Session: 13-22-02: CONCAM Distinguished Lectures on Computational Mechanics II

Paper Number: 173717

From Differentiable Splines to Digital Twins in Cardiac Simulations: Part 2 

Modern computer-aided design (CAD) and analysis workflows are being revolutionized by differentiable spline modeling frameworks. In this first part, we introduce innovations including THB-Diff, which embed truncated hierarchical B-splines (THB-splines) into differentiable programming paradigms. These frameworks allow CAD geometry to be treated as native layers in deep learning models, enabling end-to-end gradient-based optimization for shape design. Our THB-Diff module is fully integrated with PyTorch and GPU-accelerated, providing automatic differentiation of CAD geometry for backpropagation. This capability lets us perform traditional CAD operations like surface fitting and offsetting, as well as incorporate spline evaluation directly into neural networks for tasks like point cloud reconstruction. By leveraging hierarchical B-splines to enable local adaptive refinement of surfaces within the optimization loop, we enable precise control.To address the computational challenges of hierarchical splines, custom CUDA kernels are employed for efficient forward and backward passes, substantially boosting performance on GPUs. Together, these differentiable spline tools achieve significant speed-ups and accuracy gains in surface modeling.

These developments bridge the gap between CAD and AI, allowing seamless integration of precise geometry representations into machine learning workflows. By obtaining exact geometry gradients, engineers can now conduct inverse design and shape optimization directly on NURBS/THB models, rather than approximate meshes. This opens up new possibilities in design automation: complex shapes can be optimized in a GPU-accelerated, end-to-end pipeline where objectives (e.g. aerodynamic performance or structural stress) propagate gradients back to control points. We demonstrate how differentiable splines enable faster design iterations and analysis-suitable models – geometry that is immediately ready for simulation without remodeling. Key takeaways include substantial improvements in computational performance through GPU acceleration, the ability to refine models hierarchically for fine local detail, and the tight integration of AI-driven optimization with traditional CAD. This showcases how gradient-driven spline modeling elevates CAD from static design to an interactive, learning-enabled process, laying the foundation for advanced applications like real-time design feedback and automatic model generation for simulation.

Building on the above technologies, we explore a high-impact application of differentiable spline modeling in biomechanics and digital healthcare. We focus on patient-specific modeling and PDE-constrained optimization for heart valve tissues, demonstrating how spline-based design and simulation converge to form a cardiac digital twin. Specifically, we introduce ValveFit, a GPU-accelerated and differentiable B-spline surface fitting framework for reconstructing tricuspid heart valve geometry from medical images. This method addresses a critical clinical need: children with Hypoplastic Left Heart Syndrome (HLHS) undergo multiple surgeries that often increase the risk of tricuspid regurgitation. ValveFit rapidly generates a smooth, analysis-suitable valve model by deforming an idealized template via gradient-based optimization. The template’s control points are adjusted to fit noisy, sparse 4D echocardiography data through a multi-term loss function that balances anatomy fidelity with regularization to enforce smoothness and prevent self-intersections. This differentiable fitting process – essentially an AI-driven deformable registration – is robust against imaging artifacts. We validate the fitted valve models first on synthetic data with known ground-truth, confirming accuracy across varying point cloud densities and noise levels. We then successfully apply ValveFit to real HLHS patient data at different cardiac phases, showcasing its resilience to clinical imaging challenges.

Crucially, the analysis-suitability of the spline models allows direct use in fluid–structure interaction (FSI) simulations to evaluate valve function. We perform high-fidelity biomechanical simulations on the personalized valve geometries to verify that they exhibit realistic closure and stress patterns, thus serving as valid digital twins of the patients’ valves. This simulation-backed validation underlines the PDE-constrained optimization aspect: the fitted geometry can be optimized (or tuned) such that simulated performance (governed by the physics of blood flow and tissue mechanics) meets desired criteria. The clinical implications are significant. By integrating AI-driven modeling with physics-based simulation, ValveFit enables a paradigm shift in cardiac treatment planning. Clinicians could virtually test and optimize surgical repairs or prosthetic devices on a patient’s digital twin before intervention, reducing risk and personalizing therapy. The pipeline – from noisy scans to a ready-to-simulate spline model – is largely automatic and computationally efficient, thanks to GPU acceleration and differentiable programming techniques. Key takeaways include the demonstrated robustness and speed of the approach (enabling near-real-time model reconstruction), the clinical relevance of enhancing decision-making with patient-specific simulations, and the power of combining AI and advanced computational mechanics to realize predictive digital twins for the heart.

Presenting Author: Aishwarya Pawar Iowa State University

Presenting Author Biography: Aishwarya Pawar is an Assistant Professor in the Department of Mechanical Engineering at Iowa State University, where she leads the Computational Modeling and Image Analysis (CMIA) Lab. Her research lies at the intersection of computational mechanics, geometric modeling, scientific machine learning, and biomedical image analysis, with applications spanning digital twins for personalized healthcare and high-performance design automation. She earned her Ph.D. in Mechanical Engineering from Carnegie Mellon University. Her research focused on B-spline-based image segmentation, registration, and modeling of neuron growth. She completed postdoctoral research at Purdue University, contributing to the development of PDE-constrained optimization frameworks for biological growth and morphogenesis. She is affiliated with the Biomedical Engineering and Human-Computer Interaction Programs at Iowa State, and actively serves on scientific and organizing committees for conferences such as USNCCM and the International Meshing Roundtable.

Authors:

Ajith Moola Iowa State University
Aditya Balu Iowa State University
Adarsh Krishnamurthy Iowa State University
Chung-Hao Lee University of California Riverside
Ming-Chen Hsu Iowa State University
Aishwarya Pawar Iowa State University