Surface shape analysis with an application to brain surface asymmetry in schizophrenia

Abstract

Some methods for the statistical analysis of surface shapes and asymmetry are introduced. We focus on a case study where magnetic resonance images of the brain are available from groups of 30 schizophrenia patients and 38 controls, and we investigate large-scale brain surface shape differences. Key aspects of shape analysis are to remove nuisance transformations by registration and to identify which parts of one object correspond with the parts of another object. We introduce maximum likelihood and Bayesian methods for registering brain images and providing large-scale correspondences of the brain surfaces. Brain surface size-and-shape analysis is considered using random field theory, and also dimension reduction is carried out using principal and independent components analysis. Some small but significant differences are observed between the the patient and control groups. We then investigate a particular type of asymmetry called torque. Differences in asymmetry are observed between the control and patient groups, which add strength to other observations in the literature. Further investigations of the midline plane location in the 2 groups and the fitting of nonplanar curved midlines are also considered.

Discrimination surfaces with application to region‐specific brain asymmetry analysis

“…Despite the results by Brignell et al, the evidence for differences in morphological asymmetries between schizophrenic and control patients is not clear cut, and for instance, in Narr et al,(p945) it can be read as follows:…”

“…The raw data consist of n =68 3‐D MRI, gathered from a neuroscience study conducted at the University of British Columbia, Canada, and documented in Brignell et al; the study involved n D =30 schizophrenic patients and healthy controls. Some comments on the geometry of the data are in order.…”

“…Following Brignell et al, we assume the midline plane of the brain as the line of symmetry; therefore, we decompose the brain curves into left ( ) and right ( ) as follows: It is clear that from the previous decomposition. To analyze the brain asymmetries with respect to the midline plane, we rotate and reflect the functions and and also rescale the domain of both functions to the interval [0,1].…”

Shape and object data analysis

“…The joint analysis of the registration and invariant properties ('shape') in each case leads to complementary but different analyses. Another example is in comparing cortical asymmetry in schizophrenia in Brignell et al (2010), where different but complementary conclusions are obtained depending on whether one registers on a flat midline plane or on a curved midline between the hemispheres.…”

Neurological imaging: statistics behind the pictures

“…New complementary approaches extracting, modeling and analyzing geometric data derived from the raw neuroimaging data are increasingly becoming an integral component of many contemporary neuroimaging studies. Such geometric modeling techniques, derived from the raw imaging data, include shape analyses [34,35], tensor modeling and analyses [36,37], as well as tractography and white matter integrity [38,39]. These geometric techniques rely on sophisticated mathematical models to represent static or dynamic features of brain structure and function as multidimensional curved manifolds (spaces locally homeomorphic to Euclidian spaces of the same dimension with no curvature), higher-order generalizations of scalars, vectors and matrices (tensors), and topologically equivalent canonical spaces [40–42].…”