Soft Tissue Deformation Modeling Based on a Complex Variable Meshless Approach

Background: Minimally invasive interventional procedures involve needle insertion into soft tissue, which requires an accurate needle-tissue interaction model to advance a robotic-assisted puncture system. Traditional methods face challenges in dealing with stress singularity and computational complexity. Objective: The purpose of this paper is to propose an EICVMLS method to efficiently address soft tissue fracture and deformation during needle insertion, overcoming the limitations of traditional methods in terms of stress singularity and computational efficiency. Methods: A viscoelastic fracture model is developed based on fracture characteristics of different damage types in fracture mechanics, analyzing displacement and force changes at the crack tip during the needle-tissue interaction. The weak form of Galerkin integral of viscoelastic mechanics is used to realize the deformation calculation of needle and tissue by Newton-Raphson time integration, and the ontological relationship of viscoelastic fracture of soft tissue is expressed in terms of displacements computed by the EICVMLS. The computational model is validated through meshless simulations of needle insertion into bionic tissue. Results: The computational model retains the advantages of the ICVMLS method in addressing the non-fracture problem while obtaining a high-precision solution to the fracture problem during needle puncture of soft tissue without affecting the computational volume, which outperforms traditional methods in precision and efficiency. Conclusion: The EICVMLS method is proposed to address the stress singularity problem at soft tissue fracture. This high-precision computational model could be considered implemented in developing advanced robotic-assisted surgical systems in the future, enabling more precise and adaptive interventions in minimally invasive surgery.