Brain image registration using cortically constrained harmonic mappings

Abstract

Volumetric registration of brains is required for inter-subject studies of functional and anatomical data. Intensity-driven registration typically results in some degree of misalignment of cortical and gyral folds. Increased statistical power in group studies may be achieved through improved alignment of cortical areas by using sulcal landmarks. In this paper we describe a new volumetric registration method in which cortical surfaces and sulcal landmarks are accurately aligned. We first compute a one-to-one map between the two cortical surfaces constrained by a set of user identified sulcal curves. We then extrapolate this mapping from the cortical surface to the entire brain volume using a harmonic mapping procedure. Finally, this volumetric mapping is refined using an intensity driven linear elastic registration. The resulting maps retain the one-to-one correspondence between cortical surfaces while also aligning volumetric features via the intensity-driven registration. We evaluate performance of this method in comparison to other volumetric registration methods.

Fig. 1

(a) Our surface registration method involves simultaneous flattening and sulcal landmark alignment of the two cortical surfaces, which produces accurate sulcal mapping from one cortex to another. The outer grey matter/CSF surface is shown in semi-transparent grey color and the inner grey/CSF surface is opaque. Shown below are flat maps of a single hemisphere for the inner cortical surface of the two brains. (b) Mapping of the aligned sulci in the flat space and (c) sulci mapped back to the inner cortical surface of the template.

Fig. 2

(a) Illustration of the extrapolation of the surface mapping to the 3D volume by harmonic mapping. The pairs of surfaces are shown in red and green. The deformation field is represented by placing a regular grid in the central coronal slice of the brain and deforming it according to the harmonic map. The projection of this deformation onto a 2D plane is shown with the in-plane value encoded according to the adjacent color bar. (b) The result of harmonic mapping and linear elastic refinement of the subject brain to the template brain. Note that the inner and outer cortical surfaces, by constraint, are exactly matched. The linear elastic refinement produces an approximate match between subcortical structures. The deformation field here shows the result of cortically constrained intensity-driven refinement. Note that the deformations are zero at the boundary and nonzero in the vicinity of the ventricles, thalamus and other subcortical structures.

Fig. 3

Examples of surface constrained volumetric registration. (a) Original subject volume; (b) template; (c) registration of subject to template using surface constrained harmonic mapping, note that the cortical surface matches that of the template; (d) intensity-based refinement of the harmonic map of subject to template