Part II: Magnetic Resonance Imaging (MRI)
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1 Part II: Magnetic Resonance Imaging (MRI) Contents Magnetic Field Gradients Selective Excitation Spatially Resolved Reception k-space Gradient Echo Sequence Spin Echo Sequence
2 Magnetic Resonance Imaging imaging = spatial discrimination
3 What nuclei can be used for imaging? adapted from wikipedia:
4 For conventional imaging (x-ray) imaging properties are given by the geometry of the light path.
5 Electromagnetic Spectrum Frequency range for MRI: MHz Wavelength: MHz ~ 470cm
6 Magnetic Resonance Imaging Objects that are smaller than the wave length cannot be imaged (geometric imaging not possible!)
7 Magnetic Resonance Imaging Sample in a homogenous magnetic field B 0 B 0 = B 0 B 0 x All magnetic moments precess with the same frequency, i.e., with the Larmor frequency
8 Magnetic Resonance Imaging: Gradients Swichable, linear magnetic field gradients independently in x, y and z direction Magnetic Field Gradients B(x,y,z) B 0 +Gr B 0 Position (x,y,z) Gradients are used to give protons different Larmor frequencies at different positions! x Gx x ν() r ( B e Gr) G y y 0 z y z B0 Gzz
9 Magnetic Resonance Imaging: Gradients Sample in a homogenous magnetic field B 0 with gradient field G z B (x) = B 0 + G x x) B 0 x There is a 1:1 correspondence between the frequency and the position!
10 Magnetic Resonance Imaging: Slice Selection Frequency of B 1 field is = B 0 (resonance condition) B 1 : Result: 90 degrees pulse!
11 Magnetic Resonance Imaging: Slice Selection Frequency of B 1 field is > B 0 (off resonance condition) B 1 : Result: 32 degrees pulse!
12 Magnetic Resonance Imaging: Slice Selection Frequency of B 1 field is >> B 0 (off resonance condition) B 1 : Result: 1 degrees pulse!
13 Magnetic Resonance Imaging: Slice Selection eff rot dm M B dt eff B B B Effective B1 depends on frequency of B1 field:
14 Magnetic Resonance Imaging: Slice Selection RF G z Excitation profile This is not so nice, but we are close!
15 Magnetic Resonance Imaging: Slice Selection RF G z Excitation profile
16 Magnetic Resonance Imaging: Slice Selection
17 Magnetic Resonance Imaging: Spatially Resolved Reception z x RF G z G x
18 Magnetic Resonance Imaging: Spatially Resolved Reception Gradient G x S(t) x 2 x 1 x t S 1D FFT x
19 Magnetic Resonance Imaging: Spatially Resolved Reception RF S Gradient G x G z G x ADC x 2 x 1 x 1D FFT Back projection
20 Magnetic Resonance Imaging: Spatially Resolved Reception RF G z G x G y y ADC x 1D FFT Back projection
21 Magnetic Resonance Imaging: Spatially Resolved Reception RF G z G x G y y ADC x
22 Magnetic Resonance Imaging: Spatially Resolved Reception RF G z G x G y y ADC x
23 Magnetic Resonance Imaging: Spatially Resolved Reception RF G z G x G y y ADC x
24 Magnetic Resonance Imaging: Spatially Resolved Reception RF G z G x G y y ADC x
25 Magnetic Resonance Imaging: Spatially Resolved Reception RF G z G x G y y ADC x
26 Magnetic Resonance Imaging: Spatially Resolved Reception RF G z G x G y y ADC x
27 Magnetic Resonance Imaging: Spatially Resolved Reception RF G z G x G y y ADC x
28 Magnetic Resonance Imaging: Spatially Resolved Reception RF G z G x G y y ADC x Repeat n times along different angles
29 Magnetic Resonance Imaging: Spatially Resolved Reception RF reconstruction G z G x G y ADC sinogram Repeat n times along different angles
30 Magnetic Resonance Imaging: Imaging in k-space A static point source at some position r (e.g., drop of water): z r S(t) r i t S(0)e r harmonic oscillation: continous linear phase change x y Frequency is a function of time (in the presence of gradients G): (t) G(t) r S(t) S(0)e t i G(t) rdt 0 The total signal from an object with given nuclei density (r): () r z r t i (t) dt 0 S(t) ( ) e G r r d r x y
31 Magnetic Resonance Imaging: Imaging in k-space The total signal from an object with given nuclei density (r): x () r z y r t i (t) dt 0 S(t) ( ) e G r r d 1 t k(): t (t)dt 2 G 0 r With the definition of the wave-vector k k(t), we get for the total signal: i2kr S( ) ( ) e d k r r and after inversion of the signal equation: -i 2kr () S( )e d r k k
32 Magnetic Resonance Imaging: Imaging in k-space S( k) S( k(t)) = S(t) k-space image 2D FFT i2kr S( ) ( ) e d k r r -i 2kr () S( )e d r k k
33 Magnetic Resonance Imaging: k-space Properties k y k x
34 Magnetic Resonance Imaging: k-space Properties 512 x x 8
35 Magnetic Resonance Imaging: k-space Properties 512 x x 16
36 Magnetic Resonance Imaging: k-space Properties 512 x x 32
37 Magnetic Resonance Imaging: k-space Properties 512 x x 64
38 Magnetic Resonance Imaging: k-space Properties 512 x x 128
39 Magnetic Resonance Imaging: k-space Properties 512 x x 256
40 Magnetic Resonance Imaging: k-space Properties 512 x x 32
41 Magnetic Resonance Imaging: k-space Properties FOV in x-direction FOV in y-direction ky resolution in y-direction resolution in x-direction kx
42 Magnetic Resonance Imaging: k-space & Sequences k-space RF G z? G x G y ADC i2kr S( ) ( ) e d k r r S( k) S( k(t)) = S(t) k 1 t (): t (t) dt 2 G 0
43 Magnetic Resonance Imaging: Gradient Echo (GRE) k-space RF G z G x G y ADC i2kr S( ) ( ) e d k r r S( k) S( k(t)) = S(t) k 1 t (): t (t) dt 2 G 0
44 Magnetic Resonance Imaging: Gradient Echo (GRE) k-space RF G z G x G y ADC i2kr S( ) ( ) e d k r r S( k) S( k(t)) = S(t) k 1 t (): t (t) dt 2 G 0
45 Magnetic Resonance Imaging: Gradient Echo (GRE) k-space RF G z G x G y ADC i2kr S( ) ( ) e d k r r S( k) S( k(t)) = S(t) k 1 t (): t (t) dt 2 G 0
46 Magnetic Resonance Imaging: Gradient Echo (GRE) k-space RF G z G x G y ADC i2kr S( ) ( ) e d k r r S( k) S( k(t)) = S(t) k 1 t (): t (t) dt 2 G 0
47 Magnetic Resonance Imaging: Gradient Echo (GRE) k-space RF G z G x G y ADC i2kr S( ) ( ) e d k r r S( k) S( k(t)) = S(t) k 1 t (): t (t) dt 2 G 0
48 Magnetic Resonance Imaging: Gradient Echo (GRE) k-space RF G z G x G y ADC i2kr S( ) ( ) e d k r r S( k) S( k(t)) = S(t) k 1 t (): t (t) dt 2 G 0
49 Magnetic Resonance Imaging: Gradient Echo (GRE) k-space RF G z G x G y ADC i2kr S( ) ( ) e d k r r S( k) S( k(t)) = S(t) k 1 t (): t (t) dt 2 G 0
50 Magnetic Resonance Imaging: Echo Planar Imaging (EPI) k-space RF G z G x G y ADC i2kr S( ) ( ) e d k r r S( k) S( k(t)) = S(t) k 1 t (): t (t) dt 2 G 0
51 Magnetic Resonance Imaging: Spiral EPI k-space RF G z G x G y ADC i2kr S( ) ( ) e d k r r S( k) S( k(t)) = S(t) k 1 t (): t (t) dt 2 G 0
52 Magnetic Resonance Imaging: Spin Echo (SE) 180 k-space RF 90 G z G x G y ADC i2kr S( ) ( ) e d k r r S( k) S( k(t)) = S(t) k 1 t (): t (t) dt 2 G 0
53 Magnetic Resonance Imaging: Spin Echo (SE) 180 k-space RF 90 G z G x G y ADC i2kr S( ) ( ) e d k r r S( k) S( k(t)) = S(t) k 1 t (): t (t) dt 2 G 0
54 Summary: Part II Gradients induce a linear change in magnetic fields along one spatial direction. As a result, gradients induce a linear change in the larmor frequency of the magnetization with position (related by the Fourier transform). In combination with an exitation field, slice selection can be achieved. Using back transform (this is CT!), the spatial dependency in the precession frequency can be used to generate an image. The variation in the spatial frequency (and phase) from switching gradients in different orthogonal directions is stored in k-space. Fourier transform related k-space with image space. Gradient echoes are recalled with gradients, spin-echoes using a 180 pulse.
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