• boundary contidions
• carotid artery
• cfd
• hemodynamic parameters
• numerical simulations

The carotid arteries are major blood vessels in the neck that supply blood to the brain, neck, and face. There are two carotid arteries, one on the right and one on the left. In the neck, each carotid artery branches into two divisions: the internal carotid artery (ICA) supplies blood to the brain and the external carotid artery (ECA) supplies blood to the face and neck.

CFD models have become very effective tools for predicting the flow field within the carotid bifurcation, and for understanding the relationship between local hemodynamics, and the origin and progression of vascular wall pathologies. Hemodynamics is a key factor in the physiology of healthy vessels, but also in the onset of vascular wall pathologies. Geometry construction, blood characterization, and type of solver are some of the key aspects to consider.

However, the use of realistic Boundary Conditions (BCs) is critical for the accuracy of the simulation. For the carotid artery, the vessel upstream of the bifurcation Common Carotid Artery (CCA) represents the inlet. The two vessels downstream of the bifurcation, the ICA and ECA, are the two outlets. The inlet BC supplies the impulsion to the system and receives the reflected backward wave created by the distal networks. The inlet velocity profiles influence the magnitude of the hemodynamic properties of blood flow in a patient-specific carotid artery with stenosis. The employment of the BCs determines the computational cost and accuracy of the CFD simulation.

The goal of this work is to compare results obtained from CFD simulations using different outlet BCs with those extracted from MR data. The hemodynamic parameters' results are shown with the most used BCs: the transient pressure profile with the Resistance-Capacitance-Resistance (RCR), also known as the Windkessel model. Among all the imaging techniques used to extract vessel information, 4D-Flow MRI allows the acquisition of a single 3D volume covering all the vessels of interest and extracting in post-processing the single 2D plans useful for classical clinical analysis. From 4D-Flow data, a single volume deriving from the implementation of the Phase-Contrast Magnetic Resonance Angiography (PC-MRA) was obtained.
A PC-MRA was performed leveraging the blood flow encoded in three directions to compute the absolute velocity squared values combined with magnitude squared, as a noise mask. Then, with the segmentation process, each pixel/voxel of an image was associated with a label and the interesting structures were identified. The result of the segmentation process was a Standard Tessellation Language (STL) format file. The model was created with a patching operation and generated the volume mesh with the prescription of four inflation layers, to better capture Wall Shear Stress (WSS). Then, a Mesh Sensitivity Analysis was performed to determine the best element size as a compromise between accuracy and computational calculation necessary for the simulation.
Therefore, an analysis of the boundary conditions was set up with various increasingly precise approaches. For all three simulations, as inlet BC, the flow extracted from MR was used. The flow values for each outlet were compared in three simulations with increasing accuracy. From the CFD simulation with the lowest flow difference values with the MR, the results of the most significant hemodynamic parameters were collected.

In the first approach, only the flow extracted from MR data was used as inlet BC. In the second one, to make the simulation even more patient-specific, real flow data were extracted for the supra-aortic branches and carotids on selected planes. Starting from these flows, the refined RCRs were estimated. Then, in the third one, the flow values extracted at the carotid branches were used. Quantification of the relative error between simulations results and MR data were reported in term of flow peak and volumetric output, to highlight the difference between the three approaches. The main hemodynamic indices were evaluated for the simulation which revealed the lowest difference in flow with the resonance data. Moreover, a comparison between the third simulation and MR, in terms of WSS and velocity maps at different cross sections, was performed.

The differences in the WSS distribution for all analyzed instants, and more evident at the systolic peak, could be due to the MR spatial resolution. MRI-derived WSS estimations have a relative distribution that is reasonably similar to the WSS distribution derived by the CFD. These measurement errors are most significant in regions of low and complex flow, which are precisely the regions of most interest.
The major difference in terms of velocity maps was found at the level of internal/external carotid arteries due to different factors. MR imaging especially underestimates peak systolic blood flow velocities in the CCA and ICA. There is a difference in the distribution of velocities due to the combination of several intrinsic errors in the segmentation from PC-MRA mediated over the entire cardiac cycle and by possible saturation of the values due to the data acquisition phase.

This thesis work provided an evaluation of the impact of different BCs assumed for carotid arteries CFD simulations on the hemodynamic results. Hence the findings may represent a crucial aspect to be considered when any kind of approximation related to patient outlet conditions is performed.