We propose an operational method to extract the left ventricle (LV) systole dynamics using HARmonic Phase (HARP) images extracted from tagged cardiac MR sequences. Established techniques to generate HARP sequences provide independent evidence for motion extraction, in the sense that the combined linear system for scalar brightness conservation, applied to the HARP images, can be uniquely solved for a dense field of motion parameters without the need for regularization. In contrast to some of the previously proposed popular methods, no segmentation or tracking of tags over time, nor interpolation of a sparse motion field explicitly coupled to the tag pattern is required, and the problem of tag fading is bypassed. An important novelty is the incorporation of automatic local scale selection so as to obtain a robust solution, which not only yields a stable, but also a smoothly varying motion field of the (healthy) LV myocardial wall. The scheme relies on an integer parameter representing order of approximation, and allows one to simultaneously obtain a dense field of differential tensors capturing the low order differential structure of the motion field, which is useful for the computation of relevant local quantities such as strain rates and material acceleration fields. The methodology is generic and straightforward to implement, and can be generalized to 3D and, in principle, to account for higher order differential structure.
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