<title>Automated 3D nonlinear deformation procedure for determination of gross morphometric variability in human brain</title>

Abstract

Abstract We describe an automated method to register MRI volumetric datasets to a digital human brain model. The technique employs3D non-linear warping based on the estimation of local deformation fields using cross-correlation of invariant intensity featuresderived from image data. Results of the non-linear registration on a simple phantom, a complex brain phantom and real MRIdata are presented. Anatomical variability is expressed with respect to the Talairach-like standardized brain-based coordinatesystem of the model. We show that the automated non-linear registration reduces the inter-subject variability of homologouspoints in standardized space by 15% over linear registration methods. A 3D variability map is shown. 1 INTRODUCTION New imaging modalities and techniques, e.g., PET, functional MRI (fMRI), SPECT, magnetoencephalography (MEG), andEEG have made it possible to map functional areas of the human brain with respect to anatomy. Two aspects of this workrequire integration of data from different individuals: 1) The low signal associated with cognitive activation (e.g., a subtlechange in cerebral blood flow (CBF) as measured by PET) requires averaging across subjects to improve statistical significanceofmeasured CBF changes'4°. 2) Although high resolution imaging techniques such as fMRI now make it possible to measureactivation within a single subject, it will still be necessary to compare results across individuals in order to fully understandthe relationship between functional areas and the underlying gross morphology such as gyral anatomy. For both situations weideally wish to remove all morphological differences between individual brains before considering the distribution of functionalinformation superimposed on the anatomical substrate. This requires a method for deforming one brain to match another atall points, and has typically been accomplished by mapping the volumetric data into a standardized brain-based coordinatesystem24. Until recently, most centers have used linear transformations only13'15'19'25. However, previous work24'23 has shownthat even after linear mapping, there is variability of up to 1.5 cm in the position of cortical structures, which may representa significant source of error when mapping activation foci. We have shown9, that on average for points throughout the brain(cortical and sub-cortical), there is a 6-7mm anatomical variability in 3D position not accounted for by linear registration.The objective of this paper is to present an automated method of establishing the non-linear morphometric variability ina population of normal brains with 3D MRI. Non-linear warping based on homologous landmark matching2'9 has not beenpractical for routine use as a deformation/warping model because of the subjectivity involved in selecting the precise locationand number of points that define the non-linear deformation. This has lead our group and others (e.g.,16'20) to consider fullyautomated, objective non-linear mapping techniques. Our method uses non-linear 3D warping of one data set to register itwith another, based on the estimation of local deformations derived from local neighbourhood correlation of invariant featurescalculated from image data3'4.To properly assess non-linear variability it is first essential to have a well-defined 3D coordinate space where the linearcomponent of the anatomical variation is removed by application of an affine transformation. Without a priori knowledgeof anatomical variability, the best minimum variance frame cannot be defined since it is wholly dependent on the former.Therefore, we have selected a brain-based coordinate system very similar to that proposed by Talairach24. Our implementationuses a single global affine transformation whereas Talairach employs 12 piece-wise linear transformations (as implemented in