Feasibility of using intermediate x-ray energies for highly conformal extracranial radiotherapy

Treatment planning with a 2.5 MV photon beam for radiation therapy

PURPOSE

The shallow depth of maximum dose and higher dose fall-off gradient of a 2.5 MV beam along the central axis that is available for imaging on linear accelerators is investigated for treatment of shallow tumors and sparing the organs at risk (OARs) beyond it. In addition, the 2.5 MV beam has an energy bridging the gap between kilo-voltage (kV) and mega-voltage (MV) beams for applications of dose enhancement with high atomic number (Z) nanoparticles.

METHODS

We have commissioned and utilized a MATLAB-based, open-source treatment planning software (TPS), matRad, for intensity-modulated radiation therapy (IMRT) dose calculations. Treatment plans for prostate, liver, and head and neck (H&N), nasal cavity, two orbit cases, and glioblastoma multiforme (GBM) were performed and compared to a conventional 6 MV beam. Additional Monte Carlo calculations were also used for benchmarking the central axis dose.

RESULTS

Both beams had similar planning target volume (PTV) dose coverage for all cases. However, the 2.5 MV beam deposited 6%-19% less integral doses to the nasal cavity, orbit, and GBM cases than 6 MV photons. The mean dose to the heart in the liver plan was 10.5% lower for 2.5 MV beam. The difference between the doses to OARs of H&N for two beams was under 3%. Brain mean dose, brainstem, and optic chiasm max doses were, respectively, 7.5%-14.9%, 2.2%-8.1%, and 2.5%-19.0% lower for the 2.5 MV beam in the nasal cavity, orbit, and GBM plans.

CONCLUSIONS

This study demonstrates that the 2.5 MV beam can produce clinically relevant treatment plans, motivating future efforts for design of single-energy LINACs. Such a machine will be capable of producing beams at this energy beneficial for low- and middle-income countries, and investigations on dose enhancement from high-Z nanoparticles.

A fast deep learning approach for beam orientation optimization for prostate cancer treated with intensity-modulated radiation therapy

PURPOSE

Beam orientation selection, whether manual or protocol-based, is the current clinical standard in radiation therapy treatment planning, but it is tedious and can yield suboptimal results. Many algorithms have been designed to optimize beam orientation selection because of its impact on treatment plan quality, but these algorithms suffer from slow calculation of the dose influence matrices of all candidate beams. We propose a fast beam orientation selection method, based on deep learning neural networks (DNN), capable of developing a plan comparable to those developed by the state-of-the-art column generation (CG) method. Our model's novelty lies in its supervised learning structure (using CG to teach the network), DNN architecture, and ability to learn from anatomical features to predict dosimetrically suitable beam orientations without using dosimetric information from the candidate beams. This may save hours of computation.

METHODS

A supervised DNN is trained to mimic the CG algorithm, which iteratively chooses beam orientations one-by-one by calculating beam fitness values based on Karush-Kush-Tucker optimality conditions at each iteration. The DNN learns to predict these values. The dataset contains 70 prostate cancer patients - 50 training, 7 validation, and 13 test patients - to develop and test the model. Each patient's data contains 6 contours: PTV, body, bladder, rectum, and left and right femoral heads. Column generation was implemented with a GPU-based Chambolle-Pock algorithm, a first-order primal-dual proximal-class algorithm, to create 6270 plans. The DNN trained over 400 epochs, each with 2500 steps and a batch size of 1, using the Adam optimizer at a learning rate of 1 × 10-5 and a sixfold cross-validation technique.

RESULTS

The average and standard deviation of training, validation, and testing loss functions among the six folds were 0.62 ± 0.09%, 1.04 ± 0.06%, and 1.44 ± 0.11%, respectively. Using CG and supervised DNN, we generated two sets of plans for each scenario in the test set. The proposed method took at most 1.5 s to select a set of five beam orientations and 300 s to calculate the dose influence matrices for 5 beams and finally 20 s to solve the fluence map optimization (FMO). However, CG needed around 15 h to calculate the dose influence matrices of all beams and at least 400 s to solve both the beam orientation selection and FMO problems. The differences in the dose coverage of PTV between plans generated by CG and by DNN were 0.2%. The average dose differences received by organs at risk were between 1 and 6 percent: Bladder had the smallest average difference in dose received (0.956 ± 1.184%), then Rectum (2.44 ± 2.11%), Left Femoral Head (6.03 ± 5.86%), and Right Femoral Head (5.885 ± 5.515%). The dose received by Body had an average difference of 0.10 ± 0.1% between the generated treatment plans.

CONCLUSIONS

We developed a fast beam orientation selection method based on a DNN that selects beam orientations in seconds and is therefore suitable for clinical routines. In the training phase of the proposed method, the model learns the suitable beam orientations based on patients' anatomical features and omits time intensive calculations of dose influence matrices for all possible candidate beams. Solving the FMO to get the final treatment plan requires calculating dose influence matrices only for the selected beams.

Many-isocenter optimization for robotic radiotherapy

Despite significant dosimetric gains, clinical implementation of the 4π non-coplanar radiotherapy on the widely available C-arm gantry system is hindered by limited clearance, and the need to perform complex coordinated gantry and couch motion. A robotic radiotherapy platform would be conducive to such treatment but a new conflict between field size and MLC modulation resolution needs to be managed for versatile applications. This study investigates the dosimetry and delivery efficiency of purposefully creating many isocenters to achieve simultaneously high MLC modulation resolution and large tumor coverage. An integrated optimization framework was proposed for simultaneous beam orientation optimization (BOO), isocenter selection, and fluence map optimization (FMO). The framework includes a least-square dose fidelity objective, a total variation term for regularizing the fluence smoothness, and a group sparsity term for beam selection. A minimal number of isocenters were identified for efficient target coverage. Colliding beams excluded, high-resolution small-field 4π intensity-modulated radiotherapy (IMRT) treatment plans with 50 cm source-to-isocenter distance (SID-50) on 10 Head and Neck (H&N) cancer patients were compared with low-resolution large-field plans with 100 cm SID (SID-100). With the same or better target coverage, the average reduction of [Dmean, Dmax] of 20-beam SID-50 plans from 20-beam SID-100 plans were [2.09 Gy, 1.19 Gy] for organs at risk (OARs) overall, [3.05 Gy, 0.04 Gy] for parotid gland, [3.62 Gy, 5.19 Gy] for larynx, and [3.27 Gy, 1.10 Gy] for mandible. R50 and integral dose were reduced by 5.3% and 9.6%, respectively. Wilcoxon signed-rank test showed significant difference (p   <  0.05) in planning target volume (PTV) homogeneity, PTV Dmax, R50, Integral dose, and OAR Dmean and Dmax. The estimated delivery time of 20-beam [SID-50, SID-100] plans were [19, 18] min and [14, 9] min, assuming 5 fractions and 30 fractions, respectively. With clinically acceptable delivery efficiency, many-isocenter optimization is dosimetrically desirable for treating large targets with high modulation resolution on the robotic platform.

Fraction-variant beam orientation optimization for non-coplanar IMRT

Conventional beam orientation optimization (BOO) algorithms for IMRT assume that the same set of beam angles is used for all treatment fractions. In this paper we present a BOO formulation based on group sparsity that simultaneously optimizes non-coplanar beam angles for all fractions, yielding a fraction-variant (FV) treatment plan. Beam angles are selected by solving a multi-fraction fluence map optimization problem involving 500-700 candidate beams per fraction, with an additional group sparsity term that encourages most candidate beams to be inactive. The optimization problem is solved using the fast iterative shrinkage-thresholding algorithm. Our FV BOO algorithm is used to create five-fraction treatment plans for digital phantom, prostate, and lung cases as well as a 30-fraction plan for a head and neck case. A homogeneous PTV dose coverage is maintained in all fractions. The treatment plans are compared with fraction-invariant plans that use a fixed set of beam angles for all fractions. The FV plans reduced OAR mean dose and D 2 values on average by 3.3% and 3.8% of the prescription dose, respectively. Notably, mean OAR dose was reduced by 14.3% of prescription dose (rectum), 11.6% (penile bulb), 10.7% (seminal vesicle), 5.5% (right femur), 3.5% (bladder), 4.0% (normal left lung), 15.5% (cochleas), and 5.2% (chiasm). D 2 was reduced by 14.9% of prescription dose (right femur), 8.2% (penile bulb), 12.7% (proximal bronchus), 4.1% (normal left lung), 15.2% (cochleas), 10.1% (orbits), 9.1% (chiasm), 8.7% (brainstem), and 7.1% (parotids). Meanwhile, PTV homogeneity defined as D 95/D 5 improved from .92 to .95 (digital phantom), from .95 to .98 (prostate case), and from .94 to .97 (lung case), and remained constant for the head and neck case. Moreover, the FV plans are dosimetrically similar to conventional plans that use twice as many beams per fraction. Thus, FV BOO offers the potential to reduce delivery time for non-coplanar IMRT.

Deterministic direct aperture optimization using multiphase piecewise constant segmentation

PURPOSE

Direct aperture optimization (DAO) attempts to incorporate machine constraints in the inverse optimization to eliminate the post-processing steps in fluence map optimization (FMO) that degrade plan quality. Current commercial DAO methods utilize a stochastic or greedy approach to search a small aperture solution space. In this study, we propose a novel deterministic direct aperture optimization that integrates the segmentation of fluence map in the optimization problem using the multiphase piecewise constant Mumford-Shah formulation.

METHODS

The Mumford-Shah based direct aperture optimization problem was formulated to include an L2-norm dose fidelity term to penalize differences between the projected dose and the prescribed dose, an anisotropic total variation term to promote piecewise continuity in the fluence maps, and the multiphase piecewise constant Mumford-Shah function to partition the fluence into pairwise discrete segments. A proximal-class, first-order primal-dual solver was implemented to solve the large scale optimization problem, and an alternating module strategy was implemented to update fluence and delivery segments. Three patients of varying complexity-one glioblastoma multiforme (GBM) patient, one lung (LNG) patient, and one bilateral head and neck (H&N) patient with 3 PTVs-were selected to test the new DAO method. For each patient, 20 non-coplanar beams were first selected using column generation, followed by the Mumford-Shah based DAO (DAO_MS ). For comparison, a popular and successful approach to DAO known as simulated annealing-a stochastic approach-was replicated. The simulated annealing DAO (DAO_SA ) plans were then created using the same beam angles and maximum number of segments per beam. PTV coverage, PTV homogeneity D95D5, and OAR sparing were assessed for each plan. In addition, high dose spillage, defined as the 50% isodose volume divided by the tumor volume, as well as conformity, defined as the van't Riet conformation number, were evaluated.

RESULTS

DAO_MS achieved essentially the same OAR doses compared with the DAO_SA plans for the GBM case. The average difference of OAR D_max and D_mean between the two plans were within 0.05% of the plan prescription dose. The lung case showed slightly improved critical structure sparing using the DAO_MS approach, where the average OAR D_max and D_mean were reduced by 3.67% and 1.08%, respectively, of the prescription dose. The DAO_MS plan substantially improved OAR dose sparing for the H&N patient, where the average OAR D_max and D_mean were reduced by over 10% of the prescription dose. The DAO_MS and DAO_SA plans were comparable for the GBM and LNG PTV coverage, while the DAO_MS plan substantially improved the H&N PTV coverage, increasing D99 by 6.98% of the prescription dose. For the GBM and LNG patients, the DAO_MS and DAO_SA plans had comparable high dose spillage but slightly worse conformity with the DAO_MS approach. For the H&N plan, DAO_MS was considerably superior in high dose spillage and conformity to the DAO_SA . The deterministic approach is able to solve the DAO problem substantially faster than the simulated annealing approach, with a 9.5- to 40-fold decrease in total solve time, depending on the patient case.

CONCLUSIONS

A novel deterministic direct aperture optimization formulation was developed and evaluated. It combines fluence map optimization and the multiphase piecewise constant Mumford-Shah segmentation into a unified framework, and the resulting optimization problem can be solved efficiently. Compared to the widely and commercially used simulated annealing DAO approach, it showed comparable dosimetry behavior for simple plans, and substantially improved OAR sparing, PTV coverage, PTV homogeneity, high dose spillage, and conformity for the more complex head and neck plan.

An Expanded Multi-scale Monte Carlo Simulation Method for Personalized Radiobiological Effect Estimation in Radiotherapy: a feasibility study

A novel and versatile "bottom-up" approach is developed to estimate the radiobiological effect of clinic radiotherapy. The model consists of multi-scale Monte Carlo simulations from organ to cell levels. At cellular level, accumulated damages are computed using a spectrum-based accumulation algorithm and predefined cellular damage database. The damage repair mechanism is modeled by an expanded reaction-rate two-lesion kinetic model, which were calibrated through replicating a radiobiological experiment. Multi-scale modeling is then performed on a lung cancer patient under conventional fractionated irradiation. The cell killing effects of two representative voxels (isocenter and peripheral voxel of the tumor) are computed and compared. At microscopic level, the nucleus dose and damage yields vary among all nucleuses within the voxels. Slightly larger percentage of cDSB yield is observed for the peripheral voxel (55.0%) compared to the isocenter one (52.5%). For isocenter voxel, survival fraction increase monotonically at reduced oxygen environment. Under an extreme anoxic condition (0.001%), survival fraction is calculated to be 80% and the hypoxia reduction factor reaches a maximum value of 2.24. In conclusion, with biological-related variations, the proposed multi-scale approach is more versatile than the existing approaches for evaluating personalized radiobiological effects in radiotherapy.

Computerized triplet beam orientation optimization for MRI-guided Co-60 radiotherapy

PURPOSE

Magnetic resonance imaging (MRI)-guided Co-60 provides daily and intrafractional MRI soft tissue imaging for improved target and critical organ tracking. To increase delivery efficiency, the system uses three Co-60 sources at 120° apart, allowing up to 600 cGy combined dose rate at isocenter. Despite the potential tripling in output, creating a delivery plan that uses all three sources is considerably unintuitive. Here, the authors computerize the triplet orientation optimization using column generation, an approach that was demonstrated effective in integrated beam orientation and fluence optimization for noncoplanar therapies. To achieve a better plan quality without increasing the treatment time, the authors then solve a fluence map optimization (FMO) problem while regularizing the fluence maps to reduce the number of deliverable MLC segments.

METHODS

Three patients-one prostate, one lung, and one head and neck boost plan (H&N_Boost)-were evaluated in this study. For each patient, the beamlet doses were calculated using Monte Carlo, under a 0.35 T magnetic field, for 180 equally spaced coplanar beams grouped into 60 triplets. The beamlet size is 1.05 × 0.5 cm determined by the MLC leaf thickness and step size. The triplets were selected using the column generation algorithm. The FMO problem was formulated using an L2-norm dose fidelity term and an L1-norm anisotropic total variation regularization term, which allows controlling the number of MLC segments, and hence the treatment time, with minimal degradation to the dose. The authors' Fluence Regularization and Optimized Selection of Triplets (FROST) plans were compared against the clinical treatment plans (CLNs) produced by an experienced dosimetrist. PTV homogeneity, max dose, mean dose, D95, D98, and D99 were evaluated. OAR max and mean doses, as well as R50, defined as the ratio of the 50% isodose volume over the planning target volume were investigated.

RESULTS

The mean PTV D95, D98, and D99 differ by +0.04%, +0.07%, and +0.25% of the prescription dose between planning methods. The mean PTV homogeneity was virtually same with values at 0.8788 (FROST) and 0.8812 (CLN). R50 decreased by 0.67 comparing FROST to CLN. On average, FROST reduced D_max and D_mean of OARs by 7.30% and 6.08% of the prescription dose, respectively. The manual CLN planning processes required numerous trial and error runs. The FROST plans on the other hand required minimal human intervention.

CONCLUSIONS

Efficient delivery of MRI-guided Co-60 therapy needs the output of multiple sources yet suffers from unintuitive and laborious manual beam selection processes. Computerized triplet orientation optimization improves both planning efficiency and plan dosimetry. The novel fluence map regularization provides additional controls over the number of MLC segments and treatment time.

A novel software and conceptual design of the hardware platform for intensity modulated radiation therapy

PURPOSE

To deliver high quality intensity modulated radiotherapy (IMRT) using a novel generalized sparse orthogonal collimators (SOCs), the authors introduce a novel direct aperture optimization (DAO) approach based on discrete rectangular representation.

METHODS

A total of seven patients-two glioblastoma multiforme, three head & neck (including one with three prescription doses), and two lung-were included. 20 noncoplanar beams were selected using a column generation and pricing optimization method. The SOC is a generalized conventional orthogonal collimators with N leaves in each collimator bank, where N = 1, 2, or 4. SOC degenerates to conventional jaws when N = 1. For SOC-based IMRT, rectangular aperture optimization (RAO) was performed to optimize the fluence maps using rectangular representation, producing fluence maps that can be directly converted into a set of deliverable rectangular apertures. In order to optimize the dose distribution and minimize the number of apertures used, the overall objective was formulated to incorporate an L2 penalty reflecting the difference between the prescription and the projected doses, and an L1 sparsity regularization term to encourage a low number of nonzero rectangular basis coefficients. The optimization problem was solved using the Chambolle-Pock algorithm, a first-order primal-dual algorithm. Performance of RAO was compared to conventional two-step IMRT optimization including fluence map optimization and direct stratification for multileaf collimator (MLC) segmentation (DMS) using the same number of segments. For the RAO plans, segment travel time for SOC delivery was evaluated for the N = 1, N = 2, and N = 4 SOC designs to characterize the improvement in delivery efficiency as a function of N.

RESULTS

Comparable PTV dose homogeneity and coverage were observed between the RAO and the DMS plans. The RAO plans were slightly superior to the DMS plans in sparing critical structures. On average, the maximum and mean critical organ doses were reduced by 1.94% and 1.44% of the prescription dose. The average number of delivery segments was 12.68 segments per beam for both the RAO and DMS plans. The N = 2 and N = 4 SOC designs were, on average, 1.56 and 1.80 times more efficient than the N = 1 SOC design to deliver. The mean aperture size produced by the RAO plans was 3.9 times larger than that of the DMS plans.

CONCLUSIONS

The DAO and dose domain optimization approach enabled high quality IMRT plans using a low-complexity collimator setup. The dosimetric quality is comparable or slightly superior to conventional MLC-based IMRT plans using the same number of delivery segments. The SOC IMRT delivery efficiency can be significantly improved by increasing the leaf numbers, but the number is still significantly lower than the number of leaves in a typical MLC.

Energy Modulated Photon Radiotherapy: A Monte Carlo Feasibility Study

A novel treatment modality termed energy modulated photon radiotherapy (EMXRT) was investigated. The first step of EMXRT was to determine beam energy for each gantry angle/anatomy configuration from a pool of photon energy beams (2 to 10 MV) with a newly developed energy selector. An inverse planning system using gradient search algorithm was then employed to optimize photon beam intensity of various beam energies based on presimulated Monte Carlo pencil beam dose distributions in patient anatomy. Finally, 3D dose distributions in six patients of different tumor sites were simulated with Monte Carlo method and compared between EMXRT plans and clinical IMRT plans. Compared to current IMRT technique, the proposed EMXRT method could offer a better paradigm for the radiotherapy of lung cancers and pediatric brain tumors in terms of normal tissue sparing and integral dose. For prostate, head and neck, spine, and thyroid lesions, the EMXRT plans were generally comparable to the IMRT plans. Our feasibility study indicated that lower energy (<6 MV) photon beams could be considered in modern radiotherapy treatment planning to achieve a more personalized care for individual patient with dosimetric gains.

Intermediate Megavoltage Photon Beams for Improved Lung Cancer Treatments

The goal of this study is to evaluate the effects of intermediate megavoltage (3-MV) photon beams on SBRT lung cancer treatments. To start with, a 3-MV virtual beam was commissioned on a commercial treatment planning system based on Monte Carlo simulations. Three optimized plans (6-MV, 3-MV and dual energy of 3- and 6-MV) were generated for 31 lung cancer patients with identical beam configuration and optimization constraints for each patient. Dosimetric metrics were evaluated and compared among the three plans. Overall, planned dose conformity was comparable among three plans for all 31 patients. For 21 thin patients with average short effective path length (< 10 cm), the 3-MV plans showed better target coverage and homogeneity with dose spillage index R_50% = 4.68±0.83 and homogeneity index = 1.26±0.06, as compared to 4.95±1.01 and 1.31±0.08 in the 6-MV plans (p < 0.001). Correspondingly, the average/maximum reductions of lung volumes receiving 20 Gy (V_20Gy), 5 Gy (V_5Gy), and mean lung dose (MLD) were 7%/20%, 9%/30% and 5%/10%, respectively in the 3-MV plans (p < 0.05). The doses to 5% volumes of the cord, esophagus, trachea and heart were reduced by 9.0%, 10.6%, 11.4% and 7.4%, respectively (p < 0.05). For 10 thick patients, dual energy plans can bring dosimetric benefits with comparable target coverage, integral dose and reduced dose to the critical structures, as compared to the 6-MV plans. In conclusion, our study indicated that 3-MV photon beams have potential dosimetric benefits in treating lung tumors in terms of improved tumor coverage and reduced doses to the adjacent critical structures, in comparison to 6-MV photon beams. Intermediate megavoltage photon beams (< 6-MV) may be considered and added into current treatment approaches to reduce the adjacent normal tissue doses while maintaining sufficient tumor dose coverage in lung cancer radiotherapy.