A Low-Order Parametric Description of Left Ventricular Kinematics

Abstract

An approximate description for the deformation of the left ventricle (LV) throughout the cardiac cycle is developed in terms of three time-dependent parameters. The reference configuration, corresponding to end-diastole, is represented as a thick-walled prolate spheroid. By using prolate spheroidal coordinates, a three-parameter family of mappings is defined to represent the deformed shapes of the LV wall, while identically conserving wall volume. The three parameters represent lengthening with constant internal volume, contraction with reduction of internal volume, and torsion. Feasibility is illustrated using echocardiography data from a healthy subject. The reference configuration was defined by fitting observed points on LV endocardial and epicardial surfaces in long-axis images at end diastole. Time-courses of parameters defining LV kinematics were obtained for best fit to longitudinal strains, circumferential strains and rotations (LS, CS and R) obtained from speckle tracking echocardiography at 36 LV regions. Fitted versus echocardiography-measured CS, LS and R were compared at the LV base, mid-wall and apex at the endocardium and epicardium. The RMS deviation between fitted and measured peak strains was 0.06 (LS) and 0.08 (CS). Fitted and measured LV volume changes during contraction agreed closely. Circumferential variations in strain, which may be significant in normal and pathological hearts, are not represented here. The results demonstrate feasibility of a low-order description of the deformation field in the LV myocardium, based on echocardiographic imaging data. Such a description provides a basis for low-order models of LV mechanics and eventual real-time patient-specific analysis of LV mechanical parameters.