A Deep Learning Framework for Design and Analysis of Surgical Bioprosthetic Heart Valves

Figure 1. A framework for predictive biomechanics-based approach for design of BHVs. Evaluating the valve performance using finite element analysis is a critical time-consuming step in the process. DLFEA can replace compute intensive biomechanics simulations with fast valve performance evaluations.

Figure 2. The histograms (a) show the Euclidean distance and Hausdorff distance between predicted deformations from DLFEA and the simulated deformations for the test data. (b) Shows the DLFEA-predicted coaptation area compared with the coaptation area obtained from simulations. The predicted coaptation area is highly correlated (R = 0.9328) with the simulated values.

Figure 3. Illustrative examples of valve deformations and their corresponding maximum in-plane principal Green-Lagrange strains computed from isogeometric simulations and the predicted deformations using the DLFEA framework.

Figure 4. t-distributed stochastic neighborhood embedding (t-SNE) of the higher dimensional manifold learnt by DLFEA. t-SNE generates a lower dimensional embedding of the data using the learnt model, which can provide insights into the distribution of the data. This particular t-SNE shows that the different geometries are well clustered, showing that the model has reasonably learnt the effect of geometric parameters used for generating the reference configurations, although this information is not available to the model.

Figure 5. The DLFEA-predicted coaptation area variation with pressure is shown in (a) for three specific sets of reference configuration geometries. (b) Shows a similar plot with variation in material coefficient 1 (see Supplement for more details) for three specific reference configurations, pressure, and other material properties. (c) is a similar plot with variation in geometry parameter (belly curve parameter, see Supplement) for two specific material properties, and pressure. These plots are generated with 1000 intermediate values in the parameter of interest. The region estimating 10% variation of the predicted coaptation area value is highlighted.

Figure 6. NURBS-aware convolution. In order to learn from a 3D surface, we extract the control points of the NURBS surface in the parametric space, which introduces spatial structure to the control points. We restructure the control points (from the parametric space) into three channels of an image (texture representation) to perform traditional convolution operations.

Figure 7. Deep-learning-based convolutional autoencoder for predicting the output deformations and the coaptation area of the heart valve in the closed state, with the BHV leaflet reference geometry, material properties, and the aortic pressure as input. The leaflet deformations are individually learnt using a NURBS-aware convolution followed by an encoder. All the inputs are fused using the intermediate fusion layers (also called as the coding layers).