Boundary conditions by Schwarz-Christoffel mapping in anatomically accurate hemodynamics.

Appropriate velocity boundary conditions are a prerequisite in computational hemodynamics. A method for mapping analytical or experimental velocity profiles on anatomically realistic boundary cross-sections is presented. Interpolation is required because the computational and experimental domains are seldom aligned. In the absence of velocity information one alternative is the adaptation of analytical profiles based on volumetric flux constraints. The presented algorithms are based on the Schwarz-Christoffel (S-C) mapping of singly or doubly connected polygons to the unit circle or an annulus with unary external radius. S-C transformations are combined to construct a one-to-one invertible map between the target surface and the measurement domain or the support of the source analytical profile. The proposed technique permits us to segment each space separately and map one onto the other in its entirety. Tests are performed with normal velocity boundary conditions for computational simulations of blood flow in the ascending aorta and cerebrospinal fluid flow in the spinal cavity. Mappings of axisymmetric velocity profiles of the Womersley type through a simply connected circular pipe as well as through a doubly connected circular annulus, and interpolations from in-vivo phase-contrast magnetic resonance imaging velocity measurements under instantaneous volumetric flux constraints are considered.

A study on the compliance of a right coronary artery and its impact on wall shear stress.

A computational model incorporating physiological motion and uniform transient wall deformation of a branchless right coronary artery (RCA) was developed to assess the influence of artery compliance on wall shear stress (WSS). Arterial geometry and deformation were derived from modern medical imaging techniques, whereas the blood flow was solved numerically employing a moving-grid approach using a well-validated in-house finite element code. The simulation results indicate that artery compliance affects the WSS in the RCA heterogeneously, with the distal region mostly experiencing these effects. Under physiological inflow conditions, coronary compliance contributed to phase changes in the WSS time history, without affecting the temporal gradient of the local WSS nor the bounds of the WSS magnitude. Compliance does not cause considerable changes to the topology of WSS vector patterns nor to the localization of WSS minima along the RCA. We conclude that compliance is not an important factor affecting local hemodynamics in the proximal region of the RCA while the influence of compliance in the distal region needs to be evaluated in conjunction with the outflow to the myocardium through the major branches of the RCA.

Computational investigation of subject-specific cerebrospinal fluid flow in the third ventricle and aqueduct of Sylvius.

The cerebrospinal fluid flow in the third ventricle of the brain and the aqueduct of Sylvius was studied using computational fluid dynamics (CFD) based on subject-specific boundary conditions derived from magnetic resonance imaging (MRI) scans. The flow domain geometry was reconstructed from anatomical MRI scans by manual image segmentation. The movement of the domain boundary was derived from MRI brain motion scans. Velocimetric MRI scans were used to reconstruct the velocity field at the inferior end of the aqueduct of Sylvius based on the theory of pulsatile flow in pipes. A constant pressure boundary condition was assigned at the foramina of Monro. Three main flow features were observed: a fluid jet emerging from the aqueduct of Sylvius, a moderately mobile recirculation zone above the jet and a mobile recirculation below the jet. The flow in the entire domain was laminar with a maximum Reynolds number of 340 in the aqueduct. The findings demonstrate that by combining MRI scans and CFD simulations, subject-specific detailed quantitative information of the flow field in the third ventricle and the aqueduct of Sylvius can be obtained.

Computational simulation of a non-newtonian model of the blood separation process.

The aim of this work is to construct a computational fluid dynamics model capable of simulating the transient non-Newtonian process of apheresis. A Lagrangian-Eulerian model has been developed which tracks the blood particles within a two-dimensional flow configuration. Within the Eulerian method, the fluid mass and momentum conservation equations within the separator are solved using the density and the viscosity is calculated from the blood particle concentrations. Subsequently, the displacement of the blood particles is calculated with a Lagrangian method. Hawksley's model for the density of supensions is used in the variable density calculation. The viscosity is calculated with two models based on Vand's rigid particle suspension viscosity concepts, followed by the flow field calculation in the separator. Simulations were performed for various inlet hematocrit values and separator lengths. The simulations are in satisfactory agreement with experimental results reported in literature, indicating a complete separation of plasma and red blood cells (RBCs), as well as nearly complete separation of red blood cells and platelets. No hemolysis was observed in the simulations because the shear rate remained under the critical value of 150 N/m2.

Computational simulation of the blood separation process.

The aim of this work is to construct a computational fluid dynamics model capable of simulating the quasitransient process of apheresis. To this end a Lagrangian-Eulerian model has been developed which tracks the blood particles within a delineated two-dimensional flow domain. Within the Eulerian method, the fluid flow conservation equations within the separator are solved. Taking the calculated values of the flow field and using a Lagrangian method, the displacement of the blood particles is calculated. Thus, the local blood density within the separator at a given time step is known. Subsequently, the flow field in the separator is recalculated. This process continues until a quasisteady behavior is reached. The simulations show good agreement with experimental results. They shows a complete separation of plasma and red blood cells, as well as nearly complete separation of red blood cells and platelets. The white blood cells build clusters in the low concentrate cell bed.

Reconstruction of cerebrospinal fluid flow in the third ventricle based on MRI data.

A finite-volume model of the cerebrospinal fluid (CSF) system encompassing the third ventricle and the aqueduct of Sylvius was used to reconstruct CSF velocity and pressure fields based on MRI data. The flow domain geometry was obtained through segmentation of MRI brain anatomy scans. The movement of the domain walls was interpolated from brain motion MRI scans. A constant pressure boundary condition (BC) was specified at the foramina of Monro. A transient velocity BC reconstructed from velocimetric MRI scans was employed at the inferior end of the aqueduct of Sylvius. It could be shown that a combination of MRI scans and computational fluid dynamics (CFD) simulation can be used to reconstruct the flow field in the third ventricle. Pre-interventional knowledge of patient-specific CSF flow has the potential to improve neurosurgical interventions such as shunt placement in case of hydrocephalus.