The solution of Bloch equations for flowing spins during a selective pulse using a finite difference method

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

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

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.

Reduction of flow artifacts by using partial saturation in RF-spoiled gradient-echo imaging

Radiofrequency (RF)-spoiled gradient-echo imaging provides a signal intensity close to pure T(1) contrast by using spoiler gradients and RF phase cycling to eliminate net transverse magnetization. Generally, spins require many RF excitations to reach a steady-state magnetization level; therefore, when unsaturated flowing spins enter the imaging slab, they can cause undesirable signal enhancement and generate image artifacts. These artifacts can be reduced by partially saturating an outer slab upstream to drive the longitudinal magnetization close to the steady state, while the partially saturated spins generate no signal until they enter the imaging slab. In this work, magnetization evolution of flowing spins in RF-spoiled gradient-echo sequences with and without partial saturation was simulated using the Bloch equations. Next, the simulations were validated by phantom and in vivo experiments. For phantom experiments, a pulsatile flow phantom was used to test partial saturation for a range of flip angles and relaxation times. For in vivo experiments, the technique was used to image the carotid arteries, abdominal aorta, and femoral arteries of normal volunteers. All experiments demonstrated that partial saturation can provide consistent T(1) contrast across the slab while reducing inflow artifacts.

Blood velocity assessment using 3D bright-blood time-resolved magnetic resonance angiography

Blood velocity is a functional parameter that is not easily assessed noninvasively, especially in small animals. A new noninvasive method that uses magnetic resonance angiography (MRA) to measure blood flows is proposed. This method is based on the time-of-flight (TOF) phenomenon. By initially suppressing the signal from the stationary spins in the area of interest, it is possible to sequentially visualize only the signal from the moving spins entering a given volume. With this method, 3D cine images of the blood flow can be generated by positive contrast, with unparalleled spatial (<200 microm) and temporal resolutions (<10 ms/image). As a result, it is possible to measure flow in sinuous paths. The present method was applied in vivo to measure the blood velocity in mouse carotid arteries. Because of its robustness and simplicity of implementation, this method has numerous potential applications for fundamental studies in small animal models.

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.

Inflow correction of hepatic perfusion measurements usingT1-weighted, fast gradient-echo, contrast-enhanced MRI

Inflow effects were studied for T(1)-weighted, fast gradient-echo, contrast-enhanced MRI. This was done on the basis of realistic simulations (e.g., taking slice profiles into account) for unsteady flow. The area under the point spread function (PSF) was used to estimate the flow-related enhancement. A simple analytical model that accurately describes the inflow effects was derived and validated. This model was used to correct the experimental perfusion calibration curves (signal intensity vs. relaxation rate) for inflow effects. Hepatic perfusion measurements, performed on patients, were analyzed in terms of a dual-input, first-order linear model. It was shown that inflow causes incorrect perfusion input functions. The resulting estimated perfusion parameters displayed a systematic error of typically 30-40%. By performing two extra time-resolved flow measurements during the examination, one can correct the input functions.

Inversion profiles of adiabatic inversion pulses for flowing spins: the effects on labeling efficiency and labeling accuracy in perfusion imaging with pulsed arterial spin-labeling

The inversion profile of adiabatic inversion pulses is essential to the accuracy of perfusion measurement with pulsed arterial spin-labeling (ASL). In this paper, the inversion profiles for flowing spins were investigated using a numerical solution of the modified Bloch equations including a term for moving spins. Inversion profiles for spins flowing at a constant or varying velocity were examined for hyperbolic secant (HS) and frequency-offset corrected inversion (FOCI) pulses. Distortions of the inversion profiles were found for both pulses with spins flowing within physiological velocity range. The effects of the distorted profiles on labeling efficiency and labeling accuracy in the application of pulsed ASL perfusion imaging were analyzed. These effects should be taken into account in ASL techniques, in order to obtain robust and accurate perfusion measurements.

A protocol for assessing subtraction errors of arterial spin-tagging perfusion techniques in human brain

A protocol for assessing signal contributions from static tissue (subtraction errors) in perfusion images acquired with arterial spin-labeling (ASL) techniques in human brain is proposed. The method exploits the reduction of blood T(1) caused by the clinically available paramagnetic contrast agent, gadopentetate dimeglumine (Gd-DTPA). The protocol is demonstrated clinically with multislice FAIR images acquired before, during, and after Gd-DTPA administration using a range of selective inversion widths. Perfusion images acquired postcontrast for selective inversion widths large enough (threshold) to avoid interaction with the imaging slice had signal intensities reduced to noise level, as opposed to subtraction errors manifested on images acquired using inversion widths below the threshold. The need for these experiments to be performed in vivo is further illustrated by comparison with phantom results. The protocol allows a one-time calibration of relevant ASL parameters (e.g., selective inversion widths) in vivo, which may otherwise cause subtraction errors. Magn Reson Med 43:896-900, 2000. Published 2000 Wiley-Liss, Inc.

Ultra-short echo-time 2D time-of-flight MR angiography using a half-pulse excitation

Flow-related artifacts remain a significant concern for magnetic resonance (MR) angiography because their appearance in angiograms adversely impacts accuracy in evaluation of arterial stenoses. In this paper, a half-pulse excitation scheme for improved two-dimensional time-of-flight (2D TOF) angiography is described. The proposed method eliminates the need for gradient moment nulling (of all orders), providing significant reductions in spin dephasing and consequent artifactual signal loss. Furthermore, because the post-excitation refocusing and flow compensation gradients are obviated, the achievable echo time is dramatically shortened. The half-pulse excitation is employed in conjunction with a fast radial-line acquisition, allowing ultra-short echo times on the order of 250-300 microsec. Radial-line acquisition methods also provide additional benefits for flow imaging: effective mitigation of pulsatile flow artifacts, full k-space coverage, and decreased scan times. The half-pulse excitation/radial-line sequence demonstrated improved performance in initial clinical evaluations of the carotid bifurcation when compared with a conventional 2D TOF sequence.

Effects of slow flow on slice profile and NMR signal in fast imaging sequences

A computer program has been developed to evaluate the selective-slice profiles obtained in the steady state for fast gradient-echo imaging. Both spoiled and refocused gradient-echo pulse sequences have been considered. By numerically solving the Bloch equations modified for the effects of flow, for a three-dimensional volume of spins, for realistic RF excitations and linear gradient combinations, the program permits the combined effects of flow and imaging variables on the magnetization slice profile to be assessed quantitatively. We have found that the gradient pattern in gradient-echo pulse sequences is a significant factor for determining the steady-state slice profiles and the strength of the NMR signal from the flowing spins.

Velocity sensitivity of slice-selective excitation

The purpose of this study was to investigate how flow affects slice-selective excitation, particularly for radiofrequency (rf) pulses optimized for slice-selective excitation of stationary material. Simulation methods were used to calculate the slice profiles for material flowing at different velocities, using optimal flow compensation when appropriate. Four rf pulses of very different shapes were used in the simulation study: a 90 degrees linear-phase Shinnar-LeRoux pulse; a 90 degrees self-refocusing pulse; a minimum-phase Shinnar-LeRoux inversion pulse; and a SPINCALC inversion pulse. Slice profiles from simulations with a laminar flow model were compared with experimental studies for two different rf pulses using a clinical magnetic resonance imaging (MRI) system. We found that, for a given rf pulse, the effect of flow on slice-selective excitation depends on the product of the selection gradient amplitude, the component of velocity in the slice selection direction, and the square of the rf pulse duration. The shapes of the slice profiles from the Shinnar-LeRoux pulses were relatively insensitive to velocity. However, the slice profiles from the self-refocusing pulse and the SPINCALC pulse were significantly degraded by velocity. Experimental slice profiles showed excellent agreement with simulation. In conclusion, our study demonstrates that slice-selective excitation can be significantly degraded by flow depending on the velocity, the gradient amplitude, and characteristics of the rf excitation pulse used. The results can aid in the design of rf pulses for slice-selective excitation of flowing material.

Determination of the optimal imaging parameters of the RODEO pulse sequence by computer simulation

A computer program has been developed for evaluating the NMR signal response of various imaging parameters and its efficiency in fat suppression of the RODEO (ROtating Delivery of Excitation Off-resonance) pulse sequence. Both spoiled and refocused RODEO pulse sequences have been considered. By numerically solving the Bloch equation modified for a three-dimensional volume of spins, for realistic RF excitations and Lorentzian distribution of the frequency spectrum for both fat and water, the program permits the imaging contrast and fat suppression of the RODEO pulse sequences to be assessed quantitatively. We have found that excellent fat suppression can be achieved by choosing appropriate imaging parameters. Imaging contrast for different tissues can be enhanced by using longer repetition time (TR) in the spoiled scheme. The complex pattern of NMR signal response and imaging contrast has been observed in the refocused scheme.

Calculation of the magnetization distribution for fluid flow in curved vessels

The signal intensity in magnetic resonance angiography (MRA) images reflects both morphological and flow-related features of vascular anatomy. A thorough understanding of MRA, therefore, demands a careful analysis of flow-related effects. Computational fluid dynamics (CFD) methods are very powerful in determining flow patterns in 3D tortuous vessels for both steady and unsteady flow. Previous simulations of MRA images calculated the magnetization of flowing blood by tracking particles as they moved along flow streamlines that had been determined by a CFD calculation. This manuscript describes MRA simulations that use CFD calculations to determine magnetization variation at a fixed point and, therefore, do not require streamline tracking to calculate the distribution of magnetization in flowing fluids. This method inherently accounts for uniform particle density, avoids problems associated with tracking particles close to the wall, and is well-suited to modeling pulsatile flow.

Accurate velocity mapping with FAcE

Spin dislocation between the slice selection, phase encoding, and frequency encoding is a source of image distortions. Two strategies can be pursued to improve the appearance of moving spins in an image. Either the sequence is made equally sensitive to velocity-dependent dislocation artifacts for all spatial directions or the sensitivity is reduced with a shorter echo time. The first approach increases the dislocation for the phase-encoding direction and is therefore not useful if velocity maps with minimal distortion are the goal. FAcE (FID acquired echoes) is a sequence with separate sampling of the left and right k-space half-planes that allows for very short echo times. It was applied for velocity mapping of flow in the slice select direction. Special attention was paid to a compact design of the velocity-encoding select gradient to achieve short echo times even with high velocity sensitivity. Artifacts introduced by in-plane motion were studied for FAcE and conventional gradient-echo sequences, both in phantom experiments and simulation. FAcE allows for very short echo times with inherent motion compensation of the frequency-encoding gradient. Thus, both motion-related dislocation artifacts and signal voids due to coherence loss in regions with irregular flow are minimal.

MR imaging of flow through tortuous vessels: a numerical simulation

A novel computer simulation technique is presented that allows the calculation of images from Magnetic Resonance Angiography (MRA) studies of blood flow in realistic curving and branching two-dimensional vessel geometries. Fluid dynamic calculations provide flow streamlines through curved or branching vessels. MR simulations generate images for specific MR pulse sequence parameters. Simulations of steady flow in carotid bifurcation and carotid siphon geometries as imaged by a standard, flow-compensated, spoiled gradient echo sequence illustrate the major features seen in clinical time of flight MRA studies. The simulations provide insight into a number of artifacts encountered in MRA such as displacement artifacts, signal pile-up, truncation artifacts, and intravoxel phase dispersion.

Imaging of the human cardiovascular system using the rapid echo flow-rephased spin-echo technique

Using a flow-rephased spin-echo technique with a short echo time of TE = 9.7 msec, "white blood" multislice and single slice first echo images of the human heart were acquired using standard 1.5 T whole-body imagers. The technique almost completely eliminates phase shifts for flow with constant velocity and constant acceleration, so the investigations with healthy volunteers show images which are almost free of the artifacts often found in ECG-gated standard spin-echo imaging of the heart. T1-weighted images with good contrast between tissue and blood are achieved at any time during the whole heart cycle. The results obtained indicate that the technique might be helpful for imaging small vessels, vessels which contain slowly flowing blood, and vessels located in regions with static field inhomogeneities, for example, lung vessels.

The design of pulse sequences employing spatial presaturation for the suppression of flow artifacts

The use of spatial presaturation to suppress the signal, and therefore also the artifacts, from flowing blood has become an important tool in the arsenal of techniques to suppress pulsatile flow artifacts in magnetic resonance images. However, a detailed theoretical analysis of the behavior of these flow artifact suppression pulses and of the important aspects of implementing suppression pulses in combination with particular imaging sequences has yet to be presented. In this paper we present a general theoretical framework to describe the flow artifact suppression technique. This analysis addresses the following four major issues: (1) the spin washout characteristics of the imaging sequence, (2) the interference between the flow signal suppression pulses and the imaging sequence, (3) the flow velocity range for a single application of the suppression pulse, and (4) the total flow velocity range for a suppression pulse repeated with a constant time interval between applications of the pulse. The predictions of our theoretical model are confirmed by experimental measurements made with stationary and flow phantoms. The results of this investigation provide guidelines for the design of flow artifact suppression pulse sequences and, in addition, should aid in the future development and refinement of the spatial presaturation technique as applied to flow signal suppression.

MR angiography by multiple thin slab 3D acquisition

Multiple overlapping thin 3D slab acquisition is presented as a magnitude contrast (time of flight) technique which combines advantages from multiple thin slice 2D and direct 3D volume acquisitions to obtain high-resolution cross-sectional images of vessel detail. Details of implementation and example images are presented.

Interactive design of motion-compensated gradient waveforms with a personal computer spreadsheet program

A personal computer spreadsheet program was used to compute the amplitudes of the gradient pulses in motion-compensated gradient waveforms. The resulting designs for velocity-compensated, gradient-echo, frequency-encoding gradients and velocity-compensated section-select waveforms required little or no modification when implemented on two clinical magnetic resonance imagers.

Nuclear magnetic resonance velocity spectra of steady flow

Nuclear magnetic resonance (NMR) velocity spectra are a compact way to represent the flow information in a velocity-resolved image set. Fully developed steady flow in long tubes gives NMR velocity spectra with average velocities which correlate well with the values derived from the flow rate. The ratio of average velocity to peak velocity correlates well with the Reynolds number. Tubes with compressed cross sections have velocity spectra similar to those of circular tubes. Tubes with irregular walls have velocity spectra in the entrance region that are markedly different from those from smooth-walled tubes.

A technique for flow-enhanced magnetic resonance angiography of the lower extremities

A two-dimensional, flow-enhanced gradient echo pulse sequence for nuclear magnetic resonance angiography is described. It employs interleaved, presaturated slices to acquire data efficiently on imagers which favor interleaved acquisition over sequential acquisition for multislice imaging. It is useful on any imagers when the effective TR is extended to enhance the sensitivity to slow flow. The technique was applied to the region from aortic bifurcation to the iliac bifurcations of three normal volunteers. The right and left common iliac arteries and veins, the separation of the external and internal iliac arteries, and secondary branches were clearly depicted.

Motional phase artifacts in Fourier transform MRI

Most magnetic resonance imaging (MRI) techniques are subject to a "motional blurring" arising from the acquisition of data in the presence of a frequency-encoding gradient. The Fourier transform of the signal from a spin moving along a magnetic field gradient obeys an equation analogous to the free space Schrödinger equation. Computer simulations of the Bloch equations illustrate the implications of this motional blurring in MRI.

Flow-induced phase effects and compensation technique for slice-selective pulses

Flowing spins experience a time-varying frequency during the application of slice-selective radiofrequency (RF) pulses. As a result the flowing spins accumulate phase relative to stationary spins as the spins are rotated toward the transverse plane. Using finite difference techniques to solve the Bloch equations for flowing spins, the phase of the transverse magnetization after a slice-selective pulse was evaluated for varying flow velocities and for tip angles which ranged between 0 degrees and 180 degrees. The following results were obtained for constant slice thickness: (1) For a fixed tip angle, the phase varies nonlinearly with velocity. (2) For a fixed velocity, the phase varies nonlinearly with tip angle. For small tip angles the nonlinearity in the variation as a function of velocity is very small but increases for tip angles greater than 90 degrees and becomes especially severe near 180 degrees. A method is proposed to desensitize the phase of flowing spins during the application of slice-selective pulses. The compensation scheme depends upon tip angle but is virtually independent of flow velocity. The technique was tested and verified with clinical images.

A rotating phantom for the study of flow effects in MR imaging

A common type of phantom used for the study of flow effects in MR imaging is the tube phantom, where a liquid passes through a set of tubes placed in the main magnetic field of an MR scanner. Among the disadvantages with this type of phantom are that a distribution of velocities is present in each tube, and that quantifications of flow effects using tube phantoms may be very time-consuming. In this work, we describe the design and the properties of a rotating wheel flow phantom used for quantification of the effects of flow through the imaging plane as well as in the imaging plane. The proposed phantom is constructed as a rotating gel-filled wheel, surrounded by static volumes filled with the same gel, and the evaluation of the information from rotating and static parts is made with a specially designed computer program. The phantom can be used as a plug flow phantom covering simultaneously an interchangeable velocity interval, which at present has the range -52 mm/s, +52 mm/s. It is shown that the phantom gives adequate information on the dependence of pixel content on first-order motion in MR modulus and phase images. Among the fields of application are rapid calibration of MR imaging units for flow determination using phase information, as well as testing of pulse sequence characteristics and verification of theoretical predictions concerning the flow dependence in MR images.

A mathematical model for signal from spins flowing during the application of spin echo pulse sequences

Models are presented for both laminar and plug flow that predict the signal from spins flowing during the application of slice-selective spin echo pulse sequences. The models permit calculation of the total signal from a cylindrical vessel lying perpendicular to the slice and incorporate the effect of the physical displacement of the spins between successive excitations. This time-of-flight effect gives a signal which is composed of contributions from a finite number of spin populations, with each population signal weighted by the fractional volume of that spin population within the cylindrical vessel segment. The signal and fractional volume from each spin population are derived analytically for ten different spin echo pulse sequences. The models for plug and laminar flow have important application for predicting and interpreting flow effects observed in clinical images. They are shown to be useful for selecting pairs of pulse sequences that can be used to obtain digitally subtracted MR images which provide optimum contrast for flowing blood with essentially complete suppression of stationary anatomy. These models provide a means for quantitatively comparing the expected signal from flowing spins for the many techniques presently being investigated for MR angiography.