Reconstruction of 3D deformation from 2D MR velocity mapping with incompressibility constraints

This paper presents a new method for calculating 3D myocardial deformation from multislice 2D magnetic resonance velocity mapping. The method first involves the rectification of in-plane velocity distribution with a variational vector restoration method. This restored 2D velocity is then used to estimate the through-plane velocity component by applying a local incompressibility constraint. A global optimization procedure was then used to derive the velocity distribution that conforms to the incompressibility constraint. The proposed method was validated by using a simulation phantom with different levels of noise. The derived velocity field permits a full 3D deformation analysis of the myocardium.