Monica Hernandez

Non-parametric geodesic active regions: method and evaluation for cerebral aneurysms segmentation in 3DRA and CTA.

Segmentation of vascular structures is a difficult and challenging task. In this article, we present an algorithm devised for the segmentation of such structures. Our technique consists in a geometric deformable model with associated energy functional that incorporates high-order multiscale features in a non-parametric statistical framework. Although the proposed segmentation method is generic, it has been applied to the segmentation of cerebral aneurysms in 3DRA and CTA. An evaluation study over 10 clinical datasets indicate that the segmentations obtained by our method present a high overlap index with respect to the ground-truth (91.13% and 73.31%, respectively) and that the mean error distance from the surface to the ground truth is close to the in-plane resolution (0.40 and 0.38 mm, respectively). Besides, our technique favorably compares to other alternative techniques based on deformable models, namely parametric geodesic active regions and active contours without edges.

Registration of Anatomical Images Using Paths of Diffeomorphisms Parameterized with Stationary Vector Field Flows

Computational Anatomy aims for the study of variability in anatomical structures from images. Variability is encoded by the spatial transformations existing between anatomical images and a template selected as reference. In the absence of a more justified model for inter-subject variability, transformations are considered to belong to a convenient family of diffeomorphisms which provides a suitable mathematical setting for the analysis of anatomical variability. One of the proposed paradigms for diffeomorphic registration is the Large Deformation Diffeomorphic Metric Mapping (LDDMM). In this framework, transformations are characterized as end points of paths parameterized by time-varying flows of vector fields defined on the tangent space of a Riemannian manifold of diffeomorphisms and computed from the solution of the non-stationary transport equation associated to these flows. With this characterization, optimization in LDDMM is performed on the space of non-stationary vector field flows resulting into a time and memory consuming algorithm. Recently, an alternative characterization of paths of diffeomorphisms based on constant-time flows of vector fields has been proposed in the literature. With this parameterization, diffeomorphisms constitute solutions of stationary ODEs. In this article, the stationary parameterization is included for diffeomorphic registration in the LDDMM framework. We formulate the variational problem related to this registration scenario and derive the associated Euler-Lagrange equations. Moreover, the performance of the non-stationary vs the stationary parameterizations in real and simulated 3D-MRI brain datasets is evaluated. Compared to the non-stationary parameterization, our proposal provides similar results in terms of image matching and local differences between the diffeomorphic transformations while drastically reducing memory and time requirements.

Contributions to 3D diffeomorphic atlas estimation: application to brain images

This paper focuses on the estimation of statistical atlases of 3D images by means of diffeomorphic transformations. Within a Log-Euclidean framework, the exponential and logarithm maps of diffeomorphisms need to be computed. In this framework, the Inverse Scaling and Squaring (ISS) method has been recently extended for the computation of the logarithm map, which is one of the most time demanding stages. In this work we propose to apply the Baker-Campbell-Hausdorff (BCH) formula instead. In a 3D simulation study, BCH formula and ISS method obtained similar accuracy but BCH formula was more than 100 times faster. This approach allowed us to estimate a 3D statistical brain atlas in a reasonable time, including the average and the modes of variation. Details for the computation of the modes of variation in the Sobolev tangent space of diffeomorphisms are also provided.

Subject-specific modeling of intracranial aneurysms

Characterization of the blood flow patterns in cerebral aneurysms is important to explore possible correlations between the hemodynamics conditions and the morphology, location, type and risk of rupture of intracranial aneurysms. For this purpose, realistic patient-specific models are constructed from computed tomography angiography and 3D rotational angiography image data. Visualizations of the distribution of hemodynamics forces on the aneurysm walls as well as the intra-aneurysmal flow patterns are presented for a number of cerebral aneurysms of different sizes, types and locations. The numerical models indicate that there are different classes of intra-aneurysmal flow patterns, that may carry different risks of rupture.

Three-Dimensional Segmentation of Brain Aneurysms in CTA Using Non-parametric Region-Based Information and Implicit Deformable Models: Method and Evaluation

Knowledge of brain aneurysm dimensions is essential in min- imally invasive surgical interventions using Guglielmi Detachable Coils. These parameters are obtained in clinical routine using 2D maximum intensity projection images. Automated quantification of the three di- mensional structure of aneurysms directly from the 3D data set may be used to provide accurate and objective measurements of the clinically relevant parameters. In this paper we present an algorithm devised for the segmentation of brain aneurysms based on implicit deformable mod- els combined with non-parametric region-based information. This work also presents the evaluation of the method in a clinical data base of 39 cases.

Registration of anatomical images using geodesic paths of diffeomorphisms parameterized with stationary vector fields

Computational Anatomy aims for the study of the statistical variability in anatomical structures. Variability is encoded by the transformations existing among populations of anatomical images. These transformations are usually computed from diffeomorphic registration based on the large deformation paradigm. In this framework diffeomorphisms are usually computed as end points of paths on the Riemannian manifold of diffeomorphisms parameterized by non-stationary vector fields. Recently, an alternative parameterization based on stationary vector fields has been developed. In this article we propose to use this stationary parameterization for diffeomorphic registration. We formulate the variational problem related to this registration scenario and derive the associated Euler-Lagrange equations. We evaluate the performance of the non-stationary vs the stationary parameterizations in real and synthetic 3D-MRI datasets. Compared to the non-stationary parameterization, our proposal provides similar accuracy in terms of image matching and deformation smoothness while drastically reducing memory and time requirements.

Gauss-Newton optimization in Diffeomorphic registration

In this article, we propose a numerical implementation of Gauss-Newtons method for optimization in diffeomorphic registration in the large deformation diffeomorphic metric mapping framework. The computations of the Gateaux derivatives of the objective function are performed in the tangent space of the Riemannian manifold of diffeomorphisms. The resulting algorithm has been compared to gradient descent optimization in brain MRI anatomical images. The experiments have shown similar accuracy for both techniques at steady-state while Gauss-Newton has resulted to be more robust with a faster rate of convergence.

Pre-clinical evaluation of implicit deformable models for three-dimensional segmentation of brain aneurysms from CTA images

Knowledge of brain aneurysm dimensions is essential during the planning stage of minimally invasive surgical interventions using Guglielmi Detachable Coils (GDC). These parameters are obtained in clinical routine using 2D Maximum Intensity Projection images from Computed Tomographic Angiography (CTA). Automated quantification of the three dimensional structure of aneurysms directly from the 3D data set may be used to provide accurate and objective measurements of the clinically relevant parameters. The properties of Implicit Deformable Models make them suitable to accurately extract the three dimensional structure of the aneurysm and its connected vessels. We have devised a two-stage segmentation algorithm for this purpose. In the first stage, a rough segmentation is obtained by means of the Fast Marching Method combining a speed function based on a vessel enhancement filtering and a freezing algorithm. In the second stage, this rough segmentation provides the initialization for Geodesic Active Contours driven by region-based information. The latter problem is solved using the Level Set algorithm. This work presents a comparative study between a clinical and a computerized protocol to derive three geometrical descriptors of aneurysm morphology that are standard in assessing the viability of surgical treatment with GDCs. The study was performed on a data base of 40 brain aneurysms. The manual measurements were made by two neuroradiologists in two independent sessions. Both inter- and intra-observer variability and comparison with the automated method are presented. According to these results, Implicit Deformable Models are a suitable technique for this application.

Geodesic Active Regions Using Non-parametric Statistical Regional Description and Their Application to Aneurysm Segmentation from CTA

The inclusion of statistical region-based information in the Geodesic Active Contours introduces robustness in the segmentation of images with weak or inhomogeneous gradient at edges. The estimation of the Probability Density Function (PDF) for each region, involves the definition of the features that characterize the image inside the different regions. PDFs are usually modelled from the intensity values using Gaus- sian Mixture Models. However, we argue that the use of up to second order information could provide better discrimination of the different regions than based on intensity only, as the local intensity manifold is more accurately represented. In this paper, we present a non parametric estimation technique for the PDFs of the underlying tissues present in medical images with application for the segmentation of brain aneurysms in CTA data with the Geodesic Active Regions model.

Brain aneurysm segmentation in CTA and 3DRA using geodesic active regions based on second order prototype features and nonparametric density estimation

Coupling the geodesic active contours model with statistical information based on regions introduces robustness in the segmentation of images with weak or inhomogeneous gradients. In the estimation of the probability density function for each region take part the definition of the features that describe the image inside the different regions and the method of density estimation itself. A Gaussian Mixture Model is frequently proposed for density estimation. This approach is based on the assumption that the intensity distribution of the image is the most discriminant feature in a region. However, the use of second order features provides a better discrimination of the different regions, as these features represent more accurately the local properties of the image manifold. Due to the high dimensionality of the problem, the use of non parametric density estimation methods becomes necessary. In this article, we present a novel method of introducing the second order information of an image for non parametric estimation of the probability density functions of the different tissues that are present in medical images. The novelty of the method stems on the use of the response of the image under an orthogonal harmonic operator set projected onto a prototype space for feature generation. The technique described here is applied to the segmentation of brain aneurysms in Computed Tomography Angiography (CTA) and 3D Rotational Angiography (3DRA) showing a qualitative improvement from the Gaussian Mixture Model approach.