  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.
