Modelling blood flow in patients with heart valve disease using deep learning: A computationally efficient method to expand diagnostic capabilities in clinical routine

Figures

• 

  Figure 1. Surface model of the aorta and aortic valve of a typical case with severe aortic stenosis. Additionally, labels for the various parts of the aorta are provided as well as a schematic depiction of the left ventricle attached to the left-ventricular outflow tract (LVOT).

• 

  Figure 2. An example of the computational mesh structure in the aortic valve and ascending aorta used for the computational fluid dynamics simulations. The boundary layer structure used to resolve near wall flow can be seen around the valve and vessel walls.

• 

  Figure 3. Comparison between a simulation with unsteady flow boundary conditions (BC) and a steady flow BC at peak systolic flow rate for a patient with a severe aortic stenosis. Top diagram compares pressure, bottom diagram wall-shear-stress (WSS). The flow curve for the ejection phase as well as the peak-systolic flow rate were derived from left-ventricular volumetry data.

• 

  Figure 4. Deriving the compact representation (bottom plot) from the three-dimensional pressure and velocity field (top). Cross-section planes are defined along the vessel centerline. The average values of pressure on these planes are used to plot locally averaged pressure along the vessel centerline. Similarly, average values of WSS are computed from vessel sections between two adjacent cross-sections.

• 

  Figure 5. Schematic depiction of the artificial neural network (ANN) based workflow for computing pressure and wall-shear-stress (WSS) along the vessel centerline. Clinical data pre-processing includes the extraction of the vessel surface model as well as peak systolic flow rate from multiphasic computed tomography (CT) image data. Vessel centerline and cross-section shapes are then derived from the surface model and passed to the ANN directly (centerline-coordinates) and through an auto encoder, respectively. A long-short-term-memory (LSTM) recurrent neural network computes the flow states at each centerline point based on centerline coordinates, encoded cross-sections and flow rate. Lastly, a fully connected layer derives pressure and wall-shear-stress along vessel centerline from the flow states provided by the LSTM. Hidden state and input/output sizes are also provided in the schematic.

• 

  Figure 6. Top left: Distribution of maximum pressure drop (MPD) within the entire simulation data. Top right: Distribution of MPD within the set of test cases. Bottom: An exemplary depiction of CFD-based pressure and wall-shear-stress (WSS) in the compact representation (i.e., average along centerline). Additionally, the measurement points for transvalvular pressure gradient (TPG, red) and MPD (green) are shown with their respective values.

• 

  Figure 7. Scatter plots of absolute and normalized root-mean-square-errors (RMSE), calculated between computational fluid dynamics (CFD) simulations and artificial neural network (ANN)-based results for the set of 23 test cases. Top shows absolute pressure and wall-shear-stress (WSS) RMSE over CFD computed maximum pressure drop and maximum WSS, respectively. Bottom shows pressure and WSS RMSE normalized with TPG and maximum WSS, respectively.

• 

  Figure 8. Comparison of ANN and CFD-based pressure and wall-shear-stress (WSS) along vessel centerline. Cases (A–F) are ordered by descending transvalvular-pressure-gradient.