magnetic resonance imaging - ntnufolk.ntnu.no/audunfor/7. semester/[email protected] 2 why...
TRANSCRIPT
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Magnetic Resonance Imaging
Pål Erik Goa Associate Professor in Medical Imaging
Dept. of Physics [email protected]
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Why MRI?
• X-ray/CT: – Great for bone structures and high spatial resolution – Not so great for soft tissue.
• Ultrasound: – Great for real-time imaging, quick and easily available. – Not so great in terms of spatial resolution, and for imaging behind
bones/air. • Magnetic Resonance Imaging:
– Great for soft tissue, in particular brain! – Not so great for bones and close to metal implants – Spatial resolution ~1 mm.
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MRI: Main components
• Requires a large magnet to put the patient in (expensive and potentially dangerous).
• The signal is coming from the hydrogen nucleus (proton) -> water (fat).
• Radio frequency antennas (coils) are used for transmitting and receiving the signal.
• Additional coils for generating gradients in the magnetic field needed for spatial localization/coding.
• Signal is acquired in Fourier-space.
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The Magnet
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A closer look
• Magnet coils: – Superconducting wire at 4.2 K creating a strong magnetic field
(typically 1.5-3.0 T) • Shim coils:
– Fine adjustment of magnetic field • Gradient coils:
– Resistive wire creating linear gradients in the magnetic field – used for spatial encoding
• RF-coils: – Signal transmission and reception – Individually designed for different body regions
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Rf-coils
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Operator room
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Technical room
Cooling pump Gradient amplifiers
Control electronics
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Rf shielding
• To avoid artefacts in images, the magnet-room must be shielded from all electromagnetic radiation.
• Walls, floor and roof is covered by copper plates.
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MRI = Contrast Versatility
• Image contrast can be controlled and changed depending on acquisition parameters.
• Basic Image contrasts: – Relaxation times (T1, T2, T2*) – Water content (proton density)
• Image contrast can also be made sensitive to: – Diffusion, temperature, flow, oxygen content
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MR-physics: Warning
• MRI is based on the precession of the magnetic moment in protons (usually called spin).
• Is often explained using a combination of quantum physics and classical equations of motion.
• A simplified quantum picture is used to explain: – Thermal equilibrium distribution – Resonance condition
• Classical equations of motion are used to explain the rest. • Beware that the simplified quantum picture is insufficient to describe
MRI, because it does not deal with the phase of the magnetic moments.
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Proton spin
• Atomic nuclei with odd number of nuclear particles have a physical property called spin.
• Since nuclei also have electric charge, the spin gives rise to a magnetic moment.
• The simplest atomic nucleus is the hydrogen proton.
• Hydrogen is everywhere in the body through water.
• All ordinary MRI is based on the hydrogen nucleus (proton) H+ in the water molecule.
• All the properties described in the following relate to the proton spins.
S
H+
N
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Magnetic Moment
• Each spin is like a small compass needle: • The strength of this needle is called the magnetic
moment and is determined by the gyromagnetic ratio γ .
• γ is a physical constant and is different for different nuclei.
• Proton: γ = 2.68 108 rad/s/Tesla (γ = 42.58 MHz/Tesla)
S
H+
N
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Energy Levels
• If we put the spin in a magnetic field B0, two possible energy states exists (quantization):
1. Up. 2. Down.
• More energy is needed for the Down state compared to the Up state.
• Energy difference involved is given by the socalled Larmor frequency ω0:
B0
E
ΔE !E = hf = !!0!0 = "B0
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Resonance
• Whenever a spin moves between the two energy states, energy is absorbed or released:
• The energy is released as an electromagnetic wave at the
Larmor frequency:
• @1.5 T: 63.87 MHz
E
ΔE ΔE
!E = hf0 = !!0!0 = "B0
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Boltzmann distribution • Gives the probability of finding an individual spin in
one of the two possible energy states, given the thermal energy available:
• P+ = Probability of Spin Up. • P- = Probability of Spin Down. • ΔE = hf. • k = Boltzmanns constant ( 1.381 10-23 J/K) • T = Temperature (Kelvin).
P+ P! = exp "E kT( )
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Equilibrium state • The Boltzmann-distribution describes the equilibrium state:
– If left to itself, nature will relax towards this state. • Example:
– B0 = 3.0 Tesla. – T = 37 oCelcius. – P+/P- = 1.0000198. – If you have 200000 spins, 100001 will be in the Up state,
99999 in the Down state! – But: Water contains 6.7 1022 protons per ml
(67000000000000000000000). • The fraction is low, but the total number is high.
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Magnetization at equilibrium • The net magnetic moment from all
the individual spins is called the magnetization M.
• Zero magnetic field: – Arbitrary orientation of spins and
no net magnetization.
• With magnetic field: – A small majority of spins will align
with the magnetic field and create an additional field M0.
M = 0
B0
M > 0
M
M 0 =
!0"2!2
4kTB0
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• So far with quantum physics… • In the following we deal with classical equations of motion • This is possible because the QM expectation value for the
magnetic moment of individual spins follows the classical equations of motion.
• When, in the following we use the term “spin”, we don’t necessarily mean individual spins, but larger collection of spins in a coherent state.
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Precession • When put in a magnetic field:
– Spin will rotate around the applied field – Identical to the interaction between the angular moment of a
spinning top and the gravitational field. – Precession frequency (Larmor frequency) will depend on
the applied field and the magnetic moment of the nucleus:
!0 = " B0
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Magnetization vector • The magnetization vector describes the
sum of all individual magnetic moments • Equilibrium: M is directed along the z-
axes, magnitude given by the thermal equilibrium value (M0).
• The precession of spins will NOT create a net rotating M in the x-y plane, due to random phases of the individual magnetic moments. x
y
z
B0
M
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Application of rf field
• In addition to the static B0, we now apply a rotating magnetic field B1 (ω0).
• Magnetization vector will start to precess around the total magnetic field.
• Results in a spiraling motion of M if viewed in the laboratory frame of reference:
x
y
z
B0
M
B1
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Rotating frame of reference
• Used to simplify the visualization of M. • Rotates at the Larmor frequency.
• Only precession around rf-field B1 (which now appears static) is visible.
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Effect of rf-field • Excitation by radio frequency
radiation will bring the system away from its equilibrium state.
• This excitation can be described as a rotation of the magnetization vector away from the z-axis.
• The angle with which M rotates is called the flip angle and can be controlled (often 90 deg).
• The result after the rf-pulse is a net magnetization in the x’-y’ plane
x'
y'
z
B0
M
rf
90º
M
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MR-signal
• If we jump back to the laboratory reference frame, the magnetization vector will now rotate in the x-y plane at the Larmor-frequency.
• This rotating magnetic field can be detected as rf-radiation -> MR signal.
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MR-signal
x
y
z
B0
M
x
time
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Relaxation (T1) • After the rf-pulse, the spin magnetization
vector will relax back towards its equilibrium value, which is along the z-axis.
• This effect is called T1-relaxation, longitudinal relaxation or spin-lattice relaxation.
• When the x-y component of M has dissappeared completely, the MR signal is lost.
x'
y'
z
B0
M
Free Induction Decay
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Relaxation (T2) • In most cases the x-y component of the magnetization vector
disappears faster than expected from the T1-relaxation process, meaning that we loose the MRI signal faster than expected.
• This effect is called dephasing,T2-relaxation, transversal relaxation or spin-spin relaxation.
x'
y'
z
B0
M
Free induction decay
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Relaxation (T2) • We can understand this effect by introducing phase.
+
=
In phase:
+
=
Out of phase:
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Origin of dephasing • B0 is not identical all over the sample at all times, it varies slightly.
• This means rotation speed of different spins vary slightly, leading to dephasing.
• After a while, different spins are at different points along the circle.
• Eventually the spins will spread out to cover the whole circle, and the signal is lost.
Mx
x
x
y
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Rotating frame of reference • Dephasing is better visualized in the rotating frame of
reference. • Here dephasing corresponds to a fanning out of the phases of
the individual spins
z
x’
y’
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T1 versus T2 relaxation
• T1-relaxation: – the regrowth of the z-magnetization (longitudinal magn.). – Usually in the range of seconds.
• T2-relaxation: – the loss of x’y’- magnetization (transverse magn.) – Usually in the range of 100 ms.
• The two processes are usually considered independent of each other, although T2≤T1.
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Summary
• Magnetic field B0. – Resonance frequency. – Strength of equilibrium magnetization M0
• Magnetization vector. – The net magnetic field created by all the spins.
• RF-pulse. – Radio frequency radiation which rotates M away from z-axis.
• Flip Angle. – Angle which the magnetization is rotated away from z-direction.
• FID (free induction decay). – The decaying MR-signal as the system relaxes back to equilibrium.
• T1-relaxation. – Regrowth of longitudinal magnetization.
• T2-relaxation. – Loss of transverse magnetization.
f = !B0
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Weighting: motivation for T1/T2 • To adjust acquisition parameters to obtain different types of contrast
in an MR image is called weighting.
• In a proton-weighted image the contrast is due to the spin density ρ0.
• In a T1-weighted image the contrast is due to variation in the T1 values an so on….
• T1 and T2-weighted images are important because ρ0 alone does not vary much in biological tissue. However there are big variations in T1 and T2.
• In addition will pathology affect T1 and T2.
• It is important to understand how we can get T1 and T2 weighted images.
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T1-relaxation one more time…
• The relaxation of longitudinal magnetization is described by the Bloch-equation which simply stats:
– The time derivative of the z-magnetization is proportional to the distance from the equilibrium value:
• When you solve this equation you get the following expression for the z-magnetization as a function of time t (after applying a 90º-rf-pulse)
Mz = M 0 1! e! t T1"# $%
dMzdt
=1T1
M 0 ! Mz"# $%
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T1-relaxation curve
t (sec)
Mz T1 = 4 sec
T1 = 1 sec
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T2-relaxation
• The dephasing-process can similarly be described by the following Bloch-equation:
• Again we get an exponential solution (with FA = 90o):
Mxy =M0 !e"t/T 2
dMxydt
= !1T 2
Mxy
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T2 Relaxation curve
t (sec)
Mxy
T2 = 0.4 sec
T2 = 0.1 sec
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The MR sequence • An MR-experiment consists of repeated blochs of rf-
excitation pulses and signal acquisition:
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TR and TE
• TR = Repetition time – Time between successive rf-excitation pulses. – Controls T1-weighting
• TE = Echo Time – Time between rf-excitation and signal acquisition. – Controls T2-weighting
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A basic signal equation
• By varying TR we control sensitivity to tissue variations in T1.
• By varying TE we control sensitivity to tissue variations in T2.
S ! "0 i 1# e#TR /T1$% &'e
#TE /T 2
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Short TR, short TE:
• T1-weighted
S ! "0 i 1# e#TR /T1$% &'e
#TE /T 2
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T1-weighting
• Maximize T1-effects: Short TR • Minimize T2-effects: Short TE
TR (sec)
Mz
TE
Mxy
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Long TR, long TE:
• T2-weighted
S ! "0 i 1# e#TR /T1$% &'e
#TE /T 2
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T2-weighting
• Minimize T1-effects: Long TR • Maximize T2-effects: Long TE
TR (sec)
Mz
TE
Mxy
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Long TR, short TE:
• Proton weighted
S ! "0 i 1# e#TR /T1$% &'e
#TE /T 2
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Proton-weighting
• Minimize T1-effects: Long TR • Minimize T2-effects: Short TE
TR (sec)
Mz
TE
Mxy
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There is more…
• The signal decay due to dephasing happens through two separate processes: – Dynamic dephasing (T2) – Static dephasing (T2’)
• The standard FID experiment is sensitive to both processes through T2*:
1T 2 *
=1T 2
+1T 2 '
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Dynamic versus Static Dephasing
• Dynamic dephasing is the result of B0 variations in time. – Spins move around and affect each others local field. – Irreversible process. – All MR-sequences are sensitive to this.
• Static dephasing is the result of spatial BUT time constant B0 variations. – Due to imperfect magnetic field. – Reversible process. – FID sequence sensitive to this. – The spin echo is not (next slides)
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Spin-echo. • In stead of measuring the FID signal it is
possible to create an echo at a chosen time after the 90º excitation pulse.
• Is achieved by an 180º refocusing pulse • Can be understood with the help of the rotating
coordinate system:
z z 180º
Ekko
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Spin-Echo
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Spin echo versus FID 90 180 180
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Signal acquisition
• The transverse magnetization vector is a complex quantity (Magnitude and phase).
• Both signals are aquired. • Usually only the magnitude image is used. • The phase image contains mostly information about B0.
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Magnitude image Phase image
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So how to get an image?
• So far we only discussed a single MR-signal from the whole object • How to spatially code the signal will be the topic of the next
presentation.