A hybrid approach to automatic clustering of white matter fibers

NeuroImage 49 (2010) 1249–1258

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NeuroImage j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / y n i m g

A hybrid approach to automatic clustering of white matter fibers Hai Li a,b, Zhong Xue b,⁎, Lei Guo a, Tianming Liu c, Jill Hunter d, Stephen T.C. Wong b a

School of Automation, Northwestern Polytechnical University, Xi'an, China Medical Image Analysis Lab, Center for Bioengineering and Informatics, The Methodist Hospital Research Institute, and Department of Radiology, The Methodist Hospital, Weill Medical College of Cornell University, Houston, TX, USA c Department of Computer Science and Bioimaging Research Center, University of Georgia, Athens, GA, USA d Neuroradiology Section, Department of Radiology, Texas Children’s Hospital, Houston, TX, USA b

a r t i c l e

i n f o

Article history: Received 11 May 2009 Revised 22 July 2009 Accepted 6 August 2009 Available online 13 August 2009

a b s t r a c t Recently, the tract-based white matter (WM) fiber analysis has been recognized as an effective framework to study the diffusion tensor imaging (DTI) data of human brain. This framework can provide biologically meaningful results and facilitate the tract-based comparison across subjects. However, due to the lack of quantitative definition of WM bundle boundaries, the complexity of brain architecture and the variability of WM shapes, clustering WM fibers into anatomically meaningful bundles is nontrivial. In this paper, we propose a hybrid top-down and bottom-up approach for automatic clustering and labeling of WM fibers, which utilizes both brain parcellation results and similarities between WM fibers. Our experimental results show reasonably good performance of this approach in clustering WM fibers into anatomically meaningful bundles. © 2009 Elsevier Inc. All rights reserved.

Introduction Diffusion tensor imaging (DTI) allows in vivo measurement of the diffusivity of water molecules in living tissues (Le Bihan et al., 2001; Basser et al., 1994; Basser and Jones, 2002). Although the diffusivity of water molecules is generally represented as a Brownian motion, the microstructure of living tissues imposes certain constraints on this motion, which results in an anisotropic diffusion measured by DTI (Le Bihan 1991; Basser et al., 1994). The measured diffusion can be approximated by an anisotropic Gaussian model, which is parameterized by the diffusion tensor in each voxel (Basser et al., 1994) to create the tensor field. Diffusion tensor measure provides a rich data set from which a measurement of diffusion anisotropy can be obtained through the application of mathematical formulas and calculation of the underlying Eigenvalues (Moseley et al., 1990; Le Bihan et al., 2001; Basser and Jones, 2002). The recent review article Mori and Zhang (2006) provided an excellent tutorial on the principles of DTI and its applications to neuroscience. It is widely believed that DTI provides insights into the nature and degree of white matter injury that occurs in neurological diseases and sheds light on early detection and diagnosis of devastating neurological diseases. DTI has been widely used in the investigation of WM abnormality associated with various progressive neuropathologies (Werring et al., 1999; Bozzali et al., 2002; Horsfield and Jones, 2002; Moseley, 2002; Stahl et al., 2003; Sundgren et al., 2004; Park et al., 2004; Schocke et al., 2004; Eluvathingal et al., 2006), since it yields quantitative measures reflecting the integrity of WM fiber tracts. These DTI studies on

⁎ Corresponding author. E-mail address: [email protected] (Z. Xue). 1053-8119/$ – see front matter © 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2009.08.017

WM are very useful in the investigation of the abnormality that occurs on fiber pathways connecting remote computation centers of various gray matter (GM) regions. From computational quantitation perspective, most of previous clinical WM DTI studies were based on region of interests (ROI) analysis (Alexander et al., 2007; Chang et al., 2007) or voxel-based morphometry (VBM) analysis (Barnea-Goraly et al., 2004). Notably, ROIbased methods are time-consuming and their reproducibility is limited. VBM-based methods add uncertainty into the analysis since they need non-linear warping of the tensor field and re-orientation of the tensors (Ruiz-Alzola et al., 2000; Alexander et al., 2001.) Recently, a new methodology called tract-based analysis has been investigated by a variety of research groups (Shimony et al., 2002; Fillard and Gerig, 2003; Gerig et al., 2004; Brun et al., 2004; O'Donnell and Westin, 2005; Smith et al., 2006; Maddah et al., 2008). The basic idea of this methodology is to cluster the WM fibers into anatomically meaningful tracts or bundles, and then perform quantitative measurements on these clustered fiber tracts. The major advantages of this methodology include its better biological meanings and facilitation of tract-based comparisons across different subject groups. The tract-based analysis of WM fibers has raised interests from the neurology and clinical neuroscience community, e.g., GoldbergZimring et al., 2005, since this methodology provides direct quantification of the properties of the specific WM bundles rather than the individual image voxels or the entire human brain. However, clustering WM fibers into meaningful bundles is nontrivial due to the following reasons. First, although the conceptual definition of meaningful WM bundles is quite clear in neuroanatomy (Mori et al., 2005), their accurate quantitative definitions are largely unknown, e.g., where the boundaries of different WM bundles are. Second, the human brain architecture

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and its connectivity pattern is quite complex. In typical DTI tractography results, it is quite common that there are many thousands of tracked WM fibers. How to automatically assign meaningful anatomic labels to them is quite challenging. Finally, the white matter architecture of the human brain across individuals is considerably variable in terms of its geometric properties and connectivity strengths and patterns. Development of a WM fiber clustering method that could reliably and robustly work on different human brain DTI data is not easy. Due to above reasons, many existing WM fiber clustering methods need manual guidance in the clustering procedure, so that expert neuroscience knowledge could be integrated into the decision-making process of WM fiber clustering. A couple of approaches have been proposed to incorporate prior knowledge, e.g., Xia et al. (2005) and O'Donnell and Westin (2007). One popular methodology to incorporate neuroscience prior knowledge to WM fiber clustering is to use an atlas of fiber tracts and perform atlasbased warping, e.g., Maddah et al. (2005) and O'Donnell and Westin (2007). For this methodology, it needs to build up a WM atlas first, and then perform non-linear registration of DTI data across different individual brains (Yang et al., 2008). Another approach is to use anatomically defined gray matter regions to guide the clustering of WM fibers (Xia et al., 2005). In this method, connections between anatomically delineated brain regions are identified by first clustering fibers based on their terminations in anatomically defined gray matter regions, and then these connections are refined based on geometric similarity criteria. In this paper, we propose a new computational framework to automatically cluster whole brain WM fibers into biologically meaningful neuro-tracts. This framework explicitly divides 19 major WM fiber bundles into two groups based on neuroanatomical knowledge and our experimental observations. The proposed framework is a hybrid approach, that is, the bundles in the first group are consecutively clustered via top-down brain anatomy guidance, while the bundles in the second group are clustered via a similarity-based bottom-up clustering method. The major advantages of this framework are its intuitiveness, effectiveness, and biological soundness. Our experimental results demonstrate that this hybrid approach can deal

with the complexity and variability of white matter architecture of human brain. Methods Overview and pre-processing A schematic diagram of our computational framework for fiber clustering and tract-based fiber analysis is illustrated in Fig. 1a. Totally, there are six steps in this computational framework. This framework uses FSL FDT for eddy current correction and uses DTIStudio for tensor calculation and channel image generation (Fig. 1b). It then employs the multi-channel DTI segmentation method in Li et al. (2006, 2007) to perform tissue segmentation based on DTI data (Fig. 1c). The basic idea is to classify the brain into two compartments by utilizing the tissue contrast exiting in a single channel, e.g., apparent diffusion coefficient (ADC) image can be used to distinguish CSF and non-CSF, and the fractional anisotropy (FA) image can be used to separate WM from non-WM tissues. Other channels such as Eigenvalues of the tensor, relative anisotropy (RA), and volume ratio (VR) can also be used to separate tissues. Then the STAPLE algorithm (Warfield et al., 2004) is employed to combine these two-class maps to obtain a complete segmentation of CSF, GM, and WM. Afterwards, a high-dimensional registration method is adopted to register a brain atlas to the DTI data and parcellate the brain into recognized WM and GM regions (Liu et al., 2004, 2006; Shen and Davatzikos, 2002). Here, the brain atlas is the Montreal Neurological Institute (MNI) atlas. In this way, we obtain a map of labeled WM and GM structures in DTI space (Fig. 1d). Along with these procedures, the fiber tracking step is performed on the DTI data using DTIStudio with FA threshold 0.25 and angle turn threshold 70° (Fig. 1e). The focus of this paper is the fifth step of fiber clustering and the details of other steps are referred to our previous publications (Liu et al., 2004;, Li et al., 2006; Liu et al., 2006, 2007) and related work in the literature (Tibshirani et al., 2000; Ding et al., 2003; Fillard and Gerig, 2003; Gerig et al., 2004; Brun et al., 2004; O'Donnell and Westin, 2005; Mori et al., 2005; Wakana et al., 2007; Maddah et al., 2008).

Fig. 1. (a) A schematic diagram of the proposed computational framework for white matter fiber clustering and tract-based fiber analysis. This paper focuses on the fifth step, as highlighted. (b) FA image; (c) tissue segmentation map. (d) Labeled anatomical brain regions. (e) WM fibers obtained via the DTI tractography.

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Fiber clustering and labeling In general, WM fibers can be classified into 4 broad types of bundles: tracts in the brain stem, projection tracts, commissural tracts, and association tracts in the cerebral hemispheres (Mori et al., 2005; Wakana et al., 2004). The first three types of bundles could be clustered by top-down brain anatomic guidance, whereas the association bundles are relatively difficult to be clustered by anatomic guidance and need to be clustered via bottom-up similarity-based clustering. For example, the corpus callosum (CC), corticothalamic and corticofugal fibers, and cingulum (CG) can be clustered under the guidance of WM regions they penetrate. Fig. 2a shows a list of parcellated brain regions via the hybrid registration algorithm (Liu et al., 2004, 2006) that can be used to guide the fiber clustering process. However, for certain association bundles such as uncinate fasciculus (UC) and superior longitudinal fasciculus (SLF), they are entangled with other bundles (as shown in Fig. 5) and it is difficult to separate them from surrounding bundles only based on the WM regions they pass. Hence, additional information from similarity-based clustering algorithm is needed to cluster and label them. Above observations and initial experimental results motivate us to develop a hybrid approach that takes the advantages of both topdown brain anatomy-guided clustering and bottom-up similaritybased clustering to group the whole brain WM fibers. Fig. 2b lists the

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19 fiber bundles that are divided into two groups, each of which is clustered via either the top-down anatomy guided method or bottomup similarity-based clustering method. Top-down anatomy guided clustering approach Once we have the whole brain WM/GM region labels (Liu et al., 2004, 2006), the anatomy guided clustering is to group WM fibers based on the brain regions they penetrate or pass. The specific clustering procedures for the bundles in the first group in Fig. 2b are summarized as follows. Step 1: for CC bundles, we extract all the fibers penetrating corpus callosum (WM region), the left and the right frontal lobes, and group them as CC1 in Fig. 2b. In a similar way, we extract CC2 that connects the left and right parietal lobes, and CC3 that connects the occipital lobes. Figs. 3a and b provide a visualization example of the fibers penetrating the CC and the clustered results for CC1, CC2 and CC3, respectively. Step 2: to cluster projection tracts, we remove all CC bundles obtained in Step1 from the fiber set first, and then select all of the fibers penetrating right internal capsule and right frontal lobe, which are parts of corticothalamic and corticofugal fibers, denoted as PTR1. Here PTR means Projection Tract Right. Similarly, we obtain the projection tracts that penetrate the right internal capsule and parietal and occipital lobes respectively, denoted as PTR2 and PTR3. The

Fig. 2. (a) Neuroanatomical regions used in this framework. (b) The list of 19 fiber bundles.

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Fig. 3. (a) Fibers penetrating white matter region—corpus callosum (Index 61 in Fig. 2a); (b) labeled fibers of (a) based on the regions they connect. (c) Fibers penetrating right PLIC (71) and ALIC (72); (d) labeled fibers of (c) based on the regions they connect; (e) Labeled bundles of (a) based on the regions they connect after changing the extraction order (from posterior to anterior). The green arrows point to fibers at transition regions.

corresponding projection tracts that penetrate the left internal capsule and frontal, parietal and occipital lobes are denoted as PTL1, PTL2 and PTL3 respectively, as listed in Fig. 2b. Figs. 3c and d provide a visualization example of the fibers penetrating the right internal capsule and the clustered results for PTR1, PTR2 and PTR3 respectively. Step3: for the cingulum tract (CG), we select all of the fibers passing the right cingulate regions and group them as CGR. The CGL is obtained similarly for the left cingulum tract. Fig. 4a shows an example of the grouped cingulum tract. Step 4: for the inferior fronto-occipital (IFO) fasciculus tract, we select those fibers passing the right frontal lobe and occipital lobe, and group them as IFOR. Fig. 4b shows an example of the grouped fibers passing the right frontal lobe and occipital lobe. The IFOL for the left hemisphere is obtained similarly. Step 5: for the inferior longitudinal fasciculus (ILF) tract, we select the fibers passing the right occipital and temporal lobe first as shown in Fig. 4c, and then remove those fibers belonging to the IFOR obtained in Step 4 and CC obtained in Step 1, and group the remaining fibers as ILFR as shown in Fig. 4d. The ILFL for the left hemisphere is grouped in a similar way. Through the aforementioned five steps, we obtain all of the 15 fiber bundles in the first group in Fig. 2b. As shown in Figs. 3 and 4, the top-down anatomy guided clustering approach extracts the 15 major WM bundles effectively, given the results of WM tractography and whole brain parcellation. Notably, we extract the bundles in the order of from inside to outside, superior to inferior, anterior to posterior, and left to right. Also, it should be noted that the brain parcellation step (Liu et al., 2004, 2006) is performed directly on the brain tissue segmentation map on the DTI image space (Liu et al., 2007), thus avoiding the possible alignment errors in co-registration of MRI and DTI data (Liu et al., 2006). To evaluate how the bundle extraction order influences the fiber clustering result, we changed the extraction order of CC from posterior to anterior. As shown in Fig. 3e, we can see very few fibers in the transition areas (highlighted by the green arrows) that have different labels compared to the result in Fig. 3a. Quantitatively, the number of fibers with different labels is quite small, which is less than 1.5% of the total fibers.

Bottom-up similarity-based clustering approach As mentioned before, the fiber bundles in the second group in Fig. 2b are twisted with the surrounding fibers closely, and it is difficult to extract them only based on the information of brain regions they penetrate. For example, Fig. 5a shows all the fibers penetrating right front lobe and temporal lobe (denoted as set A). In set A, there are several bundles including the uncinate fasciculus (UF), superior longitudinal fasciculus (SLF), and inferior fronto-occipital fasciculus (IFO). Because IFO has already been obtained in the first group in Fig. 2a, we can remove them from set A to make the problem easier to handle. Fig. 5b shows the result after removing IFO (denoted as set B). However, it is apparent that the remaining fibers still twist together closely. To separate them, we apply an automated and robust similarity-based clustering method as follows. First, a nonlinear method of kernelprincipal component analysis (PCA) is used to project the fiber curves of set B onto the principal component space of the kernel vectors. Then, a fuzzy c-mean (FCM) algorithm is applied to automatically group the fibers in the feature space. To determine the optimal number of classes, the GAP statistics is adopted (Tibshirani et al., 2000). Finally, based on the fiber end point distributions and the fiber bundle shape patterns, we can separate and recognize IFO and UC automatically. Kernel-PCA projection. Kernel-PCA is used to project the nonlinear fiber tracts onto a linear kernel space to reduce the dimensionality of the variables. The Hausdorff distance (Corouge et al., 2004) is used as the fiber similarity metric in calculating the kernel-PCA. In O'Donnell and Westin (2005), the authors revised it to a symmetric one to retain certain information when the fiber length is mismatched. Here, we adopt a similar technique and incorporate a length mismatch factor wm,n similar (Ding et al., 2003) to give penalty to fibers with different lengths. The kernel function is defined as,
 V Km;n = wm;n exp −dm;n = σ

ð1Þ

where wm,n = sm,n/(sm + sn – sm,n) is the length mismatch factor. sm,n is the length of corresponding segment of fiber m and n. The corresponding segment is part of one fiber that has point-wise correspondence to part of another fiber. sm and sn are the lengths of fiber m and

Fig. 4. (a) Fibers penetrating cingulum (70); (b) fibers penetrating right front lobe (73) and occipital lobe (75) at the same time. (c) Fibers penetrating right occipital lobe (75) and temporal lobe. (d) Right ILFR.

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Fig. 5. An example of similarity-based fiber clustering results in the kernel space. (a) Fibers penetrating right frontal and temporal lobe, denoted as set A. (b) Fibers after removing IFOR from set A, denoted as set B. (c) Clustering results in the feature space. (d) The fibers are classified into 4 groups. The bundle colors correspond to those in (c).

  V n, respectively. dm;n = dm;n + dn;m = 2; dm,n is the Hausdorff distance, dm;n = maxpk aFm minplaFn jjpk − pl jj; and pk,pl are two points along the fibers. PCA is then performed on the kernel space K, and each column vector ki of K is projected to a lower dimensional space:
 T bi = Φ ki − k ; i = 1; N ; N ð2Þ where each column of Φ is an eigenvector of the covariance matrix of K and k̄ is the mean column vector. In this paper, σ is set as 1 voxel width. In kernel-PCA, the first 3 dimensions are chosen, which cover more than 99% energy of the whole space. After kernel-PCA, each fiber is represented as a feature vector b in the kernel-PCA space, and the FCM clustering algorithm is used to classify them into different groups. Fiber clustering by fuzzy c-means. The fuzzy c-means algorithm is applied to cluster the fibers into different groups. Suppose there are C classes, the objective function is defined as: E=

I C n o X X 2 μ i;j ‖bi −cj ‖

ð3Þ

i=1 j=1

Pc

where the fuzzy membership function μi,j is subject to j = 1 μ i;j = 1, and cj is the centroid of class j. To determine the optimal number of classes, the GAP statistics (Tibshirani et al., 2000) is employed. Basically, the GAP statistics are calculated by increasing the number of classes in Eq. (3), and the best C is determined that gives the largest change of GAP statistics when we change the number of classes from C to C + 1. Fig. 5 shows an example of the clustering results, and axes P1, P2 and P3 stand for the first three principal components. Fiber labeling by feature-based recognition. To recognize the SLF and UC bundles from the clustering result in Fig. 5d, we developed a feature-based recognition algorithm. First, using the manual fiber bundle extraction method in Wakana et al. (2007), we extract the SLF and UC bundles manually in our training dataset. Then, for each fiber end point of the labeled bundles, a closest voxel in the GM regions is identified and the GM label (obtained in step 3 in Fig. 1a) is assigned to the fiber end point as its anatomic landmark. The anatomic Table 1 The spatial matching ratio (SMR) and spatial volume agreement (SVA) results for one randomly selected case. CGR CGL IFOR IFOL ILFR SMR (%) 86.7 87.5 87.8 81.9 SVA (%) 96.7 97.2 97.8 98.2

ILFL

SLFR SLFL UCR

78.0 87.2 85.3 99.0 95.2 98.8

81.5 97.7

UCL

Average

98.3 95.9 87.1 99.2 97.9 97.8

landmark distribution of the end points of each manually labeled bundle is analyzed. Fig. 6 shows the end point landmark histograms for the bundle SLFR and UCR. Take the SLFR as an example, the bundle feature, denoted as Ps, is defined as: Ps =

N 1X H si N i=1

ð4Þ

where N is the number of training dataset (here N = 5); Hsi = ½h1 ; h2: : :h60  is the histogram of end point landmark distribution in 60 GM regions (for a complete list of these region names, please refer to Fig. 2a). Fig. 6a shows the histogram of end point landmark distribution for SLFR. Fig. 6c shows the bundle feature of SLFR obtained from Eq. (4). Similarly, Fig. 6b and d are the results for UCR. It is apparent that the bundle features for SLFR and UCR are quite different. The underlying premise of this feature definition is that fiber bundles can be uniquely identified by their connectivity patterns, that is, the brain regions they connect. With these unique bundle features, we can accurately label SLFR and UCR, as well as for SLFL and UCL. It should be noted that the clustering of bundles in the second group was performed purely based on a bottom-up approach while the recognition of them was aided by the gray matter (GM) landmarks. Therefore, clustering and recognition are two consecutive procedures in dealing with the second group of bundles. The similarity-based bottom-up fiber clustering approach is the prerequisite of the second step of landmark feature-based recognition. Without the clustering of those fibers, we cannot define the landmark-based features for each bundle. In other words, we can only define and have the bundle features for SLFR and UCR after the SLFR and UCR are clustered. The top-down approach cannot cluster the SLFR and UCR bundles without the similarity-based bottom-up approach. Results In this section, we present experimental results of the evaluation of the proposed computational framework of fiber bundle clustering and labeling. Experiment 1: visual evaluation The proposed fiber bundle clustering and labeling framework was applied to 10 testing DTI datasets and each subject's WM fibers are clustered into 19 bundles. The DTI data was acquired on a Philips 1.5 T Intera using 15-direction diffusion encoding, with b = 0 and b1 = 860 s/mm2. For more details of the DTI imaging parameters, please

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Fig. 6. Bundle feature extraction. (a) SLFR end point landmark distribution. (b) UCR end point landmark distribution. (c) Feature of SLFR. (d) Feature of UCR.

referred to Hunter et al., 2006. We performed expert visual evaluation. As shown in the fiber clustering results for 4 randomly selected cases in Fig. 7, it is evident that most of the bundles are reasonably clustered and labeled. For example, the fibers penetrating corpus callosum are consistently clustered in those bundles connecting the frontal, parietal and occipital lobes in different subjects, demonstrating that the proposed computational framework is quite effective in clustering WM fibers into bundles. Here, each of the 19 bundles is labeled by one distinct color, and the colors in different subjects are in correspondence. Experiment 2: SLF and UC labeling To evaluate the bundle labeling method the section of fiber labeling by feature-based recognition, we visually evaluated all of

the 10 cases of testing DTI dataset, and found that both of the SLF and UC were reasonably separated and successfully recognized. Fig. 8 shows the bundle labeling result of SLF and UC for one randomly selected case, which is similar to those in Fig. 6. It is also evident that the bundle feature histograms for these bundles are quite similar to those corresponding ones of training samples in Fig. 6, which significantly contributes to the successful recognition of these fiber bundles. The Euclidean distance between the SFL pattern and the feature histogram of the recognized SLF for this case is 0.1, and that for UC is 0.08. This quantitative result further demonstrates that the feature histograms for both SFL and UC are quite distinctive in description of these bundles, resulting in the successful recognition of all of SFL and UC bundles in the 10 testing DTI dataset.

Fig. 7. Result of bundle clustering and labeling for 4 subjects. Left and superior views are presented. Each bundle is labeled with a different color.

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Fig. 8. An example of SLFR and UCR labeling for one case. (a) SLFR end point distribution. (b) Labeled SLFR. (c) UCR end point distribution. (d) Labeled UCR.

Experiment 3: quantitative evaluation

two binary images. The spatial volume agreement for two bundles is defined as:

To quantitatively evaluate the proposed framework, we calculate the spatial matching ratio (SMR) and spatial volume agreement (SVA) between automatically clustered bundles and manually labeled bundles according to the guidelines in Wakana et al. (2007). Since there are totally 10 bundles which have corresponding manual extraction guidelines in Wakana et al. (2007), we only performed the quantitative evaluations for those 10 bundles (bundles 10–19 in Fig. 2b). Other 9 bundles are not included in this evaluation. We first converted all of the fiber bundles to a binary image, where voxels that the bundles penetrate are marked as 1, and other voxels are marked as 0. Then, the spatial matching ratio of two bundles is defined as:

   j V ðIa Þ − V ðIm Þj  AðBa ; Bm Þ = 1 − V ðI Þ + V ðI Þ 

MðBa ; Bm Þ =

V ðIa \ Im Þ V ðIa [ Im Þ

ð5Þ

where Ba is the automatically extracted bundle, Bm is the bundle by manual labeling, Ia is the binary map for Ba and Im is that for Bm,V() represent the non-zero voxel volume, the ∩ operator takes the intersection of two binary images, and ∪ operator takes the union of

a

ð6Þ

m

The average results of SMR and SVA for these bundles are shown in Table 1. It is apparent that the SMR and SVA are quite high for all of these 10 bundles. The average SMR and SVA are 87.1% and 97.8% respectively, demonstrating the good performance of the automated fiber clustering approach, compared to manual labeling. As an example, Fig. 9 shows the visualization of fibers clustered by automatic and manual clustering for one randomly selected case. By visual inspection, the manual clustering of WM fibers is quite close to the automatic clustering result. Quantitatively, Fig. 10 shows the volumes of 10 bundles and the volume overlaps between manual and automated clustering approaches for this case. The volumes for automated clustering approach, volumes for manual approach, and volumes of the overlap between the two approaches of these 10 bundles are (11.02, 11.77, 10.58), (31.64, 29.92, 28.73), (133.27, 139.32, 127.44), (63.50, 61.24, 56.16), (149.36, 146.45, 129.60), (66.85, 60.70, 59.40), (65.66,

Fig. 9. Visualization of automatically and manually labeled bundles. (a) Automatically labeled bundles in the right hemisphere. (b) Manually labeled bundles in the right hemisphere.

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Fig. 10. Volumes of 10 bundles in one case. Three different colors represent the bundle volumes obtained by the automatic and manual clustering methods, and the overlap volume between them.

64.04, 59.72), (16.09, 16.85, 14.80), (31.86, 32.40, 31.86), and (50.54, 52.70, 50.54), respectively. Here, the unit is 100 mm3. It is evident that the volume overlaps are quite high, demonstrating the relatively good performance of the proposed approach. Fig. 11 shows the SMR and SVA measurements for the 10 bundles averaged over 10 DTI datasets. Evidently, the average SMR (0.887± 0.04) and SVA (0.981 ± 0.008) are quite high, indicating the good performance of the proposed fiber clustering and labeling framework. Fig. 12. The comparison of the proposed automated method and manual labeling. The average FA and ADC values and their deviations of 10 labeled bundles in a randomly selected case are shown in (a) and (b) respectively.

Experiment 4: quantitative analysis for DTI scale metrics Quantitative diffusivity analysis of neuro-bundles has important applications in study of many brain diseases. In this experiment, we evaluate the accuracy of tract-based quantitative diffusivity analysis using our methods. Fig. 12 shows the average FA and ADC values of 10 bundles obtained by the proposed automatic method and expert manual labeling for a randomly selected case respectively. It can be seen that the difference between the automatically labeled result by our method and manually labeled result is quite small. For the purpose of quantitation, the scale metrics difference (SMD) is defined as: DðBa ; Bm Þ =

j Sa − Sm j Sm

ð7Þ

where Sa is the average value of a DTI metric, such as FA or ADC, in a bundle obtained by the proposed automatic method, and Sm is that for bundles obtained by expert manual labeling. Table 2 shows the SMD

results for one case. It is apparent that the average SMD is quite small (b1%), indicating that the tract-based analysis using our method is accurate, in comparison with expert manual labeling. Discussions and Conclusion In this paper, we proposed a hybrid approach to WM fiber clustering and labeling. The top-down anatomy-guided fiber clustering step in this computational framework is based on the brain parcellation results obtained by an atlas-based warping algorithm (Liu et al., 2004), which means the WM fiber clustering result is dependent on the performance of the brain parcellation algorithm. Although the hybrid volumetric and surface warping method (Liu et al., 2004) used in this paper has reasonably good performance in parcellating human brains, improved brain parcellation and recognition algorithm in the future could potentially improve the performance of the anatomy-guided WM fiber clustering step in this paper. For example, we are working towards a self-contained brain parcellation and recognition system that can potentially provide improved accuracy and reliability in segmentation and recognition of cortical structures by following the cortical folding patterns (Li et al., 2009a). We expect that this improved cortical structure segmentation can improve the top-down anatomy-guided fiber clustering. In this paper, the structural MNI brain atlas (GM/WM regions) was used to parcellate the brain via the atlas-based warping algorithm (Liu et al., 2004). An alterative methodology is to apply an atlas-based registration and warping method on DTI images of human brain. For example, we developed a diffusion tensor registration algorithm in Li et al. (2009b) by simultaneous consideration of spatial deformation

Table 2 The FA and ADC difference between the proposed automatic method and manual labeling for a randomly selected case. Difference CGR CGL IFOR IFOL ILFR ILFL SLFR SLFL UCR UCL (%)

Fig. 11. The average SMR (a) and SVA (b) for 10 bundles over 10 cases.

FA ADC

1.46 1.02 0.65 1.18 1.44 1.75 0.43 0.01 0.05 0.14 0.55 0.06 1.28 0.06

Average

1.05 0.08 0.26 0.93 0.17 0.11 0.30 0.35

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and tensor orientation in DTI images. This DTI image registration algorithm can potentially be used in the future to parcellate a subject's white matter into detailed structures by warping a WM atlas such as the one in Mori et al. (2005). This WM parcellation methodology may provide an alterative approach to, or potentially improve current anatomy-guided WM fiber clustering algorithm in this paper. It should be noted that the proposed computational framework of fiber clustering depends on the DTI tractography results. Currently, we use the streamline tractography method implemented in the DTIStudio software package distributed by the Johns Hopkins University. In the future, we will investigate how different tractography algorithms will affect the WM fiber clustering procedures in this paper. Also, different DTI imaging parameters such as spatial resolutions will be used to evaluate how this computational framework is sensitive to different imaging settings. Reproducibility studies will be carried out by performing the computational framework on DTI images of the same subject with different imaging settings in the future. In current study, only 19 bundles are involved in the WM fiber clustering process. However, there are other important WM bundles, such as fimbria and stria terminalis, which are not included in the current WM clustering procedure. The reason is that these WM bundles are relatively small, and successful clustering of them is heavily influenced by such factors as image quality, tractography method, and fiber tracking parameter. At current stage, our computational algorithms are not robust enough to extract these small WM fiber bundles. In the future, we will apply more detailed brain atlas in the anatomy-guided fiber clustering to deal with this issue. Tract-based WM fiber analysis is increasingly important to study the changes of WM bundles associated with brain diseases (Pagani et al., 2005; Corouge et al., 2006; Smith et al., 2006; Maddah et al., 2008; O'Donnell et al., 2009). Our future work will apply the proposed computational framework to study the possible WM disruptions in brain diseases such as Alzheimer's disease, autism, and schizophrenia. Also, it will be of interest to apply this computational framework to the study of longitudinal WM changes occurring in these chronic brain diseases. Acknowledgments This research work was supported by The Methodist Hospital Research Institute and the NIH Grant 5G08LM008937 (STCW). The authors would like to thank Kaiming Li from UGA for proof reading of the manuscript. References Alexander, A.L, Lee, J.E., et al., 2007. Diffusion tensor imaging of the corpus callosum in autism. Neuroimage 34, 61–73. Alexander, D.C., Pierpaoli, C., Basser, P.J., Gee, J.C., 2001. Spatial transformations of diffusion tensor magnetic resonance images. IEEE Trans. Med. Imag. 20, 1131–1139. Barnea-Goraly, N., Kwon, H., Menon, V., et al., 2004. White matter structure in autism: preliminary evidence from diffusion tensor imaging. Biol. Psychiatry 55, 323–326. Basser, P.J., Jones, D.K., 2002. Diffusion tensor MRI: theory, experimental design and data analysis-a technical review. NMR Biomed. 14, 456–467. Basser, P.J., Mattiello, J., Le Bihan, D., 1994. MR diffusion tensor spectroscopy and imaging. Biophys. J 66, 259–267. Bozzali, M., Falini, A., Franceschi, M., Cercignani, M., Zuffi, M., Scotti, G., Comi, G., Filippi, M., 2002. White matter damage in Alzheimer's disease assessed in vivo using diffusion tensor magnetic resonance imaging. J. Neurol. Neurosurg. Psychiat. 72, 742–746. Brun, A., Knutsson, H., Park, H.J., Shenton, M.E., Westin, C.-F., 2004. Clustering fiber tracts using normalized cuts. Seventh International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI 04), Lecture Notes in Computer Science. InRennes–Saint Malo, France, pp. 368–375. September. Chang, Bernard S., Katzir, Tami, Liu, Tianming, Corriveau, Kathleen, Barzillai, Mirit, Apse, Kira A., Bodell, Adria, Hackney, David, Alsop, David, Wong, Stephen, Walsh, Christopher A., 2007. A structural basis for reading fluency: White matter fiber tracts and reading disability in a neuronal migration disorder. Neurology 69, 2146–2154. Corouge, I., Gouttard, S., Gerig, G., 2004. Towards a shape model of white matter fiber bundles using diffusion tensor MRI. ISBI'04 344–347. Corouge, I., Fletcher, P.T., Joshi, S., Gouttard, S., Gerig, G., 2006. Fiber tract-oriented statistics for quantitative diffusion tensor MRI analysis. Med. Image Anal. 10 (5), 786–798.

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