Magnetic Resonance Imaging (MRI)

Transcription

1 C. A. Bouman: Digital Image Processing - January 12, Magnetic Resonance Imaging (MRI) Can be very high resolution No radiation exposure Very flexible and programable Tends to be expensive, noisy, slow

2 C. A. Bouman: Digital Image Processing - January 12, MRI Attributes Based on magnetic resonance effect in atomic species Does not require any ionizing radiation Numerous modalities Conventional anatomical scans Functional MRI (fmri) MRI Tagging Image formation RF excitation of magnetic resonance modes Magnetic field gradients modulate resonance frequency Reconstruction computed with inverse Fourier transform Fully programmable Requires an enormous (and very expensive) superconducting magnet

3 C. A. Bouman: Digital Image Processing - January 12, Magnetic Resonance Magnetic Field Procession Atom Atom will precess at the Larmor frequency ω o = LM Quantities of importance M - magnitude of ambient magnetic field ω o - frequency of procession (radians per second) L - Larmor constant. Depends on choice of atom

4 C. A. Bouman: Digital Image Processing - January 12, The MRI Magnet Liquid Helium Z axis Megnetic Field X axis Superconducting Magnet Large super-conducting magnet Uniform field within bore Very large static magnetic field of M o

5 C. A. Bouman: Digital Image Processing - January 12, Magnetic Field Gradients Magnetic field magnitude at the location(x,y,z) has the form M(x,y,z) = M o +xg x +yg y +zg z G x, G y, and G z control magnetic field gradients Gradients can be changed with time Gradients are small compared to M o For time varying gradients M(x,y,z,t) = M o +xg x (t)+yg y (t)+zg z (t)

6 C. A. Bouman: Digital Image Processing - January 12, MRI Slice Select Mo Selected Slice Magnetic Field RF Pulse Slope Gz RF Antenna Zc Z Design RF pulse to excite protons in single slice Turn offxand y gradients, i.e. G x = G y =. Set z gradient to fix positive value, G z >. Use the fact that resonance frequency is given by ω = L(M o +zg z ).

7 C. A. Bouman: Digital Image Processing - January 12, Design parameters Slice center = z c. Slice Select Pulse Design Slice thickness = z. Slice centered at z c pulse center frequency f c = LM o 2π + z clg z 2π Slice thickness z pulse bandwidth f = zlg z 2π = f o + z clg z 2π. Using these parameters, the pulse is given by s(t) = e j2πf ct sinc(t f) and its CTFT is given by ( ) (f fc ) S(f) = rect f.

8 C. A. Bouman: Digital Image Processing - January 12, How Do We Imaging Selected Slice? Y axis Selected Slice RF Antenna X axis Precessing atoms radiate electromagnetic energy at RF frequencies Strategy Vary magnetic gradients along x and y axies Measure received RF signal Reconstruct image from RF measurements

9 C. A. Bouman: Digital Image Processing - January 12, Signal from a Single Voxel RF Antenna Voxel of Selected Slice RF signal from a single voxel has the form r(x,y,t) = f(x,y)e jφ(t) f(x, y) voxel dependent weighting Depends on properties of material in voxel Quantity of interest Typically weighted by T1, T2, or T2* φ(t) phase of received signal Can be modulated usingg x andg y magnetic field gradients We assume thatφ() =

10 C. A. Bouman: Digital Image Processing - January 12, Analysis of Phase Frequency = time derivative of phase dφ(t) dt φ(t) = = LM(x,y,t) = where we define ω o = LM o k x (t) = k y (t) = t t t t LM(x,y,τ)dτ LM o +xlg x (τ)+ylg y (τ)dτ = ω o t+xk x (t)+yk y (t) LG x (τ)dτ LG y (τ)dτ

11 C. A. Bouman: Digital Image Processing - January 12, Received Signal from Voxel RF Antenna Voxel of Selected Slice RF signal from a single voxel has the form r(t) = f(x,y)e jφ(t) = f(x,y)e j (ω o t+xk x (t)+yk y (t)) = f(x,y)e jωot e j (xk x (t)+yk y (t))

12 C. A. Bouman: Digital Image Processing - January 12, Received Signal from Selected Slice Y axis Selected Slice RF Antenna X axis RF signal from the complete slice is given by R(t) = r(x, y, t)dxdy = IR IR IR IR = e jω ot f(x,y)e jωot e j (xk x (t)+yk y (t)) dxdy f(x,y)e j (xk x (t)+yk y (t)) dxdy = e jωot F( k x (t), k y (t)) weref(u,v) is the CSFT of f(x,y) IR IR

13 C. A. Bouman: Digital Image Processing - January 12, K-Space Interpretation of Demodulated Signal RF signal from the complete slice is given by F( k x (t), k y (t)) = R(t)e jω ot where k x (t) = k y (t) = Strategy t t LG x (τ)dτ LG y (τ)dτ Scan spatial frequencies by varyingk x (t) and k y (t) Reconstruct image by performing (inverse) CSFT G x (t) and G y (t) control velocity through K-space

14 C. A. Bouman: Digital Image Processing - January 12, Controlling K-Space Trajectory Relationship between gradient coil voltage and K-space L x di(t) dt L y di(t) dt using this results in = v x (t) G x (t) = M x i(t) = v y (t) G y (t) = M y i(t) k x (t) = LM x L x k y (t) = LM y L y t τ t τ v x (s)dsdτ v y (s)dsdτ v x (t) and v y (t) are like the accelerator peddles for k x (t) and k y (t)

15 C. A. Bouman: Digital Image Processing - January 12, Echo Planer Imaging (EPI) Scan Pattern A commonly used raster scan pattern through K-space Ky Serpintine Scan k x (t) = L t G x (τ)dτ = LM x L x t τ v x (s)dsdτ Kx k y (t) = L t G y (τ)dτ = LM y L y t τ v y (s)dsdτ

16 C. A. Bouman: Digital Image Processing - January 12, Gradient Waveforms for EPI Gradient waveforms in x and y look like Gx(t) Gy(t) Voltage waveforms in x and y look like Vx(t) Vy(t)