Calculation of the magnetization distribution for fluid flow in curved vessels

CMRsim-A python package for cardiovascular MR simulations incorporating complex motion and flow

PURPOSE

To present an open-source MR simulation framework that facilitates the incorporation of complex motion and flow for studying cardiovascular MR (CMR) acquisition and reconstruction.

METHODS

CMRsim is a Python package that allows simulation of CMR images using dynamic digital phantoms with complex motion as input. Two simulation paradigms are available, namely, numerical and analytical solutions to the Bloch equations, using a common motion representation. Competitive simulation speeds are achieved using TensorFlow for GPU acceleration. To demonstrate the capability of the package, one introductory and two advanced CMR simulation experiments are presented. The latter showcase phase-contrast imaging of turbulent flow downstream of a stenotic section and cardiac diffusion tensor imaging on a contracting left ventricle. Additionally, extensive documentation and example resources are provided.

RESULTS

The Bloch simulation with turbulent flow using approximately 1.5 million particles and a sequence duration of 710 ms for each of the seven different velocity encodings took a total of 29 min on a NVIDIA Titan RTX GPU. The results show characteristic phase contrast and magnitude modulation present in real data. The analytical simulation of cardiac diffusion tensor imaging with bulk-motion phase sensitivity took approximately 10 s per diffusion-weighted image, including preparation and loading steps. The results exhibit the expected alteration of diffusion metrics due to strain.

CONCLUSION

CMRsim is the first simulation framework that allows one to feasibly incorporate complex motion, including turbulent flow, to systematically study advanced CMR acquisition and reconstruction approaches. The open-source package features modularity and transparency, facilitating maintainability and extensibility in support of reproducible research.

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.

Evaluation of the impact of carotid artery bifurcation angle on hemodynamics by use of computational fluid dynamics: a simulation and volunteer study

In this study, we evaluated the hemodynamics of carotid artery bifurcation with various geometries using simulated and volunteer models based on magnetic resonance imaging (MRI). Computational fluid dynamics (CFD) was analyzed by use of OpenFOAM. The velocity distribution, streamline, and wall shear stress (WSS) were evaluated in a simulated model with known bifurcation angles (30°, 40°, 50°, 60°, derived from patients' data) and in three-dimensional (3D) healthy volunteer models. Separated flow was observed at the outer side of the bifurcation, and large bifurcation models represented upstream transfer of the point. Local WSS values at the outer bifurcation [both simulated (<30 Pa) and volunteer (<50 Pa) models] were lower than those in the inner region (>100 Pa). The bifurcation angle had a significant negative correlation with the WSS value (p<0.05). The results of this study show that the carotid artery bifurcation angle is related to the WSS value. This suggests that hemodynamic stress can be estimated based on the carotid artery geometry. The construction of a clinical database for estimation of developing atherosclerosis is warranted.

Artefacts at a glance: differentiating features of artefactual stenosis from true stenosis at the genu of the petrous internal carotid artery on TOF MRA

AIM

To investigate the distinguishing features of artefactual stenosis from true stenosis at the genu of the petrous internal carotid artery (ICA) on time of flight (TOF) magnetic resonance angiography (MRA).

MATERIALS AND METHODS

Both TOF MRA and digital subtraction angiography (DSA) were performed in 65 patients with 74 vessels who demonstrated artefactual stenosis in 43 patients with 50 vessels and true stenosis in 22 patients with 24 vessels. The following findings of the signal loss were compared between the two groups: (1) margin, (2) darkness, (3) the presence of bilaterality, (4) the presence of tandem arterial stenosis, (5) the location of the epicentre, and (6) length.

RESULTS

In five out of the six evaluated items, statistically significant differences were present between the two groups (p<0.00 in all five items). Artefactual stenosis more frequently showed signal loss with ill-defined margins (47/50), less darkness compared to the background darkness (46/50), the absence of tandem arterial stenosis (35/50), epicentre at the genu (34/50), and shorter length (2.57 ± 0.68 mm). No significant difference was noted in the presence of bilaterality of signal loss between the two groups (p=0.706).

CONCLUSION

Several MRA features can be useful for suggesting artefactual stenosis rather than true stenosis at the genu of the petrous ICA on TOF MRA.

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.

High wall shear stress and spatial gradients in vascular pathology: a review

Cardiovascular pathologies such as intracranial aneurysms (IAs) and atherosclerosis preferentially localize to bifurcations and curvatures where hemodynamics are complex. While extensive knowledge about low wall shear stress (WSS) has been generated in the past, due to its strong relevance to atherogenesis, high WSS (typically >3 Pa) has emerged as a key regulator of vascular biology and pathology as well, receiving renewed interests. As reviewed here, chronic high WSS not only stimulates adaptive outward remodeling, but also contributes to saccular IA formation (at bifurcation apices or outer curves) and atherosclerotic plaque destabilization (in stenosed vessels). Recent advances in understanding IA pathogenesis have shed new light on the role of high WSS in pathological vascular remodeling. In complex geometries, high WSS can couple with significant spatial WSS gradient (WSSG). A combination of high WSS and positive WSSG has been shown to trigger aneurysm initiation. Since endothelial cells (ECs) are sensors of WSS, we have begun to elucidate EC responses to high WSS alone and in combination with WSSG. Understanding such responses will provide insight into not only aneurysm formation, but also plaque destabilization and other vascular pathologies and potentially lead to improved strategies for disease management and novel targets for pharmacological intervention.

Endothelial cells express a unique transcriptional profile under very high wall shear stress known to induce expansive arterial remodeling

Chronic high flow can induce arterial remodeling, and this effect is mediated by endothelial cells (ECs) responding to wall shear stress (WSS). To assess how WSS above physiological normal levels affects ECs, we used DNA microarrays to profile EC gene expression under various flow conditions. Cultured bovine aortic ECs were exposed to no-flow (0 Pa), normal WSS (2 Pa), and very high WSS (10 Pa) for 24 h. Very high WSS induced a distinct expression profile compared with both no-flow and normal WSS. Gene ontology and biological pathway analysis revealed that high WSS modulated gene expression in ways that promote an anti-coagulant, anti-inflammatory, proliferative, and promatrix remodeling phenotype. A subset of characteristic genes was validated using quantitative polymerase chain reaction: very high WSS upregulated ADAMTS1 (a disintegrin and metalloproteinase with thrombospondin motif-1), PLAU (urokinase plasminogen activator), PLAT (tissue plasminogen activator), and TIMP3, all of which are involved in extracellular matrix processing, with PLAT and PLAU also contributing to fibrinolysis. Downregulated genes included CXCL5 and IL-8 and the adhesive glycoprotein THBS1 (thrombospondin-1). Expressions of ADAMTS1 and uPA proteins were assessed by immunhistochemistry in rabbit basilar arteries experiencing increased flow after bilateral carotid artery ligation. Both proteins were significantly increased when WSS was elevated compared with sham control animals. Our results indicate that very high WSS elicits a unique transcriptional profile in ECs that favors particular cell functions and pathways that are important in vessel homeostasis under increased flow. In addition, we identify specific molecular targets that are likely to contribute to adaptive remodeling under elevated flow conditions.

3D network model of NO transport in tissue

We developed a mathematical model to simulate shear stress-dependent nitric oxide (NO) production and transport in a 3D microcirculatory network based on published data. The model consists of a 100 μm × 500 μm × 75 μm rectangular volume of tissue containing two arteriole-branching trees, and nine capillaries surrounding the vessels. Computed distributions for NO in blood, vascular walls, and surrounding tissue were affected by hematocrit (Hct) and wall shear stress (WSS) in the network. The model demonstrates that variations in the red blood cell (RBC) distribution and WSS in a branching network can have differential effects on computed NO concentrations due to NO consumption by RBCs and WSS-dependent changes in NO production. The model predicts heterogeneous distributions of WSS in the network. Vessel branches with unequal blood flow rates gave rise to a range of WSS values and therefore NO production rates. Despite increased NO production in a branch with higher blood flow and WSS, vascular wall NO was predicted to be lower due to greater NO consumption in blood, since the microvascular Hct increased with redistribution of RBCs at the vessel bifurcation. Within other regions, low WSS was combined with decreased NO consumption to enhance the NO concentration.

High fluid shear stress and spatial shear stress gradients affect endothelial proliferation, survival, and alignment

Cerebral aneurysms develop near bifurcation apices, where complex hemodynamics occur: Flow impinges on the apex, accelerates into branches, then slows again distally, creating high wall shear stress (WSS) and positive and negative spatial gradients in WSS (WSSG). Endothelial responses to these kinds of high WSS hemodynamic environments are not well characterized. We examined endothelial cells (ECs) under elevated WSS and positive and negative WSSG using a flow chamber with constant-height channels to create regions of uniform WSS and converging and diverging channels to create positive and negative WSSG, respectively. Cultured bovine aortic ECs were subjected to 3.5 and 28.4 Pa with and without WSSG for 24 and 36 h. High WSS inhibited EC alignment to flow, increased EC proliferation assessed by bromodeoxyuridine incorporation, and increased apoptosis determined by terminal deoxynucleotidyl transferase dUTP-mediated nick-end labeling. These responses to high WSS were either accentuated or ameliorated by WSSG: Positive WSSG (+980 Pa/m) inhibited alignment and stimulated proliferation and apoptosis, whereas negative WSSG (-1120 Pa/m) promoted alignment and suppressed proliferation and apoptosis. These results demonstrate that ECs discriminate between positive and negative WSSG under high WSS conditions. EC responses to positive WSSG may contribute to pathogenic remodeling that occurs at bifurcations preceding aneurysm formation.

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.

Analysis of coronary bifurcations by intravascular ultrasound and virtual histology

BACKGROUND

Regional differences in shear stress have been identified as reason for early plaque formation in vessel bifurcations. We aimed to investigate regional plaque morphology and composition using intravascular ultrasound (IVUS) and virtual histology (IVUS-VH) in coronary artery bifurcations.

METHODS

We performed IVUS and IVUS-VH studies at coronary bifurcations to analyze segmental plaque burden and composition of different segments in relation to their orientation to the bifurcation.

RESULTS

A total of 236 patients with a mean age of 59±11 years (69% male) were analyzed. Plaque burden was higher at the contralateral vessel wall facing the bifurcation compared to the ipsilateral vessel wall and this difference was true for proximal and distal segments (proximal: 37±12% and 45±15% for segments at the ipsilateral and contralateral vessel wall, respectively, p<0.001; distal: 37±10% and 47±15% for segments at the ipsilateral and contralateral vessel wall, respectively, p<0.001). In addition, these segments exhibited a higher proportion of dense calcium and a lower proportion of fibrous tissue and fibro fatty tissue.

CONCLUSIONS

Segments on the contralateral wall of the bifurcation which have previously been identified as regions with low shear stress not only exhibited a higher plaque burden, but also a higher degree of calcification.

Computational study of pulsatile blood flow in prototype vessel geometries of coronary segments

The spatial and temporal distributions of wall shear stress (WSS) in prototype vessel geometries of coronary segments are investigated via numerical simulation, and the potential association with vascular disease and specifically atherosclerosis and plaque rupture is discussed. In particular, simulation results of WSS spatio-temporal distributions are presented for pulsatile, non-Newtonian blood flow conditions for: (a) curved pipes with different curvatures, and (b) bifurcating pipes with different branching angles and flow division. The effects of non-Newtonian flow on WSS (compared to Newtonian flow) are found to be small at Reynolds numbers representative of blood flow in coronary arteries. Specific preferential sites of average low WSS (and likely atherogenesis) were found at the outer regions of the bifurcating branches just after the bifurcation, and at the outer-entry and inner-exit flow regions of the curved vessel segment. The drop in WSS was more dramatic at the bifurcating vessel sites (less than 5% of the pre-bifurcation value). These sites were also near rapid gradients of WSS changes in space and time - a fact that increases the risk of rupture of plaque likely to develop at these sites. The time variation of the WSS spatial distributions was very rapid around the start and end of the systolic phase of the cardiac cycle, when strong fluctuations of intravascular pressure were also observed. These rapid and strong changes of WSS and pressure coincide temporally with the greatest flexion and mechanical stresses induced in the vessel wall by myocardial motion (ventricular contraction). The combination of these factors may increase the risk of plaque rupture and thrombus formation at these sites.

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.

Clinical implications and mechanisms of plaque rupture in the acute coronary syndromes

Coronary atherosclerosis complicated by plaque rupture or disruption and thrombosis is primarily responsible for the development of acute coronary syndromes. Plaques with a large extracellular lipid-rich core, a thin fibrous cap due to reduced collagen content and smooth muscle density, and increased numbers of activated macrophages and mast cells appear to be vulnerable to rupture. Plaque disruption tends to occur at points at which the plaque surface is weakest and most vulnerable, which coincide with points at which stresses resulting from biomechanical and hemodynamic forces acting on plaques are concentrated. Reduced matrix synthesis as well as increased matrix degradation predisposes vulnerable plaques to rupture in response to extrinsic mechanical or hemodynamic stresses. Modification of endothelial dysfunction and reduction of vulnerability to plaque rupture and thrombosis may lead to plaque stabilization. These concepts have significant clinical implications that are just beginning to be explored and incorporated into clinical practice. This article reviews the mechanism of coronary atherosclerosis development and the pathophysiology of acute coronary syndromes to provide a framework for understanding how plaque passivation might be accomplished in clinical medicine.

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

Magnetic Resonance Angiography (MRA) has become a routine imaging modality for the clinical evaluation of obstructive vascular disease. However, complex circulatory flow patterns, which redistribute the Magnetic Resonance (MR) signal in a complicated way, may generate flow artifacts and impair image quality. Numerical simulation of MRAs is a useful tool to study the mechanisms of artifactual signal production. The present study proposes a new approach to perform such simulations, applicable to complex anatomically realistic vascular geometries. Both the Navier-Stokes and the Bloch equations are solved on the same mesh to obtain the distribution of modulus and phase of the magnetization. The simulated angiography is subsequently constructed by a simple geometric procedure mapping the physical plane into the MRA image plane. Steady bidimensional numerical simulations of MRAs of an anatomically realistic severely stenotic carotid artery bifurcation are presented, for both time-of-flight and contrast-enhanced imaging modalities. These simulations are validated by qualitative comparison with flow phantom experiments performed under comparable conditions.

Association between hematological parameters and high-density lipoprotein cholesterol

PURPOSE OF REVIEW

The ability of high-density lipoprotein cholesterol to reverse atherosclerosis and reduce cardiovascular disease has been shown in several randomized controlled trials. One mechanism by which high-density lipoprotein cholesterol protects the vascular system includes hemorheology, the study of blood flow.

RECENT FINDINGS

Blood viscosity, or the resistance of flow, can be altered by red blood cell aggregation, red blood cell deformability, and plasma viscosity. Elevated high-density lipoprotein cholesterol levels may improve all of these rheological mediators. An infusion of recombinant high-density lipoprotein cholesterol can immediately release nitric oxide, a potent vasodilator and responder to changes in rheology, into the arteries by activation of endothelial nitric oxide synthase. The stimulation of nitric oxide release by high-density lipoprotein cholesterol may also alter blood rheology.

SUMMARY

In this article, we will review hemorheology, particularly blood viscosity along with other hemorheological factors, and examine their association with high-density lipoprotein cholesterol.

Computational modeling of arterial biomechanics: insights into pathogenesis and treatment of vascular disease

We review how advances in computational techniques are improving our understanding of the biomechanical behavior of the healthy and diseased cardiovascular system. Numerical modeling of biomechanics is being used in a wide variety of ways, including assessment of effects of mural and hemodynamically induced stresses on atherogenesis, development of risk measures for aneurysm rupture, improvement in interpretation of medical images, and quantification of oxygen transport in diseased and healthy arteries. Although not amenable to routine clinical use, numerical modeling of cardiovascular biomechanics is a powerful research tool.

Numerical analysis of flow through a severely stenotic carotid artery bifurcation

The results of computational simulations may supplement MR and other in vivo diagnostic techniques to provide an accurate picture of the hemodynamics in particular vessels, which may help demonstrate the risks of embolism or plaque rupture posed by particular plaque deposits. In this study, a model based on an endarterectomy specimen of the plaque in a carotid bifurcation was examined. The flow conditions include steady flow at Reynolds numbers of 300, 600, and 900 as well as unsteady pulsatile flow. Both dynamic pressure and wall shear stress are very high, with shear values up to 70 N/m2, proximal to the stenosis throat in the internal carotid artery, and both vary significantly through the flow cycle. The wall shear stress gradient is also strong along the throat. Vortex shedding is observed downstream of the most severe occlusion. Two turbulence models, the Chien and Goldberg varieties of k-epsilon, are tested and evaluated for their relevance in this geometry. The Chien model better captures phenomena such as vortex shedding. The flow distal to stenosis is likely transitional, so a model that captures both laminar and turbulent behavior is needed.

Reconstruction of blood flow patterns in a human carotid bifurcation: a combined CFD and MRI study

The carotid bifurcation is a common site for clinically significant atherosclerosis, and the development of this disease may be influenced by the local hemodynamic environment. It has been shown that vessel geometry and pulsatile flow conditions are the predominant factors that determine the detailed blood flow patterns at the carotid bifurcation. This study was initiated to quantify the velocity profiles and wall shear stress (WSS) distributions in an anatomically true model of the human carotid bifurcation using data acquired from magnetic resonance (MR) imaging scans of an individual subject. A numerical simulation approach combining the image processing and computational fluid dynamics (CFD) techniques was developed. Individual vascular anatomy and pulsatile flow conditions were all incorporated into the computer model. It was found that the geometry of the carotid bifurcation was highly complex, involving helical curvature and out-of-plane branching. These geometrical features resulted in patterns of flow and wall shear stress significantly different from those found in simplified planar carotid bifurcation models. Comparisons between the predicted flow patterns and MR measurement demonstrated good quantitative agreement.

Middle cerebral artery anatomy and characteristics of embolic signals: a dual gate computer simulation study

In terms of microembolic signal (MES) detection, the anatomy of the middle cerebral artery (MCA) mainstem has only scarcely been considered. The vessel itself, however, could be at least partly responsible for the enormous variation when calculating the essential time difference (deltat) values of MES using the dual-gate technique. Therefore, we studied the time characteristics of MES in a computer simulation applying an anatomically realistic vessel and a dual-gate TCD approach. Three different MCA anatomies and two MES to blood intensities were simulated as well as two different sample volume settings. The MES length (proximal sample volume t1; distal sample volume t2) and deltat were calculated for different angles of insonation and sample volume depths. The calculations of the time characteristics of MES showed extreme variation, with only modest changes of the insonation angle (t1 4-34 ms; deltat 9-27 ms) or the sample volume depth (t1 7-27 ms; deltat 6-32 ms). The variation could be considerably reduced with modified TCD settings i.e., a shorter gate separation combined with a shorter receiver gate time in the distal sample volume (deltat with changing insonation angles 6-19 ms; deltat with changing insonation depths 13-17 ms). These results not only urge us to a cautious interpretation of the properties of single MES, but also contribute to an understanding of the marked deltat variation using the dual-gate technique.

A numerical study of magnetic resonance images of pulsatile flow in a two dimensional carotid bifurcation: a numerical study of MR images

A numerical method to simulate magnetic resonance angiographic images is proposed. The new method greatly simplifies the calculation of the average phase in a voxel, the bottleneck of previous simulations, and reduces the computation time by more than a factor of 5. Both the Navier-Stokes and the Bloch equations are solved on the same mesh to obtain the distributions of the modulus and phase of the magnetization. The data in the frequency domain are reordered according to the gating strategy to generate the final images. Pulsatile flow through a 2D normal carotid bifurcation is considered as a test case. Images for magnetic resonance angiography with an uncompensated gradient waveform, a velocity-compensated gradient waveform and an uncompensated short-TE gradient waveform are compared. Systolic gating images are shown to have degraded image quality. Images acquired with diastolic-gating have little variation in magnetization strength throughout the pulsatile cycle and provide a better representation of the vessel lumen.

Visualizing blood flow patterns using streamlines, arrows, and particle paths

A customized computer program (MRIView) is described for visualizing and quantifying complex blood flow patterns in major vessels, using nongated and cardiac-gated three-dimensional (3D) velocity data obtained with MR velocity-encoded phase pulse sequences. Streamlines, arrows, and particle paths (collectively referred to as "paths") can be computed interactively, using both forward and backward time integration of the velocity field. The program provides interactive cross-sectional and 3D perspective visualization of the paths, with quantification and statistical analysis of average speed, through-plane velocity, cross-sectional area, and flow. Normal flow patterns in the carotid artery, basilar artery tip, ascending aorta, coronary arteries, descending aorta, and renal arteries, as well as abnormal flow patterns in basilar tip aneurysms, have been investigated. The program revealed flow patterns in these regions with features that are well known from Doppler ultrasound and other features that have not been reported previously. The association between specific abnormal flow patterns and development of atherosclerosis suggests that particle paths can be used to assess risk of plaque formation and progression, as well as to evaluate flow dynamics and vascular patency before and after vascular interventions.

Intravascular contrast agent improves magnetic resonance angiography of carotid arteries in minipigs

This study was designed to optimize three-dimensional (3D) time-of-flight (TOF) magnetic resonance angiography (MRA) sequences and to determine whether contrast-enhanced MRA could improve the accuracy of lumen definition in stenosed carotid arteries of minipigs. 3D TOF MRA was acquired with use of either an intravascular (n = 13) and/or an extravascular contrast agent (n = 5) administrated at 2 to 4 weeks after balloon-induced injury to a carotid artery in 16 minipigs. Vascular contrast, defined as signal intensity differences between blood vessels and muscle normalized to the signal intensity of muscle, was compared before and after the injection of each contrast agent and between the two agents. Different vascular patencies were observed among the animals, including completely occluded vessels (n = 5), stenotic vessels (n = 3), and vessels with no visible stenosis (n = 8). Superior vascular contrast improvement was observed for small arteries and veins and for large veins with the intravascular contrast agent when compared with the extravascular contrast agent. In addition, preliminary studies in two of the animals showed a good correlation for the extent of luminal stenosis defined by digital subtraction angiography compared with MRA obtained after administration of the intravascular contrast agent (R2 = .71, with a slope of .96 +/- .04 by a linear regression analysis). We concluded that use of an intravascular contrast agent optimizes 3D TOF MRA and may improve its accuracy compared with digital subtraction angiography.

Combined analysis of spatial and velocity displacement artifacts in phase contrast measurements of complex flows

MR phase contrast (PC) velocity imaging is a promising tool for quantifying blood flow velocity in vivo. PC velocity imaging is, however, susceptible to artifacts that result from the displacement of spins during the finite duration pulse sequences. Such displacement artifacts can lead to errors in velocity measurements, especially in the presence of oblique and accelerating flows, which are common throughout the cardiovascular system. By tracking particles (representing spins) through a computed velocity field, and assuming that spatial and velocity encodings occur at discrete times during the pulse sequence, we simulate the separate and combined effects of oblique and acceleration artifacts on PC velocity images. We demonstrate, both by simulation and MR measurement, the errors associated with such artifacts in PC velocity measurements in a representative flow geometry. Using example particle trajectories, we provide a fluid dynamic basis for characteristic phase-velocity image distortions that can arise when imaging complex, physiologically relevant flows.