G16.4427 Practical MRI 1 – 12 th February 2015 G16.4427 Practical MRI 1 Radiofrequency Pulse...

G16.4427 Practical MRI 1 – 12th February 2015

G16.4427 Practical MRI 1

Radiofrequency Pulse Shapes and Functions


Small Tip-Angle Approximation• It is easier to solve the Bloch equation after making

the following assumptions:– At equilibrium Mrot = [0 0 M0] (initial condition)– RF pulse is weak leading to a small tip angle θ < 30°

• The Bloch equations become:

= 0 Why ?

We also turn off the RF field before observing the evolution of the magnetization

No Off-Resonance Effects ωrf = ω0


Solution of the Bloch Equation• The transverse and longitudinal components are

decoupled:

• We are usually interested in the transverse component, as it determines the time signal detected:


A k-Space Analysis of Small-Tip-Angle Excitation


Useful Quantities to Describe RF Pulses• Pulse width (T)– Indicates the duration of the RF pulse– Typically measured in seconds or milliseconds

• RF bandwidth (∆f)– A measure of the frequency content of the pulse– FWHM of the frequency profile– Specified in hertz or kilohertz

• Flip angle (θ)– Describes the nutation angle produced by the pulse– Measured in radians or degrees– Calculated by finding the area underneath the envelope

of the RF pulse


RF Envelope• Denoted with B1(t) and measured in microteslas• Relatively slowly varying function of time, with

at most a few zero-crossings per millisecond• The RF pulse played at the transmit coil is a

sinusoidal carrier waveform that is modulated (i.e. multiplied) by the RF envelope

• The frequency of the RF carrier is typically set equal to the Larmor frequency ± the frequency offset required for the desired slice location


RF Envelope vs. RF CarrierRF envelope - B1(t)

RF carrier

• The RF envelope describes the pulse shape, i.e. the magnetic field in the rotating frame


SLR Pulses• For small flip-angles, the shape of an RF pulse can be

determined by inverse Fourier transformation of the desired slice profile

• The Shinnar-Le Roux (SLR) algorithm allows the inverse problem to be solved directly and efficiently without iterations– Allows the pulse designer to optimize the pulse before it’s

generated– Uses the SU(2) representation for rotations and the hard

pulse approximation to describe the effect of a soft pulse on the magnetization with 2 polynomials of complex coefficients

– Given 2 complex polynomials corresponding to the desired magnetization, the inverse SLR transform yields the RF pulse


Practical Considerations For SLR Pulses• Pulses designed with SLR account for the

nonlinearity of Bloch equations only at a single flip angle– If played at a different flip angle there will be

deviations from the desired profile• If this is an important consideration:– A set of pulses designed for different flip angles

could be stored on the MR scanner– The SLR design could be done in real time when

the operator selects the flip angle


Variable-Rate (VR) Pulses• A one-dimensional spatially selective RF pulse

that is played concurrently with a time-varying gradient is called a variable-rate (VR) pulse– Also known as VRG or VERSE pulses

• The main application is to reduce SAR– Decrease RF amplitude near the peak of the pulse


Variable-Rate (VR) Pulses• A one-dimensional spatially selective RF pulse

that is played concurrently with a time-varying gradient is called a variable-rate (VR) pulse– Also known as VRG or VERSE pulses

• The main application is to reduce SAR– Decrease RF amplitude near the peak of the pulse

• Another application is to play the RF excitation concurrently with the gradient ramps– Efficient use of the entire time allotted for the

slice-selection gradient lobe, which improves slice profile


VR-Modified SINC Pulse• To maintain the nominal flip angle when RF amplitude

is reduced, the VR pulse is proportionately stretched (time delayed). Why?

Answer: flip angle is the area under the RF envelope



is reduced, the VR pulse is proportionately stretched (time delayed).– What happens as a result?



is reduced, the VR pulse is proportionately stretched (time delayed). – As a result the RF bandwidth is decreased– The slice selection gradient amplitude must be

proportionately reduced to obtain the same slice profile

Bernstein et al. (2004)Handbook of MRI Pulse Sequences.


Off-Resonance Effects• A VR-modified pulse is designed to maintain the

original slice profile for on-resonance spins (e.g. water)– The pulse designer can dilate the RF pulse and adjust the

gradient, but has no control over the precession period of off-resonance spins

– The slice profile of off-resonance spins (e.g. fat) is distorted

On-ResonanceProfile

Off-ResonanceProfile

(Original Pulse)

Off-ResonanceProfile

(VR Pulse)



Any questions?


Basic Radiofrequency (RF) Functions


Excitation Pulses• Excitation pulses tip the magnetization vector away

from the direction of B0

– They are implemented by switching on B1(t) for a short time (200 μs to 5 ms)

– T1 and T2 relaxation during the pulse can be neglected

• They are characterized by the flip angle (θ), which is the angle between the direction of B0 and the magnetization vector after turning off RF– For non-adiabatic excitation pulses, θ is calculated as the

area under the envelope of B1(t)– Typically θ = 90° for spin echo and θ = 5-70° for gradient

echo


Slice Profile And Flip Angle• The distribution of the flip angle across the

selected slice is called the slice profile– What is the ideal slice profile?



selected slice is called the slice profile– The ideal slice profile consists of a uniform flip

angle within the desired slice and θ = 0° outside– Why it cannot be achieved in practice?



selected slice is called the slice profile– The ideal slice profile consists of a uniform flip

angle within the desired slice and θ = 0 outside– It would require a pulse of infinite duration, so

several approximations are used in practice• Problem– A hard RF pulse has a rectangular-shaped envelope.

Its pulse width is 100 μs and its flip angle (on-resonance) is 90°. What is its amplitude?


Inversion Pulses• An inversion pulse nutates the magnetization

vector from the direction of B0 to the negative B0 direction– The nominal flip angle is 180°


Examples of Inversion PulsesSLR inversion pulse Slice profile

SINC inversion pulsewith Hamming window Slice profile



Application: T1 Measurement• One popular method to measure T1 is the inversion-recovery

method– The magnetization is inverted with a 180° RF pulse and then spin-lattice

relaxation begins– After a time TI, the value of Mz is detected applying a 90° RF pulse and

measuring the FID signal– The measurement is repeated for several TI and T1 is calculated by fitting

the inversion recovery equation

t


Refocusing Pulses• Due to the gradients, local magnetic field

inhomogeneities, magnetic susceptibility variation, or chemical shift, the spins contributing to the transverse magnetization have a range of precessing frequencies– As a result there is a phase dispersion (fanning out)

• A refocusing RF pulse (typically 180°) rotates the dispersing spins about an axis in the transverse plane so the the magnetization vector will rephase (or refocus) at a later time– The refocused magnetization is known as spin echo


Graphical Explanation

tRF


Application: T2 Mapping• The simplest method to map T2 is the multi-echo method

– Multiple images are acquired with different time delays– The resulting intensities are fitted on a pixel-by-pixel basis to

extract the T2 value using the spin-spin relaxation curve

t


Any questions?


See you next Thursday!

G16.4427 Practical MRI 1 – 12 th February 2015 G16.4427 Practical MRI 1 Radiofrequency Pulse...

Documents

Transcript of G16.4427 Practical MRI 1 – 12 th February 2015 G16.4427 Practical MRI 1 Radiofrequency Pulse...