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

TL;DR

VALVEFIT tackles the challenge of generating patient-specific tricuspid valve geometries from noisy, sparse segmentation data by deforming a template B-spline surface into the target point clouds using a differentiable, GPU-accelerated optimization. The framework combines a shape-fidelity loss with novel surface-regularization terms—tangent-orthogonality, tangent-point energy to prevent self-collisions, and normal-deviation control—to yield smooth, intersection-free surfaces suitable for isogeometric analysis. Validation on synthetic benchmarks and real patient data demonstrates robustness to point density and noise, with low scaled nearest-neighbor distances (sNND) and stable performance across cardiac-cycle time points. Demonstrations include a simplified TV closure simulation showing the fitted surfaces can be directly used for biomechanical analysis, underscoring the framework’s potential for automated image-to-analysis pipelines in clinical contexts.

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.

Figures (22)

• Figure 1: Representative echocardiogram imaging data of a newborn with hypoplastic left heart syndrome (HLHS) and the segmented point cloud for the tricuspid valve (TV) apparatus: (a) coronal view and (b) 3D perspectives. Segmented points (red) for the TV annulus and segmented points (blue) for the three TV leaflets.
• Figure 2: (a) Excised porcine tricuspid valve (TV) showing the three leaflets—septal (SL), anterior (AL), and posterior (PL)—along with their commissures. (b) Point cloud representation of a patient’s TV annulus (black) and the three leaflets: SL (blue), AL (green), and PL (red). (c) Template geometry constructed using a single-patch periodic B-spline surface, shown in both top and side views. Idealized template geometry is generated with the annulus modeled as a circular ring and the leaflets with equal heights. Surface parameterization is carried out using knot vectors: $\mathcal{U} := \{0, 0, 0, 0.33, 0.66, 1, 1, 1\}$ along the axial direction and $\mathcal{V} := \{-0.3, -0.2, -0.1, 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.3\}$ along the circumferential direction.
• Figure 3: Comparison of cubic B-spline basis functions for (a) clamped and (b) unclamped knot vectors, defined as $\{0, 0, 0, 0, 1, 2, 3, 4, 5, 5, 5, 5\}$ and $\{-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8\}$, respectively.
• Figure 4: Comparison of (a) closed non-periodic and (b) closed periodic cubic B-spline curves. The periodic curve in (b) achieves $C^{2}$ continuity across the parametric boundary, whereas the non-periodic curve in (a) maintains only $C^{0}$ continuity.
• Figure 5: Effect of the Chamfer distance weight, $w_\text{CD}$, on surface fitting accuracy. (a) With no contribution from the Chamfer distance term ($w_\text{CD} = 0$), the surface fails to accurately fit to the target point cloud. (b) A moderate weight value ($w_\text{CD} = 20$) yields a well-fitted surface that accurately approximates the target point cloud. (c) An excessive large weight value ($w_\text{CD} = 500$) leads to overfitting, resulting in unnatural surface folding.