Myocardial kinematics from tagged MRI based on a 4-D B-spline model

Current research investigating the modeling of left ventricular dynamics for accurate clinical assessment of cardiac function is extensive. Magnetic resonance (MR) tagging is a functional imaging method which allows for encoding of a grid of signal voids on cardiac MR images, providing a mechanism for noninvasive measurement of intramural tissue deformations, in vivo. We present a novel technique of employing a four-dimensional (4-D) B-spline model which permits concurrent determination of myocardial beads and myocardial strains. The method entails fitting the knot planes of the 4-D B-spline model for fixed times to a sequence of triplets of orthogonal sets of tag surfaces for all imaged volumetric frames within the constraints of the modelʹs spatio-temporal internal energy. From a three-dimensional (3-D) displacement field, the corresponding long and short-axis Lagrangian normal, shear, and principal strain maps are produced. As an important byproduct, the points defined by the 3-D intersections of the triplets of orthogonal tag planes, which we refer to as myocardial beads, can easily be determined by our model. Displaying the beads as a movie loop allows for the visualization of the nonrigid movement of the left ventricle in 3-D.