Numerical simulation of magnetic resonance angiographies of an anatomically realistic stenotic carotid bifurcation

An Eulerian formulation for the computational modeling of phase-contrast MRI

PURPOSE

Computational simulation of phase-contrast MRI (PC-MRI) is an attractive way to physically interpret properties and errors in MRI-reconstructed flow velocity fields. Recent studies have developed PC-MRI simulators that solve the Bloch equation, with the magnetization transport being modeled using a Lagrangian approach. Because this method expresses the magnetization as spatial distribution of particles, influences of particle densities and their spatial uniformities on numerical accuracy are well known. This study developed an alternative method for PC-MRI modeling using an Eulerian approach in which the magnetization is expressed as a spatially smooth continuous function.

METHODS

The magnetization motion was described using the Bloch equation with an advection term and computed on a fixed grid using a finite difference method, and k-space sampling was implemented using the spoiled gradient echo sequence. PC-MRI scans of a fully developed flow in straight and stenosed cylinders were acquired to provide numerical examples.

RESULTS

Reconstructed flow in a straight cylinder showed excellent agreement with input velocity profiles and mean errors were less than 0.5% of the maximum velocity. Numerical cases of flow in a stenosed cylinder successfully demonstrated the velocity profiles, with displacement artifacts being dependent on scan parameters and intravoxel dephasing due to flow disturbances. These results were in good agreement with those obtained using the Lagrangian approach with a sufficient particle density.

CONCLUSION

The feasibility of the Eulerian approach to PC-MRI modeling was successfully demonstrated.

Development and practical evaluation of a saturation effect learning simulator for inflow magnetic resonance angiography

The quality of visualization in inflow magnetic resonance angiography (MRA) depends highly on the excitation state of the longitudinal magnetization obtained using specified imaging parameters. In addition, signal intensity changes controlled by the preparation pulse-such as inversion recovery (IR) and saturation recovery (SR)-can potentially be used as quantitative physiological values. Although having practitioners understand these relationships both qualitatively and quantitatively is important, handling clinical equipment in practical learning or experiments involves limited opportunities. The simulator corresponds to a three-dimensional spoiled gradient echo sequence and allows users to freely input multiple virtual excitation effects in space and time. The purpose of this study was to quantitatively evaluate the agreement between the measured MRAs obtained in flow phantom tests and virtual MRAs simulated under similar conditions. We imaged two vascular flow phantoms on a 3.0 T MR system using three-dimensional (3D) time-of-flight (TOF) MRA and 3D inversion recovery tissue signal suppression (IR-suppression) MRA protocols. We evaluated quantitative values for consistency between the measured and virtual MRAs images with matched spatial resolution. Then we assessed the coincidence by reformatting maximum-intensity projection images with 1 mm isotropic pixels, with it ranging from 89.6 to 92.0% and 89.1 to 92.9% for TOF MRA and IR-suppression MRA, respectively. These results may be useful as a reference index for the theoretical study of MRA images by practitioners, for complementary validation by phantom testing, or for the development of MRI-related simulators.

Numerical simulation of time-resolved 3D phase-contrast magnetic resonance imaging

A numerical approach is presented to efficiently simulate time-resolved 3D phase-contrast Magnetic resonance Imaging (or 4D Flow MRI) acquisitions under realistic flow conditions. The Navier-Stokes and Bloch equations are simultaneously solved with an Eulerian-Lagrangian formalism. A semi-analytic solution for the Bloch equations as well as a periodic particle seeding strategy are developed to reduce the computational cost. The velocity reconstruction pipeline is first validated by considering a Poiseuille flow configuration. The 4D Flow MRI simulation procedure is then applied to the flow within an in vitro flow phantom typical of the cardiovascular system. The simulated MR velocity images compare favorably to both the flow computed by solving the Navier-Stokes equations and experimental 4D Flow MRI measurements. A practical application is finally presented in which the MRI simulation framework is used to identify the origins of the MRI measurement errors.

Flow MRI simulation in complex 3D geometries: Application to the cerebral venous network

PURPOSE

Develop and evaluate a complete tool to include 3D fluid flows in MRI simulation, leveraging from existing software. Simulation of MR spin flow motion is of high interest in the study of flow artifacts and angiography. However, at present, only a few simulators include this option and most are restricted to static tissue imaging.

THEORY AND METHODS

An extension of JEMRIS, one of the most advanced high performance open-source simulation platforms to date, was developed. The implementation of a Lagrangian description of the flow allows simulating any MR experiment, including both static tissues and complex flow data from computational fluid dynamics. Simulations of simple flow models are compared with real experiments on a physical flow phantom. A realistic simulation of 3D flow MRI on the cerebral venous network is also carried out.

RESULTS

Simulations and real experiments are in good agreement. The generality of the framework is illustrated in 2D and 3D with some common flow artifacts (misregistration and inflow enhancement) and with the three main angiographic techniques: phase contrast velocimetry (PC), time-of-flight, and contrast-enhanced imaging MRA.

CONCLUSION

The framework provides a versatile and reusable tool for the simulation of any MRI experiment including physiological fluids and arbitrarily complex flow motion.

Simulation of MR angiography imaging for validation of cerebral arteries segmentation algorithms

BACKGROUND AND OBJECTIVE

Accurate vessel segmentation of magnetic resonance angiography (MRA) images is essential for computer-aided diagnosis of cerebrovascular diseases such as stenosis or aneurysm. The ability of a segmentation algorithm to correctly reproduce the geometry of the arterial system should be expressed quantitatively and observer-independently to ensure objectivism of the evaluation.

METHODS

This paper introduces a methodology for validating vessel segmentation algorithms using a custom-designed MRA simulation framework. For this purpose, a realistic reference model of an intracranial arterial tree was developed based on a real Time-of-Flight (TOF) MRA data set. With this specific geometry blood flow was simulated and a series of TOF images was synthesized using various acquisition protocol parameters and signal-to-noise ratios. The synthesized arterial tree was then reconstructed using a level-set segmentation algorithm available in the Vascular Modeling Toolkit (VMTK). Moreover, to present versatile application of the proposed methodology, validation was also performed for two alternative techniques: a multi-scale vessel enhancement filter and the Chan-Vese variant of the level-set-based approach, as implemented in the Insight Segmentation and Registration Toolkit (ITK). The segmentation results were compared against the reference model.

RESULTS

The accuracy in determining the vessels centerline courses was very high for each tested segmentation algorithm (mean error rate = 5.6% if using VMTK). However, the estimated radii exhibited deviations from ground truth values with mean error rates ranging from 7% up to 79%, depending on the vessel size, image acquisition and segmentation method.

CONCLUSIONS

We demonstrated the practical application of the designed MRA simulator as a reliable tool for quantitative validation of MRA image processing algorithms that provides objective, reproducible results and is observer independent.

Impact of bifurcation dual stenting on endothelial shear stress

Despite advances in percutaneous coronary interventions and the introduction of drug eluding stents, in-stent restenosis and stent thrombosis remain a clinically significant problem for bifurcations. The aim of this study is to determine the effect of dual bifurcation stenting on hemodynamic parameters known to influence restenosis and thrombosis. We hypothesized that double stenting, especially with a longer side branch (SB) stent, likely has a negative effect on wall shear stress (WSS), WSS gradient (WSSG), and oscillatory shear index (OSI). To test this hypothesis, we developed computational models of dual stents at bifurcations and non-Newtonian blood simulations. The models were then interfaced, meshed, and solved in a validated finite-element package. Longer and shorter stents at the SB and provisional stenting were compared. It was found that stents placed in the SB at a bifurcation lowered WSS, but elevated WSSG and OSI. Dual stenting with longer SB stent had the most adverse impact on SB endothelial WSS, WSSG, and OSI, with low WSS region up to 50% more than the case with shorter SB stent. The simulations also demonstrated flow disturbances resulting from SB stent struts protruding into the main flow field near the carina, which may have implications on stent thrombosis. The simulations predict a negative hemodynamic role for SB stenting, which is exaggerated with a longer stent, consistent with clinical trial findings that dual-stenting is comparable or inferior to provisional stenting.

FABRICATION OF 3D MILI-SCALE CHANNELS FOR HEMODYNAMIC STUDIES

3D mili-scale channel representing simplified anatomical models of blood vessels were constructed in polidimethylsiloxane (PDMS). The objective was to obtain a sequential method to fabricate transparent PDMS models from a mold produced by rapid prototyping. For this purpose, two types of casting methods were compared, a known lost-wax casting method and a casting method using sucrose. The channels fabricated by both casting methods were analyzed by Optical Microscopy, Scanning Electron Microscopy (SEM), and Energy Dispersive X-ray Spectroscopy (EDS). The lost-wax method is not ideal since the channels become contaminated during the removal process. The models produced with the lost-sucrose casting method exhibit much better optical characteristics. These models are transparent with no visible contamination, since the removing process is done by dissolution at room temperature rather than melting. They allow for good optical access for flow visualization and measurement of the velocity field by micro-Particle Image Velocimetry (μPIV). The channels fabricated by the lost-sucrose casting method were shown to be suitable for future hemodynamic studies using optical techniques.

In silico modeling of magnetic resonance flow imaging in complex vascular networks

The paper presents a computational model of magnetic resonance (MR) flow imaging. The model consists of three components. The first component is used to generate complex vascular structures, while the second one provides blood flow characteristics in the generated vascular structures by the lattice Boltzmann 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 performed by an in vitro phantom. Then, the simulation possibilities of the model are shown. Flow and MR flow imaging in complex vascular structures are presented and evaluated. Finally, the computational 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 literature. Moreover, compared to previous works on flow and MR flow imaging, this approach distinguishes itself by its computational efficiency. Such a connection of anatomy, physiology and image formation in a single computer tool could provide an in silico solution to improving our understanding of the processes involved, either considered together or separately.

Computational modeling of MR flow imaging by the lattice Boltzmann method and Bloch equation

In this work, a computational model of magnetic resonance (MR) flow imaging is proposed. The first model component provides fluid dynamics maps by applying the lattice Boltzmann method. The second one uses the flow maps and couples MR imaging (MRI) modeling with a new magnetization transport algorithm based on the Eulerian coordinate approach. MRI modeling is based on the discrete time solution of the Bloch equation by analytical local magnetization transformations (exponential scaling and rotations). Model is validated by comparison of experimental and simulated MR images in two three-dimensional geometries (straight and U-bend tubes) with steady flow under comparable conditions. Two-dimensional geometries, presented in literature, were also tested. In both cases, a good agreement is observed. Quantitative analysis shows in detail the model accuracy. Computational time is noticeably lower to prior works. These results demonstrate that the discrete time solution of Bloch equation coupled with the new magnetization transport algorithm naturally incorporates flow influence in MRI modeling. As a result, in the proposed model, no additional mechanism (unlike in prior works) is needed to consider flow artifacts, which implies its easy extensibility. In combination with its low computational complexity and efficient implementation, the model could have a potential application in study of flow disturbances (in MRI) in various conditions and in different geometries.

Targeted particle tracking in computational models of human carotid bifurcations

A significant and largely unsolved problem of computational fluid dynamics (CFD) simulation of flow in anatomically relevant geometries is that very few calculated pathlines pass through regions of complex flow. This in turn limits the ability of CFD-based simulations of imaging techniques (such as MRI) to correctly predict in vivo performance. In this work, I present two methods designed to overcome this filling problem, firstly, by releasing additional particles from areas of the flow inlet that lead directly to the complex flow region ("preferential seeding") and, secondly, by tracking particles both "downstream" and "upstream" from seed points within the complex flow region itself. I use the human carotid bifurcation as an example of complex blood flow that is of great clinical interest. Both idealized and healthy volunteer geometries are investigated. With uniform seeding in the inlet plane (in the common carotid artery (CCA)) of an idealized bifurcation geometry, approximately half the particles passed through the internal carotid artery (ICA) and half through the external carotid artery. However, of those particles entering the ICA, only 16% passed directly through the carotid bulb region. Preferential seeding from selected regions of the CCA was able to increase this figure to 47%. In the second method, seeding of particles within the carotid bulb region itself led to a very high proportion (97%) of pathlines running from CCA to ICA. Seeding of particles in the bulb plane of three healthy volunteer carotid bifurcation geometries led to much better filling of the bulb regions than by particles seeded at the inlet alone. In all cases, visualization of the origin and behavior of recirculating particles led to useful insights into the complex flow patterns. Both seeding methods produced significant improvements in filling the carotid bulb region with particle tracks compared with uniform seeding at the inlet and led to an improved understanding of the complex flow patterns. The methods described may be combined and are generally applicable to CFD studies of fluid and gas flow and are, therefore, of relevance in hemodynamics, respiratory mechanics, and medical imaging science.

Synthetic dataset generation for the analysis and the evaluation of image-based hemodynamics of the human aorta

Here, we consider the issue of generating a suitable controlled environment for the evaluation of phase contrast (PC) MRI measurements. The computational framework, tailored to build synthetic datasets, is based on a two-step approach, i.e., define and implement (1) an accurate CFD model and (2) an image generator able to mime the overall outcomes of a PC MRI acquisition starting from datasets retrieved by the computational model. About 20 different datasets were built by changing relevant image parameters (pixel size, slice thickness, time frames per cardiac cycle). Focusing our attention on the thoracic aorta, synthetic images were processed in order to: (1) verify to which extent the fluid dynamics into the aortic arch is influenced by the image parameters; (2) establish the effect of spatial and temporal interpolation. Our study demonstrates that the integral scale of the aortic bulk flow could be described satisfactorily even when using images which are nowadays acquirable with MRI scanners. However, attention must be paid to near-wall velocities that can be affected by large inaccuracy. In detail, in bulk flow regions error values are well bounded (below 5% for most of the analyzed resolutions), while errors greater than 100% are systematically present at the vessel's wall. Moreover, also the data interpolation process can be responsible for large inaccuracies in new data generation, due to the inherent complexity of the flow field in some connected regions.

Impact of main branch stenting on endothelial shear stress: role of side branch diameter, angle and lesion

In-stent restenosis and stent thrombosis remain clinically significant problems for bifurcation lesions. The objective of this study is to determine the haemodynamic effect of the side branch (SB) on main branch (MB) stenting. We hypothesize that the presence of a SB has a negative effect on MB wall shear stress (WSS), wall shear stress gradient (WSSG) and oscillatory shear index (OSI); and that the bifurcation diameter ratio (SB diameter/MB diameter) and angle are important contributors. We further hypothesized that stent undersizing exaggerates the negative effects on WSS, WSSG and OSI. To test these hypotheses, we developed computational models of stents and non-Newtonian blood. The models were then interfaced, meshed and solved in a validated finite-element package. Stents at bifurcation models were created with 30° and 70° bifurcation angles and bifurcations with diameter ratios of SB/MB = 1/2 and 3/4. It was found that stents placed in the MB at a bifurcation lowered WSS dramatically, while elevating WSSG and OSI. Undersizing the stent exaggerated the decrease in WSS, increase in WSSG and OSI, and disturbed the flow between the struts and the vessel wall. Stenting the MB at bifurcations with larger SB/MB ratios or smaller SB angles (30°) resulted in lower WSS, higher WSSG and OSI. Stenosis at the SB lowered WSS and elevated WSSG and OSI. These findings highlight the effects of major biomechanical factors in MB stenting on endothelial WSS, WSSG, OSI and suggests potential mechanisms for the potentially higher adverse clinical events associated with bifurcation stenting.

Simulation of phase contrast MRI of turbulent flow

Phase contrast MRI is a powerful tool for the assessment of blood flow. However, especially in the highly complex and turbulent flow that accompanies many cardiovascular diseases, phase contrast MRI may suffer from artifacts. Simulation of phase contrast MRI of turbulent flow could increase our understanding of phase contrast MRI artifacts in turbulent flows and facilitate the development of phase contrast MRI methods for the assessment of turbulent blood flow. We present a method for the simulation of phase contrast MRI measurements of turbulent flow. The method uses an Eulerian-Lagrangian approach, in which spin particle trajectories are computed from time-resolved large eddy simulations. The Bloch equations are solved for each spin for a frame of reference moving along the spins trajectory. The method was validated by comparison with phase contrast MRI measurements of velocity and intravoxel velocity standard deviation (IVSD) on a flow phantom consisting of a straight rigid pipe with a stenosis. Turbulence related artifacts, such as signal drop and ghosting, could be recognized in the measurements as well as in the simulations. The velocity and the IVSD obtained from the magnitude of the phase contrast MRI simulations agreed well with the measurements.

Simulation study of brain blood flow regulation by intra-cortical arterioles in an anatomically accurate large human vascular network. Part II: flow variations induced by global or localized modifications of arteriolar diameters

In a companion paper (Lorthois et al., Neuroimage, in press), we perform the first simulations of blood flow in an anatomically accurate large human intra-cortical vascular network (~10000 segments), using a 1D non-linear model taking into account the complex rheological properties of blood flow in microcirculation. This model predicts blood pressure, blood flow and hematocrit distributions, volumes of functional vascular territories, regional flow at voxel and network scales, etc. Using the same approach, we study flow reorganizations induced by global arteriolar vasodilations (an isometabolic global increase in cerebral blood flow). For small to moderate global vasodilations, the relationship between changes in volume and changes in flow is in close agreement with Grubb's law, providing a quantitative tool for studying the variations of its exponent with underlying vascular architecture. A significant correlation between blood flow and vascular structure at the voxel scale, practically unchanged with respect to baseline, is demonstrated. Furthermore, the effects of localized arteriolar vasodilations, representative of a local increase in metabolic demand, are analyzed. In particular, localized vasodilations induce flow changes, including vascular steal, in the neighboring arteriolar trunks at small distances (<300 μm), while their influence in the neighboring veins is much larger (about 1 mm), which provides an estimate of the vascular point spread function. More generally, for the first time, the hemodynamic component of various functional neuroimaging techniques has been isolated from metabolic and neuronal components, and a direct relationship with several known characteristics of the BOLD signal has been demonstrated.

Computational simulations and experimental studies of 3D phase-contrast imaging of fluid flow in carotid bifurcation geometries

PURPOSE

To evaluate the use of computational fluid dynamic (CFD)-based magnetic resonance imaging (MRI) simulations to predict the image appearance and velocity measurement of fluid flow in human carotid bifurcation geometries, and to compare the results with images from experimental MRI studies.

MATERIALS AND METHODS

Simulated particle paths were calculated from available CFD datasets of normal and moderately stenosed carotid bifurcation geometries. An MRI simulator based on the spin isochromat method was used to generate images corresponding to a 3D phase-contrast sequence with velocity encoding in three orthogonal directions. The resulting images were compared qualitatively with experimental MRI scans of the corresponding physical models.

RESULTS

The simulations predicted the main features observed in experimental studies, such as the low image intensity in regions of complex flow and the position and bright appearance of the jet in the stenosed bifurcation. Simulated velocity images also agreed well with experimental results. The effects of sequence parameters such as repetition time (TR) and echo time (TE) were readily demonstrated by the simulations.

CONCLUSION

CFD-based MRI simulations can be used to predict the appearance of MRI images of regions of physiological flow, and may be useful in the development of improved pulse sequences for flow measurement.

Numerical simulations of phase contrast velocity mapping of complex flows in an anatomically realistic bypass graft geometry

Combined in vitro experiments and numerical simulations were performed to study flow artifacts in phase contrast (PC) velocity mapping of steady flow through an anatomically realistic aortocoronary bypass graft model. The geometry was obtained through imaging and computational reconstruction of a left anterior descending (LAD) coronary artery of a porcine heart. Simulated images of through-plane velocity were obtained at selected slices of the geometry. These were then compared and contrasted with velocity images of corresponding sites that were obtained from in vitro experiments. The shift and distortion of the measured velocity profile was well predicted by the simulation, while trajectories obtained from particle tracking were shown to be useful in understanding the origins of the flow artifacts that were observed.