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

摘要

Measurement of the three-dimensional flowfield inside the cardiac chambers has proven to be a challengingtask. This is mainly due to the fact that generalizedfull-volume velocimetry techniques cannot be easilyimplemented to the heart chambers. In addition, the rapidpace of the events in the heart does not allow for accuratereal-time flow measurements in 3D using imaging modalitiessuch as magnetic resonance imaging, which neglectsthe transient variations of the flow due to averaging ofthe flow over multiple heartbeats. In order to overcomethese current limitations, we introduce a multi-planarvelocity reconstruction approach that can characterize 3Dincompressible flows based on the reconstruction of 2D velocity fields. Here, two-dimensional, two-componentvelocity fields acquired on multiple perpendicular planesare reconstructed into a 3D velocity field through Kriginginterpolation and by imposing the incompressibilityconstraint. Subsequently, the scattered experimental dataare projected into a divergence-free vector field spaceusing a fractional step approach. We validate the methodin exemplary 3D flows, including the Hill’s sphericalvortex and a numerically simulated flow downstream ofa 3D orifice. During the process of validation, differentsignal-to-noise ratios are introduced to the flow field, andthe method’s performance is assessed accordingly. Theresults show that as the signal-to-noise ratio decreases,the corrected velocity field significantly improves. Themethod is also applied to the experimental flow inside amock model of the heart’s right ventricle. Taking advantageof the periodicity of the flow, multiple 2D velocityfields in multiple perpendicular planes at different locationsof the mock model are measured while being phaselockedfor the 3D reconstruction. The results suggestthe metamorphosis of the original transvalvular vortex,which forms downstream of the inlet valve during theearly filling phase of the right ventricular model, into astreamline single-leg vortex extending toward the outlet.