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Background: CT reconstruction is of essential importance in medical imaging. In 2022, the American Association of Physicists in Medicine (AAPM) sponsored a Grand Challenge to investigate the challenging inverse problem of spectral CT reconstruction, with the aim of achieving the most accurate reconstruction results. The authors of this paper participated in the challenge and won as a runner‐up team. Purpose: This paper reports details of our PROSPECT algorithm (Prior‐based Restricted‐variable Optimization for SPEctral CT) and follow‐up studies regarding the algorithm's accuracy and enhancement of its convergence speed. Methods: We formulated the reconstruction task as an optimization problem. PROSPECT employed a one‐step backward iterative scheme to solve this optimization problem by allowing estimation of and correction for the difference between the actual polychromatic projection model and the monochromatic model used in the optimization problem. PROSPECT incorporated various forms of prior information derived by analyzing training data provided by the Grand Challenge to reduce the number of unknown variables. We investigated the impact of projection data precision on the resulting solution accuracy and improved convergence speed of the PROSPECT algorithm by incorporating a beam‐hardening correction (BHC) step in the iterative process. We also studied the algorithm's performance under noisy projection data. Results: Prior knowledge allowed a reduction of the number of unknown variables by 85.9%$85.9\%$. PROSPECT algorithm achieved the average root of mean square error (RMSE) of 3.3×10−6$3.3\,\times \,10^{-6}$ in the test data set provided by the Grand Challenge. Performing the reconstruction with the same algorithm but using double‐precision projection data reduced RMSE to 1.2×10−11$1.2\,\times \,10^{-11}$. Including the BHC step in the PROSPECT algorithm accelerated the iteration process with a 40% reduction in computation time. Conclusions: PROSPECT algorithm achieved a high degree of accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

Background: High dose rate (HDR) brachytherapy is commonly used to treat prostate cancer. Existing HDR planning systems solve the dwell time problem for predetermined catheters and a single energy source. Purpose: Additional degrees of freedom can be obtained by relaxing the catheters' pre‐designation and introducing more source types, and may have a dosimetric benefit, particularly in improving conformality to spare the urethra. This study presents a novel analytical approach to solving the corresponding HDR planning problem. Methods: The catheter and dual‐energy source selection problem was formulated as a constrained optimization problem with a non‐convex group sparsity regularization. The optimization problem was solved using the fast‐iterative shrinkage‐thresholding algorithm (FISTA). Two isotopes were considered. The dose rates for the HDR 4140 Ytterbium (Yb‐169) source and the Elekta Iridium (Ir‐192) HDR Flexisource were modeled according to the TG‐43U1 formalism and benchmarked accordingly. Twenty‐two retrospective HDR prostate brachytherapy patients treated with Ir‐192 were considered. An Ir‐192 only (IRO), Yb‐169 only (YBO), and dual‐source (DS) plan with optimized catheter location was created for each patient with N catheters, where N is the number of catheters used in the clinically delivered plans. The DS plans jointly optimized Yb‐169 and Ir‐192 dwell times. All plans and the clinical plans were normalized to deliver a 15 Gy prescription (Rx) dose to 95% of the clinical treatment volume (CTV) and evaluated for the CTV D90%, V150%, and V200%, urethra D0.1cc and D1cc, bladder V75%, and rectum V75%. Dose‐volume histograms (DVHs) were generated for each structure. Results: The DS plans ubiquitously selected Ir‐192 as the only treatment source. IRO outperformed YBO in organ at risk (OARs) OAR sparing, reducing the urethra D0.1cc and D1cc by 0.98% (p=2.22∗10−9$p\ = \ 2.22*{10^{ - 9}}$) and 1.09% (p=1.22∗10−10$p\ = \ 1.22*{10^{ - 10}}$) of the Rx dose, respectively, and reducing the bladder and rectum V75% by 0.09 (p=0.0023$p\ = \ 0.0023$) and 0.13 cubic centimeters (cc) (p=0.033$p\ = \ 0.033$), respectively. The YBO plans delivered a more homogenous dose to the CTV, with a smaller V150% and V200% by 3.20 (p=4.67∗10−10$p\ = \ 4.67*{10^{ - 10}}$) and 1.91 cc (p=5.79∗10−10$p\ = \ 5.79*{10^{ - 10}}$), respectively, and a lower CTV D90% by 0.49% (p=0.0056$p\ = \ 0.0056$) of the prescription dose. The IRO plans reduce the urethral D1cc by 2.82% (p=1.38∗10−4$p\ = \ 1.38*{10^{ - 4}}$) of the Rx dose compared to the clinical plans, at the cost of increased bladder and rectal V75% by 0.57 (p=0.0022$p\ = \ 0.0022$) and 0.21 cc (p=0.019$p\ = \ 0.019$), respectively, and increased CTV V150% by a mean of 1.46 cc (p=0.010$p\ = \ 0.010$) and CTV D90% by an average of 1.40% of the Rx dose (p=8.80∗10−8$p\ = \ 8.80*{10^{ - 8}}$). While these differences are statistically significant, the clinical differences between the plans are minimal. Conclusions: The proposed analytical HDR planning algorithm integrates catheter and isotope selection with dwell time optimization for varying clinical goals, including urethra sparing. The planning method can guide HDR implants and identify promising isotopes for specific HDR clinical goals, such as target conformality or OAR sparing. [ABSTRACT FROM AUTHOR]

Background: The intensities (i.e., number of protons in monitor unit [MU]) of deliverable proton spots need to be either zero or meet a minimum‐MU (MMU) threshold, which is a nonconvex problem. Since the dose rate is proportionally associated with the MMU threshold, higher‐dose‐rate proton radiation therapy (RT) (e.g., efficient intensity modulated proton therapy (IMPT) and ARC proton therapy, and high‐dose‐rate‐induced FLASH effect needs to solve the MMU problem with larger MMU threshold, which however makes the nonconvex problem more difficult to solve. Purpose: This work will develop a more effective optimization method based on orthogonal matching pursuit (OMP) for solving the MMU problem with large MMU thresholds, compared to state‐of‐the‐art methods, such as alternating direction method of multipliers (ADMM), proximal gradient descent method (PGD), or stochastic coordinate descent method (SCD). Methods: The new method consists of two essential components. First, the iterative convex relaxation (ICR) method is used to determine the active sets for dose‐volume planning constraints and decouple the MMU constraint from the rest. Second, a modified OMP optimization algorithm is used to handle the MMU constraint: the non‐zero spots are greedily selected via OMP to form the solution set to be optimized, and then a convex constrained subproblem is formed and can be conveniently solved to optimize the spot weights restricted to this solution set via OMP. During this iterative process, the new non‐zero spots localized via OMP will be adaptively added to or removed from the optimization objective. Results: The new method via OMP is validated in comparison with ADMM, PGD and SCD for high‐dose‐rate IMPT, ARC, and FLASH problems of large MMU thresholds, and the results suggest that OMP substantially improved the plan quality from PGD, ADMM and SCD in terms of both target dose conformality (e.g., quantified by max target dose and conformity index) and normal tissue sparing (e.g., mean and max dose). For example, in the brain case, the max target dose for IMPT/ARC/FLASH was 368.0%/358.3%/283.4% respectively for PGD, 154.4%/179.8%/150.0% for ADMM, 134.5%/130.4%/123.0% for SCD, while it was <120% in all scenarios for OMP; compared to PGD/ADMM/SCD, OMP improved the conformity index from 0.42/0.52/0.33 to 0.65 for IMPT and 0.46/0.60/0.61 to 0.83 for ARC. Conclusions: A new OMP‐based optimization algorithm is developed to solve the MMU problems with large MMU thresholds, and validated using examples of IMPT, ARC, and FLASH with substantially improved plan quality from ADMM, PGD, and SCD. [ABSTRACT FROM AUTHOR]

Background: Periodic and slow target motion is tracked by synchronous motion of the treatment beams in robotic stereotactic body radiation therapy (SBRT). However, spontaneous, non‐periodic displacement or drift of the target may completely change the treatment geometry. Simple motion compensation is not sufficient to guarantee the best possible treatment, since relative motion between the target and organs at risk (OARs) can cause substantial deviations of dose in the OARs. This is especially evident when considering the temporally heterogeneous dose delivery by many focused beams which is typical for robotic SBRT. Instead, a reoptimization of the remaining treatment plan after a large target motion during the treatment could potentially reduce the actually delivered dose to OARs and improve target coverage. This reoptimization task, however, is challenging due to time constraints and limited human supervision. Purpose: To study the detrimental effect of spontaneous target motion relative to surrounding OARs on the delivered dose distribution and to analyze how intra‐fractional constrained replanning could improve motion compensated robotic SBRT of the prostate. Methods: We solve the inverse planning problem by optimizing a linear program. When considering intra‐fractional target motion resulting in a change of geometry, we adapt the linear program to account for the changed dose coefficients and delivered dose. We reduce the problem size by only reweighting beams from the reference treatment plan without motion. For evaluation we simulate target motion and compare our approach for intra‐fractional replanning to the conventional compensation by synchronous beam motion. Results are generated retrospectively on data of 50 patients. Results: Our results show that reoptimization can on average retain or improve coverage in case of target motion compared to the reference plan without motion. Compared to the conventional compensation, coverage is improved from 87.83 % to 94.81 % for large target motion. Our approach for reoptimization ensures fixed upper constraints on the dose even after motion, enabling safer intra‐fraction adaption, compared to conventional motion compensation where overdosage in OARs can lead to 21.79 % higher maximum dose than planned. With an average reoptimization time of 6 s for 200 reoptimized beams our approach shows promising performance for intra‐fractional application. Conclusions: We show that intra‐fractional constrained reoptimization for adaption to target motion can improve coverage compared to the conventional approach of beam translation while ensuring that upper dose constraints on VOIs are not violated. [ABSTRACT FROM AUTHOR]

Purpose: Spectral computed tomography (CT) based on the photon‐counting detection system has the capability to produce energy‐discriminative attenuation maps of objects with a single scan. However, the insufficiency of photons collected into the narrow energy bins results in high quantum noise levels causing low image quality. This work aims to improve spectral CT image quality by developing a novel regularization based on framelet tensor prior. Methods: First, similar patches are extracted from highly correlated interchannel images in spectral and spatial domains, and stacked to form a third‐order tensor after vectorization along the energy channels. Second, the framelet tensor nuclear norm (FTNN) is introduced and applied to construct the regularization to exploit the sparsity embedded in nonlocal similarity of spectral images, and thus the reconstruction problem is modeled as a constrained optimization. Third, an iterative algorithm is proposed by utilizing the alternating direction method of multipliers framework in which efficient solvers are developed for each subproblem. Results: Both numerical simulations and real data verifications were performed to evaluate and validate the proposed FTNN‐based method. Compared to the analytic, TV‐based, and the state‐of‐the‐art tensor‐based methods, the proposed method achieves higher numerical accuracy on both reconstructed CT images and decomposed material maps in the mouse data indicating the capability in noise suppression and detail preservation of the proposed method. Conclusions: A framelet tensor sparsity–based iterative algorithm is proposed for spectral reconstruction. The qualitative and quantitative comparisons show a promising improvement of image quality, indicating its promising potential in spectral CT imaging. [ABSTRACT FROM AUTHOR]

Purpose: FLASH radiotherapy (RT) can potentially reduce normal tissue toxicity while preserving tumoricidal effectiveness to improve the therapeutic ratio. The key of FLASH for sparing normal tissues is to irradiate tissues with an ultra‐high dose rate (i.e., ≥40 Gy/s), for which proton RT can be used. However, currently available treatment plan optimization method only optimizes the dose distribution and does not directly optimize the dose rate. The contribution of this work to FLASH proton RT is the development of a novel treatment optimization method, that is, simultaneous dose and dose rate optimization (SDDRO), to optimize tissue‐receiving dose rate distribution as well as dose distribution. Methods: Distinguished from existing methods, SDDRO accounts for dose rate constraint and optimizes dose rate distribution. In terms of mathematical formulation, SDDRO is a constrained optimization problem with dose‐volume constraint on dose distribution, minimum dose rate constraint on dose‐averaged tissue‐receiving dose rates, minimum monitor unit constraint on spot weight, and maximum intensity constraint on beam intensity. In terms of optimization algorithm, SDDRO is solved by iterative convex relaxation and alternating direction method of multipliers. SDDRO algorithms are presented for both scenarios with either constant or variable beam intensity. Results: SDDRO was compared with intensity modulated proton therapy (IMPT) (dose optimization alone, and no dose rate optimization) using three lung cases. SDDRO substantially improved the dose rate distribution compared to IMPT, for example, increasing of the region‐of‐interest (ROI) volume (ROI = CTV_10mm: the ring sandwiched by 10 mm outer and inner expansion of CTV boundary) receiving at least 40 Gy/s from ~30–50% to at least 98%, and the lung volume receiving at least 40 Gy/s from ~30–40% to ~70–90%. Moreover, both dose and dose rate distributions from SDDRO were further considerably improved via the combined use of hypofractionation and multiple beams. Conclusions: We have developed a joint dose and dose rate optimization method for FLASH proton RT, namely SDDRO, which is first‐of‐its‐kind to the best of our knowledge. The results suggest that (a) SDDRO can substantially improve the FLASH‐dose rate coverage (e.g., in terms of dose rate volume histogram) compared to IMPT for the purpose of normal tissue sparing while preserving the dose distribution and (b) the combination of hypofractionation and multiple beams can further considerably improve the SDDRO plan quality in terms of both dose and dose rate distribution. [ABSTRACT FROM AUTHOR]

Purpose: This work aims to reduce dose delivery time of pencil beam scanning (PBS) proton plans, which is the dominant factor of total plan delivery time. A proton PBS system, such as Varian ProBeam proton therapy system, can be equipped with the proton dose rate that is linearly proportional to the minimum monitor unit (MU) (i.e., number of protons) of PBS spots before saturation. Thus dose delivery time can be potentially reduced by increasing the MU threshold. However, commercially available treatment planning systems and current methods only allow for a single MU threshold globally for all PBS spots (i.e., all energy layers), and consequently the room to increase this minimum‐MU for reducing dose delivery time is very limited since higher minimum‐MU can greatly degrade treatment plan quality. Methods: Two major innovations of this work are the proposal of using variable MU thresholds locally adaptive to each energy layer, that is, minimum‐MU‐per‐energy‐layer (MMPEL), for reducing dose delivery time, and the joint optimization of plan delivery time and plan quality. Minimum‐MU‐per‐energy‐layer is formulated as a constrained optimization problem with objectives of dose‐volume‐histogram based planning constraints and plan delivery time, and minimum‐MU constraints per energy layer for deliverable PBS spots. Minimum‐MU‐per‐energy‐layer is solved by iterative convex relaxations via alternating direction method of multipliers. Results: Representative prostate, lung, brain, head‐and‐neck, breast, liver and pancreas cases were used to validate MMPEL. Minimum‐MU‐per‐energy‐layer reduced dose delivery time to 53%, 67%, 67%, 53%, 54%, 32%, and 14% respectively while maintaining a similar plan quality. Accepting a slightly degraded plan quality that still met all physician planning constraints, the treatment time could be further reduced to 26%, 35%, 41%, 34%, 32%, 16%, and 11% respectively, or in another word MMPEL accelerated the PBS plan delivery by 2–10 fold. Conclusions: A new proton PBS treatment planning method MMPEL with variable energy‐adaptive MU thresholds is developed to optimize dose delivery time jointly with plan quality. The preliminary results suggest that MMPEL could substantially reduce dose delivery time. [ABSTRACT FROM AUTHOR]

Purpose: To present a fully automated treatment planning process for proton therapy including beam angle selection using a novel Bayesian optimization approach and previously developed constrained hierarchical fluence optimization method. Methods: We adapted our in‐house automated intensity modulated radiation therapy (IMRT) treatment planning system, which is based on constrained hierarchical optimization and referred to as ECHO (expedited constrained hierarchical optimization), for proton therapy. To couple this to beam angle selection, we propose using a novel Bayesian approach. By integrating ECHO with this Bayesian beam selection approach, we obtain a fully automated treatment planning framework including beam angle selection. Bayesian optimization is a global optimization technique which only needs to search a small fraction of the search space for slowly varying objective functions (i.e., smooth functions). Expedited constrained hierarchical optimization is run for some initial beam angle candidates and the resultant treatment plan for each beam configuration is rated using a clinically relevant treatment score function. Bayesian optimization iteratively predicts the treatment score for not‐yet‐evaluated candidates to find the best candidate to be optimized next with ECHO. We tested this technique on five head‐and‐neck (HN) patients with two coplanar beams. In addition, tests were performed with two noncoplanar and three coplanar beams for two patients. Results: For the two coplanar configurations, the Bayesian optimization found the optimal beam configuration after running ECHO for, at most, 4% of all potential configurations (23 iterations) for all patients (range: 2%–4%). Compared with the beam configurations chosen by the planner, the optimal configurations reduced the mandible maximum dose by 6.6 Gy and high dose to the unspecified normal tissues by 3.8 Gy, on average. For the two noncoplanar and three coplanar beam configurations, the algorithm converged after 45 iterations (examining <1% of all potential configurations). Conclusions: A fully automated and efficient treatment planning process for proton therapy, including beam angle optimization was developed. The algorithm automatically generates high‐quality plans with optimal beam angle configuration by combining Bayesian optimization and ECHO. As the Bayesian optimization is capable of handling complex nonconvex functions, the treatment score function which is used in the algorithm to evaluate the dose distribution corresponding to each beam configuration can contain any clinically relevant metric. [ABSTRACT FROM AUTHOR]

Purpose: We present a method for fully automated generation of high quality robust proton treatment plans using hierarchical optimization. To fill the gap between the two common extreme robust optimization approaches, that is, stochastic and worst‐case, a robust optimization approach based on the p‐norm function is used whereby a single parameter, p, can be used to control the level of robustness in an intuitive way. Methods: A fully automated approach to treatment planning using Expedited Constrained Hierarchical Optimization (ECHO) is implemented in our clinic for photon treatments. ECHO strictly enforces critical (inviolable) clinical criteria as hard constraints and improves the desirable clinical criteria sequentially, as much as is feasible. We extend our in‐house developed ECHO codes for proton therapy and integrate it with a new approach for robust optimization. Multiple scenarios accounting for both setup and range uncertainties are included (13scenarios), and the maximum/mean/dose‐volume constraints on organs‐at‐risk (OARs) and target are fulfilled in all scenarios. We combine the objective functions of the individual scenarios using the p‐norm function. The p‐norm with a parameter p=1 or p=∞ result in the stochastic or the worst‐case approach, respectively; an intermediate robustness level is obtained by employing p‐values in‐between. While the worst‐case approach only focuses on the worst‐case scenario(s), the p‐norm approach with a large p value (p≈20) resembles the worst‐case approach without completely neglecting other scenarios. The proposed approach is evaluated on three head‐and‐neck (HN) patients and one water phantom with different parameters, p∈1,2,5,10,20. The results are compared against the stochastic approach (p‐norm approach with p=1) and the worst‐case approach, as well as the nonrobust approach (optimized solely on the nominal scenario). Results: The proposed algorithm successfully generates automated robust proton plans on all cases. As opposed to the nonrobust plans, the robust plans have narrower dose volume histogram (DVH) bands across all 13 scenarios, and meet all hard constraints (i.e., maximum/mean/dose‐volume constraints) on OARs and the target for all scenarios. The spread in the objective function values is largest for the stochastic approach (p=1) and decreases with increasing p toward the worst‐case approach. Compared to the worst‐case approach, the p‐norm approach results in DVH bands for clinical target volume (CTV) which are closer to the prescription dose at a negligible cost in the DVH for the worst scenario, thereby improving the overall plan quality. On average, going from the worst‐case approach to the p‐norm approach with p=20, the median objective function value across all the scenarios is improved by 15% while the objective function value for the worst scenario is only degraded by 3%. Conclusion: An automated treatment planning approach for proton therapy is developed, including robustness, dose‐volume constraints, and the ability to control the robustness level using the p‐norm parameter p, to fit the priorities deemed most important. [ABSTRACT FROM AUTHOR]

Purpose: Dose‐volume constraints (DVCs) continue to be common features in intensity‐modulated radiation therapy (IMRT) prescriptions, but they are non‐convex and difficult to incorporate. We propose computationally efficient methods to incorporate dose‐volume constraints (DVCs) into automated IMRT planning. Methods: We propose a two‐phase approach: in phase‐1, we solve a convex approximation with DVCs. Although this convex approximation does not guarantee DVC satisfaction, it provides crucial initial information about voxels likely to receive doses below DVC thresholds. Subsequently, phase‐2 solves an optimization problem with maximum dose constraints imposed on those subthreshold voxels. We further categorize DVCs into hard‐ and soft‐DVCs, where hard‐DVCs are strictly enforced by the optimization and soft‐DVCs are encouraged in the objective function. We tested this approach in our automated treatment planning system which is based on hierarchical constrained optimization. Performance is demonstrated on a series of paraspinal, lung, oligometastasis, and prostate cases as well as a small paraspinal case for which we can computationally afford to obtain a ground‐truth by solving a non‐convex optimization problem. Results: The proposed algorithm successfully meets all the hard‐DVCs while increasing the overall computational time of the baseline planning process (without DVCs) by 20%, 10%, and 11% for paraspinal, oligometastasis, and prostate cases, respectively. For a soft‐DVC applied to the lung case, the dose‐volume histogram curve moves toward the desired direction and the computational time is increased by 11%. For a low‐resolution paraspinal case, the ground‐truth solution process using mixed‐integer programming methods required 15 h while the proposed algorithm converges in only 2 min with a proximal solution. Conclusions: A computationally tractable algorithm to handle hard‐ and soft‐DVCs is developed which is capable of satisfying DVCs without any parameter tweaking. Although the algorithm is demonstrated in our in‐house developed automated treatment planning system, it can potentially be used in any constrained optimization framework. [ABSTRACT FROM AUTHOR]

Purpose: Spatiotemporal fractionation schemes for photon radiotherapy have recently arisen as a promising technique for healthy tissue sparing. Because spatiotemporally fractionated treatments have a characteristic pattern of delivering high doses to different parts of the tumor in each fraction, uncertainty in patient positioning is an even more pressing concern than in conventional uniform fractionation. Until now, such concerns in patient setup uncertainty have not been addressed in the context of spatiotemporal fractionation. Methods: A stochastic optimization model is used to incorporate patient setup uncertainty to optimize spatiotemporally fractionated plans using expected penalties for deviations from prescription values. First, a robust uniform reference plan is optimized with a stochastic optimization model. Then, a spatiotemporal plan is optimized with a constrained stochastic optimization model that minimizes a primary clinical objective and constrains the spatiotemporal plan to be at least as good as the uniform reference plan with respect to all other objectives. A discrete probability distribution is defined to characterize the random setup error occurring in each fraction. For the optimization of uniform plans, the expected penalties are computed exactly by exploiting the symmetry of the fractions, and for the spatiotemporal plans, quasi‐Monte Carlo sampling is used to approximate the expectation. Results: Using five clinical liver cases, it is demonstrated that spatiotemporally fractionated treatment plans maintain the same robust tumor coverage as a stochastic uniform reference plan and exhibit a reduction in the expected mean BED of the uninvolved liver. This is observed for a spectrum of probability distributions of random setup errors with shifts in the patient position of up to 5 mm from the nominal position. For probability distributions with small variance in the patient position, the spatiotemporal plans exhibit an 8–30% reduction in expected mean BED in the healthy liver tissue for shifts up to 2.5 mm and reductions of 5–25% for shifts up to 5 mm. Conclusions: In the presence of patient setup uncertainty, spatiotemporally fractionated treatment plans exhibit the same robust tumor coverage as their uniformly fractionated counterparts and still retain the benefit in sparing healthy tissues. [ABSTRACT FROM AUTHOR]

Purpose: To develop and implement a fully automated approach to intensity modulated radiation therapy (IMRT) treatment planning. Method: The optimization algorithm is developed based on a hierarchical constrained optimization technique and is referred internally at our institution as expedited constrained hierarchical optimization (ECHO). Beamlet contributions to regions‐of‐interest are precomputed and captured in the influence matrix. Planning goals are of two classes: hard constraints that are strictly enforced from the first step (e.g., maximum dose to spinal cord), and desirable goals that are sequentially introduced in three constrained optimization problems (better planning target volume (PTV) coverage, lower organ at risk (OAR) doses, and smoother fluence map). After solving the optimization problems using external commercial optimization engines, the optimal fluence map is imported into an FDA‐approved treatment planning system (TPS) for leaf sequencing and accurate full dose calculation. The dose‐discrepancy between the optimization and TPS dose calculation is then calculated and incorporated into optimization by a novel dose correction loop technique using Lagrange multipliers. The correction loop incorporates the leaf sequencing and scattering effects into optimization to improve the plan quality and reduce the calculation time. The resultant optimal fluence map is again imported into TPS for leaf sequencing and final dose calculation for plan evaluation and delivery. The workflow is automated using application program interface (API) scripting, requiring user interaction solely to prepare the contours and beam arrangement prior to launching the ECHO plug‐in from the TPS. For each site, parameters and objective functions are chosen to represent clinical priorities. The first site chosen for clinical implementation was metastatic paraspinal lesions treated with stereotactic body radiotherapy (SBRT). As a first step, 75 ECHO paraspinal plans were generated retrospectively and compared with clinically treated plans generated by planners using VMAT (volumetric modulated arc therapy) with 4 to 6 partial arcs. Subsequently, clinical deployment began in April, 2017. Results: In retrospective study, ECHO plans were found to be dosimetrically superior with respect to tumor coverage, plan conformity, and OAR sparing. For example, the average PTV D95%, cord and esophagus max doses, and Paddick Conformity Index were improved, respectively, by 1%, 6%, 14%, and 15%, at a negligible 3% cost of the average skin D10cc dose. Conclusion: Hierarchical constrained optimization is a powerful and flexible tool for automated IMRT treatment planning. The dosimetric correction step accurately accounts for detailed dosimetric multileaf collimator and scattering effects. The system produces high‐quality, Pareto optimal plans and avoids the time‐consuming trial‐and‐error planning process. [ABSTRACT FROM AUTHOR]

Purpose: We study the problem of spectrum estimation from transmission data of a known phantom. The goal is to reconstruct an x‐ray spectrum that can accurately model the x‐ray transmission curves and reflects a realistic shape of the typical energy spectra of the CT system. Methods: Spectrum estimation is posed as an optimization problem with x‐ray spectrum as unknown variables, and a Kullback–Leibler (KL)‐divergence constraint is employed to incorporate prior knowledge of the spectrum and enhance numerical stability of the estimation process. The formulated constrained optimization problem is convex and can be solved efficiently by use of the exponentiated‐gradient (EG) algorithm. We demonstrate the effectiveness of the proposed approach on the simulated and experimental data. The comparison to the expectation–maximization (EM) method is also discussed. Results: In simulations, the proposed algorithm is seen to yield x‐ray spectra that closely match the ground truth and represent the attenuation process of x‐ray photons in materials, both included and not included in the estimation process. In experiments, the calculated transmission curve is in good agreement with the measured transmission curve, and the estimated spectra exhibits physically realistic looking shapes. The results further show the comparable performance between the proposed optimization‐based approach and EM. Conclusions: Our formulation of a constrained optimization provides an interpretable and flexible framework for spectrum estimation. Moreover, a KL‐divergence constraint can include a prior spectrum and appears to capture important features of x‐ray spectrum, allowing accurate and robust estimation of x‐ray spectrum in CT imaging. [ABSTRACT FROM AUTHOR]

Purpose: To investigate whether building a knowledge‐based planning (KBP) model with prostate bed plans constructed from constrained hierarchical optimization (CHO) would result in more efficient model construction with more consistent output than a model built using plans from a traditional, trial‐and‐error‐based optimization (TEO) technique. Methods: Three KBP models were constructed from plans from subsets of 58 post‐prostatectomy patients treated with intensity‐modulated radiation therapy. TEO54 was built from 54 TEO plans, selected to represent typical clinical variations in target and organ‐at‐risk sizes and shapes. CHO30 and TEO30 were built from the same 30 patients populated with CHO and TEO plans, respectively. The three models were each applied to a new set of 18 patient scans and dose–volume histogram estimates (DVHEs) were generated for rectal and bladder walls and compared for each patient. Results: CHO30 resulted in a significantly tighter range in DVHEs (P < 0.01) for both the rectal and bladder walls compared with either of the TEO models, indicating less uncertainty in the dose estimation. Plans resulting from KBP optimization using each model were very similar. Conclusion: Populating a KBP model with CHO data resulted in a high quality model. Since CHO plans can be generated automatically offline in a process that necessitates little to no user interaction, a CHO‐KBP model can quickly adapt to changes in plan evaluation criteria or planning techniques without the need to wait to accrue sufficient numbers of clinical TEO plans. This may facilitate the use of KBP approaches for initial or ongoing quality assurance procedures and plan quality audits. [ABSTRACT FROM AUTHOR]

Purpose Most radiation therapy optimization problems can be formulated as an unconstrained problem and solved efficiently by quasi-Newton methods such as the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. However, several next generation planning techniques such as total variation regularization- based optimization and MV+kV optimization, involve constrained or mixed-norm optimization, and cannot be solved by quasi-Newton methods. Using standard optimization algorithms on such problems often leads to prohibitively long optimization times and large memory requirements. This work investigates the use of a recently developed proximal operator graph solver (POGS) in solving such radiation therapy optimization problems. Methods Radiation therapy inverse treatment planning was formulated as a graph form problem, and the proximal operators of POGS for quadratic optimization were derived. POGS was exploited for the first time to impose hard dose constraints along with soft constraints in the objective function. The solver was applied to several clinical treatment sites (TG119, liver, prostate, and head&neck), and the results were compared to the solutions obtained by other commercial and non-commercial optimizers. Results For inverse planning optimization with nonnegativity box constraints on beamlet intensity, the speed of POGS can compete with that of LBFGSB in some situations. For constrained and mixed-norm optimization, POGS is about one or two orders of magnitude faster than the other solvers while requiring less computer memory. Conclusions POGS was used for solving inverse treatment planning problems involving constrained or mixed-norm formulation on several example sites. This approach was found to improve upon standard solvers in terms of computation speed and memory usage, and is capable of solving traditionally difficult problems, such as total variation regularization-based optimization and combined MV+kV optimization. [ABSTRACT FROM AUTHOR]

Purpose: To explore the potential of a novel dose-volume based metric to assist in the selection of optimal fractionation schedules for lung cancer patients. Methods: Selecting the dose per fraction that maximizes the therapeutic ratio via a linear-quadratic effect on normal tissue complication probability and tumor cell survival is an optimization problem. The mathematical solution reveals that the optimal fractionation schedule is determined by a generalized dose ratio between the normal tissue and the tumor, here termed the bifurcation number B, that can be derived from the dose-volume histogram of the normal tissue. The bifurcation number characterizes the volume effect of a normal tissue and its dependency on the fractionation schedule. The clinical relevance of the bifurcation number was evaluated in 46 patients previously treated for nonsmall cell lung cancer (NSCLC) according to various fractionation protocols. Bifurcation numbers were computed for both lung and esophagus as the normal tissues. Results: The value of the bifurcation number determines whether the volume effect reverses the traditional radiobiological advantage of small dose per fraction for the normal tissue. If B is smaller than the ratio of alpha/beta ratios between normal tissue and tumor, then a single fraction is optimal; otherwise the optimal treatment is an infinite number of doses (hence the name 'bifurcation' number). These fractionation schedules correspond clinically to hypo- and standard/hyperfractionation, respectively. Compared with traditional dose-volume metrics, the bifurcation number is a unitless ratio and independent of dose fractionation. The B-numbers derived from the clinical treatment plans are also strongly consistent with historically prescribed clinical fractionation protocols for NSCLC treatments. The B-numbers for esophagus and lung for all patients receiving a high dose per fraction protocol (>7.5 Gy/fraction) were all smaller than the B-numbers for the patients receiving standard 2 Gy/fraction, with the numbers for the 3 Gy/fraction group in between. Conclusions: The bifurcation numbers are strongly consistent with prescribed clinical fractionation protocols for NSCLC treatments. Due to their scale-free property the B-numbers may assist in the selection of an appropriate fractionation once the dose distribution has been optimized. [ABSTRACT FROM AUTHOR]

Purpose: The authors use reduced-order constrained optimization (ROCO) to create clinically acceptable IMRT plans quickly and automatically for advanced lung cancer patients. Their new ROCO implementation works with the treatment planning system and full dose calculation used at Memorial Sloan-Kettering Cancer Center (MSKCC). The authors have implemented mean dose hard constraints, along with the point-dose and dose-volume constraints that the authors used for our previous work on the prostate.Methods: ROCO consists of three major steps. First, the space of treatment plans is sampled by solving a series of optimization problems using penalty-based quadratic objective functions. Next, an efficient basis for this space is found via principal component analysis (PCA); this reduces the dimensionality of the problem. Finally, a constrained optimization problem is solved over this basis to find a clinically acceptable IMRT plan. Dimensionality reduction makes constrained optimization computationally efficient.Results: The authors apply ROCO to 12 stage III non-small-cell lung cancer (NSCLC) cases, generating IMRT plans that meet all clinical constraints and are clinically acceptable, and demonstrate that they are competitive with the clinical treatment plans. The authors also test how many samples and PCA modes are necessary to achieve an adequate lung plan, demonstrate the importance of long-range dose calculation for ROCO, and evaluate the performance of nonspecific normal tissue ('rind') constraints in ROCO treatment planning for the lung. Finally, authors show that ROCO can save time for planners, and they estimate that in the clinic, planning using their approach would save a median of 105 min for the patients in the study.Conclusions: New challenges arise when applying ROCO to the lung site, which include the lack of a class solution, a larger treatment site, an increased number of parameters and beamlets, a variable number of beams and beam arrangement, and the customary use of rinds in clinical plans to avoid high-dose areas outside the PTV. In the authors previous work, use of an approximate dose calculation in the hard constraint optimization sometimes meant that clinical constraints were not met when evaluated with the full dose calculation. This difficulty has been removed in the current work by using the full dose calculation in the hard constraint optimization. The authors have demonstrated that ROCO offers a fast and automatic way to create IMRT plans for advanced NSCLC, which extends their previous application of ROCO to prostate cancer IMRT planning. [ABSTRACT FROM AUTHOR]

Purpose: The streak artifacts caused by metal implants have long been recognized as a problem that limits various applications of CT imaging. In this work, the authors propose an iterative metal artifact reduction algorithm based on constrained optimization. Methods: After the shape and location of metal objects in the image domain is determined automatically by the binary metal identification algorithm and the segmentation of 'metal shadows' in projection domain is done, constrained optimization is used for image reconstruction. It minimizes a predefined function that reflects a priori knowledge of the image, subject to the constraint that the estimated projection data are within a specified tolerance of the available metal-shadow-excluded projection data, with image non-negativity enforced. The minimization problem is solved through the alternation of projection-onto-convex-sets and the steepest gradient descent of the objective function. The constrained optimization algorithm is evaluated with a penalized smoothness objective. Results: The study shows that the proposed method is capable of significantly reducing metal artifacts, suppressing noise, and improving soft-tissue visibility. It outperforms the FBP-type methods and ART and EM methods and yields artifacts-free images. Conclusions: Constrained optimization is an effective way to deal with CT reconstruction with embedded metal objects. Although the method is presented in the context of metal artifacts, it is applicable to general 'missing data' image reconstruction problems. [ABSTRACT FROM AUTHOR]

Purpose: To develop a technique to estimate onboard 4D-CBCT using prior information and limited-angle projections for potential 4D target verification of lung radiotherapy. Methods: Each phase of onboard 4D-CBCT is considered as a deformation from one selected phase (prior volume) of the planning 4D-CT. The deformation field maps (DFMs) are solved using a motion modeling and free-form deformation (MM-FD) technique. In the MM-FD technique, the DFMs are estimated using a motion model which is extracted from planning 4D-CT based on principal component analysis (PCA). The motion model parameters are optimized by matching the digitally reconstructed radiographs of the deformed volumes to the limited-angle onboard projections (data fidelity constraint). Afterward, the estimated DFMs are fine-tuned using a FD model based on data fidelity constraint and deformation energy minimization. The 4D digital extended-cardiac-torso phantom was used to evaluate the MM-FD technique. A lung patient with a 30 mm diameter lesion was simulated with various anatomical and respirational changes from planning 4D-CT to onboard volume, including changes of respiration amplitude, lesion size and lesion average-position, and phase shift between lesion and body respiratory cycle. The lesions were contoured in both the estimated and 'ground-truth' onboard 4D-CBCT for comparison. 3D volume percentage-difference (VPD) and center-of-mass shift (COMS) were calculated to evaluate the estimation accuracy of three techniques: MM-FD, MM-only, and FD-only. Different onboard projection acquisition scenarios and projection noise levels were simulated to investigate their effects on the estimation accuracy. Results: For all simulated patient and projection acquisition scenarios, the mean VPD (±S.D.)/COMS (±S.D.) between lesions in prior images and 'ground-truth' onboard images were 136.11% (±42.76%)/15.5 mm (±3.9 mm). Using orthogonal-view 15°-each scan angle, the mean VPD/COMS between the lesion in estimated and 'ground-truth' onboard images for MM-only, FD-only, and MM-FD techniques were 60.10% (±27.17%)/4.9 mm (±3.0 mm), 96.07% (±31.48%)/12.1 mm (±3.9 mm) and 11.45% (±9.37%)/1.3 mm (±1.3 mm), respectively. For orthogonal-view 30°-each scan angle, the corresponding results were 59.16% (±26.66%)/4.9 mm (±3.0 mm), 75.98% (±27.21%)/9.9 mm (±4.0 mm), and 5.22% (±2.12%)/0.5 mm (±0.4 mm). For single-view scan angles of 3°, 30°, and 60°, the results for MM-FD technique were 32.77% (±17.87%)/3.2 mm (±2.2 mm), 24.57% (±18.18%)/2.9 mm (±2.0 mm), and 10.48% (±9.50%)/1.1 mm (±1.3 mm), respectively. For projection angular-sampling-intervals of 0.6°, 1.2°, and 2.5° with the orthogonal-view 30°-each scan angle, the MM-FD technique generated similar VPD (maximum deviation 2.91%) and COMS (maximum deviation 0.6 mm), while sparser sampling yielded larger VPD/COMS. With equal number of projections, the estimation results using scattered 360° scan angle were slightly better than those using orthogonal-view 30°-each scan angle. The estimation accuracy of MM-FD technique declined as noise level increased. Conclusions: The MM-FD technique substantially improves the estimation accuracy for onboard 4D-CBCT using prior planning 4D-CT and limited-angle projections, compared to the MM-only and FD-only techniques. It can potentially be used for the inter/intrafractional 4D-localization verification. [ABSTRACT FROM AUTHOR]

Purpose: The authors present the application of the reduced order constrained optimization (ROCO) method, previously successfully applied to the prostate and lung sites, to the head-and-neck (H&N) site, demonstrating that it can quickly and automatically generate clinically competitive IMRT plans. We provide guidelines for applying ROCO to larynx, oropharynx, and nasopharynx cases, and report the results of a live experiment that demonstrates how an expert planner can save several hours of trial-and-error interaction using the proposed approach. Methods: The ROCO method used for H&N IMRT planning consists of three major steps. First, the intensity space of treatment plans is sampled by solving a series of unconstrained optimization problems with a parameter range based on previously treated patient data. Second, the dominant modes in the intensity space are estimated by dimensionality reduction using principal component analysis (PCA). Third, a constrained optimization problem over this basis is quickly solved to find an IMRT plan that meets organ-at-risk (OAR) and target coverage constraints. The quality of the plan is assessed using evaluation tools within Memorial Sloan-Kettering Cancer Center (MSKCC)'s treatment planning system (TPS). Results: The authors generated ten H&N IMRT plans for previously treated patients using the ROCO method and processed them for deliverability by a dynamic multileaf collimator (DMLC). The authors quantitatively compared the ROCO plans to the previously achieved clinical plans using the TPS tools used at MSKCC, including DVH and isodose contour analysis, and concluded that the ROCO plans would be clinically acceptable. In our current implementation, ROCO H&N plans can be generated using about 1.6 h of offline computation followed by 5-15 min of semiautomatic planning time. Additionally, the authors conducted a live session for a plan designated by MSKCC performed together with an expert H&N planner. A technical assistant set up the first two steps, which were performed without further human interaction, and then collaborated in a virtual meeting with the expert planner to perform the third (constrained optimization) step. The expert planner performed in-depth analysis of the resulting ROCO plan and deemed it to be clinically acceptable and in some aspects superior to the clinical plan. This entire process took 135 min including two constrained optimization runs, in comparison to the estimated 4 h that would have been required using traditional clinical planning tools. Conclusions: The H&N site is very challenging for IMRT planning, due to several levels of prescription and a large, variable number (6-20) of OARs that depend on the location of the tumor. ROCO for H&N shows promise in generating clinically acceptable plans both more quickly and with substantially less human interaction. [ABSTRACT FROM AUTHOR]