Displacement field computation from 3D echocardiographic sequences

A method for 3D displacement field computation of a beating heart from 3D echocardiographic sequences is proposed. A feature based tracking algorithm provides reliable displacement estimates for a little set of points during a cardiac cycle. A physically based constraint is used in order to reconstruct the dense displacement field in each volume point starting from the features displacements. Linear elastic theory provides this constraint. In particular the 3D volume is considered as an hookean elastic solid that fulfils the Navier equation of motion. The solution of the elastostatic problem is given by a set of coupled elliptic partial differential equations (PDE´s). The numerical solution is provided by discretizing the PDE´s and obtaining a system of algebric linear equations. Results obtained by the application of the method to real 3D echocardiographic sequences are presented