We propose a rapid interpolation method of computational fluid dynamics (CFD) solution based on the collocation method for vascular flows through the polynomial interpolation and present a proof-of-concept computation of our preliminary results. A rapid CFD can play a crucial role for some applications such as the hemodynamics assessment for human vasculature in the emergent situation. The CFD approach for the real-time assessment at the clinical level is, however, not a practical tool due to the computational complexity and the long time integration needed for the individual CFDs. We propose an efficient, accurate, yet fast interpolation method of finding CFD solutions that can be utilized for the real-time hemodynamic analysis for clinicians. The main idea of the method is to use the vascular library where vascular solutions with different parameter values are pre-computed and stored. The desired unknown CFD solution is obtained via the interpolation using the similar solutions from the library. We use the spectral collocation method for the individual CFD solutions. The collocation method makes it easier to map the solution from the physical domain to the reference domain for the interpolation using the homeomorphic transformation. The interpolation is then directly constructed using the solution fields at the collocation points. Our preliminary results for vascular flows of 3D stenosis show that the proposed method is fast and accurate.

Understanding 3D flow-velocity fields may be valuable during interventional procedures. Thus, we are developing methods to calculate 3D flow fields from single-plane angiographic sequences. The vessel geometry is selected. Flow fields are generated based on laminar flow conditions. X-ray-attenuating contrast is propagated through the vessel using the flow fields. Angiograms are generated at 30 frames/second using ray-casting. Vessel profile data are extracted from the angiograms along lines perpendicular to the vessel axis. The conversion from image intensity to contrast pathlength is determined. The contrast pathlength is calculated for each vessel-profile point, and the contrast is centered about the vessel's central plane generating a 3D contrast distribution. This procedure is repeated for each acquired angiogram. Corresponding points on the surface of the calculated contrast distributions are established for temporally adjacent distributions using estimated streamlines. Distances between corresponding points are calculated from which average velocities are calculated. These average velocities are placed at points along the streamlines, thereby generating a 3D velocity flow field in the vessel lumen. Simulations for steady flow conditions for straight vessels, curved (in-plane) vessels, and vessels with stenoses, for noiseless and noisy (10% peak contrast) angiograms were performed. The calculated and simulated 3D contrast distributions agree well for both noiseless and noisy conditions (errors < 2 voxels ~ 0.2 mm). Average absolute error of the calculated 3D flow velocities is approximately 10%. These promising initial results indicate that this technique may form the basis for calculating 3D-contrast and 3D-flow-velocity distributions from standard single-plane angiographic sequences.