Hemodynamic simulation in the left atrium and left atrial appendage

The second tutorial focuses on a left atrium geometry, collected from a published public dataset by Roney et al.[RBP+21], located here. In particular, we selected the endocardium model labeled LA_Endo_5.vtk in the dataset, representing the inner left atrium wall. The tutorial is meant to demonstrate that VaMPy is also applicable to other vascular domains, not only tubular structures.

Attention

Because VaMPy relies on vtkPolyData as input, the .vtk model needs to be converted to .vtp (or .stl) format, which can easily be performed in ParaView by using the Extract Surface filter, and saving the data as LA_Endo_5.vtp.

Meshing an atrium with appendage refinement

The morphology of the left atrium is shown in Fig. 18, and typically includes an average of four pulmonary veins leading to a large chamber where blood circulates during the atrial diastole, before being pumped through the mitral valve into the left ventricle during atrial systole. In addition, on the left side of the chamber, the left atrium harbours the left atrial appendage, a small pouch-like extension of the atrium and known to be the most prone site of blood clot formation. Hence, this region of the left atrium is of interest, similar to intracranial aneurysms as presented earlier for the artery case.

Fig. 18 The surface model considered in this tutorial, where we have pointed out two of the four pulmonary veins, the left atrial appendage, and the mitral valve.

To ensure that the hemodynamics are captured sufficiently inside the left atrial appendage, we will perform mesh generation with refinement of this particular region. To manually refine a region on the geometry, the user may provide the --refine-region flag, or -r for short. Thus, to include a user-defined area of refinement, run the following command:

$ vampy-mesh -m constant -i LA_Endo/5/LA_Endo_5.vtp -r True -el 1.5 -bl False -fli 1 -flo 3 -at 

Here, the -fli and -flo flags determine the length of the flow extensions at the inlets and outlet, respectively, and the -at flag is used to notify the pipeline that an atrium model is being meshed. By executing the command above, the mesh generation becomes semi-automated, and a render window will eventually pop up, asking the user to specify a point on the surface that will represent the region that will be refined, as shown in Figure 7. Navigate with the mouse, and press space to place a point, u to undo, and q to proceed. The rest of the meshing pipeline is automated. Alternatively, the user may supply the --region-points (-rp for short), followed by three numbers representing the \(x, y\), and \(z\) coordinates of the point, making the pipeline fully automated again. If the point is located slightly off the surface, it will stick to the closest surface point. For the point shown in Fig. 19, this would correspond to running the following command:

$ vampy-mesh -m constant -i LA_Endo/5/LA_Endo_5.vtp -r True -rp 29.8 28.7 66.5 -el 1.5 -bl False -fli 1 -flo 3 -at 

Fig. 19 Render window for placing a seed, defining which region of the geometry that will be refined.

Using the command above should result in a volumetric mesh consisting of ~3.1M tetrahedral cells, as shown in Fig. 20 displaying the refinement in the left atrial appendage, and four boundary layers.

Fig. 20 Volumetric mesh of the left atrium model, with a zoomed in view of the left atrial appendage, clipped to display the refinement and four boundary layers.

CFD simulation in the left atrium model

The resulting mesh from the previous section is now used as input to the CFD simulation, followed by computation of the hemodynamic indices. The only real difference from the artery problem from eariler is that instead of running the Artery.py problem file, we here will be solving the problem defined in Atrium.py, also located in the simulation folder. Thus, running a left atrial CFD simulation can be performed by navigating to the src/vampy/simulation folder and executing the following command:

$ oasis NSfracStep problem=Atrium mesh_path=../../../LA_Endo/5/LA_5_Endo.xml.gz T=951 dt=0.951 save_solution_after_cycle=0

Running the simulations will create the result folder results_atrium, with the results and corresponding mesh saved compactly in HDF5 format. For this demonstration, the simulation was run for one cardiac cycle, corresponding to 0.951 s, with \(\Delta t =\) 0.951 ms resulting in a total of 1000 time steps per cycle. In Fig. 21 we present the volumetric rendering of velocity, the pressure field, the Q-criterion displaying vortical structures, and three hemodynamic indices; the time averaged wall shear stress (TAWSS), the oscillatory shear index (OSI), and the relative residence time (RRT).

Fig. 21 From left to right: the volumetric rendering of velocity, the pressure field, volumetric rendering of the Q-criterion, TAWSS, OSI, and RRT.

RBP+21

Caroline H Roney, Rokas Bendikas, Farhad Pashakhanloo, Cesare Corrado, Edward J Vigmond, Elliot R McVeigh, Natalia A Trayanova, and Steven A Niederer. Constructing a human atrial fibre atlas. Annals of biomedical engineering, 49(1):233–250, 2021.