Suite of meshless algorithms for accurate computation of soft tissue deformation for surgical simulation

•Meshless algorithms for the computation of soft tissue deformation for surgical simulation.•Element Free Galerkin (EFG) is an effective meshless method for nonlinear problems.•Meshless Total Lagrangian Explicit Dynamics (MTLED) solution method bypass the traditional meshless methods.•Application of...

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Published in:Medical image analysis Vol. 56; pp. 152 - 171
Main Authors: Joldes, Grand, Bourantas, George, Zwick, Benjamin, Chowdhury, Habib, Wittek, Adam, Agrawal, Sudip, Mountris, Konstantinos, Hyde, Damon, Warfield, Simon K., Miller, Karol
Format: Journal Article
Language:English
Published: Netherlands Elsevier B.V 01.08.2019
Elsevier BV
Subjects:
Algorithms
Boundary conditions
Computation
Computer simulation
Deformation
Finite element method
Galerkin method
Integration
Mathematical analysis
Meshless methods
Meshless Total Lagrangian Explicit Dynamics
Nonlinear computational mechanics
Numerical integration
Polynomials
Precision medicine
Shape functions
Soft tissues
Surgery
Surgical mesh
Surgical simulation
Time integration
Tissues
Meshless Total Lagrangian Explicit Dynamics
Surgical simulation
Nonlinear computational mechanics
Soft tissues
ISSN:1361-8415, 1361-8423, 1361-8423
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Summary:•Meshless algorithms for the computation of soft tissue deformation for surgical simulation.•Element Free Galerkin (EFG) is an effective meshless method for nonlinear problems.•Meshless Total Lagrangian Explicit Dynamics (MTLED) solution method bypass the traditional meshless methods.•Application of a new method of imposing the essential boundary conditions. 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. [Display omitted]
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ISSN:1361-8415
1361-8423
1361-8423
DOI:10.1016/j.media.2019.06.004