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

TL;DR

This paper introduces a boundary condition-free biomechanical model-based surface matching method for intraoperative liver deformation correction, improving registration accuracy without needing boundary condition specifications.

Contribution

It proposes a modified finite element model that removes the need for boundary condition specification in liver surface registration, simplifying the process.

Findings

Outperforms or matches state-of-the-art methods across datasets.

Eliminates the need for boundary condition specification in FEM.

Uses an accelerated gradient algorithm for optimization.

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), into the strain energy term to regularize a surface matching term. We propose a 3D-3D non-rigid registration method that incorporates a modified FEM into the surface matching term. The modified FEM alleviates the need to specify boundary conditions, which is achieved by modifying the stiffness matrix of a FEM and using diagonal loading for stabilization. As a result, the modified surface matching term does not require the specification of boundary conditions or an additional strain energy term to regularize the surface matching term. Optimization is achieved through an accelerated gradient algorithm, further enhanced by our proposed method for determining the optimal step size. We evaluated our method and compared it to several state-of-the-art methods across various datasets. Our straightforward and effective approach consistently outperformed or achieved comparable performance to the state-of-the-art methods. Our code and datasets are available at https://github.com/zixinyang9109/BCF-FEM.