Meshless algorithm for soft tissue cutting in surgical simulation

Abstract

Computation of soft tissue mechanical responses for surgery simulation and image-guided surgery has been dominated by the finite element (FE) method that utilises a mesh of interconnected elements as a computational grid. Shortcomings of such mesh-based discretisation in modelling of surgical cutting include high computational cost and the need for re-meshing in the vicinity of cutting-induced discontinuity. The meshless total Lagrangian adaptive dynamic relaxation (MTLADR) algorithm we present here does not exhibit such shortcomings, as it relies on spatial discretisation in a form of a cloud of nodes. The cutting-induced discontinuity is modelled solely through changes in nodal domains of influence, which is done through efficient implementation of the visibility criterion using the level set method. Accuracy of our MTLADR algorithm with visibility criterion is confirmed against the established nonlinear solution procedures available in the commercial FE code Abaqus.

From Finite Element Meshes to Clouds of Points: A Review of Methods for Generation of Computational Biomechanics Models for Patient-Specific Applications

“…Tissue cutting simulation is also difficult, as small and poorly shaped elements can be created during the cutting process. 24,54 Meshless methods of computational mechanics have been recognized as one possible solution for some of these challenges. 30 In particular, several meshless methods for surgical simulation have been developed, implemented and tested at the Intelligent Systems for Medicine Laboratory at the University of Western Australia.…”

“…30 In particular, several meshless methods for surgical simulation have been developed, implemented and tested at the Intelligent Systems for Medicine Laboratory at the University of Western Australia. 46,54,58 In meshless methods, the field variable interpolation is constructed without the use of a predefined mesh. These methods use a set of nodes scattered within the problem domain and on its boundary (Fig.…”

Modeling Soft Tissue Damage and Failure Using a Combined Particle/Continuum Approach

“…SPH is not the only tool of this type available. Other methods, such as Peridynamics (Silling et al 2007) and the Element-Free Galerkin Method (Jin et al 2014) as well as the closely related Meshless Total Lagrangian Explicit Dynamics method (MTLED) (Miller et al 2012; Li et al 2016), may provide a good alternative to the method introduced in the current work. Note, too, that methods such as the one discussed here as well as MTLED lend themselves well to surgical simulations because of straight-forward spatial discretization as well as their algorithmic simplicity.…”

Efficient visibility criterion for discontinuities discretised by triangular surface meshes

“…Use of these so-called "cracked particles" applies only to finely cracking solids and not to deforming soft bodies with arbitrary discontinuities, and the existence of discontinuities only at particular particles limits the accuracy with which they can be modelled. Level-set functions proposed by Osher and Sethian [5] and applied to FEM crack growth modelling by Stolarska et al [6], have also been applied to the problem of using meshless methods to model surgical cutting of brain tissue in two and three dimensions by Jin et al [7]. In two dimensions, discontinuities are represented by a series of straight line segments, each of which uses the vector between the segment's beginning and end to define a level-set function with values of opposing signs on opposing sides of the segment, and another such vector and level-set function perpendicular to the end of the segment.…”