Magnetic Resonance Imaging Physical Principles Richard Watts D

Magnetic Resonance Imaging: Physical Principles Richard Watts, D. Phil. , Yi Wang, Ph. D. Weill Medical College of Cornell University, New York, USA

Physics of MRI, Lecture 1 • Nuclear Magnetic Resonance – Nuclear spins – Spin precession and the Larmor equation – Static B 0 – RF excitation – RF detection • Fourier Transforms – Continuous Fourier Transform – Discrete Fourier Transform – Fourier properties – k-space representation in MRI • Spatial Encoding – Slice selective excitation – Frequency encoding – Phase encoding – Image reconstruction 9/17/2020 2

Physics of MRI, Lecture 2 • Echo formation – Vector summation – Phase dispersion – Phase refocus • 2 D Pulse Sequences – Spin echo – Gradient echo – Echo-Planar Imaging 9/17/2020 • Medical Applications – Contrast in MRI – Bloch equation • Tissue properties – T 1 weighted imaging – T 2 weighted imaging – Spin density imaging • Examples • 3 D Imaging • Spectroscopy 3

Many spins in a voxel: vector summation spins in step spins not in step Rotating frame Lamor precession 9/17/2020 4

Phase dispersion due to perturbing B fields Spin Phase f g. Bt B = B 0 + d. Bcs + d. Bpp sampling Immediately after RF excitation 9/17/2020 sometime after RF excitation 5

Refocus spin phase – echo formation Echo Time (TE) • Invert perturbing field: d. B Phase 0 d. Bt (gradient echo, k-space sampling) • Invert spin state: Phase 0 (spin echo) 9/17/2020 d. Bt -d. B f-d. B(t-TE/2) f -f -f+d. B(t-TE/2) time 0 0 6

Spin Echo • Spins dephase with time • Rephase spins with a 180° pulse • Echo time, TE • Repeat time, TR • (Running analogy) 9/17/2020 7

Frequency encoding - 1 D imaging Spatial-varying resonance frequency during RF detection B = B 0 + Gxx S(t) ~ eig. Bt S(t) ~ m(x)eig. Gxxtdx m(x) x ikxxdx = S(k ), S(t) = m(x)e x 9/17/2020 kx = g. Gxt m(x) = FT{S(kx)} 8

Slice selection Spatial-varying resonance frequency during RF excitation w w = w 0 + g. Gzz B 1 freq band z Excited location Slice profile 9/17/2020 m+ = mx+imy ~ g b 1(t)e-ig. Gzztdt = B 1(g. Gzz) 9

rd 3 dimension – phase encoding Before frequency encoding and after slice selection, apply y-gradient pulse that makes spin phase varying linearly in y. Repeat RF excitation and detection with different gradient area. S(ky, t) = ( m+(x, y, z)dz)eikyyeig. Gxxtdxdy 9/17/2020 10

Gradient Echo FT imaging ky Readout kx 9/17/2020 Repeat with different phase-encoding amplitudes to fill k-space 11

Pulse sequence design prewinder spoiler rephasor rewinder spoiler 9/17/2020 12

X EPI (echo planar imaging) ky Y Z kx RF time Quick, but very susceptible to artifacts, particularly B 0 field inhomogeneity. Can acquire a whole image with one RF pulse – single shot EPI 9/17/2020 13

Spin Echo FT imaging ky Readout kx 9/17/2020 Repeat with different phase-encoding 14 amplitudes to fill k-space

Spin Relaxation • Spins do not continue to precess forever • Longitudinal magnetization returns to equilibrium due to spin-lattice interactions – T 1 decay • Transverse magnetization is reduced due to both spin-lattice energy loss and local, random, spin dephasing – T 2 decay • Additional dephasing is introduced by magnetic field inhomogeneities within a voxel – T 2' decay. This can be reversible, unlike T 2 decay 9/17/2020 15

Bloch Equation • The equation of MR physics • Summarizes the interaction of a nuclear spin with the external magnetic field B and its local environment (relaxation effects) 9/17/2020 16

Contrast - T 1 Decay • Longitudinal relaxation due to spin-lattice interaction • Mz grows back towards its equilibrium value, M 0 • For short TR, equilibrium moment is reduced 9/17/2020 17

Contrast - T 2 Decay • Transverse relaxation due to spin dephasing • T 2 irreversible dephasing • T 2/ reversible dephasing • Combined effect 9/17/2020 18

Free Induction Decay – Gradient echo (GRE) • Excite spins, then measure decay • Problems: – Rapid signal decay – Acquisition must be disabled during RF – Don’t get central “echo” data 9/17/2020 MR signal e-t/T 2* time 0 90 RF 19

Spin echo (SE) MR signal e-t/T 2* time 0 90 RF 9/17/2020 0 180 RF 20

MR Parameters: TE and TR • Echo time, TE is the time from the RF excitation to the center of the echo being received. Shorter echo times allow less T 2 signal decay • Repetition time, TR is the time between one acquisition and the next. Short TR values do not allow the spins to recover their longitudinal magnetization, so the net magnetization available is reduced, depending on the value of T 1 • Short TE and long TR give strong signals 9/17/2020 21

Contrast, Imaging Parameters 9/17/2020 22

Properties of Body Tissues Tissue T 1 (ms) T 2 (ms) Grey Matter (GM) 950 100 White Matter (WM) 600 80 Muscle 900 50 Cerebrospinal Fluid (CSF) 4500 2200 Fat 250 60 Blood 1200 100 -200 MRI has high contrast for different tissue types! 9/17/2020 23

MRI of the Brain - Sagittal T 1 Contrast TE = 14 ms TR = 400 ms 9/17/2020 T 2 Contrast TE = 100 ms TR = 1500 ms Proton Density TE = 14 ms TR = 1500 ms 24

MRI of the Brain - Axial T 1 Contrast TE = 14 ms TR = 400 ms 9/17/2020 T 2 Contrast TE = 100 ms TR = 1500 ms Proton Density TE = 14 ms TR = 1500 ms 25

Brain - Sagittal Multislice T 1 9/17/2020 26

Brain - Axial Multislice T 1 9/17/2020 27

Brain Tumor T 1 9/17/2020 T 2 Post-Gd T 1 28

3 D Imaging • Instead of exciting a thin slice, excite a thick slab and phase encode along both ky and kz • Greater signal because more spins contribute to each acquisition • Easier to excite a uniform, thick slab than very thin slices • No gaps between slices • Motion during acquisition can be a problem 9/17/2020 29

2 D Sequence (Gradient Echo) ky acq Gx Gy kx Gz b 1 TE TR 9/17/2020 Scan time = Ny. TR 30

3 D Sequence (Gradient Echo) acq Gx kz Gy Gz b 1 9/17/2020 kx ky Scan time = Ny. Nz. TR 31

3 D Imaging - example • Contrast-enhanced MRA of the carotid arteries. Acquisition time ~25 s. • 160 x 128 x 32 acquisition (kxkykz). • 3 D volume may be reformatted in post-processing. Volume-ofinterest rendering allows a feature to be isolated. • More on contrast-enhanced MRA later 9/17/2020 32

Spectroscopy • Precession frequency depends on the chemical environment (d. Bcs) e. g. Hydrogen in water and hydrogen in fat have a f = fwater – ffat = 220 Hz • Single voxel spectroscopy excites a small (~cm 3) volume and measures signal as f(t). Different frequencies (chemicals) can be separated using Fourier transforms • Concentrations of chemicals other than water and fat tend to be very low, so signal strength is a problem • Creatine, lactate and NAA are useful indicators of tumor types 9/17/2020 33

Spectroscopy - Example Intensity 9/17/2020 Frequency 34

Future lectures • Magnetization preparation • Perfusion and diffusion (phase and magnitude, • Functional imaging pelc) (f. MRI) • Fast imaging (fast • Cardiac imaging sequences, epi, spiral…) (coronary MRA) • Motion (artifacts, compensation, correction, navigator…) • MR angiography (TOF, PC, CE) 9/17/2020 35