Slide 1

Fund BioImag 2013 11-1 11: Echo formation and spatial encoding 1.What makes the magnetic resonance signal spatially dependent ? 2.How is the position of an MR signal identified ? Slice selection 3.What is echo formation and how is it achieved ? Echo formation Gradient echo sequence 4.How is a two-dimensional MR image encoded ? After this course you 1.Understand the principle of slice selection 2.Are familiar with dephasing and rephasing of transverse magnetization and how it leads to echo formation 3.Understand the principle of spatial encoding in MRI 4.Can describe the basic imaging sequence and the three necessary elements 5.Understand the principle of image formation in MRI and how it impacts spatial resolution Slide 2 Fund BioImag 2013 11-2 11-1. What do we know about magnetic resonance so far ? Adding a 3 rd magnetic field So far 1) Excite spins using RF field at L 2) Record time signal (Known as FID) 3) M xy decays, M z grows (T 2 and T 1 relaxation) RF coils measure signal from entire body (no spatial information) How to encode spatial position ? L=B0L=B0 B 0 : Static Magnetic Field Creates equilibrium magnetization 0.1 T to 12 T Earths field is 0.5 10 -4 T B 1 : Radiofrequency Field (RF) 0.05mT, on resonance Detection of MR signal (RF coils) Precessional Frequency Static Magnetic Field L =f(x) Magnetic field B along z varies spatially with x, y, and/or z: GxGx GyGy GzGz e.g. G=(G x,0,0) Slide 3 Fund BioImag 2013 11-3 How is the gradient field created ? One coil for each spatial dimension: G x, G y, G z Created by a set of 3 additional coils (gradient coil) G: Gradient Field 10-50 mT/m in ~100s Used to determine spatial position of signal (frequency) NB. Why are MRI scans so loud ? Lorentz-force of B z (3T) on rapidly switched current in gradient coil (wire) (~100A in ~100s) Example: z-gradient coil principle (Helmholtz pair) One gradient coil All three gradient coils B0B0 GzGz Slide 4 Fund BioImag 2013 11-4 On-resonance: Frequency RF of RF field B 1 matches the precession frequency of magnetization How is slice-selection achieved ? Only magnetization on-resonance is excited Frequency Position z RF = G z z RF Moving Frequency RF alters position of slice : RF = B 0 + G z z 0 y z x z0z0 NB. Not to confuse: (x,y) refers to spatial dimensions M xy M or M refers to transverse magnetization (in magnetization space) (coordinate systems are different, but share z) NB. Not to confuse: (x,y) refers to spatial dimensions M xy M or M refers to transverse magnetization (in magnetization space) (coordinate systems are different, but share z) Slide 5 Fund BioImag 2013 11-5 For 2D object: =Radon Transform 11-2. What is the basic principle of encoding spatial information ? frequency encoding - 1D example B z (x) Spatial-varying resonance frequency B(x) during detection Detected signal = sum of all precessing magnetization: x B z (x) = B 0 + G x x Rotating frame: B(x) = G x x What does this resemble ? = Inverse Fourier Transformation ! FT of S(t) (or S(k)) M(x) Reconstruction as in CT (in principle) Slide 6 Fund BioImag 2013 11-6 Spatial Encoding: 1D example w/o encoding w/ encoding Constant Magnetic Field Gradient: Varying Magnetic Field Fourier transformation (Frequency Decomposition) Paul Lauterbur Peter Mansfield Physiology and Medicine 2003 Two point-like objects x Slide 7 Fund BioImag 2013 11-7 Dephasing Rephasing TE y x 11-3. When is the signal maximal in the presence of G ? Echo formation: Dephasing and rephasing Phase of magnetization (t)=G y yt Gradient G y (t) Magnetization in-phase maximal signal (echo formation) S(t)=maximal (constant G y ) when t= : echo formation =TE/2: S(t) Fund BioImag 2013 11-14 Fourier or reciprocal space (k x, k y ) G x (t) Phase Encode Acq. Sampled Signal Phase Direction (y) Frequency Direction (x) One line of k-space acquired per TR MR scans are long and motion-sensitive How is the spatial information encoded in MRI ? scanning k-space (Fourier or reciprocal space) sequentially For k-space line every TR=1s: 256 2 image matrix > 4 min Subject moved head during acquisition Ghosting and ringing artifacts Maximum k x (or k y ) Resolution (Nyquist) Increment k Field-of-view center of k-space (k x,k y =0) Uniform resolution and sensitivity (Limited by voxel magnetization) Uniform resolution and sensitivity (Limited by voxel magnetization) ~ ms Slide 15 Fund BioImag 2013 11-15 8 x 8512 x 512 16 x 1632 x 32 64 x 64128 x 128256 x 256 What are some effects of incomplete sampling ? of Fourier space (k-space) Time of acquisition of center of k- space point (k x,k y =0) determines contrast of image: = Discrete FFT (periodicity + time shift) k x,k y x,y Slide 16 Fund BioImag 2013 11-16 Summary: Spatial encoding with gradients Phase encoding, echo formation + 2DFT time GyGy Dephasing at point (x,y) in space: m( )=m(0)e -i with = G y y k y y GxGx Signal S( ,t) M (t) = m(x,y,t)dxdy = m(x,y,0) e (n Gyy) e Gxx( +t) dxdy S(k x,k y ) m (x,y) e -k x x e -k y y dxdy m(t)=m( )e -i with = G x xt k x x Echo formation: (TE )=0 TE RF (B 1 ) 1234 Magnetization at time points specified: 1: (0,0,M z ) rotated by RF pulse by 0 about x: 2: (0,M z sin ,M z cos ) (0,M y,) [now only consider M xy ] Precesses with B = - G y y - G x x 3: M y (sin[- (n G y y+G x x) ], cos[- (n G y y+G x x) ] M y [sin(- x ), cos( x )], with x = G x x (rotation by angle x ) inverting gradient, i.e. B = + G x x: after another , rotates by angle + x maximal signal at TE=2 ( Gy=0) 4: M y (0,1,)= (0,M z sin ,M z cos ) Echo formation cos Btsin Bt 0 -sin Btcos Bt 0 001 *Precession matrix (for B||z) MRI measures the 2D Fourier transformation of the object (measuring the 2 nd dimension requires time!) (r,t)= (B 0 + G (t)r) nGynGy flip angle