Search results for: George Biros

Items from 1 to 20 out of 49 results

article

Simulation of glioblastoma growth using a 3D multispecies tumor model with mass effect

Shashank Subramanian, Amir Gholami, George Biros

Journal of Mathematical Biology > 2019 > 79 > 3 > 941-967

In this article, we present a multispecies reaction–advection–diffusion partial differential equation coupled with linear elasticity for modeling tumor growth. The model aims to capture the phenomenological features of glioblastoma multiforme observed in magnetic resonance imaging (MRI) scans. These include enhancing and necrotic tumor structures, brain edema and the so-called “mass effect”, a term-of-art...

article

PDE-constrained optimization in medical image analysis

Andreas Mang, Amir Gholami, Christos Davatzikos, George Biros

Optimization and Engineering > 2018 > 19 > 3 > 765-812

PDE-constrained optimization problems find many applications in medical image analysis, for example, neuroimaging, cardiovascular imaging, and oncologic imaging. We review the related literature and give examples of the formulation, discretization, and numerical solution of PDE-constrained optimization problems for medical imaging. We discuss three examples. The first is image registration, the second...

article

Low-resolution simulations of vesicle suspensions in 2D

Gökberk Kabacaoğlu, Bryan Quaife, George Biros

Journal of Computational Physics > 2018 > 357 > C > 43-77

Vesicle suspensions appear in many biological and industrial applications. These suspensions are characterized by rich and complex dynamics of vesicles due to their interaction with the bulk fluid, and their large deformations and nonlinear elastic properties. Many existing state-of-the-art numerical schemes can resolve such complex vesicle flows. However, even when using provably optimal algorithms,...

article

Far-field compression for fast kernel summation methods in high dimensions

William B. March, George Biros

Applied and Computational Harmonic Analysis > 2017 > 43 > 1 > 39-75

We consider fast kernel summations in high dimensions: given a large set of points in d dimensions (with d≫3) and a pair-potential function (the kernel function), we compute a weighted sum of all pairwise kernel interactions for each point in the set. Direct summation is equivalent to a (dense) matrix–vector multiplication and scales quadratically with the number of points. Fast kernel summation algorithms...

chapter

An N log N Parallel Fast Direct Solver for Kernel Matrices

Chenhan D. Yu, William B. March, George Biros

2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS) > 886 - 896

2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS)

Kernel matrices appear in machine learning and non-parametric statistics. Given N points in d dimensions and a kernel function that requires O(d) work to evaluate, we present an O(dN log N)-work algorithm for the approximate factorization of a regularized kernel matrix, a common computational bottleneck in the training phase of a learning task. With this factorization, solving a linear system with...

chapter

A Parallel Arbitrary-Order Accurate AMR Algorithm for the Scalar Advection-Diffusion Equation

Arash Bakhtiari, Dhairya Malhotra, Amir Raoofy, Miriam Mehl, more

SC16: International Conference for High Performance Computing, Networking, Storage and Analysis > 514 - 525

SC16: International Conference for High Performance Computing, Networking, Storage and Analysis

We present a numerical method for solving the scalar advection-diffusion equation using adaptive mesh refinement. Our solver has three unique characteristics: (1) it supports arbitrary-order accuracy in space; (2) it allows different discretizations for the velocity and scalar advected quantity; (3) it combines the method of characteristics with an integral equation formulation; and (4) it supports...

chapter

Distributed-Memory Large Deformation Diffeomorphic 3D Image Registration

Andreas Mang, Amir Gholami, George Biros

SC16: International Conference for High Performance Computing, Networking, Storage and Analysis > 842 - 853

SC16: International Conference for High Performance Computing, Networking, Storage and Analysis

We present a parallel distributed-memory algorithm for large deformation diffeomorphic registration of volumetric images that produces large isochoric deformations (locally volume preserving). Image registration is a key technology in medical image analysis. Our algorithm uses a partial differential equation constrained optimal control formulation. Finding the optimal deformation map requires the...

chapter

Modeling Glioma Growth and Mass Effect in 3D MR Images of the Brain

Cosmina Hogea, Christos Davatzikos, George Biros

Lecture Notes in Computer Science > Medical Image Computing and Computer-Assisted Intervention – MICCAI 2007 > Physiology and Physics-based Image Computing > 642-650

In this article, we propose a framework for modeling glioma growth and the subsequent mechanical impact on the surrounding brain tissue (mass-effect) in a medical imaging context. Glioma growth is modeled via nonlinear reaction-advection-diffusion, with a two-way coupling with the underlying tissue elastic deformation. Tumor bulk and infiltration and subsequent mass-effects are not regarded separately,...

chapter

Optimizing GPGPU Kernel Summation for Performance and Energy Efficiency

Jiajun Wang, Ahmed Khawaja, George Biros, Andreas Gerstlauer, more

2016 45th International Conference on Parallel Processing Workshops (ICPPW) > 123 - 132

2016 45th International Conference on Parallel Processing Workshops (ICPPW)

Kernel summation is a widely used computational kernel that involves matrix-matrix multiplication (GEMM) and matrix-vector multiplication (GEMV) computational primitives. The parallelism exhibited in kernel summation suggests performance improvement when running on GPGPU. State of the art GPU solutions apply cuBLAS library but cannot exploit much of the data locality because intermediate results are...

chapter

INV-ASKIT: A Parallel Fast Direct Solver for Kernel Matrices

Chenhan D. Yu, William B. March, Bo Xiao, George Biros

2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS) > 161 - 171

2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS)

We present a parallel algorithm for computing the approximatefactorization of an N-by-N kernel matrix. Once this factorizationhas been constructed (with N log2 N work), we can solve linearsystems with this matrix with N log N work. Kernel matricesrepresent pairwise interactions of points in metric spaces. Theyappear in machine learning, approximation theory, and computationalphysics. Kernel matrices...

chapter

Biomechanically-Constrained 4D Estimation of Myocardial Motion

Hari Sundar, Christos Davatzikos, George Biros

Lecture Notes in Computer Science > Medical Image Computing and Computer-Assisted Intervention – MICCAI 2009 > Motion Analysis, Physical Based Modelling and Image Reconstruction > 257-265

We propose a method for the analysis of cardiac images with the goal of reconstructing the motion of the ventricular walls. The main feature of our method is that the inversion parameter field is the active contraction of the myocardial fibers. This is accomplished with a biophysically-constrained, four-dimensional (space plus time) formulation that aims to complement information that can be gathered...

chapter

Robust Computation of Mutual Information Using Spatially Adaptive Meshes

Hari Sundar, Dinggang Shen, George Biros, Chenyang Xu, more

Lecture Notes in Computer Science > Medical Image Computing and Computer-Assisted Intervention – MICCAI 2007 > General Medical Image Computing - II > 950-958

We present a new method for the fast and robust computation of information theoretic similarity measures for alignment of multi-modality medical images. The proposed method defines a non-uniform, adaptive sampling scheme for estimating the entropies of the images, which is less vulnerable to local maxima as compared to uniform and random sampling. The sampling is defined using an octree partition...

chapter

Joint Segmentation and Deformable Registration of Brain Scans Guided by a Tumor Growth Model

Ali Gooya, Kilian M. Pohl, Michel Bilello, George Biros, more

Lecture Notes in Computer Science > Medical Image Computing and Computer-Assisted Intervention – MICCAI 2011 > Registration I > 532-540

This paper presents an approach for joint segmentation and deformable registration of brain scans of glioma patients to a normal atlas. The proposed method is based on the Expectation Maximization (EM) algorithm that incorporates a glioma growth model for atlas seeding, a process which modifies the normal atlas into one with a tumor and edema. The modified atlas is registered into the patient space...

chapter

An Inverse Scattering Algorithm for the Segmentation of the Luminal Border on Intravascular Ultrasound Data

E. Gerardo Mendizabal-Ruiz, George Biros, Ioannis A. Kakadiaris

Lecture Notes in Computer Science > Medical Image Computing and Computer-Assisted Intervention – MICCAI 2009 > Image Segmentation and Analysis > 885-892

Intravascular ultrasound (IVUS) is a catheter-based medical imaging technique that produces cross-sectional images of blood vessels and is particularly useful for studying atherosclerosis. In this paper, we present a novel method for segmentation of the luminal border on IVUS images using the radio frequency (RF) raw signal based on a scattering model and an inversion scheme. The scattering model...

chapter

A Framework for Online Inversion-Based 3D Site Characterization

Volkan Akçelik, Jacobo Bielak, George Biros, Ioannis Epanomeritakis, more

Lecture Notes in Computer Science > Computational Science - ICCS 2004 > Workshop on Dynamic Data Driven Applications Systems > 717-724

Our goal is to develop the capability for characterizing the three-dimensional geological structure and mechanical properties of individual sites and complete basins in earthquake-prone regions. Toward this end we present a framework that integrates in situ field testing, observations of earthquake ground motion, and inversion-based modeling.

chapter

Inversion of Airborne Contaminants in a Regional Model

Volkan Akcelik, George Biros, Andrei Draganescu, Omar Ghattas, more

Lecture Notes in Computer Science > Computational Science – ICCS 2006 > Dynamic Data Driven Application Systems (DDDAS 2006) > 481-488

We are interested in a DDDAS problem of localization of airborne contaminant releases in regional atmospheric transport models from sparse observations. Given measurements of the contaminant over an observation window at a small number of points in space, and a velocity field as predicted for example by a mesoscopic weather model, we seek an estimate of the state of the contaminant at the begining...

article

Adaptive time stepping for vesicle suspensions

Bryan Quaife, George Biros

Journal of Computational Physics > 2016 > 306 > C > 478-499

We present an adaptive high-order accurate time-stepping numerical scheme for the flow of vesicles suspended in Stokesian fluids. Our scheme can be summarized as an approximate implicit spectral deferred correction (SDC) method. Applying a fully-implicit SDC scheme to vesicle flows is prohibitively expensive. For this reason we introduce several approximations. Our scheme is based on a semi-implicit...

article

An inverse problem formulation for parameter estimation of a reaction–diffusion model of low grade gliomas

Amir Gholami, Andreas Mang, George Biros

Journal of Mathematical Biology > 2016 > 72 > 1-2 > 409-433

We present a numerical scheme for solving a parameter estimation problem for a model of low-grade glioma growth. Our goal is to estimate the spatial distribution of tumor concentration, as well as the magnitude of anisotropic tumor diffusion. We use a constrained optimization formulation with a reaction–diffusion model that results in a system of nonlinear partial differential equations. In our formulation,...

article

Boundary integral method for the flow of vesicles with viscosity contrast in three dimensions

Abtin Rahimian, Shravan K. Veerapaneni, Denis Zorin, George Biros

Journal of Computational Physics > 2015 > 298 > C > 766-786

We propose numerical algorithms for the simulation of the dynamics of three-dimensional vesicles suspended in viscous Stokesian fluid. Our method is an extension of our previous work (S.K. Veerapaneni et al., 2011) [37] to flows with viscosity contrast. This generalization requires a change in the boundary integral formulation of the solution, in which a double-layer Stokes integral is introduced,...

article

Comparison of multigrid algorithms for high‐order continuous finite element discretizations

Hari Sundar, Georg Stadler, George Biros

Numerical Linear Algebra with Applications > 22 > 4 > 664 - 680

We present a comparison of different multigrid approaches for the solution of systems arising from high‐order continuous finite element discretizations of elliptic partial differential equations on complex geometries. We consider the pointwise Jacobi, the Chebyshev‐accelerated Jacobi, and the symmetric successive over‐relaxation smoothers, as well as elementwise block Jacobi smoothing. Three approaches...

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INFONA - science communication portal

Search results for: George Biros

Simulation of glioblastoma growth using a 3D multispecies tumor model with mass effect

PDE-constrained optimization in medical image analysis

Low-resolution simulations of vesicle suspensions in 2D

Far-field compression for fast kernel summation methods in high dimensions

An N log N Parallel Fast Direct Solver for Kernel Matrices

A Parallel Arbitrary-Order Accurate AMR Algorithm for the Scalar Advection-Diffusion Equation

Distributed-Memory Large Deformation Diffeomorphic 3D Image Registration

Modeling Glioma Growth and Mass Effect in 3D MR Images of the Brain

Optimizing GPGPU Kernel Summation for Performance and Energy Efficiency

INV-ASKIT: A Parallel Fast Direct Solver for Kernel Matrices

Biomechanically-Constrained 4D Estimation of Myocardial Motion

Robust Computation of Mutual Information Using Spatially Adaptive Meshes

Joint Segmentation and Deformable Registration of Brain Scans Guided by a Tumor Growth Model

An Inverse Scattering Algorithm for the Segmentation of the Luminal Border on Intravascular Ultrasound Data

A Framework for Online Inversion-Based 3D Site Characterization

Inversion of Airborne Contaminants in a Regional Model

Adaptive time stepping for vesicle suspensions

An inverse problem formulation for parameter estimation of a reaction–diffusion model of low grade gliomas

Boundary integral method for the flow of vesicles with viscosity contrast in three dimensions

Comparison of multigrid algorithms for high‐order continuous finite element discretizations

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