Topology of optical flow in 3D echocardiography

A new approach for quantification of global strain and twist of ventricular wall is presented, it utilizes the theoretical framework of dynamical systems faking into account the large time-varying displacements that occur during the beating of the heart. Topological features of the 3D optical flow have been analysed; such features summarize the global behaviour of the motion field and can be used as cardiac function indexes. In particular the eigenvalues and eigenvectors of the vector field critical points give useful information about deformation and rotation of the entire left ventricle during cardiac cycle. The eigenvectors directions are related to the principal axis of deformation and to the rotation axis. The eigenvalues are related to deformation and rotation magnitudes, therefore they provide an estimate of the relative variation of volume and twisting for each time step