MRI Physics in a Nutshell Christian Schwarzbauer

MR images: What do we see ? MRI images are usually based on the signal from protons A Proton is the nucleus of the hydrogen atom Hydrogen is the most common element in tissue The signal from protons is due to their „spin“

The nuclear spin Elementary property of an atomic nucleus Each spin carries an elementary magnetization Spins align in an external magnetic field (like a compass needle)

Macroscopic sample

Macroscopic sample B0 M

Excitation B0 M radio waves  =  B0

 =  B0 Precession and signal induction M 123 MHz @ 3T receiver coil NMR signal

Longitudinal and transverse components Mz M Mxy

Exication with different pulse angles equilibrium state 90o pulse (maximum signal) 30o pulse 180o pulse (no signal)

Relaxation non-equilibrium state RF pulse relaxation equilibrium state

1 Ml M0 T1 2 Mt 0 T2 Relaxation Two independent relaxation processes: T1: “longitudinal relaxation time” ( 1 s) T2: “transverse relaxation time” ( 100 ms)

Relaxation Transverse Magnetization vanishes quickly (short T2) Longitudinal Magnetization relaxes slowly (long T1)

 =  B0 Signal loss due to magnetic field inhomogeneities t = 10 ms  =  B0 t = 20 ms has higher frequency than

Effective transverse relaxation (T2* < T2) Spin dephasing as a result of magnetic field inhomogeneities Transverse relaxation (T2) Effective transverse relaxation (T2* < T2)

Effective transverse relaxation time [ ms ] 20 40 60 80 No inhomogeneities (T2* = 100 ms) Moderate inhomogeneities (T2* = 40 ms) Strong inhomogeneities (T2* = 10 ms)

T2* related signal dropouts T2* reduction due to local field inhomogeneities  signal dropouts reduced T2* normal T2* (about 40 ms) EPI image

B0  =  B0 B  =  (B0 + s Gs) Gs The principle of MRI Homogeneous magnetic field B0  =  (B0 + s Gs) Add magnetic field gradient Gs B

Slice selective excitation  =  (B0 + s Gs) Gs w > w0 w = w0 RF pulse (0) w < w0 Only spins in slice of interest have frequency w0 RF pulse with frequency w0 excites only spins in slice of interest

Slice position Gs s1 s0  =  (B0 + s Gs)

Slice orientation Gs  =  (B0 + s Gs)

Mulit-slice MRI Gs 4 3 2 1  =  (B0 + s Gs)

Slice profile  =  (B0 + s Gs) Frequency (w) Dw Position (s) A rectangular-shaped frequency distribution only exists in theory Position (s) Ds

Slice profile  =  (B0 + s Gs) Frequency (w) Dw Position (s) Gaussian-shaped frequency distribution Position (s) Ds

Slice thickness (SLTH) SLTH = Full width at half maximum of the slice profile

Multi-slice MRI SLTH Gap Slice 1 Slice 2 Slice 3 Tissue in the inter-slice gap contibutes to the signal of the adjacent slices

Spatial encoding Slice selective excitation Transverse magnetization precesses in the excited slice ( =  B0)

Spatial encoding Gradient pulse in x-direction Gx

Spatial encoding Gy Gradient pulse in x-direction Gradient pulse in y-direction

Spatial encoding Gradient pulse in x-direction Gradient pulse in y-direction Signal:

Image reconstruction and k-space (Simple example: 3 x 3 matrix) Fast Fourier Transform (FFT) y ky x kx Object space (9 unknown parameters) K space

Image reconstruction and k-space (Experimental data: 128 x 128 matrix) FFT K space (raw data) Object space (image)

Conventional MRI (e.g. MP-RAGE) Gx Gy Signal acquisition (digital sampling) Selective excitation 1 kx ky K space

Conventional MRI (e.g. MP-RAGE) Gx Gy Signal acquisition (digital sampling) Selective excitation 2 kx ky K space

Conventional MRI (e.g. MP-RAGE) Gx Gy Signal acquisition (digital sampling) Selective excitation 5 kx ky K space

Conventional MRI (e.g. MP-RAGE) 1st excitation 2nd excitation nth excitation Problem: This sequence is rather slow K space is sampled line by line After each excitation one must wait for the longitudinal magnetization to recover Example: n = 256, TR = 2s T = n TR = 8.5 min

Echo-planar imaging (EPI) kx ky K space Signal acquisition (digital sampling) Gx Gy Selective excitation

EPI: A technical challenge Signal decay due to transverse relaxation (Example: T2* = 40ms) time [ ms ] 20 40 60 80 Within 80 ms the signal has decayed to nothing Complete image must be acquired in less than 80 ms (in general: T = 2 T2*) High temporal, but low spatial resolution

Acquisition time: 62.5 ms per slice EPI at the CBU Slice thickness: 3 mm Inter-slice gap: 0.75 mm (25 %) Number of slices: 32 (whole brain coverage) Matrix size: 64 x 64 Field of view: 192 x 192 mm Spatial resolution (in-plane): 3 x 3 mm Echo time (TE): 30 ms Repetition time (TR): 2000 ms Acquisition time: 62.5 ms per slice

Standard slice orientation How many slices ? 120 mm = 32 3 mm + 0.75 mm And the minimum TR ? 32 * 62.5 ms = 2000 ms 120 mm

Coronal slice orientation How many slices ? 180 mm = 48 3 mm + 0.75 mm And the minimum TR ? 48 * 62.5 ms = 3000 ms 180 mm