Introduction au cours

Fund BioImag 201311-111: Echo formation and spatial encodingWhat makes the magnetic resonance signal spatially dependent ? How is the position of an MR signal identified ? Slice selectionWhat is echo formation and how is it achieved ? Echo formationGradient echo sequenceHow is a two-dimensional MR image encoded ?After this course youUnderstand the principle of slice selectionAre familiar with dephasing and rephasing of transverse magnetization and how it leads to echo formation Understand the principle of spatial encoding in MRICan describe the basic imaging sequence and the three necessary elementsUnderstand the principle of image formation in MRI and how it impacts spatial resolution 1Fund BioImag 201311-211-1. What do we know about magnetic resonance so far ?Adding a 3rd magnetic fieldSo far1) Excite spins using RF field at L2) Record time signal (Known as FID)3) Mxy decays, Mz grows (T2 and T1 relaxation)RF coils measure signal from entire body (no spatial information) How to encode spatial position ?L=B0B0: Static Magnetic FieldCreates equilibrium magnetization0.1 T to 12 TEarths field is 0.5 10-4 TB1: Radiofrequency Field (RF)0.05mT, on resonanceDetection of MR signal (RF coils)PrecessionalFrequencyStatic Magnetic Field

wL=f(x)Magnetic field B along zvaries spatially with x, y, and/or z:

GxGyGze.g. G=(Gx,0,0)2S?Fund BioImag 201311-3How is the gradient field created ?One coil for each spatial dimension: Gx, Gy, Gz

Created by a set of 3 additional coils (gradient coil)

G: Gradient Field 10-50 mT/m in ~100sUsed to determine spatial position of signal (frequency)

NB. Why are MRI scans so loud ?Lorentz-force of Bz (3T) on rapidly switched current in gradient coil (wire) (~100A in ~100s)

Example: z-gradient coil principle (Helmholtz pair)One gradient coilAll three gradient coilsB0Gz3Fund BioImag 201311-4On-resonance: Frequency wRF of RF field B1 matches the precession frequency of magnetizationHow is slice-selection achieved ?Only magnetization on-resonance is excitedFrequencyPosition zwRF=gGzzwRFMoving Frequency wRF alters position of slice : wRF=gB0+gGzz0yzxz0NB. Not to confuse:(x,y) refers to spatial dimensionsMxy M or M refers to transverse magnetization (in magnetization space)(coordinate systems are different, but share z)Fund BioImag 201311-5For 2D object:

=Radon Transform11-2. What is the basic principle of encoding spatial information ? frequency encoding - 1D example gBz(x)Spatial-varying resonance frequency gB(x) during detectionDetected signal = sum of all precessing magnetization: xBz(x) = B0 + GxxRotating frame: B(x) = Gxx

What does this resemble ?

= Inverse Fourier Transformation !

FT of S(t) (or S(k)) M(x)

Reconstruction as in CT (in principle)

Fund BioImag 201311-6Spatial Encoding: 1D examplew/o encodingw/ encodingConstant Magnetic FieldGradient:Varying Magnetic FieldFourier transformation (Frequency Decomposition)

Paul LauterburPeter MansfieldPhysiology and Medicine2003

Two point-like objects

x

6Fund BioImag 201311-7DephasingRephasingTEyx11-3. When is the signal maximal in the presence of G ?Echo formation: Dephasing and rephasingPhase of magnetizationf(t)=GyytGradient Gy(t)Magnetization in-phase maximal signal (echo formation)

S(t)=maximal (constant Gy) when t=t: echo formationt=TE/2:S(t) 4 minSubject moved head during acquisition

Ghosting and ringing artifactsMaximum kx (or ky) Resolution (Nyquist)Increment Dk Field-of-viewcenter of k-space (kx,ky=0)Uniform resolution and sensitivity(Limited by voxel magnetization)~ msFund BioImag 201311-15

8 x 8512 x 512

16 x 16

32 x 32

64 x 64

128 x 128

256 x 256What are some effects of incomplete sampling ?of Fourier space (k-space)Time of acquisition of center of k-space point (kx,ky=0) determines contrast of image:

=Discrete FFT(periodicity + time shift)

kx,kyx,y15Fund BioImag 201311-16

Summary: Spatial encoding with gradientsPhase encoding, echo formation + 2DFT

timeGyDephasing at point (x,y) in space: m(t)=m(0)e-if with f = Gyyt kyytGxSignal S(t,t) M(t) = m(x,y,t)dxdy= m(x,y,0) eg(nDGyy)tegGxx(t+t)dxdyS(kx,ky) m(x,y) e-kxxe-kyydxdy m(t)=m(t)e-iF with F = Gxxt kxx

Echo formation: F(TE)=0TERF (B1)1234Magnetization at time points specified:1: (0,0,Mz) rotated by RF pulse by a0 about x:2: (0,Mzsina,Mzcosa)(0,My,) [now only consider Mxy]Precesses with B = -gGyy -gGxx3: My(sin[-g(nDGyy+Gxx)t], cos[-g(nDGyy+Gxx)t]My [sin(-fx), cos(fx)], with fx =gGxxt (rotation by angle fx)inverting gradient, i.e. B = +gGxx: after another t, rotates by angle +fx maximal signal at TE=2t (DGy=0)

4: My (0,1,)= (0,Mzsina,Mzcosa) Echo formationcosgBtsingBt0-singBtcosgBt0001*Precession matrix (for B||z)MRI measures the 2D Fourier transformation of the object (measuring the 2nd dimension requires time!)(r,t)=g(B0 + G (t)r)nDGyflip angle a