The work performed during the project is described in three categories.
1. Development of a 3D imaged-based computational fluid dynamics tool for high-resolution simulation of blood flow in patient-specific aortic geometries
Clinical guidelines on TAVI suggest that the hemodynamic performance of the valve is tightly linked with the morphology of the aorta, where the valve is to be implanted. The curvature of the aorta is specific for each patient, and oftentimes is already affected by the aortic valve disease (for instance, bicuspid valve patients are known for a high incidence of aortic dilation). This led us to develop and couple an image-based arterial geometry analysis tool with our legacy GPU-accelerated solver, aiming to incorporate detailed models of patient-specific aortic geometries. The resulting tool takes CT scans of the patients chests, creates suitable input models for integration into blood flow simulation tool and finally performs detailed blood flow simulations that are highly resolved in time and space. The base solver was designed to capture blood flow details such as turbulent shear stresses with high accuracy, enabling more precise predictions and laying the groundwork for more rigorous optimizations. The results produced by our flow simulation tool packed in extremely large datasets of sizes beyond 10TBs for each beat cycle, which provided unprecedented spatiotemporal detayils into the flow phenomena in the aorta.
2. For the adjoint-based methodology, we started by a simple valve design, given the complexity of the full problem in hand. Adjoint-based methods are costly in nature, given that they require several iterations of a so-called forward-backward looping procedure. Given that 3D simulations are significantly costly even using the most advanced GPUs (a single heart beat simulation required three days allocation on eight powerful P100 GPUs), performing such simulations is not practical in a repetitive fashion that is required for optimization. Therefore, we developed an optimization code based on a simplified 2D design of a prosthetic valve. Leveraging both linear and nonlinear optimization techniques which could utilize the optimization code for both route-cause identification as well as control of adverse blood flow events. Particularly, our optimization framwork took a certain geometrical mask as a user input, and could identify the most relevant root causes for an unphysiological flow (e.g. highly turbulent) to develop within the mask. In the next step, and aiming to extend our methodology to 3D environments, we explored the use of artifical neural networks together with our direct numerical simulations. In particular, we addressed an specifc type of these techniques, namely, the Physics-informed neural networks (PINNs). The PINNs approach can be challenging for unsteady flow scenarios and high geometrical details, and proved to be costly to train even in a 2D setting. Future advancements in this area could potentially be highly relevant for the optimization procedures in 3D settings.
