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Heart valve disease (HVD), a significant cardiovascular complication, is one of the leading global causes of morbidity and mortality. Treatment for HVD often involves medical devices such as bioprosthetic valves. However, the design and optimization of these devices require a thorough understanding of their biomechanical and hemodynamic interactions with patient-specific anatomical structures. Parametric procedural geometry has become a powerful tool in enhancing the efficiency and accuracy of design optimization for such devices, allowing researchers to systematically explore a wide range of possible configurations. In this work, we present a robust framework for parametric and procedural modeling of stented bioprosthetic heart valves and patient-specific aortic geometries. The framework employs non-uniform rational B-splines (NURBS)-based geometric parameterization, enabling precise control over key anatomical and design variables. By enabling a modular and expandable workflow, the framework supports iterative optimization of valve designs to achieve improved hemodynamic performance and durability. We demonstrate its applicability through simulations on bioprosthetic aortic valves, highlighting the impact of geometric parameters on valve function and their potential for personalized device design. By coupling parametric geometry with computational tools, this framework offers researchers and engineers a streamlined pathway toward innovative and patient-specific cardiovascular solutions. 

Cardiovascular disease (CVD) remains one of the leading causes of mortality worldwide. Computational medicine and digital twins hold promise in mitigating the impact and prevalence of CVD. Recent advances in image-based computational methods have enabled the quantification of functional and biologically important metrics that would otherwise be difficult to obtain from the standard of care. However, significant challenges remain due to the manual/semi-automated nature of the processes and the domain expertise required to perform them. This paper addresses these challenges by proposing a novel framework that builds on our recently developed direct point cloud-to-CFD approach using immersogeometric analysis. The proposed method leverages advanced auto-segmentation techniques to extract medically relevant geometries as point clouds, which are then directly used for CFD simulations. The framework is validated using benchmark flow problems with analytical and computational solutions and is subsequently applied to patient-specific images to demonstrate its capabilities. The results highlight the method's ability to facilitate rapid CFD simulations directly on point clouds derived from patient scans, underscoring its potential to accelerate the image-to-simulation pipeline and enable the tractability of cardiovascular digital twins. 

Point cloud representations of three-dimensional objects have remained indispensable across a diverse array of applications, given their ability to represent complex real-world geometry with just a set of points. The high fidelity and versatility of point clouds have been utilized in directly performing numerical analysis for engineering applications, bypassing the labor-intensive and time-consuming tasks of creating analysis-suitable CAD models. However, point clouds exhibit various levels of quality, often containing defects such as holes, noise, and sparse regions, leading to sub-optimal geometry representation that can impact the stability and accuracy of any analysis study. This paper aims to overcome such challenges by proposing a novel method that expands upon our recently developed direct point cloud-to-CFD approach based on immersogeometric analysis. The proposed method features a mesh-driven resampling technique to fill any unintended gaps and regularize the point cloud, making it suitable for CFD analysis. Additionally, ghost penalty stabilization is employed for incompressible flow to improve the conditioning and stability compromised by the small cut elements in immersed methods. The developed method is validated against standard benchmark geometries and real-world point clouds obtained in-house with photogrammetry. Results demonstrate the proposed framework’s robustness in facilitating CFD simulations directly on point clouds of varying quality, underscoring its potential for practical applications in analyzing real-world structures. 

Abstract We present a data-driven workflow to biological tissue modeling, which aims to predict the displacement field based on digital image correlation (DIC) measurements under unseen loading scenarios, without postulating a specific constitutive model form nor possessing knowledge of the material microstructure. To this end, a material database is constructed from the DIC displacement tracking measurements of multiple biaxial stretching protocols on a porcine tricuspid valve anterior leaflet, with which we build a neural operator learning model. The material response is modeled as a solution operator from the loading to the resultant displacement field, with the material microstructure properties learned implicitly from the data and naturally embedded in the network parameters. Using various combinations of loading protocols, we compare the predictivity of this framework with finite element analysis based on three conventional constitutive models. From in-distribution tests, the predictivity of our approach presents good generalizability to different loading conditions and outperforms the conventional constitutive modeling at approximately one order of magnitude. When tested on out-of-distribution loading ratios, the neural operator learning approach becomes less effective. To improve the generalizability of our framework, we propose a physics-guided neural operator learning model via imposing partial physics knowledge. This method is shown to improve the model's extrapolative performance in the small-deformation regime. Our results demonstrate that with sufficient data coverage and/or guidance from partial physics constraints, the data-driven approach can be a more effective method for modeling biological materials than the traditional constitutive modeling. 

Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key bottleneck in the above process is the fast construction of a ‘good’ adaptively-refined mesh. In this work, we present an efficient novel octree-based adaptive discretization approach capable of carving out arbitrarily shaped void regions from the parent domain: an essential requirement for fluid simulations around complex objects. Carving out objects produces an incomplete octree. We develop efficient top-down and bottom-up traversal methods to perform finite element computations on incomplete octrees. We validate the framework by (a) showing appropriate convergence analysis and (b) computing the drag coefficient for flow past a sphere for a wide range of Reynolds numbers (0(1-10 6 )) encompassing the drag crisis regime. Finally, we deploy the framework on a realistic geometry on a current project to evaluate COVID-19 transmission risk in classrooms.