Preclinical and clinical imaging with focus on neurology
Medical imaging:
Non-electromagnetic waves:
Ultrasonic waves: ultrasound
➢ Not for brain imaging due to skull
Electromagnetic waves:
Radio waves: MRI/ spectroscopy
• Wavelength > 109Å
• Frequency < 3*109 Hz
• Energy < 10-5 eV
X-rays: CT / RX
• Wavelength = 10Å – 0,1Å
• Frequency = 3*1017 – 3*1019 Hz
• Energy = 103 – 105 eV → low energy does not cause ionisation so is safe
Gamma waves: PET / SPECT
• Wavelength < 0,1Å
• Frequency > 3*1019
• Energy > 105
Formulas:
𝒄 =𝒇∗𝝀 (𝑐 = wave speed , 𝑓 = frequency , 𝜆 = wavelength)
𝑬 =𝒉∗𝒇 (𝐸 = photon energy , ℎ = Planck’s constant = 6,63 ∗ 10−34 𝐽𝑠 , 𝑓 = frequency)
MRI setup:
Superconducting magnet: loses all electrical resistance below critical temperature
Coil immersed in liquid Helium at 4K: no electrical resistance so current remains flowing without
energy source
➢ Transmits radio waves into the subject
Measurement: radio waves re-emitted by the subject
Magnetic field: veterinary 0,2T , clinical 3T , preclinical 7-11,5T
Preclinical MRI:
• Inhalation anesthesia: by inhalation because you have immediate control
• Stereotactic apparatus: tooth bar , ear plugs to make sure the mead is stable and has a fixed
position towards the coil
• Physiological measurements: temperature (measured by anal probe) maintained by heating ,
pCO2 , breath rate
Subject:
Imaged regions: differences in soft tissue visualized (head , neck , spine)
,Nuclei:
Necessary properties:
• Spin: only atoms with odd number of protons can have spin (pairs of spins cancel each other out)
• Charge
MRI nuclei:
• Hydrogen 1H biological abundance = 0,63 → most used
• Carbon 13C biological abundance = 0,094
• Sodium 23Na biological abundance = 0,00041
• Phosphorus 31P biological abundance = 0,0024
Magnetic momentum:
Proton = small magnet due to its spin
➢ Electrical current creates a magnetic moment 𝝁
Magnetic momentum 𝝁 ⃗
⃗ = 𝜸𝑳 (𝛾 = gyromagnetic constant , 𝐿 = angular momentum)
⃗
𝑑𝜇
Magnetic momentum change in time: ⃗⃗⃗⃗0
= 𝜇 × 𝛾𝐵
𝑑𝑡
⃗⃗⃗⃗⃗𝟎 = Larmor frequency
⃗⃗⃗⃗⃗𝟎 = −𝜸𝑩
Angular frequency of precession 𝝎
➢ Spin 𝜇 precesses around the magnetic field
➢ Angular velocity |𝜔0 | = how fast angle changes in time
Magnetic momentum components:
• 𝜇𝑥 (𝑡) = 𝜇 sin 𝜃 cos(𝜔0 𝑡 + 𝜙0 )
X and Y component oscillate
• 𝜇𝑦 (𝑡) = 𝜇 sin 𝜃 sin(𝜔0 𝑡 + 𝜙0 )
• 𝜇𝑧 (𝑡) = 𝜇 cos 𝜃 Z component doesn’t change over time
Spin component along 𝑩𝟎 : (𝑧-axis)
1
• Spin up: 𝜇𝑧 = + 𝛾 ℎ̅ 2
1
• Spin down: 𝜇𝑧 = − 𝛾 ℎ̅
2
Potential energy: interaction of magnetic moment 𝜇 in 𝐵0 field 𝑈 = −𝜇𝑧 𝐵0
1
• Spin up: 𝑈 = − 𝛾ℎ̅𝐵0
2
1
• Spin down: 𝑈 = + 2 𝛾ℎ̅𝐵0
• Equilibrium state: more spins in spin-up state → magnet puts protons in equilibrium
𝜔0 −𝛾𝐵0
Frequency: 𝑓 = 2𝜋
= 2𝜋
𝛾
➢ Bv proton: 𝑓 = 2𝜋 = 42,6𝑀𝐻𝑧/𝑇
42,6𝑀𝐻𝑧
➢ 7T magnet: 𝑓 = 𝑇
∗ 7𝑇 = 298,2𝑀𝐻𝑧
Netto magnetization:
= vector sum of individual proton magnetic moments in a voxel 𝑴 = ∑ 𝝁𝒊
No external magnetic field: magnetic moments/spins randomly oriented
External magnetic field 𝑩𝟎 : all spins distributed in spin up / spin down state
• 7 on 106 spins will be in spin up state → netto magnetization ≠ 0
• Magnetization dependent on the proton density (more protons = more excess protons in
spin up state)
• |𝑴| ∥ |𝑩𝟎 | and |𝑴|~|𝑩𝟎 |: netto magnetization is parallel and proportional to external magnetization
, Longitudinal component: 𝑀𝑧 = 𝑀0
Transversal component: 𝑀𝑥𝑦 = 0
Sensitivity: bigger 𝑀0 gives higher sensitivity
➢ Mouse brain 10x smaller in 3D (1000x less signal) so use higher 𝐵0 for adequate signal
MRI signal:
1. Magnet puts protons in equilibrium
2. RF pulse applied to disturb the equilibrium state
3. Magnetization 𝑴 gets perturbed and aligns away from 𝐵0
4. 𝑀𝑥𝑦 signal re-emits a magnetic field during relaxation
5. Change of magnetic flux through the receiver coils and induction of electromotive force = MR signal
Laboratory frame (xyz): point from where the observation is being done
➢ 𝑀 is rotating at the Larmor frequency around 𝐵0 in the z-axis
Rotating frame (x’y’z’): observation point rotating at the same angular frequency 𝜔0 around the z-axis
➢ 𝑀 is stationary in the rotating frame (appears stationary because you rotate with it)
➢ Easier to describe what happens when applying RF pulses without needing to describe
oscillations of 𝑀
MRI signal: to measure magnetization 𝑀 it must be aligned away from 𝐵0 (perturbed)
⃗⃗
𝑑𝑀
⃗⃗ × 𝛾𝐵
= 𝑀 ⃗⃗⃗⃗0 = −𝛾𝐵
⃗⃗⃗⃗0 × 𝑀
⃗⃗ = 𝜔 ⃗⃗
⃗⃗⃗⃗⃗0 × 𝑀 (Larmor frequency −𝛾𝐵0 = 𝜔0 )
𝑑𝑡
➢ 𝑀𝑧 < 𝑀0 : not measurable
➢ 𝑀𝑥𝑦 ≠ 0 : precessing with 𝜔0 → oscillating magnetic field gives MR signal
Perturbing M:
In theory: apply a very big magnetic field 𝐵1 for a short time
➢ 𝑀 would align with 𝐵0 + 𝐵1
➢ Impossible to create a huge 𝐵1 field within seconds (takes an entire day)
RF pulse frequency: apply 𝐵1 with Larmor frequency 𝜔0 to slowly turn 𝑀 away from the z-axis
𝝎
➢ RF frequency should be equal to precession frequency of the spins 𝒇 = 𝟐𝝅𝟎
➢ Spins precessing with that resonance frequency absorb the transmitted RF energy
➢ RF pulse with too much / too little energy → spins remain in same state
⃗⃗
𝜕𝑀
𝐵1 torque on 𝑀: ⃗⃗ × 𝛾𝐵
= 𝑀 ⃗⃗⃗⃗1
𝜕𝑡
➢ 𝑀 turns away from z-axis with angular frequency 𝝎 = −𝜸𝑩𝟏
Flip angle: in respect to the external magnetic field 𝜃 = 𝜔1 ∆𝑡 = −𝛾𝐵1 ∆𝑡
• Proportional to the magnitude of the 𝑩𝟏 -field
• Proportional to the time ∆𝒕 of the 𝑩𝟏 transmission
= Perturbation magnetization
, RF pulses:
90° pulse:
• 𝑴𝒛 = 𝟎
• 𝑴𝒙𝒚 = 𝑴𝟎 = maximal
Spin states:
• Spins equally distributed over spin up and spin down state
• Spinning in phase (not randomly distributed in xy plane)
180° pulse:
• 𝑴𝒛 = −𝑴𝟎
• 𝑴𝒙𝒚 = 𝟎
Spin states: most spins inverted (more in spin down state)
90° pulse:
𝑴 precesses in xy-plane with angular frequency 𝜔0 = −𝛾𝐵0
• 𝑀𝑥 = 𝑀0 sin(𝜔0 𝑡) → oscillation in vertical component
Additional magnetic induction: 𝐵 = 𝜇0 𝑀 (𝜇0 = magnetic permeability of vacuum = 4𝜋 ∗ 10−7 𝑁/𝑚²)
➢ Causes a change in magnetic flux in the receiver coils
Electromotive force: respond to the flux change by running a current through the coils to create a voltage
(electromotive force) = MR signal
➢ EMF varies with angular frequency 𝜔0 = free induction decay
Free induction decay: precession of 𝑀𝑥𝑦 around 𝐵0 (after RF pulse) induces a voltage in the receiver coil
= oscillating but decaying signal due to the gradual dephasing
Coils to perturb netto magnetization:
➢ 𝐵1 should be the same all over the subject
➢ 𝐵1 ⊥ 𝐵0
Surface coil:
+ Very sensitive: smaller loop has higher sensitivity to capture 𝑀𝑥𝑦 component
− Position dependent: high sensitivity close to the coil but sensitivity lost further from the coil
→ creates bias in MRI image
→ good to use for mouse brain
Multi-turn coil: volume coil
Bird cage coil
RF pulse characteristics:
Pulse formation: generated in RF-transmitter and becomes electromagnetic wave when transmitted
via the RF antenna
Frequency:
Optimal energy transfer: when the RF-pulse and the spins have the same resonance frequency
= Larmor frequency
Medical imaging:
Non-electromagnetic waves:
Ultrasonic waves: ultrasound
➢ Not for brain imaging due to skull
Electromagnetic waves:
Radio waves: MRI/ spectroscopy
• Wavelength > 109Å
• Frequency < 3*109 Hz
• Energy < 10-5 eV
X-rays: CT / RX
• Wavelength = 10Å – 0,1Å
• Frequency = 3*1017 – 3*1019 Hz
• Energy = 103 – 105 eV → low energy does not cause ionisation so is safe
Gamma waves: PET / SPECT
• Wavelength < 0,1Å
• Frequency > 3*1019
• Energy > 105
Formulas:
𝒄 =𝒇∗𝝀 (𝑐 = wave speed , 𝑓 = frequency , 𝜆 = wavelength)
𝑬 =𝒉∗𝒇 (𝐸 = photon energy , ℎ = Planck’s constant = 6,63 ∗ 10−34 𝐽𝑠 , 𝑓 = frequency)
MRI setup:
Superconducting magnet: loses all electrical resistance below critical temperature
Coil immersed in liquid Helium at 4K: no electrical resistance so current remains flowing without
energy source
➢ Transmits radio waves into the subject
Measurement: radio waves re-emitted by the subject
Magnetic field: veterinary 0,2T , clinical 3T , preclinical 7-11,5T
Preclinical MRI:
• Inhalation anesthesia: by inhalation because you have immediate control
• Stereotactic apparatus: tooth bar , ear plugs to make sure the mead is stable and has a fixed
position towards the coil
• Physiological measurements: temperature (measured by anal probe) maintained by heating ,
pCO2 , breath rate
Subject:
Imaged regions: differences in soft tissue visualized (head , neck , spine)
,Nuclei:
Necessary properties:
• Spin: only atoms with odd number of protons can have spin (pairs of spins cancel each other out)
• Charge
MRI nuclei:
• Hydrogen 1H biological abundance = 0,63 → most used
• Carbon 13C biological abundance = 0,094
• Sodium 23Na biological abundance = 0,00041
• Phosphorus 31P biological abundance = 0,0024
Magnetic momentum:
Proton = small magnet due to its spin
➢ Electrical current creates a magnetic moment 𝝁
Magnetic momentum 𝝁 ⃗
⃗ = 𝜸𝑳 (𝛾 = gyromagnetic constant , 𝐿 = angular momentum)
⃗
𝑑𝜇
Magnetic momentum change in time: ⃗⃗⃗⃗0
= 𝜇 × 𝛾𝐵
𝑑𝑡
⃗⃗⃗⃗⃗𝟎 = Larmor frequency
⃗⃗⃗⃗⃗𝟎 = −𝜸𝑩
Angular frequency of precession 𝝎
➢ Spin 𝜇 precesses around the magnetic field
➢ Angular velocity |𝜔0 | = how fast angle changes in time
Magnetic momentum components:
• 𝜇𝑥 (𝑡) = 𝜇 sin 𝜃 cos(𝜔0 𝑡 + 𝜙0 )
X and Y component oscillate
• 𝜇𝑦 (𝑡) = 𝜇 sin 𝜃 sin(𝜔0 𝑡 + 𝜙0 )
• 𝜇𝑧 (𝑡) = 𝜇 cos 𝜃 Z component doesn’t change over time
Spin component along 𝑩𝟎 : (𝑧-axis)
1
• Spin up: 𝜇𝑧 = + 𝛾 ℎ̅ 2
1
• Spin down: 𝜇𝑧 = − 𝛾 ℎ̅
2
Potential energy: interaction of magnetic moment 𝜇 in 𝐵0 field 𝑈 = −𝜇𝑧 𝐵0
1
• Spin up: 𝑈 = − 𝛾ℎ̅𝐵0
2
1
• Spin down: 𝑈 = + 2 𝛾ℎ̅𝐵0
• Equilibrium state: more spins in spin-up state → magnet puts protons in equilibrium
𝜔0 −𝛾𝐵0
Frequency: 𝑓 = 2𝜋
= 2𝜋
𝛾
➢ Bv proton: 𝑓 = 2𝜋 = 42,6𝑀𝐻𝑧/𝑇
42,6𝑀𝐻𝑧
➢ 7T magnet: 𝑓 = 𝑇
∗ 7𝑇 = 298,2𝑀𝐻𝑧
Netto magnetization:
= vector sum of individual proton magnetic moments in a voxel 𝑴 = ∑ 𝝁𝒊
No external magnetic field: magnetic moments/spins randomly oriented
External magnetic field 𝑩𝟎 : all spins distributed in spin up / spin down state
• 7 on 106 spins will be in spin up state → netto magnetization ≠ 0
• Magnetization dependent on the proton density (more protons = more excess protons in
spin up state)
• |𝑴| ∥ |𝑩𝟎 | and |𝑴|~|𝑩𝟎 |: netto magnetization is parallel and proportional to external magnetization
, Longitudinal component: 𝑀𝑧 = 𝑀0
Transversal component: 𝑀𝑥𝑦 = 0
Sensitivity: bigger 𝑀0 gives higher sensitivity
➢ Mouse brain 10x smaller in 3D (1000x less signal) so use higher 𝐵0 for adequate signal
MRI signal:
1. Magnet puts protons in equilibrium
2. RF pulse applied to disturb the equilibrium state
3. Magnetization 𝑴 gets perturbed and aligns away from 𝐵0
4. 𝑀𝑥𝑦 signal re-emits a magnetic field during relaxation
5. Change of magnetic flux through the receiver coils and induction of electromotive force = MR signal
Laboratory frame (xyz): point from where the observation is being done
➢ 𝑀 is rotating at the Larmor frequency around 𝐵0 in the z-axis
Rotating frame (x’y’z’): observation point rotating at the same angular frequency 𝜔0 around the z-axis
➢ 𝑀 is stationary in the rotating frame (appears stationary because you rotate with it)
➢ Easier to describe what happens when applying RF pulses without needing to describe
oscillations of 𝑀
MRI signal: to measure magnetization 𝑀 it must be aligned away from 𝐵0 (perturbed)
⃗⃗
𝑑𝑀
⃗⃗ × 𝛾𝐵
= 𝑀 ⃗⃗⃗⃗0 = −𝛾𝐵
⃗⃗⃗⃗0 × 𝑀
⃗⃗ = 𝜔 ⃗⃗
⃗⃗⃗⃗⃗0 × 𝑀 (Larmor frequency −𝛾𝐵0 = 𝜔0 )
𝑑𝑡
➢ 𝑀𝑧 < 𝑀0 : not measurable
➢ 𝑀𝑥𝑦 ≠ 0 : precessing with 𝜔0 → oscillating magnetic field gives MR signal
Perturbing M:
In theory: apply a very big magnetic field 𝐵1 for a short time
➢ 𝑀 would align with 𝐵0 + 𝐵1
➢ Impossible to create a huge 𝐵1 field within seconds (takes an entire day)
RF pulse frequency: apply 𝐵1 with Larmor frequency 𝜔0 to slowly turn 𝑀 away from the z-axis
𝝎
➢ RF frequency should be equal to precession frequency of the spins 𝒇 = 𝟐𝝅𝟎
➢ Spins precessing with that resonance frequency absorb the transmitted RF energy
➢ RF pulse with too much / too little energy → spins remain in same state
⃗⃗
𝜕𝑀
𝐵1 torque on 𝑀: ⃗⃗ × 𝛾𝐵
= 𝑀 ⃗⃗⃗⃗1
𝜕𝑡
➢ 𝑀 turns away from z-axis with angular frequency 𝝎 = −𝜸𝑩𝟏
Flip angle: in respect to the external magnetic field 𝜃 = 𝜔1 ∆𝑡 = −𝛾𝐵1 ∆𝑡
• Proportional to the magnitude of the 𝑩𝟏 -field
• Proportional to the time ∆𝒕 of the 𝑩𝟏 transmission
= Perturbation magnetization
, RF pulses:
90° pulse:
• 𝑴𝒛 = 𝟎
• 𝑴𝒙𝒚 = 𝑴𝟎 = maximal
Spin states:
• Spins equally distributed over spin up and spin down state
• Spinning in phase (not randomly distributed in xy plane)
180° pulse:
• 𝑴𝒛 = −𝑴𝟎
• 𝑴𝒙𝒚 = 𝟎
Spin states: most spins inverted (more in spin down state)
90° pulse:
𝑴 precesses in xy-plane with angular frequency 𝜔0 = −𝛾𝐵0
• 𝑀𝑥 = 𝑀0 sin(𝜔0 𝑡) → oscillation in vertical component
Additional magnetic induction: 𝐵 = 𝜇0 𝑀 (𝜇0 = magnetic permeability of vacuum = 4𝜋 ∗ 10−7 𝑁/𝑚²)
➢ Causes a change in magnetic flux in the receiver coils
Electromotive force: respond to the flux change by running a current through the coils to create a voltage
(electromotive force) = MR signal
➢ EMF varies with angular frequency 𝜔0 = free induction decay
Free induction decay: precession of 𝑀𝑥𝑦 around 𝐵0 (after RF pulse) induces a voltage in the receiver coil
= oscillating but decaying signal due to the gradual dephasing
Coils to perturb netto magnetization:
➢ 𝐵1 should be the same all over the subject
➢ 𝐵1 ⊥ 𝐵0
Surface coil:
+ Very sensitive: smaller loop has higher sensitivity to capture 𝑀𝑥𝑦 component
− Position dependent: high sensitivity close to the coil but sensitivity lost further from the coil
→ creates bias in MRI image
→ good to use for mouse brain
Multi-turn coil: volume coil
Bird cage coil
RF pulse characteristics:
Pulse formation: generated in RF-transmitter and becomes electromagnetic wave when transmitted
via the RF antenna
Frequency:
Optimal energy transfer: when the RF-pulse and the spins have the same resonance frequency
= Larmor frequency
