Quiz In a 2D spin warp or FT MR scan, aliasing should only occur a) in the slice select direction b) in the readout direction c) in the phase encoding direction Between adjacent phase encodes, the larger phase encode has an additional p phase wrap across the FOV in the y direction. Between k-space samples in the readout direction, there is a relative 2 p phase wrap across the FOV in the x direction.

Imaging Considerations We have touched earlier on some the effects that make the imaged slice magnetization look complex. Let’s quantify some of them. Main field inhomogeneity Bo inhomogeneity ( also know as shim) a) magnet 1.5 T shim specifications to 1/3 ppm (parts per million) over a 20 cm diameter sphere ~ 20 Hz at 1.5 T Is this significant?

Patient-Induced Inhomogeneity Main field inhomogeneity Tissue’s bulk magnetic susceptibility, , can vary.  varies by 10-6 to 10-5 1 ppm to 12 ppm Worst areas: tissue-air interface lung / abdomen sinus intestines Chemical Shift: Electronic shielding reduces the magnetic field seen by the fat molecules.

Patient-Induced Inhomogeneity z component of magnetic field is the field inhomogeneity term. - unintended - due to local neighborhood inhomogeneity - T2 effect T2* Varying magnetic field in immediate neighborhood (within a voxel) causes in-plane spins to dephase earlier than intended T2 decay. The faster decay has a decay constant referred to as T2*

T2* is actual decay in gradient echo experiment. T2* Equation T2* is actual decay in gradient echo experiment. T2 is actual spin-spin decay of material. We will see how to easily measure this today. Last term is decay due to local magnetic environment

Causes of Phase Error Main field inhomogeneity, patient-induced inhomogeneity, gradient non-linearity, and blood flow all cause phase errors (or frequency errors, depending on your point of view). That is, spins will resonate faster or slower than our basic formula predicts. Chemical shift is another type of phase error. Let’s study the effects of these phenomena on the two major classes of MR imaging sequences.

Gradient Echo  This is what we have studied to date: 90º RF t Gx t s(t) t t  2 Where does the gradient echo form? What happens when we push the echo time out?

2D Fourier Transform (2) 2D Fourier Transform: (2D FT or Spin Warp) 1) RF t 6GRADECH.AVI The location or phase of spins throughout the x,y plane The first time point shows the spins immediately after the RF pulse. In the left plot, no gradient is played. In the right plot, the gradient waveform has equal positive and negative areas. The marker on top labeled “MAG1” or “MAG2” gives the magnitude of the signal in each case. In the left plot, a local magnetic field distortion is present that causes the vectors to become dephased naturally and the vector sum of the vectors to become smaller over time (T2* decay). This dephasing can be observed over a period of 16 frames in the vector plot on the left. The vector sum of the magnetization vectors during T2* decay is indicated by MAG1. On the right is shown the same distribution of magnetization vectors in the same local field distortion, but with the addition of an applied magnetic field gradient along the x-direction. The vector sum of the magnetization vectors with this additional dephasing is indicated by MAG2. The additional dephasing caused by this gradient can be seen by comparing the left and right vector-field plots, as well as by comparing MAG1 and MAG2. After 8 frames, the field gradient is reversed. This can be seen by observing the behavior of the vectors in the bottom- most row on the right. As well, the value of MAG2 begins to increase. The reversed gradient undoes the dephasing of the originally applied gradient so that, after 16 frames, the vector field plots and their sums are equal. As shown here, a gradient echo does not restore the signal decay caused by field inhomogeneities or other sources of dephasing. It merely corrects its own effects.In the left plot, spins dephase due to a magnetic field inhomogeneity. Gx(t)

Susceptibility Artifacts Short echo time Water /plastic interface has large susceptibility. Notice dropout of signal around water discs in bottom image. Note: Not exactly the same slice and so bottom slice has some water signal also around discs. Longer echo time

Perils of Gradient Echo Imaging and T2* TE = 8 ms TE = 24 ms 0.17 T GE Orthopedic Scanner

Spin Echo Phenomenon

  Spin Echo Generation Spin Echo Generation: 90º 180º (a) (b) (c) (d) (e) Spin Echo Generation: Following a 90º excitation pulse, (a -b) the spin vectors begin to fan out and dephase because of precessional frequency differences (c) at time , a 180º excitation rotates all the spins about the x’ axis (d) The spin vectors continue to precess at their slightly different frequencies, rephasing at time 2 (e). (alternate to slide 7 - original caption) Nishimura Image Copyright Nishimura

Tip Bulk Magnetization y' x'

Tip Bulk Magnetization 1 y' x'

Tip Bulk Magnetization 1 y' x'

Tip Bulk Magnetization 1 y' x'

Tip Bulk Magnetization 1 y' x'

Transverse Magnetization y' Mtrans x'

T2 Decay z' s y' f x' T2 relaxation is dephasing of transverse magnetization

T2 Decay z' s y' f x' T2 relaxation is dephasing of transverse magnetization

T2 Decay z' s y' f x' T2 relaxation is dephasing of transverse magnetization

Refocusing Pulse z' s y' B 1 f x'

Refocusing Pulse z' s y' B 1 f x'

Refocusing Pulse z' s y' B 1 f x'

Rephasing z' s y' f x'

Rephasing z' s y' f x'

Rephasing z' s y' f x'

Echo Formation z' y' Mtrans x'

Spin Echoes The phase errors E are for the most part out of our control, but there is a method around them called a spin echo. Chemical shift, CS , can be compensated with techniques beyond the scope of this class. But these require more scan time also.. However, we can use a “spin echo” to correct for both effects. Spin echoes form the second major class of pulse sequences. Spin echoes use a 90º pulse as we have seen, but also a second RF pulse, a 180º pulse. Let’s first consider just the effects of off-resonance and ignore the imaging gradients. 180º 90º RF t  2

Spin Echo Generation in Rotating Frame   90º 180º (a) (b) (c) (d) (e) The phase error just prior to the 180º pulse is Just after the 180º pulse, it is Then we let the spins progress for another . A “spin echo” is said to be formed at t=2 Image Copyright Nishimura

Effect of echo delay on signal loss Effect of echo delay on susceptibility-induced signal losses: (a) TE = 15 ms (b) TE = 10 ms (c) TE = 5 ms Note artifactual signal reduction in the region of the nasal and mastoid sinuses. Notice homogeneity of water discs and air bubble appearance. image source?

Spin Echo Pulse Sequence t t Echo Time (TE) = 2 t Z grad 90 180 90 RF X Grad TE Gy Y Grad TR

Spin Echo Signal Plus X Readout Gradient 6SPINECH.AVI Left plot experiences no refocusing pulse. Right plot experiences refocusing pulse half way through time series. Sum of magnitude of spins given on top. Time series ends at echo time.

Spin Echo RF Sequence T2 T2* TE TR T2* 1 = T2 + B0

Spin Echo Sequence with 180 y pulse Fig 14.13 from Illustrator mag 120%

Spin Echo Sequence – Long Versus Short T2 long T2 long T2 short T2 short T2 T2-weighting: long TE, long TR PD-weighting: short TE, long TR

T1, T2, and Density-Weighted Images T1_brain_w_tumor.tif, t2_brain_w_tumor.tif, density_brain_w_tumor.tif From wesolak, janet, series 2, image 16, series 3, image 38, series 3, image 37 T1-weighted T2-weighted r-weighted

Scan Duration Scan Time = TR  PE  NEX TR = repetition time PE = number of phase encoding values NEX = number of excitations (averages)

Spin Echo Formation For spins to be refocused, they must experience the same magnetic field after the 180 refocusing pulse as they experienced before the 180 refocusing pulse. Thus, only dephasing due to macroscopic inhomogeneities (B0) is refocused. Dephasing due to microscopic inhomogenieties (T2) is not refocused.

Spin Echo Parameters TR TE T1-weighting short (400 msec) long (3000 msec) long (100 msec) -weighting

Signal vs Weighting T1-weighted T2-weighted r-weighted T1-weighting long T1, small signal short T1, large signal T2-weighting long T2, large signal short T2, small signal -weighting high , large signal low , small signal

Images of the Knee -weighted T2-weighted Needs longer TE

T2 & T2* Relaxation: Image Contrast Sources Mxy T2* Time T2* 1 = T2 + B0

FSE Pulse Sequence Timing Diagram 90° 180° 180° 180° 180° rf Slice Select Phase Encode Freq. Encode ETL=4 Signal ESP

Filling k-space FSE Phase Direction Frequency Direction

Scan Duration Scan Time = TR  PE/ETL  NEX TR = repetition time PE = number of phase encoding values NEX = number of excitations (averages) ETL = echo train length

T2 Weighting (Various Sequences) TR = 2500 TE = 116 ETL = 16 NEX = 2 24 slices 17 slices/pass 2 passes Time = 2:51 TR = 2500 TE = 112 ETL = N/A NEX = 1 24 slices 20 slices/pass 2 passes Time = 22:21 FSE SE

Inversion Recovery RF Sequence

Inversion Recovery (IR) Sequence & Spin Behavior

Inversion Recovery rf Slice Select Phase Encode Freq. Encode Signal TI 180° 90° 180° rf Slice Select Phase Encode Freq. Encode Signal

IR Sequence – Short Versus Long T1 Fig 14.18 from Illustrator mag 150%, separate sections

Inversion Recovery Signal Mlong short T1 longer T1 Short T1 = brighter Long T1 = darker TI

Inversion Recovery Signal Mlong short T1 longer T1 Short T1 = brighter Long T1 = null TI

Short Tau Inversion Recovery (Fat Nulled) STIR Mlong short T1 (fat) longer T1 Short T1 = null Long T1 = brighter TI

Spine: T1 versus T2 versus STIR

Inversion Recovery II IR pulse precedes T2-weighted sequence Coronal Tumor Here the inversion recovery delay is very long ( ~2 s). Here the idea is to null CSF so one can distinguish tumor from CSF. Notice tumor still has positive contrast.

MR: SNR vs Field Strength Signal - energy separation of Zeeman levels - Faraday’s Law of Induction Signal amplitude is Noise Power Receiver - electronics - patient electrons in Brownian motion Patient Patient noise dominates at most field strengths

SNR We will first consider the case where we ignore T1 and T2 of the tissue involved. leave sequence dependent effects for later

SNR Noise Power Study for impulse at x=0, y = 0 Each k-space point has signal A, noise power 2 Each sampled point is independent with respect to noise. ky Amplitude of Signal = NxNyA Noise Power = NxNy 2 Ny kx Nx sampling interval in time

voxel size since this determines the # of protons per voxel SNR voxel size since this determines the # of protons per voxel Replace A above by voxel size Together, SNR Time Resolution

Scan Time Image b) has twice the SNR as a) at an expense of four times the scan time

Axial Forearm T2-Weighted TE = 15 ms TE = 45 ms TE = 75 ms TR = 4000 ms for all Notice appearance of supinator Muscle ( arrow) on all images. One arm had an exercise protocol. Which one? What is in between arms? TE = 105 ms

q q q q TR During each TR, Mz will recover. When in steady-state, Where n-1 is the n-1th RF pulse and n is the nth RF pulse.