Transcript Relaxation times

Institute for Biomedical Engineering
EXCITE
Afternoon Hands-On MRI Sessions: fMRI & DTI
Institute for Biomedical Engineering
Contrast in MRI - Relevant Parameters
Relaxation times:

T1
Spin-lattice relaxation time (longitudinal relaxation time)
Return of spin system to equilibrium state

T2
Spin-spin relaxation time (transverse relaxation time)
Loss of phase coherence due to fluctuations of interacting
spins (‘phase memory time’)

T2*
Decay time of free induction decay
Signal loss due to magnetic field inhomogeneity (difference
in magnetic susceptibility)

ADC Apparent diffusion coefficient
Signal loss due to diffusion of water molecules in an
inhomogeneous magnetic field

k
water exchange rate
Exchange of water between macromolecule bound fraction and
bulk (free) water
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Relations and Limitations
Sensitivity:
Signal-to-Noise Ratio (SNR)
Spatial
resolution
Temporal
resolution
Signal: magnetization (number of spins, magnetic field strength, …. )
Noise: thermal noise of receiver system, physiological noise, …
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MRI Contrast
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Relaxation times
 MRI delivers good soft tissue contrast
 Tissue specific magnetic parameters for contrast
generation
 T2 / T2*: how fast is signal lost after excitation
 T1: how fast is magnetization gained back after excitation for next
experiments
 Sequence parameters and sequence type determine
contrast
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The NMR signal
+1.0
Mz
My
Mx
1-exp(-t/T1)
Relaxation
Mi(t)/Meq
Relaxation
0.0
exp(-t/T2*)
-1.0
0
0.5
time (s)
1.0
0
0.5
time (s)
1.0
0
0.5
time (s)
1.0
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T1 weighting
 Relevant parameters:
 Repetition time (TR) = time between two excitations
 Flip angle -> how much magnetization is left for next excitation
 Strong T1 weighting for large flip angle and short TR
Mz
MzA
θ
T1 Relaxation
during TR
MzB
Mxy
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T1 weighting: Example




Two metabolites with T1=500ms (blue) and T1=250ms (red)
Flip angle: 60°
Signal proportional to DMz
TR=3000ms
Mz
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Institute for Biomedical Engineering
T1 weighting: Example




Two metabolites with T1=500ms (blue) and T1=250ms (red)
Flip angle: 60°
Signal proportional to DMz
TR=300ms
Mz
time
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Institute for Biomedical Engineering
T1 weighting: Example




Two metabolites with T1=500ms (blue) and T1=250ms (red)
Flip angle: 60°
Signal proportional to DMz
TR=100ms
Mz
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Institute for Biomedical Engineering
T2 / T2* weighting
 Relevant parameter:
 Echo time (TE) = time between excitations and data acquisition
 Strong T2 weighting for long TE
Mxy
t / ms
TEshort TEmedium
TElong
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Proton density weighting
 Intensity scales with number of signal generating nuclei per
volume element
 Keep influence of relaxation times small:
 Short TE -> small effect of T2 / T2* on signal
 Long TR -> small effect of T1
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Functional MRI (fMRI)
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Functional MRI (fMRI)
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 Uses echo planar imaging (EPI) for fast
acquisition of T2*-weighted images.
 Spatial resolution:
 3 mm
 < 200 μm
(standard 1.5 T scanner)
(high-field systems)
EPI
(T2*)
 Sampling speed:
 1 slice: 50-100 ms
dropout
 Problems:
 distortion and signal dropouts in certain regions
 sensitive to head motion of subjects during scanning
 Requires spatial pre-processing and statistical
analysis.
T1
But what is it that makes T2*
weighted images “functional”?
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The BOLD contrast
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REST
neural activity   blood flow   oxyhemoglobin   T2*   MR signal
ACTIVITY
Source: Jorge Jovicich, fMRIB Brief Introduction to fMRI
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The temporal properties of the BOLD signal
 sometimes shows
initial undershoot
 peaks after 4-6
secs
 back to baseline
after approx. 30
secs
 can vary between
regions and
subjects
Peak
Brief
Stimulus
Undershoot
Initial
Undershoot
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MRI and Diffusion
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Brownian motion
 Molecules or atoms in fluids and gases move freely
 Collisions with other particles causes trembling movement
 Brownian motion: microscopic random walk of particles in
fluids of gases (R. Brown 1827)
 Brownian motion depends on thermal energy, particle
properties and fluid density
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Diffusion
 Diffusion: irreversible automatic mixing of fluids (or gases)
due to Brownian motion
 Root mean square displacement depends on diffusion
coefficient D and time t: r  2  D t
(A. Einstein)
 Diffusion coefficient D affected by cell membranes,
organelles, macromolecules (Le Bihan 1995)
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Anisotropy
 Restrictions on water diffusion usually without spherical
symmetry  anisotropic diffusion in biological tissue
 Diffusion tensor (=3x3-matrix) instead of diffusion
coefficient accounts for anisotropic diffusion in 3D
 Principal diffusion direction: direction with largest diffusion
coefficient
r1
r2
r3
Free Diffusion
Restricted Diffusion
ri  2  Di t , i  1, 2,3
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 Example: nerve fibre
 Diffusion perpendicular to fibre restricted
 Water diffusion indicates white matter organization
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Diffusion and MRI
 Diffusion leads to signal loss in MRI
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Diffusion gradients
 Signal attenuation depends on diffusion coefficient and
gradient waveforms
 GE: sum of diffusion weighting gradients zero
 SE: diffusion weighting gradients have equal area
 Single shot techniques freeze out physical motion
90°
diffusion
gradient
180° diffusion
gradient
TE
EPI readout
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Diffusion weighted imaging DWI
 b-value (=b-factor) describes diffusion weighting
analogous to TE in T2 weighted sequences
 b-value determined by diffusion weighting gradients (i.e.
gradient form, strength, distance)
signal
S  S0ebD
0 200 400 600 800 1000
b-factor
[s/mm2]
S0: signal without diffusion weighting;
D: diffusion coefficient in direction of gradient
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DTI
 Ellipsoid represents diffusion tensor
 Fibre structure via map of diffusion anisotropy: calculate
fractional anisotropy (or relative anisotropy or volume
ratio)
PS
MS
MP
S
ADC
l1
M
P
DWIs + Reference
l2
l3
3D
ellipsoid
FA
Colorcoded FA
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 Principal diffusion coefficient and vector: longest axis of
diffusion tensor
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 Brain structures via analysis of principle diffusion vectors
Pons
Medulla
Superior longitudinal
fasciculus
Corticospinal tract
Corpus callosum Tapetum
Middle cerebellar
peduncle
Medulla
Optic radiation
Superior cerebella
peduncle
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MR Angiography
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MR Angiography
Image
Slice
Image
Slice
Mz
imaging
saturation
Blood flow
Gradient echo imaging:
Don’t wait for gradient echo
 Bright signal from
unsaturated spins in slice
Saturation: apply 90°
slice-selective pulse
Stationary spins
Inflowing spins
time
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