IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 33, NO. 11, NOVEMBER 2014 2191 In Silico Modeling of Magnetic Resonance Flow Imaging in Complex Vascular Networks Krzysztof Jurczuk*, Marek Kretowski, Pierre-Antoine Eliat, Herve Saint-Jalmes, and Johanne Bezy-Wendling Abstract—The paper presents a computational model of mag- netic resonance (MR) flow imaging. The model consists of three components. The first component is used to generate complex vas- cular structures, while the second one provides blood flow charac- teristics in the generated vascular structures by the lattice Boltz- mann method. The third component makes use of the generated vascular structures and flow characteristics to simulate MR flow imaging. To meet computational demands, parallel algorithms are applied in all the components. The proposed approach is verified in three stages. In the first stage, experimental validation is per- formed by an in vitro phantom. Then, the simulation possibilities of the model are shown. Flow and MR flow imaging in complex vas- cular structures are presented and evaluated. Finally, the computa- tional performance is tested. Results show that the model is able to reproduce flow behavior in large vascular networks in a relatively short time. Moreover, simulated MR flow images are in accordance with the theoretical considerations and experimental images. The proposed approach is the first such an integrative solution in liter- ature. Moreover, compared to previous works on flow and MR flow imaging, this approach distinguishes itself by its computational ef- ficiency. Such a connection of anatomy, physiology and image for- mation in a single computer tool could provide an in silico solution to improving our understanding of the processes involved, either considered together or separately. Index Terms—Computational fluid dynamics (CFD), computa- tional modeling, magnetic resonance imaging (MRI), parallel com- puting, vascular network. I. INTRODUCTION C OMPUTATIONAL models play a very important role in science and industry. In the medical field, they are used to reproduce biological systems and equipment by using and pro- Manuscript received May 10, 2014; accepted June 14, 2014. Date of publi- cation July 09, 2014; date of current version October 28, 2014. This work was supported in part by Polonium 2012–2013 (French-Polish cooperation program) under the project “MRI analysis and modeling for tissue characterization” and in part by Bialystok University of Technologyunder Grant S/WI/2/2013 and Grant W/WI/2/2014. Asterisk indicates corresponding author. *K. Jurczuk is with the Faculty of Computer Science, Bialystok University of Technology, 15-351 Bialystok, Poland (e-mail: k.jurczuk@pb.edu.pl). M. Kretowski is with the Faculty of Computer Science, Bialystok University of Technology, 15-351 Bialystok, Poland. P. A. Eliat is with Universite de Rennes 1, PRISM, F-35000 Rennes, France, and with CNRS, UMS 3480, F-35000 Rennes, France, and also with INSERM, UMS 018, F-35000 Rennes, France. H. Saint-Jalmes is with INSERM, U1099, F-35000 Rennes, France, and with Universite de Rennes 1, LTSI, F-35000 Rennes, France, and is also with, Centre Eugene Marquis, F-35000 Rennes, France. J. Bezy-Wendling is with INSERM, U1099, F-35000 Rennes, France, and with Universite de Rennes 1, LTSI, F-35000 Rennes, France. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMI.2014.2336756 gramming mathematical formulas that describe physical pro- cesses usually in a simplified manner [1]. This artificial repre- sentation of reality allows us to perform various experiments in silico without disturbing the actual system. The advantage of using models in also evident when significant number of sce- narios are to be tested. Simultaneous simulations are often the only way to evaluate various combinations of parameters. In this paper, we deal with the modeling of magnetic res- onance imaging (MRI) of vascular structures. Such imaging, called in medicine magnetic resonance angiography (MRA) [2], is influenced not only by the standard contrast parameters of tissues (i.e., relaxation times and proton density) but also by blood behavior, e.g., flow direction, velocity and patterns. In one respect, pathology detection and characterization can be im- proved by using the intrinsic flow sensitivity of MRI. For ex- ample, flow-related signal diminution can be identified in zones of abnormal vessel widening (e.g., aneurysm [4]) or narrowing (e.g., stenosis [5]). Such vessel perturbations can lead to many serious consequences, such as cerebral hemorrhage [6], liver is- chemia with hepatic insufficiency [7], or thromboembolic pul- monary embolism [8]. Another example is the use of contrast agents transported by blood to enhance the MR signal in hyper- vascularized areas of tumoral lesions (contrast-enhanced MRA) [3]. In other respects, flow during MRI acquisition can give rise to various image artifacts (as other movements) [9]–[12]. These flow-related artifacts appear in the regions with complex vas- cular structures as well as simple straight vessels. They lead to additional difficulties in image analysis which can lead to image misinterpretation and inappropriate patient treatment. Hence, the understanding of MR flow image formation is of importance, due to clinical assessment of the disease as well as problems with artifacts. The literature includes many studies, both exper- imental and numerical, to predict the influence of flow on MRI, e.g., [11], [13]–[18] to name a few. MR flow imaging is a complicated process that involves many factors linked to anatomy, physiology, and imaging modalities. MRI sequence events (e.g., excitation, spatial encoding, etc.) are located in time over ranges usually from a few milliseconds to a few seconds. Due to the flow, magnetized fluid particles are transported during and between those MRI events and are thus subjected to constantly changing magnetic conditions [9]. Therefore, fluids in images can be visible in a totally unpredictable way. Evidently, this visibility depends on the flow pattern (e.g., turbulent, steady) and the flow charac- teristics, such as velocity and direction. In turn, the spatial and temporal flow behavior results from the topology, geometry, and physiology of the vascular structures. Even small changes 0278-0062 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.