David Legrady

Performance evaluation of scatter modeling of the GPU-based “Tera-Tomo” 3D PET reconstruction

In positron emission tomography (PET), photon scattering inside the body causes significant blurring and quantification error in the reconstructed images. To solve this problem we have developed Monte Carlo (MC) based 3D PET reconstruction algorithms implemented on the Graphics Processing Unit (GPU). Our implementation takes multiple Compton scattering into account without any significant additional cost. The performance of the scatter correction is evaluated using GATE simulation as well as by comparing reconstruction results of Tera-Tomo to the reference reconstruction implementation of the Philips Gemini TOF PET which applies attenuation correction and single scatter simulation (SSS) for scatter correction. The comparative reconstruction results are based on the NEMA NU2-2007 image quality phantom.

Gamma photon transport on the GPU for PET

This paper proposes a Monte Carlo algorithm for gamma-photon transport, that partially reuses random paths and is appropriate for parallel GPU implementation According to the requirements of the application of the simulation results in reconstruction algorithms, the method aims at similar relative rather than absolute errors of the detectors The resulting algorithm is SIMD-like, which is a requirement of efficient GPU implementation, i.e all random paths are built with the same sequence of instructions, thus can be simulated on parallel threads that practically have no conditional branches The algorithm is a combined method that separates the low-dimensional part that cannot be well mimicked by importance sampling and computes it by a deterministic quadrature, while the high-dimensional part that is made low-variation by importance sampling is handled by the Monte Carlo method The deterministic quadrature is based on a geometric interpretation of a direct, i.e non-scattered effect of a photon on all detectors.

Unbiased Light Transport Estimators for Inhomogeneous Participating Media

This paper presents a new stochastic particle model for efficient and unbiased Monte Carlo rendering of heterogeneous participating media. We randomly add and remove material particles to obtain a density with which free flight sampling and transmittance estimation are simple, while material particle properties are simultaneously modified to maintain the true expectation of the radiance. We show that meeting this requirement may need the introduction of light particles with negative energy and materials with negative extinction, and provide an intuitive interpretation for such phenomena. Unlike previous unbiased methods, the proposed approach does not require a‐priori knowledge of the maximum medium density that is typically difficult to obtain for procedural models. However, the method can benefit from an approximate knowledge of the density, which can usually be acquired on‐the‐fly at little extra cost and can greatly reduce the variance of the proposed estimators. The introduced mechanism can be integrated in participating media renderers where transmittance estimation and free flight sampling are building blocks. We demonstrate its application in a multiple scattering particle tracer, in transmittance computation, and in the estimation of the inhomogeneous air‐light integral.

Detector response function of the NanoPET™/CT system

Even with the huge advance of computers and computing power, full three dimensional reconstructions of PET and CT scans belong to the future as far as commercially available scanners and software are concerned. Recent investigations have shown that with the aid of Graphical Processing Units (GPUs) extremely high computational speed might be achieved, which lends itself to the implementation of iterative 3D reconstruction techniques. Moreover, these techniques make it possible to make use of off-line and on-the-fly Monte Carlo calculations. A consortium of several Hungarian institutions has been working on the development and optimization of a Monte Carlo supported 3D iterative reconstruction program. The in-body scatter processes are modeled by real-time Monte Carlo, however, the detector response is calculated off-line. Therefore, the effective implementation of this MC code requires the calculation of a detector response function in advance. The paper describes our analysis of the response function characteristics of the NanoPET™ (Mediso) detector system. Using MCNPX we constructed a data base consisting of 300 simulations (different incoming photon angles and energies). We studied the sensitivity of the system to several parameters. It was found that the spatial dependence is stronger than the energy dependence. At right angle (at 511 keV) the side-neighbors have an order of magnitude less probability compared to the central pixel, while for photons reaching the central pixel with 350 keV or 511 keV there is only 40% difference in the probabilities. We studied different techniques to include the response function into the MC code mentioned in order to find the optimal strategy. With the approach described in the paper a significant improvement in image quality can be obtained.

Singular value decomposition analysis of back projection operator of maximum likelihood expectation maximization PET image reconstruction

Abstract Background In emission tomography maximum likelihood expectation maximization reconstruction technique has replaced the analytical approaches in several applications. The most important drawback of this iterative method is its linear rate of convergence and the corresponding computational burden. Therefore, simplifications are usually required in the Monte Carlo simulation of the back projection step. In order to overcome these problems, a reconstruction code has been developed with graphical processing unit based Monte Carlo engine which enabled full physical modelling in the back projection. Materials and methods Code performance was evaluated with simulations on two geometries. One is a sophisticated scanner geometry which consists of a dodecagon with inscribed circle radius of 8.7 cm, packed on each side with an array of 39 × 81 LYSO detector pixels of 1.17 mm sided squares, similar to a Mediso nanoScan PET/CT scanner. The other, simplified geometry contains a 38,4mm long interval as a voxel space, detector pixels are assigned in two parallel sections each containing 81 crystals of a size 1.17×1.17 mm. Results We have demonstrated that full Monte Carlo modelling in the back projection step leads to material dependent inhomogeneities in the reconstructed image. The reasons behind this apparently anomalous behaviour was analysed in the simplified system by means of singular value decomposition and explained by different speed of convergence. Conclusions To still take advantage of the higher noise stability of the full physical modelling, a new filtering technique is proposed for convergence acceleration. Some theoretical considerations for the practical implementation and for further development are also presented.

Variance Reduction and Optimization Strategies in a Biased Woodcock Particle Tracking Framework

Abstract A novel particle tracking framework is introduced in this paper that utilizes null-collisions to sample distance to collision in Monte Carlo particle transport problems. The sampling process is described in the most general form as it covers all of the main developments concerning the Woodcock method (delta tracking). We show that none of the previously suggested modifications are optimal in terms of either variance or efficiency. Variance analysis is provided for a general transport problem along with the estimation of computational cost. Simplified models with analytic solutions are further investigated and propositions for optimal settings are discussed based on the derived equations. A well-known variance reduction technique, exponential transform, is found to be a limiting case of the biased Woodcock tracking method and comparison shows the proposed framework may outperform the exponential transform in real-case scenarios.

Multigroup Coupled Neutron-Gamma Cross-Section Library for Deterministic and Monte Carlo Borehole-Logging Analysis

Abstract A special-purpose multigroup cross-section library optimized for nuclides and reactions arising in nuclear oil well logging was prepared for use in deterministic and Monte Carlo transport codes. The library is based on the recent ENDF/B-VI.8 evaluation, which includes among others improved oxygen and chlorine cross sections. A 175-neutron and 45-gamma-ray energy group structure was selected as a way to take into account the requirements of oil well-logging applications. This library is expected to improve the prediction of the neutron and gamma spectra at the detector positions of the logging tool. For the Monte Carlo codes the library can be useful in particular in calculations requiring multigroup cross sections, like adjoint or MIDWAY methods. Furthermore, comparison of deterministic and Monte Carlo calculations using the same or similar cross sections can reveal the uncertainty linked to the computational method and model. The use of the library for the interpretation of the carbon/oxygen neutron logging measurements in boreholes was studied. Preparation and testing of this library, which is available from the Organisation for Economic Co-operation and Development/Nuclear Energy Agency Data Bank, is described.