PHANTOM project: development and validation of the pipeline from MRA acquisition to MRA simulations

ESAIM: PROCEEDINGS AND SURVEYS, December 2016, Vol. 55, p. 1-22 Emmanuel FRÉNOD, Emmanuel MAITRE, Antoine ROUSSEAU, Stéphanie SALMON and Marcela SZOPOS Editors PHANTOM PROJECT: DEVELOPMENT AND VALIDATION OF THE PIPELINE FROM MRA ACQUISITION TO MRA SIMULATIONS Alexandre Ancel 1 , Alexandre Fortin 2 , Simon Garnotel 3 , Olivia Miraucourt 2 and Ranine Tarabay 1 Abstract. The aim of this project is to validate the Vivabrain pipeline with a physical phantom from real MRI acquisition to MRI simulations through image segmentation and computational fluid dynamics (CFD) simulations. For that purpose, we set up three comparison benchmarks. The first benchmark compares dimensions of the reconstructed geometry from real MRI acquisition to the physical phantom dimensions. The second aims to validate the CFD simulations by comparing the outputs of two simulations, one carried out using Feel++ and the other using FreeFem++. The CFD outputs are also compared to MRI flow measurement data. The goal of the last comparison benchmark is to compare the MRI simulations outputs to the numerical fluid simulations. Introduction In the last 20 years, progress in medical imaging has led to the development of modalities devoted to visualizing vascular structures. These angiography images progressively proved their usefulness in various clinical applications, in particular for cerebrovascular issues. This project is within the context of the ANR project Vivabrain [2]. The goal of this project is to develop a pipeline for the generation of virtual Magnetic Resonance Angiography (MRA) of the human brain, associated to their anatomical (3D) and hemodynamic (3D+t) models (providing a ground-truth). The interdisciplinary program follows four steps, see Fig. 1. We first start from real MRA data from which we extract the vascular volumes. We then generate the 3D vascular mesh (see [12] for more details). We perform 3D+t simulations of blood flow in the complex (arterial and venous) mesh. Finally, we run the simulations of MR acquisition of angiography data from these 3D+t models. AngioTK [1] is a software framework developed in this context, using open source software. This framework takes MRI data as input and produces virtual angiographies as output. As show in Fig. 1, AngioTK proceeds in several steps: (1) Filtering: Filter the initial MRI data, to ease the extraction of arterial/venous data; (2) Segmentation: Separate the veins/arteries from the background; (3) Mesh processing: Process the segmented data to prepare it for numerical simulations. This task involves several subtasks using centerlines notably; (4) Numerical simulations: simulations of blood flow in the processed mesh (Feel++/FreeFem++); (5) Particles tracing: Generates particles for virtual angiographies; (6) Virtual angiography: Uses JEMRIS to simulate virtual angiographies. 1 University of Strasbourg, IRMA / UMR 7501, Strasbourg, France 2 University of Reims Champagne-Ardenne, LMR, Reims, France 3 University of Picardie Jules Verne, BioFlowImage Laboratory, Amiens, France c EDP Sciences, SMAI 2017 Article published online by EDP Sciences and available at http://www.esaim-proc.org or http://dx.doi.org/10.1051/proc/201655001 2 ESAIM: PROCEEDINGS AND SURVEYS MRA Medical teams (5) Particles tracing and (6) Virtual images simulation (1) Filtering and (2) Segmentation Physics teams Computer science teams Blood flow simulation Mathematics teams (4) (3) Figure 1. The Vivabrain project task loop. In this paper, our purpose is to evaluate the accuracy of the image segmentation, the (3D+t) blood flow simulations and the MRI simulations. To this end, we started from a physical phantom, see Fig. 2, so that we have an exact description of its geometry that can be used to evaluate the error made when extracting the 3D volume from the MRI segmentation. For the computational fluid dynamic validation, we have chosen to run simulations using two finite elements libraries, Feel++ [13] and FreeFem++ [10]. A first level of validation of the computational fluid dynamics (CFD) simulations is to compare the numerical outputs obtained by using Feel++ and FreeFem++ libraries, running equivalent simulations on the same mesh. The second level of comparison is to compare the Feel++ and FreeFem++ numerical output data to the experimental MRI measurements. Lastly, the validation of the MRI simulations will be performed by comparing their outputs to the MRI acquisition and to the exact geometry dimensions. The first part of this paper is dedicated to the description of the image segmentation, the numerical model and methods for the simulations of blood flow and MRI simulations. In the second part, we describe the benchmark setup used for the previously mentioned comparisons. The third part of this paper is dedicated to the image segmentation evaluation. Finally, we present the blood flow and MRI simulations results on the phantom. In particular, we run a cross-validation between the Feel++ and FreeFem++ libraries to estimate the precision of the step of blood flow simulations in the phantom and the complex cerebral venous network, which is studied in the Vivabrain project. 1. Numerical methods 1.1. Image segmentation In the first part of the pipeline, we need to extract the vascular volumes from the MRA images. Here, to segment the phantom, we use an active contour model called “snake” whose principle is to evolve a curve to detect the objects boundaries in a given image. Let Ω be a bounded open set of R2 , with ∂Ω its boundary. Let I : Ω̄ → R2 be a given image of bounded variation and C(s) : [0, 1] → R2 be a parameterized curve, at least of class C 2 . The classical snake model consists of minimizing the energy functional J1 (C) given by: Z 1 J1 (C) = α 0 |C 0 (s)|2 ds + β Z 1 0 |C 00 (s)|ds − λ Z 1 0 |∇I(C(s))|2 ds (1) ESAIM: PROCEEDINGS AND SURVEYS 3 Figure 2. The physical phantom. where α, β and λ are positive parameters. The first two terms control the smoothness of the contour (the internal energy), while the third term attracts the contour towards the object (the external energy). The snake minimizes the energy J1 (C) by trying to locate the curve at the points of maxima |∇I(C(s))|, acting as an edge-detector. In general, −|∇I| can be replaced by g(|∇I|) where g is a positive and decreasing function such 1 as limx→∞ g(x) = 0 (e.g. g(x) = 1+|x| or g(x) = exp(−x)). ITK-SNAP 1 implements the 3D geodesic active contour method developed by Caselles et al. [7], which allows topological changes of the curve, contrary to the classical snake. The new energy J2 (C) to be minimized is given by: Z 1 J2 (C) = 2 0 |C 0 (s)| · g(|∇I(C(s))|)ds (2) This is a problem of geodesic computation in a Riemannian space, according to a metric induced by the image I. This minimization problem is solved by a gradient descent which follows an evolution equation and the curve changes over time as it can be seen in Fig. 3. Figure 3. Evolution of the snake on (...truncated)