Scott Penfold

A maximum likelihood proton path formalism for application in proton computed tomography

The limited spatial resolution in proton computed tomography (pCT) in comparison to x-ray CT is related to multiple Coulomb scattering (MCS) within the imaged object. The current generation pCT design utilizes silicon detectors that measure the position and direction of individual protons prior to and post-traversing the patient to maximize the knowledge of the path of the proton within the imaged object. For efficient reconstruction with the proposed pCT system, one needs to develop compact and flexible mathematical formalisms that model the effects of MCS as the proton traverses the imaged object. In this article, a compact, matrix-based most likely path (MLP) formalism is presented employing Bayesian statistics and a Gaussian approximation of MCS. Using GEANT4 simulations in a homogeneous 20 cm water cube, the MLP expression was found to be able to predict the Monte Carlo tracks of 200 MeV protons to within 0.6 mm on average when employing 3sigma cuts on the relative exit angle and exit energy. These cuts were found to eliminate the majority of events not conforming to the Gaussian model of MCS used in the MLP derivation. M riszwana Banu

Total variation superiorization schemes in proton computed tomography image reconstruction

PURPOSE Iterative projection reconstruction algorithms are currently the preferred reconstruction method in proton computed tomography (pCT). However, due to inconsistencies in the measured data arising from proton energy straggling and multiple Coulomb scattering, the noise in the reconstructed image increases with successive iterations. In the current work, the authors investigated the use of total variation superiorization (TVS) schemes that can be applied as an algorithmic add-on to perturbation-resilient iterative projection algorithms for pCT image reconstruction. METHODS The block-iterative diagonally relaxed orthogonal projections (DROP) algorithm was used for reconstructing GEANT4 Monte Carlo simulated pCT data sets. Two TVS schemes added on to DROP were investigated; the first carried out the superiorization steps once per cycle and the second once per block. Simplifications of these schemes, involving the elimination of the computationally expensive feasibility proximity checking step of the TVS framework, were also investigated. The modulation transfer function and contrast discrimination function were used to quantify spatial and density resolution, respectively. RESULTS With both TVS schemes, superior spatial and density resolution was achieved compared to the standard DROP algorithm. Eliminating the feasibility proximity check improved the image quality, in particular image noise, in the once-per-block superiorization, while also halving image reconstruction time. Overall, the greatest image quality was observed when carrying out the superiorization once per block and eliminating the feasibility proximity check. CONCLUSIONS The low-contrast imaging made possible with TVS holds a promise for its incorporation into future pCT studies.

Monte Carlo investigation of the increased radiation deposition due to gold nanoparticles using kilovoltage and megavoltage photons in a 3D randomized cell model

PURPOSE Investigation of increased radiation dose deposition due to gold nanoparticles (GNPs) using a 3D computational cell model during x-ray radiotherapy. METHODS Two GNP simulation scenarios were set up in Geant4; a single 400 nm diameter gold cluster randomly positioned in the cytoplasm and a 300 nm gold layer around the nucleus of the cell. Using an 80 kVp photon beam, the effect of GNP on the dose deposition in five modeled regions of the cell including cytoplasm, membrane, and nucleus was simulated. Two Geant4 physics lists were tested: the default Livermore and custom built Livermore/DNA hybrid physics list. 10(6) particles were simulated at 840 cells in the simulation. Each cell was randomly placed with random orientation and a diameter varying between 9 and 13 μm. A mathematical algorithm was used to ensure that none of the 840 cells overlapped. The energy dependence of the GNP physical dose enhancement effect was calculated by simulating the dose deposition in the cells with two energy spectra of 80 kVp and 6 MV. The contribution from Auger electrons was investigated by comparing the two GNP simulation scenarios while activating and deactivating atomic de-excitation processes in Geant4. RESULTS The physical dose enhancement ratio (DER) of GNP was calculated using the Monte Carlo model. The model has demonstrated that the DER depends on the amount of gold and the position of the gold cluster within the cell. Individual cell regions experienced statistically significant (p < 0.05) change in absorbed dose (DER between 1 and 10) depending on the type of gold geometry used. The DER resulting from gold clusters attached to the cell nucleus had the more significant effect of the two cases (DER ≈ 55). The DER value calculated at 6 MV was shown to be at least an order of magnitude smaller than the DER values calculated for the 80 kVp spectrum. Based on simulations, when 80 kVp photons are used, Auger electrons have a statistically insignificant (p < 0.05) effect on the overall dose increase in the cell. The low energy of the Auger electrons produced prevents them from propagating more than 250-500 nm from the gold cluster and, therefore, has a negligible effect on the overall dose increase due to GNP. CONCLUSIONS The results presented in the current work show that the primary dose enhancement is due to the production of additional photoelectrons.

A more accurate reconstruction system matrix for quantitative proton computed tomography

An accurate system matrix is required for quantitative proton CT (pCT) image reconstruction with iterative projection algorithms. The system matrix is composed of chord lengths of individual proton path intersections with reconstruction pixels. In previous work, reconstructions were performed assuming constant intersection chord lengths, which led to systematic errors of the reconstructed proton stopping powers. The purpose of the present work was to introduce a computationally efficient variable intersection chord length in order to improve the accuracy of the system matrix. An analytical expression that takes into account the discrete stepping nature of the pCT most likely path (MLP) reconstruction procedure was created to describe an angle-dependent effective mean chord length function. A pCT dataset was simulated with GEANT4 using a parallel beam of 200 MeV protons intersecting a computerized head phantom consisting of tissue-equivalent materials with known relative stopping power. The phantom stopping powers were reconstructed with the constant chord length, exact chord length, and effective mean chord length approaches, in combination with the algebraic reconstruction technique. Relative stopping power errors were calculated for each anatomical phantom region and compared for the various methods. It was found that the error of approximately 10% in the mean reconstructed stopping power value for a given anatomical region, resulting from a system matrix with a constant chord length, could be reduced to less than 0.5% with either the effective mean chord length or exact chord length approaches. Reconstructions with the effective mean chord length were found to be approximately 20% faster than reconstructions with an exact chord length. The effective mean chord length method provides the possibility for more accurate, computationally efficient quantitative pCT reconstructions.

Dosimetric comparison of stopping power calibration with dual-energy CT and single-energy CT in proton therapy treatment planning

PURPOSE The accuracy of proton dose calculation is dependent on the ability to correctly characterize patient tissues with medical imaging. The most common method is to correlate computed tomography (CT) numbers obtained via single-energy CT (SECT) with proton stopping power ratio (SPR). CT numbers, however, cannot discriminate between a change in mass density and change in chemical composition of patient tissues. This limitation can have consequences on SPR calibration accuracy. Dual-energy CT (DECT) is receiving increasing interest as an alternative imaging modality for proton therapy treatment planning due to its ability to discriminate between changes in patient density and chemical composition. In the current work we use a phantom of known composition to demonstrate the dosimetric advantages of proton therapy treatment planning with DECT over SECT. METHODS A phantom of known composition was scanned with a clinical SECT radiotherapy CT-simulator. The phantom was rescanned at a lower X-ray tube potential to generate a complimentary DECT image set. A set of reference materials similar in composition to the phantom was used to perform a stoichiometric calibration of SECT CT number to proton SPRs. The same set of reference materials was used to perform a DECT stoichiometric calibration based on effective atomic number. The known composition of the phantom was used to assess the accuracy of SPR calibration with SECT and DECT. Intensity modulated proton therapy (IMPT) treatment plans were generated with the SECT and DECT image sets to assess the dosimetric effect of the imaging modality. Isodose difference maps and root mean square (RMS) error calculations were used to assess dose calculation accuracy. RESULTS SPR calculation accuracy was found to be superior, on average, with DECT relative to SECT. Maximum errors of 12.8% and 2.2% were found for SECT and DECT, respectively. Qualitative examination of dose difference maps clearly showed the dosimetric advantages of DECT imaging, compared to SECT imaging for IMPT dose calculation for the case investigated. Quantitatively, the maximum dose calculation error in the SECT plan was 7.8%, compared to a value of 1.4% in the DECT plan. When considering the high dose target region, the root mean square (RMS) error in dose calculation was 2.1% and 0.4% for SECT and DECT, respectively. CONCLUSIONS DECT-based proton treatment planning in a commercial treatment planning system was successfully demonstrated for the first time. DECT is an attractive imaging modality for proton therapy treatment planning owing to its ability to characterize density and chemical composition of patient tissues. SECT and DECT scans of a phantom of known composition have been used to demonstrate the dosimetric advantages obtainable in proton therapy treatment planning with DECT over the current approach based on SECT.

Review of Geant4-DNA applications for micro and nanoscale simulations

Emerging radiotherapy treatments including targeted particle therapy, hadron therapy or radiosensitisation of cells by high-Z nanoparticles demand the theoretical determination of radiation track structure at the nanoscale. This is essential in order to evaluate radiation damage at the cellular and DNA level. Since 2007, Geant4 offers physics models to describe particle interactions in liquid water at the nanometre level through the Geant4-DNA Package. This package currently provides a complete set of models describing the event-by-event electromagnetic interactions of particles with liquid water, as well as developments for the modelling of water radiolysis. Since its release, Geant4-DNA has been adopted as an investigational tool in kV and MV external beam radiotherapy, hadron therapies using protons and heavy ions, targeted therapies and radiobiology studies. It has been benchmarked with respect to other track structure Monte Carlo codes and, where available, against reference experimental measurements. While Geant4-DNA physics models and radiolysis modelling functionalities have already been described in detail in the literature, this review paper summarises and discusses a selection of representative papers with the aim of providing an overview of a) geometrical descriptions of biological targets down to the DNA size, and b) the full spectrum of current micro- and nano-scale applications of Geant4-DNA.

Development of a randomized 3D cell model for Monte Carlo microdosimetry simulations.

PURPOSE The objective of the current work was to develop an algorithm for growing a macroscopic tumor volume from individual randomized quasi-realistic cells. The major physical and chemical components of the cell need to be modeled. It is intended to import the tumor volume into GEANT4 (and potentially other Monte Carlo packages) to simulate ionization events within the cell regions. METHODS A MATLAB© code was developed to produce a tumor coordinate system consisting of individual ellipsoidal cells randomized in their spatial coordinates, sizes, and rotations. An eigenvalue method using a mathematical equation to represent individual cells was used to detect overlapping cells. GEANT4 code was then developed to import the coordinate system into GEANT4 and populate it with individual cells of varying sizes and composed of the membrane, cytoplasm, reticulum, nucleus, and nucleolus. Each region is composed of chemically realistic materials. RESULTS The in-house developed MATLAB© code was able to grow semi-realistic cell distributions (~2 × 10(8) cells in 1 cm(3)) in under 36 h. The cell distribution can be used in any number of Monte Carlo particle tracking toolkits including GEANT4, which has been demonstrated in this work. CONCLUSIONS Using the cell distribution and GEANT4, the authors were able to simulate ionization events in the individual cell components resulting from 80 keV gamma radiation (the code is applicable to other particles and a wide range of energies). This virtual microdosimetry tool will allow for a more complete picture of cell damage to be developed.

Detector development for Proton Computed Tomography (pCT)

Proton Computed Tomography (pCT) is being developed in support of proton therapy and treatment planning. The aim of pCT, to reconstruct an accurate map of the stopping power (S.P.) in a phantom and, in the future, in patients, is being pursued with a diverse list of detector systems, using the entire arsenal of tracking and energy detectors developed for High Energy Physics (HEP). The first radiographs and 3D images are being reconstructed with prototype detectors, which will be described. Most of the existing systems are being upgraded to higher proton fluxes to reduce the scanning time.

Development of Proton Computed Tomography for Applications in Proton Therapy

Determination of the Bragg peak position in proton therapy requires accurate knowledge of the electron density and ratio of effective atomic number and mass (Z/A) of the body tissues traversed. While the Z/A ratio is fairly constant for human tissues, the density of tissues varies significantly. One possibility to obtain accurate electron density information of tissues is to use protons of sufficient energy to penetrate the patient and measure their energy loss. From these transmission measurements, it is possible to reconstruct a three‐dimensional map of electron densities using algebraic techniques. The interest in proton computed tomography (pCT) has considerably increased in recent years due to the more common use of proton accelerators for cancer treatment world‐wide and a modern design concept based on current high‐energy physics technology has been suggested. This contribution gives a status update on the pCT project carried out by the pCT Collaboration, a group of institutions sharing interest and...

Characteristics of proton CT images reconstructed with filtered backprojection and iterative projection algorithms

In early studies of proton computed tomography (pCT), images were reconstructed with the fast and robust filtered backprojection (FBP) algorithm. Due to multiple Coulomb scattering of the protons within the object, the straight line path assumption of FBP resulted in poor spatial resolution. In an attempt to improve spatial resolution, a formalism to predict the proton path of maximum likelihood through the image space was created. The use of these paths with the iterative algebraic reconstruction technique (ART), have shown an improvement in spatial resolution, but also an increase in image noise, resulting in poor density resolution. In this work, we propose a reconstruction method that attempts to optimize both spatial and density resolution of pCT images. The new reconstruction approach makes use of the block-iterative diagonally relaxed orthogonal projections (DROP) algorithm with an initial FBP-reconstructed image estimate. Reconstruction of Monte Carlo simulated pCT data sets of spatial and density resolution phantoms demonstrated that the combined reconstruction approach resulted in better spatial resolution than the FBP algorithm alone and better density resolution than the DROP algorithm starting from a uniform initial image estimate.