Implementation of displacement field fitting for calculating 3D myocardial deformations from parallel-tagged MR images

The utility of using a displacement field fitting approach to reconstruct 3D myocardial deformations from sets of parallel-tagged MR images has been demonstrated (W.G. O´Dell et al., 1994). The authors´ present goal is to implement the field fitting algorithm efficiently on real heart data. A cascade of fitting steps is used: a first order global cartesian fit, followed by an n-th order global prolate spheroidal fit, followed by a local prolate spheroidal fit around each pre-selected test point. Local deformation gradient and strain tensors are then computed by taking directional derivatives of the displacement field at each test point. On a normal human volunteer, the standard deviation of error of the fitting model to the raw tag point displacement data was ~0.3 mm. Projections of representative image slices following each stage in the cascade provide a graphical validation of the technique