BACKGROUND AND PURPOSE Hemodynamics play an important role in the mechanisms that govern the initiation, growth, and possible rupture of intracranial aneurysms. The purpose of this study was to objectively characterize these dynamics, classify them, and connect them to aneurysm rupture. MATERIALS AND METHODS Image-based computational fluid dynamic simulations were used to re-create the hemodynamics of 210 patient-specific intracranial aneurysm geometries. The hemodynamics were then classified according to their spatial complexity and temporal stability by using quantities derived from vortex core lines and proper orthogonal decomposition. RESULTS The quantitative classification was compared with a previous qualitative classification performed by visual inspection. Receiver operating characteristic curves provided area-under-the-curve estimates for spatial complexity (0.905) and temporal stability (0.85) to show that the 2 classifications were in agreement. Statistically significant differences were observed in the quantities describing the hemodynamics of ruptured and unruptured intracranial aneurysms. Specifically, ruptured aneurysms had more complex and more unstable flow patterns than unruptured aneurysms. Spatial complexity was more strongly associated with rupture than temporal stability. CONCLUSIONS Complex-unstable blood flow dynamics characterized by longer core line length and higher entropy could induce biologic processes that predispose an aneurysm for rupture.

Hemodynamics is thought to be a fundamental factor in the formation, progression and rupture of cerebral aneurysms. Understanding these mechanisms is important to improve their rupture risk assessment and treatment. In this study we analyze the blood flow field in a growing cerebral aneurysm using experimental particle image velocimetry (PIV) and computational fluid dynamics (CFD) techniques. Patient-specific models were constructed from longitudinal 3D computed tomography angiography (CTA) images acquired at one-year intervals. Physical silicone models were constructed from the CTA images using rapid prototyping techniques and pulsatile flow fields were measured with PIV. Corresponding CFD models were created and run under matching flow conditions. Both flow fields were aligned, interpolated, and compared qualitatively by inspection and quantitatively by defining similarity measures between the PIV and CFD vector fields. Results showed that both flow fields were in good agreement. Specifically, both techniques provided consistent representations of the main intra-aneurysmal flow structures, and their change during the geometric evolution of the aneurysm. Despite differences observed mainly in the near wall region and the inherent limitations of each technique, the information derived is consistent and can be used to study the role of hemodynamics in the natural history of intracranial aneurysms.

Abstract. We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF), which is derived from an overapproximation of the gradient of the solution-flows. The SF measures the discrepancy between two states propagated by the system solution from two initial states lying in a well-defined region, thereby allowing LRT to compute a reachtube with a ball-overestimate in a metric where the computed enclosure is as tight as possible. To evaluate its performance, we implemented a prototype of LRT in C++/Matlab, and ran it on a set of well-established benchmarks. Our results show that LRT compares very favorably with respect to the CAPD and Flow* tools.

Unstable nonchaotic solutions embedded in the chaotic attractor can provide significant new insight into chaotic dynamics of both low-and high-dimensional systems. In particular, in turbulent fluid flows, such unstable solutions are referred to as exact coherent structures (ECS) and play an important role in both initiating and sustaining turbulence. The nature of ECS and their role in organizing spatiotemporally chaotic dynamics, however, is reasonably well understood only for systems on relatively small spatial domains lacking continuous Euclidean symmetries. Construction of ECS on large domains and in the presence of continuous translational and/or rotational symmetries remains a challenge. This is especially true for models of excitable media which display spiral turbulence and for which the standard approach to computing ECS completely breaks down. This paper uses the Karma model of cardiac tissue to illustrate a potential approach that could allow computing a new class of ECS on large domains of arbitrary shape by decomposing them into a patchwork of solutions on smaller domains, or tiles, which retain Euclidean symmetries locally.

We establish conditions for distinguishing between two topologically identical strange attractors that are enclosed by identical bounding tori, one of which is generated by a flow restricted to that torus, the other of which is generated by a flow in a different bounding torus and either imaged or lifted into the first bounding torus.