Many recent anatomical magnetic resonance image (MRI) studies on the human brain have been focused on the cerebral cortex thickness analysis, because longitudinal variations in cortical thickness are found closely correlated to either pathological (e.g.
Alzheimer’s disease) or physiological (e.g.
normal aging) development of brains. Therefore, an accurate cortical thickness measuring method with longitudinal consistency and stability, which can detect and monitor the developmental changes of cortical thickness, is highly desirable. Many cortical thickness methods have been previously proposed. They can be broadly categorized as explicit surface based, implicit surface based and probabilistic segmentation based. In the explicit surface-based methods, after the inner (WM/GM interface) and outer (GM/CSF interface) surfaces are extracted by deformable surface models (which incorporate the smoothness constraints), the thickness is defined as the distance between a pair of points from each of the two surfaces. The correspondence between the two points in the pair is found either by deformable mapping of the inner surface to the outer surface [1
], nearest point [3
] or surface normal [4
]. The disadvantages of using explicit surface are the extra computational cost and errors generated by the surface construction. In contrast, in implicit surface-based approaches, after segmentation of brain tissues, no surface mesh is explicitly constructed to represent the WM/GM and GM/CSF boundary. This makes the algorithms in this category more computationally efficient. The PDE-based [5
] method is one of the representative approaches in this category [6
]. In this method, Laplace’s equation is solved in the GM region with certain boundary conditions (by setting different constant potentials on the two boundaries). The nested sub-layers of cortex is thus revealed by the resultant iso-potentials. The cortical thickness is then defined at each point as the length of the streamline along the gradient of the defined potential field. Some of the above methods are based on a hard segmentation of brain tissues. The disadvantage of using hard segmentation is the losing of sub-voxel information, which makes the algorithms very sensitive to the segmentation errors. To overcome this limitation, methods which measure the thickness on probabilistic segmentation of GM are proposed. Diffeomorphic registration of the probabilistic segmentation image is used in [9
] to find a one-to-one correspondence of point pairs, between which cortical thickness is defined. Similarly, in [10
], thickness is defined as the minimum line integral across the probablistic GM segmentation.
The above existing methods can be considered as 3D thickness measuring approaches, because they are designed to measure the thickness temporal-independently and do not take into account the temporal correlation. In order to improve the measuring accuracy and stability in longitudinal thickness studies, in this paper, we aim to devise a 4D thickness measuring method which is capable of fully utilizing the temporal information provided by longitudinal image dataset. The reason why 4D thickness measurement is important and necessary is that, measuring cortical thickness from MR images is affected by many artifacts and noises, such as intensity inhomogeneity, partial volume (PV) effect and segmentation errors. Comparing the thickness of cortical structures (1.2 ~ 4.5mm
]) to the the resolution of MR images (≈ 1mm
), the errors introduced in the measuring process are considerably large. Therefore, if the thickness changes are evaluated as the difference between two temporal-independent 3D measurements, these errors will be amplified and result in jittery longitudinal measurements. Another fact makes the longitudinal study even more difficult is that the expected change in GM thickness during the early stages of some neurological disorders, e.g.
Alzheimer’s disease, has been shown to be less than 1mm
in most brain regions [12
]. Since the cortical structure are only a few voxels thick in the images, sub-voxel accuracy is required to detect the subtle longitudinal thickness changes. In this situation, incorporating the information from other time-points as constraints to improve the accuracy and robustness of thickness measurement becomes very important. Currently, such temporal constraints are introduced by applying some sort of regression over the independently estimated 3D measurements. The problem of this regression-based method is that it imposes overly restrictive constraints due to the limitation of the pre-assumed regression model (usually linear), without taking into account the temporal correlation. This prompts us to incorporate the temporal constraints directly into the thickness measurement process. In this paper, after getting the 4D segmentation results of the longitudinal input images using a 4D segmentation method [14
], we propose to measure the thickness on the aligned GM probability maps of different time-points in a common stereotaxic space. In this way, information from all time-points can be easily incorporated.