Mathematical modeling and computer simulation of needle insertion into soft tissue

Abstract

In this study we present a kinematic approach for modeling needle insertion into soft tissues. The kinematic approach allows the presentation of the problem as Dirichlet-type (i.e. driven by enforced motion of boundaries) and therefore weakly sensitive to unknown properties of the tissues and needle-tissue interaction. The parameters used in the kinematic approach are straightforward to determine from images. Our method uses Meshless Total Lagrangian Explicit Dynamics (MTLED) method to compute soft tissue deformations. The proposed scheme was validated against experiments of needle insertion into silicone gel samples. We also present a simulation of needle insertion into the brain demonstrating the method’s insensitivity to assumed mechanical properties of tissue.

Effective Viscoplastic-Softening Model Suitable for Brain Impact Modelling

“…In [ 14 ], the authors showed that standard linear elastic models do not accurately reflect the viscoelastic properties of porcine, soft brain tissue, since the stiffness depends on the loading rate. In [ 19 ], the authors emphasised problems with the assumptions of linear elasticity of soft brain tissue when large strains and discontinuities are present. To model the force of the interaction between the biopsy needle and the brain tissue, the authors in [ 20 ] used viscoelastic plastic properties and considered the relaxation behaviour of the material.…”

Review on Needle Insertion Haptic Simulation

“…To provide realistic force feedback behavior and overcome computing limitations of FEM based approaches (see next subsection) at the same time, Wittek et al use Meshless Total Lagrangian Explicit Dynamics to simulate tissue deformations. This model has the advantage of requiring only patient-specific geometry and two parameters (being easy to identify from intra-operative images) to render patient-specific simulations [1]. As the model computes needle-tissue interaction forces, it may be used to compute real-time force feedback in the future but this still requires some validation.…”

Simple and robust element-free Galerkin method with almost interpolating shape functions for finite deformation elasticity

“…For nonlinear problems, methods like meshless local Petrov-Galerkin (MLPG) [1,2], smooth particle hydrodynamics [3], element-free Galerkin (EFG) [4] and strong form collocation methods [5,6] have demonstrated their accuracy in several benchmark problems, in many cases superior to FE methods. Recent refinements of element-free Galerkin methods appear to be most promising, with comprehensive 3D non-linear problems solved effectively and accurately [7][8][9].…”

“…The paper is organized as follows: in Section 2 we briefly describe the components of our methodology adapted from our previous work [6,9,11], and explain improvements to the MMLS functions [10] that render them interpolating. In Section 3 we demonstrate convergence of our algorithm as well as its accuracy by comparing our results to analytical and finite element solutions.…”