Introduction:: The World Health Organization estimates 32% of the deaths worldwide are related to cardiovascular disease (CVD). Knowledge about blood flow patterns inside vasculature provides valuable information to make better treatment decisions for conditions such as aneurysms. Currently, computational fluid dynamics (CFD) can be used to estimate flow fields for vascular anatomies. However, the computation, expertise, and time consumption (hours or days) for CFD renders the technique unusable in clinic. The goal of this study is to predict 3D blood flow patterns in seconds by training a custom-designed physics-informed neural network (PINN) for cardiovascular and neurovascular geometries. For this study, we focused on cerebral aneurysms and left ventricular assist device (LVAD) scenarios. We generated datasets containing flow profiles for both of those geometries. We developed a 1D-3D convolutional neural network to make blood flow predictions for our ventricular and aneurysm test datasets, as well as tools to aid the network training process including a physics-informed component for the loss. The network achieved 93% accuracy in prediction of the flow magnitude for the test aneurysms dataset, and it was able to predict in less than one second for both the aneurysm and ventricular-LVAD datasets.


Materials and Methods::

Materials
A synthetic dataset of 2000 aneurysms of diverse aneurysmal and parent vessel morphologies was generated, and their 3D flow patterns were resolved using an automated version of MATLAB’s FEATool solver. Neural networks were constructed using Python’s Tensorflow library. For continuing our study, a dataset of synthetic ventricular geometries with implanted LVADs were constructed and their flow profiles were resolved using Ansys Fluent. Our neural network was trained using a NVIDIA GeForce RTX 3080 GPU.

Methods

We developed and trained a 1D-3D convolutional neural network to predict the 3D velocity patterns within the vascular lumen. This architecture intakes point clouds in 3D space describing an aneurysm and returns regular 3D grids with the output x, y, and z velocity profile components. Additionally, we developed tools to enhance network performance: a physics-informed loss function to enforce the law of flow conservation in the predictions, the Huber loss to enhance prediction accuracy across blood flow velocity components of widely different magnitudes, and a radial distance function (RDF) used as an auxiliary input to convey additional information about the aneurysmal shape. The physics-informed loss calculates the flowrate at different cross sections of the predicted flow profile and penalizes the network for sudden changes in flowrate. Normalized mean absolute error (NMAE) was used to characterize network performance for each component of velocity. Additionally, an analysis of the streamlines for the original velocity profile and the predicted profile was performed to assess the prediction of areas of recirculation.


Results, Conclusions, and Discussions::
Results


The network developed using our architecture and tools achieved the best performance in our test dataset compared to various networks, with a 7% error in the velocity magnitude as described by NMAE. The accuracy was maintained across the x, y, and z velocity components even in areas of vorticity where clinically relevant and hard-to-predict flow patterns exist. For some geometries in the datasets, it was noted that the y and z velocity components exhibited higher errors in areas of vorticity. Most importantly, our network produced results in less than 0.5 seconds. The network was also able to predict 3D flow patterns within the left ventricle implanted with the LVAD inflow cannula within 1 second, and captured the major stagnation zones accurately.



Conclusions

Our network’s results show promise for accurately and quickly predicting flow profiles for aneurysms geometrically similar to those in the training dataset. Usage of the Huber loss, a radial distance function additional input, and a physics loss enforcing the law of flow conservation helped produce more accurate flow patterns. Areas of vorticity, while being well preserved, were the most challenging for network prediction. We estimate that further tuning of model hyperparameters and an increased diversity of geometries in the training dataset will help the network generate better predictions.

Discussion


Our 1D-3D convolutional network was able to accurately predict flow profiles for our test aneurysm dataset in less than a second. The possibility of using a 3D point cloud and inlet velocity as inputs provides the opportunity of feeding the geometry to the network with minimal preprocessing. The initial success with our aneurysm and left ventricle models lays the foundation for our successive studies, which aims to further train our network with a new dataset of more realistic vascular geometries, which, coupled with our response times of seconds, brings it within the reach of clinical applications.






Acknowledgements (Optional): : This work was supported in part by an American Heart Association Career Development Award # 937847 to Dr. Chivukula

References (Optional): :