This paper presents a new registration algorithm, called Temporal Di eomorphic Free Form Deformation (TDFFD), and its application to motion and strain quanti cation from a sequence of 3D ultrasound (US) images. The originality of our approach resides in enforcing time consistency by representing the 4D velocity eld as the sum of continuous spatiotemporal B-Spline kernels. The spatiotemporal displacement eld is then recovered through forward Eulerian integration of the non-stationary velocity eld. The strain tensor is/ncomputed locally using the spatial derivatives of the reconstructed displacement eld. The energy functional considered in this paper weighs two terms: the image similarity and a regularization term. The image similarity metric is the sum of squared di erences between the intensities of each frame and a reference one. Any frame in the sequence can be chosen as reference. The regularization term is based on the/nincompressibility of myocardial tissue. TDFFD was compared to pairwise 3D FFD and 3D+t FFD, both/non displacement and velocity elds, on a set of synthetic 3D US images with di erent noise levels. TDFFD/nshowed increased robustness to noise compared to these two state-of-the-art algorithms. TDFFD also proved to be more resistant to a reduced temporal resolution when decimating this synthetic sequence. Finally, this synthetic dataset was used to determine optimal settings of the TDFFD algorithm. Subsequently, TDFFD/nwas applied to a database of cardiac 3D US images of the left ventricle acquired from 9 healthy volunteers and 13 patients treated by Cardiac Resynchronization Therapy (CRT). On healthy cases, uniform strain patterns were observed over all myocardial segments, as physiologically expected. On all CRT patients, the/nimprovement in synchrony of regional longitudinal strain correlated with CRT clinical outcome as quanti ed by the reduction of end-systolic left ventricular volume at follow-up (6 and 12 months), showing the potential of the proposed algorithm for the assessment of CRT.

This research has been partially funded by the Spanish Industrial and Technological Development Center (CDTI) under the CENIT Programme (cvREMOD Project), the Spanish Ministry of Science and Innovation (MICINN) and the European Regional Development Fund (ERDF) through the research project STIMATH (TIN2009-14536-C02-01), and the European Community’s Seventh Framework Program (FP7/2007-2013) under the euHeart project (FP7-ICT-2007-2-224495).