Realistic simulation of the 3-D growth of brain tumors in MR images coupling diffusion with biomechanical deformation
TL;DR: A new model to simulate the three-dimensional (3-D) growth of glioblastomas multiforma (GBMs), the most aggressive glial tumors, and a new coupling equation taking into account the mechanical influence of the tumor cells on the invaded tissues are proposed.
Abstract: We propose a new model to simulate the three-dimensional (3-D) growth of glioblastomas multiforma (GBMs), the most aggressive glial tumors. The GBM speed of growth depends on the invaded tissue: faster in white than in gray matter, it is stopped by the dura or the ventricles. These different structures are introduced into the model using an atlas matching technique. The atlas includes both the segmentations of anatomical structures and diffusion information in white matter fibers. We use the finite element method (FEM) to simulate the invasion of the GBM in the brain parenchyma and its mechanical interaction with the invaded structures (mass effect). Depending on the considered tissue, the former effect is modeled with a reaction-diffusion or a Gompertz equation, while the latter is based on a linear elastic brain constitutive equation. In addition, we propose a new coupling equation taking into account the mechanical influence of the tumor cells on the invaded tissues. The tumor growth simulation is assessed by comparing the in-silico GBM growth with the real growth observed on two magnetic resonance images (MRIs) of a patient acquired with 6 mo difference. Results show the feasibility of this new conceptual approach and justifies its further evaluation.
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TL;DR: This paper attempts to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain, and provides an extensive account of registration techniques in a systematic manner.
Abstract: Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: 1) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; 2) longitudinal studies, where temporal structural or anatomical changes are investigated; and 3) population modeling and statistical atlases used to study normal anatomical variability. In this paper, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this paper is to provide an extensive account of registration techniques in a systematic manner.
1,434 citations
Cites methods from "Realistic simulation of the 3-D gro..."
...In [181], after an initial a ne registration between a normal atlas and the patient's image, a coupled model that predicts the anisotropic evolution of the tumor as well as its mass-e ect was applied....
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TL;DR: The state of the art in segmentation, registration and modeling related to tumor-bearing brain images with a focus on gliomas is reviewed, giving special attention to recent developments in radiological tumor assessment guidelines.
Abstract: MRI-based medical image analysis for brain tumor studies is gaining attention in recent times due to an increased need for efficient and objective evaluation of large amounts of data. While the pioneering approaches applying automated methods for the analysis of brain tumor images date back almost two decades, the current methods are becoming more mature and coming closer to routine clinical application. This review aims to provide a comprehensive overview by giving a brief introduction to brain tumors and imaging of brain tumors first. Then, we review the state of the art in segmentation, registration and modeling related to tumor-bearing brain images with a focus on gliomas. The objective in the segmentation is outlining the tumor including its sub-compartments and surrounding tissues, while the main challenge in registration and modeling is the handling of morphological changes caused by the tumor. The qualities of different approaches are discussed with a focus on methods that can be applied on standard clinical imaging protocols. Finally, a critical assessment of the current state is performed and future developments and trends are addressed, giving special attention to recent developments in radiological tumor assessment guidelines.
765 citations
Cites background or methods from "Realistic simulation of the 3-D gro..."
...Clatz et al. (2005a) tackled the problem of non-rigidly registering intraoperative MR images to pre-operative scans....
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...Most models simulate proliferation based on a reactiondiffusion equation and couple this with a bio-mechanical model for the mass-effect (Clatz et al. (2005b), Hogea et al. (2007b), Hogea et al. (2008b), Hogea et al. (2008a), Prastawa et al. (2009))....
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TL;DR: Three experiments are reported that identify the best spatial normalization for structurally damaged brains and establish whether differences among normalizations have a significant effect on inferences about functional activations.
272 citations
Cites background from "Realistic simulation of the 3-D gro..."
...The importance of these issues is reflected on the large body of work modeling the effect of lesions on anatomy (Cuadra et al., 2004; Mohamed et al., 2006; Xue et al., 2006; Dawant et al., 2002; Clatz et al., 2005)....
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TL;DR: This paper extends Nadaraya-Watson kernel regression by recasting the regression problem in terms of Fréchet expectation, and uses the infinite dimensional manifold of diffeomorphic transformations, with an associated metric, to study the small scale changes in anatomy.
Abstract: Regression analysis is a powerful tool for the study of changes in a dependent variable as a function of an independent regressor variable, and in particular it is applicable to the study of anatomical growth and shape change. When the underlying process can be modeled by parameters in a Euclidean space, classical regression techniques (Hardle, Applied Nonparametric Regression, 1990; Wand and Jones, Kernel Smoothing, 1995) are applicable and have been studied extensively. However, recent work suggests that attempts to describe anatomical shapes using flat Euclidean spaces undermines our ability to represent natural biological variability (Fletcher et al., IEEE Trans. Med. Imaging 23(8), 995---1005, 2004; Grenander and Miller, Q. Appl. Math. 56(4), 617---694, 1998).
In this paper we develop a method for regression analysis of general, manifold-valued data. Specifically, we extend Nadaraya-Watson kernel regression by recasting the regression problem in terms of Frechet expectation. Although this method is quite general, our driving problem is the study anatomical shape change as a function of age from random design image data.
We demonstrate our method by analyzing shape change in the brain from a random design dataset of MR images of 97 healthy adults ranging in age from 20 to 79 years. To study the small scale changes in anatomy, we use the infinite dimensional manifold of diffeomorphic transformations, with an associated metric. We regress a representative anatomical shape, as a function of age, from this population.
260 citations
Additional excerpts
...A number of longitudinal growth models have been developed to provide this type of analysis to time-series imagery of a single subject (e.g., Beg 2003; Clatz et al. 2005; Miller 2004; Thompson et al. 2000)....
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TL;DR: The two main goals are to improve the deformable registration from images of brain tumor patients to a common stereotactic space, thereby assisting in the construction of statistical anatomical atlases and to develop predictive capabilities for glioma growth, after the model parameters are estimated for a given patient.
Abstract: We present a framework for modeling gliomas growth and their mechanical impact on the surrounding brain tissue (the so-called, mass-effect) We employ an Eulerian continuum approach that results in a strongly coupled system of nonlinear Partial Differential Equations (PDEs): a reaction-diffusion model for the tumor growth and a piecewise linearly elastic material for the background tissue To estimate unknown model parameters and enable patient-specific simulations we formulate and solve a PDE-constrained optimization problem Our two main goals are the following: (1) to improve the deformable registration from images of brain tumor patients to a common stereotactic space, thereby assisting in the construction of statistical anatomical atlases; and (2) to develop predictive capabilities for glioma growth, after the model parameters are estimated for a given patient To our knowledge, this is the first attempt in the literature to introduce an adjoint-based, PDE-constrained optimization formulation in the context of image-driven modeling spatio-temporal tumor evolution In this paper, we present the formulation, and the solution method and we conduct 1D numerical experiments for preliminary evaluation of the overall formulation/methodology
240 citations
References
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Book•
01 Apr 2003
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
Abstract: Preface 1. Background in linear algebra 2. Discretization of partial differential equations 3. Sparse matrices 4. Basic iterative methods 5. Projection methods 6. Krylov subspace methods Part I 7. Krylov subspace methods Part II 8. Methods related to the normal equations 9. Preconditioned iterations 10. Preconditioning techniques 11. Parallel implementations 12. Parallel preconditioners 13. Multigrid methods 14. Domain decomposition methods Bibliography Index.
13,484 citations
Additional excerpts
...We propose to “slice” every tetrahedron, and include a voxel in a tetrahedron if its barycentric coordinates are positive....
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01 Aug 1987
TL;DR: In this paper, a divide-and-conquer approach is used to generate inter-slice connectivity, and then a case table is created to define triangle topology using linear interpolation.
Abstract: We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.
13,231 citations
Book•
01 Jul 1981TL;DR: This chapter discusses the mechanics of Erythrocytes, Leukocytes, and Other Cells, and their role in Bone and Cartilage, and the properties of Bioviscoelastic Fluids, which are a by-product of these cells.
Abstract: Prefaces. 1. Introduction: A sketch of the History and Scope of the Field. 2. The Meaning of the Constitutive Equation. 3. The Flow Properties of Blood. 4. Mechanics of Erythrocytes, Leukocytes, and Other Cells. 5. Interaction of Red Blood Cells with Vessel Wall, and Wall Shear with Endothelium. 6 Bioviscoelastic Fluids. Bioviscoelastic Solids. 8. Mechanical Properties and Active Remodeling of Blood Vessels. 9. Skeletal Muscle. 10. Heart Muscle. 11. Smooth Muscles. 12. Bone and Cartilage. Indices
6,027 citations
Book•
01 Jan 1982
TL;DR: Elements finis Reference Record created on 2004-09-07, modified on 2016-08-08.
Abstract: Keywords: Methode des elements finis ; Mathematique ; Elements finis Reference Record created on 2004-09-07, modified on 2016-08-08
5,049 citations
"Realistic simulation of the 3-D gro..." refers background or methods in this paper
...We use the classical continuum mechanics formalism ([31, p. 28]) to describe the mechanical behavior of the brain parenchyma....
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...…mechanical problem is obtained by minimizing the potential energy functional (20) Then, combining (17) and (15) with (20) we can explicitly compute the potential energy The minimization condition can indeed be written as a linear system (21) Details of the matrix computation can be found in [42]....
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TL;DR: In this paper, the median of the squared residuals is used to resist the effect of nearly 50% of contamination in the data in the special case of simple least square regression, which corresponds to finding the narrowest strip covering half of the observations.
Abstract: Classical least squares regression consists of minimizing the sum of the squared residuals. Many authors have produced more robust versions of this estimator by replacing the square by something else, such as the absolute value. In this article a different approach is introduced in which the sum is replaced by the median of the squared residuals. The resulting estimator can resist the effect of nearly 50% of contamination in the data. In the special case of simple regression, it corresponds to finding the narrowest strip covering half of the observations. Generalizations are possible to multivariate location, orthogonal regression, and hypothesis testing in linear models.
3,713 citations
"Realistic simulation of the 3-D gro..." refers background in this paper
...GBMs can, thus, be described as a combination of two different growth models depending on the considered tumor area (central active or external)....
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