Cardiac motion recovery using an incompressible B-solid model

B-spline based deformable model is commonly used in recovering three-dimensional (3D) cardiac motion from tagged MRI due to its compact description, localized continuity and control flexibility. However, existing approaches usually ignore an important well-known fact that myocardial tissue is incompressible. In this paper, we propose to reconstruct 3D cardiac motion from tagged MRI using an incompressible B-solid model. We demonstrate that cardiac motion recovery can be achieved more with greater accuracy by considering both smoothness and incompressibility of the myocardium. Specifically, our incompressible B-solid model is formulated as a 3D tensor product of B-splines, where each piece of B-spline represents a smooth and divergence-free displacement field of myocardium with respect to radial, longitudinal and circumferential direction, respectively. We further formulate the fitting of the incompressible B-solid model as an optimization problem and solve it with a two-stage algorithm. Finally, the 3D myocardium strains are obtained from the reconstructed incompressible displacement fields and visualized in a comprehensive way. The proposed method is evaluated on both synthetic and in vivo human datasets. Comparisons with state-of-the-art methods are also conducted to validate the proposed method. Experimental results demonstrate that our method has a higher accuracy and more stable volume-preserving ability than previous methods, yielding an average displacement error of 0.21 mm and a Jacobian determinant mean of 1.029.