Local vs Global Descriptors of Hippocampus Shape Evolution for Alzheimer’s Longitudinal Population Analysis

Abstract

In the context of Alzheimer's disease (AD), state-of-the-art methods separating normal control (NC) from AD patients or CN from progressive MCI (mild cognitive impairment patients converting to AD) achieve decent classification rates. However, they all perform poorly at separating stable MCI (MCI patients not converting to AD) and progressive MCI. Instead of using features extracted from a single temporal point, we address this problem using descriptors of the hippocampus evolutions between two time points. To encode the transformation, we use the framework of large deformations by diffeomorphisms that provides geodesic evolutions. To perform statistics on those local features in a common coordinate system, we introduce an extension of the Kärcher mean algorithm that defines the template modulo rigid registrations, and an initialization criterion that provides a final template leading to better matching with the patients. Finally, as local descriptors transported to this template do not directly perform as well as global descriptors (e.g. volume difference), we propose a novel strategy combining the use of initial momentum from geodesic shooting, extended Kärcher algorithm, density transport and integration on a hippocampus subregion, which is able to outperform global descriptors.

Longitudinal deformation models, spatial regularizations and learning strategies to quantify Alzheimer's disease progression

“…Achieving results higher than the ones reported in Fiot et al (2012), which uses non-linear SVM classifier, our method provides in addition coefficient maps with direct anatomical interpretation.…”

“…Moreover, the linear classification model used in this paper is simpler than the non-linear SVM used in Fiot et al (2012). SVM is a very powerful approach, which has been widely studied and successfully used.…”

Geometry of Image Registration: The Diffeomorphism Group and Momentum Maps

“…Since computing the parallel transport of the momentum along geodesics is numerically quite challenging, a first-order approximation called Schild's ladder was proposed in [38] as an alternative. Other methods that depend only on the end-deformation and not on the whole geodesic path were considered and compared in [20]. From the viewpoint of applications, there is, as of now, no consensus about which is the most appropriate method for the transport of deformation momenta.…”

“…First, the expression on the right side must not depend on g and second we have to show that γ V is independent of I 0 . As a first step we note that any X g ∈ T g G is of the form Xg with X ∈ g and thus we can rewrite the condition in the infimum of (20) as…”

Detection of Conversion from Mild Cognitive Impairment to Alzheimer's Disease Using Longitudinal Brain MRI

“…Similarly, Lorenzi et al ( 2015a ) summarizes the longitudinal change of each structure as a regional flux computed from the longitudinal deformation between the baseline and follow-up images. Fiot et al ( 2012 , 2014 ) directly use the longitudinal deformation of the hippocampus to distinguish between MCIs and MCIc, but without considering other brain structures.…”