directly segment the thalamic nuclei in standard 3T T1-weighted images using ... with seven subjects by comparing the shape-based segmentations on 3T.
Thalamic Nuclei Segmentation in Clinical 3T T1-weighted Images Using High-Resolution 7T Shape Models Yuan Liu, Pierre-François D'Haese, Allen T. Newton, Benoit M. Dawant Dept. of Electrical Eng. and Comp. Science, Vanderbilt University, Nashville, TN, USA ABSTRACT Accurate and reliable identification of thalamic nuclei is important for surgical interventions and neuroanatomical studies. This is a challenging task due to their small sizes and low intra-thalamic contrast in standard T1-weighted or T2weighted images. Previously proposed techniques rely on diffusion imaging or functional imaging. These require additional scanning and suffer from the low resolution and signal-to-noise ratio in these images. In this paper, we aim to directly segment the thalamic nuclei in standard 3T T1-weighted images using shape models. We manually delineate the structures in high-field MR images and build high resolution shape models from a group of subjects. We then investigate if the nuclei locations can be inferred from the whole thalamus. To do this, we hierarchically fit joint models. We start from the entire thalamus and fit a model that captures the relation between the thalamus and large nuclei groups. This allows us to infer the boundaries of these nuclei groups and we repeat the process until all nuclei are segmented. We validate our method in a leave-one-out fashion with seven subjects by comparing the shape-based segmentations on 3T images to the manual contours. Results we have obtained for major nuclei (dice coefficients ranging from 0.57 to 0.88 and mean surface errors from 0.29mm to 0.72mm) suggest the feasibility of using such joint shape models for localization. This may have a direct impact on surgeries such as Deep Brain Stimulation procedures that require the implantation of stimulating electrodes in specific thalamic nuclei. Keywords: Thalamic nuclei segmentation, shape models, 7T, computer-assisted surgery, functional surgery
1. INTRODUCTION The thalamus serves as the central relay station for the brain that processes and relays sensory and motor signals between different subcortical regions and the cerebral cortex. It can be divided into several neuronal clusters referred to as nuclei, each possibly subdivided into sub-nuclei. A number of diseases, including Parkinson’s disease, multiple sclerosis, and chronic pain syndrome, are associated with some of these nuclei [1-3]. Stimulating by means of Deep Brain Stimulation electrodes or ablating by means of radiosurgery specific nuclei, e.g., the ventral intermediate nucleus for movement disorders, can reduce symptoms associated with these diseases [4]. Thalamic nuclei are traditionally identified by their distinct cyto- and myelo-architecture on histology [5]. Surgical planning which targets these nuclei is often based on pre-operatively acquired magnetic resonance (MR) images using T1-weighted (T1-w) or T2-weighted (T2-w) sequences. Unfortunately, direct anatomical delineation of such nuclei in these images is challenging due to their small size and low intra-thalamic image contrast. As an alternative, diffusion tensor MR-imaging (DTI) has been used to detect the orientations of neuronal pathways. By assessing local tensor inhomogeneity or cortical structural connectivity patterns, the thalamus can be parcellated into different nuclei [6-8]. In addition to DTI, others seek to segment the nuclei based on the functional connectivity in the thalamo-cortical system, either via task-related functional MRI (fMRI) [9] or resting state fMRI [10]. These techniques, however, require additional scanning and suffer from the low spatial resolution and signal-to-noise ratio (SNR) of clinical DTI and fMRI, as well as from high fiber orientation variability for DTI. Results obtained with these techniques also need further validation because they typically lack a ground truth. To validate those segmentations and provide reliable information for surgical procedures, many on-going efforts are dedicated to developing novel imaging protocols to enhance the intra-thalamic contrast. Rapid development of high-field MR imaging techniques has led to improvements in image quality with higher resolution and SNR. For instance, Newton et al. have recently proposed an approach for thalamus imaging at 7T, which relies on acquiring various magnetizationprepared rapid acquisition gradient-echo (MPRAGE) images with different TI values and susceptibility weighted images
(SWI) [11]. However, the long scanning time required by these methods and the clinical unavailability of high-field imaging prevent their clinical use. Despite the difficulties in clinical translation, high field images with improved image qualities could be used to produce a set of image volumes commonly referred to as atlases in which the structures are localized. Atlas-based techniques could then be used to project these structures onto the clinical 3T T1-w image through image registration. Registration between atlases and clinical images are usually accurate and reliable in high-contrasted regions, but in homogenous regions such as in the thalamus, the transformations are mainly controlled by the smoothness of the deformation field. Because of this, the shape of the intra-thalamic structures may not be preserved when projected from the atlas to the target volume, thus resulting in inaccurate localization of those nuclei and unrealistic shapes. In this paper, we propose an alternative approach, which is to segment thalamic nuclei in clinically acquired 3T images using statistical shape models. We manually segment thalamic nuclei from a set of high-field sequences acquired as in [11] and build high-resolution shape models from a group of subjects. We then test the hypothesis that the shapes of these nuclei can be localized by fitting these models in a hierarchical fashion, starting with the boundary of the thalamus.
2. METHODS In this section of the paper, we present our methods for thalamic nuclei segmentation. First, we discuss the images we have acquired, the thalamic structures we have delineated and their hierarchical relationship. In the following sections we detail our methods for building the statistical shape models and for hierarchically fitting these models to infer the boundary of the nuclei. 2.1 Image data In this study, seven healthy subjects (five male, two female) have been scanned using a 7T whole body MRI scanner with a 32 channel receive-only head coil. For each subject, three different types of images have been acquired. These include a standard T1-w image, a set of MPRAGE sequences, and high resolution SWIs. The T1-w image is acquired
(a)
(b)
(c)
(d)
(e)
(f)
Figure 1. A slice of all the images that have been acquired for one subject. Top left panel (a) is the 3T T1-w image. Panels (b)-(e) show a series of 7T images acquired with different parameters; these are T1-w, MPRAGE (TI=400), MPRAGE (TI=640), MPRAGE (TI=960), MPRAGE (TI=1120), axial SWI, and coronal SWI, respectively. All images show the same half brain region to illustrate the range of contrast achievable when varying acquisition parameters. Panel (f) shows contours that have been manually delineated by combining the information provided by the multiple image volumes.
with 352×352×350 voxels and 0.7mm isotropic voxel size in the axial direction. The MPRAGE sequences are acquired by varying TI values with an inversion prepulse (FOV=246×246×174.3mm, voxel=0.7×0.7×0.7mm, TR/TE/TIs=4.74/2.1/ 400, 640, 960, and 1120ms, shot interval=4500ms). The SWIs are acquired both axially and coronally using slice selective gradient echo (FOV= 240×180mm, voxel=0.24×0.24×1mm, #sl=60, θ=45°, TR/TE=1952.3/23.1ms). Each of the sequences is rigidly registered to the T1-w to be overlaid in our visualization and segmentation tool for manual delineation of the thalamus and thalamic nuclei. Alongside with the 7T acquisition, a T1-w MR volume has also been acquired at 3T with 256×256×170 voxels and 1 mm isotropic voxels (TR=7.92ms, TE=3.65ms). This clinical 3T T1-w volume serves as the target image for automatic segmentation of thalamic nuclei. Figure 1 shows a portion of one slice in the deep brain in all images for one volunteer, with the panel (a) being the clinical 3T T1-w image and panels (b)-(e) the seven 7T sequences. 2.2 Thalamic nuclei groups Figure 1 illustrates the range of contrast that can be achieved and the complementary nature of the series of images for the visualization of the deep brain nuclei. Individual nuclei were manually segmented based on manual analysis of individual images as well as images in combination, and the locations of nuclei were compared to those of the Morel atlas [5]. Based on the available contrast information, a total of 19 substructures have been delineated. Their names and their spatial hierarchy as suggested by Morel et al. [5] are shown in Figure 2. These include (I) the anterior ventral dorsal nucleus (AVD), the anterior medial nucleus (AM), and the lateral dorsal nucleus (LD) from the anterior group; (II) the mediodorsal nucleus (MD), the central medial nucleus (CeM), the habenula (Hb), and the ventral tier from the medial group, where the ventral tier contains (i) the parafascicular (Pf), (ii) the centre median (CM), and (iii) the central lateral nucleus (CL); (III) the ventral anterior nucleus (VA), the ventral lateral nucleus (VL), and the ventral posterior lateral nucleus (VPL) from the lateral group, where the VL is subdivided into (i) the ventral lateral anterior nucleus (VLa) and (ii) the ventral lateral posterior nucleus (VLp); (IV) pulvinar (Pu), the lateral posterior nucleus (LP), and the limitans (Li) from the posterior group, where the pulvinar is subdivided into (i) the anterior pulvinar (PuA), (ii) the lateral pulvinar (PuL), (iii) the medial and inferior pulvinar (PuMI); (V) the mammillothalamic tract (mtt) from the thalamic fiber tracts. 2.3 Statistical shape model creation Our goal is to segment the thalamic nuclei in clinically available 3T T1-w images, in which these nuclei are not visible. As in clinical images only the external boundary of the thalamus can be visualized, we test the hypothesis that models built from high field images that are fitted to the thalamus can predict the location of thalamic nuclei. We use standard statistical shape models [12] to capture the shape variations. This requires localizing homologous points across shapes, estimating the covariance matrix of these points, and computing the eigenvectors of this covariance matrix, which are called eigenshapes or modes of variation. 2.3.1 Correspondence establishment To establish the point correspondence between training shapes, we randomly select one subject from the set of training subjects as the reference/atlas volume and we register the other subjects to this volume using the 7T T1-w images. A a. Perform global affine, local affine, and non-rigid registration of training volumes to reference volume b. Project reference surfaces into training subject space using transformations in (a) c. Register the projected thalamus surfaces to the subject’s thalamus surface d. Calculate a TPS transformation from the registration result in (c) e. Apply this TPS transform to the rest of projected reference surfaces in (b) f. Register the transformed surfaces from (e) to the subject’s segmented surfaces Figure 2. Hierarchical relationship of the thalamus and the thalamic nuclei.
Figure 3. Establishment of point correspondence for surfaces in the training set.
three-step image registration process is performed, including 1) a global affine registration using an intensity-based technique with mutual information as a similarity measure [13-14], 2) a local affine registration which restricts the computation of the mutual information to the deep brain region, and 3) a nonrigid registration using the Adaptive Bases Algorithm [15]. Structures in the atlas, represented as triangulated meshes, can be projected onto the subject space using the inverses transformations. Correspondence for the thalamus is established first by non-rigidly registering the thalamus surface projected from the atlas to segmented surface in the subject’s volume. This is done with an automated algorithm developed in house that acts as a 3D snake [16] and minimizes the surface distances while preserving the smoothness and curvature of the mesh. This outputs a surface that aligns almost perfectly with the subject’s segmented surface. Vertex correspondence between these surfaces is thus established. We also estimate a thin-plate-spline (TPS) transformation [17] from this non-rigid surface registration and this transformation is used to establish point correspondences for the internal structures. Correspondence for the internal thalamic structures is established by projecting surfaces from the atlas using imagebased transformations, followed by the previously estimated TPS transformation. A non-rigid surface registration is then performed between the transformed surface and the manual surface of the subject. Occasionally this surface registration algorithm fails because of large shape differences between two meshes. When this is the case, we manually adjust the transformed surface to bring it closer to the subject’s manual surface, and re-run the surface registration algorithm. Repeating this process correspondence for all structures between the training subjects is established. This is illustrated in Figure 3. 2.3.2 Joint hierarchical modeling To model the relationship between the thalamus and the nuclei, a straightforward way would be to build a large shape model that contains the thalamus and all the 19 nuclei. However, incorporating so many structures into one model increases its complexity, which could not be captured with the size of the training set we currently have. Therefore, instead of jointly modeling all the 19 nuclei with the thalamus we use a hierarchical approach that follows the decomposition shown in Figure 2. Starting at the top level of the hierarchy, we first jointly model the thalamus and the general nuclei groups. At the next level, each group is jointly modeled with its subdivisions, and the process is repeated until the leaf nodes are reached. The individual shapes at each hierarchy level are shown in Figure 4. To group the nuclei as specified in Figure 2 and illustrated in Figure 4, we combine the surfaces of the nuclei in this group into one mesh but remove the inner boundaries where two nuclei are adjacent to each other. Identification of vertices that belong to inner boundaries is done on the reference subject by computing the distance from each vertex to each other surface based on its distance map obtained by a fast marching method [18]. Once such vertices are identified, this is subsequently applied to the rest of the subjects via the established vertex correspondence.
Figure 4. Individual shapes used for modeling at each level. For each the left is a 3D visualization and the right a coronal view overlaid on one slice.
2.3.3 Modes of variation estimation Once correspondence is established and joint relationships are determined, training surfaces can be rigidly registered to the reference surfaces with 7-DOF transformation (three rotations, three translations, one isotropic scaling) using a standard Procrustes approach [19]. This is performed separately for individual joint models, i.e., only the surfaces involved in this model are co-registered to build this particular model. This allows measuring the anatomical variations of thalamic structures at different scales using different models across the training set. To build the shape model, we
perform the following procedure as described by Cootes et al. [12]. First a mean shape of the co-registered corresponding point set is extracted and the covariance matrix is computed as the deviation of the point set from the mean shape. The eigenvectors of the covariance matrix represent the modes of variation and their associated eigenvalues the explained variance in the training set. A new shape can then be approximated by adding a linearly weighted sum of the eigenvectors within three standard deviations of the mean to the mean shape: 𝑥 = 𝑥̅ + 𝑃𝑏
(1)
where 𝑥̅ is the mean shape, 𝑃 is a set of modes of variation, and 𝑏 is the parameters that determines the new shape 𝑥. Figure 5 shows an example of such shape model, which jointly models the VLa and the VLp. It presents the mean shape and its first three modes of variations. It appears that the first mode of the variation is capturing changes in anteriorposterior and left-right directions, the second mode in the superior-inferior direction, and the third mode in local structures. For this shape model, the first three eigenmodes explains 80% of the shape variation.
Figure 5. Instances of the statistical shape model for VLa and VLp. The middle row is the mean shape, and the rest of the shapes are generated by varying the first three modes of variation between +3√𝜆𝑖 (top row) and −3√𝜆𝑖 (bottom row) where 𝜆𝑖 is the corresponding eigenvalue. The mean shape is shown as a semi-transparent structure together with the shape variations.
2.4 Segmentation using the hierarchical shape model In this work, we assume that the thalamus as a whole has been segmented, which could be done with a number of tools such as FreeSurfer [20]. We estimate the position of the thalamic nuclei in the clinical 3T T1-w image given the thalamus and the shape models as inputs. 2.4.1 Shape initialization Given a segmentation of the thalamus surface in a new 3T volume, to use our models to segment the thalamic nuclei, we first establish a correspondence between the thalamus surfaces. This is achieved by means of image-based registration and surface-based registration, as we have done during the model creation stage. However in this case, the image-based registration is performed between the atlas 7T T1-w and the subject 3T T1-w images. 2.4.2 Hierarchical weighted fitting After the corresponding thalamus surface is estimated, a hierarchical shape fitting algorithm is applied to localize each nucleus. We start by fitting the joint model at the top level to the thalamus. This joint shape includes the thalamus and all general nuclei groups. The fitting to this joint model is done by weighting the thalamus surface points as 1 and the rest as 0. Neglecting the alignment, the shape 𝑥𝑛𝑒𝑤 estimated in a weighted fashion given the current joint shape 𝑥𝑐𝑢𝑟 is obtained by: 𝑥𝑛𝑒𝑤 = 𝑥̅ + 𝑃𝑏, 𝑏 = (𝑃𝑇 𝑊 𝑇 𝑊𝑃)−1 𝑃𝑇 𝑊 𝑇 𝑊 ∙ (𝑥𝑐𝑢𝑟 − 𝑥̅ )
(2)
where 𝑊 is a diagonal matrix formed by weights for each surface point, with value 1 for thalamus and 0 for the rest. This permits us to infer the position of the general nuclei groups. Subsequently, given the external boundary of the nuclei group estimated from the previous level, the internal boundary between the subdivisions of the group are inferred by fitting the external boundary to the corresponding joint shape model. After the shape fitting we have observed that the external boundary of the fitted thalamus did not exactly fall on the boundary of the segmented thalamus. We attribute this small fitting error to the small size of our training set. To correct for this fitting error, we estimate a TPS transformation between the original thalamus boundary and the fitted boundary and we apply it to all the boundary points localized by the model. This correction is performed after each shape fitting step, i.e., at each level in the hierarchy. 2.4.3 Validation We test our approach by performing segmentations on the 3T T1-w images of seven subjects in a leave-one-out fashion, i.e., the volume being segmented is left out of the model construction. This requires the 7T T1-w volume to be rigidly registered to the 3T T1-w volume and all manual structures delineated in 7T volumes projected to the 3T T1-w space for each subject. As one subject is randomly chosen to serve as the reference to establish the point correspondence, this one is excluded from testing, which leaves six leave-one-out rounds. As mentioned earlier, we assume the thalamus has already been well segmented, and we use this manual segmentation as an input to feed our algorithm. To validate the accuracy of our results, we compute dice coefficients and mean surface errors between the segmentations obtained with our method and the manual segmentations in the 3T space.
3. RESULTS Figure 6 presents qualitatively the results obtained with our method for one subject. The segmented meshes are rigidly transformed to the subject 7T space and overlaid on different 7T sequences for visualization. As this figure shows, our automatic segmentations agree well with the manual delineations while preserving realistic nuclei shapes.
Figure 6. Qualitative visualization of the thalamic nuclei segmentation. Top row is the manual delineation, and the bottom row is the results obtained by shape models. From left to right: segmentations overlaid on an axial SWI slice, a coronal MPRAGE slice with TI=640, a sagittal MPRAGE slice with TI=960, and their 3D visualizations in two different orientations.
Figure 7 and 8 show the dice coefficients and mean surface errors (MSE) (in millimeter) for each nucleus for the six leave-one-out segmentation results respectively. Table I reports the mean and the standard deviation (in parenthesis) of dice and MSE as well as the volume (in mm3 or voxel3) of the manual segmentations, all computed in 3T T1-w space.
For most of the nuclei, mean dice values range from 0.57 to 0.88 and MSE from 0.29mm to 0.72mm. For tiny and elongated structures with only around 20 voxel3 such as the Hb and Li, the dice coefficients suffer from low value and high variability. This is expected as dice values are sensitive to the size and the shape of the structures; a small deviation from the ground truth could result in small dice values. Their mean surface errors are also somewhat larger than the surface error of other structures. The worst results are obtained for the mtt fiber tract which is a tubular structure that runs ventro-dorsally and traverses the lateral thalamic group before reaching its terminal point. This is because the shape of the mtt and its relative position with respect other thalamus structures vary significantly across subjects, which cannot be captured well by the joint models. More image information is thus needed to constrain the internal boundary of the nuclei within the thalamus to improve the segmentation accuracy. Nevertheless, these are encouraging results for structures with sizes ranging from 43mm3 (AM) to 1215mm3 (VLp), especially for AVD, MD, VA, VLa, VLp, LP, PuMI, PuL with around 0.8 dice values and 0.5mm MSE.
Figure 7. Boxplot of dice coefficients of each nucleus for all six subjects.
Figure 8. Boxplot of mean surface errors (in millimeter) of each nucleus for all six subjects.
TABLE I. Mean and standard deviation of the dice and MSE of the segmentation result, as well as the volumes (in mm3 or voxel3) of the manual delineations of the thalamic nuclei. Name
AVD
0.77 (0.07) 0.42 MSE (0.11) 207 Volume (47) Dice
AM
LD
MD
CM
Pf
CL
CeM
Hb
VA
VLa
VLp
VPL
LP
0.58 (0.13) 0.47 (0.16) 43 (21)
0.72 (0.11) 0.37 (0.18) 164 (56)
0.83 (0.05) 0.52 (0.11) 821 (79)
0.67 (0.10) 0.65 (0.18) 207 (61)
0.57 (0.12) 0.38 (0.15) 65 (20)
0.58 (0.12) 0.56 (0.13) 586 (127)
0.71 (0.18) 0.29 (0.09) 75 (34)
0.36 (0.26) 0.73 (0.35) 25 (11)
0.76 (0.07) 0.48 (0.23) 385 (190)
0.76 (0.13) 0.50 (0.19) 227 (106)
0.85 (0.03) 0.46 (0.09) 1215 (241)
0.79 (0.06) 0.49 (0.10) 231 (56)
0.73 (0.09) 0.59 (0.31) 333 (63)
PuMI PuA 0.88 (0.04) 0.41 (0.13) 1123 (206)
0.60 (0.10) 0.72 (0.12) 146 (71)
PuL
Li
mtt
0.83 (0.04) 0.43 (0.16) 278 (119)
0.40 (0.19) 0.54 (0.18) 19 (6)
0.16 (0.12) 1.35 (0.58) 63 (23)
4. CONCLUSIONS In this paper, we have proposed a method for thalamic nuclei segmentation in a standard 3T T1-w image by relying on the shape of the thalamus and shape models jointly built to capture the relationship between the thalamus and the internal nuclei in a hierarchical fashion. On the testing subjects we have used in this study, the segmentations obtained with our method agree well with the manual delineations and also preserve realistic shapes, indicating the potential of such shape models to segment the internal nuclei. Although the 7T image taken as a set provide enough information for manual delineation of the internal nuclei, none of them alone is sufficient to localize the entire external boundary of each nucleus. This complicates the manual segmentation task and introduces error in the manual delineation. To quantify this error we need to repeat the manual segmentation, which we plan to do. Also, as indicated by the shape models, more training subjects are required to better capture inter-subject variations in our model. We are in the process of scanning more subjects in our 7T scanner to build better shape models. This paper presents results that can be achieved using only shape information for segmentation, i.e., the shape of the thalamus. In a traditional active shape framework, an iterative search is performed to drive each vertex of the surface to a well-contrasted boundary point while constraining the shape of the surface with the models. Unfortunately, in 3T T1-w image, limited contrast is available within the thalamus region. However, with specifically designed MR sequences that could be acquired in clinically acceptable time, this issue might be alleviated. A few anchor landmarks may be derived from the better-contrasted images to further guide the segmentation. Our current framework could be easily modified to account for such local appearance information if available. In the future, we plan to acquire 3T MPRAGE images to enhance the contrast in the thalamus region. We also plan to explore the utility of integrating structural diffusivity information provided by diffusion imaging into our framework.
5. ACKNOWLEDGEMENTS This work was supported by NIH grant R01-EB006136 from the National Institute of Biomedical Imaging and Bioengineering and Vanderbilt Initiative in Surgery and Engineering Fellowship. The content is solely the responsibility of the authors and does not necessarily represent the official views of this institute.
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