An inhomogeneous most likely path formalism for proton computed tomography

A Monte-Carlo-based study of a single-2D-detector proton-radiography system

PURPOSE

To assess the feasibility of a proton radiography (pRG) system based on a single thin pixelated detector for water-equivalent path length (WEPL) and relative stopping power (RSP) measurements.

METHODS

A model of a pRG system consisting of a single pixelated detector measuring energy deposition and proton fluence was investigated in a Geant4-based Monte Carlo study. At the position directly after an object traversed by a broad proton beam, spatial 2D distributions are calculated of the energy deposition in, and the number of protons entering the detector. Their ratio relates to the 2D distribution of the average stopping power of protons in the detector. The system response is calibrated against the residual range in water of the protons to provide the 2D distribution of the WEPL of the object. The WEPL distribution is converted into the distribution of the RSP of the object. Simulations have been done, where the system has been tested on 13 samples of homogeneous materials of which the RSPs have been calculated and compared with RSPs determined from simulations of residual-range-in-water, which we refer to as reference RSPs.

RESULTS

For both human-tissue- and non-human-tissue-equivalent materials, the RSPs derived with the detector agree with the reference values within 1%.

CONCLUSION

The study shows that a pRG system based on one thin pixelated detection screen has the potential to provide RSP predictions with an accuracy of 1%.

The role of Monte Carlo simulation in understanding the performance of proton computed tomography

Proton computed tomography (pCT) is a promising tomographic imaging modality allowing direct reconstruction of proton relative stopping power (RSP) required for proton therapy dose calculation. In this review article, we aim at highlighting the role of Monte Carlo (MC) simulation in pCT studies. After describing the requirements for performing proton computed tomography and the various pCT scanners actively used in recent research projects, we present an overview of available MC simulation platforms. The use of MC simulations in the scope of investigations of image reconstruction, and for the evaluation of optimal RSP accuracy, precision and spatial resolution omitting detector effects is then described. In the final sections of the review article, we present specific applications of realistic MC simulations of an existing pCT scanner prototype, which we describe in detail.

Energy-adaptive calculation of the most likely path in proton CT

This note addresses an issue faced by every proton computed tomography (CT) reconstruction software: the modelling and the parametrisation of the multiple Coulomb scattering power for the estimation of the most likely path (MLP) of each proton. The conventional approach uses a polynomial model parameterised as a function of depth for a given initial beam energy. This makes it cumbersome to implement a software that works for proton CT data acquired with an arbitrary beam energy or with energy modulation during acquisition. We propose a simple way to parametrise the scattering power based on the measured proton CT list-mode data only and derive a compact expression for the MLP based on a conventional MLP model. Our MLP does not require any parameter. The method assumes the imaged object to be homogeneous, as most conventional MLPs, but requires no information about the material as opposed to most conventional MLP expressions which often assume water to infer energy loss. Instead, our MLP automatically adapts itself to the energy-loss which actually occurred in the object and which is one of the measurements required for proton CT reconstruction. We validate our MLP method numerically and find excellent agreement with conventional MLP methods.

Calculating 1/β2p2 for most likely path estimates for protons and helium ions using an analytical model

In ion computed tomography, limited spatial resolution can be related to the non-straight path of ions resulting from multiple Coulomb scattering in the object to be imaged. By including sophisticated path estimates such as most likely path (MLP) or optimized cubic spline into the image reconstruction algorithm, the achieved spatial resolution can be substantially improved compared to assuming a simple straight line path only. The typically used implementation of the MLP is a matrix-based approach employing Bayesian statistics and modelling multiple Coulomb scattering as Gaussian distribution. For the elements of the scattering matrices, the term 1/β(w)²p(w)², depending on the momentum and velocity of an ion within a phantom depth w, has to be known and integrated along the depth w. Usually, this term is extracted from a Monte Carlo simulation and approximated by a polynomial fit to solve the integral. In the present study, an existing analytical model for ion ranges and stopping powers was used to calculate 1/β(w)²p(w)² and the scattering matrices for the MLP and was tested for protons and helium ions. The model was investigated for 10 cm to 40 cm water targets and initial energies ranging from 150 MeV to 300 MeV for protons and 150 MeV/u to 300 MeV/u for helium ions. In all cases, the calculated value obtained for 1/β(w)²p(w)² was compared to a GATE simulation. The difference between root-mean-square errors of MLP estimates using calculated and simulated 1/β(w)²p(w)² values were found to be smaller than 3 μm for all investigated water targets and energies.

Machine learning for proton path tracking in proton computed tomography

A Machine Learning approach to the problem of calculating the proton paths inside a scanned object in proton Computed Tomography is presented. The method is developed in order to mitigate the loss in both spatial resolution and quantitative integrity of the reconstructed images caused by multiple Coulomb scattering of protons traversing the matter. Two Machine Learning models were used: a forward neural network (NN) and the XGBoost method. A heuristic approach, based on track averaging was also implemented in order to evaluate the accuracy limits on track calculation, imposed by the statistical nature of the scattering. Synthetic data from anthropomorphic voxelized phantoms, generated by the Monte Carlo (MC) Geant4 code, were utilized to train the models and evaluate their accuracy, in comparison to a widely used analytical method that is based on likelihood maximization and Fermi-Eyges scattering model. Both NN and XGBoost model were found to perform very close or at the accuracy limit, further improving the accuracy of the analytical method (by 12% in the typical case of 200 MeV protons on 20 cm of water object), especially for protons scattered at large angles. Inclusion of the material information along the path in terms of radiation length did not show improvement in accuracy for the phantoms simulated in the study. A NN was also constructed to predict the error in path calculation, thus enabling a criterion to filter out proton events that may have a negative effect on the quality of the reconstructed image. By parametrizing a large set of synthetic data, the Machine Learning models were proved capable to bring-in an indirect and time efficient way-the accuracy of the MC method into the problem of proton tracking.

Artificial intelligence supported single detector multi-energy proton radiography system

Proton radiography imaging was proposed as a promising technique to evaluate internal anatomical changes, to enable pre-treatment patient alignment, and most importantly, to optimize the patient specific CT number to stopping-power ratio conversion. The clinical implementation rate of proton radiography systems is still limited due to their complex bulky design, together with the persistent problem of (in)elastic nuclear interactions and multiple Coulomb scattering (i.e. range mixing). In this work, a compact multi-energy proton radiography system was proposed in combination with an artificial intelligence network architecture (ProtonDSE) to remove the persistent problem of proton scatter in proton radiography. A realistic Monte Carlo model of the Proteus^®One accelerator was built at 200 and 220 MeV to isolate the scattered proton signal in 236 proton radiographies of 80 digital anthropomorphic phantoms. ProtonDSE was trained to predict the proton scatter distribution at two beam energies in a 60%/25%/15% scheme for training, testing, and validation. A calibration procedure was proposed to derive the water equivalent thickness image based on the detector dose response relationship at both beam energies. ProtonDSE network performance was evaluated with quantitative metrics that showed an overall mean absolute percentage error below 1.4% ± 0.4% in our test dataset. For one example patient, detector dose to WET conversions were performed based on the total dose (ITotal), the primary proton dose (IPrimary), and the ProtonDSE corrected detector dose (ICorrected). The determined WET accuracy was compared with respect to the reference WET by idealistic raytracing in a manually delineated region-of-interest inside the brain. The error was determined 4.3% ± 4.1% forWET(ITotal),2.2% ± 1.4% forWET(IPrimary),and 2.5% ± 2.0% forWET(ICorrected).

The impact of path estimates in iterative ion CT reconstructions for clinical-like cases

Ion computed tomography (CT) promises to mitigate range uncertainties inherent in the conversion of x-ray Hounsfield units into ion relative stopping power (RSP) for ion beam therapy treatment planning. To improve accuracy and spatial resolution of ion CT by accounting for statistical multiple Coulomb scattering deflection of the ion trajectories from a straight line path (SLP), the most likely path (MLP) and the cubic spline path (CSP) have been proposed. In this work, we use FLUKA Monte Carlo simulations to investigate the impact of these path estimates in iterative tomographic reconstruction algorithms for proton, helium and carbon ions. To this end the ordered subset simultaneous algebraic reconstruction technique was used and coupled with a total variation superiorization (TVS). We evaluate the image quality and dose calculation accuracy in proton therapy treatment planning of cranial patient anatomies. CSP and MLP generally yielded nearly equal image quality with an average RSP relative error improvement over the SLP of 0.6%, 0.3% and 0.3% for proton, helium and carbon ion CT, respectively. Bone and low density materials have been identified as regions of largest enhancement in RSP accuracy. Nevertheless, only minor differences in dose calculation results were observed between the different models and relative range errors of better than 0.5% were obtained in all cases. Largest improvements were found for proton CT in complex scenarios with strong heterogeneities along the beam path. The additional TVS provided substantially reduced image noise, resulting in improved image quality in particular for soft tissue regions. Employing the CSP and MLP for iterative ion CT reconstructions enabled improved image quality over the SLP even in realistic and heterogeneous patient anatomy. However, only limited benefit in dose calculation accuracy was obtained even though an ideal detector system was simulated.

First application of the GPU-based software framework TIGRE for proton CT image reconstruction

In proton therapy, the knowledge of the proton stopping power, i.e. the energy deposition per unit length within human tissue, is essential for accurate treatment planning. One suitable method to directly measure the stopping power is proton computed tomography (pCT). Due to the proton interaction mechanisms in matter, pCT image reconstruction faces some challenges: the unique path of each proton has to be considered separately in the reconstruction process adding complexity to the reconstruction problem. This study shows that the GPU-based open-source software toolkit TIGRE, which was initially intended for X-ray CT reconstruction, can be applied to the pCT image reconstruction problem using a straight line approach for the proton path. This simplified approach allows for reconstructions within seconds. To validate the applicability of TIGRE to pCT, several Monte Carlo simulations modeling a pCT setup with two Catphan® modules as phantoms were performed. Ordered-Subset Simultaneous Algebraic Reconstruction Technique (OS-SART) and Adaptive-Steepest-Descent Projection Onto Convex Sets (ASD-POCS) were used for image reconstruction. Since the accuracy of the approach is limited by the straight line approximation of the proton path, requirements for further improvement of TIGRE for pCT are addressed.

A novel proton counting detector and method for the validation of tissue and implant material maps for Monte Carlo dose calculation

The presence of artificial implants complicates the delivery of proton therapy due to inaccurate characterization of both the implant and the surrounding tissues. In this work, we describe a method to characterize implant and human tissue mimicking materials in terms of relative stopping power (RSP) using a novel proton counting detector. Each proton is tracked by directly measuring the deposited energy along the proton track using a fast, pixelated spectral detector AdvaPIX-TPX3 (TPX3). We considered three scenarios to characterize the RSPs. First, in-air measurements were made in the presence of metal rods (Al, Ti and CoCr) and bone. Then, measurements of energy perturbations in the presence of metal implants and bone in an anthropomorphic phantom were performed. Finally, sampling of cumulative stopping power (CSP) of the phantom were made at different locations of the anthropomorphic phantom. CSP and RSP information were extracted from energy spectra at each beam path. To quantify the RSP of metal rods we used the shift in the most probable energy (MPE) of CSP from the reference CSP without a rod. Overall, the RSPs were determined as 1.48, 2.06, 3.08, and 5.53 from in-air measurements; 1.44, 1.97, 2.98, and 5.44 from in-phantom measurements, for bone, Al, Ti and CoCr, respectively. Additionally, we sampled CSP for multiple paths of the anthropomorphic phantom ranging from 18.63 to 25.23 cm deriving RSP of soft tissues and bones in agreement within 1.6% of TOPAS simulations. Using minimum error of these multiple CSP, optimal mass densities were derived for soft tissue and bone and they are within 1% of vendor-provided nominal densities. The preliminary data obtained indicates the proposed novel method can be used for the validation of material and density maps, required by proton Monte Carlo Dose calculation, provided by competing multi-energy computed tomography and metal artifact reduction techniques.