Stopping-power ratio estimation for proton radiotherapy using dual-energy computed tomography and prior-image constrained denoising

BACKGROUND

Dual-energy computed tomography (DECT) is a promising technique for estimating stopping-power ratio (SPR) for proton therapy planning. It is known, however, that deriving electron density (ED) and effective atomic number (EAN) from DECT data can cause noise amplification in the resulting SPR images. This can negate the benefits of DECT.

PURPOSE

This work introduces a new algorithm for estimating SPR from DECT with noise suppression, using a pair of CT scans with spectral separation. The method is demonstrated using phantom measurements.

MATERIALS AND METHODS

An iterative algorithm is presented, reconstructing ED and EAN with noise suppression, based on Prior Image Constrained Denoising (PIC-D). The algorithm is tested using a Siemens Definition AS+ CT scanner (Siemens Healthcare, Forchheim, Germany). Three phantoms are investigated: a calibration phantom (CIRS 062M), a QA phantom (CATPHAN 700), and an anthropomorphic head phantom (CIRS 731-HN). A task-transfer function (TTF) and the noise power spectrum are derived from SPR images of the QA phantom for the evaluation of image quality. Comparisons of accuracy and noise for ED, EAN, and SPR are made for various versions of the algorithm in comparison to a solution based on Siemens syngo.via Rho/Z software and the current clinical standard of a single-energy CT stoichiometric calibration. A gamma analysis is also applied to the SPR images of the head phantom and water-equivalent distance (WED) is evaluated in a treatment planning system for a proton treatment field.

RESULTS

The algorithm is effective at suppressing noise in both ED and EAN and hence also SPR. The noise is tunable to a level equivalent to or lower than that of the syngo.via Rho/Z software. The spatial resolution (10% and 50% frequencies in the TTF) does not degrade even for the highest noise suppression investigated, although the average spatial frequency of noise does decrease. The PIC-D algorithm showed better accuracy than syngo.via Rho/Z for low density materials. In the calibration phantom, it was superior even when excluding lung substitutes, with root-mean-square deviations for ED and EAN less than 0.3% and 2%, respectively, compared to 0.5% and 3%. In the head phantom, however, the SPR accuracy of the PIC-D algorithm was comparable (excluding sinus tissue) to that derived from syngo.via Rho/Z: less than 1% error for soft tissue, brain, and trabecular bone substitutes and 5-7% for cortical bone, with the larger error for the latter likely related to the phantom geometry. Gamma evaluation showed that PIC-D can suppress noise in a patient-like geometry without introducing substantial errors in SPR. The absolute pass rates were almost identical for PIC-D and syngo.via Rho/Z. In the WED evaluations no general differences were shown.

CONCLUSIONS

The PIC-D DECT algorithm provides scanner-specific calibration and tunable noise suppression. It is vendor agnostic and applicable to any pair of CT scans with spectral separation. Improved accuracy to current methods was not clearly demonstrated for the complex geometry of a head phantom, but the suppression of noise without spatial resolution degradation and the possibility of incorporating constraints on image properties, suggests the usefulness of the approach.

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.

Mixed stochastic-deterministic time-dependent density functional theory: application to stopping power of warm dense carbon

Warm dense matter (WDM) describes an intermediate phase, between condensed matter and classical plasmas, found in natural and man-made systems. In a laboratory setting, WDM is often created dynamically. It is typically laser or pulse-power generated and can be difficult to characterize experimentally. Measuring the energy loss of high energy ions, caused by a WDM target, is both a promising diagnostic and of fundamental importance to inertial confinement fusion research. However, electron coupling, degeneracy, and quantum effects limit the accuracy of easily calculable kinetic models for stopping power, while high temperatures make the traditional tools of condensed matter, e.g. time-dependent density functional theory (TD-DFT), often intractable. We have developed a mixed stochastic-deterministic approach to TD-DFT which provides more efficient computation while maintaining the required precision for model discrimination. Recently, this approach showed significant improvement compared to models when compared to experimental energy loss measurements in WDM carbon. Here, we describe this approach and demonstrate its application to warm dense carbon stopping across a range of projectile velocities. We compare direct stopping-power calculation to approaches based on combining homogeneous electron gas response with bound electrons, with parameters extracted from our TD-DFT calculations.

Dual-layer spectral CT for proton, helium, and carbon ion beam therapy planning of brain tumors

Pretreatment computed tomography (CT) imaging is an essential component of the particle therapy treatment planning chain. Treatment planning and optimization with charged particles require accurate and precise estimations of ion beam range in tissues, characterized by the stopping power ratio (SPR). Reduction of range uncertainties arising from conventional CT-number-to-SPR conversion based on single-energy CT (SECT) imaging is of importance for improving clinical practice. Here, the application of a novel imaging and computational methodology using dual-layer spectral CT (DLCT) was performed toward refining patient-specific SPR estimates. A workflow for DLCT-based treatment planning was devised to evaluate SPR prediction for proton, helium, and carbon ion beam therapy planning in the brain. DLCT- and SECT-based SPR predictions were compared in homogeneous and heterogeneous anatomical regions. This study included eight patients scanned for diagnostic purposes with a DLCT scanner. For each patient, four different treatment plans were created, simulating tumors in different parts of the brain. For homogeneous anatomical regions, mean SPR differences of about 1% between the DLCT- and SECT-based approaches were found. In plans of heterogeneous anatomies, relative (absolute) proton range shifts of 0.6% (0.4 mm) in the mean and up to 4.4% (2.1 mm) at the distal fall-off were observed. In the investigated cohort, 12% of the evaluated organs-at-risk (OARs) presented differences in mean or maximum dose of more than 0.5 Gy (RBE) and up to 6.8 Gy (RBE) over the entire treatment. Range shifts and dose differences in OARs between DLCT and SECT in helium and carbon ion treatment plans were similar to protons. In the majority of investigated cases (75th percentile), SECT- and DLCT-based range estimations were within 0.6 mm. Nonetheless, the magnitude of patient-specific range deviations between SECT and DLCT was clinically relevant in heterogeneous anatomical sites, suggesting further study in larger, more diverse cohorts. Results indicate that patients with brain tumors may benefit from DLCT-based treatment planning.

Dose measurement in the TEM and STEM

Practical aspects of dosimetry are considered, including the measurement of electron-beam current and current density. Complications that arise in the case of a focused probe or a STEM image are discussed and solutions proposed. Advantages of expressing the radiation dose in Grays are listed and a simple formula given for converting electron fluence to Gray units, based on a near constancy of the stopping power per atomic electron. Comparisons with stopping-power calculations and EELS measurements suggest that this formula is accurate to within 5%. Based on the stopping power formula, a new way of measuring the local mass-thickness of light-element specimens is proposed. The average energy loss per inelastic collision is shown to be higher than previous expectations.

Accuracy of proton stopping power estimation of silicone breast implants with single and dual-energy CT calibration techniques

A major contributing factor to proton range uncertainty is the conversion of computed tomography (CT) Hounsfield Units (HU) to proton relative stopping power (RSP). This uncertainty is elevated with implanted devices, such as silicone breast implants when computed with single energy CT (SECT). In recent years, manufacturers have introduced implants with variations in gel cohesivity. Deriving the RSP for these implants from dual-energy CT (DECT) can result in a marked reduction of the error associated with SECT. In this study, we investigate the validity of DECT calibration of HU to RSP on silicone breast implants of varying cohesivity levels. A DECT capable scanner was calibrated using the stoichiometric method of Bourque et al for SECT and DECT using a tissue substitute phantom. Three silicone breast implants of increasing gel cohesivity were measured in a proton beam of clinical energy to determine ground-truth RSP and water equivalent thickness (WET). These were compared to SECT-derived RSP at three CT spectrum energies and DECT with two energy pairs (80/140 kVp and 100/140 kVp) as obtained from scans with and without an anthropomorphic phantom. The RSP derived from parameters estimates from CT vendor-specific software (syngo.via) was compared. The WET estimates from SECT deviated from MLIC ground truth approximately +11%-19%, which would result in overpenetration if used clinically. Both the Bourque calibration and syngo.via WET estimates from DECT yielded error ≤0.5% from ground truth; no significant difference was found between models of varying gel cohesivity levels. WET estimates without the anthropomorphic phantom were significantly different than ground truth for the Bourque calibration. From these results, gel cohesivity had no effect on proton RSP. User-generated DECT calibration can yield comparably accurate RSP estimates for silicone breast implants to vendor software methods. However, care must be taken to account for beam hardening effects.

MeV TOF SIMS Analysis of Hybrid Organic/Inorganic Compounds in the Low Energy Region

The low energy range (a few 100 keV to a few megaelectronvolts) primary ion mode in MeV secondary ion mass spectrometry (MeV SIMS) and its potential in exploiting the capabilities of conventional (keV) SIMS and MeV SIMS simultaneously were investigated. The aim is to see if in this energy range of both types of materials, inorganic and organic, can be simultaneously analyzed. A feasibility study was conducted, first by analyzing the dependence of secondary ion yields in indium tin oxide (ITO, In₂O₅Sn) and leucine (C₆H₁₃NO₂) on various primary ion energies and charge states of a Cu beam, within the scope of equal influence of electronic and nuclear stopping. Expected behavior was observed for both targets (mainly nuclear sputtering for ITO and electronic sputtering for leucine). MeV SIMS images of samples containing separate regions of Cr and leucine were obtained using both keV and MeV primary ions. On the basis of the image contrast and measured data, the benefit of a low energy beam is demonstrated by Cr⁺ intensity leveling with leucine [M + H]⁺ intensity, as opposed to a significant contrast at a higher energy. It is estimated that, by lowering the energy, the leucine [M + H]⁺ yield efficiency lowers roughly 20 times as a price for gaining about 10 times larger efficiency of Cr⁺ yield, while the leucine [M + H]⁺ yield still remains sufficiently pronounced.

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.

Helium CT: Monte Carlo simulation results for an ideal source and detector with comparison to proton CT

PURPOSE

To evaluate the accuracy of relative stopping power and spatial resolution of images reconstructed with simulated helium CT (HeCT) in comparison to proton CT (pCT).

METHODS

A Monte Carlo (MC) study with the TOPAS tool was performed to compare the accuracy of relative stopping power (RSP) reconstruction and spatial resolution of low-fluence HeCT to pCT, both using 200 MeV/u particles. An ideal setup consisting of a flat beam source and a totally absorbing energy-range detector was implemented to estimate the theoretically best achievable RSP accuracy for the calibration and reconstruction methods currently used for pCT. The phantoms imaged included a cylindrical water phantom with inserts of different materials, sizes, and positions, a Catphan phantom with a module containing high-contrast line pairs (CTP528) and a module with cylindrical inserts of different RSP (CTP404), as well as a voxelized 10-year-old female phantom. Dose to the cylindrical water phantom was also calculated. The RSP accuracy was studied for all phantoms except the CTP528 module. The latter was used for the estimation of the spatial resolution, evaluated as the modulation transfer function (MTF) at 10%.

RESULTS

An overall error under 0.5% was achieved for HeCT for the water phantoms with the different inserts, in all cases better than that for pCT, in some cases by a factor 3. The inserts in the CTP404 module were reconstructed with an average RSP accuracy of 0.3% for HeCT and 0.2% for pCT. Anatomic structures (brain, bones, air cavities, etc.) in the digitized head phantom were well recognizable and no artifacts were visible with both HeCT and pCT. The three main tissue materials (soft tissue, brain, and cranium) were well identifiable in the reconstructed RSP-volume distribution with both imaging modalities. Using 360 projection angles, the spatial resolution was 4 lp/cm for HeCT and 3 lp/cm for pCT. Generally, spatial resolution increased with the number of projection angles and was always higher for HeCT than for pCT for the same number of projections. When HeCT and pCT scan were performed to deliver the same dose in the phantom, the resolution for HeCT was higher than pCT.

CONCLUSION

MC simulations were used to compare HeCT and pCT image reconstruction. HeCT images had similar or better RSP accuracy and higher spatial resolution compared to pCT. Further investigation of the potential of helium ion imaging is warranted.

A linear, separable two-parameter model for dual energy CT imaging of proton stopping power computation

PURPOSE

To evaluate the accuracy and robustness of a simple, linear, separable, two-parameter model (basis vector model, BVM) in mapping proton stopping powers via dual energy computed tomography (DECT) imaging.

METHODS

The BVM assumes that photon cross sections (attenuation coefficients) of unknown materials are linear combinations of the corresponding radiological quantities of dissimilar basis substances (i.e., polystyrene, CaCl2 aqueous solution, and water). The authors have extended this approach to the estimation of electron density and mean excitation energy, which are required parameters for computing proton stopping powers via the Bethe-Bloch equation. The authors compared the stopping power estimation accuracy of the BVM with that of a nonlinear, nonseparable photon cross section Torikoshi parametric fit model (VCU tPFM) as implemented by the authors and by Yang et al. ["Theoretical variance analysis of single- and dual-energy computed tomography methods for calculating proton stopping power ratios of biological tissues," Phys. Med. Biol. 55, 1343-1362 (2010)]. Using an idealized monoenergetic DECT imaging model, proton ranges estimated by the BVM, VCU tPFM, and Yang tPFM were compared to International Commission on Radiation Units and Measurements (ICRU) published reference values. The robustness of the stopping power prediction accuracy of tissue composition variations was assessed for both of the BVM and VCU tPFM. The sensitivity of accuracy to CT image uncertainty was also evaluated.

RESULTS

Based on the authors' idealized, error-free DECT imaging model, the root-mean-square error of BVM proton stopping power estimation for 175 MeV protons relative to ICRU reference values for 34 ICRU standard tissues is 0.20%, compared to 0.23% and 0.68% for the Yang and VCU tPFM models, respectively. The range estimation errors were less than 1 mm for the BVM and Yang tPFM models, respectively. The BVM estimation accuracy is not dependent on tissue type and proton energy range. The BVM is slightly more vulnerable to CT image intensity uncertainties than the tPFM models. Both the BVM and tPFM prediction accuracies were robust to uncertainties of tissue composition and independent of the choice of reference values. This reported accuracy does not include the impacts of I-value uncertainties and imaging artifacts and may not be achievable on current clinical CT scanners.

CONCLUSIONS

The proton stopping power estimation accuracy of the proposed linear, separable BVM model is comparable to or better than that of the nonseparable tPFM models proposed by other groups. In contrast to the tPFM, the BVM does not require an iterative solving for effective atomic number and electron density at every voxel; this improves the computational efficiency of DECT imaging when iterative, model-based image reconstruction algorithms are used to minimize noise and systematic imaging artifacts of CT images.

Handling Density Conversion in TPS

Conversion from CT value to density is essential to a radiation treatment planning system. Generally CT value is converted to the electron density in photon therapy. In the energy range of therapeutic photon, interactions between photons and materials are dominated with Compton scattering which the cross-section depends on the electron density. The dose distribution is obtained by calculating TERMA and kernel using electron density where TERMA is the energy transferred from primary photons and kernel is a volume considering spread electrons. Recently, a new method was introduced which uses the physical density. This method is expected to be faster and more accurate than that using the electron density. As for particle therapy, dose can be calculated with CT-to-stopping power conversion since the stopping power depends on the electron density. CT-to-stopping power conversion table is also called as CT-to-water-equivalent range and is an essential concept for the particle therapy.

The sensitivity of backscattering coefficients to elastic scattering cross-sections and electron stopping powers

The sensitivity of Monte Carlo estimates of backscattering coefficients η to the accuracy of their input data is examined by studying the percentage change in η due to changes of 10% and 20% in the differential elastic scattering cross-section dσ/dΩ and corresponding changes in the stopping power S(E) in the primary energy range 200-10,000 eV. To a good approximation equivalent elastic and inelastic scattering changes produce equal and opposite shifts in η, a result consistent with predictions of transport theory. For medium to high atomic numbers an x% error in the specification of either S(E) or dσ/dΩ produces a percentage change in η significantly less than x%, while at low atomic number Δη/η increases approximately linearly with ln E so that Monte Carlo predictions are then more sensitive to parameter precision at high energy.

Surface excitations in electron spectroscopy. Part I: dielectric formalism and Monte Carlo algorithm

The theory describing energy losses of charged non-relativistic projectiles crossing a planar interface is derived on the basis of the Maxwell equations, outlining the physical assumptions of the model in great detail. The employed approach is very general in that various common models for surface excitations (such as the specular reflection model) can be obtained by an appropriate choice of parameter values. The dynamics of charged projectiles near surfaces is examined by calculations of the induced surface charge and the depth- and direction-dependent differential inelastic inverse mean free path (DIIMFP) and stopping power. The effect of several simplifications frequently encountered in the literature is investigated: differences of up to 100% are found in heights, widths, and positions of peaks in the DIIMFP. The presented model is implemented in a Monte Carlo algorithm for the simulation of the electron transport relevant for surface electron spectroscopy. Simulated reflection electron energy loss spectra are in good agreement with experiment on an absolute scale. Copyright © 2012 John Wiley & Sons, Ltd.