title: Multi-resolutional shape features via non-Euclidean wavelets: applications to statistical analysis of cortical thickness.
abstract: Statistical analysis on arbitrary surface meshes such as the cortical surface is an important approach to understanding brain diseases such as Alzheimer's disease (AD). Surface analysis may be able to identify specific cortical patterns that relate to certain disease characteristics or exhibit differences between groups. Our goal in this paper is to make group analysis of signals on surfaces more sensitive. To do this, we derive multi-scale shape descriptors that characterize the signal around each mesh vertex, i.e., its local context, at varying levels of resolution. In order to define such a shape descriptor, we make use of recent results from harmonic analysis that extend traditional continuous wavelet theory from the Euclidean to a non-Euclidean setting (i.e., a graph, mesh or network). Using this descriptor, we conduct experiments on two different datasets, the Alzheimer's Disease NeuroImaging Initiative (ADNI) data and images acquired at the Wisconsin Alzheimer's Disease Research Center (W-ADRC), focusing on individuals labeled as having Alzheimer's disease (AD), mild cognitive impairment (MCI) and healthy controls. In particular, we contrast traditional univariate methods with our multi-resolution approach which show increased sensitivity and improved statistical power to detect a group-level effects. We also provide an open source implementation.
authors.affiliation: Department of Computer Sciences, University of Wisconsin-Madison, Madison, WI 53706, USA; Geriatric Research Education and Clinical Center, William S. Middleton Memorial Veteran's Hospital, Madison, WI 53705, USA. Electronic address: wonhwa@cs.wisc.edu.
authors.forename: Won Hwa
authors.initials: WH
authors.lastname: Kim
authors.affiliation: Department of Computer Sciences, University of Wisconsin-Madison, Madison, WI 53706, USA; Department of Biostatistics & Med. Informatics, University of Wisconsin-Madison, Madison, WI 53705, USA; Geriatric Research Education and Clinical Center, William S. Middleton Memorial Veteran's Hospital, Madison, WI 53705, USA. Electronic address: vsingh@biostat.wisc.edu.
authors.forename: Vikas
authors.initials: V
authors.lastname: Singh
authors.affiliation: Department of Biostatistics & Med. Informatics, University of Wisconsin-Madison, Madison, WI 53705, USA.
authors.forename: Moo K
authors.initials: MK
authors.lastname: Chung
authors.affiliation: Department of Computer Sciences, University of Wisconsin-Madison, Madison, WI 53706, USA.
authors.forename: Chris
authors.initials: C
authors.lastname: Hinrichs
authors.affiliation: Department of Computer Sciences, University of Wisconsin-Madison, Madison, WI 53706, USA.
authors.forename: Deepti
authors.initials: D
authors.lastname: Pachauri
authors.affiliation: Geriatric Research Education and Clinical Center, William S. Middleton Memorial Veteran's Hospital, Madison, WI 53705, USA; Wisconsin Alzheimer's Disease Research Center, University of Wisconsin School of Medicine and Public Health, Madison, WI 53792, USA.
authors.forename: Ozioma C
authors.initials: OC
authors.lastname: Okonkwo
authors.affiliation: Geriatric Research Education and Clinical Center, William S. Middleton Memorial Veteran's Hospital, Madison, WI 53705, USA; Wisconsin Alzheimer's Disease Research Center, University of Wisconsin School of Medicine and Public Health, Madison, WI 53792, USA.
authors.forename: Sterling C
authors.initials: SC
authors.lastname: Johnson
mesh_terms: D000368:Aged; D000544:Alzheimer Disease / Q000473:pathology*; D002540:Cerebral Cortex / Q000033:anatomy & histology* / Q000473:pathology*; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D008297:Male; D058067:Wavelet Analysis
keywords: Alzheimer's disease; Cortical thickness discrimination; Graph wavelets; Multi-resolution analysis; Non-Euclidean wavelet; Shape analysis