10th Annual Meeting of the Organization for Human Brain Mapping

Abstract Number: 2990

Nonparametric estimation of cortical thickness
Moo K. Chung1,2,3 , Shijie Tang,1
1Department of Statistics, 2Department of Biotatistics and Medical Informatics, 3Keck Laboratory for Functional Brain Imaging and Behavior, University of Wisconsin-Madison

The cerebral cortex has the topology of a 2D highly convoluted sheet. The cortical thickness that measures the distance between the outer and inner cortical surfaces has been used to characterize the brain shape [1]. There are many different techniques to measure the cortical thickness [1, 2, 3, 4]. Which method one uses, the thickness measurements are always contaminated with noise. The noise may come from a scanner or due to partial volume effect. To increase the signal-to-noise ratio and to increase Gausianess that is needed in the random fields theory, diffusion smoothing has been used so far [1]. We present a completely new smoothing technique that is simpler than diffusion smoothing.

T1 weighted MRIs are segmented and cortical thickness maps are computed based on deformable surface algorithm presented in [2] using FreeSurfer package. The triangular mesh generated in this way has about 300,000 triangle elements in average, which is the sufficient mesh resolution for 1mm resolution MRI obtained from 3T GE scanner. The cortical thickness measurement is assumed to follow the additive model of true signal plus noise. The true cortical thickness is assumed to be a continuous functional data that can be estimated via the Nadaraya-Waton (NW) smoother. The NW kernel smoothing is essentially a Gaussian kernel smoothing for sparse data. The amount of smoothing can be increased by iteratively applying NW kernel smoothing.

Single iteration of Gaussian kernel smoothing takes about 1 min in Pentium M-processor machine which is compatible to the speed of diffusion smoothing. Figure 1 is the cortical thickness measurements obtained from FreeSurfer and Figure 2 is the NW kernel estimation of the thickness measure which shows huge reduction of noise. Figure 3 is the local comparison of the thickness maps before and after smoothing. The thickness maps are deformed onto a sphere to show hidden sulcal regions. Figure 4 is an application of the NW kernel estimation for smoothing out noisy brain surface. To show the effect of surface regularization, artificially large white noise has been added to the coordinates of the mesh.

This work was funded by WARF. The authors wish to thank Bruce Fischl and his research staff for valuable advice on segmentation.

[1] Chung, M.K., Worsley, K.J., Robbins, S., Paus, P., Taylor, J., Giedd, J.N., Rapoport, J.L., Evans, A.C. (2003) Deformation-Based Surface Morphometry with an Application to Gray Matter Deformation, NeuroImage. 18:198-213.
[2] Fischl, B. and Dale, A.M. (2000) Measuring the thickness of the human cerebral cortex from magnetic resonance images, PNAS 97:11050-11055.
[3] Jones, et al. (2000) Three-dimensional mapping of cortical thickness using Laplace’s equation, Human Brain Mapping 11:12-32.
[4] Miller, M.I. et al. (2000) Bayesian construction of geometrically based cortical thickness metrics. NeuroImage. 12:676-687.

Figure 1. Cortical thickness measurement

Figure 2. Cortical thickness estimation

Figure 3. Comparision of before and after smoothing

Figure 4. Nonparametric estimation of noise brain surface