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Fast and Analytical EAP Approximation from a 4th-Order Tensor

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying struct...

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Detalles Bibliográficos
Autores principales: Ghosh, Aurobrata, Deriche, Rachid
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2012
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3546486/
https://www.ncbi.nlm.nih.gov/pubmed/23365552
http://dx.doi.org/10.1155/2012/192730
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author Ghosh, Aurobrata
Deriche, Rachid
author_facet Ghosh, Aurobrata
Deriche, Rachid
author_sort Ghosh, Aurobrata
collection PubMed
description Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.
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spelling pubmed-35464862013-01-30 Fast and Analytical EAP Approximation from a 4th-Order Tensor Ghosh, Aurobrata Deriche, Rachid Int J Biomed Imaging Research Article Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data. Hindawi Publishing Corporation 2012 2012-12-30 /pmc/articles/PMC3546486/ /pubmed/23365552 http://dx.doi.org/10.1155/2012/192730 Text en Copyright © 2012 A. Ghosh and R. Deriche. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Ghosh, Aurobrata
Deriche, Rachid
Fast and Analytical EAP Approximation from a 4th-Order Tensor
title Fast and Analytical EAP Approximation from a 4th-Order Tensor
title_full Fast and Analytical EAP Approximation from a 4th-Order Tensor
title_fullStr Fast and Analytical EAP Approximation from a 4th-Order Tensor
title_full_unstemmed Fast and Analytical EAP Approximation from a 4th-Order Tensor
title_short Fast and Analytical EAP Approximation from a 4th-Order Tensor
title_sort fast and analytical eap approximation from a 4th-order tensor
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3546486/
https://www.ncbi.nlm.nih.gov/pubmed/23365552
http://dx.doi.org/10.1155/2012/192730
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