JBiSEJournal of Biomedical Science and Engineering1937-6871Scientific Research Publishing10.4236/jbise.2013.63A042JBiSE-29493ArticlesBiomedical&Life Sciences Automated measurement of three-dimensional cerebral cortical thickness in Alzheimer’s patients using localized gradient vector trajectory in fuzzy membership maps hiakiTokunaga1HidetakaArimura2*TakashiYoshiura3TomoyukiOhara4YasuoYamashita5KoujiKobayashi1TaikiMagome5YasuhikoNakamura1HiroshiHonda3HidekiHirata2MasafumiOhki2FukaiToyofuku2Division of Radiology, Department of Medical Technology, Kyushu University Hospital, Fukuoka, JapanDepartment of Health Sciences, Graduate School of Medical Sciences, Kyushu University, Fukuoka, JapanDepartment of Clinical Radiology, Graduate School of Medical Sciences, Kyushu University, Fukuoka, JapanDepartment of Neuropsychiatry, Graduate School of Medical Sciences, Kyushu University, Fukuoka, JapanDepartment of Health Sciences, Faculty of Medical Sciences, Kyushu University, Fukuoka, Japan* E-mail:arimurah@med.kyushu-u.ac.jp(HA);29032013060332733614 January 201322 February 2013 28 February 2013© Copyright 2014 by authors and Scientific Research Publishing Inc. 2014This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/

Our purpose in this study was to develop an automated method for measuring three-dimensional (3D) cerebral cortical thicknesses in patients with Alzheimer’s disease (AD) using magnetic resonance (MR) images. Our proposed method consists of mainly three steps. First, a brain parenchymal region was segmented based on brain model matching. Second, a 3D fuzzy membership map for a cerebral cortical region was created by applying a fuzzy c-means (FCM) clustering algorithm to T1-weighted MR images. Third, cerebral cortical thickness was three- dimensionally measured on each cortical surface voxel by using a localized gradient vector trajectory in a fuzzy membership map. Spherical models with 3 mm artificial cortical regions, which were produced using three noise levels of 2%, 5%, and 10%, were employed to evaluate the proposed method. We also applied the proposed method to T1-weighted images obtained from 20 cases, i.e., 10 clinically diagnosed AD cases and 10 clinically normal (CN) subjects. The thicknesses of the 3 mm artificial cortical regions for spherical models with noise levels of 2%, 5%, and 10% were measured by the proposed method as 2.953 ± 0.342, 2.953 ± 0.342 and 2.952 ± 0.343 mm, respectively. Thus the mean thicknesses for the entire cerebral lobar region were 3.1 ± 0.4 mm for AD patients and 3.3 ± 0.4 mm for CN subjects, respectively (p < 0.05). The proposed method could be feasible for measuring the 3D cerebral cortical thickness on individual cortical surface voxels as an atrophy feature in AD.

Alzheimer’s Disease (AD); Fuzzy C-Means Clustering (FCM); Three-Dimensional Cerebral Cortical Thickness; Localized Gradient Vector1. INTRODUCTION

Alzheimer’s disease (AD) is a major health and social problem in advanced countries with long life expectancy, such as Japan and the United States of America. According to recent estimates, as many as 2.4 million to 4.5 million Americans and 1.8 million Japanese have AD [1, 2]. AD is associated with atrophy of gray matter in the cerebral cortex, which leads to morphological changes, i.e., a decrease in the thickness of the cerebral cortex or an increase in the volume of cerebrospinal fluid (CSF) in the cerebral sulci and lateral ventricles (LVs), which can be measured in magnetic resonance (MR) images. Furthermore, the atrophy of gray matter occurring in early stages of AD is localized to specific regions such as the hippocampus, amygdala, entorhinal area, and medialtemporal cortex [3,4]. Querbes et al. [5] reported that patients with AD in early stages can be diagnosed using a normalized thickness index-based criterion. Because palliative medicines can delay the progression of AD, early diagnosis and treatment are highly important [6,7]. Therefore, neuroradiologists attempt to subjectively estimate the degree of atrophy by analyzing atrophic morphological changes on MR images such as the cerebral cortical thickness, but a diagnosis based on such analysis is not quantitative or reproducible.

Several methods have been developed for quantitative measurement of cerebral cortical thickness between the white matter and cortical surfaces based on the analysis coupled surfaces propagation using the level set method [8], Laplace’s equation from mathematical physics [9], the average least distance [10], the distance between linked vertices [11], and normal vectors derived using the level set method [12].

In the method of Jones et al. [9], the cortical thicknesses were measured by means of gradient vector trajectries in a virtual electromagnetic field, which was constructed to be analogous to the neuronal sublayers between the cortical surface and white matter surface. Their method, in which the gradient vectors were orthogonal to the nested sublayers, is considered to be reliable. Acosta et al. [13] developed a voxel-based method that is both accurate and computationally efficient by extending Jones’s method to a Lagrangian-Eulerian approach. A hollow sphere with an inner radius of 20 mm and external radius of 23 mm has a cortical thickness of 3 mm similar to the cerebral cortex, was constructed to evaluate their method. Their results showed that the cortical thickness was 3.04 ± 0.02 mm with a voxel size of 1 mm, which seems to be accurate and reliable. Therefore, in this study we adopted Jones’s basic idea for the measurement of the cortical thickness, which is to use the trajectory of the gradient vector in some 3D space, but we used a different method for calculating the gradient vectors.

Previous methods for measuring cortical thickness depended on the accuracy of determination of the boundary between the cerebral cortex and white matter regions. However, it can be very difficult to determine the boundary in the case of diffuse neuronal cell death, since the edges of white matter regions may be blurred or voxels of the cortex and white matter in the boundary may be mixed, making them appear fuzzy. In addition, past studies have not considered the voxel value information in MR images, which could include the atrophy information in the cerebral cortex. To overcome these issues, we employed fuzzy c-means (FCM) clustering [14-17]. We assumed that the 3D membership map in the FCM clustering can express the fuzzy boundary between the cerebral cortex and white matter regions, and the fuzzy framework can incorporate voxel value information related to the AD atrophy.

Our purpose in this study was to develop an automated method for measuring the 3D cerebral cortical thicknesses in AD patients based on 3D fuzzy membership maps derived from T1-weighted images, which includes atrophy information in the cerebral cortical regions. In the proposed method, the boundary between the cortical and white matter regions is determined on each cortical surface voxel by using membership profiles on trajectories of local gradient vectors in a fuzzy membership map, so that the white matter regions do not have to be segmented.

2. MATERIALS AND METHODS2.1. Overall Algorithm

Figure 1 shows the overall scheme for measurement of the 3D cerebral cortical thickness. The proposed method consisted of mainly three steps as follows.

1) Segmentation of the brain parenchymal region based on a brain model matching.

2) Creation of a fuzzy membership map for the cerebral cortical region based on the FCM clustering algorithm [14-17].

3) Calculation of the cerebral cortical thickness using localized gradient vector trajectories in fuzzy membership maps.

2.2. Segmentation of the Brain Parenchymal Region2.2.1. Initial Brain Parenchymal Region Based on Histogram Analysis

The background (BG) and CSF regions were removed from an original T1-weighted image based on a histogram analysis. Figure 2 shows a histogram of the original T1-weighted image. The histogram of the T1- weighted image could be divided into four portions that included three peaks, which correspond to the BG (the largest peak), CSF (the second largest peak), and the brain parenchyma and fat regions (the third largest peak), respectively. The two threshold values, TBG and TCSF, for reducing the BG and CSF regions, respectively, are shown in Figure 2. The inset figure shows the enlarged histogram without the background peak. The threshold value, TBG, for the background region was determined as TBG = MBG + kBGSDBG, where MBG and SDBG are the mean value and the standard deviation (SD), respectively. The values MBG and SDBG were determined from the first largest peak with more than a certain number of pixels, which was empirically set as 300,000 pixels in this study, and kBG is the constant, which was empirically set as 1.0. Similarly, the threshold value for reducing the CSF region, TCSF, was determined as TCSF = MCSF + kCSFSDCSF,

where MCSF and SDCSF are the mean value and the standard deviation, respectively, and kCSF is the constant, which was empirically set at –0.25. After reducing the CSF region, the initial brain parenchymal region was segmented by applying morphological processing and extracting the largest region.

2.2.2. Segmentation of the Brain Parenchymal Region with Brain Model Matching

Figure 3 shows a flowchart for the segmentation of the brain parenchymal region using a brain model matching. The brain parenchymal model image shown in Figure 4(a) was manually created from a T1-weighted image of a cognitively normal (CN) subject, whose brain seemed to be of average size and shape (female, 71 years old; mini-mental state examination (MMSE) score: 30). A voxel value similar to those in the white matter regions was assigned to holes of the CSF regions in the LVs to avoid removing some portions of the brain parenchyma by the holes of lateral ventricles due to misregistration. The brain parenchymal region was segmented by registering and masking of the brain model image to each head region, in which the BG and CSF regions were removed, based on a global linear registration of an affine transformation [18,19] and a local non-linear registration of the free-form deformation (FFD) [20-23]. Figure 4 shows images of the segmentation of a brain parenchymal region: (a) an original brain model image; (b) a brain model image after global registration to a normalized image; (c) an image after local registration; (d) a brain parenchymal mask image; (e) a head region after removing CSF regions; and (f) a brain parenchymal region extracted from the head region (e) by the brain mask image (d).

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