ANALYSIS OF GROWTH IN THE DEVELOPING BRAIN USING NON-RIGID REGISTRATION P. Aljabar 1 , K.K. Bhatia 1 , J.V. Hajnal 2 , J.P. Boardman 2 , L. Srinivasan 2 , M.A. Rutherford 2 , L.E. Dyet 3 , A.D. Edwards 2 , D. Rueckert 1 1 Visual Information Processing, Department of Computing 2 Imaging Sciences Department 3 Division of Clinical Sciences, Faculty of Medicine Imperial College London,London, SW7 2AZ, U.K. ABSTRACT This work describes and compares two different methods for iden- tifying growth patterns in preterm infants during the second year of development. One method is based on creating anatomical atlases from the population of subjects within each timepoint and using the transformation between atlases at different timepoints to create aver- age volume change maps. The second method uses multiple longitu- dinal intra-subject registrations to produce individual volume change maps. These maps are then transformed into a common coordi- nate system and averaged with the method used for atlas creation. We show that there is a reasonable level of agreement between the two methods and both generate plausible growth patterns implying that either could be used to track development during this period of growth. 1. INTRODUCTION Preterm birth has a significant effect on the developing brain, and infants born preterm commonly display neuropsychiatric problems during childhood [1][2][3]. It is therefore important to be able to determine the structural changes that occur in the brain in the early years. We have previously used deformation-based morphometry to study differences between term-born infants and preterm infants at term equivalent age [4][5]. By analyzing deformation fields pro- duced by non-rigid registration between subjects, quantitative volu- metric changes between the two groups can be obtained. However, such studies do not indicate how the brain of preterm infants develops with time. In this work, we focus on regional volu- metric changes due to growth of structures in the preterm brain from one to two years. Older children (over three years) have been the subjects of previous longitudinal studies [6], but we are not aware of studies of brain development between one and two years, despite the fact that significant growth occurs during this period. In this study, we compare two methods to map the average growth from one to two years. In the first method, we created separate at- lases, representing the average shape of the population at one year and at two years of age. The atlases at each timepoint were then reg- istered and used to generate maps of regional brain growth. In the second method, the subjects were longitudinally registered to obtain separate growth maps for each individual. The individual growth maps were then registered and combined in an average population space using the same method that generated the anatomical atlases. A number of methods have recently been proposed to create av- erage or template free atlases [7][8][9][10][11][12]. For the purposes of this study, we have chosen to average non-rigid deformations [13]. However, it is additionally necessary to account for overall growth in brain size and shape as well as local development of structures within the brain. We have therefore also averaged the global compo- nent of the transformations, so that the resulting atlas lies in a space representing both the global and local average. 2. MATERIALS AND METHODS For this study, we use data presented in a previous study [4]. These contained T1 images of preterm infants scanned at term equivalent age (44 images) at one year (7 images) and at two years (7 images). The one and two year images represent repeat scans of the same children. The images were acquired using A 1.5T Eclipse MR sys- tem (Philips Medical Systems, Cleveland, Ohio), TR = 30ms, TE = 4.5ms, flip angle = 30 o with a voxel size of 1 × 1 × 1.6mm 3 . In order to visualise typical growth patterns atlases were gener- ated at each timepoint to represent the average shape and size of the population. Several methods have been used to construct such at- lases [9][10][11][12][13][14]. In this study, we have chosen a refer- ence subject at each timepoint and registered the remaining images at the same timepoint with the reference. The resulting transformations are then averaged in order to remove any potential shape or size bias towards the chosen reference. Clearly, global affine changes play a significant part in developmental growth. The global shape and scale changes within the transformations between subjects are therefore averaged separately from the non-linear part of the transformations. Section 2.1 presents the global scale and shape averaging method. The non-linear components of the transformation are averaged using a method similar to that presented in [13] as is described in 2.2. 2.1. Affine Registration After registering subject images {I1,...,In} with the reference im- age for each timepoint, an estimate of the global transformations from the reference to each of the subjects can be represented by homogeneous transformation matrices {T g i } , i =1,...,n where the superscript indicates ’global’. Each global transformation T g i can be decomposed into a rigid and a non-rigid (affine) component T g i = R g i ◦ A g i where the matrix A g i represents only the scale and skew parameters. Because we aim to correct only for global shape and size differ- ences, it is not necessary to average the rigid components of these transformations. These global shape and size differences are repre- sented by the affine matrices {A g i }. The average affine matrix Aav