An improved Bayesian tensor regularization and sampling algorithm to track neuronal fiber pathways in the language circuit
Purpose: The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with functionally important regions in the human brain. The functional activations in the brain normally occur in the gray matter regions. Hence the...
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| Published in | Medical physics (Lancaster) Vol. 37; no. 8; pp. 4274 - 4287 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
American Association of Physicists in Medicine
01.08.2010
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0094-2405 2473-4209 0094-2405 |
| DOI | 10.1118/1.3456113 |
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| Abstract | Purpose:
The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with functionally important regions in the human brain. The functional activations in the brain normally occur in the gray matter regions. Hence the fibers bordering these regions are weakly myelinated, resulting in poor performance of conventional tractography methods to trace the fiber links between them. A lower fractional anisotropy in this region makes it even difficult to track the fibers in the presence of noise. In this work, the authors focused on a stochastic approach to reconstruct these fiber pathways based on a Bayesian regularization framework.
Methods:
To estimate the true fiber direction (propagation vector), thea priori and conditional probability density functions are calculated in advance and are modeled as multivariate normal. The variance of the estimated tensor element vector is associated with the uncertainty due to noise and partial volume averaging (PVA). An adaptive and multiple sampling of the estimated tensor element vector, which is a function of the pre-estimated variance, overcomes the effect of noise and PVA in this work.
Results:
The algorithm has been rigorously tested using a variety of synthetic data sets. The quantitative comparison of the results to standard algorithms motivated the authors to implement it forin vivo DTI data analysis. The algorithm has been implemented to delineate fibers in two major language pathways (Broca’s to SMA and Broca’s to Wernicke’s) across 12 healthy subjects. Though the mean of standard deviation was marginally bigger than conventional (Euler’s) approach [P. J. Basser
et al.
, “In vivo fiber tractography using DT-MRI data,” Magn. Reson. Med.
44(4), 625–632 (2000)], the number of extracted fibers in this approach was significantly higher. The authors also compared the performance of the proposed method to Lu’s method [Y. Lu
et al.
, “Improved fiber tractography with Bayesian tensor regularization,” Neuroimage
31(3), 1061–1074 (2006)] and Friman’s stochastic approach [O. Friman
et al.
, “A Bayesian approach for stochastic white matter tractography,” IEEE Trans. Med. Imaging
25(8), 965–978 (2006)]. Overall performance of the approach is found to be superior to above two methods, particularly when the signal-to-noise ratio was low.
Conclusions:
The authors observed that an adaptive sampling of the tensor element vectors, estimated as a function of the variance in a Bayesian framework, can effectively delineate neuronal fibers to analyze the structure-function relationship in human brain. The simulated andin vivo results are in good agreement with the theoretical aspects of the algorithm. |
|---|---|
| AbstractList | Purpose:
The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with functionally important regions in the human brain. The functional activations in the brain normally occur in the gray matter regions. Hence the fibers bordering these regions are weakly myelinated, resulting in poor performance of conventional tractography methods to trace the fiber links between them. A lower fractional anisotropy in this region makes it even difficult to track the fibers in the presence of noise. In this work, the authors focused on a stochastic approach to reconstruct these fiber pathways based on a Bayesian regularization framework.
Methods:
To estimate the true fiber direction (propagation vector), the
a priori
and conditional probability density functions are calculated in advance and are modeled as multivariate normal. The variance of the estimated tensor element vector is associated with the uncertainty due to noise and partial volume averaging (PVA). An adaptive and multiple sampling of the estimated tensor element vector, which is a function of the pre-estimated variance, overcomes the effect of noise and PVA in this work.
Results:
The algorithm has been rigorously tested using a variety of synthetic data sets. The quantitative comparison of the results to standard algorithms motivated the authors to implement it for
in vivo
DTI data analysis. The algorithm has been implemented to delineate fibers in two major language pathways (Broca’s to SMA and Broca’s to Wernicke’s) across 12 healthy subjects. Though the mean of standard deviation was marginally bigger than conventional (Euler’s) approach [
P. J. Basser et al., “In vivo fiber tractography using DT-MRI data,” Magn. Reson. Med. 44(
4
), 625–632 (2000)
], the number of extracted fibers in this approach was significantly higher. The authors also compared the performance of the proposed method to Lu’s method [
Y. Lu et al., “Improved fiber tractography with Bayesian tensor regularization,” Neuroimage 31(
3
), 1061–1074 (2006)
] and Friman’s stochastic approach [
O. Friman et al., “A Bayesian approach for stochastic white matter tractography,” IEEE Trans. Med. Imaging 25(
8
), 965–978 (2006)
]. Overall performance of the approach is found to be superior to above two methods, particularly when the signal-to-noise ratio was low.
Conclusions:
The authors observed that an adaptive sampling of the tensor element vectors, estimated as a function of the variance in a Bayesian framework, can effectively delineate neuronal fibers to analyze the structure-function relationship in human brain. The simulated and
in vivo
results are in good agreement with the theoretical aspects of the algorithm. Purpose: The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with functionally important regions in the human brain. The functional activations in the brain normally occur in the gray matter regions. Hence the fibers bordering these regions are weakly myelinated, resulting in poor performance of conventional tractography methods to trace the fiber links between them. A lower fractional anisotropy in this region makes it even difficult to track the fibers in the presence of noise. In this work, the authors focused on a stochastic approach to reconstruct these fiber pathways based on a Bayesian regularization framework. Methods: To estimate the true fiber direction (propagation vector), thea priori and conditional probability density functions are calculated in advance and are modeled as multivariate normal. The variance of the estimated tensor element vector is associated with the uncertainty due to noise and partial volume averaging (PVA). An adaptive and multiple sampling of the estimated tensor element vector, which is a function of the pre‐estimated variance, overcomes the effect of noise and PVA in this work. Results: The algorithm has been rigorously tested using a variety of synthetic data sets. The quantitative comparison of the results to standard algorithms motivated the authors to implement it forin vivo DTI data analysis. The algorithm has been implemented to delineate fibers in two major language pathways (Broca's to SMA and Broca's to Wernicke's) across 12 healthy subjects. Though the mean of standard deviation was marginally bigger than conventional (Euler's) approach [P. J. Basser et al., “In vivo fiber tractography using DT‐MRI data,” Magn. Reson. Med. 44(4), 625–632 (2000)], the number of extracted fibers in this approach was significantly higher. The authors also compared the performance of the proposed method to Lu's method [Y. Lu et al., “Improved fiber tractography with Bayesian tensor regularization,” Neuroimage 31(3), 1061–1074 (2006)] and Friman's stochastic approach [O. Friman et al., “A Bayesian approach for stochastic white matter tractography,” IEEE Trans. Med. Imaging 25(8), 965–978 (2006)]. Overall performance of the approach is found to be superior to above two methods, particularly when the signal‐to‐noise ratio was low. Conclusions: The authors observed that an adaptive sampling of the tensor element vectors, estimated as a function of the variance in a Bayesian framework, can effectively delineate neuronal fibers to analyze the structure‐function relationship in human brain. The simulated andin vivo results are in good agreement with the theoretical aspects of the algorithm. The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with functionally important regions in the human brain. The functional activations in the brain normally occur in the gray matter regions. Hence the fibers bordering these regions are weakly myelinated, resulting in poor performance of conventional tractography methods to trace the fiber links between them. A lower fractional anisotropy in this region makes it even difficult to track the fibers in the presence of noise. In this work, the authors focused on a stochastic approach to reconstruct these fiber pathways based on a Bayesian regularization framework.PURPOSEThe purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with functionally important regions in the human brain. The functional activations in the brain normally occur in the gray matter regions. Hence the fibers bordering these regions are weakly myelinated, resulting in poor performance of conventional tractography methods to trace the fiber links between them. A lower fractional anisotropy in this region makes it even difficult to track the fibers in the presence of noise. In this work, the authors focused on a stochastic approach to reconstruct these fiber pathways based on a Bayesian regularization framework.To estimate the true fiber direction (propagation vector), the a priori and conditional probability density functions are calculated in advance and are modeled as multivariate normal. The variance of the estimated tensor element vector is associated with the uncertainty due to noise and partial volume averaging (PVA). An adaptive and multiple sampling of the estimated tensor element vector, which is a function of the pre-estimated variance, overcomes the effect of noise and PVA in this work.METHODSTo estimate the true fiber direction (propagation vector), the a priori and conditional probability density functions are calculated in advance and are modeled as multivariate normal. The variance of the estimated tensor element vector is associated with the uncertainty due to noise and partial volume averaging (PVA). An adaptive and multiple sampling of the estimated tensor element vector, which is a function of the pre-estimated variance, overcomes the effect of noise and PVA in this work.The algorithm has been rigorously tested using a variety of synthetic data sets. The quantitative comparison of the results to standard algorithms motivated the authors to implement it for in vivo DTI data analysis. The algorithm has been implemented to delineate fibers in two major language pathways (Broca's to SMA and Broca's to Wernicke's) across 12 healthy subjects. Though the mean of standard deviation was marginally bigger than conventional (Euler's) approach [P. J. Basser et al., "In vivo fiber tractography using DT-MRI data," Magn. Reson. Med. 44(4), 625-632 (2000)], the number of extracted fibers in this approach was significantly higher. The authors also compared the performance of the proposed method to Lu's method [Y. Lu et al., "Improved fiber tractography with Bayesian tensor regularization," Neuroimage 31(3), 1061-1074 (2006)] and Friman's stochastic approach [O. Friman et al., "A Bayesian approach for stochastic white matter tractography," IEEE Trans. Med. Imaging 25(8), 965-978 (2006)]. Overall performance of the approach is found to be superior to above two methods, particularly when the signal-to-noise ratio was low.RESULTSThe algorithm has been rigorously tested using a variety of synthetic data sets. The quantitative comparison of the results to standard algorithms motivated the authors to implement it for in vivo DTI data analysis. The algorithm has been implemented to delineate fibers in two major language pathways (Broca's to SMA and Broca's to Wernicke's) across 12 healthy subjects. Though the mean of standard deviation was marginally bigger than conventional (Euler's) approach [P. J. Basser et al., "In vivo fiber tractography using DT-MRI data," Magn. Reson. Med. 44(4), 625-632 (2000)], the number of extracted fibers in this approach was significantly higher. The authors also compared the performance of the proposed method to Lu's method [Y. Lu et al., "Improved fiber tractography with Bayesian tensor regularization," Neuroimage 31(3), 1061-1074 (2006)] and Friman's stochastic approach [O. Friman et al., "A Bayesian approach for stochastic white matter tractography," IEEE Trans. Med. Imaging 25(8), 965-978 (2006)]. Overall performance of the approach is found to be superior to above two methods, particularly when the signal-to-noise ratio was low.The authors observed that an adaptive sampling of the tensor element vectors, estimated as a function of the variance in a Bayesian framework, can effectively delineate neuronal fibers to analyze the structure-function relationship in human brain. The simulated and in vivo results are in good agreement with the theoretical aspects of the algorithm.CONCLUSIONSThe authors observed that an adaptive sampling of the tensor element vectors, estimated as a function of the variance in a Bayesian framework, can effectively delineate neuronal fibers to analyze the structure-function relationship in human brain. The simulated and in vivo results are in good agreement with the theoretical aspects of the algorithm. The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with functionally important regions in the human brain. The functional activations in the brain normally occur in the gray matter regions. Hence the fibers bordering these regions are weakly myelinated, resulting in poor performance of conventional tractography methods to trace the fiber links between them. A lower fractional anisotropy in this region makes it even difficult to track the fibers in the presence of noise. In this work, the authors focused on a stochastic approach to reconstruct these fiber pathways based on a Bayesian regularization framework. To estimate the true fiber direction (propagation vector), the a priori and conditional probability density functions are calculated in advance and are modeled as multivariate normal. The variance of the estimated tensor element vector is associated with the uncertainty due to noise and partial volume averaging (PVA). An adaptive and multiple sampling of the estimated tensor element vector, which is a function of the pre-estimated variance, overcomes the effect of noise and PVA in this work. The algorithm has been rigorously tested using a variety of synthetic data sets. The quantitative comparison of the results to standard algorithms motivated the authors to implement it for in vivo DTI data analysis. The algorithm has been implemented to delineate fibers in two major language pathways (Broca's to SMA and Broca's to Wernicke's) across 12 healthy subjects. Though the mean of standard deviation was marginally bigger than conventional (Euler's) approach [P. J. Basser et al., "In vivo fiber tractography using DT-MRI data," Magn. Reson. Med. 44(4), 625-632 (2000)], the number of extracted fibers in this approach was significantly higher. The authors also compared the performance of the proposed method to Lu's method [Y. Lu et al., "Improved fiber tractography with Bayesian tensor regularization," Neuroimage 31(3), 1061-1074 (2006)] and Friman's stochastic approach [O. Friman et al., "A Bayesian approach for stochastic white matter tractography," IEEE Trans. Med. Imaging 25(8), 965-978 (2006)]. Overall performance of the approach is found to be superior to above two methods, particularly when the signal-to-noise ratio was low. The authors observed that an adaptive sampling of the tensor element vectors, estimated as a function of the variance in a Bayesian framework, can effectively delineate neuronal fibers to analyze the structure-function relationship in human brain. The simulated and in vivo results are in good agreement with the theoretical aspects of the algorithm. Purpose: The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with functionally important regions in the human brain. The functional activations in the brain normally occur in the gray matter regions. Hence the fibers bordering these regions are weakly myelinated, resulting in poor performance of conventional tractography methods to trace the fiber links between them. A lower fractional anisotropy in this region makes it even difficult to track the fibers in the presence of noise. In this work, the authors focused on a stochastic approach to reconstruct these fiber pathways based on a Bayesian regularization framework. Methods: To estimate the true fiber direction (propagation vector), thea priori and conditional probability density functions are calculated in advance and are modeled as multivariate normal. The variance of the estimated tensor element vector is associated with the uncertainty due to noise and partial volume averaging (PVA). An adaptive and multiple sampling of the estimated tensor element vector, which is a function of the pre-estimated variance, overcomes the effect of noise and PVA in this work. Results: The algorithm has been rigorously tested using a variety of synthetic data sets. The quantitative comparison of the results to standard algorithms motivated the authors to implement it forin vivo DTI data analysis. The algorithm has been implemented to delineate fibers in two major language pathways (Broca’s to SMA and Broca’s to Wernicke’s) across 12 healthy subjects. Though the mean of standard deviation was marginally bigger than conventional (Euler’s) approach [P. J. Basser et al. , “In vivo fiber tractography using DT-MRI data,” Magn. Reson. Med. 44(4), 625–632 (2000)], the number of extracted fibers in this approach was significantly higher. The authors also compared the performance of the proposed method to Lu’s method [Y. Lu et al. , “Improved fiber tractography with Bayesian tensor regularization,” Neuroimage 31(3), 1061–1074 (2006)] and Friman’s stochastic approach [O. Friman et al. , “A Bayesian approach for stochastic white matter tractography,” IEEE Trans. Med. Imaging 25(8), 965–978 (2006)]. Overall performance of the approach is found to be superior to above two methods, particularly when the signal-to-noise ratio was low. Conclusions: The authors observed that an adaptive sampling of the tensor element vectors, estimated as a function of the variance in a Bayesian framework, can effectively delineate neuronal fibers to analyze the structure-function relationship in human brain. The simulated andin vivo results are in good agreement with the theoretical aspects of the algorithm. |
| Author | Anderson, Adam W. Wu, Xi Mishra, Arabinda Gore, John C. Ding, Zhaohua |
| Author_xml | – sequence: 1 givenname: Arabinda surname: Mishra fullname: Mishra, Arabinda email: arabinda.mishra@vanderbilt.edu organization: Institute of Imaging Science, Vanderbilt University, Nashville, Tennessee 37232 – sequence: 2 givenname: Adam W. surname: Anderson fullname: Anderson, Adam W. organization: Institute of Imaging Science, Vanderbilt University, Nashville, Tennessee 37232 and Department of Biomedical Engineering, Vanderbilt University, Nashville, Tennessee 37232 – sequence: 3 givenname: Xi surname: Wu fullname: Wu, Xi organization: Institute of Imaging Science, Vanderbilt University, Nashville, Tennessee 37232 – sequence: 4 givenname: John C. surname: Gore fullname: Gore, John C. organization: Institute of Imaging Science, Vanderbilt University, Nashville, Tennessee 37232 and Department of Biomedical Engineering, Vanderbilt University, Nashville, Tennessee 37232 – sequence: 5 givenname: Zhaohua surname: Ding fullname: Ding, Zhaohua organization: Institute of Imaging Science, Vanderbilt University, Nashville, Tennessee 37232; Department of Biomedical Engineering, Vanderbilt University, Nashville, Tennessee 37232; and Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, Tennessee 37232 |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/20879588$$D View this record in MEDLINE/PubMed |
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| Copyright | American Association of Physicists in Medicine 2010 American Association of Physicists in Medicine Copyright © 2010 American Association of Physicists in Medicine 2010 American Association of Physicists in Medicine |
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| Keywords | Hotelling transform Bayes decision rule diffusion tensor imaging (DTI) |
| Language | English |
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| Notes | 0094‐2405/2010/37(8)/4274/14/$30.00 Author to whom correspondence should be addressed. Electronic mail arabinda.mishra@vanderbilt.edu Telephone: (615) 322‐6213; Fax: (615) 322‐0734. ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 Author to whom correspondence should be addressed. Electronic mail: arabinda.mishra@vanderbilt.edu; Telephone: (615) 322-6213; Fax: (615) 322-0734. |
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The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with... The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with... |
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| SubjectTerms | Algorithms Anisotropy Bayes decision rule Bayes Theorem biodiffusion biomedical MRI brain Brain - anatomy & histology Computer Simulation Data analysis Diffusion diffusion tensor imaging (DTI) Diffusion Tensor Imaging - methods Eigenvalues Hotelling transform Humans Image Enhancement - methods Image Interpretation, Computer-Assisted - methods image reconstruction Imaging, Three-Dimensional - methods Interpolation Language medical image processing Models, Neurological Models, Statistical MRI: anatomic, functional, spectral, diffusion Nerve Net - anatomy & histology Neural Pathways - anatomy & histology neurophysiology Optical fiber testing Pattern Recognition, Automated - methods probability Probability density functions Probability theory Radiation Imaging Physics Reproducibility of Results Sample Size Sensitivity and Specificity smoothing methods Stochastic modeling stochastic processes Tensor methods tracking |
| Title | An improved Bayesian tensor regularization and sampling algorithm to track neuronal fiber pathways in the language circuit |
| URI | http://dx.doi.org/10.1118/1.3456113 https://onlinelibrary.wiley.com/doi/abs/10.1118%2F1.3456113 https://www.ncbi.nlm.nih.gov/pubmed/20879588 https://www.proquest.com/docview/756297387 https://pubmed.ncbi.nlm.nih.gov/PMC2921424 |
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