A MATHEMATICAL MODEL OF SINGLE-PHOTON EMISSION COMPUTED TOMOGRAPHY (RADON TRANSFORM, COMPTON SCATTER, ATTENUATION, NUCLEAR MEDICINE).

Persistent Link:
http://hdl.handle.net/10150/188142
Title:
A MATHEMATICAL MODEL OF SINGLE-PHOTON EMISSION COMPUTED TOMOGRAPHY (RADON TRANSFORM, COMPTON SCATTER, ATTENUATION, NUCLEAR MEDICINE).
Author:
CLOUGH, ANNE VIRGINIA.
Issue Date:
1986
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Single-photon emission computed tomography (SPECT) is a nuclear-medicine imaging technique that has been shown to provide clinically useful images of radionuclide distributions within the body. The problem of quantitative determination of tomographic activity images from a projection data set leads to a mathematical inverse problem which is formulated as an integral equation. The solution of this problem then depends on an accurate mathematical model as well as a reliable and efficient inversion algorithm. The effects of attenuation and Compton scatter within the body have been incorporated into the model in the hopes of providing a more physically realistic mathematical model. The attenuated Radon transform is the mathematical basis of SPECT. In this work, the case of constant attenuation is reviewed and a new proof of the Tretiak-Metz algorithm is presented. A space-domain version of the inverse attenuated Radon transform is derived. A special case of this transform that is applicable when the object is rotationally symmetric, the attenuated Abel transform is derived, and its inverse is found. A numerical algorithm for the implementation of the inverse attenuated Radon transform with constant attenuation is described and computer simulations are performed to demonstrate the results of the inversion procedure. With the use of the single-scatter approximation and an energy-windowed detector, the effects of Compton scatter are incorporated into the model. The data is then taken to be the sum of primary photons and single-scattered photons. The scattered photons are modeled by a scatter operator acting on the original activity distribution within the object where the operator consists of convolution with a given analytic kernel followed by a boundary cut-off operation. A solution is given by first applying the inverse attenuated Radon transform to the data set. This leads to a Fredholm integral equation to which a Neumann series solution is constructed. Again simulations are performed to validate the accuracy of the assumptions within the model as well as to numerically demonstrate the reconstruction procedure.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Tomography, Emission -- Mathematical models.; Nuclear medicine.; Imaging systems in medicine -- Mathematical models.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Barrett, Harry

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleA MATHEMATICAL MODEL OF SINGLE-PHOTON EMISSION COMPUTED TOMOGRAPHY (RADON TRANSFORM, COMPTON SCATTER, ATTENUATION, NUCLEAR MEDICINE).en_US
dc.creatorCLOUGH, ANNE VIRGINIA.en_US
dc.contributor.authorCLOUGH, ANNE VIRGINIA.en_US
dc.date.issued1986en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractSingle-photon emission computed tomography (SPECT) is a nuclear-medicine imaging technique that has been shown to provide clinically useful images of radionuclide distributions within the body. The problem of quantitative determination of tomographic activity images from a projection data set leads to a mathematical inverse problem which is formulated as an integral equation. The solution of this problem then depends on an accurate mathematical model as well as a reliable and efficient inversion algorithm. The effects of attenuation and Compton scatter within the body have been incorporated into the model in the hopes of providing a more physically realistic mathematical model. The attenuated Radon transform is the mathematical basis of SPECT. In this work, the case of constant attenuation is reviewed and a new proof of the Tretiak-Metz algorithm is presented. A space-domain version of the inverse attenuated Radon transform is derived. A special case of this transform that is applicable when the object is rotationally symmetric, the attenuated Abel transform is derived, and its inverse is found. A numerical algorithm for the implementation of the inverse attenuated Radon transform with constant attenuation is described and computer simulations are performed to demonstrate the results of the inversion procedure. With the use of the single-scatter approximation and an energy-windowed detector, the effects of Compton scatter are incorporated into the model. The data is then taken to be the sum of primary photons and single-scattered photons. The scattered photons are modeled by a scatter operator acting on the original activity distribution within the object where the operator consists of convolution with a given analytic kernel followed by a boundary cut-off operation. A solution is given by first applying the inverse attenuated Radon transform to the data set. This leads to a Fredholm integral equation to which a Neumann series solution is constructed. Again simulations are performed to validate the accuracy of the assumptions within the model as well as to numerically demonstrate the reconstruction procedure.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectTomography, Emission -- Mathematical models.en_US
dc.subjectNuclear medicine.en_US
dc.subjectImaging systems in medicine -- Mathematical models.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorBarrett, Harryen_US
dc.identifier.proquest8613427en_US
dc.identifier.oclc697514303en_US
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