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Objective. Algorithmic differentiation (AD) can be a useful technique to numerically optimize design and algorithmic parameters by, and quantify uncertainties in, computer simulations. However, the effectiveness of AD depends on how "well-linearizable" the software is. In this study, we assess how promising derivative information of a typical proton computed tomography (pCT) scan computer simulation is for the aforementioned applications. Approach. This study is mainly based on numerical experiments, in which we repeatedly evaluate three representative computational steps with perturbed input values. We support our observations with a review of the algorithmic steps and arithmetic operations performed by the software, using debugging techniques. Main results. The model-based iterative reconstruction (MBIR) subprocedure (at the end of the software pipeline) and the Monte Carlo (MC) simulation (at the beginning) were piecewise differentiable. Jumps in the MBIR function arose from the discrete computation of the set of voxels intersected by a proton path. Jumps in the MC function likely arose from changes in the control flow that affect the amount of consumed random numbers. The tracking algorithm solves an inherently non-differentiable problem. Significance. The MC and MBIR codes are ready for the integration of AD, and further research on surrogate models for the tracking subprocedure is necessary., Comment: 27 pages, 11 figures

Proton Computed Tomography (CT) is a prototype imaging modality for the reconstruction of the Relative Stopping Power of a patient, for more accurate calculations of the dose distributions in proton therapy dose planning. The measurements needed for the reconstruction of a proton CT image are: i) each initial proton vector incident on the imaged object, ii) each proton vector incident on the front face of the detector and iii) the stopping depth of each proton in the detector. In this study, a track reconstruction algorithm is adapted for a planned pixel-based particle-tracking range telescope for proton CT, called the Digital Tracking Calorimeter (DTC). The algorithm is based on the track-following scheme, in which a growing track searches for deeper-laying activated pixels, while minimizing the accumulated angular change. The algorithm is applied to Monte Carlo-simulated output of the DTC, showing that the DTC is able to reconstruct the tracks and find the depths of up to several hundred simultaneous proton tracks., Comment: 7 pages, 10 figures. Accepted in the "Connecting the Dots 2018" proceedings to be published by EPJ Web of Conferences

The Monte Carlo (MC) simulation method is a powerful tool for radiation physicists, and several general-purpose software packages are commonly applied in a myriad of different radiation physics fields today. In medical physics, charged particle detectors for proton Computed Tomography are under development, a modality introduced in order to increase the accuracy of proton radiation therapy. MC simulations are helpful during the development and optimization phase of such detector systems. In order to justify the usage of MC for such purposes, the simulation output must be validated against experimental or theoretical data, or even cross-checked between different MC software packages. In this study, we compare three general-purpose MC software packages (GATE/Geant4, MCNP6 and FLUKA) with respect to how they predict the spatial distribution of the stopping position of protons. They are compared to each other and to semi-empirical data, using the mean proton range, the longitudinal and lateral variation of individual proton ranges, and the fraction of primary protons lost to nuclear interactions. This comparison is performed in two homogeneous materials and in a detector geometry designed for proton Computed Tomography. The three MC software packages agree well, and sufficiently reproduce the semi-empirical data. Some discrepancies are observed, such as less lateral beam spreading in GATE/Geant4, and a small deficiency in the MCNP6 proton range in water: This is consistent with previously published data. Due to the general agreement, the choice of simulation framework may be made on personal preferences. It is important to note that the choice of physics packages, simulation parameter settings and material definitions are important aspects when performing MC simulations, both during the preparation, execution and interpretation of the simulation results., Comment: 14 pages, 5 figures, submitted to Radiation Physics and Chemistry (IRRMA X Proceedings)

An accurate calculation of proton ranges in phantoms or detector geometries is crucial for decision making in proton therapy and proton imaging. To this end, several parameterizations of the range-energy relationship exist, with different levels of complexity and accuracy. In this study we compare the accuracy four different parameterizations models: Two analytical models derived from the Bethe equation, and two different interpolation schemes applied to range-energy tables. In conclusion, a spline interpolation scheme yields the highest reproduction accuracy, while the shape of the energy loss-curve is best reproduced with the differentiated Bragg-Kleeman equation., Comment: 5 pages, 3 figures, submitted to Radiation Physics and Chemistry

Radiation therapy with protons as of today utilizes information from x-ray CT in order to estimate the proton stopping power of the traversed tissue in a patient. The conversion from x-ray attenuation to proton stopping power in tissue introduces range uncertainties of the order of 2-3% of the range, uncertainties that are contributing to an increase of the necessary planning margins added to the target volume in a patient. Imaging methods and modalities, such as Dual Energy CT and proton CT, have come into consideration in the pursuit of obtaining an as good as possible estimate of the proton stopping power. In this study, a Digital Tracking Calorimeter is benchmarked for proof-of-concept for proton CT purposes. The Digital Tracking Calorimeteris applied for reconstruction of the tracks and energies of individual high energy protons. The presented prototype forms the basis for a proton CT system using a single technology for tracking and calorimetry. This advantage simplifies the setup and reduces the cost of a proton CT system assembly, and it is a unique feature of the Digital Tracking Calorimeter. Data from the AGORFIRM beamline at KVI-CART in Groningen in the Netherlands and Monte Carlo simulation results are used to in order to develop a tracking algorithm for the estimation of the residual ranges of a high number of concurrent proton tracks. The range of the individual protons can at present be estimated with a resolution of 4%. The readout system for this prototype is able to handle an effective proton frequency of 1 MHz by using 500 concurrent proton tracks in each readout frame, which is at the high end range of present similar prototypes. A future further optimized prototype will enable a high-speed and more accurate determination of the ranges of individual protons in a therapeutic beam., Comment: 21 pages, 8 figures