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Purpose: The purpose of this study was to develop a simple flexible method for accurate estimation of stopping power ratio (SPR) and mean excitation energy (I) using relative electron density (ρ e). Materials and Methods: The model was formulated using empirical relationships between SPR, mean excitation energy I, and relative electron density. Some examples were implemented, and a comparison was carried out using other existing methods. The needed coefficients in the model were estimated using optimization tools. Basis vector method (BVM) and Hunemohr and Saito (H-S) method were applied to estimate the ρ e used in the application section. 80 kVp and 150 kVpSn were used as low and high energy, respectively, for the implementation of dual-energy methods. Results: All the examples of the proposed method considered have modeling error that is ≤0.32% and testing root mean square error (RMSE) ≤0.92% for SPR with a mean error close to 0.00%. The method was able to achieve modeling RMSE of 2.12% for mean excitation energy with room for improvement. Similar or better results were achieved in application to BVM. Conclusion: The method showed robustness in application by achieving lower testing error than other presented methods in most cases. It achieved accurate estimation which can be improved using the machine learning algorithm since it is flexible to implement in terms of the function (model) degree and tissue classification.

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Objective. Range uncertainty in proton therapy is an important factor limiting clinical effectiveness. Magnetic resonance imaging (MRI) can measure voxel-wise molecular composition and, when combined with kilovoltage CT (kVCT), accurately determine mean ionization potential (Im), electron density, and stopping power ratio (SPR). We aimed to develop a novel MR-based multimodal method to accurately determine SPR and molecular compositions. This method was evaluated in tissue-mimicking andex vivoporcine phantoms, and in a brain radiotherapy patient.Approach. Four tissue-mimicking phantoms with known compositions, two porcine tissue phantoms, and a brain cancer patient were imaged with kVCT and MRI. Three imaging-based values were determined: SPRCM(CT-based Multimodal), SPRMM(MR-based Multimodal), and SPRstoich(stoichiometric calibration). MRI was used to determine two tissue-specific quantities of the Bethe Bloch equation (Im, electron density) to compute SPRCMand SPRMM. Imaging-based SPRs were compared to measurements for phantoms in a proton beam using a multilayer ionization chamber (SPRMLIC).Main results. Root mean square errors relative to SPRMLICwere 0.0104(0.86%), 0.0046(0.45%), and 0.0142(1.31%) for SPRCM, SPRMM, and SPRstoich, respectively. The largest errors were in bony phantoms, while soft tissue and porcine tissue phantoms had <1% errors across all SPR values. Relative to known physical molecular compositions, imaging-determined compositions differed by approximately ≤10%. In the brain case, the largest differences between SPRstoichand SPRMMwere in bone and high lipids/fat tissue. The magnitudes and trends of these differences matched phantom results.Significance. Our MR-based multimodal method determined molecular compositions and SPR in various tissue-mimicking phantoms with high accuracy, as confirmed with proton beam measurements. This method also revealed significant SPR differences compared to stoichiometric kVCT-only calculation in a clinical case, with the largest differences in bone. These findings support that including MRI in proton therapy treatment planning can improve the accuracy of calculated SPR values and reduce range uncertainties.

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BACKGROUND: Extended field-of-view (eFOV) methods have been proposed to generate larger demonstration FOVs for computed tomography (CT) simulators with a limited scanning FOV (sFOV) size in order to ensure accurate dose calculation and patient collision avoidance. Although the efficacy of these strategies has been evaluated for photon applications, the effect of stopping power ratio (SPR) estimation on proton therapy has not been studied. This study investigated the effect of an eFOV approach on the accuracy of SPR to water estimation in homogeneous and heterogeneous phantoms. MATERIALS AND METHODS: To simulate patient geometries, tissue-equivalent material (TEM) and customized extension phantoms were used. The TEM phantom supported various rod arrangements through predefined holes. Images were reconstructed to three FOV sizes using a commercial eFOV technique. A single-energy CT stoichiometric method was used to generate Hounsfield unit (HU) to SPR (HU-to-SPR) conversion curves for each FOV. To investigate the effect of rod location in the sFOV and eFOV regions, eight TEM rods were placed at off-center distances in the homogeneous phantom and scanned individually. Similarly, 16 TEM rods were placed in the heterogeneous TEM phantom and scanned simultaneously. RESULTS: The conversion curves derived from the sFOV and eFOV data were identical. The average SPR differences of soft-tissue, bone, and lung materials for rods placed at various off-center locations were 3.3%, 4.8%, and 39.6%, respectively. In the heterogeneous phantom, the difference was within 1.0% in the absence of extension. However, in the presence of extension, the difference increased to 2.8% for all rods, except for lung materials, whose difference was 4.8%. CONCLUSIONS: When an eFOV method is used, the SPR variation in phantoms considerably increases for all TEM rods, especially for lung TEM rods. This phenomenon may substantially increase the uncertainty of HU-to-SPR conversion. Therefore, image reconstruction with a standard FOV size is recommended.

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BACKGROUND AND PURPOSE: Studies have shown large variations in stopping-power ratio (SPR) prediction from computed tomography (CT) across European proton centres. To standardise this process, a step-by-step guide on specifying a Hounsfield look-up table (HLUT) is presented here. MATERIALS AND METHODS: The HLUT specification process is divided into six steps: Phantom setup, CT acquisition, CT number extraction, SPR determination, HLUT specification, and HLUT validation. Appropriate CT phantoms have a head- and body-sized part, with tissue-equivalent inserts in regard to X-ray and proton interactions. CT numbers are extracted from a region-of-interest covering the inner 70% of each insert in-plane and several axial CT slices in scan direction. For optimal HLUT specification, the SPR of phantom inserts is measured in a proton beam and the SPR of tabulated human tissues is computed stoichiometrically at 100 MeV. Including both phantom inserts and tabulated human tissues increases HLUT stability. Piecewise linear regressions are performed between CT numbers and SPRs for four tissue groups (lung, adipose, soft tissue, and bone) and then connected with straight lines. Finally, a thorough but simple validation is performed. RESULTS: The best practices and individual challenges are explained comprehensively for each step. A well-defined strategy for specifying the connection points between the individual line segments of the HLUT is presented. The guide was tested exemplarily on three CT scanners from different vendors, proving its feasibility. CONCLUSION: The presented step-by-step guide for CT-based HLUT specification with recommendations and examples can contribute to reduce inter-centre variations in SPR prediction.

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The stopping-power ratio (SPR) of body tissues relative to water depends on the particle energy and mean excitation energy (I value) of the tissues. Effective energies to minimize the range error in proton therapy and ion beam therapy with helium, carbon, oxygen, and neon ions and elemental I values have been updated in recent studies. We investigated the effects of these updates on SPR estimation for computed tomography-based treatment planning. The updates led to an increase of up to 0.5% in the SPRs of soft tissues, whereas they led to a decrease of up to 1.9% in the SPRs of bone tissues compared with the current clinical settings. For 44 proton beams planned for 15 randomly sampled patients, the mean water-equivalent target depth change was - 0.2 mm with a standard deviation of 0.2 mm. The maximum change was - 0.6 mm, which we consider to be insignificant in clinical practice.

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The errors on the stopping power ratio (SPR) of mouthpiece samples from ERKODENT were evaluated. Erkoflex and Erkoloc-pro from ERKODENT and samples that combined Erkoflex and Erkoloc-pro were computed tomography (CT)-scanned using head and neck (HN) protocol at the East Japan Heavy Ion Center (EJHIC), and the values were averaged to obtain the CT number. The integral depth dose of the Bragg curve with and without these samples was measured for 292.1, 180.9, and 118.8 MeV/u of the carbon-ion pencil beam using an ionization chamber with concentric electrodes at the horizontal port of the EJHIC. The average value of the water equivalent length (WEL) of each sample was obtained from the difference between the range of the Bragg curve and the thickness of the sample. To calculate the difference between the theoretical and measured values, the theoretical CT number and SPR value of the sample were calculated using the stoichiometric calibration method. Compared with the Hounsfield unit (HU)-SPR calibration curve used at the EJHIC, the SPR error on each measured and theoretical value was calculated. The WEL value of the mouthpiece sample had an error of approximately 3.5% in the HU-SPR calibration curve. From this error, it was evaluated that for a mouthpiece with a thickness of 10 mm, a beam range error of approximately 0.4 mm can occur, and for a mouthpiece with a thickness of 30 mm, a beam range error of approximately 1 mm can occur. For a beam passing through the mouthpiece in HN treatment, it would be practical to consider a mouthpiece margin of 1 mm to avoid beam range errors if ions pass through the mouthpiece.

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Radiotherapy with protons or light ions can offer accurate and precise treatment delivery. Accurate knowledge of the stopping power ratio (SPR) distribution of the tissues in the patient is crucial for improving dose prediction in patients during planning. However, materials of uncertain stoichiometric composition such as dental implant and restoration materials can substantially impair particle therapy treatment planning due to related SPR prediction uncertainties. This study investigated the impact of using dual-energy computed tomography (DECT) imaging for characterizing and compensating for commonly used dental implant and restoration materials during particle therapy treatment planning. Radiological material parameters of ten common dental materials were determined using two different DECT techniques: sequential acquisition CT (SACT) and dual-layer spectral CT (DLCT). DECT-based direct SPR predictions of dental materials via spectral image data were compared to conventional single-energy CT (SECT)-based SPR predictions obtained via indirect CT-number-to-SPR conversion. DECT techniques were found overall to reduce uncertainty in SPR predictions in dental implant and restoration materials compared to SECT, although DECT methods showed limitations for materials containing elements of a high atomic number. To assess the influence on treatment planning, an anthropomorphic head phantom with a removable tooth containing lithium disilicate as a dental material was used. The results indicated that both DECT techniques predicted similar ranges for beams unobstructed by dental material in the head phantom. When ion beams passed through the lithium disilicate restoration, DLCT-based SPR predictions using a projection-based method showed better agreement with measured reference SPR values (range deviation: 0.2 mm) compared to SECT-based predictions. DECT-based SPR prediction may improve the management of certain non-tissue dental implant and restoration materials and subsequently increase dose prediction accuracy.

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An important source of uncertainty in proton therapy treatment planning is the assignment of stopping-power ratio (SPR) from CT data. A commercial product is now available that creates an SPR map directly from dual-energy CT (DECT). This paper investigates the use of this new product in proton treatment planning and compares the results to the current method of assigning SPR based on a single-energy CT (SECT). Two tissue surrogate phantoms were CT scanned using both techniques. The SPRs derived from single-energy CT and by DirectSPR™ were compared to measured values. SECT-based values agreed with measurements within 4% except for low density lung and high density bone, which differed by 13% and 8%, respectively. DirectSPR™ values were within 2% of measured values for all tissues studied. Both methods were also applied to scanned containers of three types of animal tissue, and the expected range of protons of two different energies was calculated in the treatment planning system and compared to the range measured using a multi-layer ion chamber. The average difference between range measurements and calculations based on SPR maps from dual- and single-energy CT, respectively, was 0.1 mm (0.07%) versus 2.2 mm (1.5%). Finally, a phantom was created using a layer of various tissue surrogate plugs on top of a 2D ion chamber array. Dose measurements on this array were compared to predictions using both single- and dual-energy CTs and SPR maps. While standard gamma pass rates for predictions based on DECT-derived SPR maps were slightly higher than those based on single-energy CT, the differences were generally modest for this measurement setup. This study showed that SPR maps created by the commercial product from dual-energy CT can successfully be used in RayStation to generate proton dose distributions and that these predictions agree well with measurements.

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PURPOSE: To assess treatment planning system (TPS) accuracy in estimating the stopping-power ratio (SPR) of immobilization devices commonly used in proton therapy and to evaluate the dosimetric effect of SPR estimation error for a set of clinical treatment plans. METHODS: Computed tomography scans of selected clinical immobilization devices were acquired. Then, the water-equivalent thickness (WET) and SPR values of these devices based on the scans were estimated in a commercial TPS. The reference SPR of each device was measured using a multilayer ion chamber (MLIC), and the differences between measured and TPS-estimated SPRs were calculated. These findings were utilized to calculate corrected dose distributions of 15 clinical proton plans for three treatment sites: extremity, abdomen, and head-and-neck. The original and corrected dose distributions were compared using a set of target and organs-at-risk (OARs) dose-volume histogram (DVH) parameters. RESULTS: On average, the TPS-estimated SPR was 19.5% lower (range, -35.1% to 0.2%) than the MLIC-measured SPR. Due to the relatively low density of most immobilization devices used, the WET error was typically <1 mm, but up to 2.2 mm in certain devices. Overriding the SPR of the immobilization devices to the measured values did not result in significant changes in the DVH metrics of targets and most OARs. However, some critical OARs showed noticeable changes of up to 6.7% in maximum dose. CONCLUSIONS: The TPS tends to underestimate the SPR of selected proton immobilization devices by an average of about 20%, but this does not induce major WET errors because of the low density of the devices. The dosimetric effect of this SPR error was negligible for most treatment sites, although the maximum dose of a few OARs exhibited noticeable variations.

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In this work, we conducted experiments to validate the proton physics models of Geant4 (version 10.6). The stopping power ratios (SPRs) of 11 inserts, such as acrylic, delrin, high density polyethylene, and polytetrafluoroethylene, etc, were measured using a superconducting synchrocyclotron that produces a scattering proton beam. The SPRs of the inserts were also calculated based on Geant4 simulation with six physics lists, i.e. QGSP_ FTFP_ BERT, QGSP_BIC_HP, QGSP_BIC, QGSP_FTFP_BERT, QSGP_BERT, and QBBC. The calculated SPRs were compared to the experimental SPRs, and relative per cent error was used to quantify the accuracy of the simulated SPRs of inserts. The comparison showed that the five physics lists generally agree well with the experimental SPRs with a relative difference of less than 1%. The lowest overall percentage error was observed for QGSP_FTFP_BERT and the highest overall percentage error was observed for QGSP_BIC_HP. The 0.1 mm range cut value consistently led to higher percentage error for all physics lists except for QGSP_BIC_HP and QBBC. Based on the validation, we recommend QGSP_BERT_HP physics list for proton dose calculation.

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In particle therapy treatment planning, dose calculation is conducted using patient-specific maps of tissue ion stopping power ratio (SPR) to predict beam ranges. Improving patient-specific SPR prediction is therefore essential for accurate dose calculation. In this study, we investigated the use of the Spectral CT 7500, a second-generation dual-layer spectral computed tomography (DLCT) system, as an alternative to conventional single-energy CT (SECT) for patient-specific SPR prediction. This dual-energy CT (DECT)-based method allows for the direct prediction of SPR from quantitative measurements of relative electron density and effective atomic number using the Bethe equation, whereas the conventional SECT-based method consists of indirect image data-based prediction through the conversion of calibrated CT numbers to SPR. The performance of the Spectral CT 7500 in particle therapy treatment planning was characterized by conducting a thorough analysis of its SPR prediction accuracy for both tissue-equivalent materials and common non-tissue implant materials. In both instances, DLCT was found to reduce uncertainty in SPR predictions compared to SECT. Mean deviations of 0.7% and 1.6% from measured SPR values were found for DLCT- and SECT-based predictions, respectively, in tissue-equivalent materials. Furthermore, end-to-end analyses of DLCT-based treatment planning were performed for proton, helium, and carbon ion therapies with anthropomorphic head and pelvic phantoms. 3D gamma analysis was performed with ionization chamber array measurements as the reference. DLCT-predicted dose distributions revealed higher passing rates compared to SECT-predicted dose distributions. In the DLCT-based treatment plans, measured distal-edge evaluation layers were within 1 mm of their predicted positions, demonstrating the accuracy of DLCT-based particle range prediction. This study demonstrated that the use of the Spectral CT 7500 in particle therapy treatment planning may lead to better agreement between planned and delivered dose compared to current clinical SECT systems.

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PURPOSE: To present a proton computed tomography (pCT) reconstruction approach that models the integral depth dose (IDD) of the clinical scanning proton beam into beamlets. Using a multilayer ionization chamber (MLIC) as the imager, the proposed pCT system and the reconstruction approach can minimize extra ambient neutron dose and simplify the beamline design by eliminating an additional collimator to confine the proton beam. METHODS: Monte Carlo simulation was applied to digitally simulate the IDDs of the exiting proton beams detected by the MLIC. A forward model was developed to model each IDD into a weighted sum of percentage depth doses of the constituent beamlets separated laterally by 1 mm. The water equivalent path lengths (WEPLs) of the beamlets were determined by iteratively minimizing the squared L2-norm between the forward projected and simulated IDDs. The final WEPL values were reconstructed to pCT images, that is, proton stopping power ratio (SPR) maps, through simultaneous algebraic reconstruction technique with total variation regularization. The reconstruction process was tested with a digital cylindrical water-based phantom and an ICRP adult reference computational phantom. The mean of SPR within regions of interest (ROIs) and the WEPL along a 4 mm-wide beam ( WEP L 4 mm ${\rm{WEP}}{{\rm{L}}_{4{\rm{mm}}}}$ ) were compared with the reference values. The spatial resolution was analyzed at the edge of a cortical insert of the cylindrical phantom. RESULTS: The percentage deviations from reference SPR were within ±1% in all selected ROIs. The mean absolute error of the reconstructed SPR was 0.33%, 0.19%, and 0.27% for the cylindrical phantom, the adult phantom at the head and lung region, respectively. The corresponding percentage deviations from reference WEP L 4 mm ${\rm{WEP}}{{\rm{L}}_{4{\rm{mm}}}}$ were 0.48 ± 0.64%, 0.28 ± 0.48%, and 0.22 ± 0.49%. The full width at half maximum of the line spread function (LSF) derived from the radial edge spread function (ESF) of a cortical insert was 0.13 cm. The frequency at 10% of the modulation transfer function (MTF) was 6.38 cm-1 . The mean signal-to-noise ratio (SNR) of all the inserts was 2.45. The mean imaging dose was 0.29 and 0.25 cGy at the head and lung region of the adult phantom, respectively. CONCLUSION: A new pCT reconstruction approach was developed by modeling the IDDs of the uncollimated scanning proton beams in the pencil beam geometry. SPR accuracy within ±1%, spatial resolution of better than 2 mm at 10% MTF, and imaging dose at the magnitude of mGy were achieved. Potential side effects caused by neutron dose were eliminated by removing the extra beam collimator.

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BACKGROUND/AIM: This study evaluated the calculation accuracy of the stopping power ratio (SPR) using dual-energy computed tomography with fast kilovoltage switching (FKSCT) for particle therapy. MATERIALS AND METHODS: A tissue characterization phantom with various reference materials was scanned to obtain single-energy computed tomography (SECT) images and generate virtual monochromatic images at 77 keV (VMI77keV) and 140 keV (VMI140keV), water density (WD) images, and effective Z (Zeff) images. For SECT, VMI77keV and VMI140keV lookup tables were generated to convert the measured Hounsfield value into the theoretical SPR for a normal phantom size. Subsequently, the reference materials were scanned in small and large phantoms. The SPR was calculated using the lookup tables of SECT (SPRSECT) images, VMI77keV (SPR77keV), and VMI140keV (SPR140keV), and it was derived from the WD and Zeff (SPRWD). RESULTS: In the normal-sized phantom, the overall mean difference between SPRWD and theoretical SPR was -0.3%, and remained below 2% for most reference materials. For the large phantom, the overall mean absolute difference for SPR140keV (3.0%, p=0.006) and SPRWD (3.2%, p=0.002) for the reference materials was significantly lower than that for SPRSECT (5.9%). For the small phantom, a significant reduction in the mean difference in the SPR calculation was observed in SPR77keV (1.0%, p=0.001) and SPR140keV (1.1%, p=0.013) compared with SPRSECT (2.2%). CONCLUSION: VMI140keV generated using FKSCT significantly improves the estimation accuracy of SPR compared with SECT. Thus, FKSCT may be used to improve the dose calculation accuracy for treatment planning of particle therapy.

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Accurate radiation dosimetry is required for radiation protection in various environments. Therefore, dosemeters and dose-rate meters must be calibrated in standard radiation fields. The National Metrology Institute of Japan (NMIJ) expands the energy range of x-ray reference field measurement up to 450 kV using a cylindrical graphite-walled cavity ionization chamber. Departure from the condition of the Spencer-Attix cavity theory was evaluated by comparing the measurement results obtained using the cavity ionization and the free-air ionization chambers, which are used as the primary standard up to a tube voltage of 250 kV. The calibration coefficients found using the spherical ionization chamber were in good agreement with those obtained by the free-air ionization chamber within relative standard uncertainties (k = 1) for N-200 and N-250 x-ray fields. Consistent calibration coefficients were obtained in the energy range 300-450 kV.

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The two-parameter-fitting method (PFM) is commonly used to calculate the stopping-power ratio (SPR). This study proposes a new formalism: a three-PFM, which can be used in multiple spectral computed tomography (CT). Using a photon-counting CT system, seven rod-shaped samples of aluminium, graphite, and poly(methyl methacrylate) (PMMA), and four types of biological phantom materials were placed in a water-filled sample holder. The X-ray tube voltage and current were set at 150 kV and 40 µA, respectively, and four CT images were obtained at four threshold settings. A semi-empirical correction method that corrects the difference between the CT values from the photon-counting CT images and theoretical values in each spectral region was also introduced. Both the two- and three-PFMs were used to calculate the effective atomic number and electron density from multiple CT numbers. The mean excitation energy was calculated via parameterisation with the effective atomic number, and the SPR was then calculated from the calculated electron density and mean excitation energy. Then, the SPRs from both methods were compared with the theoretical values. To estimate the noise level of the CT numbers obtained from the photon-counting CT, CT numbers, including noise, were simulated to evaluate the robustness of the aforementioned PFMs. For the aluminium and graphite, the maximum relative errors for the SPRs calculated using the two-PFM and three-PFM were 17.1% and 7.1%, respectively. For the PMMA and biological phantom materials, the maximum relative errors for the SPRs calculated using the two-PFM and three-PFM were 5.5% and 2.0%, respectively. It was concluded that the three-PFM, compared with the two-PFM, can yield SPRs that are closer to the theoretical values and is less affected by noise.

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PURPOSE: This paper presents a novel method for the calculation of three-dimensional (3D) Bragg-Gray water-to-detector stopping power ratio (sw,det ) distributions for proton and carbon ion beams. METHODS: Contrary to previously published fluence-based calculations of the stopping power ratio, the sw,det calculation method used in this work is based on the specific way GATE/Geant4 scores the energy deposition. It only requires the use of the so-called DoseActor, as available in GATE, for the calculation of the sw,det at any point of a 3D dose distribution. The simulations are performed using GATE-RTion v1.0, a dedicated GATE release that was validated for the clinical use in light ion beam therapy. RESULTS: The Bragg-Gray water-to-air stopping power ratio (sw,air ) was calculated for monoenergetic proton and carbon ion beams with the default stopping power data in GATE-RTion v1.0 and the new ICRU90 recommendation. The sw,air differences between the use of the default and the ICRU90 configuration were 0.6% and 5.4% at the physical range (R80 - 80% dose level in the distal dose fall-off) for a 70 MeV proton beam and a 120 MeV/u carbon ion beam, respectively. For protons, the sw,det results for lithium fluoride, silicon, gadolinium oxysulfide, and the active layer material of EBT2 (radiochromic film) were compared with the literature and a reasonable agreement was found. For a real patient treatment plan, the 3D distributions of sw,det in proton beams were calculated. CONCLUSIONS: Our method was validated by comparison with available literature data. Its equivalence with Bragg-Gray cavity theory was demonstrated mathematically. The capability of GATE-RTion v1.0 for the sw,det calculation at any point of a 3D dose distribution for simple and complex proton and carbon ion plans was presented.

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PURPOSE: To investigate and quantify the potential benefits associated with the use of stopping-power-ratio (SPR) images created from dual-energy computed tomography (DECT) images for proton dose calculation in a clinical proton treatment planning system (TPS). MATERIALS AND METHODS: The DECT and single-energy computed tomography (SECT) scans obtained for 26 plastic tissue surrogate plugs were placed individually in a tissue-equivalent plastic phantom. Relative-electron density (ρe) and effective atomic number (Z eff) images were reconstructed from the DECT scans and used to create an SPR image set for each plug. Next, the SPR for each plug was measured in a clinical proton beam for comparison of the calculated values in the SPR images. The SPR images and SECTs were then imported into a clinical TPS, and treatment plans were developed consisting of a single field delivering a 10 × 10 × 10-cm3 spread-out Bragg peak to a clinical target volume that contained the plugs. To verify the accuracy of the TPS dose calculated from the SPR images and SECTs, treatment plans were delivered to the phantom containing each plug, and comparisons of point-dose measurements and 2-dimensional γ-analysis were performed. RESULTS: For all 26 plugs considered in this study, SPR values for each plug from the SPR images were within 2% agreement with measurements. Additionally, treatment plans developed with the SPR images agreed with the measured point dose to within 2%, whereas a 3% agreement was observed for SECT-based plans. γ-Index pass rates were > 90% for all SECT plans and > 97% for all SPR image-based plans. CONCLUSION: Treatment plans created in a TPS with SPR images obtained from DECT scans are accurate to within guidelines set for validation of clinical treatment plans at our center. The calculated doses from the SPR image-based treatment plans showed better agreement to measured doses than identical plans created with standard SECT scans.

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PURPOSE: To study the accuracy with which proton stopping power ratio (SPR) can be determined with dual-energy computed tomography (DECT) for small structures and bone-tissue-air interfaces like those found in the head or in the neck. METHODS: Hollow cylindrical polylactic acid (PLA) plugs (3 cm diameter, 5 cm height) were 3D printed containing either one or three septa with thicknesses tsepta  = 0.8, 1.6, 3.2, and 6.4 mm running along the length of the plug. The cylinders were inserted individually into a tissue-equivalent head phantom (16 cm diameter, 5 cm height). First, DECT scans were obtained using a Siemens SOMATOM Definition Edge CT scanner. Effective atomic number (Zeff ) and electron density (ρe ) images were reconstructed from the DECT to produce SPR-CT images of each plug. Second, independent elemental composition analysis of the PLA plastic was used to determine the Zeff and ρe for calculating the theoretical SPR (SPR-TH) using the Bethe-Bloch equation. Finally, for each plug, a direct measurement of SPR (SPR-DM) was obtained in a clinical proton beam. The values of SPR-CT, SPR-TH, and SPR-DM were compared. RESULTS: The SPR-CT for PLA agreed with SPR-DM for tsepta  ≥ 3 mm (for CT slice thicknesses of 0.5, 1.0, and 3.0 mm). The density of PLA was found to decrease with thickness when tsepta  < 3 mm. As tsepta (and density) decreased, the SPR-CT values also decreased, in good agreement with SPR-DM and SPR-TH. CONCLUSION: Overall, the DECT-based SPR-CT was within 3% of SPR-TH and SPR-DM in the high-density gradient regions of the 3D-printed plugs for septa greater than ~ 3mm in thickness.

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PURPOSE: Dual-energy CT (DECT) has been shown to have a great potential in reducing the uncertainty in proton stopping power ratio (SPR) estimation, when compared to current standard method - the stoichiometric method based on single-energy CT (SECT). However, a few recent studies indicated that imaging noise may have a substantial impact on the performance of the DECT-based approach, especially at a high noise level. The goal of this study is to quantify the uncertainty in SPR and range estimation caused by noise in the DECT-based approach under various conditions. METHODS: Two widely referred parametric DECT methods were studied: the Hünemohr-Saito (HS) method and the Bourque method. Both methods were calibrated using Gammex tissue substitute inserts scanned on the Siemens Force DECT scanner. An energy pair of 80 and 150 kVp with a tin filter was chosen to maximize the spectral separation. After calibrating the model with the Gammex phantom, CT numbers were synthesized using the density and elemental composition from ICRU 44 human tissues to be used as a reference, in order to evaluate the impact of noise alone while putting aside other sources of uncertainty. Gaussian noise was introduced to the reference CT numbers and its impact was measured with the difference between estimated SPR and its noiseless reference SPR. The uncertainty caused by noise was divided into two independent categories: shift of the mean SPR and variation of SPR. Their overall impact on range uncertainty was evaluated on homogeneous and heterogeneous tissue samples of various water equivalent path lengths (WEPL). RESULTS: Due to the algorithms being nonlinear and/or having hard thresholds in the CT number to SPR mapping, noise in the CT numbers induced a shift in the mean SPR from its noiseless reference SPR. The degree of the mean shift was dependent on the algorithm and tissue type, but its impact on the SPR uncertainty was mostly small compared to the variation. All mean shifts observed in this study were within 0.5% at a noise level of 2%. The ratio of the influence of variation to mean shift was mostly greater than 1, indicating that variation more likely determined the uncertainty caused by noise. Overall, the range uncertainty (95th percentile) caused by noise was within 1.2% and 1.0% for soft and bone tissues, respectively, at 2% noise with 50 voxels. This value can be considered an upper limit as more voxels and lower noise level rapidly decreased the uncertainty. CONCLUSIONS: We have systematically evaluated the impact of noise to the DECT-based SPR estimation and identified under various conditions that the variation caused by noise is the dominant uncertainty-contributing component. We conclude that, based on the noise level and tumor depth, it is important to estimate and include the uncertainty due to noise in estimating the overall range uncertainty before implementing a small margin in the range of 1%.

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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.

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