Objectives: Small field of view gamma detection and imaging technologies for monitoring in vivo tracer uptake are rapidly expanding and being introduced for bed-side imaging and image guided surgical procedures. The Hybrid Gamma Camera (HGC) has been developed to enhance the localization of targeted radiopharmaceuticals during surgical procedures; for example in sentinel lymph node (SLN) biopsies and for bed-side imaging in procedures such as lacrimal drainage imaging and thyroid scanning. In this study, a prototype anthropomorphic head and neck phantom has been designed, constructed, and evaluated using representative modelled medical scenarios to study the capability of the HGC to detect SLNs and image small organs. Methods: An anthropomorphic head and neck phantom has been designed to mimic the adult head and neck including some internal organs and tissues of interest, such as the thyroid gland and sentinel lymph nodes. The design of the head and neck phantom included an adjustable inner jig holding the simulated SLNs and thyroid gland. The simulated thyroid gland was designed and 3D printed taking into consideration the size and the shape of a healthy adult thyroid gland. The inner sealed space of the thyroid was filled with 15MBq of 99mTc through two upper filling valves. Sealed micro-tubes (0.2ml) have been employed to simulate SLNs containing various 99mTc activity concentrations ranging between 0.1MBq and 1MBq, and can be positioned at any desired place in the head and neck region. An active background was simulated through mixing 10MBq of 99mTc solution with the water used to fill the outer shell of the head and neck phantom. Results: The head and neck phantom was employed to simulate a situation where there are four SLNs distributed at two different vertical levels and at two depths within the neck. Contrast to noise ratio (CNR) calculations were performed for the detected SLNs at an 80mm distance between both pinhole collimators (i.e. 0.5mm and 1.0mm diameters) and the surface of the head and neck phantom with a 100s acquisition time. The recorded CNR values for the simulated SLNs are higher when the HGC was fitted with the 1.0mm diameter pinhole collimator. For instance, the recorded CNR values for the superficially simulated SLN containing 0.1MBq of 99mTc using 0.5mm and 1.0mm diameter pinhole collimators are 6.48 and 16.42, respectively (~87% difference). The anatomical context provided by the hybrid imaging aided the localization process of radioactivity accumulation in simulated SLNs. Gamma and hybrid optical images were acquired using the HGC with both available pinhole collimators for the simulated thyroid gland. The thyroid images produced varied in terms of spatial resolution and detectability. The count profiles through the middle of the simulated thyroid gland images provided by both pinhole collimators were obtained. The HGC could clearly differentiate the individual peaks of both thyroid lobes in the gamma image produced by the 0.5mm pinhole collimator. In contrast, the recorded count profile for the acquired image using the 1.0mm diameter pinhole collimator showed broader peaks for both lobes, reflecting the degradation of the spatial resolution with increasing the diameter of the pinhole collimator. Conclusion: The capability of the HGC has been evaluated utilizing a prototype anthropomorphic head and neck phantom, and the gamma and hybrid images obtained demonstrate that it is ideally suited for intraoperative SLNs detection and small organ imaging. The standardization of test phantoms and protocols for SFOV portable gamma systems will provide an opportunity to collect data across various medical centers and research groups. Moreover, it will provide a technical baseline for researchers and clinical practitioners to consider when assessing their SFOV gamma imaging systems. The anthropomorphic head and neck phantom described is cost effective, reproducible, flexible and anatomically representative.
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New types of modules named Fully Small Dual Stable Modules and Principally Small Dual Stable are studied and investigated. Both concepts are generalizations of Fully Dual Stable Modules and Principally Dual Stable Modules respectively. Our new concepts coincide when the module is Small Quasi-Projective, and by considering other kind of conditions. Characterizations and relations of these concepts and the concept of Small Duo Modules are investigated, where every fully small dual stable R-module M is small duo and the same for principally small dual stable.
Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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Let be a commutative ring with unity and let be a non-zero unitary module. In
this work we present a -small projective module concept as a generalization of small
projective. Also we generalize some properties of small epimorphism to δ-small
epimorphism. We also introduce the notation of δ-small hereditary modules and δ-small
projective covers.
Let be a commutative ring with identity , and be a unitary (left) R-module. A proper submodule of is said to be quasi- small prime submodule , if whenever with and , then either or . In this paper ,we give a comprehensive study of quasi- small prime submodules.
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In this paper, we introduce the concept of e-small M-Projective modules as a generalization of M-Projective modules.
Let R be an associative ring with identity and let M be a unitary left R–module. As a generalization of small submodule , we introduce Jacobson–small submodule (briefly J–small submodule ) . We state the main properties of J–small submodules and supplying examples and remarks for this concept . Several properties of these submodules are given . Also we introduce Jacobson–hollow modules ( briefly J–hollow ) . We give a characterization of J–hollow modules and gives conditions under which the direct sum of J–hollow modules is J–hollow . We define J–supplemented modules and some types of modules that are related to J–supplemented modules and int
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A submodule Ϝ of an R-module Ε is called small in Ε if whenever , for some submodule W of Ε , implies . In this paper , we introduce the notion of Ζ-small submodule , where a proper submodule Ϝ of an R-module Ε is said to be Ζ-small in Ε if , such that , then , where is the second singular submodule of Ε . We give some properties of Ζ-small submodules . Moreover , by using this concept , we generalize the notions of hollow modules , supplement submodules, and supplemented modules into Ζ-hollow modules, Ζ-supplement submodules, and Ζ-supplemented modules. We study these concepts and provide some of their relations .
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The main goal of this paper is to give a new generalizations for two important classes in the category of modules, namely the class of small submodules and the class of hollow modules. They are purely small submodules and purely hollow modules respectively. Various properties of these classes of modules are investigated. The relationship between purely small submodules and P-small submodules which is introduced by Hadi and Ibrahim, is studied. Moreover, another characterization of purely hollow modules is considered.
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