One-Dimensional and Three-Dimensional Models of Cerebrovascular Flow

Abstract

The Circle of Willis is a ring-like structure of blood vessels found beneath the hypothalamus at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. One-dimensional (1D) and three-dimensional (3D) computational fluid dynamics (CFD) models of the Circle of Willis have been created to provide a simulation tool which can potentially be used to identify at-risk cerebral arterial geometries and conditions and replicate clinical scenarios, such as occlusions in afferent arteries and absent circulus vessels. Both models capture cerebral haemodynamic autoregulation using a proportional-integral (PI) controller to modify efferent artery resistances to maintain optimal efferent flow rates for a given circle geometry and afferent blood pressure. The models can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures. The 1D model is particularly relevant in this instance, with its fast solution time suitable for real-time clinical decisions. Results show the excellent correlation between models for the transient efferent flux profile. The assumption of strictly Poiseuille flow in the 1D model allows more flow through the geometrically extreme communicating arteries than the 3D model. This discrepancy was overcome by increasing the resistance to flow in the anterior communicating artery in the 1D model to better match the resistance seen in the 3D results.

Group-wise construction of reduced models for understanding and characterization of pulmonary blood flows from medical images

“…It can also be drastically reduced when lower-dimensional models (i.e. 1D wave propagation or 0D lumped models) can efficiently replace 3D models (Moore et al, 2005;Blanco et al, 2009;Grinberg et al, 2011;Formaggia et al;Reymond et al, 2012). However, 3D models are really warranted when pressure losses and velocity features are largely determined by the interplay between hemodynamics and complex geometry Keshavarz-Motamed et al (2012); Itu et al (2013), as in these repaired ToF cases.…”

Modelling of flow through the circle of Willis and cerebral vasculature

“…Missing PCoA has been better modelled in previous CFD studies of CoW [14,15,17,18,19,20] and we plan to incorporate such a method in our model. Currently, our model has only one-way coupling between 3D CFD and the vascular tree fractal models.…”

“…They compared flow resistances calculated from flow simulations with those obtained using a vascular bed model based on parallel resistors. Moore et al [17,18] modelled three anatomical variations and showed the flow redistribution with these anatomical variations. Kim et al [19,20] modelled three patient-specific geometries and found communicating arteries play an important role in the cerebral autoregulation mechanism.…”

“…Alnaes et al [21] modelled three geometric variants of the posterior part of the CoW and showed that differences in vessel radii and bifurcation angle influence the wall shear stress. Most of these CFD models included autoregulation [14,15,[17][18][19][20] and only Kim et al [19] and Kim [20] modelled flexible walls.…”

“…In the CFD simulations of the CoW the vascular bed resistance models used for the outlet boundary conditions include: network of resistors [16,19,20], porous media as terminating blocks [14,15,17,18], constant pressure [21] and calculating flow resistance of branching tree models [16]. Cebral et al [16] recommended using arterial models to specify outflow conditions and include arterial compliance.…”