VALVEFIT: An analysis-suitable B-spline-based surface fitting framework for patient-specific modeling of tricuspid valves

Abstract

Patient-specific computational modeling of the tricuspid valve (TV) is vital for the clinical assessment of heart valve diseases. However, this process is hindered by limitations inherent in the medical image data, such as noise and sparsity, as well as by complex valve dynamics. We present VALVEFIT, a novel GPU-accelerated and differentiable B-spline surface fitting framework that enables rapid reconstruction of smooth, analysis-suitable geometry from point clouds obtained via medical image segmentation. We start with an idealized TV B-spline template surface and optimize its control point positions to fit segmented point clouds via an innovative loss function, balancing shape fidelity and mesh regularization. Novel regularization terms are introduced to ensure that the surface remains smooth, regular, and intersection-free during large deformations. We demonstrate the robustness and validate the accuracy of the framework by first applying it to simulation-derived point clouds that serve as the ground truth. We further show its robustness across different point cloud densities and noise levels. Finally, we demonstrate the performance of the framework toward fitting point clouds obtained from real patients at different stages of valve motion. An isogeometric biomechanical valve simulation is then performed on the fitted surfaces to show their direct applicability toward analysis. VALVEFIT enables automated patient-specific modeling with minimal manual intervention, paving the way for the future development of direct image-to-analysis platforms for clinical applications.