arXiv subjects

George C. Bourantas

Publications and source records attributed to George C. Bourantas.

5 recordsLinked to original sources

arXiv2022

Generation of Patient-specific Structured Hexahedral Mesh of Aortic Aneurysm Wall

Abdominal Aortic Aneurysm (AAA) is an enlargement in the lower part of the main artery Aorta by 1.5 times its normal diameter. AAA can cause death if rupture occurs. Elective surgeries are recommended to prevent rupture based on geometrical measurements of AAA diameter and diameter growth rate. Reliability of these geometric parameters to predict the AAA rupture risk has been questioned, and biomechanical assessment has been proposed to distinguish between patients with high and low risk of rupture. Stress in aneurysm wall is the main variable of interest in such assessment. Most studies use finite element method to compute AAA stress. This requires discretising patient-specific geometry (aneurysm wall and intraluminal thrombus ILT) into finite elements/meshes. Tetrahedral elements are most commonly used as they can be generated in seemingly automated and effortless way. In practice, however, due to complex aneurysm geometry, the process tends to require time consuming mesh optimisation to ensure sufficiently high quality of tetrahedral elements. Furthermore, ensuring solution convergence requires large number of tetrahedral elements, which leads to long computation times. In this study, we focus on generation of hexahedral meshes as they are known to provide converged solution for smaller number of elements than tetrahedral meshes. Generation of hexahedral meshes for continua with complex/irregular geometry, such as aneurysms, requires analyst interaction. We propose a procedure for generating high quality patient-specific hexahedral discretisation of aneurysm wall using the algorithms available in commercial software package for mesh generation. For aneurysm cases, we demonstrate that the procedure facilitates patient-specific mesh generation within timeframe consistent with clinical workflow constraints while requiring only limited input from the analyst.

cs.CE↗

arXiv2022

Recovery by discretization corrected particle strength exchange (DC PSE) operators

A new recovery technique based on discretization corrected particle strength exchange (DC PSE) operators is developed in this paper. DC PSE is a collocation method that can be used to compute derivatives directly at nodal points, instead of by projection from Gauss points as is done in many finite element-based recovery techniques. The proposed method is truly meshless and does not require patches of elements to be defined, which makes it generally applicable to point clouds and arbitrary element topologies. Numerical examples show that the proposed method is accurate and robust.

math.NA↗

arXiv2022

Patient-specific solution of the electrocorticography forward problem in deforming brain

Invasive intracranial electroencephalography (iEEG) or electrocorticography (ECoG) measures electric potential directly on the surface of the brain and can be used to inform treatment planning for epilepsy surgery. Combined with numerical modeling they can further improve accuracy of epilepsy surgery planning. Accurate solution of the iEEG or ECoG forward problem, which is a crucial prerequisite for solving the inverse problem in epilepsy seizure onset zone localization, requires accurate representation of the patient's brain geometry and tissue electrical conductivity after implantation of electrodes. However, implantation of subdural grid electrodes causes the brain to deform, which invalidates preoperatively acquired image data. Moreover, postoperative magnetic resonance imaging (MRI) is incompatible with implanted electrodes and computed tomography (CT) has insufficient range of soft tissue contrast, which precludes both MRI and CT from being used to obtain the deformed postoperative geometry. In this paper, we present a biomechanics-based image warping procedure using preoperative MRI for tissue classification and postoperative CT for locating implanted electrodes to perform non-rigid registration of the preoperative image data to the postoperative configuration. We solve the iEEG forward problem on the predicted postoperative geometry using the finite element method (FEM) which accounts for patient-specific inhomogeneity and anisotropy of tissue conductivity. Results for the simulation of a current source in the brain show large differences in electric potential predicted by the models based on the original images and the deformed images corresponding to the brain geometry deformed by placement of invasive electrodes. Computation of the lead field matrix (useful for solution of the iEEG inverse problem) also showed significant differences between the different models.

physics.med-ph↗

arXiv2019

Cell-based Maximum Entropy Approximants for Three Dimensional Domains: Application in Large Strain Elastodynamics using the Meshless Total Lagrangian Explicit Dynamics Method

We present the Cell-based Maximum Entropy (CME) approximants in E3 space by constructing the smooth approximation distance function to polyhedral surfaces. CME is a meshfree approximation method combining the properties of the Maximum Entropy approximants and the compact support of element-based interpolants. The method is evaluated in problems of large strain elastodynamics for three-dimensional (3D) continua using the well-established Meshless Total Lagrangian Explicit Dynamics (MTLED) method. The accuracy and efficiency of the method is assessed in several numerical examples in terms of computational time, accuracy in boundary conditions imposition, and strain energy density error. Due to the smoothness of CME basis functions, the numerical stability in explicit time integration is preserved for large time step. The challenging task of essential boundary conditions imposition in non-interpolating meshless methods (e.g., Moving Least Squares) is eliminated in CME due to the weak Kronecker-delta property. The essential boundary conditions are imposed directly, similar to the Finite Element Method. CME is proven a valuable alternative to other meshless and element-based methods for large-scale elastodynamics in 3D.

math.NA↗

arXiv2019

An explicit meshless point collocation solver for incompressible Navier-Stokes equations

We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow domain. We compute the spatial derivatives using the Meshless Point Collocation (MPC) method. We verify the accuracy of the numerical scheme for commonly-used benchmark problems including lid-driven cavity flow, flow over a backward-facing step and vortex shedding behind a cylinder. We have examined the applicability of the proposed scheme by considering flow cases with complex geometries, such as flow in a duct with cylindrical obstacles, flow in a bifurcated geometry, and flow past complex-shaped obstacles. Our method offers high accuracy and excellent computational efficiency as demonstrated by the verification examples, while maintaining a stable time step comparable to that used in unconditionally stable implicit methods.

physics.comp-ph↗