Nikola Kosturski

Supercomputer Simulation of Radio‐frequency Hepatic Tumor Ablation

We simulate the thermal and electrical processes, involved in the radio‐frequency (RF) ablation procedure. The mathematical model consists of two parts—electrical and thermal. The energy from the applied AC voltage is determined first, by solving the Laplace equation to find the potential distribution. After that, the electric field intensity and the current density are directly calculated. Finally, the heat transfer equation is solved to determine the temperature distribution. Heat loss due to blood perfusion is also accounted for.The representation of the computational domain is based on a voxel mesh. Both partial differential equations are discretized in space via linear conforming FEM. After the space discretization, the backward Euler scheme is used for the time stepping.Large‐scale linear systems arise from the FEM discretization. Moreover, they are ill‐conditioned, due to the strong coefficient jumps and the complex geometry of the problem. Therefore, efficient parallel solution methods are required.The developed parallel solver is based on the preconditioned conjugate gradient (PCG) method. As a preconditioner, we use BoomerAMG—a parallel algebraic multigrid implementation from the package Hypre, developed in LLNL, Livermore.Parallel numerical tests, performed on the IBM Blue Gene/P massively parallel computer are presented.We simulate the thermal and electrical processes, involved in the radio‐frequency (RF) ablation procedure. The mathematical model consists of two parts—electrical and thermal. The energy from the applied AC voltage is determined first, by solving the Laplace equation to find the potential distribution. After that, the electric field intensity and the current density are directly calculated. Finally, the heat transfer equation is solved to determine the temperature distribution. Heat loss due to blood perfusion is also accounted for.The representation of the computational domain is based on a voxel mesh. Both partial differential equations are discretized in space via linear conforming FEM. After the space discretization, the backward Euler scheme is used for the time stepping.Large‐scale linear systems arise from the FEM discretization. Moreover, they are ill‐conditioned, due to the strong coefficient jumps and the complex geometry of the problem. Therefore, efficient parallel solution methods are require...

Numerical homogenization of bone microstructure

The presented study is motivated by the development of methods, algorithms, and software tools for μFE (micro finite element) simulation of human bones The voxel representation of the bone microstructure is obtained from a high resolution computer tomography (CT) image The considered numerical homogenization problem concerns isotropic linear elasticity models at micro and macro levels.

Comparison of Two Techniques for Radio‐frequency Hepatic Tumor Ablation through Numerical Simulation

We simulate the thermal and electrical processes, involved in the radio‐frequency ablation procedure. In this study, we take into account the observed fact, that the electrical conductivity of the hepatic tissue varies during the procedure. With the increase of the tissue temperature to a certain level, a sudden drop of the electrical conductivity is observed. This variation was neglected in some previous studies.The mathematical model consists of two parts—electrical and thermal. The energy from the applied AC voltage is determined first, by solving the Laplace equation to find the potential distribution. After that, the electric field intensity and the current density are directly calculated. Finally, the heat transfer equation is solved to determine the temperature distribution. Heat loss due to blood perfusion is also accounted for.The simulations were performed on the IBM Blue Gene/P massively parallel computer.

Computer Simulation of RF Liver Ablation on an MRI Scan Data

Radio-frequency (RF) ablation is a low invasive technique for treatment of liver tumors. An RF-probe is inserted in the patients liver and a ground pad is applied to the skin. Then the tumor is heated with RF current. The heat causes the destruction of tumor cells. We use the finite element method (FEM) to simulate and analyze various aspects of the procedure. A 3D image of the patients liver is obtained from a magnetic resonance imaging (MRI) scan. Then, the geometry for the RFprobe and the ground pad is added. Our focus is on the influence of the position of the ground pads on the ablation process. Our simulation is based on an unstructured mesh. The size of the mesh is large due to the complexity of the domain. We discretize and solve the problem on a parallel computer using MPI for the parallelization. The presented numerical tests are performed on IBM Blue Gene/P machine at BGSC. The parallel efficiency of the incorporated Boomer AMG solver is demonstrated as well.

Balancing the communications and computations in parallel FEM simulations on unstructured grids

We consider large scale finite element modeling on 3D unstructured grids. Large scale problems imply the use of parallel hardware and software. In general, the computational process on unstructured grids includes: mesh generation, mesh partitioning, optional mesh refinement, discretization, and the solution. The impact of the domain partitioning strategy on the performance of the discretization and solution stages is studied. Our investigations are focused on the Blue Gene/P massively parallel computer. The mapping of the communications to the underlying 3D tours interconnect topology is considered as well. As a sample problem, we consider the simulation of the thermal and electrical processes, involved in the radio-frequency (RF) ablation procedure. RF ablation is a low invasive technique for the treatment of hepatic tumors, utilizing AC current to destroy the tumor cells by heating.

Improving the efficiency of parallel FEM simulations on voxel domains

In this work, we consider large-scale finite element modeling on voxel grids. We are targeting the IBM Blue Gene/P computer, which features a 3D torus interconnect. Our previous parallelization approach was to divide the domain in one spatial direction only, which lead to limited parallelism. Here, we extend it to all three spatial directions in order to match the interconnect topology. As a sample problem, we consider the simulation of the thermal and electrical processes, involved in the radio-frequency (RF) ablation procedure. RF ablation is a low invasive technique for the treatment of hepatic tumors, utilizing AC current to destroy the tumor cells by heating. A 3D voxel approach is used for finite element method (FEM) approximation of the involved partial differential equations. After the space discretization, the backward Euler scheme is used for the time stepping. We study the impact of the domain partitioning on the performance of a parallel preconditioned conjugate gradient (PCG) solver for the arising large linear systems. As a preconditioner, we use BoomerAMG --- a parallel algebraic multigrid implementation from the package Hypre, developed in LLNL, Livermore. The implementation is tested on the IBM Blue Gene/P massively parallel computer.

Comparative analysis of mesh generators and MIC(0) preconditioning of FEM elasticity systems

In this study, the topics of grid generation and FEM applications are studied together following their natural synergy. We consider the following three grid generators: Triangle, NETGEN and Gmsh. The quantitative analysis is based on the number of elements/nodes needed to obtain a triangulation of a given domain, satisfying a certain minimal angle condition. After that, the performance of two displacement decomposition (DD) preconditioners that exploit modified incomplete Cholesky factorization MIC(0) is studied in the case of FEM matrices arising from the discretization of the two-dimensional equations of elasticity on nonstructured grids.

Performance Analysis of MG Preconditioning on Intel Xeon Phi: Towards Scalability for Extreme Scale Problems with Fractional Laplacians

The Intel Xeon Phi architecture is currently a popular choice for supercomputers, with many entries of the Top 500 list, using it either as main processors or as accelerators/coprocessors. In this paper, we explore the performance and scalability of the Intel Xeon Phi chips in the context of large sparse linear systems, commonly arising from the discretization of PDEs. At the first step, the PCG [1] is applied as a basic iterative solution method in the case of sparse SPD problems. The parallel multigrid (MG) implementation from Trilinos ML package is utilized as a preconditioner. A matrix free algebraic multilevel solver is used to reduce the memory requirements, thus allowing the cores to be more efficiently utilized. The second part of the paper is devoted to the fractional Laplacian, that is, we consider the equation \(-\varDelta ^\alpha {\mathbf {u}} = {\mathbf {f}}\), \(0<\alpha < 1\), Open image in new window . The related elliptic boundary value problem describes anomalous diffusion phenomena also referred to as super-diffusion. The implemented method approximates the solution of the nonlocal problem by a series of local elliptic problems. The currently available numerical methods for fractional diffusion Laplacian have computational complexity, comparable e.g., to the complexity of solving local elliptic problem in Open image in new window . The presented parallel results are for \(\varOmega =(0,1)^3\), including meshes of very large scale. The numerical experiments are run on the Avitohol computer at the Institute of Information and Communication Technologies, IICT-BAS. The presented results show very good scalability when the CPU-cores and MIC work together for a certain number of compute nodes.

MIC(0) DD Preconditioning of FEM Elasticity Systems on Unstructured Tetrahedral Grids

In this study, the topics of grid generation and FEM applications are studied together following their natural synergy. We consider the following three grid generators: NETGEN, TetGen and Gmsh. The qualitative analysis is based on the range of the dihedral angles of the triangulation of a given domain. After that, the performance of two displacement decomposition (DD) preconditioners that exploit modified incomplete Cholesky factorization MIC(0) is studied in the case of FEM matrices arising from the discretization of the three-dimensional equations of elasticity on unstructured tetrahedral grids.

Thermoelectrical Tick Removal Process Modeling

Ticks are widespread ectoparasites. They feed on blood of animals like birds and mammals, including humans. They are carriers and transmitters of pathogens, which cause many diseases, including tick-borne meningoencephalitis, lyme borreliosis, typhus to name few. The best way to prevent infection is to remove the ticks from the host as soon as possible. The removal usually is performed mechanically by pulling the tick. This however is a risky process. Tick irritation or injury may result in it vomiting infective fluids.