Physics of MR Image Acquisition

Physics of MR Image Acquisition HST-583, Fall 2002 Review: -MRI: Overview - MRI: Spatial Encoding MRI Contrast: Basic sequences - Gradient Echo - Spin Echo - Inversion Recovery : Functional Magnetic Resonance Imaging: Data Acquisition and Analysis Harvard-MIT Division of Health Sciences and Technology Dr. Jorge Jovicich

Overview of an MRI procedure Subject Safety screening Magnetic field Relaxation processes Tissue protons align with magnetic field (equilibrium state) RF pulses Protons absorb RF energy (excited state) Spatial encoding using magnetic field gradients Larmor Equation ω 0 = γ B 0 Relaxation processes Protons emit RF energy (return to equilibrium state) NMR signal detection Repeat RAW DATA MATRIX Fourier transform IMAGE S (t1,t2) S (x1,x2)

Dynamics of the Magnetization Geometrical description: damped precession B 0 M 0 RF ω = γ 0 B 0 B 0 B 0 B 0 B 0 NMR signal M 0 M (t) M (t) M (t) Equilibrium time Equilibrium Mathematical Description: precession + relaxation (Bloch equations) d r M ( t ) dt = r M ( t ) γ r B ext ( t) ( M x î + M y ĵ) T 2 * (M z M 0 ) T 1 ˆk

Spatial Encoding in MRI Key concept: ω ( r ) = γ (B 0 + G.r) Slice Selection -Location - Thickness - Rephasing/Refocussing Frequency Encoding - Fourier Transform -FOV - Gradient Echo Formation Phase Encoding - Phase / Frequency Equivalency -FOV

Slice Selection RF excitation (selective bandwidth) + magnetic field gradient RF pulse properties shape & duration frequency (w o ) bandwidth (bw) Magnetic field gradient (Gz) B B o ( ) ω ( r ) = γ B 0 + G.r w G z w o bw Schematically RF G z z o z Slice parameters z Phase Slice thickness ( z): bw = γ G z z Slice center (z o ): w o = γ G z z o

Pulse sequence so far RF slice select G z t t MR signal from whole Selected slice S(t) T 2 * Sample points Courtesy of L. Wald t

Frequency Encoding After slice selection all spins in the selected plane have the same frequency and phase (a) Signal is acquired while a magnetic field gradient G x is on (b) G x (a) (b) Gradient field y x 63 MHz 64 MHz 65 MHz x w (x) = γ G x x

Pulse sequence so far RF slice select freq. encode (read-out) G z G x S(t) t Signal dephases rapidly t t Sample points Courtesy of L. Wald t

More signal can be obtained: RF slice select freq. encode (read-out) G z G x S(t) + - Dephase Rephase Sample points Acquisition window t We can save some time

Pulse sequence so far RF slice select G z freq. encode (read-out) G x - + Gradient Echo S(t) Sample points Acquisition window t

Frequency Encoding S (t) Measured signal: time domain Fourier transform S (ω) Frequency spectrum: 1D x-projection time δt Sampling time δt=1/ bw rec N x : number of samples bw rec Receiver bandwidth (bw ) rec frequency ω ( r ) = γ (B 0 + G.r) Acquisition time (t acq ): t = N δt = N / bw acq x x rec Relevant parameters Resolution (δx): δx = FOV x / Nx Field of view (FOV x ): bw = γ G FOV rec x x

We could have measured exactly the same information differently: RF So far we ve used ONE RF excitation and we ve acquired Nx sampling points while the read-out gradient was ON slice select G z freq. encode (read-out) G x - + Each S(t) Sample points Acquisition window t

Let s look at one arbitrary sampled point in the MR signal RF RF G z G z G x - + = G x - S(t) + = - t - S(t) depends on net dephasing during t Same net dephasing S(t)

We can do the same for all Nx sampled points: RF Measure one point after dephasing gradient G z G x - RF G z Net negative dephasing G x RF G z Repeat experiment Nx times to sample all points Net zero dephasing G x + Net positive dephasing

We could have measured exactly the same information differently: RF S (t) Measured signal: time domain slice select G z time phase G x FT encode Frequency spectrum: 1D x-projection S(t) S (ω) Repeat Nx times frequency

Basic Gradient Echo Sequence RF α TE TR α Gz Slice Gy Phase Gx Read

Conventional spin-warp MRI sequence θ Repeat N phase times k phase G G slice phase RF N phase N phase G read TE k read Signal 0 Prephase t acq N read time TR Prephase The signal we measure is in γ t spatial frequency space (k-space) k (t ) = G (t ') dt ' 2π 0 N read

Pulse Sequences & Image Contrast Contents: Definition of Contrast Contrast parameters Concept of MRI contrast weighting Properties of pulse sequences & sequence parameters

Image Contrast Definition Goal: maximise the contrast ( USEFUL IMAGES! ) Contrast: difference in MR signals between different tissues Tissue 1 Tissue 2 Water protons T1, T2, T2 *, ρ, T1, T2, T2 *, ρ, mobility/environment: Diffusion, Flow Diffusion, Flow MR signal: S1 S2 Contrast to Noise ratio: CNR = S σ 1 S noise 2 Some examples?

Image Contrast: What can we manipulate? Tissue Properties: fixed Tissue T1 (ms) T2 (ms) ρ* Fat 260 84 0.90 White Matter 780 90 0.72 Gray Matter 920 100 0.84 CSF 3000 300 1.00 ρ*: % H 2 O relative to CSF Experimental Variables Pulse sequence Pulse sequence parameters - Repetition time: TR - Echo time: TE - Inversion time: TI - RF flip angle: α Contrast agent What s the effect of these variables?

Image Contrast: Weighting the MR Signal General MRI pulse sequence: combination of contrasts Signal Intensity: S(x,y) = k ρ T 1 T 2 Contrast Weighting: maximize one term, minimize the others Example: T 1 -weighting S(x,y) = k ρ T 1 T 2 by choosing adequate sequence & sequence parameters Some examples?

Typical MRI sequences Gradient Echo: - Proton Density weighting - T1 weighting - T2* weighting Spin Echo: - Proton Density weighting - T1 weighting - T2 weighting - Double echo: PD & T2 weighting Inversion Recovery: - MP-RAGE: for high T1 contrast - FLAIR: for PD or T2 weighting without CSF signal

Basic Gradient Echo Sequence RF α TE TR α Slice Phase Read MR Signal: S GRE TR TE M 0 sin α 1 exp exp T 1 T 2 = *

RF Repetition Time (TR): T1 contrast TR encode encode encode Voltage (Signal) Mxy Mz WM GM GM: gray matter (long T1) WM: white matter (short T1) time Courtesy of L. Wald

Gradient Echo Sequence S GRE TR TE M 0 sin α 1 exp exp T 1 T 2 = * * * Proton Density weighting T1 weighting T2* weighting ( TR >>T1, short TE, sin α ~ 1 ) ( TR ~ T1, short TE, sin α ~ 1 ) ( TR >>T1, TE ~ T2* ) Water density Gray / White matter / CSF Hemorrhage

Gradient Echo Sequence Proton Density Weighting T 1 Weighting FLASH FA = 3 o FA = 5 o FA = 30 o Manipulating contrast with flip angle Courtesy of A. Dale and B. Fischl

Basic Spin-Echo Sequence Excitation Pulse τ Refocusing Pulse τ RF 90 o 180 o Slice Phase TE Read Spin Echo

Spin-Echo Sequence: The MR Signal TR τ τ TE TR TE SSE = M 0 1 exp exp T 1 T 2

Spin Echo Sequence S GRE TR TE M 0 sin α 1 exp exp T 1 T = 2 Proton Density weighting T1 weighting T2 weighting ( TR >>T1, short TE, sin α ~ 1 ) ( TR ~ T1, short TE, sin α ~ 1 ) ( TR >>T1, TE ~ T2 ) Water density Gray / White matter / CSF Hemorrhage

RF 90 o Double Spin Echo Sequence τ τ τ τ 180 o 180 o Slice Phase TE 1 TE 2 Read Echo 1 Echo 2

Inversion Recovery Inversion Pulse RF Excitation Pulse TI 180 o 180 o 90 o τ Refocusing Pulse τ Slice Phase TE Read Magnetization Preparation Spin Echo

Enhanced T 1 -weighting: Inversion Recovery M 0 180 o TI GM CSF TE 90 o 180o Spin Echo Mz(t) -M o 180 o Inversion: prepare magnetization prior to Spin Echo detection Signal ρ (1 2e TI / T 1 + e TR / T 1 ) e TE / T 2

Fluid Attenuation Inversion Recovery (FLAIR) Mz(t) M 0 180 o TI GM TE 90 o 180o -M o CSF Spin Echo Signal null at: TI = ln(2)* T1

Physics of MR Image Acquisition HST-583, Fall 2002 Review: -MRI: Overview - MRI: Spatial Encoding MRI Contrast: Basic sequences - Gradient Echo - Spin Echo - Inversion Recovery