Cardiac Fiber Unfolding by Semidefinite Programming

Diffusion-tensor imaging allows noninvasive assessment of the myocardial fiber architecture, which is fundamental in understanding the mechanics of the heart. In this context, tractography techniques are often used for representing and visualizing cardiac fibers, but their output is only qualitative. We introduce here a new framework toward a more quantitative description of the cardiac fiber architecture from tractography results. The proposed approach consists in taking three-dimensional (3-D) fiber tracts as inputs, and then unfolding these fibers in the Euclidean plane under local isometry constraints using semidefinite programming. The solution of the unfolding problem takes the form of a Gram matrix which defines the two-dimensional (2-D) embedding of the fibers and whose spectrum provides quantitative information on their organization. Experiments on synthetic and real data show that unfolding makes it easier to observe and to study the cardiac fiber architecture. Our conclusion is that 2-D embedding of cardiac fibers is a promising approach to supplement 3-D rendering for understanding the functioning of the heart.