One of the problems needs to be considered is how to assure the continuity of the tangent vector’s direction as described in Eq. (8). In this study, we used the dot product of tangent vectors obtained in the previous step and the one got in the present step. If the result is positive we keep the sign of the current eigenvector; if the result is negative we reverse its sign. For termination, one of the criteria we used is the extent of anisotropy. The fractional anisotropy of the gray matter is typically in the range of 0.1-0.2 [10], by which an empirically value of 0.2 is used as the threshold for termination. Another criterion is the directional change between adjacent pixels. For this purpose, we check the trajectory deflection angles in the tracking process and the algorithm terminates when the angle change becomes too large. The continuity in the fiber orientation can be expressed as:
3 Experimental Results
Fig. 4 shows the tracking results of the first two synthetic data sets by using the STT and improved STT methods, respectively. The first pixels of each column are seed points used for tracking. Fig. 5 shows the corresponding trajectories of the synthetic 3-D fiber model. All points in the first slice (z=1) are used as the seed points for tracking. It is evident from these figures that STT cannot follow the true fiber tracts and can cause severe deviation from the real fiber orientation. The improved STT, on the other hand, is much more robust that can obtain the whole trajectories.
176 M. Bai and S. Luo
Fig.4. (a)-(c) show tTracking results for the synthetic data set shown in Fig. 2(a) by using STT, and improved STT with and respectively, (d)-(e) are the racking results for the synthetic data set shown in Fig. 2(b), with STT and improved STT, respectively. For STT, when tracking reaches the area of spherical tensor, the process misses the right direction and is terminated. For the improved STT, the tracking process can handle the isotropic point and keep tracking until the end of the fiber tract.
Fig. 5. The tracking result for the 3-D fiber model by using STT (left) and improved STT (right) respectively.
As shown in Fig. 6, nerve fiber tracts inside the ROI for the in vivo data set are almost parallel, without intersection or branching. The tracking results of two methods did not show significant differences.
However, in regions where the distribution of the nerve fiber is complex, e.g. when there are fiber crossing or fiber branching, the STT method is no longer being able to delineate the true fiber path when reaching the “crossing” area. The improved STT can resolve this problem and continue with the tracking process. It is evident that STT is sensitive to noise and has difficulty propagating through spherical and planar
Improved Fiber Tracking for Diffusion Tensor MRI 177 tensors. The modified STT method improves the overall stability of tracking process and significantly decreases the uncertainty of fiber tracking
Fig. 6. In vivo tracking results when the fiber shape is relatively simple. (a) shows the selected ROI (in green square), and (b) is the corresponding FA, (c) the tracking result of STT, and (d) is the tracking result of improved STT with
Fig. 7. Tracking results where fiber shape is complex. (a) shows a selected ROI (in green square), and (b) is the corresponding FA, and (c) is the tracking result of STT, (d) improved STT with
4 Discussion and Conclusion
In this paper, we have presented an improved STT method for fiber tracking with DT- MRI. The synthetic tensor field data sets are of practical value for validating the fiber tracking method. It is worth noting that the synthesized tensor fields in this study is relatively simple and further studies are needed to create realistic and more complex fiber models. They should include the consideration of properties such as fiber curvature and connection between fiber orientations. Although the improved STT method can overcome some disadvantages of STT, it still uses PDD as fiber tracking direction, and the problem that tracking result deviates from the real trajectory due to image noise or partial volume effect is unsolved. The issue of how to best map the real fiber tract from DT-MRI voxels should be investigated further.
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Rapid and Automatic Extraction of the Modified Talairach Cortical Landmarks from MR Neuroimages
Qingmao Hu, Guoyu Qian, Wieslaw L. Nowinski Bioinformatics Institute, Singapore 138671
{huqm, qiangy, wieslaw}@bii.a-star.edu.sg
Abstract. An automatic algorithm to locate the modified Talairach cortical landmarks is proposed. Firstly, three planes containing the landmarks are de- termined, and the optimum thresholds robust to noise and inhomogeneity are calculated based on range-constrained thresholding. Then, the planes are seg- mented with the chosen thresholds and morphological operations. Finally the segmentation is refined and landmarks are located. The algorithm has been validated against 62 T1-weighted and SPGR MR diversified datasets. For each dataset, it takes less than 2 seconds on Pentium 4 (2.6 GHz) to extract the 6 modified Talairach cortical landmarks. The average landmark location error is below 1 mm. The algorithm is robust and accurate as the factors influencing the determination of cortical landmarks are carefully compensated. A low compu- tational cost results from selecting three 2D planes to process and employing only simple operations. The algorithm is suitable for both research and clinical applications.
1 Introduction
The Talairach transformation ([9]), despite its limitation ([7]), is the most popular way to normalize brains. It is solely determined when the midsagittal plane (MSP), position of the anterior commissure (AC) and posterior commissure (PC), and local- ization of the 6 Talairach cortical landmarks are available. So far, the Talairach corti- cal landmarks are determined manually ([3]). Nowinski ([7]) studied the drawbacks of the existing Talairach cortical landmarks and proposed the modified Talairach cortical landmarks. Automatic identification of either the Talairach or modified Ta- lairach cortical landmarks from MR neuroimages is difficult due to the inherent na- ture of the MR neuroimages: noisy, gray level intensity inhomogeneity, the partial volume effect due to big voxel sizes, sagittal sinus/meninges connected to the cortex, closeness of the cortex to the optic nerves both spatially and in gray levels.
This paper focuses on robust and fast extraction of the 6 modified Talairach corti- cal landmarks based on anatomic knowledge and range-constrained thresholding.
The algorithm has been tested against 62 T1-weighted and SPGR morphological MR datasets, both phantom and real datasets with numerous variations in imaging pa- rameters (noise levels, inhomogeneities, voxel sizes, scanning orientations).
G.-Z. Yang and T. Jiang (Eds.): MIAR 2004, LNCS 3150, pp. 179-187, 2004.
© Springer-Verlag Berlin Heidelberg 2004
180 Q. Hu, G. Qian, and W.L. Nowinski
2 Material and Method