Variable precision registration via wavelets: Optimal spatial scales for inter-subject registration of functional MRI

Abstract

The detection of significantly activated brain regions in multi-subject functional magnetic resonance imaging (fMRI) studies almost invariably entails the coregistration of individual subjects' data in a standard space. Here, we investigate how sensitivity to detect loci of generic activation in such studies may be conditioned by the precision of anatomical registration. We describe a novel algorithm, implemented in the wavelet domain, for inhomogeneous deformation of individual images to match a template. The algorithm matches anatomical features in a coarse-to-fine fashion, first minimising a cost function in terms of relatively coarse spatial features and then proceeding iteratively to match the images in terms of progressively more detailed anatomical features. Applying the method to data acquired from two groups of 12 healthy volunteers (with mean age 27 and 70 years, respectively), during performance of a paired associate learning task, we show that geometrical overlap between template and individual images is monotonically improved, compared to an affine transform, by additional inhomogeneous deformations informed by more detailed features. Likewise, sensitivity to detect activated voxels can be substantially improved, by a factor of 4 or more, if wavelet-mediated deformations informed by medium-sized anatomical features are applied in addition to a preliminary affine transform. However, sensitivity to detect activated voxels was reduced by “over-registering” data or matching anatomical features at the finest scales of the wavelet transform. The benefits of variable precision registration are particularly salient for data acquired in older subjects, which showed evidence of greater inter-subject anatomic variability and generally required more extensive local deformation to achieve a satisfactory match to the template image. We conclude that major benefits in sensitivity to detect functional activation in multi-subject fMRI studies can be attained with an inhomogeneous deformation applied over appropriate spatial scales.

Introduction

Image registration has a central role in the fMRI processing pipeline, correcting for subject motion in preprocessing and, moreover, differences in inter-subject anatomy. The low signal-to-noise ratio of BOLD activation (Parrish et al., 2000) leads inevitably to the necessity for multi-subject studies. To identify regions activated by a particular stimulus or cognitive task across a group of subjects, or regional differences between groups, the image data are mapped onto a reference image in a known coordinate system. In doing so, it is implicitly assumed that each voxel location represents the same anatomical location in all images and statistical inference then typically proceeds on a voxelwise basis.

Image registration algorithms that deform an image onto a fixed template have three essential components: a cost function that measures the similarity between images, a parameterised mapping from the native space of the deformable image to the standard space of the fixed template and a strategy for searching the parameter space of the mapping. The intention is then to search for the optimal parameters of the mapping that minimise (or maximise) the cost function. This cost function may either be based on the intensity of all non-zero voxels or on the correspondence of anatomical landmarks. It may also be constrained to avoid unphysical mappings that contain features such as ‘foldings’ or ‘tearings’.

Image registration is central in the debate over the origins of differences observed with tissue morphometry; that is, the statistical analysis of spatially normalised, segmented, high-resolution structural MRI data (Bookstein, 2001, Ashburner and Friston, 2001, Friston and Ashburner, 2004, Davatizikos, 2004). In this context, criticism has been focused on whether the differences observed are so confounded by residual mis-alignment as to be uninterpretable. More fundamentally, the question has been raised as to whether it is possible to automatically determine any neuroanatomically meaningful mapping at all. If such an ideal mapping were indeed available, there would still remain the mis-registration of anatomy across a population due to the marked biological variability of brain structures between individuals (Thompson et al., 1998, Juch et al., 2005). Whilst this debate has been conducted in relation to structural data, the arguments can be translated to discussions of functional data. The dilemma we are thus presented with is how to obtain patterns of activation (or differential activation) elicited by cognitive paradigms, eschewing inter-subject variability, without the prospect of an algorithm capable of exact one-to-one mappings.

The effect of inhomogeneous spatial normalisation on patterns of brain functional activation has not been extensively considered. Gee et al. (1997) noted that an inhomogeneous deformation yields improved performance over affine mappings alone in fMRI, with similar results in PET (Crivello et al., 2002). It would therefore appear that insufficient alignment of images results in a loss of sensitivity. But is it possible to ‘over-register’ the data? That is, would a mapping parameterised to operate at finer spatial scales than the coarsest common features of the images actually provide a non-optimal solution?

We describe a method of registration that poses the problem of anatomical mapping in the wavelet domain. This multi-resolution basis for registration means that the lower and upper spatial scales of the displacement field can be varied systematically in a search for the mapping that maximises the observed activation. To illustrate this approach, we apply it to fMRI data acquired from two groups of subjects (young and older healthy volunteers) during performance of a paired associate learning task. The quality of registration achieved by using various ranges of scales of the wavelet transform is quantified in terms of the final value of the cost function as well as geometric measures of the overlap between the image volumes. These metrics can also be compared to a “bottom line” measure—the number of generically activated voxels identified following variable precision registration.