Journal of Magnetic Resonance 229 (2013) 2–11

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Journal of Magnetic Resonance

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Recent advances in Flow MRI

Lynn F. Gladden ⇑, Andrew J. SedermanUniversity of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, UK

a r t i c l e i n f o a b s t r a c t

Article history:Received 2 November 2012Available online 29 November 2012

Keywords:FlowVelocityFlow MRIMulti-phase flowTurbulence

1090-7807/$ - see front matter � 2013 Published byhttp://dx.doi.org/10.1016/j.jmr.2012.11.022

⇑ Corresponding author.E-mail address: lfg1@cam.ac.uk (L.F. Gladden).

The past five years have seen exciting new developments in Flow MRI. Two-dimensional images are nowroutinely acquired in 100–200 ms and, in some cases, acquisition times of 5–10 ms are possible. This hasbeen achieved not only by advances in the implementation of existing pulse sequences but also in dataacquisition strategies, such as Compressed Sensing and Bayesian approaches, and technical advices inparallel imaging and signal enhancement methods. In particular, the short imaging timescales that arenow achieved offer significant opportunities in the study of transient flow phenomena.

� 2013 Published by Elsevier Inc.

1. Introduction

Magnetic resonance (MR) techniques are well-established astools for measuring flows in medical and non-medical systems.Here, we will consider applications of Flow MRI to non-medicalsystems and, in particular, applications in science and engineeringwhere the intrinsic ability of MR to probe non-invasively, opticallyopaque, multi-component systems provides insights which, inmany cases, cannot be provided by other (i.e., non-MR) techniques.The application of Flow MRI to systems of interest to physical sci-entists and engineers has been limited by typical imaging times oforder minutes. Since the system under study is required to be at‘steady state’ during image acquisition, such image acquisitiontimes mean that Flow MRI has not been able to address flowingsystems which change rapidly with time. It follows that a primarymotivation for much of the research in the field of Flow MRI hasbeen directed towards rapid data acquisition over a range of flowvelocities, with the requirement that the data remain quantitative.This requirement is important if Flow MRI data are to be of value innon-medical applications where they are often used in the contextof developing theoretical models and numerical simulation codesof fluid flows.

In the following article recent advances are presented undertwo headings: (i) imaging pulse sequences, and (ii) new methodol-ogies, the latter including new data acquisition strategies andimage reconstruction methods which are employing concepts frominformation theory, hardware developments and briefly touchingon the opportunities offered by signal enhancement techniques.Of course, in practice all of these developments can be brought

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together as required to optimise the data acquisition for a specificapplication. We then consider how these advances are being usedin different applications with a particular focus on achievements inthe fast imaging of flows.

2. Principles of Flow MRI

The principles of Flow MRI are explained in detail by Callaghan[1,2]. At the simplest level, Flow MRI is a straightforward combina-tion of an imaging sequence with an MR flow measurement suchthat the resulting image or spatially-resolved profile comprisesan array of pixels, each pixel being encoded with a measure ofmolecular displacement over the timescale of the MR flow encod-ing timescale. Of course, the way the two elements are selectedand combined is essential to producing a quantitative measure ofthe particular characteristic of fluid flow that is desired.

As is well known the signal, S(k), acquired in the MRIexperiment is written:

SðkÞ ¼ZZZ

qðrÞ exp i2pk � r½ �dr ð1Þ

where q(r), is the spatial distribution of the nuclear spin density;i.e., the image. We use the standard k-space notation introducedby Mansfield [3] and hence k is defined as

k ¼ cGt2p

ð2Þ

where G is the applied magnetic field gradient employed to give thespatially resolved measurement; c is the gyromagnetic ratio and t isthe time for which the gradient G is applied. Fourier transformationof Eq. (1) gives

L.F. Gladden, A.J. Sederman / Journal of Magnetic Resonance 229 (2013) 2–11 3

qðrÞ ¼ZZZ

SðkÞ exp½�i2pk � r�dk: ð3Þ

It therefore follows that the Fourier transform of M � N k-spacedata points will produce an image, q(r), of dimensions M � N. Inconventional imaging, all M � N data points in k-space must be ac-quired to produce a fully resolved real-space image.

There have been a number of reviews on the use of MRI as a toolto study flow and translational motion in non-medical researchareas [2,4–6]. Translational motion in MR can be measured bytime-of-flight (TOF) [7,8] and phase shift methods. We will restrictourselves to consideration of phase-shift or phase-contrast dis-placement measurement and will not, to any great extent, considermeasurements of diffusion; (i.e. Pulsed Field Gradient (PFG), orPulsed Gradient Spin Echo (PGSE) NMR). The dynamic range ofphase-shift velocity imaging can be adjusted from just a fewlm s�1 up to 10–100 m s�1. It is limited at lower velocities to dis-placements due to self diffusion and at higher velocities to resi-dence time in the coil. The principle of phase-shift velocityimaging is understood by considering the effects of the appliedgradient G(t) on the phase, /(t), of moving spins. If the spatial loca-tion of the spin is time dependent, r(t), and the frequency of pre-cession is given by xðrÞ ¼ cðB0 þ G � rÞ then, in the rotatingframe, the phase shift /(t) will be given by

/ðtÞ ¼ cZ t

0GðtÞrðtÞdt: ð4Þ

If the time-dependent position of the given set of spins is expandedas:

rðtÞ ¼ r0 þ v0t þ 12

a0t2 þ . . . ; ð5Þ

then the time-dependent phase accrued by the spins will be:

/ðtÞ ¼ c r0

Z t

0GðtÞdtþ v0

Z t

0tGðtÞdtþ 1

2a0

Z t

0t2GðtÞdtþ . . .

� �: ð6Þ

The integrals are the successive moments (M0, M1, M2, . . .) ofthe magnetic field gradient such that the zeroth moment, M0,causes a phase shift proportional to position r0; the first moment,M1, a phase shift proportional to velocity v0, and so on. Thus by

π/2 π (a)

r.f.

Greadread

Gphase

τe

G

e

slice

δ

gtime

Δ

TR

Fig. 1. (a) A schematic of a simple spin echo Flow MRI pulse sequence. Several timescaletime for velocity measurement, D, the spatial encoding time, se and the repetition timSchematic representation of the k-space raster.

designing an appropriate gradient waveform, such as a bipolar pairor equivalently a pair of gradients of same polarity either side of ap pulse, the resulting phase will have a zero M0 but a non-zero M1;i.e., the phase will be proportional to velocity but be independentof position (assuming higher order motion effects are negligible).The velocity is then calculated as:

v ¼ /cM1

ð7Þ

where v and M1 are the velocity and moment in a single direction.Experimentally this is often done with two values of M1 and a veloc-ity is calculated from the difference in phase.

A simple velocity-imaging pulse sequence is shown in Fig. 1which illustrates that there are several significant timescales in avelocity-imaging pulse sequence. The time for velocity measure-ment, D; the spatial encoding time, se; and the repetition time,TR, along with the number of repeated cycles that are acquired,all influence the image acquisition time. As D, se and TR are variedso does the applicability of a pulse sequence to a specific system ofinterest. If the entire image can be acquired in a time much shorterthan the change in the velocity of the system under study then theimage can be considered a ‘snapshot’. It is important to note that ifthe velocity encode and spatial encode occur at different times, thevelocity measurement corresponds not to the position where it isspatially encoded but to where it was velocity encoded.

3. Imaging pulse sequences

The nature of the imaging sequence used is determined by thenature of the system to be studied (e.g., its magnetic heterogeneity,T2; T

�2, etc.). Here we will consider imaging sequences increasingly

used to image flowing systems in non-medical MRI; namely, EPI,spiral, RARE, FLASH, and SPI (and SPRITE). Table 1 summarisesthe relative strengths and weaknesses of each with regard to theirimplementation in Flow MRI studies, and compares them to thesimple spin-echo Flow MRI measurement shown in Fig. 1.

EPI (Echo Planar Imaging) and spiral techniques offer the fastestimage acquisition times but are not suitable (i.e. robust) for appli-cation to all systems, especially where there are spatial or temporal

kphase

nts

kreadpoi

N

M points

(b)

s which must be considered when imaging transient flows are shown including thee, TR. d Is the timescale over which the flow encoding gradients are applied. (b)

Table 1Comparison of pulse sequences in their application to velocity imaging. Timescales and spatial resolutions are approximate and will be system-dependent. Approximate guides:spatial resolution – high (<50 lm), moderate (50–500 lm), low (>500 lm). T2 – long (>0.5 s), moderate (20–500 ms), short (2–20 ms), very short (<2 ms). T�2 – long (>50 ms),moderate (5–50 ms), short (0.5–5 ms), very short (<0.5 ms).

Pulse sequence Time to acquirevelocity image

Velocity measured Comments

Single spin echo 1–100 min Up to 5 m s�1 Slow acquisition but applicable to most relaxation times. Suitable for shortT2 and short T�2. Acquisition time decreases as T1 decreases. High spatialresolution possible. Too slow to capture transient behaviour.

EPI 20–100 ms 1–100 cm s�1 Applicable to transient systems characterised by long T�2 (sE 10–100 ms).Less sensitive to gradient imperfections than spiral sequences.

Spiral 3–25 ms Up to 5 m s�1 Can probe systems with shorter T�2 than EPI (since sE 3–25 ms). Possibilityof small tip angle excitation and rapid image frame rate. More compleximage reconstruction than EPI.

RARE 2–10 s Up to 10 cm s�1 Higher spatial resolution achieved than with EPI and spiral. Appropriate forstudying slowly changing systems. Requires long T2 but can cope with quiteshort T�2 (sE = 50–500 ms). Usually too slow to capture transient behaviour.

FLASH >150 ms 50 cm s�1 Best for short T1 (<50 ms) to achieve rapid recycle, short T2; moderatelyshort T�2. Low SNR leads to low-moderate spatial resolution. Very robust.Usually too slow to capture transient behaviour.

SPI (SPRITE) Seconds to hours (time-averaged) 0.5–50 m s�1 Suitable for very short T�2. Too slow to capture transient behaviour.

4 L.F. Gladden, A.J. Sederman / Journal of Magnetic Resonance 229 (2013) 2–11

fluctuations in B0. In particular, it is worth highlighting the oppor-tunities for using spiral trajectory sampling schemes, considered asa sub-set of under-sampling schemes, which can be employed ifthe requirement for rectilinear sampling (and constant gradients/gradient switching that result from this) is removed. Clearly ifthe number of points sampled in k-space is reduced, then the asso-ciated image acquisition times are also reduced. Spiral samplingwas first demonstrated by Ahn et al. [9]; a typical pulse sequenceis shown in Fig. 2. Among its advantages are a circularly symmetricT�2 weighting and an oscillating gradient waveform without anydiscontinuities. In addition, the two principal advantages for mea-suring flows (and multiphase flows, in particular) are the efficientcovering of k-space and a reduced propensity to motion artifacts.Shorter readout times than for rectilinear EPI make it more appli-cable to samples with magnetic distortion and, since imaging timesare reduced, transient processes characterised by shorter-time-scale velocity fluctuations can be imaged. Additionally, spiral imag-ing samples all four quadrants of k-space in an interleaved fashion,which acts to compensate for the accumulation of image phase dueto motion [10]. Spiral Flow MRI has only recently been demon-strated in non-medical applications [11]. Many different spiral tra-jectories can be constructed, from a simple Archimedean spiral tovariable density and sparse spirals which may be used to optimizegradient parameters or minimize imaging times.

Where EPI and spiral schemes are not appropriate RARE, FLASH,SPI and SPRITE become the imaging techniques of choice for spe-cific flow systems. The RARE (Rapid Acquisition with RelaxationEnhancement) technique [12] acquires a whole two-dimensional(2D) image from a single excitation and records successive linesof k-space by refocusing magnetization. Unlike EPI, the refocusingis done by the application of a radio-frequency (r.f.) pulse to refo-cus the spin echo (or stimulated echo) for each line in k-space, andtherefore RARE acquisitions are much more robust to off-reso-nance effects and local field heterogeneities than EPI. Typical imag-ing times for a 128 � 128 image are 350 ms but flow imaging withRARE usually requires 4 excitations, separated by TR and so imag-ing times are typically�5 s. Two recent applications of RARE veloc-ity imaging are those of Amar et al. [13] and Shiko et al. [14]. Theformer addresses the imaging of flow fields inside a liquid dropletand will be discussed in more detail later. The latter reports single-shot 2D velocity images acquired at 390 lm � 390 lm spatial res-olution acquired every 5.2 s to study the evolution of the flow fieldaround a pharmaceutical tablet as it dissolves in a flow-throughdissolution test cell.

FLASH (Fast Low Angle SHot) [15] is a gradient echo imagingsequence based on the recall of only a small amount of the

longitudinal magnetization, with r.f. excitation angles of typically5–10�. This small tip angle comes at the price of lower signal-to-noise ratio (SNR) but because the magnetization is freshly excitedit is a more robust sequence than either EPI or RARE. In the case ofFLASH, velocity encoding can be implemented either before theimaging sequence or after each excitation [16]. Despite the lowSNR of this technique, it provides a very useful tool because of itsrobustness, particularly for low-resolution imaging where SNR isless likely to be a problem. FLASH velocity imaging has been rela-tively little used in non-medical Flow MR but a good example isthat of Reyes et al. [17], who have used a FLASH variant to measuregas–liquid flow in a horizontal pipe. FLASH has, of course, beenused directly as a fast imaging protocol to record ‘movies’ of flow-ing systems by tracking moving interfaces in two-phase flows; anexample of the latter in application to the study of gas–solid fluid-ised beds has been reported by Müller et al. [18].

Finally we note SPI (Single-Point Imaging) and its variantSPRITE (Single-Point Ramped Imaging with T1 Enhancement).These acquire only a single point of k-space from each excitationpulse. It follows that SPI is unlikely to be used where ultimatetime resolution is required but it is an extremely robust technique– similar to FLASH but with artifacts caused by dephasing duringthe read gradient also removed – particularly suited to multi-phasesystems characterised by large magnetic field gradients. It is alsocapable of measuring extremely high velocities as the velocityand spatial encoding are done simultaneously and D is primarilylimited by the gradient switching time. Measurements of velocitiesas fast as 50 m s�1 have been reported [19] using this techniqueand it is usually coil residence time or image blurring that placesthe limit on the velocities that can be measured. Similarly to RAREand FLASH, the velocity encoding can be done as a precursor to theimaging sequence or after each excitation. It is this second variantthat is of interest when measuring high velocity flows.

4. New methodologies

In addition to advances in the implementation of the aforemen-tioned pulse sequences, there are also advances being made inother areas of MR and metrology in general which are being dem-onstrated to decrease data acquisition times and open up newapplications amenable to study by MR. These are not particularto velocity imaging as distinct to conventional imaging. All of themare now being employed in Flow MRI both by themselves or incombination with one another and, in some applications, havethe potential to transform the use of Flow MRI in non-medical

(a) α

r.f.

Gread1

Gread2 Δ

Gsliceδ

g

kread2

kread1

(b)

time

Fig. 2. (a) Schematic of the pulse sequence used for spiral velocity imaging and (b) the corresponding k-space trajectory used for spiral imaging.

L.F. Gladden, A.J. Sederman / Journal of Magnetic Resonance 229 (2013) 2–11 5

applications. In particular, we consider Compressed Sensing,Bayesian MR, parallel imaging and signal enhancement techniques.

Compressed Sensing extends the concepts of data compressionto the acquisition of signals. The logic behind Compressed Sensingis straightforward – if it is possible to compress an image, say, intoa dataset comprising far fewer data points, then it should be possi-ble to acquire fewer data points in the first instance. Simply fromthe perspective of data acquisition times, we see immediately thatthis makes it possible to acquire data at a faster rate given thatfewer data points are required for each image frame. Hollandet al. [20] reported a method for reducing the data acquisitiontimes in phase-encoded velocity imaging using Compressed Sens-ing. In that work it was shown that when sampling only 30% ofthe full k-space data, it was possible to recover an image of fluidflow through a packed bed with a relative error of 11%. Such reduc-tion in acquisition times can also be exploited in acquiring imagesat higher spatial resolution which, in turn, increase the accuracy ofthe measurements by reducing errors arising from partial volumeeffects. Fig. 3 shows a comparison of velocity maps for SF6 flowingthrough a packed bed of 5 mm diameter spheres using a conven-tional full k-space acquisition and a Compressed Sensing recon-struction where only 33% (28 points in the phase-encodingdirection) of k-space was sampled. The acquisition time for bothimages was the same. This example shows that Compressed Sens-ing reconstruction allows images at high spatial resolution to beacquired without reduction in SNR in the final image. Pines andco-workers have use Compressed Sensing in combination with re-motely detected MRI techniques to study flow and mixing inmicrofluidics devices [21,22].

Bayesian MR approaches extend the concept of under-samplingyet further and no longer even require the acquisition of an image

velocity(a) (b)(mm s-1)

263

mm 175

mm

mm

27

27

88

00

8827 mm27 mm -88

Fig. 3. Implementation of Compressed Sensing with Flow MRI. Images of thevelocity distribution for SF6 flow through a packed bed of 5 mm diameter spheres.(a) Velocity image obtained with a fully-sampled k-space data set and recon-structed using a conventional Fourier transform. The resolution is460 lm � 460 lm � 1.5 mm. (b) Velocity image reconstructed using CompressedSensing at a resolution of 350 lm � 350 lm � 1.5 mm. The acquisition time forboth (a) and (b) was 19 min. The flow rate of SF6 was (15 ± 1) � 10�6 m3 s�1. TheCompressed Sensing reconstruction allows images at higher spatial resolution to beacquired with no loss of SNR.

from which data of interest are obtained. The recent example wehighlight here addresses two-phase gas–liquid bubbly flow inwhich we seek information on the characteristics of the gas-bubblesize distribution [23]. The conventional approach to studying thissystem would be to acquire an image of the flow and determinethe bubble size from a number of images. However, this cannotbe done for gas–liquid systems of industrial interest because ofthe rapid temporal variations in the flow field, high shear ratesand short nuclear spin relaxation times. The basic principle ofthe Bayesian approach is that either through an analytical ap-proach or by numerical simulation, the k-space ‘signatures’ of bub-ble-size distributions defined by specific statistical parameters areobtained (the likelihood function). k-space data acquired on thereal system are then compared with the k-space ‘signatures’employing a statistical analysis to identify which of these predictedk-space responses best matches the experimental data. Central tothe Bayesian approach is that we need to articulate the questionto which we need to know the answer. In the present example,we do not wish to now the spatial distribution of bubbles, we re-quire the bubble-size distribution only. All that is required in theexperiment is that the bubble-size distributions remains constantduring the timescale the measurement – the measurement is ro-bust to the spatial position of bubbles. For this specific system ofa gas–liquid bubbly flow, not only can we now study a flowing sys-tem that could not have been studied by conventional MRI but alsowe can obtain a measurement of gas bubble size from as few as 40k-space measurements as opposed to the 256 � 256 data arraythat would have been required to produce an image of sufficientresolution to identify and size individual bubbles.

Parallel imaging strategies also speed up image acquisition (or,of course, improve SNR) but this time by using multiple receivecoils, the signal from which is combined to reconstruct the image.Parallel reconstruction algorithms can be divided into two maingroups. Those that reconstruct the overall image from the imagesproduced by each coil, e.g. SENSE, and those that reconstruct inFourier space from the frequency signals of each coil, e.g. GRAPPA.The ‘acceleration factor’ is limited by the number of receive coilsand the geometry but can increase image speeds by over an orderof magnitude. Parallel imaging methods are now used widely inmedical MRI but have yet to make significant impact in non-med-ical applications. Hennig and co-workers have been at the forefrontof research in this field; a recent example of their work being theoptimization of parallel imaging for Dynamic Phase Contrast (PC)MRI with multidirectional velocity encoding which employed theGRAPPA approach [24]. With the recent independent develop-ments in Compressed Sensing and parallel imaging exciting oppor-tunities are opening up in combining the two approaches; a recentreport being that of Hsiao et al. [25].

Finally, we note the potential of signal enhancement tech-niques. There is much interest in employing parahydrogen-in-duced polarization (PHIP) [26], proton-electron double resonance

6 L.F. Gladden, A.J. Sederman / Journal of Magnetic Resonance 229 (2013) 2–11

imaging (PEDRI) [27] and dissolution dynamic nuclear polarization[28] to increase MRI signal. Lingwood and co-workers [29] have re-cently employed Overhauser dynamic nuclear polarization to am-plify the signal of water flowing through a cylindrical expansion.It was shown that the transient path of the water shortly afterinjection was more effectively captured using the DNP prepolar-ised water than by using conventional phase shift velocity imagingof thermally polarised water. A quite different approach to signalenhancement is that of remote detection MRI pioneered by Pinesand co-workers [30]. In combination with Compressed Sensing thishas been shown to give signal enhancements of order 106 for imag-ing microchannel flows [21,22].

We will now consider some of the more recent non-medicalapplications of these approaches emphasizing the nature of theinformation obtained from the various measurements. Necessarilyin a short review of this nature there are many more excellentexamples that could have been included. However, the examplesdiscussed are selected to give an overview of the diverse natureof the systems studied and the information that can be obtainedusing current Flow MRI techniques.

5. Single-phase flows

In single-phase flow, significant interest focuses on unsteadystate flows and the transition to turbulence. The substantial break-through in this area was that of Kose [31] who was the first to ap-ply EPI to turbulent flows. Sederman et al. [32] then extended thatwork so that a series of velocity images could be acquired from asingle excitation pulse with the phase of the signal measured ineach image being dependent only on the velocity in the directionof the velocity gradient immediately preceding the image and onthe phase measured in the previous image. It is therefore possibleto measure 3 orthogonal components of the velocity field from asingle excitation or the same component in a repeated fashion tomeasure velocity fluctuations or acceleration. Fig. 4 shows velocityimages at a range of Reynolds numbers up to 5000. Elkins and co-workers (e.g., [33]) have reported time-averaged imaging of turbu-lent flows in a number of geometries such as heat exchangers andaerofoils, but the use of velocity encoded SPRITE [19] has enabledthe highest velocities to be imaged. In this paper, time-averaged

Re =1250

3300 4200

1700

Fig. 4. Three orthogonal component velocity images of pipe flow (i.d. 29 mm) acquired a(f) 5000. The colour scale identifies the magnitude of the z-velocity, and ranges from zerofor d–f. The flow velocity in the plane of the image (i.e. x–y) is shown by the vectors on eet al. [32] reproduced by permission of Elsevier.)

velocity imaging of turbulent gas flow over a bluff body and aroundan aerofoil was measured and compared to CFD modelling, asshown in Fig. 5. This technique can image highly turbulent flows(Reynolds number up to 150,000 for the aerofoil) and velocitiesup to 50 m s�1.

Unsteady flows of a different nature are those which are associ-ated with some form of periodic behaviour. In these applicationsgated acquisitions are employed so that signal averaging is per-formed over acquisitions recorded at the same point in successivecycles. Two recent examples are those of Shiko et al. [34] and Valla-tos et al. [35]. Shiko et al. used this approach to study the flow fieldin USP 4 dissolution test cells which are used widely in the phar-maceutical industry for in vitro testing of the dissolution behaviourof controlled release pharmaceutical delivery systems. Such testcells are operated with a peristaltic pump which gives a pulsatileflow; hence the need to gate the image acquisition thereby avoid-ing artefacts in the final image. This work showed that even whenoperating such devices within the guidelines, a given delivery sys-tem would be exposed to significantly different flow fields andhence shear stresses at its surface, thereby giving rise to varyingdissolution behaviour depending on the precise test cell configura-tion used. Vallatos et al. used synchronized acquisitions to charac-terise stationary and translating vortex flow in a Couette cell.

MR has also been used to investigate transient flow phenomenain complex fluids such as wormlike micelle systems. These systemsare known to exhibit a range of interesting transient flow phenom-ena such as shear banding and have been studied extensively byCallaghan and co-workers [e.g., 36,37]. The ability to image rapidlyalso allows us to look at the rheology of complex fluids under un-steady-state conditions. Davies et al. [38] extended the GERVAISsequence to record velocity profiles recorded over millisecondtimescales through a wide-gap Couette Rheo NMR cell. A variabledelay time between a control signal to initiate a transition in flowand the start of the measurement sequence allowed investigationof the transient evolution of the velocity field following a stepchange in rotation rate. The transient rheological response wascompared between a shear banding micellar solution of cetylpyrid-iniumchloride/sodium salicylate in brine and a low molecularweight polydimethylsiloxane (PDMS) oil. In the case of the micellarsolution, an elastic shear wave was sent to propagate across the

0 0

2vav 1.5vav

vz vz

5000

2500

x

y

z

t increasing Reynolds number of (a) 1250, (b) 1700, (c) 2500, (d) 3300, (e) 4200, andto twice the average velocity for a–c and from zero to 1.5 times the average velocityach image. The vector scale bar on each image corresponds to 1 cm s�1. (Sederman

Fig. 5. SPRITE velocity imaging. The images are sensitized to the component of fluidvelocity from left to right. (a) SPRITE MRI velocity image (b) computational fluiddynamics (CFD) map for a velocity inlet condition of uniform mean velocity17 m s�1. (Newling et al. [19] reproduced by permission of the American PhysicalSociety.)

L.F. Gladden, A.J. Sederman / Journal of Magnetic Resonance 229 (2013) 2–11 7

cell following commencement of shear stress while an oscillatory‘recoil’ was observed following cessation of shear stress. In contrastthe PDMS oil exhibited a purely viscous response as expected foran incompressible Newtonian fluid. This technique clearly haspotential applications across a wide range of transient rheologicalinvestigations, particularly with respect to optically opaquematerials.

6. Two-phase flows

Current Flow MRI studies of two-phase flows fall into threemain themes of gas–liquid flows in reactor environments; liquid–liquid and gas–liquid bubbly flows, and gas–solid (or granular)flows.

Over the past decade there has been a considerable amount ofwork addressing gas–liquid flows in packed-beds of particles, oftenreferred to as fixed-bed or trickle-bed reactors and commonly usedin the chemical industry. These are cylindrical columns packedwith particles of a few mm diameter in which gas and liquid areflowed through the bed at relatively low flow rates for which thegas and liquid distribution is stable with time. To date the majorityof reports have focused on imaging the liquid distribution and li-quid flow velocity within the beds. However, the long-term moti-vation for much of this work is to use Flow MRI data to aid thedevelopment and implementation of numerical simulations ofthese two-phase flows. To do this not only do we need to be ableto image both the gas and liquid velocities but, ideally, we wishto image both flow fields at the same spatial resolution so that

we can study the adjacent gas–liquid velocities across an interfaceto help identify closure relationships that can then be used in sim-ulations. Figs. 6 and 7 show the quality of data that can be achievedfor these systems [39]. In Fig. 6, the flow field through a packing of5 mm spheres contained within a 4 cm diameter column is shown.3D visualisation of the vx, vy and vz components was achieved at aspatial resolution of 266 lm in each of the x, y and z directions.Fig. 7 shows both the gas and liquid velocity fields in a similarbed. 19F imaging is used to image a gas flow of SF6 within thebed. However, whilst the spatial resolution of the liquid velocityimage is 177 lm, that of the gas velocity image is 708 lm. In morerecent work both gas and liquid velocity fields have been acquiredat a spatial resolution of �240 lm, Compressed Sensing Flow MRIhaving been used to increase the spatial resolution at which thegas velocity image could be acquired.

An area of particular current interest is that of two-phase gas–liquid and liquid–liquid systems in which bubbles exist within acontinuous phase. The work that initiated interest in this areawas that of Han et al. [40] who measured the internal recirculatingvelocity field in a falling water drop where the drop was falling at2 m s�1 and the residence time in the coil was only 10 ms. Signal-averaging over many drops was achieved by triggering the pulsesequence when a drop broke a light beam above the imaging sec-tion. Data from 33,800 water drops were acquired in a total of 10 hto complete a 3D image of ‘the’ drop. Two more recent examples,are those of Amar et al. [41], using a RARE-based approach, andTayler et al. [42], using an EPI-based approach. Both works imple-ment ‘single-shot’ variants of the respective pulse sequences. Wewill consider first the RARE-based approach which is known bythe acronym FLow Imaging Employing Single-Shot ENcoding (FLI-ESSEN). FLIESSEN introduces a velocity encode pair for each phaseencode step. Because of the careful cancellation of motion artifacts,it was shown to be suitable for imaging high velocity flows. FLIES-SEN provides an extremely elegant measurement of the internaldynamics of toluene droplets levitating in a counterflow of waterduring mass transfer of acetone from the water phase into the dropin the presence of surface-active impurities. Fig. 8 shows velocitymaps measured within a 32 mL toluene drop levitated in waterwith 2.8% of acetone initially in the water phase for 0, 4 and15 min. The approach was used to image the impact of even smallconcentrations of acetone on accumulation of surfactants at thesurface of the drop. It is worth noting that, because of the inclusionof the extra gradients, the echo time and overall acquisition timerestricts image acquisition times to typically 1–2 s and wouldtherefore not be a technique of choice for highly transient flows.Tayler et al. [42] employed a straightforward extension of theEPI-based sequence GERVAIS to implement a ‘snap-shot’ techniquewhich acquired both reference and velocity encoded phase imagesfollowing a single excitation; 3-component velocity vector imageswere generated in under 125 ms. The technique was applied to im-age the velocity field within a droplet of decane as it moved up-ward through a column of water. Fig. 9 shows images of theinternal flow field within two decane droplets. In this examplethe decane oil droplets were of approximate diameter 10 mmand were rising within a 12 mm diameter column. Spatial resolu-tion in the 2D images was 117 lm � 234 lm.

More recently, Gladden and co-workers have employed a rangeof MR methods to measure different characteristics of gas–liquidbubbly flows. Three papers in particular have addressed the ul-tra-fast imaging of flow fields around gas bubbles rising througha liquid-filled (water) column. The first of these papers [43] consid-ered in detail the artifacts associated with the application of spiralimaging to produced time-resolved velocity measurements in un-steady state systems. In particular, this work showed that spiralimaging, in contrast to EPI, was robust to the accrual of velocityproportionate phase during imaging. Application of spiral imaging

speed (mm s−1)

0 40 16080 120160 mm s−1

yx

z

Fig. 6. 3D visualization of the vx, vy, vz components of the liquid flow field during trickle flow. The gas and liquid superficial velocities are 52.4 mm s�1 and 2.3 mm s�1

respectively. The field-of-view was 34 mm � 34 mm � 68 mm, giving an isotropic voxel resolution of 266 lm. The bed was operated at atmospheric pressure. Packingelements are shown as grey; the gas is not shown (transparent). The liquid filled regions of the bed are identified as light blue. The flow vectors identify the direction andmagnitude of the flow. For clarity, the magnitude is also colour-coded according to the colour scale shown. (For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)

yy

x

i l l it [ 1]gas axial velocity [mm s−1]

96−48 0 48 9648liquid axial velocity [mm s−1]

0 48liquid axial velocity [mm s 1]

264231231− 0

Fig. 7. Gas and liquid velocity map of SF6 (red/yellow) and water (blue/green)during trickle flow. The gas and liquid superficial velocities were 8.7 mm s�1 and2.3 mm s�1 respectively. The bed was operated at a pressure of 4.7 bara. (Forinterpretation of the references to colour in this figure legend, the reader is referredto the web version of this article.)

100

0

Fig. 8. Velocity maps measured using FLIESSEN for a 32 mL toluene drop levitatedin water with 2.8% of acetone initially in the water phase for time 0 (left), 4(middle), and 15 min (right). The velocity scale is in mm s�1. (Amar et al. [41]Reproduced by permission of Wiley-Blackwell.)

8 L.F. Gladden, A.J. Sederman / Journal of Magnetic Resonance 229 (2013) 2–11

to unsteady state flow in a pipe (Reynolds number, Re = 500–12,000; equivalent to superficial velocities of 3.1–75.0 cm s�1)was reported. Images were acquired at a rate of 91 frames per sec-ond (fps) with an in-plane spatial resolution of 313 lm � 313 lm.Comparison of acquisitions made with the spiral sampling protocoland the approach of GERVAIS-EPI also allows us to compare mea-surements made in the Eulerian and Largragian frames respec-

tively. A second application of the spiral velocity imaging to gas–liquid bubbly flow was also reported in which bubble rise couldbe tracked in ‘real time’ along with the z-component of the liquidvelocity around the rising bubble. 2D longitudinal velocity imageswere acquired at a rate of 55 fps, with an in-plane spatial resolu-tion of 390 lm � 586 lm. This work was extended in applicationto study bubbly flows at gas voidages as high as 41% [44]. Fromthese images, two measurements of bubble size were obtained(one on the basis of volume and the other on the basis of projectedradius), which allowed the quantification of both the bubble-sizedistribution and bubble shape – and hence interfacial surface area.By acquiring these data at different vertical positions along theheight of the column it was possible to track bubble size and shapeduring bubble rise. More recently, Compressed Sensing has beencombined with spiral imaging to acquire 2D velocity maps at a rateof 188 frames per second [45]. Fig. 10 shows velocity maps for theliquid flow field around air bubbles rising through stagnant water.The bubbles are of spherically equivalent radius 1.4 mm and thepipe diameter is 16 mm. Flow vectors are measured in the x, yand z directions with a spatial resolution of 390 lm � 586 lm fora field of view of 20 mm � 30 mm. Complete 2D maps of the 3 flowvectors are acquired at a rate of 63 fps. In Fig. 10 distinct featuresare observed in the flow such as potential flow about the bubblenose and periodic vortex shedding in the bubble wake, which

11.27.8 9.5

axial velocity (cm s-1)

4.4 cm s-1transverse velocity:

(a) (b)

Fig. 9. (a) Schematic of system highlighting the plane being imaged. (b) Single shotGERVAIS images of the internal flow field of two droplets of decane captured as thedrops rose through a column of distilled water. Note that the signal from the waterin these images has been suppressed.

15 9 ms 31 8 ms0 ms 15.9 ms 31.8 ms0 ms

63 6 ms 79 5 ms47 7 ms 63.6 ms 79.5 ms47.7 ms

z

x 14 714 7xy 14.7-14.7

l it ( -1)y

y-velocity (cm s-1)26 7 1i l l i 26.7 cm s-1in-plane velocity:

15 9 ms 31 8 ms0 ms 15.9 ms 31.8 ms0 ms

63 6 ms 79 5 ms47 7 ms 63.6 ms 79.5 ms47.7 ms

z

x 14 714 7xy 14.7-14.7

l it ( -1)y

y-velocity (cm s-1)26 7 1i l l i 26.7 cm s-1in-plane velocity:

Fig. 10. Velocity maps about a single bubble rising freely through stagnant solution.The location of the bubble was identified from the signal intensity maps, and ishighlighted by the filled white ellipses. The acquisition rate was 63 fps. The spatialresolution is 390 lm � 586 lm for a field of view of 20 mm � 30 mm.

(b) direction of(a) 0 mswakeyy

αβ αβx

direction ofbubble motion

15.9 ms

(c)π α

2π/2

0

βy0α

,

−π/2x

i l l it 14 4 1

π/2β

zin-plane velocity: 14.4 cm s-1

-π-8.9 26.9

z velocity (cm s-1)0 200 400 600 800

time (ms)- time (ms)

Fig. 11. (a) Example velocity maps recorded immediately under a static bubble ofspherically equivalent radius 1.4 mm. These data were acquired at a rate of 63 fps,and at a spatial resolution of 390 lm � 390 lm for a field of view of20 mm � 20 mm. (b) Schematic of the transverse plane wake structure orientationas a function of time. (c) The changing direction of bubble motion and secondarywake orientation as a function of time. The antiphase nature of the bubble motionand the wake orientation are consistent with the transverse wake vorticity beingdirectly coupled with bubble secondary motions.

L.F. Gladden, A.J. Sederman / Journal of Magnetic Resonance 229 (2013) 2–11 9

was seen to occur at rate of 12.6 ± 1.1 Hz. To enable the observa-tion of several complete cycles of the bubble wake dynamics,experiments were performed on a bubble held within the imagingcoil against a downward flow. Fig. 11 shows velocity fields in thehorizontal plane behind this static bubble. Transverse vorticesare seen to circle about local minima in the axial velocity, suggest-ing a coupling between the primary and secondary vorticity inbubble wakes. The orientation of the path and secondary wake rel-ative to the bubble centroid are defined in Fig. 11b, and the mannerin which these orientations change are juxtaposed in Fig. 11c. The

orientation of the bubble and wake are antiphase, which reflectsthat the direction of bubble motion consistently changes to opposethe direction of core wake flow. The wake direction changes fol-lowing each vortex shedding event (every 80 ms), therefore drivingthe realignment of the bubble path. Whilst this particular study fo-cused on the behaviour of single bubbles, initial data were also re-ported showing that this approach may enable us to explore howlarge-scale vortex chains are generated by the wake behaviour ofindividual bubbles in a swarm of bubbles. The SPRITE techniquehas also been used to measure average gas–liquid distributionsand average velocities in horizontal bubbly flows [46]. The veryshort encoding times used by SPRITE make it an ideal techniquefor studying such dynamic systems with moving interfaces.Although only 2D depth-averaged images were acquired, theextension to 3D acquisition is trivial if the flow characteristicsand flow rates remain constant for the imaging period.

Finally, on this topic of gas–liquid bubbly flow, Holland et al.[23] have applied Bayesian MR to characterize bubble-size distri-butions for swarms of bubbles rising within a column of stagnantwater. Even given the developments made using spiral and Com-pressed Sensing spiral approaches, it remains impossible to acquire2D images of fast moving bubbly-flows at high gas voidage. In par-ticular, the fastest image acquisition times are too slow to avoidtemporal blurring, and as mentioned earlier, MR measurementscannot be implemented successfully because of the high shearrates and short relaxation times characterising these systems. Inthe example reported in [23], bubble-size distributions were mea-sured for systems in which the gas voidage was in the range 2–15%.For a low gas voidage of 2%, the Bayesian MR measurements werecompared with optical measurements of bubble size, and werefound to be in excellent agreement. At the upper limit, the gas bub-ble size could not be measured using optical techniques.

Finally we consider gas–solid flows. Most of these studies haveemployed Flow MRI to study gas–solid systems of relevance to flu-idized beds, another type of reactor commonly employed in thechemical industry. However, more fundamental studies have been

10 L.F. Gladden, A.J. Sederman / Journal of Magnetic Resonance 229 (2013) 2–11

reported, including the works of Fukushima and co-workers [e.g.,47] on the flow of granular media in horizontal rotating cylinders.Further, Huntley and co-workers [48] have used Flow MRI to try tounderstand the fundamentals of granular dynamics in a simplevibrating fluidized bed. In this work a gated acquisition was usedto measure the spatial distribution and the velocity distributionassociated with particles in a bed vibrating at 31–50 Hz. The posi-tion and velocity of the particles was tracked as a function of thephase of the vibration. These data were then used for comparisonwith a time-varying 1D hydrodynamic model using the experimen-tal parameters as input to the simulation code; this led to a newexplanation being developed for the characteristics of the granulartemperature in these systems.

Finally, considering gas–solid fluidized beds, reports of gas andsolids motion in these systems were reported as long ago as 2002[49,50]. Since then much of this work has focused on measuringvoidage distributions and tracking bubble and slug rise in thesegranular systems using MRI [e.g., 51]. In particular, the theme ofusing Flow MRI to validate and develop numerical simulationcodes, as discussed earlier for gas–liquid flows in trickle-bed reac-tors, is of much current interest. An example is found in the workof Müller et al. [52] who imaged the velocity fields of solids in agas–solid fluidized bed from which the spatially-resolved granulartemperature was obtained. These data were used to study the ef-fect of simulation parameters such as the coefficient of restitutionand drag-force correlation employed on the ability of the simula-tion to predict the velocity distributions determined by Flow MRI.

7. Summary

The last 5 years has seen advances in Flow MRI which will havea significant impact on how MR will be used to study flowing sys-tems. Flow rates from microns per second through to meters persecond can now be measured, and timescales of measurementare just a few milliseconds. Indeed, the data acquisition rates thatcan be achieved are, for some systems, now competitive with thoseachieved by laser-based velocimetry methods. Of course, Flow MRIhas the added advantage that it can be used in optically opaquesystems. As expertise in pulse sequence implementation for study-ing flowing systems increases alongside advances in hardware anddata acquisition and signal processing protocols we can expect tosee exciting new applications of MR to flowing systems. The big-gest impact is likely to be in the field of multi-phase flows whichare notoriously difficult to study using non-MR techniques andwhich are of immense interest and importance throughout scienceand engineering.

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