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A Bloch-Torrey Equation for Diffusion in a Deforming Media

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Title: A Bloch-Torrey Equation for Diffusion in a Deforming Media
Authors: Rohmer, Damien, Gullberg, Grant T.
Contributors: United States. Department of Energy. Office of Science., National Institutes of Health (U.S.)
Publisher Information: Office of Scientific and Technical Information (OSTI), 2006.
Publication Year: 2006
Subject Terms: In Vivo, Geometry, Brain, General and miscellaneous//mathematics, Curvilinear Coordinates, Organs Mri Bloch Equations Diffusion Deforming Media Continuummechanics, MRI Bloch Equations diffusion deforming media continuum mechanics, Classical and quantum mechanics, Diffusion, and information science, Mri Bloch Equations Diffusion Deforming Media Continuummechanics, computing, Radiology and nuclear medicine, Classical and quantum mechanics, general physics, Magnetic Resonance, general physics, General and miscellaneous//mathematics, computing, and information science
Description: Author(s): Rohmer, Damien; Gullberg, Grant T. | Abstract: Diffusion Tensor Magnetic Resonance Imaging (DTMRI) technique enables the measurement of diffusion parameters and therefore, informs on the structure of the biological tissue. This technique is applied with success to the static organs such as brain. However, the diffusion measurement on the dynamically deformable organs such as the in-vivo heart is a complex problem that has however a great potential in the measurement of cardiac health. In order to understand the behavior of the Magnetic Resonance (MR)signal in a deforming media, the Bloch-Torrey equation that leads the MR behavior is expressed in general curvilinear coordinates. These coordinates enable to follow the heart geometry and deformations through time. The equation is finally discretized and presented in a numerical formulation using implicit methods, in order to get a stable scheme that can be applied to any smooth deformations. Diffusion process enables the link between the macroscopic behavior of molecules and the microscopic structure in which they evolve. The measurement of diffusion in biological tissues is therefore of major importance in understanding the complex underlying structure that cannot be studied directly. The Diffusion Tensor Magnetic Resonance Imaging(DTMRI) technique enables the measurement of diffusion parameters and therefore provides information on the structure of the biological tissue. This technique has been applied with success to static organs such as the brain. However, diffusion measurement of dynamically deformable organs such as the in-vivo heart remains a complex problem, which holds great potential in determining cardiac health. In order to understand the behavior of the magnetic resonance (MR) signal in a deforming media, the Bloch-Torrey equation that defines the MR behavior is expressed in general curvilinear coordinates. These coordinates enable us to follow the heart geometry and deformations through time. The equation is finally discretized and presented in a numerical formulation using implicit methods in order to derive a stable scheme that can be applied to any smooth deformations.
Document Type: Report
Article
File Description: application/pdf; Text
DOI: 10.2172/919380
Access URL: https://digital.library.unt.edu/ark:/67531/metadc890298/m2/1/high_res_d/919380.pdf
https://escholarship.org/content/qt3zp3z6pw/qt3zp3z6pw.pdf?t=lnpqxp
https://digital.library.unt.edu/ark:/67531/metadc890298/m2/1/high_res_d/919380.pdf
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https://escholarship.org/uc/item/3zp3z6pw.pdf
https://digital.library.unt.edu/ark:/67531/metadc890298/
https://escholarship.org/uc/item/3zp3z6pw
Accession Number: edsair.doi.dedup.....5b95cade35d7b912725b4669b296d0ac
Database: OpenAIRE
Description
Abstract:Author(s): Rohmer, Damien; Gullberg, Grant T. | Abstract: Diffusion Tensor Magnetic Resonance Imaging (DTMRI) technique enables the measurement of diffusion parameters and therefore, informs on the structure of the biological tissue. This technique is applied with success to the static organs such as brain. However, the diffusion measurement on the dynamically deformable organs such as the in-vivo heart is a complex problem that has however a great potential in the measurement of cardiac health. In order to understand the behavior of the Magnetic Resonance (MR)signal in a deforming media, the Bloch-Torrey equation that leads the MR behavior is expressed in general curvilinear coordinates. These coordinates enable to follow the heart geometry and deformations through time. The equation is finally discretized and presented in a numerical formulation using implicit methods, in order to get a stable scheme that can be applied to any smooth deformations. Diffusion process enables the link between the macroscopic behavior of molecules and the microscopic structure in which they evolve. The measurement of diffusion in biological tissues is therefore of major importance in understanding the complex underlying structure that cannot be studied directly. The Diffusion Tensor Magnetic Resonance Imaging(DTMRI) technique enables the measurement of diffusion parameters and therefore provides information on the structure of the biological tissue. This technique has been applied with success to static organs such as the brain. However, diffusion measurement of dynamically deformable organs such as the in-vivo heart remains a complex problem, which holds great potential in determining cardiac health. In order to understand the behavior of the magnetic resonance (MR) signal in a deforming media, the Bloch-Torrey equation that defines the MR behavior is expressed in general curvilinear coordinates. These coordinates enable us to follow the heart geometry and deformations through time. The equation is finally discretized and presented in a numerical formulation using implicit methods in order to derive a stable scheme that can be applied to any smooth deformations.
DOI:10.2172/919380