Identification of Young’s Modulus and Equivalent Spring Constraint Boundary Conditions of the Object With Incomplete Displacement Boundary Conditions

Abstract

Abstract In endoscopic surgery, the surgical navigation needs to calculate the internal deformation of the soft tissue by biomechanical model which needs to determine the elastic properties and boundary conditions. However, these information cannot be obtained accurately in a real operation scenario. For example, only a limited portion of a liver surface can be observed in a hepatic surgery under endoscope while its elastic properties remain unknown. 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. Biomechanical models of the soft tissue have been thoroughly studied in recent years. In these studies, boundary conditions play an important role in identification of elastic properties for mechanical model based methods. But they rarely combine these unknown conditions together to construct the model, and instead set boundary conditions or elastic properties as known for simplification. In this paper, we present a novel method to identify the Young’s modulus and equivalent spring constraint boundary conditions of a partially observed soft object with incomplete boundary conditions. The spring constraint boundary condition is applied to alternate the conventional displacement boundary conditions (e.g. free constraint and fixed constraint) and an inverse algorithm based on the standard finite element method (FEM) and Gauss-Newton (GN) method is developed, which takes external forces and displacements of observable nodes as inputs. A series of numerical simulation experiments are implemented and the analysis of simulation results show the feasibility of the proposed method.