Magnetic Resonance Elastography

27.05.2013

Dario Bashir-Elahi

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From Palpation to Magnetic Resonance Elastography

Breast MRE-Images revealing a tumor. [1]

MRI: MRE:

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Dynamic MRE

[2][2]

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Elasticity

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Hooke's law

=E dudx

=E LL

Hooke's law:

Local Hooke's law:

u = Displacement, du/dx := strain( )

u r 1 u r 2 u r 3 u r 4

[3]

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Strain and Stress

=G =K VV

=−E

bb

Transverse contraction

Compression Shear

Torsion

2 elastic parameters sufficient for full description!

[5] [5][4]]

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Elasticity

Generalize Hookes law to 3D:

ji=F iA j

ij=12duidx j

du jdx i

=2G Tr

Stress tensor:

Strain tensor:

2 Material Paramaters:G = shear modulus,λ = Lamé constant

→ Hooke's law:

( )

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▽ x v=0

→ longitudinal (=compression) waves

▽w=0

→ transversal (=shear) waves

v− 1c l2̈v=0 w− 1

c s2̈w=0

c l2=2G c s=G

2 separate waves u=v+w:

Mechanical waves

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Mechanical waves in soft tissue

● Usually:

Density: kg/L

Velocities: m/s ( )

Concentrate on shear wave!

● Parameters obtained from wave equation:

● Parameters of interest:

≈1c s≪cL≈1500 G≪

G=cs2

G ,

E ,G =¿ .≈3GG 2 G

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MRE

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Create harmonic (shear) wave

r=r0 u0 cos k r0− t

Generating the displacement pattern

Position of dm:

[7]

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Phase image

S k =∫d 3r m r eir e ik r

mr e ir =F−1[ S ] r

arg ( ) = me i

Encode quantity into !

S k =∫d 3r mr ei k rMRI-Signal:

Introduce phase factor:

Fouriertransform:

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The motion encoding gradient

Add Motion encoding gradient „MEG“:

r =∫0Tdt Gt ⋅r

[8]

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Motion Encoding

Time delay

MEG:

Wave:

G= G0 cos t

r=r0 u0 cos t−k r0

r =∫0NTdt Gt ⋅r0

r = NT2

G u0cos −k r0

NT

∝uElinminate via measurement with :−G0

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A simple phase image

2s2=cs

2=G

Frequency = 250 Hz

1

2

3

[2]

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Reconstructed Elastogram

Local Frequency Estimation „LFE“

[2] [2]

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Viscoelasticity

Elasticity

= f

Viscosity

= f ̇

Viscoelasticity

Dispersion :

Attenuation :

G, λ → G(ω), λ(ω)

G, λ → G=G'+iG'', λ=λ'+iλ''{ e i k r− t=ei k ' r−t er

...

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(Dis-)Advantages of MRE

● Based on MRI → High resolution Expensive Cumbersome Slow (US-Elastography → Real-Time-Imaging)

● No restriction to field of view (USE → acoustic window)

● Lower depth limitation (Sound only for excitation not read-out)

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Applications

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Liver fibrosis● Excessive creation of tissue

● Impaired liver functionality● Can lead to cirrhosis – potentialy fatal● Reversible● Nearly invisible to usual Imaging● Raises tissue stiffness

● Aims of imaging:● (Early) detection● Check on treatment progress

Best results : MRE

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Liver fibrosis II

Healthy liver

Cirrhoticliver

MRI Wave image Elastogram

[9]

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Brain MRE

Elastic properties (in vivo) largely uncertain.Cranium blocks out Ultrasound.

MRE:Test for correlation: stiffness change – Alzheimer/Multiple sclerosis/...Results:G → possible decrease with ageG → strong decrease with AD / MS

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Brain elasticity and aging

Distribution of springpot parameter μ based on age. [10]

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Further Applications

Identifying Breast cancer:Detectable by common imaging techniquesMRE : verify findings

Skeletal muscle:Tissue stiffness dependant on contraction stateMRE: Reveal/characterize muscular diseaseComplication: Loss of isotropy.

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MRE: Breast cancer

Breast MRE-Images revealing a tumor. [1]

MRI: MRE:

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Thank you for your attention!

Questions?

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Sources• Brandt, Dahmen: Mechanik. Springer-Verlag Berlin 2005 4.Auflage

• [7] R. Muthupillai et al (1996): Magnetic resonance imaging of transverse acoustic strain waves. Magn Reson Med, 36: 266–274

• R. Muthupillai et al: Magnetic resonance elastography by direct visualization of propagating acoustic strain waves. Science 269, 1854-1857

• K J Parker et al (2011): Imaging the elastic properties of tissue: the 20 year perspective Phys. Med. Biol. 56 R1

• [9] Mariappan, Y. K., Glaser, K. J. and Ehman, R. L. (2010), Magnetic resonance elastography: A review. Clin. Anat., 23: 497–511

• A. Manduca et al(2001):Magnetic resonance elastography: non-invasive mapping of tissue elasticity. Med. Image Anal. 5: 237-254

• [1] Glaser, K. J., Manduca, A. and Ehman, R. L. (2012), Review of MR elastography applications and recent developments. J. Magn. Reson. Imaging, 36: 757–774

• I. Sack et al (2008): Assessment of liver viscoelasticity using multifrequency MR elastography. Magn Reson Med, 60: 373–379

• [8] Dieter Klatt et al (2007): Phys. Med. Biol. 52 7281• [10] Sack I, Streitberger K-J, Krefting D, Paul F, Braun J (2011) The Influence of

Physiological Aging and Atrophy on Brain Viscoelastic Properties in Humans. PLoS ONE 6(9): e23451

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Futher image sources• [2] Raja Muthupillai, R. L. Ehman (1996) : Magnetic resonance elastography

Nature Medicine 2, 601 - 603

• [3] http://mb-s1.upb.de/home/Faculties.IV.IPW.LTM.Projekte.E-MechLAB/Wiki-Areal/Bilder/thermische_dehnung1.jpg

• [4] http://www.tf.uni-kiel.de/matwis/amat/mw1_ge/kap_7/illustr/g_und_k.gif• [5] http://www.ipf.uni-stuttgart.de/lehre/online-skript/deformierbar/deform.gif• [6] http://kilby.sac.on.ca/faculty/akowalts/old-images/eqwaves.gif

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MRE in numbers

MRE = „Extension“ to MRI

Elastogram Resolution : ~ 1/4 of MRI-Resolution

rises with frequency νDisplacement Sensitivity: ~ 100 nm

Frequency range:

Vibration

Accessible 10 - 1000 Hz Usual < 200 Hz

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Time propagation

r ∝cos k r

Propagate wavemap via time-delay of G(t) contained in .