A convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections. The formula is approximate but has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation. It reduces to the standard fan-beam formula in the plane that is perpendicular to the axis of rotation and contains the point source. The algorithm is applied to a mathematical phantom as an example of its performance.

Practical cone-beam algorithm

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Published by the American Association of Physicists in Medicine DISCLAIMER: This publication is based on sources and information believed to be reliable, but the AAPM and the editors disclaim any warranty or liability based on or relating to the contents of this publication. The AAPM does not endorse any products, manufacturers, or suppliers. Nothing in this publication should be interpreted as implying such endorsement. PREFACE This document is the report of a task group of the Radiation Therapy Committee of the American Association of Physicists in Medicine and supersedes the recommendations of AAPM Report 13 (AAPM, 1984). The purpose of the report is twofold. First, the advances in radiation oncology in the decade since AAPM Report 13 (AAPM, 1984) necessitated a new document on quality assurance (QA). Second, developments in the principles of quality assurance and continuing quality improvement necessitated a report framed in this context. The title \" Comprehensive Quality Assurance for Radiation Oncology \" may need clarification. While the report emphasizes the physical aspects of QA and does not attempt to discuss issues that are essentially medical (e.g., the decision to treat, the prescription of dose), it by no means neglects issues in which the physical and medical issues intertwine, often in a complex manner. The integrated nature of QA in radiation oncology makes it impossible to consider QA as limited to, for example, checking machine output or calibrating brachytherapy sources. QA activities cover a very broad range, and the work of medical physicists in this regard extends into a number of areas in which the actions of radiation oncologists, radiation therapists, 1 dosimetrists, accelerator engineers, and medical physicists are important. Moreover, this is true for each of the disciplines-each has special knowledge and expertise which affects the quality of treatment , and each discipline overlaps the others in a broad \" gray zone. \" It is important not only to understand each discipline's role in QA, but to clarify this zone so that errors do not \" fall between the cracks. \" This report therefore attempts to cover the physical aspects of QA both in a narrow or traditional sense and in a more integrated sense. The report comprises 2 parts: Part A is for administrators, and Part B is a code of practice in six sections. The first section of Part B describes a comprehensive quality assurance program in which the importance of a written procedural …

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Comprehensive QA for radiation oncology: report of AAPM Radiation Therapy Committee Task Group 40.

Solar Probe Plus (SPP) will be the first spacecraft to fly into the low solar corona. SPP’s main science goal is to determine the structure and dynamics of the Sun’s coronal magnetic field, understand how the solar corona and wind are heated and accelerated, and determine what processes accelerate energetic particles. Understanding these fundamental phenomena has been a top-priority science goal for over five decades, dating back to the 1958 Simpson Committee Report. The scale and concept of such a mission has been revised at intervals since that time, yet the core has always been a close encounter with the Sun. The mission design and the technology and engineering developments enable SPP to meet its science objectives to: (1) Trace the flow of energy that heats and accelerates the solar corona and solar wind; (2) Determine the structure and dynamics of the plasma and magnetic fields at the sources of the solar wind; and (3) Explore mechanisms that accelerate and transport energetic particles. The SPP mission was confirmed in March 2014 and is under development as a part of NASA’s Living with a Star (LWS) Program. SPP is scheduled for launch in mid-2018, and will perform 24 orbits over a 7-year nominal mission duration. Seven Venus gravity assists gradually reduce SPP’s perihelion from 35 solar radii (
 $R_{S}$
 ) for the first orbit to ${<}10~R_{S}$
 for the final three orbits. In this paper we present the science, mission concept and the baseline vehicle for SPP, and examine how the mission will address the key science questions

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The Solar Probe Plus Mission: Humanity’s First Visit to Our Star

A group of algorithms is presented generalizing the fast Fourier transform to the case of noninteger frequencies and nonequispaced nodes on the interval $[ - \pi ,\pi ]$. The schemes of this paper are based on a combination of certain analytical considerations with the classical fast Fourier transform and generalize both the forward and backward FFTs. Each of the algorithms requires $O(N\cdot \log N + N\cdot \log (1/\varepsilon ))$ arithmetic operations, where $\varepsilon $ is the precision of computations and N is the number of nodes. The efficiency of the approach is illustrated by several numerical examples.

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Fast Fourier transforms for nonequispaced data

Several different mathematical methods are described which use the observed line-of-sight component of the photospheric magnetic field to determine the magnetic field of the solar corona in the current-free (or potential-field) approximation. Discussed are (1) a monopole method, (2) a Legendre polynomial expansion assuming knowledge of the radial photospheric magnetic field, (3) a Legendre polynomial expansion obtained from the line-of-sight photospheric field by a least-meansquare technique, (4) solar wind simulation by zero-potential surfaces in the corona, (5) corrections for the missing flux due to magnetograph saturation. We conclude (1) that the field obtained from the monopole method is not consistent with the given magnetic data because of non-local effects produced by monopoles on a curved surface, (2) that the field given by a Legendre polynomial (which is fitted to the measured line-of-sight magnetic field) is a rigorous and self-consistent solution with respect to the available data, (3) that it is necessary to correct for the saturation of the magnetograph (at about 80 G) because fields exceeding 80 G provide significant flux to the coronal field, and (4) that a zero-potential surface at 2.5 solar radii can simulate the effect of the solar wind on the coronal magnetic field.

Magnetic Fields and the Structure of the Solar Corona. I: Methods of Calculating Coronal Fields

Introduction. The five main parts of SAS and SPSS.- Programming conventions.- Typographic conventions.- Installing & updating R.- Running R.- Help and documentation.- Programming language basics.- Data Acquisition.- Selecting Variables - Var, Variables=.- Selecting observations - where, if select if, filter.- Selecting both variables and observations.- Converting data structures.- Data management.- Recoding variables. Value labels or formats (& measurement level).- Variable labels.- Generating data.- How R stores data.- Managing your files and workspace.- Graphics overview.- Traditional graphics.- The ggplot2 package.- Statistics.- Summary.- Conclusion.- Appendix A.- Appendix B.- Appendix C.- Bibliography.

Image reconstruction from projections : implementation and applications

A system and method for selecting from a set of output actions for combinatory situations such as medical diagnosis defined by a plurality of input parameters. A decision making structure is established by an expert having a plurality of linked nodes. Random values of the input parameters are generated, which includes biasing the random values by a function of a preceding response. The steps are repeated until a sufficient number of responses having a predetermined statistical significance is achieved for each node. After this set up and teaching, the accuracy of the system's predictions may be verified against actual responses by the expert. The decision making structure may be interrogated by entering a situation to be analyzed. The path the expert would take through the decision making structure is predicted by determining the probability of the expert's response at each node in the structure to arrive at an output action. A plurality of structures may be established, one for each individual expert, allowing interrogation of any or all of the decision making structures.

Interactive statistical system and method for predicting expert decisions

A computational solution of the inverse problem in radiation-therapy treatment planning

The primary aim of this study was to determine whether optimized photodynamic therapy(PDT) treatment planning (seeking optimized positions, lengths, and strengths of the light sources to satisfy a given dose prescription) can improve dose coverage to the prostate and the sparing of critical organs relative to what can be achieved by the standard PDT plan. The Cimmino algorithm and search procedures based on that algorithm were tested for this purpose. A phase I motexafin lutetium (MLu)-mediated photodynamic therapy protocol is ongoing at the University of Pennsylvania. PDT for the prostate is performed with cylindrical diffusing fibers of various lengths inserted perpendicular to a base plate to obtain longitudinal coverage by a matrix of parallel catheters. The standard plan for the protocol uses sources of equal strength with equal spaced ( 1 - cm ) loading. Uniform optical properties were assumed. Our algorithms produce plans that cover the prostate and spare the urethra and rectum with less discrepancy from the dose prescription than the standard plan. The Cimmino feasibility algorithm is fast enough that changes to the treatment plan may be made in the operating room before and during PDT to optimize light delivery.

Martin D. Altschuler

Papers

Magnetic Fields and the Structure of the Solar Corona. I: Methods of Calculating Coronal Fields

Image reconstruction from projections : implementation and applications

Interactive statistical system and method for predicting expert decisions

A computational solution of the inverse problem in radiation-therapy treatment planning

Optimized interstitial PDT prostate treatment planning with the Cimmino feasibility algorithm.