Spatial Resolution of Shapes in Gamma Camera Imaging Using an Exact Formula for Solid Angle of View

Modeling of the tomographic weights usually incorporates angle of view, decay and attenuation. A usual assumption is that the gamma camera is a long way from the object, this leads to the approximation that the angle of view subtending the front of the collimator tube is the same as that subtending the back (Weir & Green, 1994). However, if the distance between camera and subject is small then this approximation may not be good enough and artifacts may be produced. In this paper, the derivations of the angle of view and the solid angle of view are analyzed considering distances when the camera is close to the body. The solid angle is explained by an appropriate formula which is defined as the exact solid angle of view. The effect of the solid angle of view for different distances is examined. A comparison between exact solid angle and the approximate solid angle formula of Weir and Green (1994) is presented. Finally the effects of the two formulae on reconstruction are studied using simulated data from circular gamma camera rotation systems. Comparison between the resolution could be achieved by applying multiresolutio-multigrid approaches. DOI: 10.4018/ijsbbt.2012010104 36 International Journal of Systems Biology and Biomedical Technologies, 1(1), 35-51, January-March 2012 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. the position of the object. This dependence is due to both the characteristics of the collimator and the position of the camera detector. It is common to assume that the gamma camera is a long way from the subject; this leads to the approximation that the angle subtending the front of the collimator tube is the same as that subtending the back. If however, the distance between camera and subject is small, then this approximation may not be good enough and artifacts may be produced (Jaszczak et al., 1981). In this work a derivation of the exact solid angle of view is studied for distances when the camera is close to the body. The effects of the solid angle of view for different distances are examined and a comparison between exact and approximate solid angle formula of view is presented. Finally an analysis of various distances using different camera measurements is presented for both formulae. PHYSICS OF GAMMA CAMERA Gamma camera imaging is a modern medical diagnostic technique, based to study function rather than form. The patient is injected with or inhales an appropriate drug, which became concentrated in the organ of interest. Photons emission occurs in the organ at a rate ranging spatially according to the concentration and measurements of this concentration can be made by counting emitted photons in the gamma camera. The physical and operational details of the gamma camera are described by Larsson (1980). The gamma camera rotated about an axis through the patient to collect a sequence of projections from the body at numerous equally spaced angles. The session begins with the gamma camera directly above and facing the patient. In this potion, the camera detects and records photons leaving the patient’s body in a certain time period after 20 seconds. The camera then rotates about an axis parallel to the table, stops after 64 degrees and collects counts at the new angle. This process is repeated until the gamma camera return to its original position directly above the patient. The majority of emissions are never recorded by the system since their path is not towards the camera. The camera has a lead parallel-hole collimator which further limits the number of recorded emissions by only emitted photons whose path is nearly exactly perpendicular to the surface of the camera. Figure 1 demonstrates the basic component of a gamma camera and the various paths that an emitted photon can take: (1) photon emitted away from the camera, (2) photon emitted and scattered away from the camera, (3) photon absorbed inside the subject, (4) photon emitted away from the camera but scattered through collimator, (5) photon emitted directly through the collimator, (6) photon directed towards camera, but at an angle preventing it from passing through collimator. The method of data collection means that the 3D object is divided up into multiple 2D projections and each projection is represented by a set of discrete 1D profile. Each point on the profile represents the linear sum, in the absence of attenuation, of the emissions along the line of view of the detectors through the collimator. A common way of displaying the data is by taking all 1D profile corresponding to a cross sectional slice through the object. This type of representation has been referred to as a sinogram, where the horizontal axis represents camera angles and the vertical the detectors along each 1D cross-sectional profile (Figure 2). MODELING OF THE WEIGHT Reliable reconstruction depends on detailed knowledge of the weights. Accurate modeling of the weights is important since in practice they are unknown. Based on the literature (Weir & Green, 1994; Jaszczak et al., 1981; Green, 1990) {αts} denotes the conditional probability that an emission at pixel s is detected in tube t and their modeling depends on the geometry of the gamma camera system, the physical shape of the body and the properties of the emitted photons. (Geman et al., 1991) studied the modeling of the weights {αts}, which determine the rela15 more pages are available in the full version of this document, which may be purchased using the "Add to Cart" button on the product's webpage: www.igi-global.com/article/spatial-resolution-shapes-gammacamera/63045?camid=4v1 This title is available in InfoSci-Journals, InfoSci-Journal Disciplines Medicine, Healthcare, and Life Science. Recommend this product to your librarian: www.igi-global.com/e-resources/libraryrecommendation/?id=2