Eulerian and Lagrangian approaches to compute residence-time in aneurysms

Flow stagnation is an important hemodynamic feature in aneurysms and plays a major role in biochemical transport and thrombus formation. Several Eulerian and Lagrangian approaches have been used in the literature to quantify flow stagnation. However, the connection between these approaches is not obvious, and the physiological implication of each method is not well understood. In this study, several measures of flow stagnation and residence-time are computed in patient-specific abdominal aortic and cerebral aneurysm models. In the Eulerian framework, advection-diffusion-(reaction) equations were solved using the Eulerian residence-time and virtual ink methods. Point-wise residence-time was computed as the inverse of time-average velocity magnitude. Finally, the recent concept of Eulerian indicators was used to quantify mobility and stagnation. In the Lagrangian framework, particle residence-time and mean exposure time were computed via discrete particle tracking of massless tracers. We present a thorough comparison of the six different measures of residence-time and discuss the implications of each method.