MRI Flashcards
What sort of nuclei possess spin angular momentum, J
Nuclei with odd number of protons, neutrons or both
Magenetic moment equation,Mu
Mu = (gyrometric ratio)(spin angular momentum)
Precession torque equation
tau = mu x B = (mu)Bsin(theta)
Why does precession occur
nuclear magnetic moment in a magnetic field experiences torque
Larmor equation
Frequency of precession
w= (gyrometric ratio)(Applied magnetic field - B0)
Magnitude of spin angular momentum
|J| = hbar [I(I+1)]^(1/2)
Where I is spin quantum number
How many spin states denototed by spin quantum number
(2I+1)
Potential energy of magnetic moment
work done rotatinf magnetic moment in B-field
E = -(mu).B = -(gyrometeric ratio)(J in Z direction)(B0)
How is spin state distributed in thermal equilibrium
seperated by deltaE according to Boltzman distribution
ndown/ nup = exp(-deltaE/ KbT)
Spin state distribution in the high temperature limit
ndown/ nup = 1-([(hbar)(gyrometric const)(B0)]/KbT)
Why can magnetisation within a material be detected by NMR
Population differences arisen by small excess of spins in the low energy state causes a net bulk magnetaisation in a material - can a;sp be increased by using a static magnetic field to polarise nuclear spins
At what angle fo spins precess to the Z-axis at random phase
54degrees
What is the bulk magnetisation in NMR
M = sum of spin magnetic moments
Safety issues of static field
Projectile effect
Moving in spatial static fields causes the body to experience varying fields causing dizziness, metallic taste and flashing light sensation
What is the Larmor frequency at 1T
42.57MHz
How RF excitation occur in NMR (QM)?
- Applying RF energy spins tips spins and brings into phase Causing MO to be tipped from the longitudinal plant to the transverse plant
What does a 90degree pulse do?
equalizes the population of spin states and brings spins into phase
How RF excitation occur in NMR (CM)?
Apply B field oscillating at frequency ~ Larmor frequency and oriented in Bz direction
What is the purpose of applying a magnetic field oscillating at a frequency in NMR or MRI experiments?
To excite the magnetization in the sample, particularly by aligning with the Larmor frequency.
What is the total B1 field expression, and why is the anticlockwise rotating component neglected?
The total
B1(t) = 2B1cos(wt)i
cos(ωt)i, and the anticlockwise component Ba(t) is neglected due to being off-resonance.
How does the rotating frame of reference simplify the analysis of the B1 field in NMR or MRI experiments?
It allows for the consideration of the B1 field as stationary for the component at
+ω1
+ω1, simplifying the analysis while the component at −ω1rotates at −ω2 and can be ignored due to being off-resonance.
How do you relate the lab frame and kav frame
- z’ = z
- x’ rotating at frequency with respect to x.
- y’ rotating at frequency with respect to y
What is the relationship between the rate of change of a vector in the lab frame and rotating frame?
The relationship is given by
dr/dt =
(w × r) +(∂r/∂t)
How is the magnetization described in the rotating frame?
In the rotating frame, the magnetization is described by
dM/dt = Gyrometeric ratio(M x (B+(w/t))
What is the effective field experienced by the magnetization in the rotating frame?
The effective field Beff is given by Beff = (B0 - wRADIOFREQ/ gyrometric ratio)+B1
What does the effective field represent in the rotating frame?
In the rotating frame, the magnetization precesses around the effective field B eff
What does ‘on resonance’ mean? What does this cayse
RF field is applied at Larmor frequency of spins
Effective field in rotating frame of Beff is aligned w x’ axis
What does 180 pulses do
Flips magnetisation to -z
Called inverted
Pulse can refocus magnitisation
What do 90 degree pulses do?
Flips magnetisation to xy plane
called excited or saturated
After 90 degree, Mz=0 and Mxy = M0
What does a tip/flup angle pulse (Alpha) acting on equilibrium magnetisation do?
Reduces Mz from M0 to M0cos(alpha)
Increases Mxy to M0sin(alpha)
What are the safety issues of radiofrequencies?
- Tissue heating
- More dangerous in poorly perfused organs
-Pt to be kept in low humidity - skin burns
Steps of signal detection
90degree pulse tips magnetisation into x-y plane (phase coherence)
RF pulse is switched off
Transverse xy magnetisation caused by pulse, processes about B0 at larmor freq
Rotating magnetisation causes oscillating emf
Causes pick up coil in receiver to be tuned to RF freq
What is Phase sensitive detection?
PSD is a technique used to compare the signal from precessing spins with a reference frequency, allowing for the digitization and storage of only the frequency difference, typically in the audio range.
Why is the oscillator frequency (ω0)
generally set to be approximately equal to the mean Larmor frequency (ωL) of the sample? in PSD
Setting (ω0) close to (ωL) simplifies the detection and analysis of the signal by focusing on the difference between these frequencies, which is critical for imaging encoding and spectroscopy.
What does the exponential decay rate T2∗ indicate in the context of FID?
T2∗ represents the rate at which the signal decays due to inhomogeneities in the magnetic field and interactions within the sample, with the signal typically decaying to nothing in a time equal to 5T2∗
What is the purpose of Quadrature Phase Sensitive Detection in NMR?
Quadrature Phase Sensitive Detection allows for the distinction between positive and negative frequency differences relative to a reference, enhancing the analysis of NMR signals.
How does Quadrature Detection work?
It employs two PSDs with a 90-degree phase shift between reference signals, enabling the separate detection of real and imaginary components of the signal, which correspond to the cosine and sine of the frequency difference, respectively.
What is Free Induction Decay (FID) in NMR?
FID is the signal detected in NMR that oscillates at the difference between the Larmor and oscillator frequencies (ωL−ω0)and decays exponentially with a characteristic time T2∗
3 Steps of a MRI scanner
1 - Production of RF pulses
2- Signal Detection
3- Gradient
How do MRI produce signals
Computer send pulse to waveform controller.
Frequency synthesiser produces RF freq (usually set at Larmor freq)
Multiplied by RF pulse envelope in mixer
giving RF pulse consisting of an RF carrier frequency modulated at audio-frequencieS
pulse is then passed to an RF
amplifier before being sent to the RF coil
How do MRI detect signals?
Reference signal from synthesiser is passed through quadrature splitter producing two reference signals at 90 degrees out of pjse
Signal detected by RF coil sends pre amp- so SNR is dominated by coil and sample not electronics
mixed with ref signals in two quadrature phase sensitive detectors - demodulated signals to audio frequencies
Sent to two analogue digital converters and sent to computer to be processed and stored
What are gradients in MRI?
Gradients encode image information
Waveform controller produces analogue gradent waveforms amplified by gradient amplifiers,
