Suite of Meshless Algorithms for Accurate Computation of Soft Tissue Deformation for Surgical Simulation

TL;DR

This paper introduces a suite of advanced meshless algorithms based on EFG and MMLS techniques for precise simulation of soft tissue deformation in surgical planning, overcoming key limitations of existing meshless methods.

Contribution

It develops novel MTLED algorithms with improved boundary condition enforcement and adaptive integration, enhancing accuracy and applicability for large deformation soft tissue modeling.

Findings

Demonstrated superior accuracy over traditional FEM in large deformation scenarios.

Validated methods through comparisons with ABAQUS simulations.

Successfully applied to realistic brain-shift prediction.

Abstract

The ability to predict patient-specific soft tissue deformations is key for computer-integrated surgery systems and the core enabling technology for a new era of personalized medicine. Element-Free Galerkin (EFG) methods are better suited for solving soft tissue deformation problems than the finite element method (FEM) due to their capability of handling large deformation while also eliminating the necessity of creating a complex predefined mesh. Nevertheless, meshless methods based on EFG formulation, exhibit three major limitations: i) meshless shape functions using higher order basis cannot always be computed for arbitrarily distributed nodes (irregular node placement is crucial for facilitating automated discretization of complex geometries); ii) imposition of the Essential Boundary Conditions (EBC) is not straightforward; and, iii) numerical (Gauss) integration in space is not exact as meshless shape functions are not polynomial. This paper presents a suite of Meshless Total Lagrangian Explicit Dynamics (MTLED) algorithms incorporating a Modified Moving Least Squares (MMLS) method for interpolating scattered data both for visualization and for numerical computations of soft tissue deformation, a novel way of imposing EBC for explicit time integration, and an adaptive numerical integration procedure within the Meshless Total Lagrangian Explicit Dynamics algorithm. The appropriateness and effectiveness of the proposed methods is demonstrated using comparisons with the established non-linear procedures from commercial finite element software ABAQUS and experiments with very large deformations. To demonstrate the translational benefits of MTLED we also present a realistic brain-shift computation.