High-Dimensional Deformation Fields for Longitudinal Intraindividual Volumetry of Cerebral Infarction

The aim of this study is the analysis of 3D morphological changes of human brains after cerebral infarction. The change of brain volume caused by the infarction is measured by high-dimensional transformations. These are determined by a multiresolution full multigrid (FMG) movement model [4], resulting in a precise correlation of homologous structures. Thus, volume changes are detected with subvoxel accuracy to determine volume changes between the infarct and remote brain regions without manual interaction. High-dimensional transformations are determined by application of the theory according to Navier-Lamee. Volumes are modelled as an elastic medium. For complex deformations the elastic model is extended to a movement model and the total spatial differences are divided into discrete steps. The gray-value forces driving the movement of each voxel in the source object are determined by minimizing the gray-value difference between source and reference volume. The movement of each voxel is controlled by the data itself and smoothed with respect to noise by the elasticity properties defined by the Lamee parameters for each step. The numerical effort is overcome by a combined multiresolution, full-multigrid method and the correlation of homologous structures improved by application of the Scale-Space theory. To avoid rotational transformations, coarse and fine alignment is achieved by the extended principle axes theory [2, 3] and by a cross-correlation based procedure using a matrix-norm [1]. The MRI data sets are acquired at different times, enabling the determination of morphological changes over time. The application of the FMG model enables the investigation of morphological brain changes over time. Furthermore, it is possible to detect ischemia-induced spatial distortions and plastic alterations, as the changes of the volume are exactly determined by the deformation fields. The results show, that even small infarcts result in morphological changes not only adjacent to the ischemic area but also in remote areas and in some cases the contralateral hemisphere. Supported by the Deutsche Forschungsgemeinschaft (SFB 194 A6, A13, B2). References: [1] Schormann T, Dabringhaus A, Zilles K. Bioimaging 1993; 1: 19–28. [2] Schormann T, Zilles K. IEEE TMI 1997; 16: 942–947. [3] Schormann T, Zilles K. Human Brain Mapping 1998a; 6: 339–347hf. [4] Schormann T. Method for computing and displaying 2D- and 3D-spatial differences of structures. Int. Patent PCT/EP99/04442 (1998b).