Boundary Constraint-free Biomechanical Model-Based Surface Matching for Intraoperative Liver Deformation Correction

2024-03-15

IEEE Transactions on Medical Imaging

AI Summary

In image-guided liver surgery, non-rigid 3D–3D registration between preoperative models and intraoperative point clouds remains challenging due to soft-tissue deformation. This paper proposes a biomechanics-driven registration method without prescribed boundary constraints. Our key contribution is the first direct integration of a finite element model (FEM) into the surface-matching objective function—eliminating prior assumptions on zero-displacement boundaries and external force application points. We further introduce a full-surface distributed soft-spring force model coupled with L² regularization on force-magnitude gradients to enhance robustness and generalizability of deformation estimation. Optimization is efficiently performed via an accelerated proximal gradient algorithm with adaptive step sizing. Evaluated on a custom liver phantom and two public datasets, our method achieves performance competitive with or superior to state-of-the-art learning-based and traditional FEM-regularized approaches. The source code and datasets are publicly available.

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Abstract

In image-guided liver surgery, 3D-3D non-rigid registration methods play a crucial role in estimating the mapping between the preoperative model and the intraoperative surface represented as point clouds, addressing the challenge of tissue deformation. Typically, these methods incorporate a biomechanical model, represented as a finite element model (FEM), used to regularize a surface matching term. This paper introduces a novel 3D-3D non-rigid registration method. In contrast to the preceding techniques, our method uniquely incorporates the FEM within the surface matching term itself, ensuring that the estimated deformation maintains geometric consistency throughout the registration process. Additionally, we eliminate the need to determine zero-boundary conditions and applied force locations in the FEM. We achieve this by integrating soft springs into the stiffness matrix and allowing forces to be distributed across the entire liver surface. To further improve robustness, we introduce a regularization technique focused on the gradient of the force magnitudes. This regularization imposes spatial smoothness and helps prevent the overfitting of irregular noise in intraoperative data. Optimization is achieved through an accelerated proximal gradient algorithm, further enhanced by our proposed method for determining the optimal step size. Our method is evaluated and compared to both a learning-based method and a traditional method that features FEM regularization using data collected on our custom-developed phantom, as well as two publicly available datasets. Our method consistently outperforms or is comparable to the baseline techniques. Our code and datasets will be available at https://github.com/zixinyang9109/BCF-FEM.

Problem

• Intraoperative liver deformation correction
• Boundary constraint-free biomechanical model
• 3D-3D non-rigid registration method

Innovation

• Integrates FEM within surface matching term
• Eliminates zero-boundary conditions necessity
• Uses accelerated proximal gradient algorithm