Population based analysis of directional information in serial deformation tensor morphometry

Abstract

Deformation morphometry provides a sensitive approach to detecting and mapping subtle volume changes in the brain. Population based analyses of this data have been used successfully to detect characteristic changes in different neurodegenerative conditions. However, most studies have been limited to statistical mapping of the scalar volume change at each point in the brain, by evaluating the determinant of the Jacobian of the deformation field. In this paper we describe an approach to spatial normalisation and analysis of the full deformation tensor. The approach employs a spatial relocation and reorientation of tensors of each subject. Using the assumption of small changes, we use a linear modeling of effects of clinical variables on each deformation tensor component across a population. We illustrate the use of this approach by examining the pattern of significance and orientation of the volume change effects in recovery from alcohol abuse. Results show new local structure which was not apparent in the analysis of scalar volume changes.

Fig. 1

Using non-rigid registration to capture local shape differences between subjects from the transformations T_Rn. To examine common patterns across subjects, maps of shape measures derived from these transformations may be transformed and compared in the common anatomical space.

Fig. 2

A comparison of the voxel F statistics showing the local quality of fits for conventional analyses using the scalar Jacobian determinant (bottom row) and the individual Jacobian matrix elements (top row).

Fig. 3

(a) A comparison of the effect maps for the difference between groups (abstainers vs relapsers) for the scalar volume change maps (bottom) and the directional models (top). Directional effects are shown by three effect vectors whose length indicates the relative size of the effect and the colour indicates direction of effect. Enlargements of an area are shown for one slice in (b) and (c).