Longitudinal cortical thickness estimation using Khalimsky's cubic complex

Longitudinal measurements of cortical thickness is a current hot topic in medical imaging research. Measuring the thickness of the cortex through time is normally hindered by the presence of noise, partial volume (PV) effects and topological defects, but mainly by the lack of a common directionality in the measurement to ensure consistency. In this paper, we propose a 4D pipeline (3D + time) using the Khalimsky cubic complex for the extraction of a topologically correct Laplacian field in an unbiased temporal group-wise space. The thickness at each time point is then obtained by integrating the probabilistic segmentation (transformed to the group-wise space) modulated by the Jacobian determinant of its deformation field through the group-wise Laplacian field. Experiments performed on digital phantoms show that the proposed method improves the time consistency of the thickness measurements with a statistically significant increase in accuracy when compared to two well established 3D techniques and a 3D version of the same method. Furthermore, quantitative analysis on brain MRI data showed that the proposed algorithm is able to retrieve increasingly significant time consistent consistent group differences between the cortical thickness of AD patients and controls.