Computing cardiac strain from variational optical flow in four-dimensional echocardiography

Myocardial strain is important to assess cardiac function and diagnose cardiovascular disease. Despite the adoption of 4D (volume + time) echocardiography for diagnostic and therapeutic purposes, current clinical practice often relies exclusively on 2D measurements of strain or flow information resulting from Doppler echography. However, strain is a 3D measure of deformation in the radial, circumferential and longitudinal directions and therefore full 3D strain, and in particular out-of- sagittal plane strain components, include important information for diagnostic purposes since they provide additional information on the manner in which the heart lengthens and contracts during diastole and systole. In our prior work, we have developed robust variational optical flow methods to estimate dense myocardial motion. In this study, we extend this methodology to track ventricular outlines, which are subsequently used to compute displacement and deformation fields. This in turn is used to compute volumetric estimates of strain. We test our methods on a dataset of 4D ultrasound acquired in vivo from seven patients, and find good agreement with physiological precepts.