Automatic online and real-time tumour motion monitoring during stereotactic liver treatments on a conventional linac by combined optical and sparse monoscopic imaging with kilovoltage x-rays (COSMIK).

The purpose of this study was to develop, validate and clinically demonstrate fully automatic tumour motion monitoring on a conventional linear accelerator by combined optical and sparse monoscopic imaging with kilovoltage x-rays (COSMIK). COSMIK combines auto-segmentation of implanted fiducial markers in cone-beam computed tomography (CBCT) projections and intra-treatment kV images with simultaneous streaming of an external motion signal. A pre-treatment CBCT is acquired with simultaneous recording of the motion of an external marker block on the abdomen. The 3-dimensional (3D) marker motion during the CBCT is estimated from the auto-segmented positions in the projections and used to optimize an external correlation model (ECM) of internal motion as a function of external motion. During treatment, the ECM estimates the internal motion from the external motion at 20 Hz. KV images are acquired every 3 s, auto-segmented, and used to update the ECM for baseline shifts between internal and external motion. The COSMIK method was validated using Calypso-recorded internal tumour motion with simultaneous camera-recorded external motion for 15 liver stereotactic body radiotherapy (SBRT) patients. The validation included phantom experiments and simulations hereof for 12 fractions and further simulations for 42 fractions. The simulations compared the accuracy of COSMIK with ECM-based monitoring without model updates and with model updates based on stereoscopic imaging as well as continuous kilovoltage intrafraction monitoring (KIM) at 10 Hz without an external signal. Clinical real-time tumour motion monitoring with COSMIK was performed offline for 14 liver SBRT patients (41 fractions) and online for one patient (two fractions). The mean 3D root-mean-square error for the four monitoring methods was 1.61 mm (COSMIK), 2.31 mm (ECM without updates), 1.49 mm (ECM with stereoscopic updates) and 0.75 mm (KIM). COSMIK is the first combined kV/optical real-time motion monitoring method used clinically online on a conventional accelerator. COSMIK gives less imaging dose than KIM and is in addition applicable when the kV imager cannot be deployed such as during non-coplanar fields.

Potential improvements of lung and prostate MLC tracking investigated by treatment simulations.

PURPOSE/OBJECTIVES: Intrafraction tumor motion during external radiotherapy is a challenge for the treatment accuracy. A novel technique to mitigate the impact of tumor motion is real-time adaptation of the multileaf collimator (MLC) aperture to the motion, also known as MLC tracking. Although MLC tracking improves the dosimetric accuracy, there are still residual errors. Here, we investigate and rank the performance of five prediction algorithms and seven improvements of an MLC tracking system by extensive tracking treatment simulations. MATERIALS AND METHODS: An in-house-developed MLC tracking simulator that has been experimentally validated against an electromagnetic-guided MLC tracking system was used to test the prediction algorithms and tracking system improvements. The simulator requires a Dicom treatment plan and a motion trajectory as input and outputs all motion of the accelerator during MLC tracking treatment delivery. For lung tumors, MLC tracking treatments were simulated with a low and a high modulation VMAT plan using 99 patient-measured lung tumor trajectories. For prostate, tracking was also simulated with a low and a high modulation VMAT plan, but with 695 prostate trajectories. For each simulated treatment, the tracking error was quantified as the mean MLC exposure error, which is the sum of the overexposed area (irradiated area that should have been shielded according to the treatment plan) and the underexposed area (shielded area that should have been irradiated). First, MLC tracking was simulated with the current MLC tracking system without prediction, with perfect prediction (Perfect), and with the following five prediction algorithms: linear Kalman filter (Kalman), kernel density estimation (KDE), linear adaptive filtering (LAF), wavelet-based multiscale autoregression (wLMS), and time variant seasonal autoregression (TVSAR). Next, MLC tracking was simulated using the best prediction algorithm and seven different tracking system improvements: no localization signal latency (a), doubled maximum MLC leaf speed (b), halved MLC leaf width (c), use of Y backup jaws to track motion perpendicular to the MLC leaves (d), dynamic collimator rotation for alignment of the MLC leaves with the dominant target motion direction (e), improvements 4 and 5 combined (f), and all improvements combined (g). RESULTS: All results are presented as the mean residual MLC exposure error compared to no tracking. In the prediction study, the residual MLC exposure error was 47.0% (no prediction), 45.1% (Kalman), 43.8% (KDE), 43.7% (LAF), 42.1% (wLMS), 40.1% (TVSAR), and 36.5% (Perfect) for lung MLC tracking. For prostate MLC tracking, it was 66.0% (no prediction), 66.9% (Kalman), and 63.4% (Perfect). For lung with TVSAR prediction, the residual MLC exposure error for the seven tracking system improvements was 37.2%(1), 38.3%(2), 37.4%(3), 34.2%(4), 30.6%(5), 27.7%(6), and 20.7%(7). For prostate with no prediction, the residual MLC exposure error was 61.7%(1), 61.4%(2), 55.4%(3), 57.2%(4), 47.5%(5), 43.7%(6), and 38.7%(7). CONCLUSION: For prostate, MLC tracking was slightly better without prediction than with linear Kalman filter prediction. For lung, the TVSAR prediction algorithm performed best. Dynamic alignment of the collimator with the dominant motion axis was the most efficient MLC tracking improvement except for lung tracking with the low modulation VMAT plan, where jaw tracking was slightly better.

Beam angle evaluation to improve inter-fraction motion robustness in pelvic lymph node irradiation with proton therapy.

BACKGROUND: Proton therapy dose distributions are sensitive to range variations, e.g. arising from inter-fraction organ motion. The aim of this study was to evaluate the inter-fraction motion robustness of proton beams from different beam angles in irradiation of pelvic lymph nodes (LNs). MATERIAL AND METHODS: Planning CT (pCT) and multiple repeat CT (rCT) scans of 18 prostate cancer patients were used. Considering left and right LNs separately, the average water equivalent path length (WEPL) over all ray paths in the beams eye view of the LNs were calculated for all gantry/couch angle combinations across all rCTs versus the corresponding pCT. Single beam proton plans were optimized on the pCT for all gantry angles (0° couch) and were re-calculated on all rCTs for each respective patient. WEPL and dose parameters were extracted and a statistical clustering analysis performed to identify patient sub-populations in terms of patterns in which angles were robust. RESULTS: The WEPL analysis showed a general pattern of least variation for 0° couch beam angles where three minima were found across gantry angles for the left LNs and two for the right LNs. The clustering analysis identified three patient sub-groups for the left LNs and two groups for the right LNs. The dose calculations showed similar results as the WEPL variation, e.g. for the left LNs angles around 25°-35°, 100°-110°, and 160°-170° were consistently preferable for both target and organs at risk. CONCLUSIONS: Sub-populations of patients with similar patterns of WEPL variations across beam angles were identified. The most robust angles found for WEPL variations were also confirmed by the dose/volume analysis.

An experimentally validated couch and MLC tracking simulator used to investigate hybrid couch-MLC tracking.

PURPOSE/OBJECTIVE: Couch and MLC tracking are two novel techniques to mitigate intrafractional tumor motion on a conventional linear accelerator, but both techniques still have residual dosimetric errors. Here, we first propose and experimentally validate a software tool to simulate couch and MLC tracking, and then use the simulator to study hybrid couch-MLC tracking for improved tracking performance. MATERIALS AND METHODS: The tracking simulator requires a treatment plan and a motion trajectory as input and simulates the delivered monitor units and motion of all accelerator parts as function of time. The simulator outputs accelerator log files synchronized with the target motion as well as the MLC exposure error, which is a simple dose error surrogate. A series of couch and MLC tracking experiments were used to determine appropriate parameters for the simulator dynamics and to validate the simulator by its ability to reproduce the experimental tracking accuracy. Three hybrid couch-MLC tracking strategies were investigated. All strategies divided the target motion in beam's eye view into motion perpendicular and parallel to the MLC leaves. In the hybrid strategies, couch tracking compensated for the following target motion components (in order of decreasing couch tracking contribution): (a) all perpendicular motion, (b) residual perpendicular motion less than half a leaf width, and (c) persistent residual perpendicular motion that was stable at a time scale of 1s. MLC tracking compensated for the remaining target motion. All tracking strategies were simulated with two prostate and two lung cancer single-arc VMAT plans using 695 prostate trajectories and 160 lung tumor trajectories. The tracking error was quantified as the MLC exposure error. The couch motion was quantified as the mean speed, acceleration, and jerk of the couch. RESULTS: The simulator reproduced the experimental gantry position with a mean (maximum) root-mean-square (rms) error of 0.07°(0.2°). The geometrical rms tracking error was reproduced with mean (maximum) absolute errors of 0.20 mm(0.23 mm) and 0.1 mm(0.23 mm) for MLC tracking parallel and perpendicular to the MLC leaves, and 0.40 mm(0.46 mm), 0.09 mm(0.25 mm), and 0.20 mm(0.46 mm) for couch tracking in the left-right, anterior-posterior, and cranio-caudal directions. The MLC exposure error of VMAT MLC tracking was reproduced with a mean absolute error of 5.6%. All hybrid tracking strategies reduced the couch motion relative to pure couch tracking and improved the tracking accuracy compared with pure MLC tracking. The mean MLC exposure error reduction relative to no tracking was 66.6% (couch tracking), 72.9% (hybrid (1)), 70.2% (2), 59.1% (3), and 55.6% (MLC tracking) for lung tumor motion and 76.5% (couch tracking), 76.1% (1), 74.3% (2), 72.3% (3), and 35.9% (MLC tracking) for prostate motion. For prostate motion, pure MLC tracking resulted in rather large MLC exposure errors that were more than halved with all hybrid tracking strategies. CONCLUSION: A couch and MLC tracking simulator was developed and experimentally validated against a series of tracking experiments. All hybrid couch-MLC tracking strategies improved MLC tracking. Two strategies also improved couch tracking of lung tumors. In particular, MLC tracking of prostate may be greatly improved by a modest degree of couch motion.

Volumetric modulated arc therapy with dynamic collimator rotation for improved multileaf collimator tracking of the prostate.

PURPOSE: To improve MLC tracking of prostate VMAT plans by dynamic rotation of the collimator to align the MLC leaves with the dominant prostate motion direction. METHODS: For 22 prostate cancer patients, two dual arc VMAT plans were made with (1) fixed collimators (45° and 315°) and (2) a rotating collimator that aligned the MLC leaves with the dominant prostate motion direction (population-based first principal component). The fixed and rotating collimator plan quality was compared using selected dose-volume indices. Next, MLC tracking treatments were simulated with 695 patient-measured prostate traces. The MLC exposure error (under- and overexposed MLC area in beam's eye view) was calculated as a surrogate for the MLC tracking error. Finally, motion including dose reconstruction was performed for 35 motion traces for one patient, and the root-mean-square dose error was compared with the MLC exposure error. RESULTS: Rotating collimator VMAT plans were of similar quality as the fixed collimator plans, but significantly improved MLC tracking with 33% lower MLC exposure errors (p≪0.0001). The reductions in MLC exposure error correlated significantly with dose error reductions. CONCLUSION: Prostate VMAT plans with rotating collimator were of similar quality as fixed collimator plans, but more suitable for MLC tracking with significantly better agreement between planned and delivered dose distributions. MLC tracking for prostate cancer patients can therefore be improved without the requirement of additional efforts or hardware changes.

Cardiac and respiration induced motion of mediastinal lymph node targets in lung cancer patients throughout the radiotherapy treatment course.

BACKGROUND AND PURPOSE: Involved mediastinal lymph nodes (LNs) are often included in the radiotherapy target for lung cancer patients. Their motion may differ from the primary tumor motion, possibly undermining the loco-regional control. This study determines the detailed differential target motion throughout the treatment course. MATERIAL AND METHODS: Ten lung cancer patients with 2-4 fiducial markers implanted in LN targets received IMRT with a daily pre-treatment cone-beam CT (CBCT) scan. Offline, the 3D trajectory of the markers was determined from their projected trajectory in the CBCT projections. Frequency analysis was performed to separate the intrafraction motion into a respiratory and cardiac component. The mean setup error of the markers and the motion range were used to calculate margins required for LN targets when setup is based on soft-tissue match. RESULTS: Respiration motion was largest in the CC direction and more prominent for more caudal LNs. Cardiac motion was often (73%) largest in the AP direction and tended to be largest for more cranial LNs. Margins for intrafraction motion and daily baseline shifts of LNs were 4.8mm (LR), 6.0mm (CC) and 6.7mm (AP). CONCLUSIONS: Detailed mapping showed that LN motion was in general governed by breathing, but some LNs had substantial cardiac induced motion.

Electromagnetic guided couch and multileaf collimator tracking on a TrueBeam accelerator.

PURPOSE: Couch and MLC tracking are two promising methods for real-time motion compensation during radiation therapy. So far, couch and MLC tracking experiments have mainly been performed by different research groups, and no direct comparison of couch and MLC tracking of volumetric modulated arc therapy (VMAT) plans has been published. The Varian TrueBeam 2.0 accelerator includes a prototype tracking system with selectable couch or MLC compensation. This study provides a direct comparison of the two tracking types with an otherwise identical setup. METHODS: Several experiments were performed to characterize the geometric and dosimetric performance of electromagnetic guided couch and MLC tracking on a TrueBeam accelerator equipped with a Millennium MLC. The tracking system latency was determined without motion prediction as the time lag between sinusoidal target motion and the compensating motion of the couch or MLC as recorded by continuous MV portal imaging. The geometric and dosimetric tracking accuracies were measured in tracking experiments with motion phantoms that reproduced four prostate and four lung tumor trajectories. The geometric tracking error in beam's eye view was determined as the distance between an embedded gold marker and a circular MLC aperture in continuous MV images. The dosimetric tracking error was quantified as the measured 2%/2 mm gamma failure rate of a low and a high modulation VMAT plan delivered with the eight motion trajectories using a static dose distribution as reference. RESULTS: The MLC tracking latency was approximately 146 ms for all sinusoidal period lengths while the couch tracking latency increased from 187 to 246 ms with decreasing period length due to limitations in the couch acceleration. The mean root-mean-square geometric error was 0.80 mm (couch tracking), 0.52 mm (MLC tracking), and 2.75 mm (no tracking) parallel to the MLC leaves and 0.66 mm (couch), 1.14 mm (MLC), and 2.41 mm (no tracking) perpendicular to the leaves. The motion-induced gamma failure rate was in mean 0.1% (couch tracking), 8.1% (MLC tracking), and 30.4% (no tracking) for prostate motion and 2.9% (couch), 2.4% (MLC), and 41.2% (no tracking) for lung tumor motion. The residual tracking errors were mainly caused by inadequate adaptation to fast lung tumor motion for couch tracking and to prostate motion perpendicular to the MLC leaves for MLC tracking. CONCLUSIONS: Couch and MLC tracking markedly improved the geometric and dosimetric accuracies of VMAT delivery. However, the two tracking types have different strengths and weaknesses. While couch tracking can correct perfectly for slowly moving targets such as the prostate, MLC tracking may have considerably larger dose errors for persistent target shift perpendicular to the MLC leaves. Advantages of MLC tracking include faster dynamics with better adaptation to fast moving targets, the avoidance of moving the patient, and the potential to track target rotations and deformations.

A method for evaluation of proton plan robustness towards inter-fractional motion applied to pelvic lymph node irradiation.

BACKGROUND: The benefit of proton therapy may be jeopardized by dose deterioration caused by water equivalent path length (WEPL) variations. In this study we introduced a method to evaluate robustness of proton therapy with respect to inter-fractional motion and applied it to irradiation of the pelvic lymph nodes (LNs) from different beam angles. Patient- versus population-specific patterns in dose deterioration were explored. MATERIAL AND METHODS: Patient data sets consisting of a planning computed tomography (pCT) as well as multiple repeat CT (rCT) scans for three patients were used, with target volumes and organs at risk (ORs) outlined in all scans. Single beam spot scanning proton plans were optimized for the left and right LN targets separately, across all possible beam angle configurations (5° angle intervals). Isotropic margins of 0, 3, 5 and 7 mm from the clinical target volume (CTV) to the planning target volume (PTV) were investigated. The optimized fluence maps for the pCT for each beam were applied onto all rCTs and the dose distributions were re-calculated. WEPL variation for each beam angle was computed by averaging over beams eye view WEPL distributions. RESULTS: Similarity in deterioration patterns were found for the investigated patients, with beam angles delivering less dose to rectum, bladder and overall normal tissue identified around 40° and around 150°-160° for the left LNs, and corresponding angles for the right LNs. These angles were also associated with low values of WEPL variation. CONCLUSION: We have established and explored a method to quantify the robustness towards inter-fractional motion of single beam proton plans treating the pelvic LNs from different beam configurations and with different CTV to PTV margins. For the patients investigated we were able to identify beam orientations that were robust to dose deterioration in the target and ORs.

Moving metal artifact reduction in cone-beam CT scans with implanted cylindrical gold markers.

PURPOSE: Implanted gold markers for image-guided radiotherapy lead to streaking artifacts in cone-beam CT (CBCT) scans. Several methods for metal artifact reduction (MAR) have been published, but they all fail in scans with large motion. Here the authors propose and investigate a method for automatic moving metal artifact reduction (MMAR) in CBCT scans with cylindrical gold markers. METHODS: The MMAR CBCT reconstruction method has six steps. (1) Automatic segmentation of the cylindrical markers in the CBCT projections. (2) Removal of each marker in the projections by replacing the pixels within a masked area with interpolated values. (3) Reconstruction of a marker-free CBCT volume from the manipulated CBCT projections. (4) Reconstruction of a standard CBCT volume with metal artifacts from the original CBCT projections. (5) Estimation of the three-dimensional (3D) trajectory during CBCT acquisition for each marker based on the segmentation in Step 1, and identification of the smallest ellipsoidal volume that encompasses 95% of the visited 3D positions. (6) Generation of the final MMAR CBCT reconstruction from the marker-free CBCT volume of Step 3 by replacing the voxels in the 95% ellipsoid with the corresponding voxels of the standard CBCT volume of Step 4. The MMAR reconstruction was performed retrospectively using a half-fan CBCT scan for 29 consecutive stereotactic body radiation therapy patients with 2-3 gold markers implanted in the liver. The metal artifacts of the MMAR reconstructions were scored and compared with a standard MAR reconstruction by counting the streaks and by calculating the standard deviation of the Hounsfield units in a region around each marker. RESULTS: The markers were found with the same autosegmentation settings in 27 CBCT scans, while two scans needed slightly changed settings to find all markers automatically in Step 1 of the MMAR method. MMAR resulted in 15 scans with no streaking artifacts, 11 scans with 1-4 streaks, and 3 scans with severe streaking artifacts. The corresponding numbers for MAR were 8 (no streaks), 1 (1-4 streaks), and 20 (severe streaking artifacts). The MMAR method was superior to MAR in scans with more than 8 mm 3D marker motion and comparable to MAR for scans with less than 8 mm motion. In addition, the MMAR method was tested on a 4D CBCT reconstruction for which it worked equally well as for the 3D case. The markers in the 4D case had very low motion blur. CONCLUSIONS: An automatic method for MMAR in CBCT scans was proposed and shown to effectively remove almost all streaking artifacts in a large set of clinical CBCT scans with implanted gold markers in the liver. Residual streaking artifacts observed in three CBCT scans may be removed with better marker segmentation.

A method for selection of beam angles robust to intra-fractional motion in proton therapy of lung cancer.

BACKGROUND: Proton therapy offers the potential for sparing the normal tissue surrounding the target. However, due to well-defined proton ranges around the Bragg peak, dose deposition is more sensitive to changes in the water equivalent path length (WEPL) than with photons. In this study, we assess WEPL variations caused by breathing-induced motion for all possible beam angles in a series of lung cancer patients. By studying the association between measures for WEPL variation and breathing-induced target dose degradation we aimed to develop and explore a tool to identify beam angles that are robust to patient-specific patterns of intra-fractional motion. MATERIAL AND METHODS: Using four-dimensional computed tomography (4DCT) images of three lung cancer patients we evaluated the impact of the WEPL changes on target dose coverage for a series of coplanar single-beam plans. The plans were optimised for the internal target volume (ITV) at the maximum intensity projection (MIP) CT for every 3° gantry interval. The plans were transferred to the ten 4DCT phases and the average reduction in ITV V95 over the ten phases, relative to the original MIP CT calculation, was quantified. The target dose reduction was associated with the mean difference between the WEPL and the phase-averaged WEPL computed for all beam rays across all possible gantry-couch angle combinations. RESULTS: The gantry-couch angle maps showed areas of both high and low WEPL variation, with overall quite similar patterns yet with individual differences reflecting differences in tumour position and breathing-induced motion. The coplanar plans showed a strong association between WEPL changes and ITV V95 reduction, with a correlation coefficient ranging between 0.92 and 0.98 for the three patients (p < 0.01). CONCLUSION: We have presented a 4DCT-based method to quantify WEPL changes during the breathing cycle. The method identified proton field gantry-couch angle combinations that were either sensitive or robust to WEPL changes. WEPL variations along the beam path were associated with target under-dosage.

Clinical use of iterative 4D-cone beam computed tomography reconstructions to investigate respiratory tumor motion in lung cancer patients.

BACKGROUND: Cone beam computed tomography (CBCT) provides means for respiratory resolved volumetric imaging of the thorax. However, merely sorting the acquired projections into respiratory phases and performing a series of conventional three-dimensional (3D) reconstructions lead to clinically prohibitive reconstruction artifacts. This problem can be mitigated by iterative 4D reconstruction. We present a clinical evaluation of two iterative 4D-CBCT reconstruction algorithms during stereotactic body radiation therapy. MATERIAL AND METHODS: Two types of iterative 4D-CBCT reconstructions were performed utilizing: 1) total variation (TV) minimization; and 2) optical flow (OF) based deformable registration between phases. The reconstructions were initially evaluated on a lung phantom with a moveable target insert. Subsequently, 4D-CBCT reconstructions were performed for 19 patients on 2-3 CBCT projection datasets previously acquired for conventional 3D-CBCT reconstruction (∼650 half-fan projections per scan in a full one-minute gantry rotation). The 4D reconstructions were imported into a treatment planning system, where the gross tumor volume (GTV) was delineated and used to extract the tumor motion amplitude. RESULTS: For both phantom and patient scans, the iterative 4D-CBCT reconstructions had sufficient quality for GTV delineation when the breathing period was faster than 3.5 seconds (15 of 19 patients), but not for slower breathing periods (4 patients). The 3D tumor motion amplitude for the patients was significantly lower (p = 10(-6), Wilcoxon signed rank test) in the OF reconstructions (mean 4.0 mm) than in the TV reconstructions (mean 5.3 mm). CONCLUSION: TV and OF iterative 4D-CBCT reconstruction of the thorax in a lung phantom and for 19 patients was demonstrated from standard CBCT scans and used to estimate the daily lung tumor motion.

LET-painting increases tumour control probability in hypoxic tumours.

LET-painting was suggested as a method to overcome tumour hypoxia. In vitro experiments have demonstrated a well-established relationship between the oxygen enhancement ratio (OER) and linear energy transfer (LET), where OER approaches unity for high-LET values. However, high-LET radiation also increases the risk for side effects in normal tissue. LET-painting attempts to restrict high-LET radiation to compartments that are found to be hypoxic, while applying lower LET radiation to normoxic tissues. Methods. Carbon-12 and oxygen-16 ion treatment plans with four fields and with homogeneous dose in the target volume, are applied on an oropharyngeal cancer case with an identified hypoxic entity within the tumour. The target dose is optimised to achieve a tumour control probability (TCP) of 95% when assuming a fully normoxic tissue. Using the same primary particle energy fluence needed for this plan, TCP is recalculated for three cases assuming hypoxia: first, redistributing LET to match the hypoxic structure (LET-painting). Second, plans are recalculated for varying hypoxic tumour volume in order to investigate the threshold volume where TCP can be established. Finally, a slight dose boost (5-20%) is additionally allowed in the hypoxic subvolume to assess its impact on TCP. Results. LET-painting with carbon-12 ions can only achieve tumour control for hypoxic subvolumes smaller than 0.5 cm(3). Using oxygen-16 ions, tumour control can be achieved for tumours with hypoxic subvolumes of up to 1 or 2 cm(3). Tumour control can be achieved for tumours with even larger hypoxic subvolumes, if a slight dose boost is allowed in combination with LET-painting. Conclusion. Our findings clearly indicate that a substantial increase in tumour control can be achieved when applying the LET-painting concept using oxygen-16 ions on hypoxic tumours, ideally with a slight dose boost.

Stopping power for particle therapy: the generic library libdEdx and clinically relevant stopping-power ratios for light ions.

PURPOSE: Stopping-power data enter at a number of different places in particle therapy and their uncertainties have a direct impact on the accuracy of the therapy, e.g., in treatment planning. Furthermore, for clinical quality assurance, the particle beam stopping-power ratios (STPR) have to be known accurately for dosimetry. METHODS: An open-source computer library called libdEdx (library for energy loss per unit path length, dE/dx, calculations) is developed, providing stopping-power data from data tables and computer programs as well as a stopping-power formula comprising a large list of target materials. Calculations of STPR in the case of spread-out Bragg-peaks (SOBP) are performed with the Monte Carlo transportation code SHIELD-HIT (SHIELD-Heavy Ion Transport) using different ions relevant for particle therapy. RESULTS: For SOBP the water-to-air STPR depends on the residual range and is qualitatively very similar for different ions; however, small quantitative differences exist between the considered ion species. CONCLUSIONS: libdEdx allows for a convenient and efficient treatment of stopping powers in numerical applications. It can be applied to estimate the dependence on the accuracy of the stopping power and to provide data for an extended number of target materials. The STPR for SOBP for different ions are found to be qualitatively the same which may allow for an analytical description valid for all ions.