A theoretical investigation of adequate range uncertainty margins in proton treatment planning to preserve tumor control probability.

Background: Proton dose distributions are sensitive to range uncertainties, resulting in margins added to ensure adequate tumor control probability (TCP). We investigated the required margin and dose shape needed to ensure adequate TCP, for representative tumor cell distributions in the clinical target volume (CTV). Material and methods: A mechanistic tumor response model, validated for lung tumors, was used to estimate TCP. The tumor cell distribution ( ρ ) was assumed to decrease exponentially in the CTV with decay parameter λ toward the outer border ( xCTVmax ). It was investigated if a gradual dose fall-off could reduce the dose to normal tissues outside the CTV, while achieving adequate TCP. For various values of xCTVmax and λ, we derived adequate uniform dose margins ( m ), coupled to linear dose fall-off regions ( Δx, Δxnom=Δx-0.9 cm), that ensured TCP>TCPlimit, while delivering the least mean dose outside the CTV. To account for variabilities in patients and tumor types, variable probabilities ( p ) of finding tumor cells in the non-GTV part of the CTV for a given patient were also tested. Dose from a single beam or two opposing beams was simulated under the influence of a typical stopping power ratio uncertainty of 3.5%. Results: For large λ and xCTVmax, a dose distribution with a shallower dose fall-off ( Δx>0 ) was advantageous, and m could be smaller than xCTVmax. In the case of small xCTVmax values, however, a conventional dose distribution ( Δx=0 ) would generally perform better. For no CTV, m=0.4 cm in the case of two opposing beams, while it was 0.7 cm for a single beam, however, for two opposing beams Δx=1.2 cm ( Δxnom=0.3 cm), while it was zero for a single beam. Conclusion: The details of the underlying cancer cell distribution characteristics do impact the adequate dose arrangements, and for opposing beams a non-conventional dose distribution shape is often advantageous.

Simultaneous Reduction of Number of Spots and Energy Layers in Intensity Modulated Proton Therapy for Rapid Spot Scanning Delivery.

Reducing proton treatment time improves patient comfort and decreases the risk of error from intra-fractional motion, but must be balanced against clinical goals and treatment plan quality. We formulated the proton treatment planning problem as a convex optimization problem with a cost function consisting of a dosimetric plan quality term plus a weighted $l_1$ regularization term. We iteratively solved this problem and adaptively updated the regularization weights to promote the sparsity of both the spots and energy layers. The proposed algorithm was tested on four head-and-neck cancer patients, and its performance was compared with existing standard $l_1$ and group $l_2$ regularization methods. We also compared the effectiveness of the three methods ($l_1$, group $l_2$, and reweighted $l_1$) at improving plan delivery efficiency without compromising dosimetric plan quality by constructing each of their Pareto surfaces charting the trade-off between plan delivery and plan quality. The reweighted $l_1$ regularization method reduced the number of spots and energy layers by an average over all patients of 40% and 35%, respectively, with an insignificant cost to dosimetric plan quality. From the Pareto surfaces, it is clear that reweighted $l_1$ provided a better trade-off between plan delivery efficiency and dosimetric plan quality than standard $l_1$ or group $l_2$ regularization, requiring the lowest cost to quality to achieve any given level of delivery efficiency. In summary, reweighted $l_1$ regularization is a powerful method for simultaneously promoting the sparsity of spots and energy layers at a small cost to dosimetric plan quality. This sparsity reduces the time required for spot scanning and energy layer switching, thereby improving the delivery efficiency of proton plans.

Simultaneous reduction of number of spots and energy layers in intensity modulated proton therapy for rapid spot scanning delivery.

BACKGROUND: Reducing proton treatment time improves patient comfort and decreases the risk of error from intrafractional motion, but must be balanced against clinical goals and treatment plan quality. PURPOSE: To improve the delivery efficiency of spot scanning proton therapy by simultaneously reducing the number of spots and energy layers using the reweighted l 1 $l_1$ regularization method. METHODS: We formulated the proton treatment planning problem as a convex optimization problem with a cost function consisting of a dosimetric plan quality term plus a weighted l 1 $l_1$ regularization term. We iteratively solved this problem and adaptively updated the regularization weights to promote the sparsity of both the spots and energy layers. The proposed algorithm was tested on four head-and-neck cancer patients, and its performance, in terms of reducing the number of spots and energy layers, was compared with existing standard l 1 $l_1$ and group l 2 $l_2$ regularization methods. We also compared the effectiveness of the three methods ( l 1 $l_1$ , group l 2 $l_2$ , and reweighted l 1 $l_1$ ) at improving plan delivery efficiency without compromising dosimetric plan quality by constructing each of their Pareto surfaces charting the trade-off between plan delivery and plan quality. RESULTS: The reweighted l 1 $l_1$ regularization method reduced the number of spots and energy layers by an average over all patients of 40 % $40\%$ and 35 % $35\%$ , respectively, with an insignificant cost to dosimetric plan quality. From the Pareto surfaces, it is clear that reweighted l 1 $l_1$ provided a better trade-off between plan delivery efficiency and dosimetric plan quality than standard l 1 $l_1$ or group l 2 $l_2$ regularization, requiring the lowest cost to quality to achieve any given level of delivery efficiency. CONCLUSIONS: Reweighted l 1 $l_1$ regularization is a powerful method for simultaneously promoting the sparsity of spots and energy layers at a small cost to dosimetric plan quality. This sparsity reduces the time required for spot scanning and energy layer switching, thereby improving the delivery efficiency of proton plans.

Proton and photon radiotherapy in stage III NSCLC: Effects on hematological toxicity and adjuvant immune therapy.

BACKGROUND AND PURPOSE: Concurrent chemo-radiotherapy (CCRT) followed by adjuvant durvalumab is standard-of-care for fit patients with unresectable stage III NSCLC. Intensity modulated proton therapy (IMPT) results in different doses to organs than intensity modulated photon therapy (IMRT). We investigated whether IMPT compared to IMRT reduce hematological toxicity and whether it affects durvalumab treatment. MATERIALS AND METHODS: Prospectively collected series of consecutive patients with stage III NSCLC receiving CCRT between 06.16 and 12.22 (staged with FDG-PET-CT and brain imaging) were retrospectively analyzed. The primary endpoint was the incidence of lymphopenia grade ≥ 3 in IMPT vs IMRT treated patients. RESULTS: 271 patients were enrolled (IMPT: n = 71, IMRT: n = 200) in four centers. All patients received platinum-based chemotherapy. Median age: 66 years, 58 % were male, 36 % had squamous NSCLC. The incidence of lymphopenia grade ≥ 3 during CCRT was 67 % and 47 % in the IMRT and IMPT group, respectively (OR 2.2, 95 % CI: 1.0-4.9, P = 0.03). The incidence of anemia grade ≥ 3 during CCRT was 26 % and 9 % in the IMRT and IMPT group respectively (OR = 4.9, 95 % CI: 1.9-12.6, P = 0.001). IMPT was associated with a lower rate of Performance Status (PS) ≥ 2 at day 21 and 42 after CCRT (13 % vs. 26 %, P = 0.04, and 24 % vs. 39 %, P = 0.02). Patients treated with IMPT had a higher probability of receiving adjuvant durvalumab (74 % vs. 52 %, OR 0.35, 95 % CI: 0.16-0.79, P = 0.01). CONCLUSION: IMPT was associated with a lower incidence of severe lymphopenia and anemia, better PS after CCRT and a higher probability of receiving adjuvant durvalumab.

Distributed and scalable optimization for robust proton treatment planning.

BACKGROUND: The importance of robust proton treatment planning to mitigate the impact of uncertainty is well understood. However, its computational cost grows with the number of uncertainty scenarios, prolonging the treatment planning process. PURPOSE: We developed a fast and scalable distributed optimization platform that parallelizes the robust proton treatment plan computation over the uncertainty scenarios. METHODS: We modeled the robust proton treatment planning problem as a weighted least-squares problem. To solve it, we employed an optimization technique called the alternating direction method of multipliers with Barzilai-Borwein step size (ADMM-BB). We reformulated the problem in such a way as to split the main problem into smaller subproblems, one for each proton therapy uncertainty scenario. The subproblems can be solved in parallel, allowing the computational load to be distributed across multiple processors (e.g., CPU threads/cores). We evaluated ADMM-BB on four head-and-neck proton therapy patients, each with 13 scenarios accounting for 3 mm setup and 3.5% range uncertainties. We then compared the performance of ADMM-BB with projected gradient descent (PGD) applied to the same problem. RESULTS: For each patient, ADMM-BB generated a robust proton treatment plan that satisfied all clinical criteria with comparable or better dosimetric quality than the plan generated by PGD. However, ADMM-BB's total runtime averaged about 6 to 7 times faster. This speedup increased with the number of scenarios. CONCLUSIONS: ADMM-BB is a powerful distributed optimization method that leverages parallel processing platforms, such as multicore CPUs, GPUs, and cloud servers, to accelerate the computationally intensive work of robust proton treatment planning. This results in (1) a shorter treatment planning process and (2) the ability to consider more uncertainty scenarios, which improves plan quality.

The relative biological effectiveness of carbon ion radiation therapy for early stage lung cancer.

BACKGROUND AND PURPOSE: Carbon ion radiation therapy (CIRT) is recognized as an effective alternative treatment modality for early stage lung cancer, but a quantitative understanding of relative biological effectiveness (RBE) compared to photon therapy is lacking. In this work, a mechanistic tumor response model previously validated for lung photon radiotherapy was used to estimate the RBE of CIRT compared to photon radiotherapy, as a function of dose and the fractionation schedule. MATERIALS AND METHODS: Clinical outcome data of 9 patient cohorts (394 patients) treated with CIRT for early stage lung cancer, representing all published data, were included. Fractional dose, number of fractions, treatment schedule, and local control rates were used for model simulations relative to standard photon outcomes. Four parameters were fitted: α, α/ß, and the oxygen enhancement ratios of cells either accessing only glucose, not oxygen (OERI), or cells dying from starvation (OERH). The resulting dose-response relationship of CIRT was compared with the previously determined dose-response relationship of photon radiotherapy for lung cancer, and an RBE of CIRT was derived. RESULTS: Best-fit CIRT parameters were: α = 1.12 Gy-1 [95%-CI: 0.97-1.26], α/ß = 23.9 Gy [95%-CI: 8.9-38.9], and the oxygen induced radioresistance of hypoxic cell populations were characterized by OERI = 1.08 [95%-CI: 1.00-1.41] (cells lacking oxygen but not glucose), and OERH = 1.01 [95%-CI: 1.00-1.44] (cells lacking oxygen and glucose). Depending on dose and fractionation, the derived RBE ranges from 2.1 to 1.5, with decreasing values for larger fractional dose and fewer number of fractions. CONCLUSION: Fitted radiobiological parameters were consistent with known carbon in vitro radiobiology, and the resulting dose-response curve well-fitted the reported data over a wide range of dose-fractionation schemes. The same model, with only a few fitted parameters of clear mechanistic meaning, thus synthesizes both photon radiotherapy and CIRT clinical experience with early stage lung tumors.

Automated proton treatment planning with robust optimization using constrained hierarchical optimization.

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.

Automating proton treatment planning with beam angle selection using Bayesian optimization.

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.

Theoretical and experimental analysis of photon counting detector CT for proton stopping power prediction.

PURPOSE: Photon counting detectors (PCDs) are being introduced in advanced x-ray computed tomography (CT) scanners. From a single PCD-CT acquisition, multiple images can be reconstructed, each based on only a part of the original x-ray spectrum. In this study, we investigated whether PCD-CT can be used to estimate stopping power ratios (SPRs) for proton therapy treatment planning, both by comparing to other SPR methods proposed for single energy CT (SECT) and dual energy CT (DECT) as well as to experimental measurements. METHODS: A previously developed DECT-based SPR estimation method was adapted to PCD-CT data, by adjusting the estimation equations to allow for more energy spectra. The method was calibrated directly on noisy data to increase the robustness toward image noise. The new PCD SPR estimation method was tested in theoretical calculations as well as in an experimental setup, using both four and two energy bin PCD-CT images, and through comparison to two other SPR methods proposed for SECT and DECT. These two methods were also evaluated on PCD-CT images, full spectrum (one-bin) or two-bin images, respectively. In a theoretical framework, we evaluated the effect of patient-specific tissue variations (density and elemental composition) and image noise on the SPR accuracy; the latter effect was assessed by applying three different noise levels (low, medium, and high noise). SPR estimates derived using real PCD-CT images were compared to experimentally measured SPRs in nine organic tissue samples, including fat, muscle, and bone tissues. RESULTS: For the theoretical calculations, the root-mean-square error (RMSE) of the SPR estimation was 0.1% for the new PCD method using both two and four energy bins, compared to 0.2% and 0.7% for the DECT- and SECT-based method, respectively. The PCD method was found to be very robust toward CT image noise, with a RMSE of 2.7% when high noise was added to the CT numbers. Introducing tissue variations, the RMSE only increased to 0.5%; even when adding high image noise to the changed tissues, the RMSE stayed within 3.1%. In the experimental measurements, the RMSE over the nine tissue samples was 0.8% when using two energy bins, and 1.0% for the four-bin images. CONCLUSIONS: In all tested cases, the new PCD method produced similar or better results than the SECT- and DECT-based methods, showing an overall improvement of the SPR accuracy. This study thus demonstrated that PCD-CT scans will be a qualified candidate for SPR estimations.

Inter-centre variability of CT-based stopping-power prediction in particle therapy: Survey-based evaluation.

BACKGROUND AND PURPOSE: Stopping-power ratios (SPRs) are used in particle therapy to calculate particle range in patients. The heuristic CT-to-SPR conversion (Hounsfield Look-Up-Table, HLUT), needed for treatment planning, depends on CT-scan and reconstruction parameters as well as the specific HLUT definition. To assess inter-centre differences in these parameters, we performed a survey-based qualitative evaluation, as a first step towards better standardisation of CT-based SPR derivation. MATERIALS AND METHODS: A questionnaire was sent to twelve particle therapy centres (ten from Europe and two from USA). It asked for details on CT scanners, image acquisition and reconstruction, definition of the HLUT, body-region specific HLUT selection, investigations of beam-hardening and experimental validations of the HLUT. Technological improvements were rated regarding their potential to improve SPR accuracy. RESULTS: Scan parameters and HLUT definition varied widely. Either the stoichiometric method (eight centres) or a tissue-substitute-only HLUT definition (three centres) was used. One centre combined both methods. The number of HLUT line segments varied widely between two and eleven. Nine centres had investigated influence of beam-hardening, often including patient-size dependence. Ten centres had validated their HLUT experimentally, with very different validation schemes. Most centres deemed dual-energy CT promising for improving SPR accuracy. CONCLUSIONS: Large inter-centre variability was found in implementation of CT scans, image reconstruction and especially in specification of the CT-to-SPR conversion. A future standardisation would reduce time-intensive institution-specific efforts and variations in treatment quality. Due to the interdependency of multiple parameters, no conclusion can be drawn on the derived SPR accuracy and its inter-centre variability.

Chemically tuned linear energy transfer dependent quenching in a deformable, radiochromic 3D dosimeter.

Most solid-state detectors, including 3D dosimeters, show lower signal in the Bragg peak than expected, a process termed quenching. The purpose of this study was to investigate how variation in chemical composition of a recently developed radiochromic, silicone-based 3D dosimeter influences the observed quenching in proton beams. The dependency of dose response on linear energy transfer, as calculated through Monte Carlo simulations of the dosimeter, was investigated in 60 MeV proton beams. We found that the amount of quenching varied with the chemical composition: peak-to-plateau ratios (1 cm into the plateau) ranged from 2.2 to 3.4, compared to 4.3 using an ionization chamber. The dose response, and thereby the quenching, was predominantly influenced by the curing agent concentration, which determined the dosimeter's deformation properties. The dose response was found to be linear at all depths. All chemical compositions of the dosimeter showed dose-rate dependency; however this was not dependent on the linear energy transfer. Track-structure theory was used to explain the observed quenching effects. In conclusion, this study shows that the silicone-based dosimeter has potential for use in measuring 3D-dose-distributions from proton beams.

Validation of proton stopping power ratio estimation based on dual energy CT using fresh tissue samples.

Dual energy CT (DECT) has been shown, in theoretical and phantom studies, to improve the stopping power ratio (SPR) determination used for proton treatment planning compared to the use of single energy CT (SECT). However, it has not been shown that this also extends to organic tissues. The purpose of this study was therefore to investigate the accuracy of SPR estimation for fresh pork and beef tissue samples used as surrogates of human tissues. The reference SPRs for fourteen tissue samples, which included fat, muscle and femur bone, were measured using proton pencil beams. The tissue samples were subsequently CT scanned using four different scanners with different dual energy acquisition modes, giving in total six DECT-based SPR estimations for each sample. The SPR was estimated using a proprietary algorithm (syngo.via DE Rho/Z Maps, Siemens Healthcare, Forchheim, Germany) for extracting the electron density and the effective atomic number. SECT images were also acquired and SECT-based SPR estimations were performed using a clinical Hounsfield look-up table. The mean and standard deviation of the SPR over large volume-of-interests were calculated. For the six different DECT acquisition methods, the root-mean-square errors (RMSEs) for the SPR estimates over all tissue samples were between 0.9% and 1.5%. For the SECT-based SPR estimation the RMSE was 2.8%. For one DECT acquisition method, a positive bias was seen in the SPR estimates, having a mean error of 1.3%. The largest errors were found in the very dense cortical bone from a beef femur. This study confirms the advantages of DECT-based SPR estimation although good results were also obtained using SECT for most tissues.

A robust empirical parametrization of proton stopping power using dual energy CT.

PURPOSE: In this study the authors present a new method for estimation of proton stopping power ratios (SPRs) using dual energy CT (DECT), which is robust toward CT noise. The authors propose a parametrization for SPR based directly on the CT numbers in a DECT image set, whereby the intermediate steps of estimating the relative electron density, ρe, and mean excitation energy, I, are avoided. METHODS: The SPR parametrization proposed in this study is a purely empirical fit based on the theoretical SPR values for a list of 34 reference human tissues. To investigate the SPR estimation made with this new method the authors performed a calibration and an evaluation with the method. The authors initially calculated CT numbers using CT energy spectrum characterization parameters obtained from calibration based on a Gammex 467 electron density calibration phantom. These CT numbers were fitted to the theoretical SPR for the reference human tissues using the new SPR parametrization presented in this study. The method was evaluated based on theoretical CT numbers for the reference human tissues. The root-mean-square error (RMSE) of the SPR and the proton range error from the continuous slowing down approximation were calculated for the reference human tissues. To test the stability of the parametrization the authors varied the density and elemental composition of the reference human tissues and calculated their new SPR estimates. Further, clinically realistic noise values were added to the theoretical CT numbers to investigate how CT noise affected the estimated water equivalent range through 10 cm of the reference human tissues. All results for the new SPR parametrization were compared to the results obtained using two previously published DECT methods for SPR estimation. Comparisons were also made to a single energy CT (SECT) SPR estimation method, the stoichiometric method, which is commonly used in clinical practise for proton therapy treatment planning. RESULTS: The RMSE for the SPR of the 34 reference human tissues using the new SPR parametrization was 0.12%, compared to 0.19% and 0.28% for the two previously published DECT methods. The SPR parametrization was more stable toward variations of the calcium content in the reference human tissues, but less stable toward density variations and changes to the hydrogen content than the two other DECT methods. When adding noise to the theoretical CT numbers the SPR parametrization gave the lowest water equivalent range errors of all four tested SPR estimation methods (maximum error reduced to 0.4 mm). In all cases tested, the new SPR parametrization outperformed the SECT stoichiometric method. CONCLUSIONS: The new SPR parametrization gave lower RMSEs than the two other published DECT methods, and was in particular more robust against added noise. The method has potential for reducing range uncertainty margins in treatment planning of proton therapy.