MRI Pulse Sequences: IR, EPI, PC, 2D and 3D Lawrence P. Panych Radiology Department Brigham and Women’s Hospital Harvard Medical School

Selective Excitation RF mz mz mz mz my my my my mx mx mx mx mz mz mz mz my my my my mx mx mx mx mz mz mz mz my my my my mx mx mx mx Excite magnetization in transverse plane where it can be detected

Special gradient coils give a linear variation of mz my mx w1 w2 w3 w4 Resonant frequency, w x Good reason that data comes Fourier encoded. In general, is not that easy to locally interrogate the spin system. In response to an interrogation the spins all `talk’ at once and we only have one listening device. To localize information, an effective way is to vary the frequency of the local responses, record the responses over the full frequency spectrum and then do a frequency analysis. Special gradient coils give a linear variation of field strength with spatial location. The result is a proportional mapping between resonant frequency and spatial location

Gradient on during RF With an applied field Excite spins here With an applied field gradient, the resonant frequency varies with position Excite spins here

Slice selection with shaped RF Excite spins here Resonant frequency varies with position Excite spins here

Slice selection with shaped RF

my mx mz

Fourier Encoding – 2D example, 2x2 FOV Initial State After RF Excitation my my a b mx a b mx mz mz y c d c d In exploring non-Fourier encoding it is best to first be clear about Fourier encoding. I find a simple 2x2 example to be useful to follow the steps in Fourier encoded MRI. Imagine that we are resolving 4 voxels within the imaging volume. The system is represented by 4 magnetization vectors arranged as shown Initially, along Mz. After RF excitation, magnetization vector is titled to produce some component in the transverse plane. In the 2x2 example, the transverse components are encoded on two separate excitations using x and y gradients to manipulate the phases of each vector. RF Pulse x There are 4 unknowns (a-d), therefore, we need 4 measurements. Since there are 2 dimensions, we need 2 spatial gradients.

Fourier Encoding (Step 1) t0 t1 t2 a b c d Initially after excitation, all vectors are aligned. Assume that the goal is to detemine the magnitudes of the individual vectors, [abcd]. What we record is a phase sensitive signal proportional to the vector magnitudes. On first excitation, at t1 before the effect of any gradients is felt, signal A is recorded and is equal to a+b+c+d. A second measurement is acquired at t2 at which time the effect of the x gradient is to change the phase of magnetization vectors on the right side of the volume. RF excitation Y Gradient Off X Gradient On Signal at time t1 = A = a + b + c + d Signal at time t2 = B = a - b + c - d

Fourier Encoding (Step 2) t0 t1 t2 a b c d So far only have 2 measurements but have 4 variables. Also, there has not been any variation in the vertical direction. Therefore, organize a 2nd encoding step. This time put on a y gradient right after the excitation to invert the phase of the mag vectors at the bottom. At t1, signal C is recorded as above. At t2, the effect of the x gradient is again to invert the phase of mag vectors on the right side of the volume. A final signal D is recorded. RF excitation Y Gradient On X Gradient On Signal at time t1 = C = a + b - c - d Signal at time t2 = D = a - b - c + d

Fourier Encoding – Matrix Representation System of Equations: Alternate Form: From 1st Excitation: A = a + b + c + d B = a - b + c - d From 2nd Excitation: C = a + b - c - d D = a - b - c + d A 1 1 1 1 a B 1 -1 1 -1 b C 1 1 -1 -1 c D 1 -1 -1 1 d = A B 1 1 a b 1 1 C D 1 -1 c d 1 -1 Summary. Four equations and 4 unknowns. Can solve for [a,b,c,d]. Easy to invert the 4x4 matrix above. Can represent in an alterative form showing explicitly the encoding matrices for the vertical and horizontal directions. = Image matrix Data matrix (k-space) Horizontal (x) Encoding Vertical (y) Encoding

Fourier Encoding - using gradients to encode phase B A + B A - B 2 4 8 x = A B C D A + B + C + D A - iB - C + iD A - B + C - D A + iB - C - iD x = A B C D E F G H x

Fy Fx Echo-Planar Imaging (EPI) A B D C a b d c t0 t1 t2 t3 t4 c d Xgrad Ygrad Initially after excitation, all vectors are aligned. Assume that the goal is to detemine the magnitudes of the individual vectors, [abcd]. What we record is a phase sensitive signal proportional to the vector magnitudes. On first excitation, at t1 before the effect of any gradients is felt, signal A is recorded and is equal to a+b+c+d. A second measurement is acquired at t2 at which time the effect of the x gradient is to change the phase of magnetization vectors on the right side of the volume. A = a + b + c + d A B D C a b d c Fy Fx B = a - b + c - d RF C = a - b - c + d D = a + b - c - d k-space image space

Fy Fx Echo-Planar Imaging (EPI) Xgrad Ygrad 3 5 7 9 11 Xgrad Ygrad RF 2 4 6 8 10 12 ………. 1 2 3 4 5 6 7 8 9 10 11 12 Fy Fx Initially after excitation, all vectors are aligned. Assume that the goal is to detemine the magnitudes of the individual vectors, [abcd]. What we record is a phase sensitive signal proportional to the vector magnitudes. On first excitation, at t1 before the effect of any gradients is felt, signal A is recorded and is equal to a+b+c+d. A second measurement is acquired at t2 at which time the effect of the x gradient is to change the phase of magnetization vectors on the right side of the volume. k-space data acquired in 1 shot

Echo-Planar Imaging (EPI) 3 5 7 9 11 Xgrad RF 2 4 6 8 10 12 ………. time Variable acquisition time for each k-space line results in image distortion. What is the TE?

Single Value Single Echo EPI TE TE ? TE ? RF NxN shots N shots 1 shot Gx Gy Acquire Single Value TE N shots Gx Gy Acquire TE ? Single Echo 1 shot Gx Gy Acquire TE ? EPI

General Structure of a MR Pulse Sequence Preparation Excitation Evolution Encode/Acquire Variation in TR delay Alter T1 weighting Variation in TE delay Alter T2 weighting

General Structure of a MR Pulse Sequence Preparation Excitation Evolution Encode/Acquire Saturation pulse or Inversion pulse Velocity encoding or Diffusion encoding

Phase Contrast MR Pulse Sequences Preparation Excitation Evolution Encode/Acquire Velocity encoding gradient

Bi-polar gradient pulse Resonant frequency x Position of static spins

Bi-polar gradient pulse Resonant frequency x Position of static spins

Bi-polar gradient pulse Resonant frequency x Position of static spins

Bi-polar gradient pulse Resonant frequency x Position of static spins

Bi-polar gradient pulse Resonant frequency x Position of static spins

Resonant frequency x

Resonant frequency x

Resonant frequency x

Resonant frequency x

What happens if spins are not static ?

Resonant frequency x Position of moving spins

Resonant frequency x Position of moving spins

Resonant frequency x Position of moving spins

Resonant frequency x Position of moving spins

Resonant frequency x Position of moving spins

Resonant frequency x Position of moving spins

Resonant frequency x Position of moving spins

Resonant frequency x Position of moving spins

Resonant frequency x Position of moving spins

Inversion Recovery MR Pulse Sequences Preparation Excitation Evolution Encode/Acquire TI Inversion pulse

Inversion Recovery MR Pulse Sequences Mz Mz Gray Matter White Matter Blood MS lesion CSF Recovery of Mz after IR pulse Mz = Mo (1 - 2exp(-TI/T1)) -Mz TI Gray matter = 950ms, White matter = 650ms, CSF = 4200ms, Blood = 1200ms, MS lesions = 1300

Inversion Recovery - Gray/White Contrast Mz Gray Matter White Matter Mz (White Matter) - Mz (Gray Matter) TI

Inversion Recovery - Flow Sensitive Mz Blood Blood Null point TI Acquisition 1 Acquisition 2 Non-selective inversion Not flow sensitive Selective inversion Flow sensitive Selected Slice

Inversion Recovery - Fluid Suppression Other spins have mostly recovered Mz CSF CSF Null point TI