title: A novel cortical thickness estimation method based on volumetric Laplace-Beltrami operator and heat kernel.
abstract: Cortical thickness estimation in magnetic resonance imaging (MRI) is an important technique for research on brain development and neurodegenerative diseases. This paper presents a heat kernel based cortical thickness estimation algorithm, which is driven by the graph spectrum and the heat kernel theory, to capture the gray matter geometry information from the in vivo brain magnetic resonance (MR) images. First, we construct a tetrahedral mesh that matches the MR images and reflects the inherent geometric characteristics. Second, the harmonic field is computed by the volumetric Laplace-Beltrami operator and the direction of the steamline is obtained by tracing the maximum heat transfer probability based on the heat kernel diffusion. Thereby we can calculate the cortical thickness information between the point on the pial and white matter surfaces. The new method relies on intrinsic brain geometry structure and the computation is robust and accurate. To validate our algorithm, we apply it to study the thickness differences associated with Alzheimer's disease (AD) and mild cognitive impairment (MCI) on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. Our preliminary experimental results on 151 subjects (51 AD, 45 MCI, 55 controls) show that the new algorithm may successfully detect statistically significant difference among patients of AD, MCI and healthy control subjects. Our computational framework is efficient and very general. It has the potential to be used for thickness estimation on any biological structures with clearly defined inner and outer surfaces.
authors.affiliation: School of Information and Electrical Engineering, Ludong University, Yantai, China; School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ, USA.
authors.forename: Gang
authors.initials: G
authors.lastname: Wang
authors.affiliation: School of Information and Electrical Engineering, Ludong University, Yantai, China.
authors.forename: Xiaofeng
authors.initials: X
authors.lastname: Zhang
authors.affiliation: School of Information and Electrical Engineering, Ludong University, Yantai, China.
authors.forename: Qingtang
authors.initials: Q
authors.lastname: Su
authors.affiliation: School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ, USA.
authors.forename: Jie
authors.initials: J
authors.lastname: Shi
authors.affiliation: Department of Neurology, Mayo Clinic Arizona, Scottsdale, AZ, USA; Arizona Alzheimer's Consortium, Phoenix, AZ, USA.
authors.forename: Richard J
authors.initials: RJ
authors.lastname: Caselli
authors.affiliation: School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ, USA; Arizona Alzheimer's Consortium, Phoenix, AZ, USA. Electronic address: ylwang@asu.edu.
authors.forename: Yalin
authors.initials: Y
authors.lastname: Wang
mesh_terms: D000368:Aged; D000465:Algorithms; D000544:Alzheimer Disease / Q000473:pathology*; D002540:Cerebral Cortex / Q000473:pathology*; D060825:Cognitive Dysfunction / Q000473:pathology*; D005260:Female; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008297:Male; D009929:Organ Size; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: Cortical thickness; False discovery rate; Heat kernel; Spectral analysis; Tetrahedral mesh