Assessing the accuracy of two-dimensional phase-contrast MRI measurements of complex unsteady flows

Use of real-time phase-contrast MRI to quantify the effect of spontaneous breathing on the cerebral arteries

Quantification of the effect of breathing on the cerebral circulation provides a better mechanistic understanding of the brain's circulatory system and is important in the early diagnosis of certain neurological diseases. However, conventional cine phase-contrast (CINE-PC) MRI cannot be used in this field of study because it only provides an average cardiac cycle flow curve reconstructed from multiple cardiac cycles. Unlike CINE-PC, phase-contrast echo-planar imaging (EPI-PC) can be used to quantify the blood flow rate in "real-time" and thus assess the effect of breathing on blood flow. Here, we first used post-processing software (developed in-house) to determine the feasibility of quantifying cerebral arterial blood flow with EPI-PC (relative to CINE-PC) in 16 participants. In a second step, we developed a new time-domain method for quantifying the intensity and the phase shift of the effects of breathing on the mean flow rate, stroke volume, cardiac period and amplitude of cerebral blood flow (in 10 participants). Our results showed that EPI-PC can quantify cerebral arterial blood flow rate with much the same degree of accuracy as CINE-PC but is more strongly influenced by differences in magnetic susceptibility. We found that breathing affected the mean flow rate, stroke volume and cardiac period of cerebral arterial blood flow.

Inter- and Intra-Rater Reliability of Individual Cerebral Blood Flow Measured by Quantitative Vessel-Flow Phase-Contrast MRI

Vessel flow quantification by two-dimensional (2D) phase-contrast magnetic resonance imaging (PC-MRI) using a three-dimensional (3D) magnetic resonance angiography (MRA) model to measure cerebral blood flow has unclear analytical reliability. The present study aimed to determine the inter- and intra-rater reliability of quantitative vessel-flow PC-MRI and potential factors influencing its consistency. We prospectively recruited 30 Asian participants (aged 20-90 years; 16 women; 22 healthy and 8 stroke patients) for performing 1.5-T MR equipped with a head coil. Each participant was first scanned for time-of-flight magnetic resonance angiography (TOF-MRA) images for localization of intracranial arteries. The 2D PC-MRI for each cerebral artery (total 13 arteries in fixed order) was performed twice by two well-trained operators in optimal position. Using the same 3D MRA as a map and facilitated with the non-invasive optimal vessel analysis (NOVA) system, each scan was taken on a plane perpendicular to the target artery. Two consecutive full 13-artery scans were performed at least 15 min apart after participants were removed from the scanner table and then repositioned. A total of four PC flow images obtained from each target artery were transmitted to a workstation facilitated with the NOVA system. Flow data were calculated semi-automatically by the NOVA system after a few simple steps. Two-way mixed-effect models and standard errors of measurements were used. In 13 cerebral arteries, repeatability, using the intra-rater estimate expressed as the average-measures intraclass correlation coefficient, ranged from 0.641 to 0.954, and reproducibility, using the inter-rater estimate, ranged from 0.672 to 0.977. Except in the middle cerebral artery and the distal segment of the anterior cerebral artery, repeatability and reproducibility were excellent (intraclass correlation coefficient exceeded 0.8). The use of quantitative vessel-flow PC-MRI is a precise means to measure blood flow in most target cerebral arteries. This was evidenced by inter-rater and intra-rater correlations that were good/excellent, indicating good reproducibility and repeatability.

Comparison of hemodialysis arteriovenous fistula blood flow rates measured by Doppler ultrasound and phase-contrast magnetic resonance imaging

OBJECTIVE

The objective of this study was to compare blood flow rates measured by Doppler ultrasound (DUS) and phase-contrast magnetic resonance imaging (MRI) in patients having a hemodialysis arteriovenous fistula (AVF) and to identify scenarios in which there was significant discordance between these two approaches.

METHODS

Blood flow rates in the proximal artery (PA) and draining vein (DV) of newly created upper extremity AVFs were measured and compared using DUS and phase-contrast MRI at 1 day, 6 weeks, and 6 months postoperatively.

RESULTS

Blood flow rates in the PA measured by DUS (1155 ± 907 mL/min, mean ± standard deviation) and by MRI (1170 ± 657 mL/min) were not statistically different (P = .812) based on 78 data pairs from 49 patients. DV DUS flow (1277 ± 995 mL/min) and MRI flow (1130 ± 655 mL/min) were also not statistically different (P = .071) based on 64 data pairs. In both PA and DV, the two methods substantially agreed with each other (Cohen κ: PA, 0.66; DV, 0.67) when flow rates were put into four clinically relevant categories (<300, 300-599, 600-1499, and ≥1500 mL/min). The Bland-Altman analyses of DUS and MRI flow identified six and four outliers for PA and DV, respectively. Seven outliers had higher DUS than MRI flow, with all DUS scan sites having a large lumen or significant local curvature; the other three had lower DUS flow, partly due to an underestimation of lumen diameter by DUS.

CONCLUSIONS

DUS and MRI flow rates are generally comparable in both PA and DV. When DUS is used for flow measurements, careful attention to accurate lumen diameter measurements is needed and scan sites with marked curvature should be avoided. Our result may improve the accuracy of DUS-measured AVF blood flow rate.

Magnetic particle imaging for in vivo blood flow velocity measurements in mice

Magnetic particle imaging (MPI) is a new imaging technology. It is a potential candidate to be used for angiographic purposes, to study perfusion and cell migration. The aim of this work was to measure velocities of the flowing blood in the inferior vena cava of mice, using MPI, and to evaluate it in comparison with magnetic resonance imaging (MRI). A phantom mimicking the flow within the inferior vena cava with velocities of up to 21 cm s^-1 was used for the evaluation of the applied analysis techniques. Time-density and distance-density analyses for bolus tracking were performed to calculate flow velocities. These findings were compared with the calibrated velocities set by a flow pump, and it can be concluded that velocities of up to 21 cm s^-1 can be measured by MPI. A time-density analysis using an arrival time estimation algorithm showed the best agreement with the preset velocities. In vivo measurements were performed in healthy FVB mice (n  =  10). MRI experiments were performed using phase contrast (PC) for velocity mapping. For MPI measurements, a standardized injection of a superparamagnetic iron oxide tracer was applied. In vivo MPI data were evaluated by a time-density analysis and compared to PC MRI. A Bland-Altman analysis revealed good agreement between the in vivo velocities acquired by MRI of 4.0  ±  1.5 cm s^-1 and those measured by MPI of 4.8  ±  1.1 cm s^-1. Magnetic particle imaging is a new tool with which to measure and quantify flow velocities. It is fast, radiation-free, and produces 3D images. It therefore offers the potential for vascular imaging.

A Method for In Vitro TCPC Compliance Verification

The Fontan procedure is a common palliative intervention for sufferers of single ventricle congenital heart defects that results in an anastomosis of the venous return to the pulmonary arteries called the total cavopulmonary connection (TCPC). Local TCPC and global Fontan circulation hemodynamics are studied with in vitro circulatory models because of hemodynamic ties to Fontan patient long-term complications. The majority of in vitro studies, to date, employ a rigid TCPC model. Recently, a few studies have incorporated flexible TCPC models, but provide no justification for the model material properties. The method set forth in this study successfully utilizes patient-specific flow and pressure data from phase contrast magnetic resonance images (PCMRI) (n = 1) and retrospective pulse-pressure data from an age-matched patient cohort (n = 10) to verify the compliance of an in vitro TCPC model. These data were analyzed, and the target compliance was determined as 1.36 ± 0.78 mL/mm Hg. A method of in vitro compliance testing and computational simulations was employed to determine the in vitro flexible TCPC model material properties and then use those material properties to estimate the wall thickness necessary to match the patient-specific target compliance. The resulting in vitro TCPC model compliance was 1.37 ± 0.1 mL/mm Hg—a value within 1% of the patient-specific compliance. The presented method is useful to verify in vitro model accuracy of patient-specific TCPC compliance and thus improve patient-specific hemodynamic modeling.

Computational fluid dynamics simulations of blood flow regularized by 3D phase contrast MRI

Background

Phase contrast magnetic resonance imaging (PC-MRI) is used clinically for quantitative assessment of cardiovascular flow and function, as it is capable of providing directly-measured 3D velocity maps. Alternatively, vascular flow can be estimated from model-based computation fluid dynamics (CFD) calculations. CFD provides arbitrarily high resolution, but its accuracy hinges on model assumptions, while velocity fields measured with PC-MRI generally do not satisfy the equations of fluid dynamics, provide limited resolution, and suffer from partial volume effects. The purpose of this study is to develop a proof-of-concept numerical procedure for constructing a simulated flow field that is influenced by both direct PC-MRI measurements and a fluid physics model, thereby taking advantage of both the accuracy of PC-MRI and the high spatial resolution of CFD. The use of the proposed approach in regularizing 3D flow fields is evaluated.

Methods

The proposed algorithm incorporates both a Newtonian fluid physics model and a linear PC-MRI signal model. The model equations are solved numerically using a modified CFD algorithm. The numerical solution corresponds to the optimal solution of a generalized Tikhonov regularization, which provides a flow field that satisfies the flow physics equations, while being close enough to the measured PC-MRI velocity profile. The feasibility of the proposed approach is demonstrated on data from the carotid bifurcation of one healthy volunteer, and also from a pulsatile carotid flow phantom.

Results

The proposed solver produces flow fields that are in better agreement with direct PC-MRI measurements than CFD alone, and converges faster, while closely satisfying the fluid dynamics equations. For the implementation that provided the best results, the signal-to-error ratio (with respect to the PC-MRI measurements) in the phantom experiment was 6.56 dB higher than that of conventional CFD; in the in vivo experiment, it was 2.15 dB higher.

Conclusions

The proposed approach allows partial or complete measurements to be incorporated into a modified CFD solver, for improving the accuracy of the resulting flow fields estimates. This can be used for reducing scan time, increasing the spatial resolution, and/or denoising the PC-MRI measurements.

Measurement with microscopic MRI and simulation of flow in different aneurysm models

PURPOSE

The impact and the development of aneurysms depend to a significant degree on the exchange of liquid between the regular vessel and the pathological extension. A better understanding of this process will lead to improved prediction capabilities. The aim of the current study was to investigate fluid-exchange in aneurysm models of different complexities by combining microscopic magnetic resonance measurements with numerical simulations. In order to evaluate the accuracy and applicability of these methods, the fluid-exchange process between the unaltered vessel lumen and the aneurysm phantoms was analyzed quantitatively using high spatial resolution.

METHODS

Magnetic resonance flow imaging was used to visualize fluid-exchange in two different models produced with a 3D printer. One model of an aneurysm was based on histological findings. The flow distribution in the different models was measured on a microscopic scale using time of flight magnetic resonance imaging. The whole experiment was simulated using fast graphics processing unit-based numerical simulations. The obtained simulation results were compared qualitatively and quantitatively with the magnetic resonance imaging measurements, taking into account flow and spin-lattice relaxation.

RESULTS

The results of both presented methods compared well for the used aneurysm models and the chosen flow distributions. The results from the fluid-exchange analysis showed comparable characteristics concerning measurement and simulation. Similar symmetry behavior was observed. Based on these results, the amount of fluid-exchange was calculated. Depending on the geometry of the models, 7% to 45% of the liquid was exchanged per second.

CONCLUSIONS

The result of the numerical simulations coincides well with the experimentally determined velocity field. The rate of fluid-exchange between vessel and aneurysm was well-predicted. Hence, the results obtained by simulation could be validated by the experiment. The observed deviations can be caused by the noise in the measurement and by the limited resolution of the simulation. The resulting differences are small enough to allow reliable predictions of the flow distribution in vessels with stents and for pulsed blood flow.

High-resolution MRI velocimetry compared with numerical simulations

Alterations of the blood flow are associated with various cardiovascular diseases. Precise knowledge of the velocity distribution is therefore important for understanding these diseases and predicting the effect of different medical intervention schemes. The goal of this work is to estimate the precision with which the velocity field can be measured and predicted by studying two simple model geometries with NMR micro imaging and computational fluid dynamics. For these initial experiments, we use water as an ideal test medium. The phantoms consist of tubes simulating a straight blood vessel and a step between two tubes of different diameters, which can be seen as a minimal model of the situation behind a stenosis. For both models, we compare the experimental data with the numerical prediction, using the experimental boundary conditions. For the simpler model, we also compare the data to the analytical solution. As an additional validation, we determine the divergence of the velocity field and verify that it vanishes within the experimental uncertainties. We discuss the resulting precision of the simulation and the outlook for extending this approach to the analysis of specific cases of arteriovascular problems.

A flow quantification method using fluid dynamics regularization and MR tagging

This paper presents a new method for improved flow analysis and quantification using MRI. The method incorporates fluid dynamics to regularize the flow quantification from tagged MR images. Specifically, the flow quantification is formulated as a minimization problem based on the following: 1) the Navier-Stokes equation governing the fluid dynamics; 2) the flow continuity equation and boundary conditions; and 3) the data consistency constraint. The minimization is carried out using a genetic algorithm. This method is tested using both computer simulations and MR flow experiments. The results are evaluated using flow vector fields from the computational fluid dynamics software package as a reference, which show that the new method can achieve more realistic and accurate flow quantifications than the conventional method.

Supraceliac and Infrarenal Aortic Flow in Patients with Abdominal Aortic Aneurysms: Mean Flows, Waveforms, and Allometric Scaling Relationships

PURPOSE

Hemodynamic forces are thought to play a critical role in abdominal aortic aneurysm (AAA) growth. In silico and in vitro simulations can be used to study these forces, but require accurate aortic geometries and boundary conditions. Many AAA simulations use patient-specific geometries, but utilize inlet boundary conditions taken from a single, unrelated, healthy young adult.

METHODS

In this study, we imaged 43 AAA patients using a 1.5 T MR scanner. A 24-frame cardiac-gated one-component phase-contrast magnetic resonance imaging sequence was used to measure volumetric flow at the supraceliac (SC) and infrarenal (IR) aorta, where flow information is typically needed for simulation. For the first 36 patients, individual waveforms were interpolated to a 12-mode Fourier curve, peak-aligned, and averaged. Allometric scaling equations were derived from log-log plots of mean SC and IR flow vs. body mass, height, body surface area (BSA), and fat-free body mass. The data from the last seven patients were used to validate our model.

RESULTS

Both the SC and IR averaged waveforms had the biphasic shapes characteristic of older adults, and mean SC and IR flows over the cardiac cycle were 51.2 ± 10.3 and 17.5 ± 5.44 mL/s, respectively. Linear regression of the log-log plots revealed that BSA was most strongly predictive of mean SC (R² = 0.29) and IR flow (R² = 0.19), with the highest combined R². When averaged, the measured and predicted waveforms for the last seven patients agreed well.

CONCLUSIONS

We present a method to estimate SC and IR mean flows and waveforms for AAA simulation.

Quantification of hemodynamic wall shear stress in patients with bicuspid aortic valve using phase-contrast MRI

Bicuspid aortic valve (BAV) is often concomitant with aortic dilatation, aneurysm, and dissection. This valve lesion and its complications may affect positional and temporal wall shear stress (WSS), a parameter reported to regulate transcriptional events in vascular remodeling. Thus, this pilot study seeks to determine if the WSS in the ascending aorta (AAo) of BAV patients differs from control patients. Phase-contrast magnetic resonance imaging (PC-MRI) was used to perform flow analysis at the level of the AAo in 15 BAV and 15 control patients. Measurement of the aorta dimensions, flow rates, regurgitant fraction (RF), flow reversal ratio (FRR), temporal and spatial WSS, and shear range indices (SRI) were performed. The BAV and control group showed a significant difference between the circumferentially averaged WSS (p=0.03) and positional WSS at systole (minimum p<0.001). Regressions found that SRI (r=0.77, p<0.001), RF (r=0.68, p<0.001), and WSS at systole (r=0.66, p<0.001) were correlated to AAo size. The spatial distribution and magnitude of systolic WSS in BAV patients (-6.7+/-4.3 dynes/cm2) differed significantly from control patients (-11.5+/-6.6 dynes/cm2, p=0.03). The SRI metric, a measure of shear symmetry along the lumen circumference, was also significantly different (p=0.006) and indicated a heterogenic pattern of dilatation in the BAV patients.

Comparison of CFD and MRI Flow and Velocities in an In Vitro Large Artery Bypass Graft Model

Bypass graft failures have been attributed to various hemodynamic factors, including flow stasis and low shear stress. Ideally, surgeries would minimize the occurrence of these detrimental flow conditions, but surgeons cannot currently assess this. Numerical simulation techniques have been proposed as one method for predicting changes in flow distributions and patterns from surgical bypass procedures, but comparisons against experimental results are needed to assess their usefulness. Previous in vitro studies compared simulated results against experimentally obtained measurements, but they focused on peripheral arteries, which have lower Reynolds numbers than those found in the larger arteries. In this study, we compared simulation results against measurements obtained using magnetic resonance imaging (MRI) techniques for a phantom model of a stenotic vessel with a bypass graft under conditions suitable for surgical planning purposes and with inlet Reynolds numbers closer to those found inthe larger arteries. Comparisons of flow rate and velocity profiles were performed at maximum and minimum flows at four locations and used simulation results that were temporally and spatially averaged, key postprocessing when comparing against phase contrast MRI measurements. The maximum error in the computed volumetric flow rates was 6% of the measured values, and excellent qualitative agreement was obtained for the through-plane velocity profiles in both magnitude and shape. The in-plane velocities also agreed reasonably well at most locations.

Four-dimensional magnetic resonance velocity mapping of blood flow patterns in the aorta in patients with atherosclerotic coronary artery disease compared to age-matched normal subjects

PURPOSE

To test the hypothesis that age and atherosclerotic coronary artery disease (CAD) may influence aortic blood flow patterns.

MATERIALS AND METHODS

A total of 21 patients with CAD, 37-86 years old, were studied, together with 20 age-matched normal subjects. Time-resolved, three-direction velocity data over an entire volume were obtained with sequential single-slice two-dimensional cardiac-gated magnetic resonance (MR) velocity-encoded phase-contrast sequences.

RESULTS

In both normal subjects and CAD patients, the time it took for particles to travel from aortic valve to descending aorta was significantly longer in the elderly age group than in the younger (37-46 years old). This time was significantly longer in patients than in normal subjects. Systolic velocities were significantly higher in young normal subjects than in elderly normal subjects, and significantly lower in CAD patients than in age-matched normal subjects. Retrograde velocity was higher in CAD patients than in normal subjects, and higher in elderly CAD patients than in young.

CONCLUSION

CAD patients have abnormal blood flow patterns in the aorta compared with age-matched normal subjects, especially young patients ages 37-46. The aging process has a similar effect on blood flow patterns as atherosclerosis. Ascending aorta flow is chaotic in some very elderly normal subjects and in CAD patients of all ages. Chaotic aortic flow may result in reduced blood flow into the coronary arteries.

The influence of out-of-plane geometry on pulsatile flow within a distal end-to-side anastomosis

We present an experimental and computational investigation of time-varying flow in an idealized fully occluded 45 degrees distal end-to-side anastomosis. Two geometric configurations are assessed, one where the centerlines of host and bypass vessels lie within a plane, and one where the bypass vessel is deformed out of the plane of symmetry, respectively, termed planar and non-planar. Flow experiments were conducted by magnetic resonance imaging in rigid wall models and computations were performed using a high order spectral/hp algorithm. Results indicate a significant change in the spatial distribution of wall shear stress and a reduction of the time-averaged peak wall shear stress magnitude by 10% in the non-planar model as compared to the planar configuration. In the planar geometry the stagnation point follows a straight-line path along the host artery bed with a path length of 0.8 diameters. By contrast in the non-planar case the stagnation point oscillates about a center that is located off the symmetry plane intersection with the host artery bed wall, and follows a parabolic path with a 0.7 diameter longitudinal and 0.5 diameter transverse excursion. A definition of the oscillatory shear index (OSI) is introduced that varies between 0 and 0.5 and that accounts for a continuous range of wall shear stress vector angles. In both models, regions of elevated oscillatory shear were spatially associated with regions of separated or oscillating stagnation point flow. The mean oscillatory shear magnitude (considering sites where OSI>0.1) in the non-planar geometry was reduced by 22% as compared to the planar configuration. These changes in the dynamic behavior of the stagnation point and the oscillatory shear distribution introduced by out-of-plane graft curvature may influence the localization of vessel wall sites exposed to physiologically unfavorable flow conditions.