Relative stopping power resolution in time-of-flight proton CT.

Objective.Proton computed tomography (CT) is similar to x-ray CT but relies on protons rather than photons to form an image. In its most common operation mode, the measured quantity is the amount of energy that a proton has lost while traversing the imaged object from which a relative stopping power map can be obtained via tomographic reconstruction. To this end, a calorimeter which measures the energy deposited by protons downstream of the scanned object has been studied or implemented as energy detector in several proton CT prototypes. An alternative method is to measure the proton's residual velocity and thus its kinetic energy via the time of flight (TOF) between at least two sensor planes. In this work, we study the RSP resolution, seen as image noise, which can be expected from TOF proton CT systems.Approach.We rely on physics models on the one hand and statistical models of the relevant uncertainties on the other to derive closed form expressions for the noise in projection images. The TOF measurement error scales with the distance between the TOF sensor planes and is reported as velocity error in ps/m. We use variance reconstruction to obtain noise maps of a water cylinder phantom given the scanner characteristics and additionally reconstruct noise maps for a calorimeter-based proton CT system as reference. We use Monte Carlo simulations to verify our model and to estimate the noise due to multiple Coulomb scattering inside the object. We also provide a comparison of TOF helium and proton CT.Main results.We find that TOF proton CT with 30 ps m-1velocity error reaches similar image noise as a calorimeter-based proton CT system with 1% energy error (1 sigma error). A TOF proton CT system with a 50 ps m-1velocity error produces slightly less noise than a 2% calorimeter system. Noise in a reconstructed TOF proton CT image is spatially inhomogeneous with a marked increase towards the object periphery. Our modelled noise was consistent with Monte Carlo simulated images. TOF helium CT offers lower RSP noise at equal fluence, but is less advantageous at equal imaging dose.Significance.This systematic study of image noise in TOF proton CT can serve as a guide for future developments of this alternative solution for estimating the residual energy of protons and helium ions after the scanned object.

Comparative accuracy and resolution assessment of two prototype proton computed tomography scanners.

BACKGROUND: Improving the accuracy of relative stopping power (RSP) in proton therapy may allow reducing range margins. Proton computed tomography (pCT) has been shown to provide state-of-the-art RSP accuracy estimation, and various scanner prototypes have recently been built. The different approaches used in scanner design are expected to impact spatial resolution and RSP accuracy. PURPOSE: The goal of this study was to perform the first direct comparison, in terms of spatial resolution and RSP accuracy, of two pCT prototype scanners installed at the same facility and by using the same image reconstruction algorithm. METHODS: A phantom containing cylindrical inserts of known RSP was scanned at the phase-II pCT prototype of the U.S. pCT collaboration and at the commercially oriented ProtonVDA scanner. Following distance-driven binning filtered backprojection reconstruction, the radial edge spread function of high-density inserts was used to estimate the spatial resolution. RSP accuracy was evaluated by the mean absolute percent error (MAPE) over the inserts. No direct imaging dose estimation was possible, which prevented a comparison of the two scanners in terms of RSP noise. RESULTS: In terms of RSP accuracy, both scanners achieved the same MAPE of 0.72% when excluding the porous sinus insert from the evaluation. The ProtonVDA scanner reached a better overall MAPE when all inserts and the body of the phantom were accounted for (0.81%), compared to the phase-II scanner (1.14%). The spatial resolution with the phase-II scanner was found to be 0.61 lp/mm, while for the ProtonVDA scanner somewhat lower at 0.46 lp/mm. CONCLUSIONS: The comparison between two prototype pCT scanners operated in the same clinical facility showed that they both fulfill the requirement of an RSP accuracy of about 1%. Their spatial resolution performance reflects the different design choices of either a scanner with full tracking capabilities (phase-II) or of a more compact tracker system, which only provides the positions of protons but not their directions (ProtonVDA).

Quantification of biological range uncertainties in patients treated at the Krakow proton therapy centre.

BACKGROUND: Variable relative biological effectiveness (vRBE) in proton therapy might significantly modify the prediction of RBE-weighted dose delivered to a patient during proton therapy. In this study we will present a method to quantify the biological range extension of the proton beam, which results from the application of vRBE approach in RBE-weighted dose calculation. METHODS AND MATERIALS: The treatment plans of 95 patients (brain and skull base patients) were used for RBE-weighted dose calculation with constant and the McNamara RBE model. For this purpose the Monte Carlo tool FRED was used. The RBE-weighted dose distributions were analysed using indices from dose-volume histograms. We used the volumes receiving at least 95% of the prescribed dose (V95) to estimate the biological range extension resulting from vRBE approach. RESULTS: The vRBE model shows higher median value of relative deposited dose and D95 in the planning target volume by around 1% for brain patients and 4% for skull base patients. The maximum doses in organs at risk calculated with vRBE was up to 14 Gy above dose limit. The mean biological range extension was greater than 0.4 cm. DISCUSSION: Our method of estimation of biological range extension is insensitive for dose inhomogeneities and can be easily used for different proton plans with intensity-modulated proton therapy (IMPT) optimization. Using volumes instead of dose profiles, which is the common method, is more universal. However it was tested only for IMPT plans on fields arranged around the tumor area. CONCLUSIONS: Adopting a vRBE model results in an increase in dose and an extension of the beam range, which is especially disadvantageous in cancers close to organs at risk. Our results support the need to re-optimization of proton treatment plans when considering vRBE.

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.

Study of relationship between dose, LET and the risk of brain necrosis after proton therapy for skull base tumors.

PURPOSE: We investigated the relationship between RBE-weighted dose (DRBE) calculated with constant (cRBE) and variable RBE (vRBE), dose-averaged linear energy transfer (LETd) and the risk of radiographic changes in skull base patients treated with protons. METHODS: Clinical treatment plans of 45 patients were recalculated with Monte Carlo tool FRED. Radiographic changes (i.e. edema and/or necrosis) were identified by MRI. Dosimetric parameters for cRBE and vRBE were computed. Biological margin extension and voxel-based analysis were employed looking for association of DRBE(vRBE) and LETd with brain edema and/or necrosis. RESULTS: When using vRBE, Dmax in the brain was above the highest dose limits for 38% of patients, while such limit was never exceeded assuming cRBE. Similar values of Dmax were observed in necrotic regions, brain and temporal lobes. Most of the brain necrosis was in proximity to the PTV. The voxel-based analysis did not show evidence of an association with high LETd values. CONCLUSIONS: When looking at standard dosimetric parameters, the higher dose associated with vRBE seems to be responsible for an enhanced risk of radiographic changes. However, as revealed by a voxel-based analysis, the large inter-patient variability hinders the identification of a clear effect for high LETd.

A comparison of direct reconstruction algorithms in proton computed tomography.

Several direct algorithms have been proposed to take into account the non-linear path of protons in the reconstruction of a proton CT (pCT) image. This paper presents a comparison between five of them, in terms of spatial resolution and relative stopping power (RSP) accuracy. Our comparison includes (1) a distance-driven algorithm extending the filtered backprojection to non-linear trajectories (DD), (2) an algorithm reconstructing a pCT image from optimized projections (ML), (3) a backproject-then-filter approach using a 2D cone filter (BTF), (4) a differentiated backprojection algorithm based on the inversion of the Hilbert transform (DBP), and (5) an algorithm using a 2D directional ramp filter (DR). We have simulated a single tracking pCT set-up using Geant4 through GATE, with a proton source and two position, direction and energy detectors upstream and downstream from the object. Tracker uncertainties were added on the position and direction measurements. A Catphan 528 phantom and a spiral phantom were simulated to measure the spatial resolution and a Gammex 467 phantom was used for the RSP accuracy. Each proton's trajectory was estimated using a most likely path (MLP) formalism. The spatial resolution was evaluated using the frequency corresponding to a modulation transfer function of 10% of its peak value and the RSP accuracy using the mean values in the inserts of the Gammex phantom. In terms of spatial resolution, it was shown that, for ideal trackers, the DR and BTF methods offer a slightly better resolution since each proton is directly binned in the image grid according to its MLP. However, all methods but the ML show comparable resolution when using realistic trackers. Regarding the RSP, three algorithms (DR, DD and BTF) show a mean relative error inside the inserts about 0.1%. As the DR and BTF methods are more computationally expensive, the DD-which allows the same spatial resolution in realistic conditions and the same accuracy-and the DBP-which has a fairly good accuracy (<0.2%) and allows reconstruction from truncated data-can be used for a reduced reconstruction time.

Effects of transverse heterogeneities on the most likely path of protons.

The use of a most likely path (MLP) formalism for protons to account for the effects of multiple Coulomb scattering has improved the spatial resolution in proton computed tomography (pCT). However, this formalism assumes a homogeneous medium and a continuous scattering of protons. In this paper, we quantify the path prediction error induced by transverse heterogeneities to assess whether correcting for such errors might improve the spatial resolution of pCT. To this end, we have tracked protons trajectories using Monte Carlo simulations in several phantoms with different heterogeneities. Our results show that transverse heterogeneities induce non Gaussian spatial distributions leading to errors in the prediction of the MLP, reaching 0.4 mm in a 20 cm wide simulated heterogeneity and 0.13 mm in a realistic phantom. It was also shown that when the spatial distributions have more than one peak, a most likely path, if any, has yet to be defined. Transverse heterogeneities also affect energy profiles, which could explain some of the artifacts described in other works and could make the energy cuts usually performed to exclude nuclear events less efficient.