Prediction of 3D Cardiovascular hemodynamics before and after coronary artery bypass surgery via deep learning

Figures

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  Fig. 1. Comparison of velocity fields from CFD and deep learning (DL) methods, using a sample with a stenosis rate of 85%. a–d Are streamline diagrams of the entire cardiovascular internal flow field before and after CABG obtained from CFD and DL. The position indicated by the black arrow in a–d is the vortex region of ascending aorta. The position indicated by the red arrow in c, d is the grafts. e–h Are streamline diagrams of the coronary artery and grafts flow field. The blood flow velocity inside the coronary artery is smaller than that in the aorta, which means that it is difficult to clearly show the distribution of the internal flow field in the coronary artery under the same velocity color bar. Therefore, the coronary flow field is displayed separately. The position indicated by the blue arrow in g–h is the connection site between the graft and the LAD. i, j Are cross-sectional views of the velocity distribution, respectively from (i): RA branch; (ii): the proximal end of LAD before stenosis; (iii): the distal end of LAD after stenosis; (iv): descending aorta; (v): graft. (v) can reflect laminar flow in the graft. The comparison results confirm the high consistency of the…

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  Fig. 2. Comparison of pressure field from CFD and deep learning (DL), using a sample with a stenosis rate of 85%. Because the CFD outlet boundary was set as zero pressure condition, the pressure value in this figure was actually the pressure difference relative to the coronary outlet. a–d Are pressure distribution cloud maps of the entire cardiovascular before and after CABG obtained from CFD and DL. e, f Are cross-sectional views of the pressure distribution, respectively from (i): the proximal end of LAD before stenosis; (ii): the distal end of LAD after stenosis; (iii): descending aorta; iv): graft. The comparison results confirm the high consistency of the pressure field obtained by the two methods. The results of coronary pressure prediction can help us calculate FFR to further evaluate the performance of our deep learning method.

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  Fig. 3. Comparison of FFR and improved blood flow obtained from CFD and deep learning. a Is a scatterplot of FFR values from CFD (FFRCFD) and deep learning (FFRDL). b Is a scatterplot of improved blood flow values from CFD (FLOWCFD) and deep learning (FLOWDL). c, d Are Bland–Altman analysis plot of corresponding (a, b). The hemodynamic results used to calculate FFR and improved blood flow are from 100 cardiovascular models in the test set.

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  Fig. 4. Prediction error analysis. Using a model in the preoperative test set as a sample, a shows the vortex regions in its CFD simulation flow field, which are mostly distributed in the aorta and superior aortic branch artery rather than the grafts and coronary arteries. Compared to the entire model, the number of points in the vortex region of grafts and coronary arteries only accounted for 0.1% of all query points. For most models, there is an obvious vortex region in the ascending aorta area circled by the red box. In order to clearly indicate the distribution of points with high prediction errors (MRE > 10%), b shows the points with high errors in deep learning predicted velocity field of the same model as (a) (the circled area). The distribution of these points is highly consistent with the vortex region in (a), which proves that the error mainly comes from the vortex region of the aorta and superior aortic branch artery. c Shows the prediction errors along to the different size of training set only in the vortex region. c Shows the influence of the training set size on MRE of the vortex region. We fix the test set and increase the size of the training set from 10% to 100%. Then…

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  Fig. 5. Deep learning network construction. The network takes N points with three-dimensional spatial components of x, y, and z (for pressure, the three-component values are the same) as input. After feature extraction and stitching layer processing, spatial relationships are introduced to extract and reproduce the relationship between model geometry and hemodynamic. The Maxpooling layer resolves the disorder of the point cloud. The output of the network is the hemodynamic three-dimensional spatial components of N points in corresponding query point cloud.