Three-dimensional mapping of cortical thickness using Laplace's equation

We present a novel, computerized method of examining cerebral cortical thic kness. The normal cortex varies in thickness from 2 to 4 mm, reflecting the morphology of neuronal sublayers. Cortical pathologies often manifest abno rmal variations in thickness, with examples of Alzheimer's disease and cort ical dysplasia as thin and thick cortex, respectively. Radiologically, imag es are 2-D slices through a highly convoluted 3-D object. Depending on the relative orientation of the slices with respect to the object, it is imposs ible to deduce abnormal cortical thickness without additional information f rom neighboring slices. We approach the problem by applying Laplace's Equat ion (del(2)psi = 0) from mathematical physics. The volume of the cortex is represented as the domain for the solution of the differential equation, wi th separate boundary conditions at the gray-white junction and the gray-CSF junction. Normalized gradients of psi form a vector field, representing ta ngent vectors along field lines connecting both boundaries. We define the c ortical thickness at any point in the cortex to be the pathlength along suc h lines. Key advantages of this method are that it is fully three-dimension al, and the thickness is uniquely defined for any point in the cortex. We p resent graphical results that may cortical thickness everywhere in a normal brain. Results show global variations in cortical thickness consistent wit h known neuroanatomy. The application of this technique to visualization of cortical thickness in brains with known pathology has broad clinical impli cations. Hum. Brain Mapping 11:12-32, 2000. (C) 2000 Wiley-Liss, Inc.