Identification of Young’s modulus and equivalent spring constraint boundary conditions of the soft tissue with locally observed displacements for endoscopic liver surgery

Abstract

In endoscopic surgery, the surgical navigation system needs to calculate the deformation of soft tissue by biomechanical model which requires elastic properties and boundary conditions. However, patient-specific elastic parameters and boundary conditions of soft tissue are hard to measure accurately from the preoperative images, especially the boundary conditions will change during the operation due to the ligament cutting. In addition, simple boundary conditions such as fixed constraints and free-force constraints are not physically adequate to simulate the elastic effect of ligaments attached to the liver. In this paper, we present a novel method to identify the Young’s modulus and equivalent spring constraint boundary conditions of a locally observed soft tissue. Based on the spring constraint boundary condition, a two-step inverse algorithm is developed based on the finite element method (FEM) with integration of energy regularized Gauss-Newton (GN) method and ${\mathcal{l}}_1$-regularized method, which takes external forces and displacements of observable nodes as inputs. A series of numerical simulations and physical hydrogel phantom experiments were conducted. The results of simulation and physical experiments show that the Young’s modulus and equivalent spring constraint boundary conditions identified by the proposed method agree well with their setup true values.

Keywords:

• Finite element method
• unknown boundary condition
• spring constraint boundary condition
• inverse problem

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Major Scientific Research Instrument Development Project of National Natural Science Foundation of China (NSFC) (Grant No. 81827804), Zhejiang Provincial Natural Science Foundation of China (grant no. LSD19H180004), Science Fund for Creative Group of NSFC (No. 51821903).