Simulation of in-plane flow imaging

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.

Coupling synthetic and real-world data for a deep learning-based segmentation process of 4D flow MRI

BACKGROUND AND OBJECTIVE

Phase contrast magnetic resonance imaging (4D flow MRI) is an imaging technique able to provide blood velocity in vivo and morphological information. This capability has been used to study mainly the hemodynamics of large vessels, such as the thoracic aorta. However, the segmentation of 4D flow MRI data is a complex and time-consuming task. In recent years, neural networks have shown great accuracy in segmentation tasks if large datasets are provided. Unfortunately, in the context of 4D flow MRI, the availability of these data is limited due to its recent adoption in clinical settings. In this study, we propose a pipeline for generating synthetic thoracic aorta phase contrast magnetic resonance angiography (PCMRA) to expand the limited dataset of patient-specific PCMRA images, ultimately improving the accuracy of the neural network segmentation even with a small real dataset.

METHODS

The pipeline involves several steps. First, a statistical shape model is used to synthesize new artificial geometries to improve data numerosity and variability. Secondly, computational fluid dynamics simulations are employed to simulate the velocity fields and, finally, after a downsampling and a signal-to-noise and velocity limit adjustment in both frequency and spatial domains, volumes are obtained using the PCMRA formula. These synthesized volumes are used in combination with real-world data to train a 3D U-Net neural network. Different settings of real and synthetic data are tested.

RESULTS

Incorporating synthetic data into the training set significantly improved the segmentation performance compared to using only real data. The experiments with synthetic data achieved a DICE score (DS) value of 0.83 and a better target reconstruction with respect to the case with only real data (DS = 0.65).

CONCLUSION

The proposed pipeline demonstrated the ability to increase the dataset in terms of numerosity and variability and to improve the segmentation accuracy for the thoracic aorta using PCMRA.

Simulation of phase contrast angiography for renal arterial models

BACKGROUND

With the development of versatile magnetic resonance acquisition techniques there arises a need for more advanced imaging simulation tools to enable adequate image appearance prediction, measurement sequence design and testing thereof. Recently, there is a growing interest in phase contrast angiography (PCA) sequence due to the capabilities of blood flow quantification that it offers. Moreover, as it is a non-contrast enhanced protocol, it has become an attractive option in areas, where usage of invasive contrast agents is not indifferent for the imaged tissue. Monitoring of the kidney function is an example of such an application.

RESULTS

We present a computer framework for simulation of the PCA protocol, both conventional and accelerated with echo-planar imaging (EPI) readout, and its application to the numerical models of kidney vasculatures. Eight patient-specific renal arterial trees were reconstructed following vessel segmentation in real computed tomography angiograms. In addition, a synthetic model was designed using a vascular tree growth simulation algorithm. The results embrace a series of synthetic PCA images of the renal arterial trees giving insight into the image formation and quantification of kidney hemodynamics.

CONCLUSIONS

The designed simulation framework enables quantification of the PCA measurement error in relation to ground-truth flow velocity data. The mean velocity measurement error for the reconstructed renal arterial trees range from 1.5 to 12.8% of the aliasing velocity value, depending on image resolution and flip angle. No statistically significant difference was observed between measurements obtained using EPI with a number of echos (NETL) = 4 and conventional PCA. In case of higher NETL factors peak velocity values can be underestimated up to 34%.

Dissipative particle dynamics of diffusion-NMR requires high Schmidt-numbers

We present an efficient mesoscale model to simulate the diffusion measurement with nuclear magnetic resonance (NMR). On the level of mesoscopic thermal motion of fluid particles, we couple the Bloch equations with dissipative particle dynamics (DPD). Thereby we establish a physically consistent scaling relation between the diffusion constant measured for DPD-particles and the diffusion constant of a real fluid. The latter is based on a splitting into a centre-of-mass contribution represented by DPD, and an internal contribution which is not resolved in the DPD-level of description. As a consequence, simulating the centre-of-mass contribution with DPD requires high Schmidt numbers. After a verification for fundamental pulse sequences, we apply the NMR-DPD method to NMR diffusion measurements of anisotropic fluids, and of fluids restricted by walls of microfluidic channels. For the latter, the free diffusion and the localisation regime are considered.

Bloch-based MRI system simulator considering realistic electromagnetic fields for calculation of signal, noise, and specific absorption rate

PURPOSE

To describe and introduce new software capable of accurately simulating MR signal, noise, and specific absorption rate (SAR) given arbitrary sample, sequence, static magnetic field distribution, and radiofrequency magnetic and electric field distributions for each transmit and receive coil.

THEORY AND METHODS

Using fundamental equations for nuclear precession and relaxation, signal reception, noise reception, and calculation of SAR, a versatile MR simulator was developed. The resulting simulator was tested with simulation of a variety of sequences demonstrating several common imaging contrast types and artifacts. The simulation of intravoxel dephasing and rephasing with both tracking of the first order derivatives of each magnetization vector and multiple magnetization vectors was examined to ensure adequate representation of the MR signal. A quantitative comparison of simulated and experimentally measured SNR was also performed.

RESULTS

The simulator showed good agreement with our expectations, theory, and experiment.

CONCLUSION

With careful design, an MR simulator producing realistic signal, noise, and SAR for arbitrary sample, sequence, and fields has been created. It is hoped that this tool will be valuable in a wide variety of applications.

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.

Simulation of High-Resolution Magnetic Resonance Images on the IBM Blue Gene/L Supercomputer Using SIMRI

Medical imaging system simulators are tools that provide a means to evaluate system architecture and create artificial image sets that are appropriate for specific applications. We have modified SIMRI, a Bloch equation-based magnetic resonance image simulator, in order to successfully generate high-resolution 3D MR images of the Montreal brain phantom using Blue Gene/L systems. Results show that redistribution of the workload allows an anatomically accurate 256³ voxel spin-echo simulation in less than 5 hours when executed on an 8192-node partition of a Blue Gene/L system.

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.

Bloch simulations with intra-voxel spin dephasing

A common problem in simulations of MRI-experiments based on the numerical solution of the Bloch equations is the finite number of isochromats used in the calculations. This usually results in false or spurious signals and is a source of various differences between calculated and experimentally obtained data. In this paper, we are proposing a technique representing each sample voxel by a central and three additional isochromats, slightly shifted in orthogonal directions from center, thus providing a linear approximation of intra-voxel dephasing. This approach allows for further improvement and precision of the calculated NMR signal and virtually avoids the problem related to an finite set of isochromats. Here we provide details of the algorithm together with examples of simulations which prove the efficiency of this approach.

The effect of physiological noise in phase functional magnetic resonance imaging: from blood oxygen level-dependent effects to direct detection of neuronal currents

Recently, the possibility to use both magnitude and phase image sets for the statistical evaluation of fMRI has been proposed, with the prospective of increasing both statistical power and the spatial specificity. In the present work, several issues that affect the spatial and temporal stability in fMRI phase time series in the presence of physiologic noise processes are reviewed, discussed and illustrated by experiments performed at 3 T. The observed phase value is a fingerprint of the underlying voxel averaged magnetic field variations. Those related to physiological processes can be considered static or dynamic in relation to the temporal scale of a 2D acquisition and will play out on different spatial scales as well: globally across the entire images slice, and locally depending on the constituents and their relative fractions inside the MRI voxel. The 'static' respiration-induced effects lead to magneto-mechanic scan-to-scan variations in the global magnetic field but may also contribute to local BOLD fluctuations due to respiration-related variations in arterial carbon dioxide. Likewise, the 'dynamic' cardiac-related effects will lead to global susceptibility effects caused by pulsatile motion of the brain as well as local blood pressure-related changes in BOLD and changes in blood flow velocity. Finally, subject motion may lead to variations in both local and global tissue susceptibility that will be especially pronounced close to air cavities. Since dissimilar manifestations of physiological processes can be expected in phase and in magnitude images, a direct relationship between phase and magnitude scan-to-scan fluctuations cannot be assumed a priori. Therefore three different models were defined for the phase stability, each dependent on the relation between phase and magnitude variations and the best will depend on the underlying noise processes. By experiments on healthy volunteers at rest, we showed that phase stability depends on the type of post-processing and can be improved by reducing the low-frequency respiration-induced mechano-magnetic effects. Although the manifestations of physiological noise were in general more pronounced in phase than in magnitude images, due to phase wraps and global Bo effects, we suggest that a phase stability similar to that found in magnitude could theoretically be achieved by adequate correction methods. Moreover, as suggested by our experimental data regarding BOLD-related phase effects, phase stability could even supersede magnitude stability in voxels covering dense microvascular networks with BOLD-related fluctuations as the dominant noise contributor. In the interest of the quality of both BOLD-based and nc-MRI methods, future studies are required to find alternative methods that can improve phase stability, designed to match the temporal and spatial scale of the underlying neuronal activity.

Efficient simulation of magnetic resonance imaging with Bloch-Torrey equations using intra-voxel magnetization gradients

The process of image formation in magnetic resonance imaging (MRI) can be simulated by means of an iterative solution of Bloch-Torrey equations. This is a useful accessory to analyze the influence of sample properties, sequence parameters and hardware specifications on the MRI signal. In this paper, a computer algorithm is presented which is based on calculating partial derivatives of the magnetization vector. This technique allows more efficient simulation than summation of isochromats (the latter being commonly employed for this purpose) and, as a result, the effect of diffusion on the MRI signal can be calculated iteratively. A detailed description of the algorithm is given, and its feasibility for different applications is studied. It is shown that the algorithm is most applicable to simulating the effect of field perturbations, i.e. intra-voxel dephasing, but is also useful for other typical imaging experiments and the simulation of diffusion weighting.

The SIMRI project: a versatile and interactive MRI simulator

This paper gives an overview of SIMRI, a new 3D MRI simulator based on the Bloch equation. This simulator proposes an efficient management of the T2* effect, and in a unique simulator integrates most of the simulation features that are offered in different simulators. It takes into account the main static field value and enables realistic simulations of the chemical shift artifact, including off-resonance phenomena. It also simulates the artifacts linked to the static field inhomogeneity like those induced by susceptibility variation within an object. It is implemented in the C language and the MRI sequence programming is done using high level C functions with a simple programming interface. To manage large simulations, the magnetization kernel is implemented in a parallelized way that enables simulation on PC grid architecture. Furthermore, this simulator includes a 1D interactive interface for pedagogic purpose illustrating the magnetization vector motion as well as the MRI contrasts.