. The treatment-planning algorithm is based on region of interest (ROI) adjoint functions and a greedy heuristic. As defined in this work, the adjoint function of an ROI is the sensitivity of the average dose in the ROI to a unit-strength brachytherapy source at any seed position. The greedy heuristic uses a ratio of target and critical structure adjoint functions to rank seed positions according to their ability to irradiate the target ROI while sparing critical structure ROIs. Because seed positions are ranked in advance and because the greedy heuristic does not modify previously selected seed positions, the greedy heuristic constructs a complete seed configuration quickly. Isodose surface constraints determine the search space and the needle constraint limits the number of needles. This study additionally includes a methodology that scans possible combinations of these constraint values automatically. This automated selection scheme saves the user the effort of manually searching constraint values. With this method, clinically acceptable treatment plans are obtained in less than 2 min. For comparison, the branch-and-bound method used to solve a mixed integer-programming model took close to 2.5 h to arrive at a feasible solution. Both methods achieved good treatment plans, but the speedup provided by the greedy heuristic was a factor of approximately 100. This attribute makes this algorithm suitable for intra-operative real-time treatment planning.

A finite size pencil beam algorithm for IMRT dose optimization: density corrections

For beamlet-based IMRT optimization, fast and less accurate dose computation algorithms are frequently used, while more accurate algorithms are needed to recompute the final dose for verification. In order to speed up the optimization process and ensure close proximity between dose in optimization and verification, proper consideration of dose gradients and tissue inhomogeneity effects should be ensured at every stage of the optimization. Due to their speed, pencil beam algorithms are often used for precalculation of beamlet dose distributions in IMRT treatment planning systems. However, accounting for tissue heterogeneities with these models requires the use of approximate rescaling methods. Recently, a finite size pencil beam (fsPB) algorithm, based on a simple and small set of data, was proposed which was specifically designed for the purpose of dose pre-computation in beamlet-based IMRT. The present work describes the incorporation of 3D density corrections, based on Monte Carlo simulations in heterogeneous phantoms, into this method improving the algorithm accuracy in inhomogeneous geometries while keeping its original speed and simplicity of commissioning. The algorithm affords the full accuracy of 3D density corrections at every stage of the optimization, hence providing the means for density related fluence modulation like penumbra shaping at field edges.

Application of an inverse kernel concept to Monte Carlo based IMRT

Inverse treatment planning by means of pencil beam algorithms can lead to errors in the calculation of dose in areas without secondary electron equilibrium. Monte Carlo (MC) simulations give accurate results in such areas but result in increased computation times. We present a new, so-called inverse kernel concept that offers MC precision in inverse treatment planning with acceptable computation times and memory consumption. Inverse kernels are matrices that describe the dose contribution from all bixels of a beam to a distinct voxel of the patient phantom. The concept is similar to other generalized pencil-beam concepts, except that inverse kernel elements are precalculated using a single MC simulation and stored as binary trees. In this procedure a modified MC code (XVMC) is applied to trace the photon history for each dose deposition. Iterative optimization is then applied in a second step. The inverse process is separated into (i) a slower MC simulation and (ii) a faster iterative optimization, followed by (iii) the segmentation procedure, and (iv) a final MC dose calculation step including a segment weight reoptimization. Inverse kernel optimization, or IKO, with segmentation and reoptimization steps is demonstrated by means of a lung cancer case. To demonstrate the superiority of an inverse MC system over pencil-beam or collapsed-cone based systems, the final result of the IKO is compared to plans where all segments have been calculated by pencil beam or collapsed cone, respectively. Dose-volume histograms and dose-difference histograms show remarkable differences, which can be attributed to systematic errors in both algorithms. IKO is a precise, nonhybrid, inverse MC treatment planning system which suits current clinical needs, as several optimization steps can follow one single MC-simulation step for a distinct beam setup.

Efficient schemes for robust IMRT treatment planning

We use robust optimization techniques to formulate an IMRT treatment planning problem in which the dose matrices are uncertain, due to both dose calculation errors and interfraction positional uncertainty of tumour and organs. When the uncertainty is taken into account, the original linear programming formulation becomes a second-order cone program. We describe a novel and efficient approach for solving this problem, and present results to compare the performance of our scheme with more conventional formulations that assume perfect knowledge of the dose matrix.

Improving IMRT dose accuracy via deliverable Monte Carlo optimization for the treatment of head and neck cancer patients

The purpose of this work is to investigate the effect of dose-calculation accuracy on head and neck (H&N) intensity modulated radiation therapy (IMRT) plans by determining the systematic dose-prediction and optimization-convergence errors (DPEs and OCEs), using a superposition/convolution (SC) algorithm. Ten patients with locally advanced H&N squamous cell carcinoma who were treated with simultaneous integrated boost IMRT were selected for this study. The targets consisted of gross target volume (GTV), clinical target volume (CTV), and nodal target volumes (CTV nodes). The critical structures included spinal cord, parotid glands, and brainstem. For all patients, three IMRT plans were created: A: an SC optimized plan (SCopt), B: an SCopt plan recalculated with Monte Carlo [MC(SCopt)], and C: an MC optimized plan (MCopt). For each structure, DPEs and OCEs were estimated as DPE(SC)=D(B)-D(A) and OCE(SC)=D(C)-D(B) where A, B, and C stand for the three different optimized plans as defined above. Deliverable optimization was used for all plans, that is, a leaf-sequencing step was incorporated into the optimization loop at each iteration. The range of DPE(SC) in the GTV D98 varied from -1.9% to -4.9%, while the OCE(SC) ranged from 0.9% to 7.0%. The DPE(SC) in the contralateral parotid D50 reached 8.2%, while the OCE(SC) in the contralateral parotid D50 varied from 0.91% to 6.99%. The DPE(SC) in cord D2 reached -3.0%, while the OCE(SC) reached to -7.0%. The magnitude of the DPE(SC) and OCE(SC) differences demonstrate the importance of using the most accurate available algorithm in the deliverable IMRT optimization process, especially for the estimation of normal structure doses.

Direct aperture optimization for IMRT using Monte Carlo generated beamlets

This work introduces an EGSnrc-based Monte Carlo (MC) beamlet does distribution matrix into a direct aperture optimization (DAO) algorithm for IMRT inverse planning. The technique is referred to as Monte Carlo-direct aperture optimization (MC-DAO). The goal is to assess if the combination of accurate Monte Carlo tissue inhomogeneity modeling and DAO inverse planning will improve the dose accuracy and treatment efficiency for treatment planning. Several authors have shown that the presence of small fields and/or inhomogeneous materials in IMRT treatment fields can cause dose calculation errors for algorithms that are unable to accurately model electronic disequilibrium. This issue may also affect the IMRT optimization process because the dose calculation algorithm may not properly model difficult geometries such as targets close to low-density regions (lung, air etc.). A clinical linear accelerator head is simulated using BEAMnrc (NRC, Canada). A novel in-house algorithm subdivides the resulting phase space into 2.5 X 5.0 mm2 beamlets. Each beamlet is projected onto a patient-specific phantom. The beamlet dose contribution to each voxel in a structure-of-interest is calculated using DOSXYZnrc. The multileaf collimator (MLC) leaf positions are linked to the location of the beamlet does distributions. The MLC shapes are optimized using direct aperture optimization (DAO). A final Monte Carlo calculation with MLC modeling is used to compute the final dose distribution. Monte Carlo simulation can generate accurate beamlet dose distributions for traditionally difficult-to-calculate geometries, particularly for small fields crossing regions of tissue inhomogeneity. The introduction of DAO results in an additional improvement by increasing the treatment delivery efficiency. For the examples presented in this paper the reduction in the total number of monitor units to deliver is approximately 33% compared to fluence-based optimization methods.

Dose heterogeneity in the target volume and intensity-modulated radiotherapy to escalate the dose in the treatment of non–small-cell lung cancer

PURPOSE

To quantify the dose escalation achievable in the treatment of non-small-cell lung cancer (NSCLC) by allowing dose heterogeneity in the target volume or using intensity-modulated radiotherapy (IMRT), or both.

METHODS AND MATERIALS

Computed tomography data and contours of 10 NSCLC patients with limited movements of the tumor and representing a broad spectrum of clinical cases were selected for this study. Four irradiation techniques were compared: two conformal (CRT) and two IMRT techniques, either prescribing a homogeneous dose in the planning target volume (PTV) (CRT(hom) and IMRT(hom)) or allowing dose heterogeneity (CRT(inhom) and IMRT(inhom)). The dose heterogeneity was allowed only toward high doses, i.e., the minimum dose in the target for CRT(inhom) and IMRT(inhom) could not be lower than for the corresponding homogeneous plan. The dose in the PTV was escalated (fraction size of 2.25 Gy) until either an organ at risk reached the maximum allowed dose or the mean PTV dose reached a maximum level set at 101.25 Gy.

RESULTS

When small and convex tumors were irradiated, CRT(hom) could achieve the maximum dose of 101.25 Gy, whereas for bigger and/or concave PTVs the dose level achievable with CRT(hom) was significantly lower, in 1 case even below 60 Gy. The CRT(inhom) allowed on average a 6% dose escalation with respect to CRT(hom). The IMRT(hom) achieved in all except 1 case a mean PTV dose of at least 75 Gy. The gain in mean PTV dose of IMRT(hom) with respect to CRT(hom) ranged from 7.7 to 14.8 Gy and the IMRT(hom) plans were always more conformal than the corresponding CRT(hom) plans. The IMRT(inhom) provided an additional advantage over IMRT(hom) of at least 5 Gy. For all CRT plans the achievable dose was determined by the lung dose threshold, whereas for more than half of the IMRT plans the esophagus was the dose-limiting organ. The IMRT plans were deliverable with 10-12 segments per beam and did not produce an increase of lung volume irradiated at low doses (<20 Gy).

CONCLUSIONS

The dose in NSCLC treatments can be escalated by loosening the constraints on maximum dose in the target volume or using IMRT, or both. For large and concave tumors, an average dose escalation of 6% and 17% was possible when dose heterogeneity and IMRT were applied alone. When they were combined, the average dose increase was as high as 35%. Intensity-modulated RT delivered in a static mode can produce homogeneous dose distributions in the target and does not lead to an increase of lung volume receiving (very) low doses, even down to 5 Gy.

Treatment planning for prostate brachytherapy using region of interest adjoint functions and a greedy heuristic

We have developed an efficient treatment-planning algorithm for prostate implants that is based on region of interest (ROI) adjoint functions and a greedy heuristic. For this work, we define the adjoint function for an ROI as the sensitivity of the average dose in the ROI to a unit-strength brachytherapy source at any seed position. The greedy heuristic uses a ratio of target and critical structure adjoint functions to rank seed positions according to their ability to irradiate the target ROI while sparing critical structure ROIs. This ratio is computed once for each seed position prior to the optimization process. Optimization is performed by a greedy heuristic that selects seed positions according to their ratio values. With this method, clinically acceptable treatment plans are obtained in less than 2 s. For comparison, a branch-and-bound method to solve a mixed integer-programming model took more than 50 min to arrive at a feasible solution. Both methods achieved good treatment plans, but the speedup provided by the greedy heuristic was a factor of approximately 1500. This attribute makes this algorithm suitable for intra-operative real-time treatment planning.

Importance of accurate dose calculations outside segment edges in intensity modulated radiotherapy treatment planning

BACKGROUND AND PURPOSE

To assess the effect of differences in the calculation of the dose outside segment edges on the overall dose distribution and the optimisation process of intensity modulated radiation therapy (IMRT) treatment plans.

PATIENTS AND METHODS

Accuracy of dose calculations of two treatment planning systems (TPS1 and TPS2) was assessed, to ensure that they are both suitable for IMRT treatment planning according to published guidelines. Successively, 10 treatment plans for patients with prostate and head and neck tumours were calculated in both systems. The calculations were compared in selected points as well as in combination with volumetric parameters concerning the planning target volume (PTV) and organs at risk.

RESULTS

For both planning systems, the calculations agree within 2.0% or 3 mm with the measurements in the high-dose region for single and multiple segment dose distributions. The accuracy of the dose calculation is within the tolerances proposed by recent recommendations. Below 35% of the prescribed dose, TPS1 overestimates and TPS2 underestimates the measured dose values, TPS2 being closer to the experimental data. The differences between TPS1 and TPS2 in the calculation of the dose outside segments explain the differences (up to 50% of the local value) found in point dose comparisons. For the prostate plans, the discrepancies between the TPS do not translate into differences in PTV coverage, normal tissue complication probability (NTCP) values and results of the plan optimisation process. The dose-volume histograms (DVH) of the rectal wall differ below 60 Gy, thus affecting the plan optimisation if a cost function would operate in this dose region. For the head and neck cases, the two systems give different evaluations of the DVH points for the PTV (up to 22% differences in target coverage) and the parotid mean dose (1.0-3.0 Gy). Also the results of the optimisation are influenced by the choice of the dose calculation algorithm.

CONCLUSIONS

In IMRT, the accuracy of the dose calculation outside segment edges is important for the determination of the dose to both organs at risks and target volumes and for a correct outcome of the optimisation process. This aspect should therefore be of major concern in the commissioning of a TPS intended for use in IMRT. Fulfilment of the accuracy criteria valid for conformal radiotherapy is not sufficient. Three-dimensional evaluation of the dose distribution is needed in order to assess the impact of dose calculation accuracy outside the segment edges on the total dose delivered to patients treated with IMRT.

Simulations for inverse radiation therapy treatment planning using a dynamic MLC algorithm

The inverse radiation treatment planning model for a dynamic multileaf collimator (MLC) is used to find the optimal solution of planning problem. The model for dynamic MLC is explained in Tervo et al (2003 Appl. Math. Comput. 135 227-50). The advantage of this model is that it optimizes leaf velocity parameters directly. Our algorithm uses a gradient-based local optimization method. Two patient cases, prostate carcinoma and tonsilla carcinoma, are studied. Field arrangements are pre-selected and velocity parameters for MLC leaves are optimized to obtain the prescribed dose in the patient space. In both simulated cases, high dose distribution conforms the planning target volume well and organs-at-risk are saved in most parts. Simulations show that the model has its functionality in patient treatments, although it is still formal and needs further development.

A Monte Carlo tutorial and the application for radiotherapy treatment planning

Monte Carlo-based treatment planning algorithms are advancing rapidly and will certainly be implemented as part of conventional treatment planning systems in the near future. This paper was designed as a basic tutorial for using the Monte Carlo method as applied to radiotherapy treatment planning. The tutorial addresses the basic transport differences between photon and electron transport as well as the sampling distributions. The implementation of a virtual linac source model and the conversion from the Monte Carlo source modeling reference plane into the treatment reference plane is discussed. The implementation of a thresholding algorithm for converting CT electron density to patient specific materials is also presented. A 6-field prostate boost treatment is used to compare a conventional treatment planning algorithm (pencil beam model) with a Monte Carlo simulation algorithm. The agreement between the 2 calculation methods is good based upon the qualitative comparison of the isodose distribution and the dose-volume histograms for the prostate and the rectum. The effects of statistical uncertainty on the Monte Carlo calculation are also presented.

A method for photon beam Monte Carlo multileaf collimator particle transport

Monte Carlo (MC) algorithms are recognized as the most accurate methodology for patient dose assessment. For intensity-modulated radiation therapy (IMRT) delivered with dynamic multileaf collimators (DMLCs), accurate dose calculation, even with MC, is challenging. Accurate IMRT MC dose calculations require inclusion of the moving MLC in the MC simulation. Due to its complex geometry, full transport through the MLC can be time consuming. The aim of this work was to develop an MLC model for photon beam MC IMRT dose computations. The basis of the MC MLC model is that the complex MLC geometry can be separated into simple geometric regions, each of which readily lends itself to simplified radiation transport. For photons, only attenuation and first Compton scatter interactions are considered. The amount of attenuation material an individual particle encounters while traversing the entire MLC is determined by adding the individual amounts from each of the simplified geometric regions. Compton scatter is sampled based upon the total thickness traversed. Pair production and electron interactions (scattering and bremsstrahlung) within the MLC are ignored. The MLC model was tested for 6 MV and 18 MV photon beams by comparing it with measurements and MC simulations that incorporate the full physics and geometry for fields blocked by the MLC and with measurements for fields with the maximum possible tongue-and-groove and tongue-or-groove effects, for static test cases and for sliding windows of various widths. The MLC model predicts the field size dependence of the MLC leakage radiation within 0.1% of the open-field dose. The entrance dose and beam hardening behind a closed MLC are predicted within +/- 1% or 1 mm. Dose undulations due to differences in inter- and intra-leaf leakage are also correctly predicted. The MC MLC model predicts leaf-edge tongue-and-groove dose effect within +/- 1% or 1 mm for 95% of the points compared at 6 MV and 88% of the points compared at 18 MV. The dose through a static leaf tip is also predicted generally within +/- 1% or 1 mm. Tests with sliding windows of various widths confirm the accuracy of the MLC model for dynamic delivery and indicate that accounting for a slight leaf position error (0.008 cm for our MLC) will improve the accuracy of the model. The MLC model developed is applicable to both dynamic MLC and segmental MLC IMRT beam delivery and will be useful for patient IMRT dose calculations, pre-treatment verification of IMRT delivery and IMRT portal dose transmission dosimetry.

[IMCO(++)--a Monte Carlo based IMRT system]

The application of intensity modulated radiotherapy (IMRT) to dose escalation in the target volume sets particular demands in terms of accuracy of dose calculation. Dose calculation errors due to approximations are compensated by the optimization algorithm, a procedure that ultimately leads to incorrect fluence modulation. Such inaccuracies affect particularly the dose distribution in areas with secondary electron disequilibrium. In case tissues heterogeneity predominates, conventional dose calculation methods (such as Pencil Beam) can produce relative errors up to more than 10%. The accuracy can be significantly improved by the application of a Monte-Carlo (MC) algorithm. This paper describes a MC-based inverse treatment planning algorithm (IMCO++), based on a non-iterative approach with a feedback-controlling process. The convergence behavior of IMCO++ was investigated and the used MC dose-calculation codes MMms and XVMC were compared by means of a heterogeneous phantom. IMCO++ plans were optimized in various phantoms. All plans showed conformity in terms of dose distribution of the target volume and dose reduction in risk organs (according to the requirements of the target parameter), as well as a very fast convergence of the algorithm (in less than 10 optimization steps).

Monte Carlo simulation for MLC-based intensity-modulated radiotherapy

This article describes photon beam Monte Carlo simulation for multi leaf collimator (MLC)-based intensity-modulated radiotherapy (IMRT). We present the general aspects of the Monte Carlo method for the non-Monte Carloist with an emphasis given to patient-specific radiotherapy application. Patient-specific application of the Monte Carlo method can be used for IMRT dose verification, inverse planning, and forward planning in conventional conformal radiotherapy. Because it is difficult to measure IMRT dose distributions in heterogeneous phantoms that approximate a patient, Monte Carlo methods can be used to verify IMRT dose distributions that are calculated using conventional methods. Furthermore, using Monte Carlo as the dose calculation method for inverse planning results in better-optimized treatment plans. We describe both aspects and present our recent results to illustrate the discussion. Finally, we present current issues related to clinical implementation of Monte Carlo dose calculation. Monte Carlo is the most recent, and most accurate, method of radiotherapy dose calculation. It is currently in the process of being implemented by various treatment planning vendors and will be available for clinical use in the immediate future.

The effect of dose calculation accuracy on inverse treatment planning

The effect of dose calculation accuracy during inverse treatment planning for intensity modulated radiotherapy (IMRT) was studied in this work. Three dose calculation methods were compared: Monte Carlo, superposition and pencil beam. These algorithms were used to calculate beamlets. which were subsequently used by a simulated annealing algorithm to determine beamlet weights which comprised the optimal solution to the objective function. Three different cases (lung, prostate and head and neck) were investigated and several different objective functions were tested for their effect on inverse treatment planning. It is shown that the use of inaccurate dose calculation introduces two errors in a treatment plan, a systematic error and a convergence error. The systematic error is present because of the inaccuracy of the dose calculation algorithm. The convergence error appears because the optimal intensity distribution for inaccurate beamlets differs from the optimal solution for the accurate beamlets. While the systematic error for superposition was found to be approximately 1% of Dmax in the tumour and slightly larger outside, the error for the pencil beam method is typically approximately 5% of Dmax and is rather insensitive to the given objectives. On the other hand, the convergence error was found to be very sensitive to the objective function, is only slightly correlated to the systematic error and should be determined for each case individually. Our results suggest that because of the large systematic and convergence errors, inverse treatment planning systems based on pencil beam algorithms alone should be upgraded either to superposition or Monte Carlo based dose calculations.

[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.

Acceleration of dose calculations for intensity-modulated radiotherapy

The requirements and trade-offs between accuracy and speed for radiotherapy dose computations have been discussed for decades. Inverse planning used for intensity-modulated radiotherapy (IMRT) optimization imposes additional demands on dose calculation since it is an iterative process in which dose calculations might be repeated many (10's to 1000's) of times. This work discusses the accuracy and speed issues as related to IMRT dose calculations. A hybrid dose calculation method which accelerates the optimization process is proposed and applied in which a fast-pencil beam (PB) model is used for initial optimization iterations, followed by superposition/convolution (SC) calculations. Optimization dose results are compared for pure PB optimization, pure SC optimization, and PB optimization followed by SC optimization. Plans were evaluated in terms of isodose coverage, dose-volume histograms, and total dose calculation time for five head and neck cases with diverse locations, sizes, and shapes for tumors and critical structures. Patient plans were designed for nine equispaced beams. For one patient, an additional five-beam configuration was tested. We found that gross features of intensity distributions resulting from all schemes were similar, however there were differences in the fine detail. Differences were small between composite dose distributions optimized with PB and SC methods, yet differences in individual beam dose distributions were quite significant. When the SC method was used to compute dose following optimization with PB method, dose differences were reduced significantly both for composite plans and for individual beams. Substantial overall timesavings were observed, allowing IMRT dose planning to become a more interactive activity.

The effect of statistical uncertainty on inverse treatment planning based on Monte Carlo dose calculation

The effect of the statistical uncertainty, or noise, in inverse treatment planning for intensity modulated radiotherapy (IMRT) based on Monte Carlo dose calculation was studied. Sets of Monte Carlo beamlets were calculated to give uncertainties at Dmax ranging from 0.2% to 4% for a lung tumour plan. The weights of these beamlets were optimized using a previously described procedure based on a simulated annealing optimization algorithm. Several different objective functions were used. It was determined that the use of Monte Carlo dose calculation in inverse treatment planning introduces two errors in the calculated plan. In addition to the statistical error due to the statistical uncertainty of the Monte Carlo calculation, a noise convergence error also appears. For the statistical error it was determined that apparently successfully optimized plans with a noisy dose calculation (3% 1sigma at Dmax), which satisfied the required uniformity of the dose within the tumour, showed as much as 7% underdose when recalculated with a noise-free dose calculation. The statistical error is larger towards the tumour and is only weakly dependent on the choice of objective function. The noise convergence error appears because the optimum weights are determined using a noisy calculation, which is different from the optimum weights determined for a noise-free calculation. Unlike the statistical error, the noise convergence error is generally larger outside the tumour, is case dependent and strongly depends on the required objectives.

Validation of a Monte Carlo dose calculation tool for radiotherapy treatment planning

A new EGS4/PRESTA Monte Carlo user code, MCDOSE, has been developed as a routine dose calculation tool for radiotherapy treatment planning. It is suitable for both conventional and intensity modulated radiation therapy. Two important features of MCDOSE are the inclusion of beam modifiers in the patient simulation and the implementation of several variance reduction techniques. Before this tool can be used reliably for clinical dose calculation, it must be properly validated. The validation for beam modifiers has been performed by comparing the dose distributions calculated by MCDOSE and the well-benchmarked EGS4 user codes BEAM and DOSXYZ. Various beam modifiers were simulated. Good agreement in the dose distributions was observed. The differences in electron cutout factors between the results of MCDOSE and measurements were within 2%. The accuracy of MCDOSE with various variance reduction techniques was tested by comparing the dose distributions in different inhomogeneous phantoms with those calculated by DOSXYZ without variance reduction. The agreement was within 1.0%. Our results demonstrate that MCDOSE is accurate and efficient for routine dose calculation in radiotherapy treatment planning, with or without beam modifiers.

Energy- and intensity-modulated electron beams for radiotherapy

This work investigates the feasibility of optimizing energy- and intensity-modulated electron beams for radiation therapy. A multileaf collimator (MLC) specially designed for modulated electron radiotherapy (MERT) was investigated both experimentally and by Monte Carlo simulations. An inverse-planning system based on Monte Carlo dose calculations was developed to optimize electron beam energy and intensity to achieve dose conformity for target volumes near the surface. The results showed that an MLC with 5 mm leaf widths could produce complex field shapes for MERT. Electron intra- and inter-leaf leakage had negligible effects on the dose distributions delivered with the MLC, even at shallow depths. Focused leaf ends reduced the electron scattering contributions to the dose compared with straight leaf ends. As anticipated, moving the MLC position toward the patient surface reduced the penumbra significantly. There were significant differences in the beamlet distributions calculated by an analytic 3-D pencil beam algorithm and the Monte Carlo method. The Monte Carlo calculated beamlet distributions were essential to the accuracy of the MERT dose distribution in cases involving large air gaps, oblique incidence and heterogeneous treatment targets (at the tissue-bone and bone-lung interfaces). To demonstrate the potential of MERT for target dose coverage and normal tissue sparing for treatment of superficial targets, treatment plans for a hypothetical treatment were compared using photon beams and MERT.

Denoising of electron beam Monte Carlo dose distributions using digital filtering techniques

The Monte Carlo (MC) method has long been viewed as the ultimate dose distribution computational technique. The inherent stochastic dose fluctuations (i.e. noise), however, have several important disadvantages: noise will affect estimates of all the relevant dosimetric and radiobiological indices, and noise will degrade the resulting dose contour visualizations. We suggest the use of a post-processing denoising step to reduce statistical fluctuations and also improve dose contour visualization. We report the results of applying four different two-dimensional digital smoothing filters to two-dimensional dose images. The Integrated Tiger Series MC code was used to generate 10 MeV electron beam dose distributions at various depths in two different phantoms. The observed qualitative effects of filtering include: (a) the suppression of voxel-to voxel (high-frequency) noise and (b) the resulting contour plots are visually more comprehensible. Drawbacks include, in some cases, slight blurring of penumbra near the surface and slight blurring of other very sharp real dosimetric features. Of the four digital filters considered here, one, a filter based on a local least-squares principle, appears to suppress noise with negligible degradation of real dosimetric features. We conclude that denoising of electron beam MC dose distributions is feasible and will yield improved dosimetric reliability and improved visualization of dose distributions.

Monte Carlo dose computation for IMRT optimization

A method which combines the accuracy of Monte Carlo dose calculation with a finite size pencil-beam based intensity modulation optimization is presented. The pencil-beam algorithm is employed to compute the fluence element updates for a converging sequence of Monte Carlo dose distributions. The combination is shown to improve results over the pencil-beam based optimization in a lung tumour case and a head and neck case. Inhomogeneity effects like a broader penumbra and dose build-up regions can be compensated for by intensity modulation.