Hippocampus-specific fMRI group activation analysis using the continuous medial representation

Abstract

We present a new shape-based approach for regional group activation analysis in fMRI studies. The method restricts anatomical normalization, spatial smoothing and random effects statistical analysis to the space inside and around a structure of interest. Normalization involves finding intersubject correspondences between manually outlined masks, and it leverages the continuous medial representation, which makes it possible to extend surface-based shape correspondences to the space inside and outside of structures. Our approach is an alternative to whole-brain normalization in cases where the latter may fail due to anatomical variability or pathology. It also provides an opportunity to analyze the shape and thickness of structures concurrently with functional activation. We apply the technique to the hippocampus and evaluate it using data from a visual scene encoding fMRI study, where activation in the hippocampus is expected. We produce detailed statistical maps of hippocampal activation, as well as maps comparing activation inside and outside of the hippocampus. We find that random effects statistics computed by the new approach are more significant than those produced using the Statistical Parametric Mapping framework (Friston, K.J., Holmes, A.P., Worsley, K.J., Poline, J.-P., Firth, C.D., Frackowiak, R.S.J. 1994, Statistical parametric maps in functional imaging: a general linear approach. Human Brain Mapping, 2(4): 189-210) at low levels of smoothing, suggesting that greater specificity can be achieved by the new method without a severe tradeoff in sensitivity.

Fig. 1

An illustration of medial geometry and the cm-rep method with 2D examples. a. The medial axis (skeleton) of a 2D object is a curve or a set of curves. The boundary is symmetric across the medial axis. b. The skeleton of a 3D object is like a scaffold formed by surface patches called medial manifolds. c. The cm-rep method describes objects in terms of medial geometry. First, a synthetic skeleton is defined, shown here as a curve specified by a set of control points, with each control point assigned a radius value. d. The interpolation of radius values along the curve leads to a continuum of circles and a definition of a solid object. The boundary of this object can be expressed analytically if the synthetic skeleton satisfies certain constraints (see text). e. A cm-rep model can be deformed to optimally fit a given object. The number of medial axis branches in the cm-rep model is held fixed, so the model might not fit the target object perfectly, as shown here. However, for some applications and some classes of anatomical structures, the approximation is accurate enough to be useful. f. The interior of a cm-rep model can be parametrized using a curvilinear coordinate system whose one axis follows the synthetic skeleton and whose other axis extends from the skeleton to the boundary and is orthogonal to the boundary. This coordinate system is used to assign correspondences between objects.

Fig. 2

Three steps of constructing a cm-rep. a. Medial manifold m(u) with a color plot of the scalar field ρ(u). b. The radial scalar field R(u) computed by solving the Poisson PDE (3) on the medial manifold. c. Boundary surface b^±(u) resulting from inverse skeletonization.

Fig. 3

The shape-based coordinate system induced by a cm-rep. a. A slice through the hippocampus in a T1 weighted MRI, to which a cm-rep template has been fitted. b, c. The values of the coordinates u¹, u², which span the medial manifold, plotted at each point in the hippocampus using a color map. d. The values of the ξ coordinate, which goes from the medial manifold to the boundary.

Fig. 4

Hippocampus segmentation result for a single subject, shown in sagittal, coronal, axial and 3D views. All four views are available to the rater during segmentation.

Fig. 5

Random effects maps computed in the hippocampus using the structure-specific approach. The columns in this table correspond to different smoothing levels, and the rows correspond to different voxel sizes in EPI data as well as different ways of smoothing the EPI data in the hippocampus (mask-based non-uniform smoothing vs. isotropic Gaussian smoothing). The color map corresponds to the standard z-statistic.

Fig. 6

Superior view of the 12 maps plotted in Fig. 5.

Fig. 7

Projection of the anatomical labels of adjacent anatomical structures on the hippocampus boundary. Projections are based on a single-subject anatomical atlas (Tzourio-Mazoyer et al., 2002) and are intended to give a rough idea of the structures' locations relative to the hippocampus.

Fig. 8

Statistical group-level comparison of intra-hippocampal vs. extra-hippocampal activation. Positive values in the z-map correspond to greater intra-hippocampal activation.

Fig. 9

Top: sagittal and coronal slices through the right hippocampus in the mean anatomical image generated using whole-brain normalization to the MNI template. Bottom: probability map formed by projecting hippocampus segmentations into template space.

Fig. 10

Comparison of minimal FDR-adjusted p-values between the structure-specific method and whole-brain SPM2 analysis. The minimal p-values for the structure-specific method with isotropic Gaussian smoothing are shown as dashed horizontal lines, and the minimal p-values for mask-based anisotropic smoothing are shown as dotted horizontal lines. Since in the whole-brain method, there is not exact definition of the hippocampus in the space of the anatomical template, we compute and plot minimal p-values over a sequence of regions associated with increasing probability of “being the hippocampus” (see text for precise definition). The x-axis in the plots above corresponds to this hippocampus probability, and the y-axis plots the p-value on a logarithmic scale.

Fig. 11

Empirical cumulative distribution functions (CDFs) of t-statistic maps computed for the right hippocampus using hippocampus-specific analysis (HSA) and whole-brain analysis (WBA). The dashed line represents HSA with non-uniform mask-based smoothing, and the dotted line corresponds to HSA with uniform Gaussian smoothing. Solid lines represent regions R_1/4, R_1/2 and R_3/4 defined in the MNI template space, corresponding to increasing probability of “being the hippocampus.”