Quantitative assessment of 4D hemodynamics in cerebral aneurysms using proper orthogonal decomposition

Abstract

Background and purpose: The comparison of different time-varying three-dimensional hemodynamic data (4D) is a formidable task. The purpose of this study is to investigate the potential of the proper orthogonal decomposition (POD) for a quantitative assessment.

Methods: The complex spatial-temporal flow information was analyzed using proper orthogonal decomposition to reduce the complexity of the system. PC-MRI blood flow measurements and computational fluid dynamic simulations of two subject-specific IAs were used to compare the different flow modalities. The concept of Modal Assurance Criterion (MAC) provided a further detailed objective characterization of the most energetic individual modes.

Results: The most energetic flow modes were qualitatively compared by visual inspection. The distribution of the kinetic energy on the modes was used to quantitatively compare pulsatile flow data, where the most energetic mode was associated to approximately 90% of the total kinetic energy. This distribution was incorporated in a single measure, termed spectral entropy, showing good agreement especially for Case 1.

Conclusion: The proposed quantitative POD-based technique could be a valuable tool to reduce the complexity of the time-dependent hemodynamic data and to facilitate an easy comparison of 4D flows, e.g., for validation purposes.

Keywords: Computational fluid dynamics (CFD); Flow visualization; Intracranial aneurysms; Phase-Contrast Magnetic Resonance Imaging (PC-MRI); Proper orthogonal decomposition (POD); Quantitative comparison.