LV motion estimation based on the integration of continuum mechanics and estimation theory

This paper presents a scheme based on the integration of continuum mechanics and estimation theory to characterize the complex nonrigid motion of the left ventricle (LV) over a sequence of 3D images. The proposed scheme is implemented in a hierarchical fashion so that both the global and local motion and deformation can be analyzed. First, global motion and deformation are analyzed and compensated by applying the `Chen surface' modeling. Parametric representation of left ventricle surfaces are also obtained based on the segmented 3D images. Then, we develop a local motion estimation model assuming that thin slice of endocardium surface can be considered as an incompressible medium and can be characterized by the constraint of incompressibility derived from continuum mechanics. This constraint of continuum mechanics is integrated with the correlation functions derived from the estimation theory. The correlation functions are computed from the original intensity images and can be used to measure confidence of the estimation. An overall objective function can therefore be constructed as the weighted sum of the incompressibility and a motion discontinuity-preserving smoothness constraint with the corresponding correlation functions. The optimal estimation of the local deformation is obtained by minimizing this objective function. Since the proposed scheme is based on a physics model, the results are therefore more consistent with the heart function. This integrated scheme allows the point correspondences to depart slightly from the manually segmented surfaces in the region of strong uncertainty. The proposed scheme is able to generate consistent 3D motion vectors for a sequence of cardiac images. 3D visualization of the displacements is also investigated.