Kinematics of the heart: strain-rate imaging from time-resolved three-dimensional phase contrast MRI

A four-dimensional mapping (three spatial dimensions + time) of myocardial strain-rate would help to describe the mechanical properties of the myocardium, which affect important physiological factors such as the pumping performance of the ventricles. Strain-rate represents the local instantaneous deformation of the myocardium and can be calculated from the spatial gradients of the velocity field. Strain-rate has previously been calculated using one-dimensional (ultrasound) or two-dimensional (2-D) magnetic resonance imaging) techniques. However, this assumes that myocardial motion only occurs in one direction or in one plane, respectively. This paper presents a method for calculation of the time-resolved three-dimensional (3-D) strain-rate tensor using velocity vector information in a 3-D spatial grid during the whole cardiac cycle. The strain-rate tensor provides full information of both magnitude and direction of the instantaneous deformation of the myocardium. A method for visualization of the full 3-D tensor is also suggested. The tensors are visualized using ellipsoids, which display the principal directions of strain-rate and the ratio between strain-rate magnitude in each direction. The presented method reveals the principal strain-rate directions without a priori knowledge of myocardial motion directions.