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Current ultrasound methods for measuring myocardial strain are often limited to measurements in one or two dimensions. Cardiac motion and deformation however are truly 3D. With the introduction of matrix transducer technology, 3D ultrasound imaging of the heart has become feasible but suffers from low temporal and spatial resolution, making 3D strain estimation challenging. In this paper, it is shown that spatio- temporal elastic registration of currently available 3D volumetric ultrasound data sets can be used to measure the full 3D strain tensor. The method is validated using simulated data sets of the left ventricle. The regional motion of the ventricle was estimated with an accuracy of 10.14 plusmn 3.70% to 26.40 plusmn 11.95%, depending on the noise level and heart rate.