DTI Fiber Tract-Oriented Quantitative and Visual Analysis of White Matter Integrity

Transcription

1 DTI Fiber Tract-Oriented Quantitative and Visual Analysis of White Matter Integrity Xuwei Liang, Ning Cao, and Jun Zhang Department of Computer Science, University of Kentucky, USA, Abstract. A new fiber tract-oriented quantitative and visual analysis scheme using diffusion tensor imaging (DTI) is developed to study the regional micro structural white matter changes along major fiber bundles which may not be effectively revealed by existing methods due to the curved spatial nature of neuronal paths. Our technique is based on DTI tractography and geodesic path mapping, which establishes correspondences to allow cross-subject evaluation of diffusion properties by parameterizing the fiber pathways as a function of geodesic distance. A novel isonodes visualization scheme is proposed to render regional statistical features along the fiber pathways. Assessment of the technique reveals specific anatomical locations along the genu of the corpus callosum paths with significant diffusion property changes in the amnestic mild cognitive impairment subjects. The experimental results show that this approach is promising and may provide a sensitive technique to study the integrity of neuronal connectivity in human brain. 1 Introduction The diffusion tensor imaging (DTI) technique has raised hopes to assess brain disorders by detecting white matter (WM) changes through monitoring the change of diffusion properties. The fractional anisotropy (FA), a quantitative measure of the degree of anisotropy, can be used to probe the integrity of the brain WM [1]. The mean diffusivity (MD) value is a quantitative measure of the bulk mean motion of water and is used to study pathological changes in cerebral tissue [2]. Region-of-interest (ROI) [3] and voxel based morphometric (VBM) [4] have been used in medical literatures with DTI. But there are known limitations with these approaches [5]. DTI based tractography enables selective reconstruction of specific neuronal pathways [6, 7] and can be used to represent and measure the structural connectivity in human brains. However, due to the curved spatial nature of the fiber tracts, most approaches proposed so far do not evaluate regional diffusion property changes along the fiber bundles. Neither were interactive visualization techniques used to aid understanding of WM abnormalities. Human brain neuronal paths represent comparable structural connectivity and Technical Report CMIDA-HiPSCCS , Department of Computer Science, University of Kentucky, Lexington, KY, 2008.

2 exhibit a variety of geospatial information across subjects. ROI based methodology usually samples only one or more intersections along the fiber bundles. Operator-introduced errors are inherent due to the manual placements of ROIs. VBM is based on correspondences of voxels indices and does not sufficiently take the aforementioned geospatial variations into account. This motivates the need for a new analysis method. The main goals of this study were twofold: 1) to develop an effective method to measure the regional micro structural WM changes along the major fiber bundles; and 2) to interactively visualize hidden regional statistical features in vivo for better understanding. Our approach is based on DTI tractography and geodesic path mapping, which establishes correspondences to allow direct crosssubject evaluation of diffusion properties along the tractography-extracted fiber tracts by parameterizing the space of the computed pathways as isonodes, a function of the geodesic distance. The second objective was achieved by employing our proposed isonodes visualization scheme. An experiment was conducted to assess this new technique. 2 Methodology 2.1 DTI Data Calculation and Fiber Tracking We used our home-developed software package to process the DTI data and track fibers. The tensor calculation is based on the Stejskal-Tanner equation. The diffusion properties, FA, MD and eigenvectors of the diffusion tensor, were calculated and saved as image files. In this study, the genu of the corpus callosum (GCC) paths were reconstructed using the backward streamline tractography technique [8]. This approach treats the entire brain as the tracking source region and only those reconstructed fiber tracts which pass through the predefined ROI (target) are counted. Therefore, one voxel may have more than one fiber tracts passing through and the tracking results are significantly improved [8, 9]. A fixed size ROI, worked as the target region of the fiber tracking, was manually placed in the center area of GCC to minimize the misregistration effect. In this way, voxels that were around the ventricles and at the edge of a fiber bundle were then excluded. FA indexed color maps were employed to validate the reconstructed fiber tracts. Figure 1 shows the GCC fiber tracts based on a tensor averaged image from all subjects. 2.2 Geodesics and Geodesic Path Mapping Fiber tracts extracted from each individual subject were stored as sets of curvilinear polylines. One fiber tract is a 3D curve r(s) on a Riemannian manifold Ω. The tangent space τ on a Riemannian manifold is equivalent to the vector space of the primary eigenvectors e = (e 1, e 2, e 3 ) T. To obtain a distance between two points of a connected Riemannian manifold, we simply have to take the minimum length among the smooth curves joining these points. The curves satisfying

3 Fig. 1. The reconstructed GCC fiber tracts overlapped on a tensor averaged FA map of all subjects. The left-hand and right-hand side subfigures are in sagittal and axial views respectively. this minimum for any two points of the manifold are called geodesics. Geodesic distance of two points c 1 and c 2 on a fiber r(s) is obtained by integrating e (s) along r Dist(c 1, c 2 ) = s2 s 1 e (s)ds. (1) Let I = [a, b] be an interval on a fiber curve r(s), which is defined as a natural sequence of points r(s) = (x(s), y(s), z(s)) or a sequence of point vectors of a moving point on the image set r(i) of curve r. With these definitions, we can now map a fiber r(s) : Ω [a, b] by equation (1). After this mapping, two distinct points on two distinct fibers my share one common geodesic distance Dist(s). In the implementation, for each fiber bundle (a set of fiber tracts), we set up common starting points and parameterized each fiber by a fixed geodesic arc-length. These common starting points and fixed arc-length geodesic path parameterizations establish correspondences across subjects as well as individual fiber tracts. 2.3 Isonodes To facilitate the use of visual analysis techniques in our research, here we define a new concept, isonodes. Isonodes are a three-dimensional analog of a collection of nodes. They are a group of points of a constant geodesic arc-length within a volume space of fiber tracts. Similar to isosurface, they form a level set of a continuous function of geodesic distance whose domain is three-dimensional space. Isonodes are rendered quickly since they can be displayed as simple points or polygons. They can be used in tractography related volume dataset visualization schemes in medical imaging, allowing researchers to study inherently associated local features along major fiber bundles.

4 2.4 Local Diffusion Property Calculation Fig. 2. Isonodes association. In the left-hand side subfigure, a group of isonodes are assigned one distinct color and circled. The bottom starting point plane is blue. The right-hand side subfigure depicts the parameterized GCC paths from fiber tracts in Figure 1. Fiber tracts are in red and a series of isonodes are in yellow. The middle blue plane represents the common starting points. Geodesic distances were calculated bi-directionally originating from the starting point plane. To distinguish these two directions, isonodes on the left-hand and right-hand sides of the starting point plane were negatively and positively indexed by geodesic arc-length. Equipped with the above techniques, we modeled a set of fiber bundles from N subjects as B = (F 1,..., F k,..., F N ), with the k-th fiber bundle F k = (f 1,..., f i,..., f n ) and the i-th fiber f i = (d 1,..., d j,..., d m ), where d j is the j-th node s geodesic distance on the i-th fiber curve from its starting point. In our analysis, diffusion properties were carried as attributes on each node [9]. Then the local diffusion property calculation becomes straightforward by simply associating the previous defined isonodes. This is depicted in Figure 2. Let Ψ i be attribute values on the i-th fiber pathway and d j the geodesic distance of the j-th node in the curvilinear structure. Then the geodesic path for the k-th fiber bundle with average attribute Φ k is computed as Φ k (d j ) = 1 n n Ψ i (d j ), j = 1,..., m. i=1 We adopted the same scheme of coalescing fiber bundles among subjects for the purpose of group comparisons. The mean attribute values Φ(d j ) across N subjects at the j-th node is Φ(d j ) = 1 N 2.5 Quantitative Analysis N Φ k (d j ), j = 1,..., m. k=1 A non-paired student t-test was employed to evaluate the group difference in MD and FA between mild cognitive impairment (MCI) participants and controls for

5 the entire region of the computed WM pathways. The integrity of these white matter fiber tracts was further evaluated by performing a non-paired student t- tests on isonodes across subjects along the geodesic paths. Since two comparisons (FA and MD)were performed for each of the DTI data set, Bonferroni corrected p values were considered as statistically significant in this study. 2.6 Isonodes Visualization Scheme Each group of isonodes can be associated with their distinct local statistical feature in addition to their inherent attribute, a unique geodesic arc-length. We rendered all the calculated isonodes overlapped on the reconstructed fiber paths. In the process, each set of isonodes are positioned by its geodesic distance along the fiber bundles and are color coded by their discovered statistical features. Different color schemes and thresholds can be interactively selected by a user depending on applications and confidence levels to obtain better understanding of the diffusion property changes along the neuronal path. 3 Experiment and Result 3.1 Subjects and Data Acquisition Thirty-four subjects (17 MCI participants, 17 healthy elderly adults) underwent MRI-based DTI. Patient information and DTI data acquisition procedures are detailed in a previous work [4]. Possible effects of gender and age have been previously tested and excluded. Four control and two MCI subjects were removed from the experiment since their reconstructed GCC tracts were not long enough to reach the GCC forceps. 3.2 Group Difference in FA and MD Values Group differences of mean FA and MD values between the MCI and control subject groups for the entire computed GCC pathways are listed in Table 1. We found significantly reduced FA and elevated MD in the MCI subject groups. Table 1. Mean (± SD) values for the FA and MD measures for computed GCC pathways for MCI and normal control groups. The unit of MD is (10 6 mm 2 /sec). GCC tracts Normal Control MCI p-value df FA 0.56 ± ± MD 844 ± ± The scatter plots in Figure 3 depict the distributions of the FA and MD value of the entire region of the GCC paths in normal control and amnestic MCI subjects separately.

6 FA Control MCI MD Control MCI Fig. 3. Scatter plots of the FA (left) and MD (right) values of the entire region of GCC in normal control and amnestic MCI subjects. The unit of MD is (mm 2 /sec). 3.3 Micro Structural WM Changes along GCC Bundle We also found specific anatomical locations along the GCC paths with significantly reduced FA and elevated MD in the MCI subjects. The results are plotted in Figure 4. Figure 5 visualizes the computed isonodes color indexed by their p- values of the aforementioned comparison overlapped on the reconstructed GCC paths. 4 Discussion A novel fiber tract-oriented visual analysis technique is presented to inspect and visualize the regional micro structural WM alterations along major fiber bundles which may not be effectively revealed by existing ROI and VBM methods due to the curved spatial nature of the fiber tracts. This method minimizes the ROI technique s shortcomings by representing the whole neuronal paths of interest with the automatically extracted fiber tracts. As opposed to VBM, it associates the fiber tract geospatial information by establishing correspondences on geodesic distance mapping. Evaluating this approach on the GCC paths, we found significantly reduced FA and elevated MD measures for the entire computed pathways between the amnestic MCI and control subject groups. In this method, we treat each individual subject s GCC as a specific common ROI (neuronal path of interest) based on the assumption that they represent the same functional connectivity and hence are comparable even though they may have different geospatial orientation. Furthermore, the regional micro structural alterations of WM integrity along the GCC bundles in MCI participants were effectively explored and visualized in vivo. There are a number of limitations with this method. This technique is dependent on the validation of extracted fiber tracts which is an ongoing research area. The reconstructed fiber tracts for all individual subjects need to be validated

7 FA Control MCI p-value Geodesic Distance Geodesic Distance MD Control MCI Geodesic Distance p-value Geodesic Distance Fig. 4. Statistical analysis of regional micro structural FA and MD alterations along the GCC paths. Negative and positive geodesic indices are in accordance with the left and right parts of the starting point plane (indexed by 0) in Figure 2 s right-hand side subfigure. The geodesic distance unit is 0.3mm. The unit of MD is (mm 2 /sec). by experts before any statistical analysis is performed. It requires that every subject s fiber tracts be extracted with approximately the same length, as we can only analyze the common section of fiber tracts among all subjects. This will prevent us from probing the whole neuronal paths in small sampled experiments. One solution to mitigate this situation is to collect a relatively large number of samples, so excluding some of the samples from the experiment will not affect the statistical analysis results. Another approach is to explore improved fiber tracking algorithms. Furthermore, it is appropriate to apply this method in fiber bundles rather than fast dispersing fibers. Experimental results of this study are in agreement with previous amnestic MCI findings [4]. This shows that this new analysis method is promising and may provide a sensitive approach to determining the integrity of neuronal traffics in amnestic MCI.

8 Fig. 5. Visualizations of regional micro structural FA (left) and MD (right) alterations along the GCC tracts. p values greater than 0.06 were rendered as 0.06 for simplicity. 5 Acknowledgements The research work of J. Zhang was supported in part by the US National Science Foundation under grant CCF and CCF , in part by the National Institutes of Health under grant 1R01HL , in part by the Kentucky Science and Engineering Foundation under grant KSEF , and in part by the Alzheimer s Association under grant NIRG References [1] Basser, P., Jones, D.: Diffusion-tensor MRI: Theory, experimental design and data analysis- a technical review. NMR in Biomedicine 15(7-8) (2002) [2] Le Bihan, D., Mangin, J., Poupon, C., Clark, C., Pappata, S., Molko, N., Chabriat, H.: Diffusion tensor imaging: Concepts and applications. Journal of Magnetic Resonance Imaging 13(4) (2001) [3] Zhang, Y., Schuff, N., Jahng, G.H., Bayne, W., Mori, S., Schad, L., Mueller, S., Du, A.T., Kramer, J., Yaffe, K., Chui, H., Jagust, W., Miller, B., Weiner, M.: Diffusion tensor imaging of cingulum fibers in mild cognitive impairment and Alzheimer disease. Neurology 68(1) (2007) [4] Rose, S., McMahon, K., Janke, A., O dowd, B., Zubicaray, G.d., Strudwick, M., Chalk, J.: MRI diffusion indices and neuropsychological performance in amnestic mild cognitive impairment. Journal of Neurology, Neurosurgery, and Psychiatry 77 (2006) [5] Smith, S., Jenkinson, M., Johansen-Berg, H., Rueckert, D., Nichols, T., Mackay, C., Watkins, K., Ciccarelli, O., Cader, M., Matthews, P., et al.: Tract-based spatial statistics: Voxelwise analysis of multi-subject diffusion data. Neuroimage 31(4) (2006) [6] Zhang, J., Kang, N., Rose, S.: Approximating anatomical brain connectivity with diffusion tensor MRI using kernel-based diffusion simulations. In: Proceedings of Information Processing in Medical Imaging. Volume 19., Springer (2005) [7] Kang, N., Zhang, J., Carlson, E., Gembris, D.: White matter fiber tractography via anisotropic diffusion simulation in the human brain. IEEE Transactions on Medical Imaging 24(9) (2005)

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