Computational simulation of turbulent signal loss in 2D time-of-flight magnetic resonance angiograms

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.

Assessment of Complex Flow Patterns in Patients With Carotid Webs, Patients With Carotid Atherosclerosis, and Healthy Subjects Using 4D Flow MRI

BACKGROUND

Carotid webs (CaWs) are fibromuscular projections in the internal carotid artery (ICA) that cause mild luminal narrowing (<50%), but may be causative in up to one-third of seemingly cryptogenic strokes. Understanding hemodynamic alterations caused by CaWs is imperative to assessing stroke risk. Time-Average Wall Shear Stress (TAWSS) and Oscillatory Shear Index (OSI) are hemodynamic parameters linked to vascular dysfunction and thrombosis.

PURPOSE

To test the hypothesis: "CaWs are associated with lower TAWSS and higher OSI than mild atherosclerosis or healthy carotid bifurcation."

STUDY TYPE

Prospective study.

POPULATION

A total of 35 subjects (N = 14 bifurcations with CaW, 11F, age: 49 ± 10, 10 mild atherosclerosis 6F, age: 72 ± 9, 11 healthy 9F, age: 42 ± 13).

FIELD STRENGTH/SEQUENCE

4D flow/STAR-MATCH/3D TOF/3T MRI, CTA.

ASSESSMENT

4D Flow velocity data were analyzed in two ways: 1) 3D ROI in the ICA bulbar segment (complex flow patterns are expected) was used to quantify the regions with low TAWSS and high OSI. 2) 2D planes were placed perpendicular to the centerline of the carotid bifurcation for detailed analysis of TAWSS and OSI.

STATISTICAL TESTS

Independent-samples Kruskal-Wallis-H test with 0.05 used for statistical significance.

RESULTS

The percent surface area where low TAWSS was present in the ICA bulb was 12.3 ± 8.0% (95% CI: 7.6-16.9) in CaW subjects, 1.6 ± 1.9% (95% CI: 0.2-2.9) in atherosclerosis, and 8.5 ± 7.7% (95% CI: 3.6-13.4) in healthy subjects, all differences were statistically significant (ƞ2 = 0.3 [95% CI: 0.05-0.5], P-value CaW vs. healthy = 0.2). OSI had similar values in the CCA between groups (ƞ2 = 0.07 [95% CI: 0.0-0.2], P-value = 0.5), but OSI was significantly higher downstream of the bifurcation in CaW subjects compared to atherosclerosis and normal subjects. OSI returned to similar values between groups 1.5 diameters distal to the bifurcation (ƞ2 = 0.03 [95% CI: 0.0-0.2], P-value = 0.7).

CONCLUSION

Lower TAWSS and higher OSI are present in the ICA bulb in patients with CaW when compared to patients with atherosclerotic or healthy subjects.

EVIDENCE LEVEL

2 TECHNICAL EFFICACY: Stage 2.

Subjects with carotid webs demonstrate pro-thrombotic hemodynamics compared to subjects with carotid atherosclerosis

Carotid artery webs (CaW) are non-atherosclerotic projections into the vascular lumen and have been linked to up to one-third of cryptogenic strokes in younger patients. Determining how CaW affects local hemodynamics is essential for understanding clot formation and stroke risk. Computational fluid dynamics simulations were used to investigate patient-specific hemodynamics in carotid artery bifurcations with CaW, bifurcations with atherosclerotic lesions having a similar degree of lumen narrowing, and with healthy carotid bifurcations. Simulations were conducted using segmented computed tomography angiography geometries with inlet boundary conditions extracted from 2D phase contrast MRI scans. The study included carotid bifurcations with CaW (n = 13), mild atherosclerosis (n = 7), and healthy bifurcation geometries (n = 6). Hemodynamic parameters associated with vascular dysfunction and clot formation, including shear rate, oscillatory shear index (OSI), low velocity, and flow stasis were calculated and compared between the subject groups. Patients with CaW had significantly larger regions containing low shear rate, high OSI, low velocity, and flow stasis in comparison to subjects with mild atherosclerosis or normal bifurcations. These abnormal hemodynamic metrics in patients with CaW are associated with clot formation and vascular dysfunction and suggest that hemodynamic assessment may be a tool to assess stroke risk in these patients.

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.

Segmentation of intracranial vessels and aneurysms in phase contrast magnetic resonance angiography using multirange filters and local variances

Segmentation of intensity varying and low-contrast structures is an extremely challenging and rewarding task. In computer-aided diagnosis of intracranial aneurysms, segmenting the high-intensity major vessels along with the attached low-contrast aneurysms is essential to the recognition of this lethal vascular disease. It is particularly helpful in performing early and noninvasive diagnosis of intracranial aneurysms using phase contrast magnetic resonance angiographic (PC-MRA) images. The major challenges of developing a PC-MRA-based segmentation method are the significantly varying voxel intensity inside vessels with different flow velocities and the signal loss in the aneurysmal regions where turbulent flows occur. This paper proposes a novel intensity-based algorithm to segment intracranial vessels and the attached aneurysms. The proposed method can handle intensity varying vasculatures and also the low-contrast aneurysmal regions affected by turbulent flows. It is grounded on the use of multirange filters and local variances to extract intensity-based image features for identifying contrast varying vasculatures. The extremely low-intensity region affected by turbulent flows is detected according to the topology of the structure detected by multirange filters and local variances. The proposed method is evaluated using a phantom image volume with an aneurysm and four clinical cases. It achieves 0.80 dice score in the phantom case. In addition, different components of the proposed method-the multirange filters, local variances, and topology-based detection-are evaluated in the comparison between the proposed method and its lower complexity variants. Owing to the analogy between these variants and existing vascular segmentation methods, this comparison also exemplifies the advantage of the proposed method over the existing approaches. It analyzes the weaknesses of these existing approaches and justifies the use of every component involved in the proposed method. It is shown that the proposed method is capable of segmenting blood vessels and the attached aneurysms on PC-MRA images.

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.

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 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.

Vascular segmentation of phase contrast magnetic resonance angiograms based on statistical mixture modeling and local phase coherence

In this paper, we present an approach to segmenting the brain vasculature in phase contrast magnetic resonance angiography (PC-MRA). According to our prior work, we can describe the overall probability density function of a PC-MRA speed image as either a Maxwell-uniform (MU) or Maxwell-Gaussian-uniform (MGU) mixture model. An automatic mechanism based on Kullback-Leibler divergence is proposed for selecting between the MGU and MU models given a speed image volume. A coherence measure, namely local phase coherence (LPC), which incorporates information about the spatial relationships between neighboring flow vectors, is defined and shown to be more robust to noise than previously described coherence measures. A statistical measure from the speed images and the LPC measure from the phase images are combined in a probabilistic framework, based on the maximum a posteriori method and Markov random fields, to estimate the posterior probabilities of vessel and background for classification. It is shown that segmentation based on both measures gives a more accurate segmentation than using either speed or flow coherence information alone. The proposed method is tested on synthetic, flow phantom and clinical datasets. The results show that the method can segment normal vessels and vascular regions with relatively low flow rate and low signal-to-noise ratio, e.g., aneurysms and veins.

Velocity imaging of highly turbulent gas flow

We introduce a noninvasive, quantitative magnetic resonance imaging (MRI) wind-tunnel measurement in flowing gas (>10 m s(-1)) at high Reynolds numbers (Re>10(5)). The method pertains to liquids and gases, is inherently three dimensional, and extends the range of Re to which MRI is applicable by orders of magnitude. There is potential for clear time savings over traditional pointwise techniques. The mean velocity and turbulent diffusivity of gas flowing past a bluff obstruction and a wing section at realistic stall speeds were measured. The MRI data are compared with computational fluid dynamics.

Time-of-flight quantitative measurements of blood flow in mouse hindlimbs

PURPOSE

To evaluate the feasibility of using time-of-flight (TOF) imaging to directly measure hindlimb blood flow in a mouse model of peripheral vascular disease.

MATERIALS AND METHODS

Four tubes were imaged simultaneously (diameters = 0.39 mm, 0.59 mm, and two at 1.46 mm) with a 1.0 mM copper sulfate solution for 19 flow velocities. In vivo measurements were performed in the hindlimbs of three mouse strains-C57BL/6 (N = 5), BALB/c (N = 5), and 129S2/Sv (N = 5)-three weeks after femoral artery ligation with a calibration standard.

RESULTS

The flow phantom showed that the intensity was linear (r2 = 0.92) over the pertinent blood flow velocities in the mouse hindlimbs. Measurements of the blood flow in the distal hindlimbs in different strains of mice (combination of both the venous and arterial flows) were obtained 21 days after right-sided femoral artery occlusion. The results showed that under similar conditions of anesthesia and temperature, SV129 mice on the nonligated side had the highest flows (0.50 +/- 0.07 mL/minute), followed by C57BL/6 (0.28 +/- 0.04 mL/minute) and BALB/c (0.23 +/- 0.05 mL/minute), P < 0.02. The ligated side measurements (SV129, 0.31 +/- 0.05 mL/minute (P = 0.02); C57BL/6, 0.21 +/- 0.02 mL/minute (P = 0.13); and BALB/c, 0.12 +/- 0.02 mL/minute (P= 0.06)) showed a trend in BALB/c and C57BL/6 and significant differences in SV129 for incomplete recovery three weeks after surgery, compared to the nonligated side.

CONCLUSION

Two-dimensional TOF imaging permits quantitative in vivo measurements of hindlimb blood flow in a mouse model of peripheral vascular disease without the need of contrast injection, offering advantages of serial imaging not limited by tissue penetration.

Fusing speed and phase information for vascular segmentation of phase contrast MR angiograms

This paper presents a statistical approach to aggregating speed and phase (directional) information for vascular segmentation of phase contrast magnetic resonance angiograms (PC-MRA). Rather than relying on speed information alone, as done by others and in our own work, we demonstrate that including phase information as a priori knowledge in a Markov random field (MRF) model can improve the quality of segmentation. This is particularly true in the region within an aneurysm where there is a heterogeneous intensity pattern and significant vascular signal loss. We propose to use a Maxwell-Gaussian mixture density to model the background signal distribution and combine this with a uniform distribution for modelling vascular signal to give a Maxwell-Gaussian-uniform (MGU) mixture model of image intensity. The MGU model parameters are estimated by the modified expectation-maximisation (EM) algorithm. In addition, it is shown that the Maxwell-Gaussian mixture distribution (a) models the background signal more accurately than a Maxwell distribution, (b) exhibits a better fit to clinical data and (c) gives fewer false positive voxels (misclassified vessel voxels) in segmentation. The new segmentation algorithm is tested on an aneurysm phantom data set and two clinical data sets. The experimental results show that the proposed method can provide a better quality of segmentation when both speed and phase information are utilised.

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.

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.

2D-TOF MRA Follow-up Study of Percutaneous Transluminal Angioplasty for Severely Stenotic Cervical Internal Carotid Artery

Percutaneous transluminal angioplasty (PTA) for severe arteriosclerotic stenosis in the cervical internal carotid artery (ICA) was successfully carried out in 23 cases between December 1994 and August 1996. In order to analyze the condition of the cervical ICA in the early stage after PTA, 12 stenotic lesions of 11 cases were exposed to follow-up study of stenotic cervical ICA after PTA with magnetic resonance angiography (MRA) 1 to 150 days postoperatively. In six lesions, the diameter of the cervical ICA was dilated sequentially.

In another four lesions, the diameter of the cervical ICA was decreased in the first three weeks and dilated over the next three weeks. Angiographically, these lesions had a small intimal flap at the balloon dilated portion, which was speculated to cause the turbulent flow in the first stage. In the remaining 2 lesions, restenotic changes in cervical ICAs were observed within three weeks after PTA.

Follow-up angiography was performed over three months after PTA in five cases of this series and compared with MRA. Consequently, the diameters of the cervical ICA between angiography and MRA were closely correlated.

The evaluation of the lesion after PTA of the cervical ICA demonstrated that MRA is beneficial, but within three weeks after PTA, caution should be paid for underestimation of the small intimal flap on MRA.