Three-dimensional reconstruction of cardiac flows based on multi-planar velocity fields

Measurement of the three-dimensional flow field inside the cardiac chambers has proven to be a challenging task. This is mainly due to the fact that generalized full-volume velocimetry techniques cannot be easily implemented to the heart chambers. In addition, the rapid pace of the events in the heart does not allow for accurate real-time flow measurements in 3D using imaging modalities such as magnetic resonance imaging, which neglects the transient variations of the flow due to averaging of the flow over multiple heartbeats. In order to overcome these current limitations, we introduce a multi-planar velocity reconstruction approach that can characterize 3D incompressible flows based on the reconstruction of 2D velocity fields. Here, two-dimensional, two-component velocity fields acquired on multiple perpendicular planes are reconstructed into a 3D velocity field through Kriging interpolation and by imposing the incompressibility constraint. Subsequently, the scattered experimental data are projected into a divergence-free vector field space using a fractional step approach. We validate the method in exemplary 3D flows, including the Hill’s spherical vortex and a numerically simulated flow downstream of a 3D orifice. During the process of validation, different signal-to-noise ratios are introduced to the flow field, and the method’s performance is assessed accordingly. The results show that as the signal-to-noise ratio decreases, the corrected velocity field significantly improves. The method is also applied to the experimental flow inside a mock model of the heart’s right ventricle. Taking advantage of the periodicity of the flow, multiple 2D velocity fields in multiple perpendicular planes at different locations of the mock model are measured while being phase-locked for the 3D reconstruction. The results suggest the metamorphosis of the original transvalvular vortex, which forms downstream of the inlet valve during the early filling phase of the right ventricular model, into a streamline single-leg vortex extending toward the outlet.