Novel feature-based visualization of the unsteady blood flow in intracranial aneurysms with the help of proper orthogonal decomposition (POD)

The recognition and interpretation of pulsatile subject-specific blood flow is a challenging task. Animations of various quantities - such as blood flow velocity, pressure, or wall shear stress - can be depicted to visualize the complex time-varying flow features, normally in a region of interest. Traditional visualization methods however can hardly convey the dynamic information of the system. Proper orthogonal decomposition (POD), a mathematical tool, allows for the complex spatial-temporal information to be decomposed into individual spatial modes. In the present study, the most energetic blood flow features are extracted with the help of POD analysis. The first mode, representing the most energetic flow feature, characterizes the temporal mean of the flow velocity. It is considered as the primary flow. The second most energetic mode corresponds to the secondary flow features. Visualization techniques combining the primary and the secondary flows are suggested in the present paper in order to create a simplified visualization of the unsteady blood flow. The methods are presented for intracranial aneurysms for both measured as well as simulated data, illustrating the application for Phase-Contrast Magnetic Resonance Imaging (PC-MRI) and computational fluid dynamics (CFD) results.