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Thoracic aortic aneurysm (TAA) growth is currently assessed by changes in maximal aortic diameter (i.e., radial growth of the vessel). However, there is growing awareness that longitudinal aortic growth (i.e., elongation) is an important metric of disease status, albeit one that is difficult to measure using current clinical techniques. Previously we have proposed a method to assess 3D changes in aortic wall growth/deformation using deformable image registration with interpolation of the spatial Jacobian determinant to the aortic surface. Here we propose a method to re-orient the Jacobian into directional components relative to the aortic surface rather than the image space, allowing clinicians and researchers to isolate and study the pathologic effects of each directional component of growth separately. To this end, we first perform a deformable image registration between two aortic geometries. Second, we segment the aortic surface and centerline in the fixed image, and use the resulting geometry to construct anatomically-based local coordinate systems at each voxel of the aortic surface. Using the Jacobian matrix field resulting from the deformable registration, we can obtain the anatomically oriented Jacobian components by rotating the Jacobian matrix at each voxel so that it is aligned with the anatomically based local coordinate system. Through experiments on toy cylinders and real clinical cases, we show clear differences between the Jacobian determinant and its directional components, with the directional Jacobian component being able to remove one directional change (e.g., longitudinal) while maintaining the other (e.g., cross-sectional).
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