A practical approach for estimation of patient-specific intra-aneurysmal flows using variational data assimilation

Abstract

Evaluation of hemodynamics is crucial to predict growth and rupture of cerebral aneurysms. Variational data assimilation (DA) is a powerful tool to characterize patient-specific intra-aneurysmal flows. The DA method inversely estimates a boundary condition in fluid equations using personalized flow data; however, its high computational cost in optimization problems makes its use impractical. This study proposes a practical DA approach to evaluate patient-specific intra-aneurysmal flows. To estimate personalized flows, a variational DA method was combined with computational fluid dynamics (CFD) analysis and observed intra-aneurysmal velocity data, and an inverse problem was solved to estimate the spatiotemporal velocity profile at a boundary of the aneurysm neck. To circumvent an ill-posed inverse problem, model order reduction based on a Fourier series expansion was used to describe temporal changes in state variables. In numerical validation using synthetic data from a direct CFD analysis, the present DA method achieved excellent agreement with the ground truth, with a velocity mismatch of approximately 18%. In flow estimations for three patient-specific datasets, the velocity mismatch for the present DA method was markedly lower than that for the direct CFD analysis and would mitigate unphysical velocity distributions in flow data from phase contract magnetic resonance imaging. By focusing only on the intra-aneurysmal region, the present DA approach provides an attractive way to evaluate personalized flows in aneurysms with greater reliability than conventional CFD and better efficiency than existing DA approaches.