Analysis of imaging axes significance in motion artifact suppression technique (MAST): MRI of turbulent flow and motion

Recently, a new technique has been demonstrated which effectively refocusses the dephasing effects of spins moving during application of MR imaging gradients. This paper presents an analysis of imaging axes significance in spin dephasing for motion occurring along the slice select, read and phase-encoding directions. A flow phantom under constant flow conditions in all experiments was used to provide complete spin dephasing when "traditional" imaging gradients were used. The MAST technique was used to refocus along various combinations of imaging axes, and variable number of terms from the Taylor expansion of motion along them. Results indicate that motion along any imaging axis can be refocussed effectively when MAST gradients are used along only the slice select and read axis.     

Rapid spectroscopic velocity quantification using periodically oscillating gradients

In this work two spectroscopic methods are described which allow rapid flow velocity quantification in the presence of a parabolic velocity distribution. This method requires only a single excitation and is based on flow encoding by periodically oscillating gradients. In the shown spin echo variant additional refocusing pulses correct for field inhomogeneities. A theoretical model is introduced, which describes the course of the derived spectra even in high flow region, where a significant part of the encoded spins leaves the sensitive area of the coil during data acquisition (outflow-effect). It was demonstrated that both methods can quantify flow velocities within the velocity range of 1mm/s up to 36 cm/s in the presence of a parabolic flow velocity distribution. The maximum velocity of the parabolic distribution is indicated in this method by a peak in the acquired spectrum from which the velocity could be quantified. Flow velocity quantification by periodically oscillating gradients seems a reasonable and fast alternative to established imaging techniques.     

CSF flow artifact reduction using cardiac cycle ordered phase-encoding method

The flow effects appear as a change of phase as well as signal intensity in NMR imaging. Since the flow of blood and CSF (cerebrospinal fluid) is pulsatile due to the heart pumping, their velocities are not constant during NMR imaging. This type of velocity fluctuation such as the blood or CSF flow induces irregular flow-dependent phase shifts, which have been one of the main causes of flow artifacts in NMR imaging. In order to reduce the flow artifacts, especially the CSF flow artifacts, a new cardiac cycle ordered phase encoding method is proposed and has been studied. This proposed technique utilizes the cardiac cycle as a precursor for the phase encoding gradients similar to the ROPE (respiratory ordered phase encoding) technique which has been used for respiratory motion artifact reduction. The basic concept and its applications are discussed together with the experimental results obtained with human volunteers using the KAIS 2.0 2.0 T whole-body NMR imaging system.     

Measurement of pulsatile flow using MRI and a Bayesian technique of probability analysis

This work shows that complete spatial information of periodic pulsatile fluid flows can be rapidly obtained by Bayesian probability analysis of flow encoded magnetic resonance imaging data. These data were acquired as a set of two-dimensional images (complete two-dimensional sampling of k-space or reciprocal position space) but with a sparse (six point) and nonuniform sampling of q-space or reciprocal displacement space. This approach enables more precise calculation of fluid velocity to be achieved than by conventional two q-sample phase encoding of velocities, without the significant time disadvantage associated with the complete flow measurement required for Fourier velocity imaging. For experimental comparison with the Bayesian analysis applied to nonuniformly sampled q-space data, a Fourier velocity imaging technique was used with one-dimensional spatial encoding within a selected slice and a uniform sampling of q-space using 64 values of the pulsed gradients to encode fluid flow. Because the pulsatile flows were axially symmetric within the resolution of the experiment, the radial variation of fluid velocity, in the direction of the pulsed gradients, was reconstructed from one-dimensional spatial projections of the velocity by exploiting the central slice theorem. Data were analysed for internal consistency using linearised flow theories. The results show that nonuniform q-space sampling followed by Bayesian probability analysis is at least as accurate as the combined uniform q-space sampling with Fourier velocity imaging and projection reconstruction method. Both techniques give smaller errors than a two-point sampling of q-space (the conventional flow encoding experiment).     

Synchronized EPI phase contrast velocimetry in a mixing reactor

Notwithstanding its widespread use in cardiovascular and functional MRI studies, Echo Planar Imaging (EPI) has only recently been subjected to systematic validation studies. Most velocity measurement studies employing such ultrafast MRI methods involve the use of phantoms characterized by rigid or deformable solid motion. The current implementation involves a rotating phantom (angular velocity up to 10.5 rpm) with a superimposed swirling liquid flow (with axial velocities ranging between 0.145 and 0.27 cm/s) of water doped with copper sulfate. The standard implementation of single-shot EPI with phase contrast velocity encoding allows the complete mapping of the Eulerian velocity field in slices perpendicular to the rotation axis following a subtractive procedure requiring the synchronized acquisition of each velocity component on each selected transverse slice during two revolutions of the rotor. The image acquisition time is 100 ms (per velocity component) at each 64 x 64 slice. In addition to acquiring full-field velocity data for future direct comparisons with other techniques, EPI is employed here for the first time to reconstruct the three-dimensional flow field between the blades of a partitioned pipe mixer.     

A single-scan method for measuring flow along an arbitrary direction

In this article, we demonstrate a single-scan method to measure an average flow velocity vector along an arbitrary direction. This method is based on the MMME sequence and utilizes static and pulsed magnetic field gradients along multiple directions for the optimal determination of flow velocity components in three-dimensional space. Experimentally measured average flow velocities from the flow induced phase shift with a single-scan MMME sequence show excellent agreements with the known flow rate, and the signal decay of each echo due to a velocity distribution is also quantitatively verified with known laminar flow patterns.     

Concomitant magnetic field gradients and their effects on imaging at low magnetic field strengths

Low-field NMR imaging systems which use large amplitude field gradient pulses (e.g., in flow velocity encoding) may be subject to the undesirable effects of concomitant gradients. We demonstrate the effects of these extra gradients, which arise from Maxwell's equations, and show that the resultant image phase shifts and amplitude changes are consistent with theory.     

Altered Phase Interactions between Spontaneous Blood Pressure and Flow Fluctuations in Type 2 Diabetes Mellitus: Nonlinear Assessment of Cerebral Autoregulation

Cerebral autoregulation is an important mechanism that involves dilatation and constriction in arterioles to maintain relatively stable cerebral blood flow in response to changes of systemic blood pressure. Traditional assessments of autoregulation focus on the changes of cerebral blood flow velocity in response to large blood pressure fluctuations induced by interventions. This approach is not feasible for patients with impaired autoregulation or cardiovascular regulation. Here we propose a newly developed technique—the multimodal pressure-flow (MMPF) analysis, which assesses autoregulation by quantifying nonlinear phase interactions between spontaneous oscillations in blood pressure and flow velocity during resting conditions. We show that cerebral autoregulation in healthy subjects can be characterized by specific phase shifts between spontaneous blood pressure and flow velocity oscillations, and the phase shifts are significantly reduced in diabetic subjects. Smaller phase shifts between oscillations in the two variables indicate more passive dependence of blood flow velocity on blood pressure, thus suggesting impaired cerebral autoregulation. Moreover, the reduction of the phase shifts in diabetes is observed not only in previously-recognized effective region of cerebral autoregulation (<0.1 Hz), but also over the higher frequency range from ∼0.1 to 0.4 Hz. These findings indicate that type 2 diabetes mellitus alters cerebral blood flow regulation over a wide frequency range and that this alteration can be reliably assessed from spontaneous oscillations in blood pressure and blood flow velocity during resting conditions. We also show that the MMPF method has better performance than traditional approaches based on Fourier transform, and is more suitable for the quantification of nonlinear phase interactions between nonstationary biological signals such as blood pressure and blood flow.     

Velocity encoding and velocity compensation for multi-spoke RF excitation

PurposeTo investigate velocity encoded and velocity compensated variants of multi-spoke RF pulses that can be used for flip-angle homogenization at ultra-high fields (UHF). Attention is paid to the velocity encoding for each individual spoke pulse and to displacement artifacts that arise in Fourier transform imaging in the presence of flow.Theory and methodsA gradient waveform design for multi-spoke excitation providing an algorithm for minimal TE was proposed that allows two different encodings. Such schemes were compared to an encoding approach that applies an established scheme to multi-spoke excitations. The impact on image quality and quantitative velocity maps was evaluated in phantoms using single- and two-spoke excitations. Additional validation measurements were obtained in-vivo at 7 T.ResultsPhantom experiments showed that keeping the first gradient moment constant for all k-space lines eliminates any displacements in phase-encoding and slice-selection direction for all spoke pulses but leads to artifacts for non-zero velocity components along readout direction. Introducing variable but well-defined first gradient moments in the phase-encoding direction creates displacements along the velocity vector and thus minimizes velocity-induced geometrical distortions. Phase-resolved mean volume flow in the ascending and descending aorta obtained from two-spoke excitation showed excellent agreement with single-spoke excitation over the cardiac cycle (mean difference 0.8 ± 16.2 ml/s).ConclusionsThe use of single- and multi-spoke RF pulses for flow quantification at 7 T with controlled displacement artifacts has been successfully demonstrated. The presented techniques form the basis for correct velocity quantification and compensation not only for conventional but also for multi-spoke RF pulses allowing in-plane B₁⁺ homogenization using parallel transmission at UHF.     

Flow encoded NMR spectroscopy for quantification of metabolite flow in intact plants

An NMR flow quantification technique applicable to metabolite flow in plants is presented. It combines flow sensitive magnetization preparation with slice selective spectroscopy. Flow encoded NMR spectroscopy is described to quantify, for the first time, flow velocities of metabolites in plants non-invasively. Flow sensitivity is introduced by magnetization preparation based on a stimulated echo experiment, prior to slice selective spectroscopy. For flow quantification eight different flow-weighted spectra are collected. With this flow preparation very slow flow velocities down to 0.1mm/s can be detected and small amounts of flowing metabolites can be observed despite the large background signal of stationary and flowing water. Important sequence optimization steps include appropriate choice of experimental parameters used for flow encoding as well as complete balancing of eddy currents from the flow encoding gradients. The method was validated in phantom experiments and applied in vivo. Examples of quantitative flow measurements of water and metabolites in phantoms and plants are provided to demonstrate the reliability and the performance of flow encoded spectroscopy.     

Self-gated Fourier velocity encoding

Self-gating is investigated to improve the velocity resolution of real-time Fourier velocity encoding measurements in the absence of a reliable electrocardiogram waveform (e.g., fetal magnetic resonance or severe arrhythmia). Real-time flow data are acquired using interleaved k-space trajectories which share a common path near the origin of k-space. These common data provide a rapid self-gating signal that can be used to combine the interleaved data. The combined interleaves cover a greater area of k-space than a single real-time acquisition, thereby providing higher velocity resolution for a given aliasing velocity and temporal resolution. For example, this approach provided velocity spectra with a temporal resolution of 19 ms and velocity resolution of 22 cm/s over an 818 cm/s field-of-view. The method was validated experimentally using a computer-controlled pulsatile flow apparatus and applied in vivo to measure aortic-valve flow in a healthy volunteer.     

Velocity and diffusion imaging in dynamic NMR microscopy

The imposition of resolution gradients in a pulsed-gradient spin-echo (PGSE) NMR sequence induces motionally dependent phase and amplitude modulation in the image, a technique which we have termed dynamic NMR microscopy. Fourier analysis of this modulation gives a dynamic displacement profile for each pixel which can then be analyzed to obtain velocity and diffusion maps. The application of this method at high spatial resolution is motivated by a desire to measure vascular flow in living plants and variations in molecular self-diffusion under the influence of velocity shear in narrow capillaries. The theory of dynamic NMR microscopy is presented and potential artifacts discussed, including the effect of slice selection gradients, PGSE gradient nonuniformity, and specific problems associated with the measurement of self-diffusion in the presence of velocity gradients. It is demonstrated that a double-echo PGSE pulse sequence can be used to restore coherent phase shifts associated with steady-state flow, and examples of self-diffusion maps and signed velocity maps from sequences of phase-encoded images obtained by projection reconstruction are given. This method has been applied at 20,um transverse resolution in laminar capillary flow.     

A method for MR quantification of flow velocities in blood and CSF using interleaved gradient-echo pulse sequences

The aim of this study was to establish a rapid method for in vivo quantification of a large range of flow velocities using phase information. A basic gradient-echo sequence was constructed, in which flow was encoded along the slice selection direction by variation of the amplitude of a bipolar gradient without changes in sequence timings. The influence of field inhomogeneities and eddy currents was studied in a 1.5 T scanner. From the basic sequence, interleaved sequences for calibration and in vivo flow determination were constructed, and flow information was obtained by pairwise subtraction of velocity-encoded from velocity non-encoded phase images. Calibration was performed in a nongated mode using flow phantoms, and the results were compared with theoretically calculated encoding efficiencies. In vivo flow was studied in healthy volunteers in three different areas using cardiac gating; central blood flow in the great thoracic vessels, peripheral blood flow in the popliteal vessels, and flow of cerebrospinal fluid (CSF) in the cerebral aqueduct. The results show good agreement with results obtained with other techniques. The proposed method for flow determination was shown to be rapid and flexible, and we thus conclude that it seems well suited for routine clinical MR examinations.     

Instantaneous velocity measurement of dynamic deformation by digital holographic interferometry

A novel method for the instantaneous velocity measurement of dynamic deformation by digital holographic interferometry is proposed. During dynamic deformation, a series of digital holograms is recorded by a high-speed camera. At each pixel of the phase difference maps, phase and amplitude information are combined as complex phasor (CP). Each pixel can be then considered as an independent sensor and a sequence of complex phasors of such a sensor is analyzed by short time Fourier transform (STFT) along the time axis. A fast iterative algorithm is developed for the computation of instantaneous velocity. The displacement of each pixel can also be obtained by integration of the instantaneous velocity over time and phase unwrapping process is thus avoided. The performance of the proposed CP method is compared experimentally with the commonly used digital phase subtraction method.     

Quantification of complex flow using MR phase imaging--a study of parameters influencing the phase/velocity relation.

In this study, we describe how motion-induced phase angle is affected by different flow models and imaging parameters when using the MR flow phase mapping technique. In a phantom with straight as well as constricted tubes, simulating healthy and stenotic vessels, nonpulsatile flow in the velocity range 0-1 m/sec was maintained. The phase/velocity relation was studied for various degrees of complex flow caused by the constriction, and regions with a breakdown in linearity were determined. Further studies in these regions were made regarding the influence of pulse sequence parameters on the phase/velocity relation. The results showed that in poststenotic areas characterized by so-called separated flow, the phase/velocity relation became nonlinear due to dephasing effects. In regions with fully developed turbulent flow in straight tubes, however, no breakdown in linearity was observed. Parameters seen to have a substantial influence on the phase/velocity relation were first- and second-order velocity encoding and voxel size. Finally, a pilot in vivo demonstration of complex flow was done using a sequence designed to be robust with respect to linearity of the phase/velocity relation. The results indicate that the MR phase mapping technique can be used to measure flow quantitatively in regions with complex flow. This opens possibilities for future clinical use of the technique in the study of areas of complex flow such as valvular heart disease.     

Application of k- and q-space encoding NMR techniques on granular media in a 3D model fluidized bed reactor

A combination of PFG-NMR imaging and velocity encoding methods was applied to investigate the dynamic behavior of a bed of poppy seeds subjected to air flow, representing a model setup for fluidized bed reactors. The particle motion is described both from a statistical point of view, by determining propagators and dispersion coefficients representing an average over the whole bed volume, as well as combined with spatial resolution by generating velocity maps. Velocity images of different horizontal slices in the bed confirm the notion of a toroidal particle flow pattern inside the shallow granular bed. Despite the need of considerable averaging due to the random motion of the relatively few particles in the bed, quantitative velocity images and statistical information about the random particle motion can be obtained from monitoring the fluid component in the seeds by conventional spin-echo techniques.     

Conduction-electron drift velocity measurement via electron spin resonance

In analogy with NMR, motion induced phase shift of pulsed ESR signals enables in principle the direct detection of electron drift velocity or electronic current, respectively. Overcoming the difficulties with additional magnetic field gradients induced by the current itself, we succeeded in demonstrating the detection of electron flow via ESR. Measuring the electron drift velocity in the organic conductor (fluoranthene)2PF6 the microscopic Ohmic law could be observed in a current range of more than +/-0.25 A.     

Behavior of the Melt in the Vertical Bridgman Method with a Low Axial Temperature Gradient

The thermal conditions for the growth of Ge crystals with a diameter of 50 mm by the vertical Bridgman method in the case of low thermal-gravitational convection are studied using model experiments. Distilled water being hydrodynamically similar to the Ge melt is used as the model liquid. When modelling by means of the light cut method, it is established that mixture particles move along the heat flow direction from top to bottom. It is shown that an axial temperature gradient of 2 K/cm or more increases the contribution of thermal diffusion to mass transfer at a vertical flow rate of 0.09 mm/s or more. The numerical simulation of thermal convection in the Oberbeck–Boussinesq approximation confirms the absence of convection under the given thermal conditions. However, the deviation of the container axis from the vertical by 0.5° during the process of crystal growth contributes to the increase in the flow rates in the liquid phase up to 0.55 mm/s.     

In vitro experiments on ICOSA6 4D flow MRI measurement for the quantification of velocity and turbulence parameters

PurposeTo perform comprehensive in vitro experiments using six-directional icosahedral flow encoding (ICOSA6) 4D flow magnetic resonance imaging (MRI) under various scan conditions to analyze the robustness of velocity and turbulence quantification.Materials and methodsIn vitro flow phantoms with steady flow rates of 10 and 20 L/min were scanned using both conventional 4D flow MRI and ICOSA6. Experiments focused on comparisons between ICOSA6 and conventional four point (4P) methods, and the effects of contrast agents, velocity encoding range (Venc), and scan direction on velocity and turbulence quantification.ResultsThe results demonstrated that 1) ICOSA6 improves the velocity-to-noise ratio (VNR) of velocity estimation by 33% (on average) and results in similar turbulent kinetic energy (TKE) estimation as the 4P method. 2) Measurements with a contrast agent resulted in more than a 2.5 fold increase in average VNR. However, the improvement of total TKE quantification was not obvious. 3) TKE estimation was less affected by Venc and the scan direction, whereas turbulence production (TP) estimation was largely affected by these measurement conditions. The effects of Venc and scan direction accounted for less than 11.63% of TKE estimation, but up to 33.89% of TP estimation.ConclusionThe ICOSA6 scheme is compatible with conventional 4D flow MRI for velocity and TKE measurement. Contrast agents are effective at increasing VNR, but not signal-to-noise ratio for TKE quantification. The effects of Venc and scan direction influence total TP more than total TKE.