Computational issues and algorithm assessment for shock/turbulence interaction problems

The paper provides an overview of the challenges involved in the computation of flows with interactions between turbulence, strong shockwaves, and sharp density interfaces. The prediction and physics of such flows is the focus of an ongoing project in the Scientific Discovery through Advanced Computing (SciDAC) program. While the project is fundamental in nature, there are many important potential applications of scientific and engineering interest ranging from inertial confinement fusion to exploding supernovae. The essential challenges will be discussed, and some representative numerical results that highlight these challenges will be shown. In addition, the overall approach taken in this project will be outlined

The contest between internal and external-beam dosimetry: The Zeno's paradox of Achilles and the tortoise.

Radionuclide therapy, also called molecular radiotherapy (MRT), has come of age, with several novel radiopharmaceuticals being approved for clinical use or under development in the last decade. External beam radiotherapy (EBRT) is a well-established treatment modality, with about half of all oncologic patients expected to receive at least one external radiation treatment over their disease course. The efficacy and the toxicity of both types of treatment rely on the interaction of radiation with biological tissues. Dosimetry played a fundamental role in the scientific and technological evolution of EBRT, and absorbed doses to the target and to the organs at risk are calculated on a routine basis. In contrast, in MRT the usefulness of internal dosimetry has long been questioned, and a structured path to include absorbed dose calculation is missing. However, following a similar route of development as EBRT, MRT treatments could probably be optimized in a significant proportion of patients, likely based on dosimetry and radiobiology. In the present paper we describe the differences and the similarities between internal and external-beam dosimetry in the context of radiation treatments, and we retrace the main stages of their development over the last decades

Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor–Green vortex, Shu–Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results

Inter-comparison of quantitative imaging of lutetium-177 (177Lu) in European hospitals

Background: This inter-comparison exercise was performed to demonstrate the variability of quantitative SPECT/CT imaging for lutetium-177 (177Lu) in current clinical practice. Our aim was to assess the feasibility of using international inter-comparison exercises as a means to ensure consistency between clinical sites whilst enabling the sites to use their own choice of quantitative imaging protocols, specific to their systems. Dual-compartment concentric spherical sources of accurately known activity concentrations were prepared and sent to seven European clinical sites. The site staff were not aware of the true volumes or activity within the sources—they performed SPECT/CT imaging of the source, positioned within a water-filled phantom, using their own choice of parameters and reported their estimate of the activities within the source. Results: The volumes reported by the participants for the inner section of the source were all within 29% of the true value and within 60% of the true value for the outer section. The activities reported by the participants for the inner section of the source were all within 20% of the true value, whilst those reported for the outer section were up to 83% different to the true value. Conclusions: A variety of calibration and segmentation methods were used by the participants for this exercise which demonstrated the variability of quantitative imaging across clinical sites. This paper presents a method to assess consistency between sites using different calibration and segmentation methods

An Improved High Order Finite Difference Method for Non-conforming Grid Interfaces for the Wave Equation

This paper presents an extension of a recently developed high order finite difference method for the wave equation on a grid with non-conforming interfaces. The stability proof of the existing methods relies on the interpolation operators being norm-contracting, which is satisfied by the second and fourth order operators, but not by the sixth order operator. We construct new penalty terms to impose interface conditions such that the stability proof does not require the norm-contracting condition. As a consequence, the sixth order accurate scheme is also provably stable. Numerical experiments demonstrate the improved stability and accuracy property

Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations

Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not perfect and there remain some issues. Concerning robustness, DG has undergone an extensive transformation over the past seven years into its modern form that provides statements on solution boundedness for linear and nonlinear problems. This chapter takes a constructive approach to introduce a modern incarnation of the DG spectral element method for the compressible Navier-Stokes equations in a three-dimensional curvilinear context. The groundwork of the numerical scheme comes from classic principles of spectral methods including polynomial approximations and Gauss-type quadratures. We identify aliasing as one underlying cause of the robustness issues for classical DG spectral methods. Removing said aliasing errors requires a particular differentiation matrix and careful discretization of the advective flux terms in the governing equations.Comment: 85 pages, 2 figures, book chapte

3-D Image-Based Dosimetry in Radionuclide Therapy

Radionuclide therapy is the use of radioactive drugs for internal radiotherapy, mainly for the treatment of metastatic disease. As opposed to systemic cancer therapies in general, the use of radioactively labeled drugs results not only in a targeted therapy but also the possibility of imaging the distribution of the drug during therapy. From such images, the absorbed doses delivered to tumors and organs at risk can be calculated. Calculation of the absorbed dose from 3-D images such as single-photon emission computed tomography (SPECT)/CT, and in some cases positron emission tomography (PET)/CT, relies on image-based activity quantification. Quantification is accomplished by modeling the physics involved in the image-formation process, and applying image-processing methods. From a time-sequence of such quantitative images, the absorbed doses are then calculated. Although individual-patient dosimetry is a standard component of other forms of radiotherapy, it is still overlooked in the majority of radionuclide therapies. In this review, we summarize the physical and technical problems that need to be addressed in image-based dosimetry. The focus is on SPECT, since most of the radionuclides used are single-photon emitters, although the use of PET is also discussed. Practical issues of relevance for the practical implementation of personalized dosimetry in radionuclide therapy are also highlighted

Peptide Receptor Radionuclide Therapy – Prospects for Personalised Treatment

Peptide receptor radionuclide therapy is a type of molecular radiotherapy that has been used in the treatment of patients with neuroendocrine tumours for over two decades. It is not until recently, however, that it has achieved regulatory approval. The currently approved treatment regimen is a one-size-fits-all scheme, i.e. all patients receive a fixed activity of the radiopharmaceutical (177Lu-DOTATATE) and a fixed number of treatment cycles. Several research groups around the world have studied different approaches of further improving on the results of peptide receptor radionuclide therapy, with many promising retrospective and prospective clinical studies having been published over the years. In this overview, we summarise some of the most promising strategies identified so far

Computational issues and algorithm assessment for shock/turbulence interaction problems

The paper provides an overview of the challenges involved in the computation of flows with interactions between turbulence, strong shockwaves, and sharp density interfaces. The prediction and physics of such flows is the focus of an ongoing project in the Scientific Discovery through Advanced Computing (SciDAC) program. While the project is fundamental in nature, there are many important potential applications of scientific and engineering interest ranging from inertial confinement fusion to exploding supernovae. The essential challenges will be discussed, and some representative numerical results that highlight these challenges will be shown. In addition, the overall approach taken in this project will be outlined