• Journal of Biomedical Engineering Research
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• v.28 no.6
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• pp.817-824
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• 2007

Tractography using Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is a method to determine the architecture of axonal fibers in the central nervous system by computing the direction of the principal eigenvector in the white matter of the brain. However, the fiber tracking methods suffer from the noise included in the diffusion tensor images that affects the determination of the principal eigenvector. As the fiber tracking progresses, the accumulated error creates a large deviation between the calculated fiber and the real fiber. This problem of the DT-MRI tractography is known mathematically as the ill-posed problem which means that tractography is very sensitive to perturbations by noise. To reduce the noise in DT-MRI measurements, a tensor-valued median filter which is reported to be denoising and structure-preserving in fiber tracking, is applied in the tractography. In this paper, we proposed the modified gradient descent method which converges fast and accurately to the optimal tensor-valued median filter by changing the step size. In addition, the performance of the modified gradient descent method is compared with others. We used the synthetic image which consists of 45 degree principal eigenvectors and the corticospinal tract. For the synthetic image, the proposed method achieved 4.66%, 16.66% and 15.08% less error than the conventional gradient descent method for error measures AE, AAE, AFA respectively. For the corticospinal tract, at iteration number ten the proposed method achieved 3.78%, 25.71 % and 11.54% less error than the conventional gradient descent method for error measures AE, AAE, AFA respectively.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.47 no.4
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• pp.30-39
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• 2010

Since Diffusion tensor from Diffusion Tensor Magnetic Resonance Imaging(DT-MRI) is so sensitive to noise, the principle eigenvector(PEV) calculated from Diffusion tensor could be erroneous. Tractography obtained from PEV could be deviated from the real fiber tract. Therefore regularization process is needed to eliminate noise. In this paper, to reduce noise in DT-MRI measurements, the Dyadic Sorting(DS) method as regularization of the eigenvalue and the eigenvector is applied in the tractography. To resort the eigenvalues and the eignevectors, the DS method uses the intervoxel overlap function which can measure the overlap between eigenvalue-eigenvector pairs in the $3\times3$ pixel. In this paper, we applied the DS method to the three-dimensional volume. We discuss the error analysis and numerical study to the synthetic and the experimental data. As a result, we have shown that the DS method is more efficient than the median filtering methods as much as 79.97%~83.64%, 85.62%~87.76% in AAE, AFA respectively for the corticospinal tract of the experimental data.

• Proceedings of the KSMRM Conference
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• 2008.04a
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• pp.76-81
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• 2008

• Investigative Magnetic Resonance Imaging
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• v.11 no.2
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• pp.110-118
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• 2007

Purpose: The objective of this work to construct eigenvalue maps that have information of magnitude of three primary diffusion directions using diffusion tensor images. Materials and Methods: To construct eigenvalue maps, we used a 3.0T MRI scanner. We also compared the Moore-Penrose pseudo-inverse matrix method and the SVD (single value decomposition) method to calculate magnitude of three primary diffusion directions. Eigenvalue maps were constructed by calculating of magnitude of three primary diffusion directions. We did investigate the relationship between eigenvalue maps and fractional anisotropy map. Results: Using Diffusion Tensor Images by diffusion tensor imaging sequence, we did construct eigenvalue maps of three primary diffusion directions. Comparison between eigenvalue maps and Fractional Anisotropy map shows what is difference of Fractional Anisotropy value in brain anatomy. Furthermore, through the simulation of variable eigenvalues, we confirmed changes of Fractional Anisotropy values by variable eigenvalues. And Fractional anisotropy was not determined by magnitude of each primary diffusion direction, but it was determined by combination of each primary diffusion direction. Conclusion: By construction of eigenvalue maps, we can confirm what is the reason of fractional anisotropy variation by measurement the magnitude of three primary diffusion directions on lesion of brain white matter, using eigenvalue maps and fractional anisotropy map.

• Progress in Medical Physics
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• v.18 no.4
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• pp.214-220
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• 2007

Diffusion tensor tractorgraphy which is based on line propagation method with brute force approach is implemented and the vector correlation function is proposed in addition to the conventional fractional anisotrophy value as a criterion to select seed points. For the whole tractography, the proposed method used 41 % less seed points than the conventional brute force approach for $FA{\geq}0.3$ and most of the fiber tracks in the outer region of white matter were removed. For the corticospinal tract passing through region of interest, the proposed method has produced similar results with 50% less seed points than conventional one.