Modelling of strain tensors in cardiac kinematics

Abstract: The heart wall consists of three distinct layers: the inner endocardium, the middle myocardium and the outer epicardium. The myocardium is the functional tissue that endows the heart with its ability to pump blood, and consists primarily of locally parallel muscle fibers. The orientation of these muscle fibers change with position in the wall. The myofibers have been shown to be arranged parallel in sheets that are rotated around the fiber direction relative to the radial direction of the left ventricle. During a cardiac beat there are local shortenings and lengthenings in the myocardium, both within and between myolaminar sheets. The mechanism by which the local shortening or lengthening is translated into the large and complex motions of the ventricle has to be studied on a local level, by studying deformation. A parameter that describes deformation is strain. The scope of the current project is to perform detailed studies of cardiac strain, particularly during diastole. There exist several definitions of strain tensors and the focus in this project is on the Lagrangian strain tensor.The myocardial bead array gives kinematic measures of the myocardium toestimate strain in the left ventricular wall of the pumping heart. During surgery, radiopaque beads are inserted into the myocardium along three transmural columns, with typically four to six beads in each column. The 4D coordinates of the beads are acquired with high resolution using time-resolved biplane cineradiography.This thesis presents a method for strain estimation from myocardial coordinate data. This strain estimation method is tailored for the transmural bead array and fits a polynomial to the bead coordinates. A benefit with the polynomial method is its ability to avoid loss of accuracy for the case of a missing bead, e.g. due to problems sometimes encountered during surgery or during the recovery period. The polynomial strain estimation method is applied to coordinate data from a transmural bead array to quantify diastolic myocardial strain in the ovine heart. This reveals transmural strain inhomogeneities during diastole in the ovine heart.