Experimental implementation of a joint statistical image reconstruction method for proton stopping power mapping from dual-energy CT data

Machine Learning Approach and Model for Predicting Proton Stopping Power Ratio and Other Parameters Using Computed Tomography Images

Purpose

The purpose of this study was to accurately estimate proton stopping power ratio (SPR), relative electron density ρ e, effective atomic number (Z eff), and mean excitation energy (I) using one simple robust model and design a machine learning algorithm that will lead to automation.

Methods

Empirical relationships between computed tomography (CT) number and SPR, ρ e (Z eff) and I were used to formulate a model that predicts all the four parameters using linear attenuation coefficients which can be converted to CT numbers. The results of these models were compared with the results of other existing models. Thirty-three ICRU human tissues were used as modeling data and 12 Gammex inserts as testing data for the machine learning algorithm designed. More ways of tissue classification were introduced to improve accuracy. In the examples, the dual energy methods were implemented using 80 kVp and 150 kVP/Sn.

Results

The proposed method gave modeling root mean square error (RMSE) near 1% at maximum for the case of SPR and ρ e for both single and dual-energy CT approaches considered with modeling RMSE of 0.32% for ρ e and 0.38% for SPR as modeling RMSE with room for improvement (this can be done by adjusting the model number of terms as well as the parameters). The method was able to achieve modeling RMSE of 1.11% for I and 1.66% for Z ef f. The mean error for all the estimated quantities was near 0.00%. In most cases, the proposed method has lower testing RMSE and mean error compare to the other methods presented in the study.

Conclusion

The proposed method proves to be more flexible and robust among all presented methods since it has lower testing error in most cases and can be improved based on data using the machine learning algorithm. The algorithm can also improve estimation by adjusting the model as well as aid in automation and it's easy to implement.

Estimation of Proton Stopping Power Ratio and Mean Excitation Energy Using Electron Density and Its Applications via Machine Learning Approach

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.

Enhancement of Stopping Power Ratio (SPR) Estimation Accuracy through Image-Domain Dual-Energy Computer Tomography for Pencil Beam Scanning System: A Simulation Study

Our study aims to quantify the impact of spectral separation on achieved theoretical prediction accuracy of proton-stopping power when the volume discrepancy between calibration phantom and scanned object is observed. Such discrepancy can be commonly seen in our CSI pediatric patients. One of the representative image-domain DECT models is employed on a virtual phantom to derive electron density and effective atomic number for a total of 34 ICRU standard human tissues. The spectral pairs used in this study are 90 kVp/140 kVp, without and with 0.1 mm to 0.5 mm additional tin filter. The two DECT images are reconstructed via a conventional filtered back projection algorithm (FBP) on simulated noiseless projection data. The best-predicted accuracy occurs at a spectral pair of 90 kVp/140 kVp with a 0.3 mm tin filter, and the root-mean-squared average error is 0.12% for tissue substitutes. The results reveal that the selected image-domain model is sensitive to spectral pair deviation when there is a discrepancy between calibration and scanning conditions. This study suggests that an optimization process may be needed for clinically available DECT scanners to yield the best proton-stopping power estimation.

Motion-compensated scheme for sequential scanned statistical iterative dual-energy CT reconstruction

Objective.Dual-energy computed tomography (DECT) has been widely used to reconstruct numerous types of images due its ability to better discriminate tissue properties. Sequential scanning is a popular dual-energy data acquisition method as it requires no specialized hardware. However, patient motion between two sequential scans may lead to severe motion artifacts in DECT statistical iterative reconstructions (SIR) images. The objective is to reduce the motion artifacts in such reconstructions.Approach.We propose a motion-compensation scheme that incorporates a deformation vector field into any DECT SIR. The deformation vector field is estimated via the multi-modality symmetric deformable registration method. The precalculated registration mapping and its inverse or adjoint are then embedded into each iteration of the iterative DECT algorithm.Main results.Results from a simulated and clinical case show that the proposed framework is capable of reducing motion artifacts in DECT SIRs. Percentage mean square errors in regions of interest in the simulated and clinical cases were reduced from 4.6% to 0.5% and 6.8% to 0.8%, respectively. A perturbation analysis was then performed to determine errors in approximating the continuous deformation by using the deformation field and interpolation. Our findings show that errors in our method are mostly propagated through the target image and amplified by the inverse matrix of the combination of the Fisher information and Hessian of the penalty term.Significance.We have proposed a novel motion-compensation scheme to incorporate a 3D registration method into the joint statistical iterative DECT algorithm in order to reduce motion artifacts caused by inter-scan motion, and successfully demonstrate that interscan motion corrections can be integrated into the DECT SIR process, enabling accurate imaging of radiological quantities on conventional SECT scanners, without significant loss of either computational efficiency or accuracy.

Dual- and multi-energy CT for particle stopping-power estimation: current state, challenges and potential

Range uncertainty has been a key factor preventing particle radiotherapy from reaching its full physical potential. One of the main contributing sources is the uncertainty in estimating particle stopping power (ρ_s) within patients. Currently, theρ_sdistribution in a patient is derived from a single-energy CT (SECT) scan acquired for treatment planning by converting CT number expressed in Hounsfield units (HU) of each voxel toρ_susing a Hounsfield look-up table (HLUT), also known as the CT calibration curve. HU andρ_sshare a linear relationship with electron density but differ in their additional dependence on elemental composition through different physical properties, i.e. effective atomic number and mean excitation energy, respectively. Because of that, the HLUT approach is particularly sensitive to differences in elemental composition between real human tissues and tissue surrogates as well as tissue variations within and among individual patients. The use of dual-energy CT (DECT) forρ_sprediction has been shown to be effective in reducing the uncertainty inρ_sestimation compared to SECT. The acquisition of CT data over different x-ray spectra yields additional information on the material elemental composition. Recently, multi-energy CT (MECT) has been explored to deduct material-specific information with higher dimensionality, which has the potential to further improve the accuracy ofρ_sestimation. Even though various DECT and MECT methods have been proposed and evaluated over the years, these approaches are still only scarcely implemented in routine clinical practice. In this topical review, we aim at accelerating this translation process by providing: (1) a comprehensive review of the existing DECT/MECT methods forρ_sestimation with their respective strengths and weaknesses; (2) a general review of uncertainties associated with DECT/MECT methods; (3) a general review of different aspects related to clinical implementation of DECT/MECT methods; (4) other potential advanced DECT/MECT applications beyondρ_sestimation.

Towards subpercentage uncertainty proton stopping-power mapping via dual-energy CT: Direct experimental validation and uncertainty analysis of a statistical iterative image reconstruction method

PURPOSE

To assess the potential of a joint dual-energy computerized tomography (CT) reconstruction process (statistical image reconstruction method built on a basis vector model (JSIR-BVM)) implemented on a 16-slice commercial CT scanner to measure high spatial resolution stopping-power ratio (SPR) maps with uncertainties of less than 1%.

METHODS

JSIR-BVM was used to reconstruct images of effective electron density and mean excitation energy from dual-energy CT (DECT) sinograms for 10 high-purity samples of known density and atomic composition inserted into head and body phantoms. The measured DECT data consisted of 90 and 140 kVp axial sinograms serially acquired on a Philips Brilliance Big Bore CT scanner without beam-hardening corrections. The corresponding SPRs were subsequently measured directly via ion chamber measurements on a MEVION S250 superconducting synchrocyclotron and evaluated theoretically from the known sample compositions and densities. Deviations of JSIR-BVM SPR values from their theoretically calculated and directly measured ground-truth values were evaluated for our JSIR-BVM method and our implementation of the Hünemohr-Saito (H-S) DECT image-domain decomposition technique for SPR imaging. A thorough uncertainty analysis was then performed for five different scenarios (comparison of JSIR-BVM stopping-power ratio/stopping power (SPR/SP) to International Commission on Radiation Measurements and Units benchmarks; comparison of JSIR-BVM SPR to measured benchmarks; and uncertainties in JSIR-BVM SPR/SP maps for patients of unknown composition) per the Joint Committee for Guides in Metrology and the Guide to Expression of Uncertainty in Measurement, including the impact of uncertainties in measured photon spectra, sample composition and density, photon cross section and I-value models, and random measurement uncertainty. Estimated SPR uncertainty for three main tissue groups in patients of unknown composition and the weighted proportion of each tissue type for three proton treatment sites were then used to derive a composite range uncertainty for our method.

RESULTS

Mean JSIR-BVM SPR estimates deviated by less than 1% from their theoretical and directly measured ground-truth values for most inserts and phantom geometries except for high-density Delrin and Teflon samples with SPR error relative to proton measurements of 1.1% and -1.0% (head phantom) and 1.1% and -1.1% (body phantom). The overall root-mean-square (RMS) deviations over all samples were 0.39% and 0.52% (head phantom) and 0.43% and 0.57% (body phantom) relative to theoretical and directly measured ground-truth SPRs, respectively. The corresponding RMS (maximum) errors for the image-domain decomposition method were 2.68% and 2.73% (4.68% and 4.99%) for the head phantom and 0.71% and 0.87% (1.37% and 1.66%) for the body phantom. Compared to H-S SPR maps, JSIR-BVM yielded 30% sharper and twofold sharper images for soft tissues and bone-like surrogates, respectively, while reducing noise by factors of 6 and 3, respectively. The uncertainty (coverage factor k = 1) of the DECT-to-benchmark values comparison ranged from 0.5% to 1.5% and is dominated by scanning-beam photon-spectra uncertainties. An analysis of the SPR uncertainty for patients of unknown composition showed a JSIR-BVM uncertainty of 0.65%, 1.21%, and 0.77% for soft-, lung-, and bony-tissue groups which led to a composite range uncertainty of 0.6-0.9%.

CONCLUSIONS

Observed JSIR-BVM SPR estimation errors were all less than 50% of the estimated k = 1 total uncertainty of our benchmarking experiment, demonstrating that JSIR-BVM high spatial resolution, low-noise SPR mapping is feasible and is robust to variations in the geometry of the scanned object. In contrast, the much larger H-S SPR estimation errors are dominated by imaging noise and residual beam-hardening artifacts. While the uncertainties characteristic of our current JSIR-BVM implementation can be as large as 1.5%, achieving < 1% total uncertainty is feasible by improving the accuracy of scanner-specific scatter-profile and photon-spectrum estimates. With its robustness to beam-hardening artifact, image noise, and variations in phantom size and geometry, JSIR-BVM has the potential to achieve high spatial-resolution SPR mapping with subpercentage accuracy and estimated uncertainty in the clinical setting.

A Beam-Specific Optimization Target Volume for Stereotactic Proton Pencil Beam Scanning Therapy for Locally Advanced Pancreatic Cancer

PURPOSE

We investigate two margin-based schemes for optimization target volumes (OTV), both isotropic expansion (2 mm) and beam-specific OTV, to account for uncertainties due to the setup errors and range uncertainties in pancreatic stereotactic pencil beam scanning (PBS) proton therapy. Also, as 2-mm being one of the extreme sizes of margin, we also study whether the plan quality of 2-mm uniform expansion could be comparable to other plan schemes.

METHODS AND MATERIALS

We developed 2 schemes for OTV: (1) a uniform expansion of 2 mm (OTV2mm) for setup uncertainty and (2) a water equivalent thickness-based, beam-specific expansion (OTVWET) on beam direction and 2 mm expansion laterally. Six LAPC patients were planned with a prescribed dose of 33 Gy (RBE) in 5 fractions. Robustness optimization (RO) plans on gross tumor volumes, with setup uncertainties of 2 mm and range uncertainties of 3.5%, were implemented as a benchmark.

RESULTS

All 3 optimization schemes achieved decent target coverage with no significant difference. The OTV2mm plans show superior organ at risk (OAR) sparing, especially for proximal duodenum. However, OTV2mm plans demonstrate severe susceptibility to range and setup uncertainties with a passing rate of 19% of the plans meeting the goal of 95% volume covered by the prescribed dose. The proposed dose spread function analysis shows no significant difference.

CONCLUSIONS

The use of OTVWET mimics a union volume for all scenarios in robust optimization but saves optimization time noticeably. The beam-specific margin can be attractive to online adaptive stereotactic body proton therapy owing to the efficiency of the plan optimization.

Learning-Based Stopping Power Mapping on Dual-Energy CT for Proton Radiation Therapy

Purpose

Dual-energy computed tomography (DECT) has been used to derive relative stopping power (RSP) maps by obtaining the energy dependence of photon interactions. The DECT-derived RSP maps could potentially be compromised by image noise levels and the severity of artifacts when using physics-based mapping techniques. This work presents a noise-robust learning-based method to predict RSP maps from DECT for proton radiation therapy.

Materials and Methods

The proposed method uses a residual attention cycle-consistent generative adversarial network to bring DECT-to-RSP mapping close to a 1-to-1 mapping by introducing an inverse RSP-to-DECT mapping. To evaluate the proposed method, we retrospectively investigated 20 head-and-neck cancer patients with DECT scans in proton radiation therapy simulation. Ground truth RSP values were assigned by calculation based on chemical compositions and acted as learning targets in the training process for DECT datasets; they were evaluated against results from the proposed method using a leave-one-out cross-validation strategy.

Results

The predicted RSP maps showed an average normalized mean square error of 2.83% across the whole body volume and an average mean error less than 3% in all volumes of interest. With additional simulated noise added in DECT datasets, the proposed method still maintained a comparable performance, while the physics-based stoichiometric method suffered degraded inaccuracy from increased noise level. The average differences from ground truth in dose volume histogram metrics for clinical target volumes were less than 0.2 Gy for D_95% and D_max with no statistical significance. Maximum difference in dose volume histogram metrics of organs at risk was around 1 Gy on average.

Conclusion

These results strongly indicate the high accuracy of RSP maps predicted by our machine-learning–based method and show its potential feasibility for proton treatment planning and dose calculation.

Impact of bowtie filter and detector collimation on multislice CT scatter profiles: A simulation study

PURPOSE

To investigate via Monte Carlo simulations, the impact of scan subject size, antiscatter grid (ASG), collimator size, and bowtie filter on the distribution of scatter radiation in a typical realistically modeled third generation 16 slice diagnostic computed tomography (CT) scanner.

METHODS

Full radiation transport was simulated with Geant4 in a realistic CT scanner geometric model, including the imaging phantom, bowtie filter (BTF), collimators and detector assembly, except for the ASGs. An analytical method was employed to quantify the probable transmission through the ASG of each photon intersecting the detector array. Normalized scatter profiles (NSP) and scatter-to-primary-ratio (SPR) profiles were simulated for 90 and 140 kVp beams for different size phantoms and slice thicknesses. The impact of CT scatter on the reconstructed attenuation coefficient factor was also studied as were the modulating effects of phantom- and patient-tissue heterogeneities on scatter profiles. A method to characterize the relative spatial frequency content of sinogram signals was developed to assess the latter.

RESULTS

For the 21.4-cm diameter phantom, NSP and SPR increase linearly with collimator opening for both tube potentials, with the 90 kVp scan exhibiting slightly larger NSP and SPR. The BTF modestly modulates scatter under the phantom center, reducing the prominent off-axis lobes by factors of 1.1-1.3. The ASG reduces scatter on the central axis NSP threefold, and reduces scatter at the detectors outside the phantom shadow by factors of 25 to 500. For the phantoms with diameters of 27 and 32 cm, the scatter increases roughly three- and fourfold, respectively, demonstrating that scatter monotonically increases with phantom size, despite deployment of the ASG and BTF. In the absence of a scan subject, the ASG reduces the signal profile arising photons scattered by the BTF. Without ASG, the in-air scatter profile is relatively flat compared to the scatter profile when the ASG is present. For both 90 and 140 kVp photon spectra, the calculated attenuation coefficient decreases linearly with increasing collimation size. For both homogeneous and heterogeneous objects, NSPs are dominated by low spatial frequency content compared to the primary signal. However, the SPR, which quantifies the local magnitude of nonlinear detector response and is dominated by the high frequency content of the primary profile, can contribute strongly to high-spatial frequency streaking artifacts near high-density structures in reconstructed image artifacts.

CONCLUSION

Public-domain Monte Carlo codes, Geant-4 in particular, is a feasible method for characterizing CT detector response to scattered- and off-focal radiation. Our study demonstrates that the ASG substantially reduces the scatter radiation and reshapes scatter-radiation profiles and affects the accuracy with which the detector array can measure narrow-beam attenuation due its inability to distinguish between true uncollided primary and narrow-angle coherently scattered photons. Hence, incorporating the impact of detector array collimation into the forward-projection signal formation models used by iterative reconstruction algorithms is necessary to use CT for accurately characterizing material properties. While tissue heterogeneities exercise a modest influence on local NPS shape and magnitude, they do not add significant high spatial frequency content.

Initial Validation of Proton Dose Calculations on SPR Images from DECT in Treatment Planning System

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.

Status and innovations in pre-treatment CT imaging for proton therapy

Pre-treatment CT imaging is a topic of growing importance in particle therapy. Improvements in the accuracy of stopping-power prediction are demanded to allow for a dose conformality that is not inferior to state-of-the-art image-guided photon therapy. Although range uncertainty has been kept practically constant over the last decades, recent technological and methodological developments, like the clinical application of dual-energy CT, have been introduced or arise at least on the horizon to improve the accuracy and precision of range prediction. This review gives an overview of the current status, summarizes the innovations in dual-energy CT and its potential impact on the field as well as potential alternative technologies for stopping-power prediction.

Fast-switching dual energy cone beam computed tomography using the on-board imager of a commercial linear accelerator

To evaluate fast-kV switching (FS) dual energy (DE) cone beam computed tomography (CBCT) using the on-board imager (OBI) of a commercial linear accelerator to produce virtual monoenergetic (VM) and relative electron density (RED) images. Using an polynomial attenuation mapping model, CBCT phantom projections obtained at 80 and 140 kVp with FS imaging, were decomposed into equivalent thicknesses of aluminum (Al) and polymethyl methacrylate (PMMA). All projections were obtained with the titanium foil and bowtie filter in place. Basis material projections were then recombined to create VM images by using the linear attenuation coefficients at the specified energy for each material. Similarly, RED images were produced by replacing the linear attenuation values of Al and PMMA by their respective RED values in the projection space. VM and RED images were reconstructed using Feldkamp-Davis-Kress (FDK) and an iterative algorithm (iCBCT, Varian Medical Systems). Hounsfield units (HU), contrast-to-noise ratio (CNR) and RED values were compared against known values. The results after VM-CBCT production showed good material decomposition and consistent HU_VM values, with measured root mean square errors (RMSE) from theoretical values, after FDK reconstruction, of 20.5, 5.7, 12.8 and 21.7 HU for 50, 80, 100 and 150 keV, respectively. The largest CNR improvements, when compared to polychromatic images, were observed for the 50 keV VM images. Image noise was reduced up to 28% in the VM-CBCT images after iterative image reconstruction. RED values measured for our method resulted in a mean percentage error of 0.0%  ±  1.8%. This study describes a method to generate VM-CBCT and RED images using FS-DE scans obtained using the OBI of a linac, including the effects of the bowtie filter. The creation of VM and RED images increases the dynamic range of CBCT images, and provides additional data that may be used for adaptive radiotherapy, and on table verification for radiotherapy treatments.

Low-dose photon counting CT reconstruction bias reduction with multi-energy alternating minimization algorithm

Photon counting CT (PCCT) is an x-ray imaging technique that has undergone great development in the past decade. PCCT has the potential to improve dose efficiency and low-dose performance. In this paper, we propose a statistics-based iterative algorithm to perform a direct reconstruction of material-decomposed images. Compared with the conventional sinogram-based decomposition method which has degraded performance in low-dose scenarios, the multi-energy alternating minimization algorithm for photon counting CT (MEAM-PCCT) can generate accurate material-decomposed image with much smaller biases.

Determination of proton stopping power ratio with dual-energy CT in 3D-printed tissue/air cavity surrogates

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 t_septa  = 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 (Z_eff ) and electron density (ρ_e ) 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 Z_eff and ρ_e 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 t_septa  ≥ 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 t_septa  < 3 mm. As t_septa (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.