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

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.

Study of graphics libraries related to the problem of visualization of electrical impedance tomography images

“…A series of software products for the EIT [20,21] do not involve real-time reconstruction of the conductivity field in real-time. Unlike [3], this paper does not set the task of adapting the model to each individual patient, and the principles outlined in [3] do not allow their application for dynamic visualization of the EIT. It can also be noted that the graphics libraries and their specifics for medical visualization were not compared in the reviewed papers [3][4][5][6][7][8][9].…”

“…Visualization of data, obtained from medical and biological examination of a human is a significant area. Thus, paper [3] analyzes the construction of a three-dimensional model of the object under study based on the data obtained during tomographic measurements. The specific feature of this approach is the dynamic construction of a model, depending on the individual characteristics of a patient.…”

Kalman Filter Finite Element Method for Real-Time Soft Tissue Modeling

“…In order to represent the state space model, the displacement, velocity and acceleration are considered as the unknown variables for soft tissue deformation. Rewrite (19) as…”

“…Thus, we can readily have U t+θ t from (19). Since the Wilson − θ scheme is unconditionally stable when θ ≥1.37, in this paper the integration constant is set as θ = 1.4 [31].…”

“…Nevertheless, this technique requires the hardware component of GPU for implementation. The total Lagrangian formulation combines the precomputation of spatial derivatives with the explicit integration to reduce the FEM computing time [18], [19]. However, it does not accept topological alternations in the model and its solution is stable subject to small steps only.…”