Stiffness matrix representation of hyper-elasticity for surgical simulation and navigation

Area of Science:

• Computational mechanics
• Biomedical engineering
• Medical simulation

Background:

• Physics-based simulation is crucial for industry and clinical applications, particularly in surgical simulation for training and navigation.
• Conventional linear Finite Element Method (FEM) simulations lack accuracy for non-linear organ tissue responses and interactivity.
• Hyper-elasticity (HE) models organ material behavior more accurately than linear models.

Purpose of the Study:

• To develop a real-time and interactive surgical simulation and navigation system.
• To incorporate hyper-elasticity (HE) for more accurate modeling of organ tissue non-linear responses.
• To extend linear FEM for efficient simulation of complex material behaviors.

Main Methods:

• Proposed a novel method to decompose the stress-strain relationship of hyper-elastic (HE) materials.
• Constructed a stiffness matrix by extending linear FEM for efficient simulation.
• Validated the method using a kidney model to demonstrate deformation.

Main Results:

• The proposed method accurately simulates non-linear FEM deformation, achieving accuracy comparable to existing non-linear FEM analyses.
• Achieved shorter calculation times compared to conventional non-linear FEM analysis.
• Successfully demonstrated organ deformation simulation, specifically with a kidney model.

Conclusions:

• The novel approach enables accurate and efficient real-time simulation of hyper-elastic organ tissue deformation.
• This method enhances the potential for realistic surgical training and intra-operative navigation.
• Extending linear FEM provides a viable solution for interactive and accurate non-linear biomechanical simulations.