Implementation of a Modified Moving Least Squares Approximation for Predicting Soft Tissue Deformation Using a Meshless Method

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

“…A modified moving least squares approximation which can handle more nodal distributions without loss of accuracy is an example of a recent step in this direction. 21,59 Determining patient-specific material properties has been a subject of research effort in the last 20-30 years. 36 However, despite substantial progress, including recent advances in MR elastography, 11,93 in vivo quantification of soft tissue material properties still remains an unsolved challenge.…”

“…Recent developments in meshless algorithms eliminate some of these deficiencies and make meshless methods even more suitable for computational biomechanics applications. They include a more efficient method for handling discontinuities, 45 modified moving least squares approximation which can handle more nodal distributions without loss of accuracy 21,59 and incorporation of fuzzy tissue classification method within the meshless computational framework which makes it possible to assign material properties at integration points of a computational grid directly from the medical images without segmentation. Assignment of material properties directly from the medical images using fuzzy tissue classification was successfully applied in the context of computation of the brain and abdominal organ deformations when treating soft tissues as a hyperelastic neo-Hookean material.…”

Computational monitoring in real time: review of methods and applications

“…To overcome this challenge, coupling of meshless and finite element discretisation with essential boundary conditions imposed through finite element shape functions Krongauz and Belytschko 1996;Zhang et al 2014) and Lagrange multipliers (Belytschko et al 1994 have been used. Recently Chowdhury et al (2015) proposed and verified application of Modified Moving Least Squares (MMLS) with polynomial (quadratic) bases (Joldes et al 2015a) and regularised weight functions for imposition of essential boundary conditions within the Galerkin-type meshless computation framework. As the MLS shape functions are not polynomials and their local support may not align with the integration cells, background integration using Gaussian quadrature may prove difficult to quantify errors.…”

“…Detailed description of this example is provided in Chowdhury et al (2017). The model was implemented using Meshless Total Lagrangian Explicit Dynamics (MTLED) method developed by Horton et al (2010), Chowdhury et al (2015), Joldes et al (2015a, c) with the Modified Moving Least Square (MMLS) shape functions. The essential boundary conditions (at the rigidly constrained edge of the beam) were imposed using recently developed Essential Boundary Conditions Imposition in Explicit Meshless (EBCIEM) method by Joldes et al (2017).…”

“…This problem is not limited Fig. 15 Computation of deformations of cantilever beam subjected to bending using Galerkin-type Meshless Total Lagrangian Explicit Dynamics (MTLED) method developed by Horton et al (2010), Chowdhury et al (2015), Joldes et al (2015a, c), Chowdhury et al (2017) with the Modified Moving Least Squarse (MMLS) shape functions by Chowdhury et al (2017). The figure shows the differences (in mm) between the analytical solution from Timoshenko and Goodier (1970) and the deformations computed using MTLED.…”