A one-dimensional computational model for blood flow in an elastic blood vessel with a rigid catheter.

Strokes are one of the leading causes of death in the United States. Stroke treatment involves removal or dissolution of the obstruction (usually a clot) in the blocked artery by catheter insertion. A computer simulation to systematically plan such patient-specific treatments needs a network of about 105 blood vessels including collaterals. The existing computational fluid dynamic (CFD) solvers are not employed for stroke treatment planning as they are incapable of providing solutions for such big arterial trees in a reasonable amount of time. This work presents a novel one-dimensional mathematical formulation for blood flow modeling in an elastic blood vessel with a centrally placed rigid catheter. The governing equations are first-order hyperbolic partial differential equations, and the hypergeometric function needs to be computed to obtain the characteristic system of these hyperbolic equations. We employed the Discontinuous Galerkin method to solve the hyperbolic system and validated the implementation by comparing it against a well-established 3D CFD solver using idealized vessels and a realistic truncated arterial network. The results showed clinically insignificant differences in steady flow cases, with overall variations between 1D and 3D models remaining below 10%. Additionally, the solver accurately captured wave reflection phenomena at domain discontinuities in unsteady cases. A primary advantage of this model over 3D solvers is its ease in obtaining a discretized geometry of complex vasculatures with multiple arterial branches. Thus, the 1D computational model offers good accuracy and applicability in simulating complex vasculatures, demonstrating promising potential for investigating patient-specific endovascular interventions in strokes.

CFD for evaluation and treatment planning of aneurysms: review of proposed clinical uses and their challenges.

Computational fluid dynamics (CFD) has been used for several years to identify mechanical risk factors associated with aneurysmal evolution and rupture as well as to understand flow characteristics before and after surgical treatments in order to help the clinical decision making process. We used the keywords, "CFD" and "aneurysms" to search recent publications since about 2000, and categorized them into (i) studies of rupture risk factors and (ii) investigations of pre- and post-evaluations of surgical treatment with devices like coils and flow diverters (FD). This search enables us to examine the current status of CFD as a clinical tool and to determine if CFD can potentially become an important part of the routine clinical practice for the evaluation and treatment of aneurysms in near future. According to previous reports, it has been argued that CFD has become a quite robust non-invasive tool for the evaluation of surgical devices, especially in the early stages of device design and it has also been applied successfully to the study of rupture risk assessment. However, we find that due to the large number of pre-processing inputs further efforts of validation and reproducibility of CFD with larger clinical datasets are still essential to identify standardized mechanical risk factors. As a result, we identify the following needs to have a robust CFD tool for clinical use: (i) more reliability tests through validation studies, (ii) analyses of larger generalized clinical datasets to find converging universal risk parameters, (iii) fluid structure interaction (FSI) analyses to better understand the detailed vascular remodeling processes associated with aneurysm growth, evolution and rupture, and (iv) better coordinated and organized communications and collaborations between engineers and clinicians.

Hemodynamics of Cerebral Aneurysms.

The initiation and progression of cerebral aneurysms are degenerative processes of the arterial wall driven by a complex interaction of biological and hemodynamic factors. Endothelial cells on the artery wall respond physiologically to blood-flow patterns. In normal conditions, these responses are associated with nonpathological tissue remodeling and adaptation. The combination of abnormal blood patterns and genetics predisposition could lead to the pathological formation of aneurysms. Here, we review recent progress on the basic mechanisms of aneurysm formation and evolution, with a focus on the role of hemodynamic patterns.