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 prop...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.展开更多
As stochastic gradient and Skorohod integral operators, is an adjoint pair of unbounded operators on Guichardet Spaces. In this paper, we define an adjoint pair of operator , where with being the conditional expectati...As stochastic gradient and Skorohod integral operators, is an adjoint pair of unbounded operators on Guichardet Spaces. In this paper, we define an adjoint pair of operator , where with being the conditional expectation operator. We show that (resp.) is essentially a kind of localization of the stochastic gradient operators (resp. Skorohod integral operators δ). We examine that and satisfy a local CAR (canonical ani-communication relation) and forms a mutually orthogonal operator sequence although each is not a projection operator. We find that is s-adapted operator if and only if is s-adapted operator. Finally we show application exponential vector formulation of QS calculus.展开更多
文摘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.
文摘As stochastic gradient and Skorohod integral operators, is an adjoint pair of unbounded operators on Guichardet Spaces. In this paper, we define an adjoint pair of operator , where with being the conditional expectation operator. We show that (resp.) is essentially a kind of localization of the stochastic gradient operators (resp. Skorohod integral operators δ). We examine that and satisfy a local CAR (canonical ani-communication relation) and forms a mutually orthogonal operator sequence although each is not a projection operator. We find that is s-adapted operator if and only if is s-adapted operator. Finally we show application exponential vector formulation of QS calculus.
