dynamic mri imaging transport and structure in transient ... · pdf filefluid flows porous...

Andy Sederman

Department of Chemical Engineering and Biotechnology, Cambridge

Dynamic MRI – Imaging Transport and

Structure in Transient Systems

The current team

Sponsors

Johnson Matthey, ExxonMobil, Shell, BP, Schlumberger,

AstraZeneca, GlaxoSmithKline, Merck Sharp & Dohme, NPL

Overview

• Introduction to MRI (and Chemical Engineering)

• Fast velocity imaging of fluids – dynamic flows

turbulent liquid flows

two phase flows

• chemical shift separation with compressed sensing

do we need an image?

• Bayesian analysis of acquired data

• Pharmaceutical dissolution testing

• Conclusions

What is Chemical Engineering? – and why use MR?

chemical process

technologypharmaceutical industryoil industry

many different chemical species

chemical reaction

fluid flows

porous media

optically opaque

The application of physical and life sciences to understand and develop

processes and products

• Sample all of k and after FT we have a fully resolved image

k2

k-space raster

k1

image

FT

How to get a 2-D image with MRI: k-space

π2

γ tGk

rrkrk dS π2iexp)()(

krkkr dS π2iexp)()(

FT

rGr γ)(

Velocity imaging of flow in a pipe

• Steady flow up to Re ~ 2200

laminar Newtonian flow, parabolic velocity profile

• Onset of turbulence at higher Re

time varying flow

vdRe

0

10

20

30

40

50

60

70

-8 -4 0 4 8

ExperimentalAnalyticalV

elo

cit

y (

mm

s-1

)

Position (mm)

0.0 mm/s

10.0 mm/s

vz

y

x

Range of applicability

• Quantitative relationship between phase and displacement

measurement over wide range of velocities 10-6-102 m s-1

‘velocity’ over different timescales 10-3-101 s

Flow through single cell Flow over bluff body

van de Meent AJS, LFG et al.,

J. Fluid Mech, 642, 5 (2010)

MRI

Model

Newling et al., Phys. Rev.

Lett., 93(15), 154503 (2004)

• Many systems of practical interest demonstrate some

change with time

changing velocity

changing structure

• Imaging approaches to dynamic processes

time averaged

• image over long times compared to fluctuations

‘snapshot’ imaging

• speed up acquisitions

periodic systems

• triggered acquisitions

• How can MRI velocity imaging be used?

Dynamic processes

p/2 p p

d

D

Turbulent velocity imaging

ultra-fast velocity imaging sequence: GERVAIS

GERVAIS J Magn. Reson. 166 (2004) 182

Gradient Echo Rapid Velocity and Acceleration

Imaging Sequence

ky

k-space raster

kx

2D image time:

1 velocity component in 20 ms

3 velocity components in 60 ms

0 0

2vav 1.5vav

vz vzRe =1250

3300 4200 5000

1700 2500

x

y

z

Turbulent velocity imaging

Sederman et al., JMR, (2004)Pipe diameter: 29 mm, 1400 m × 700 m

Can we image even faster?

• We want to reduce timescales further

• 60 ms is still long for many systems

• Can we acquire all data points in a more efficient and

robust way?

faster images

minimise errors for high velocity flows

fast continuous image acquisition

• Do we need to acquire all of our k-space data points?

under-sampling – ‘sparse’ acquisition

non-FT reconstruction

Spiral imaging and compressed sensing

ky

k-space raster

kx


r.f.

Gread 1

Gread 2

Gslice

Gvel

a

time

d

D

ky

k-space raster

kx

• Benefits

‘simple’ MRI pulse sequence

faster coverage of k-space – for given hardware limitations

robustness to velocity effects

short recycle ‘movie’ acquisition


r.f.

Gread 1

Gread 2

Gslice

Gvel

a

time

d

D

ky

k-space raster

kx

Andrew BlakeMicrosoft Research/Alan Turing Institute

• Compressed sensing

if an image can be represented in some transform

domain by significantly fewer data points, it must be

possible to acquire fewer data points in the first place

Spiral and CS: results

• High resolution pipe flow velocity images at Re = 5000

acquire 28% cf fully sampled image

64 × 64 pixels, resolution of 325 m × 325 m

repetition time of 5.3 ms, 188 fps

0z-

vel

oci

ty (

cm s

-1)

47

CS-Spiral velocity imaging of single bubbles

velocity images of water around a rising air

bubble

• single component velocity images in 5.3

ms

• 3-component velocity images in 16 ms

(63 fps)

• spatial resolution 390 m × 586 m

• field-of-view: 20 mm × 30 mm

• vortex shedding at a rate of 12.6 ± 1.1 Hz

• droplet rise velocity = 21 cm s-1

-15

y-v

elo

city

(cm

s-1

)

15

26.7 cm s-1in-plane (x-z) velocity:

25 m

m

x

z

y

Tayler Phys. Rev. Lett. (2012)

-8.9 26.9z-velocity (cm s-1)

in-plane velocity: 14.4 cm s-1

x

y

z

x

z

Why do bubbles wobble?

Phys. Rev. Lett. 108 (2012) 264505

direction of

bubble motion

direction

of wake

ab

y

x

0 200 400 600 800-p

0

p

p/2

p/2

a ,

b

time (ms)

b

a

-8.9 26.9z-velocity (cm s-1)

in-plane velocity: 14.4 cm s-1

x

y

z

x

z

Why do bubbles wobble?

• in addition to the counter-rotating vortices in longitudinal plane, there

exists a secondary mode of vorticity in the horizontal plane

•direct coupling between direction of bubble path and secondary

vortex; secondary vortices reverse direction following every

shedding event

Can we extend this to liquid-liquid flows?

• Chemical shift differences between peaks in spectra

lead to extra signal dephaseing

chemical shift artefacts

• Similar proton densities

difficult to distinguish phases

ky

k-space raster

sparse spiral sampling

kx

ky

k-space raster

sparse perturbed spiral sampling

kx

Simultaneous measurement of oil and water flow fields50 cSt PDMS droplet rising through water

laboratory frame droplet framex

y

z

in-plane velocity7.2 cm s-1

droplet frame:

laboratory frame:

14.4 cm s-1

-14.4

14.4

z-velo

city (cm

s-1)

pipe diameter = 2 cm; droplet rise velocity = 7.1 cm s-1

data acquisition time = 31.8 ms

spatial resolution = 540 m 540 m; image slice thickness = 500 m

Tayler et al. Phys. Rev. E 89 (2014) 063009

Conventional

kx

ky

full sampling

Fourier

transform

Compressed

sensing

kx

sparse sampling

CS

reconstruction

increasing sparsity

faster acquisition

Why take an image? – A Bayesian approach

Conventional

kx

ky

full sampling

Fourier

transform

Bayesian

model +

Bayes’ theorem

kx

ky

selective sampling

pro

bab

ilit

y

size

increasing sparsity

faster acquisition

Compressed

sensing

kx

sparse sampling

CS

reconstruction


ky

kx

FT

10-10

10-9

10-8

10-7

10-6

-800 -400 0 400 800

sign

al

inte

nsi

ty (

a.u

.)

k (m-1

)

0

2 10-9

4 10-9

6 10-9

8 10-9

0 10 20 30 40

f(x)

x (mm)

10-10

10-9

10-8

10-7

10-6

-800 -400 0 400 800

sig

nal in

ten

sit

y (

a.u

.)

k (m-1

)

0

2 10-9

4 10-9

6 10-9

8 10-9

0 10 20 30 40

f(x)

x (mm)

FT

4 mm bubble16 mm bubble


0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3 4 5 6

pro

bab

ilit

y d

ensi

ty (

mm

-1)

diameter (mm)

optical

MR

Distribution I Distribution II

Bayesian bubble size measurement

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3 4 5 6

pro

bab

ilit

y d

ensi

ty (

mm

-1)

diameter (mm)

Optical techniques cannot

be used at high voidage

Distribution III

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3 4 5 6

pro

bab

ilit

y d

ensi

ty (

mm

-1)

diameter (mm)

optical

MR

comparison with optical measurements

Time resolved result

• Surfactants decrease the surface tension and, therefore, the bubble size

• Change in bubble size tracked in real time as a pulse of surfactant is

injected at the base of a bubble column

• Bubble size monitored every 3 s

air

pump

z

y water

overflow

0.0

0.2

0.4

0.6

0.8

0 200 400 600 800

rzrxsurfactant on?

voidage

r z,x (

mm

)

time (s)

0.0

0.1

0.2

0 200 400 600 800

void

age

time (s)

bubble size voidage

surfactant flow onsurfactant

solutionx

rx

rz

×

•

Summary

• MRI velocity imaging can be used to develop the

understanding of many dynamic processes

• More ‘intelligent’ data acquisition and reconstruction can

help to increase imaging speeds

image acquisition times as short as 5 ms

• Sometimes the important information can be obtained without

the need for an image

Bayesian analysis

dynamic mri imaging transport and structure in transient ... · pdf filefluid flows porous...

Documents