Samenvatting
Summary Advanced Imaging Techniques
Samenvatting in het Engels van het vak Advanced Imaging Techniques (8VC00), dat informatie bevat over MRI en US.
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Voorbeeld 4 van de 40 pagina's
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Voorbeeld van de inhoud
Summary Advanced imaging techniques MRI DYWLecture 1 MRI: CH 2 – 8
Magnetic resonance imaging (MRI): high-end imaging modality that provides superior image quality
for soft tissues.
- Deals with much lower energies than X-ray thus also lower frequencies, since the energy of
an electromagnetic wave is directly proportional to its frequency 𝐸𝐸 = ℎ𝜐𝜐.
- The wave lengths are also much longer in the radio frequency window, therefore the
electromagnetic pulse used in MRI to get a signal is called an RF pulse.
Any spinning charged particle creates a electromagnetic field. The magnetic component of this field
causes certain nuclei to act like a bar magnet. In MRI a charged nuclei, hydrogen nucleus, is used
which is a single positive charged proton.
- Each nuclei have specific energy levels related to the spin quantum number.
- If there is an even number of protons in the nucleus, every proton would be paired (for each
up there is a down) and thus cancel each other out. The net magnetic field would be zero.
- If there is an odd number of protons, there always exists one proton that is unpaired which
points either north or south and gives a net magnetic field or magnetic dipole moment. These
can be used for imaging in MR.
If spinning, unpaired protons are placed in an external magnetic field (𝐵𝐵0 ), they will line up with that
magnetic field. The spin can be in the parallel (up) or the anti-parallel (down) state, where the parallel
state has a slightly lower energy state. If the spin is exposed to a magnetic field that oscillates at that
frequency, then the particles in the lower energy state may get excited to the higher energy state.
Over time, the excited particle may relax towards the lower energy state, If this happens, they emit a
photon with the same frequency.
- If the classic particle is not in equilibrium, pointing along 𝐵𝐵0 , it will precess around 𝐵𝐵0 .
• The rotation frequency is given by the Larmor equation: 𝜔𝜔 = 𝛾𝛾𝐵𝐵0 and 𝑓𝑓 = 𝛾𝛾𝐵𝐵0 with
𝛾𝛾 = 2𝜋𝜋𝛾𝛾 and 𝛾𝛾 = 267.6 ∙ 106 rad s-1 T-1 for proton.
- If an RF wave of a specific frequency is sent into the patient, some spins will change their
alignment as a result of this new magnetic field. After RF pulse, they generate a signal as they
return to their original alignment.
A spin is represented by an arrow, starting at the origin of a system of coordinates, where the z-axis is
along the direction of the magnetic field. Thus, in equilibrium a spin is orientated along the z-axis. Here
the standard coordinate system, laboratory frame of reference, is used.
- If an additional magnetic field 𝐵𝐵1 (generated by the RF pulse) along the x-axis, which oscillates
in time with the Larmour frequency, is applied. The spin will start to precess around this field
and will thus tip away from and precess around the z-axis.
• The magnitude of 𝐵𝐵1 -field and the time duration of the RF pulse determine the flip
angle 𝜃𝜃.
Constant 𝐵𝐵1 -field magnitude during pulse: 𝜃𝜃 = 𝛾𝛾𝐵𝐵1 Δ𝑡𝑡.
Time-dependent 𝐵𝐵1 -field magnitude: 𝜃𝜃 = 𝛾𝛾∫ 𝐵𝐵1 (𝑡𝑡)𝑑𝑑𝑑𝑑.
- Rotating frame of reference, the system of coordinates rotates around the z-axis with the
Larmour frequency.
After the RF pulse the magnetization has two components, each relaxing independently towards their
equilibrium state:
1
,Summary Advanced imaging techniques MRI DYW
- 𝑴𝑴𝒛𝒛 : z-component of the magnetization of the spin, 𝑀𝑀𝑍𝑍 = 𝑀𝑀0 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐.
𝑡𝑡
−
• 𝑀𝑀𝑧𝑧 = 𝑀𝑀0 �1 − 𝑒𝑒 𝑇𝑇1 �.
• 𝑇𝑇1 is the spin-lattice relaxation time, it refers to the time it takes for the spins to give
the energy they obtained from the RF pulse back to the surrounding lattice in order
to go back to their equilibrium state.
- 𝑴𝑴𝑻𝑻 : transverse component of the magnetization of the spin, 𝑀𝑀𝑇𝑇 = 𝑀𝑀0 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠.
𝑡𝑡
−
• 𝑀𝑀𝑇𝑇 = 𝑀𝑀0 𝑒𝑒 𝑇𝑇2 , with 𝑇𝑇2 typically smaller than 𝑇𝑇1 thus transverse relaxation is much
faster than longitudinal relaxation.
• 𝑇𝑇2 is the transverse relaxation time excluding external field inhomogeneities.
Dephasing: every spin is a tiny magnet and influences the magnetic field of their neighbouring spin,
resulting in that the spins not all precess at the same Larmour frequency. Spins that feel a higher
magnetic field strength rotate faster and start to run ahead in the rotating frame of reference. Spins
that feel a lower magnetic field strength rotate slower and start to lag behind in the rotating frame of
reference. As a result, the 𝑀𝑀𝑇𝑇 shrinks which results in faster decay of transverse magnetization in
comparison to regrowth of longitudinal magnetization.
- Δ𝜙𝜙(𝑡𝑡) = 𝛾𝛾Δ𝐵𝐵0 𝑡𝑡.
Susceptibility (𝑋𝑋): indicates to what extent an external magnetic field is amplified by the material.
They affect in MRI, by making the local field slightly higher resulting in addition 𝐵𝐵0 field
inhomogeneities:
- 𝐵𝐵 = 𝜇𝜇𝜇𝜇 = 𝜇𝜇0 𝜇𝜇𝑟𝑟 𝐻𝐻 = 𝜇𝜇0 (1 + 𝑋𝑋)𝐻𝐻, with 𝜇𝜇 is the permeability.
External field inhomogeneities: inevitable field inhomogeneities of the 𝐵𝐵0 field. Not only caused by
the 𝐵𝐵0 inhomogeneity of the main magnet but also by susceptibility differences between tissues.
- 𝑇𝑇2∗ is the transverse relaxation time including external field inhomogeneities, which is always
shorter than 𝑇𝑇2 .
1 1
• = + 𝛾𝛾Δ𝐵𝐵0 .
𝑇𝑇2∗ 𝑇𝑇2
• As a result of the 𝑇𝑇2∗ decay, the amplitude of that signal decreases along the very same
curve.
At time of RF pulse, the values of 𝑀𝑀𝑍𝑍 become the values of 𝑀𝑀𝑇𝑇 (90𝑜𝑜 flip), after this 𝑀𝑀𝑇𝑇 decays with 𝑇𝑇2∗
decay. The signal of tissue type depends on spin density (𝜌𝜌), 𝑇𝑇1 and 𝑇𝑇2 (or 𝑇𝑇2∗ ). The exact signal
amplitude of a tissue in a MRI image also depends on the setting of TE and TR.
𝑇𝑇𝑇𝑇
−
- Calculate signal of tissue with 𝑀𝑀𝑧𝑧 before 90𝑜𝑜 pulse is 𝑀𝑀𝑧𝑧 (𝑇𝑇𝑇𝑇) = 𝜌𝜌 �1 − 𝑒𝑒 𝑇𝑇1 �, because 𝑀𝑀0 =
𝑇𝑇𝑇𝑇
−
𝜌𝜌 and 𝑡𝑡 = 𝑇𝑇𝑇𝑇. Then 𝑀𝑀𝑇𝑇 after 90𝑜𝑜 pulse can be calculated 𝑀𝑀𝑇𝑇 = 𝑀𝑀𝑍𝑍 (𝑇𝑇𝑇𝑇) ∙ 𝑒𝑒 𝑇𝑇2 where 𝑀𝑀0 =
𝑀𝑀𝑧𝑧 (𝑇𝑇𝑇𝑇) and 𝑡𝑡 = 𝑇𝑇𝑇𝑇.
• If 𝑇𝑇1 becomes smaller, then the recovery of magnetization is faster.
• If 𝑇𝑇2 becomes smaller, then the signal will decay faster.
- Echo time (TE): the time from the center of the RF pulse to the actual measurement and
determines the contrast.
• A short TE results in image intensities dominated by spin densities, reduction of 𝑇𝑇2
effect.
• A long TE results in image intensities dominated by 𝑇𝑇2 values, enhancing of 𝑇𝑇2 effect.
2
,Summary Advanced imaging techniques MRI DYW
- Repetition time (TR): time between two RF pulses, since one single free induction decay (FID),
the decaying MRI signal after an RF pulse as a result of 𝑇𝑇2∗ decay will not provide a whole
image.
• If TR >> 𝑇𝑇1 , then the 𝑀𝑀𝑍𝑍 will fully recovered before the next RF pulse is applied,
resulting in an image which will contain no 𝑇𝑇1 information. Reduction of 𝑇𝑇1 effect.
• If TR = 𝑇𝑇1 (in the same range), then a modest loss of signal for shorter 𝑇𝑇1 values will
be achieved. This will result in a decreased SNR, but the contrast between tissues with
different 𝑇𝑇1 values will increase.
• If TR << 𝑇𝑇1 , then only very little magnetization is recovered before the next pulse and
very little signal is available for this and all subsequent measurements. Enhancing of
𝑇𝑇1 effect.
- Spin-density-weighted Long TR, short TE Hight 𝜌𝜌 tissue is bright
𝑇𝑇2 -weighted Long TR, long TE High 𝑇𝑇2 tissue is bright
𝑇𝑇1 -weighted Short TR, short TE Short 𝑇𝑇1 tissue is bright
𝑜𝑜
Inversion recovery sequence (IRS): uses a 180 RF pulse (inversion pulse) as a pre-pulse before the
actual imaging sequence. The duration between these is the inversion recovery time (TI) of the
sequence. By choosing an appropriate TI, the tissue type with one distinct 𝑇𝑇1 can be nulled and will
give zero signal in the image. It applies: 𝑇𝑇𝑇𝑇 = 𝑇𝑇1 ln (2).
- Negative 𝑀𝑀𝑧𝑧 to flip at 90𝑜𝑜 pulse, so there is 𝑀𝑀𝑇𝑇 after pulse and therefore also signal but with
opposite phase.
- If the longitudinal 𝑀𝑀𝑧𝑧 start in equilibrium, after a RF pulse of 180𝑜𝑜 the longitudinal
𝑡𝑡
−
magnetization behaves like: 𝑀𝑀𝑧𝑧 (𝑡𝑡) = 𝑀𝑀0 �1 − 2𝑒𝑒 𝑇𝑇1 �.
- If the longitudinal 𝑀𝑀𝑧𝑧 is not in equilibrium, for example because TR is too short for complete
regrowth, and 𝑀𝑀𝑧𝑧 after a 180𝑜𝑜 RF pulse is 𝑀𝑀𝑝𝑝 then the longitudinal magnetization behaves
𝑡𝑡 𝑡𝑡
− 𝑀𝑀𝑝𝑝 −
like: 𝑀𝑀𝑧𝑧 (𝑡𝑡) = 𝑀𝑀0 �1 − 𝑒𝑒 𝑇𝑇1 + 𝑒𝑒 𝑇𝑇1 �, 𝑀𝑀𝑧𝑧 shortly before the second 90𝑜𝑜 pulse.
𝑀𝑀0
•𝑀𝑀𝑝𝑝 is if the flip angle is not equal to 90𝑜𝑜 or 180𝑜𝑜 , it can be used to determine how the
recovery curve goes.
- Two common inversion recovery sequences:
• FLAIR (fluid attenuated IR): suppresses cerebrospinal fluid in the lateral ventricles.
• STIR (short tau IR): suppresses fat with inversion pulse before sequence.
Spin echo sequence: right after a 90𝑜𝑜 pulse, the spins will start dephasing, which result in 𝑇𝑇2∗ decay of
𝑇𝑇𝑇𝑇
the 𝑀𝑀𝑇𝑇 . Then a 180𝑜𝑜 pulse is applied at 𝑡𝑡 = .
2
- The spins that were fast and were running ahead, are now inverted and are running behind.
They are still faster and will catch up with the other spins.
- The spins that were slow and were running behind are now inverted and are running ahead,.
They are still slower and the rest of the spins will catch up with them.
- At 𝑡𝑡 = 𝑇𝑇𝑇𝑇, the spins will have fully realigned and the echo appears in the signal detection line.
• However, not all signal is realigned, only 𝐵𝐵0 -deviation that are static in time can be
compensated. Dephasing that originate from random 𝐵𝐵0 fluctuations (movement of
molecules) and spin-to-spin interaction cannot be retrieved, also called 𝑇𝑇2 decay.
• The signal decay that originates from random molecule movement, spin-spin
interactions and static 𝐵𝐵0 -deviation is called 𝑇𝑇2∗ decay.
3
, Summary Advanced imaging techniques MRI DYW
Lecture 2 MRI: CH 9 – 11
The Fourier transform provides a frequency spectrum of a signal, shows for every frequency how
strong the frequency is present in the original signal. It converts a signal from the time domain to the
frequency domain.
∞
- 𝐹𝐹 (𝜔𝜔) = ∫−∞ 𝑓𝑓(𝑡𝑡)𝑒𝑒 −𝑖𝑖𝑖𝑖𝑖𝑖 𝑑𝑑𝑑𝑑, with 𝜔𝜔 = 2𝜋𝜋𝜋𝜋.
- The original function can be retrieved from the Fourier transform by the inverse Fourier
∞
transform: 𝑓𝑓(𝑡𝑡) = ∫−∞ 𝐹𝐹 (𝜔𝜔)𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖 𝑑𝑑𝑑𝑑.
• Real part of a real function refers to cosine functions.
• Imaginary part of a real function refers to sine functions.
- 2D function like 𝑧𝑧 = 𝑓𝑓(𝑥𝑥, 𝑦𝑦).
• Fourier transform: 𝐹𝐹�𝑘𝑘𝑥𝑥 , 𝑘𝑘𝑦𝑦 � = ∫ ∫ 𝑓𝑓(𝑥𝑥, 𝑦𝑦)𝑒𝑒 −2𝜋𝜋𝑘𝑘𝑥𝑥 𝑥𝑥 𝑒𝑒 −𝑖𝑖2𝜋𝜋𝑘𝑘𝑦𝑦 𝑦𝑦 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑.
• Inverse Fourier transform: 𝐹𝐹 (𝑥𝑥, 𝑦𝑦) = ∫ ∫ 𝑓𝑓�𝑘𝑘𝑥𝑥 , 𝑘𝑘𝑦𝑦 �𝑒𝑒 𝑖𝑖2𝜋𝜋𝑘𝑘𝑥𝑥 𝑥𝑥 𝑒𝑒 𝑖𝑖2𝜋𝜋𝑘𝑘𝑦𝑦 𝑦𝑦 𝑑𝑑𝑘𝑘𝑥𝑥 𝑑𝑑𝑘𝑘𝑦𝑦 .
Discrete Fourier transform: for discrete functions with a finite domain.
𝑁𝑁−1 ( ) −𝑖𝑖𝜔𝜔𝑘𝑘 (𝑡𝑡𝑛𝑛 −𝑡𝑡0 )
- 𝐹𝐹 (𝜔𝜔𝑘𝑘 ) = ℱ�𝑓𝑓(𝑡𝑡𝑛𝑛 )� = ∑𝑛𝑛=0 𝑓𝑓 𝑡𝑡𝑛𝑛 𝑒𝑒 .
- The original time series can be reconstructed using the inverse discrete Fourier transform:
1
𝑓𝑓(𝑡𝑡𝑛𝑛 ) = ℱ −1 �𝐹𝐹 (𝜔𝜔𝑘𝑘 )� = ∑𝑁𝑁−1
𝑘𝑘=0 𝐹𝐹 (𝜔𝜔𝑘𝑘 )𝑒𝑒
𝑖𝑖𝜔𝜔𝑘𝑘 (𝑡𝑡𝑛𝑛 −𝑡𝑡0 )
.
𝑁𝑁
- For a Fourier transform of the signal on time domain [𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚 ] and spacing Δ𝑡𝑡, 𝐹𝐹(𝑓𝑓), has a
frequency domain 𝑓𝑓 [𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚 ] and spacing Δ𝑓𝑓.
1
• If 𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚 becomes larger (longer sampling), Δ𝑓𝑓 becomes smaller with Δ𝑓𝑓 = .
𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚 −𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚
• If Δ𝑡𝑡 becomes smaller (denser sampling), 𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚 becomes larger (more frequency
1
components included) with 𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚 = −𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚 = .
2Δ𝑡𝑡
- 2D function:
𝑀𝑀
−𝑖𝑖2𝜋𝜋𝑘𝑘𝑥𝑥 𝑥𝑥𝑛𝑛 −𝑖𝑖2𝜋𝜋𝑘𝑘𝑦𝑦 𝑦𝑦𝑚𝑚
• Fourier transform: 𝐹𝐹�𝑘𝑘𝑥𝑥 , 𝑘𝑘𝑦𝑦 � = ∑𝑁𝑁
𝑛𝑛=1 ∫𝑚𝑚=1 𝑓𝑓 (𝑥𝑥𝑛𝑛 , 𝑦𝑦𝑚𝑚 )𝑒𝑒 𝑒𝑒 .
1 𝑀𝑀
• Inverse Fourier transform: 𝐹𝐹 (𝑥𝑥, 𝑦𝑦) = ∑𝑘𝑘𝑥𝑥 ∑𝑘𝑘𝑦𝑦 ∫𝑚𝑚=1 𝐹𝐹 (𝑥𝑥𝑛𝑛 , 𝑦𝑦𝑚𝑚 )𝑒𝑒 𝑖𝑖2𝜋𝜋𝑘𝑘𝑥𝑥 𝑥𝑥𝑛𝑛 𝑒𝑒 𝑖𝑖2𝜋𝜋𝑘𝑘𝑦𝑦 𝑦𝑦𝑚𝑚 .
𝑁𝑁𝑁𝑁
Symmetry rules:
- For real functions, the Fourier transform is symmetric: 𝐹𝐹 (𝜔𝜔) = 𝐹𝐹(−𝜔𝜔) and 𝑅𝑅𝑅𝑅{𝐹𝐹 (𝜔𝜔)} =
𝑅𝑅𝑅𝑅{𝐹𝐹 (−𝜔𝜔)} and 𝐼𝐼𝐼𝐼{𝐹𝐹 (𝜔𝜔)} = −𝐼𝐼𝐼𝐼{𝐹𝐹 (−𝜔𝜔)}.
𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖 −𝑒𝑒 −𝑖𝑖𝑖𝑖𝑖𝑖
• Real part: cos(𝜔𝜔𝜔𝜔) = .
2
𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖 −𝑒𝑒 −𝑖𝑖𝑖𝑖𝑖𝑖
• Imaginary part: sin(𝜔𝜔𝜔𝜔) = .
2𝑖𝑖
−𝑖𝑖𝑖𝑖2 𝑡𝑡 �
• Thus: 𝑅𝑅𝑅𝑅�𝐹𝐹 (−𝜔𝜔2 )𝑒𝑒 + 𝑅𝑅𝑅𝑅�𝐹𝐹 (𝜔𝜔2 )𝑒𝑒 𝑖𝑖𝜔𝜔2 𝑡𝑡 � = 2𝑅𝑅𝑅𝑅{𝐹𝐹 (𝜔𝜔2 )} cos(𝜔𝜔2 𝑡𝑡).
- For even functions (symmetric), the Fourier transform is purely real.
- For uneven functions (anti-symmetric), the Fourier transform is purely imaginary.
- For the Fourier transform of a real image:
• The real part of the Fourier transform has point-symmetry (rotational symmetry over
180𝑜𝑜 , 𝑅𝑅𝑅𝑅�𝐹𝐹�𝑘𝑘𝑥𝑥 , 𝑘𝑘𝑦𝑦 �� = 𝑅𝑅𝑅𝑅�𝐹𝐹�−𝑘𝑘𝑥𝑥 , −𝑘𝑘𝑦𝑦 ��.
• The imaginary part of the Fourier transform is anti-point-symmetrical:
𝐼𝐼𝐼𝐼�𝐹𝐹�𝑘𝑘𝑥𝑥 , 𝑘𝑘𝑦𝑦 �� = −𝐼𝐼𝐼𝐼�𝐹𝐹�−𝑘𝑘𝑥𝑥 , −𝑘𝑘𝑦𝑦 ��.
A 2D Fourier domain, k-space, has coordinates 𝑘𝑘𝑥𝑥 and 𝑘𝑘𝑦𝑦 .
4
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Opgericht in 2010, al 14 jaar dé plek om samenvattingen te kopen