Incompressible Phase Registration for Motion Estimation from Tagged Magnetic Resonance Images

Tagged magnetic resonance imaging has been used for decades to observe and quantify motion and strain of deforming tissue. Three-dimensional (3D) motion estimation has been challenging due to a tradeoff between slice density and acquisition time. Typically, sparse collections of tagged slices are processed to obtain two-dimensional motion, which are then combined into 3D motion using interpolation methods. This paper proposes a new method by reversing this process: first interpolating tagged slices and then directly estimating motion in 3D. We propose a novel image registration framework that uses the concept of diffeomorphic registration with a key novelty that defines a similarity metric involving the simultaneous use of three harmonic phase volumes. The other novel aspect is the use of the harmonic magnitude to enforce incompressibility in the tissue region. The final motion estimates are dense, incompressible, diffeomorphic, and invertible at a 3D voxel level. The approach was evaluated using simulated phantoms and human tongue motion data in speech. Compared with an existing method, it shows major advantages in reducing processing complexity, improving computation speed, allowing running motion calculations, and increasing noise robustness, while maintaining a good accuracy.