Principles of Magnetic Resonance Imaging
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1 Principles of Magnetic Resonance Imaging Hi Klaus Scheffler, PhD Radiological Physics University of 1 Biomedical Magnetic Resonance: 1 Introduction
2 Magnetic Resonance Imaging Contents: Hi 1 Introduction 2 Nuclear Magnetic Moments 3 Motion of Magnetization 4 Excitation and reception 5 Magnetic Resonance Imaging 6 Contrast 2 Biomedical Magnetic Resonance: 1 Introduction
3 Biomedical Magnetic Resonance History: Hi Biomedical Magnetic Resonance: 1 Introduction
4 Biomedical Magnetic Resonance Today: Hi 4 Biomedical Magnetic Resonance: 1 Introduction
5 Nuclear Magnetic Moments Hi Properties of a nucleus: Nuclues is charged (multiples of e+) + For example: 1 H, 13 C, 19 F, 31 P Some nuclei have a spin angular momentum J: J = ħi (I multiples of ½) Then, they have a dipolar magnetic moment : = J = ħi Biomedical Magnetic Resonance: 2 Nuclear Magnetic Moments ħ = Planck s quantum constant = gyromagnetic ration 5
6 Nuclear Magnetic Moments Hi Nucleus in a magnetic field: z = ½ ħ z = -½ ħ We assume I=½ ( 1 H, 13 C, 19 F, 31 P) Then, the magnetic moment along the field is: z = ħm = ±½ ħ B 0 B 0 The magnetic moment z is parallel or antiparallel to the field B 0 Biomedical Magnetic Resonance: 2 Nuclear Magnetic Moments ħ = Planck s quantum constant = gyromagnetic ration 6
7 Nuclear Magnetic Moments Hi Nucleus in a magnetic field: In an external magnetic field, spin up or spin down are associated to different energy levels: E m = - z B 0 = - ħb 0 m, m = ±½. E = +½ ħb 0, E = -½ ħb 0 E = ħb 0 Biomedical Magnetic Resonance: 2 Nuclear Magnetic Moments ħ = Planck s quantum constant = gyromagnetic ration 7
8 Nuclear Magnetic Moments Hi n B n n1/2 n 1/2 kt 2 B S 0 In thermal equilibrium, there are different probabilities for spin up and down occupation (Boltzmann statistics). The difference in occupation n is given by: k B : Boltzmann constant T S : Temperature Biomedical Magnetic Resonance: 2 Nuclear Magnetic Moments n n n 1/2 1/2 n B 0 2kT B S 8
9 Hi Macroscopic magnetization: Nuclear Magnetic Moments Visible magnetization: M 0 iz i Sum (macroscopic Magnetization along B 0 ): n B n M n B T B z z 0 0( S) 2kT B S 4kT B S 0 Biomedical Magnetic Resonance: 2 Nuclear Magnetic Moments 0 (T S ): magnetic susceptibility k B : Boltzmann constant 9
10 Hi Magnetization and magnetic field: Motion of Magnetization N S N = = = = W E S M 0 N S 10 Biomedical Magnetic Resonance: 3 Motion of Magnetization
11 Hi Magnetization and magnetic field: Motion of Magnetization S S S N N N B 0 B 0 B 0 11 Biomedical Magnetic Resonance: 3 Motion of Magnetization
12 Hi Magnetization and magnetic field: Motion of Magnetization? B 0 M 0 B 0 M 0 B 0 M 0 12 Biomedical Magnetic Resonance: 3 Motion of Magnetization
13 Motion of Magnetization Hi Magnetization and magnetic field: Nuclues is charged (multiples of e+) = Σ + Some nuclei have a spin angular momentum J: J = ħi (I multiples of ½) M 0 Then, they have a dipolar magnetic moment : = J = ħi Biomedical Magnetic Resonance: 3 Motion of Magnetization ħ = Planck s quantum constant = gyromagnetic ration 13
14 Hi Magnetization and magnetic field: Motion of Magnetization = S M 0 N B 0 M 0 14 Biomedical Magnetic Resonance: 3 Motion of Magnetization
15 Motion of Magnetization Hi Magnetization and magnetic field: gravity S S N N B 0 B 0 gravity B 0 M 0 Biomedical Magnetic Resonance: 3 Motion of Magnetization 15
16 Hi Motion of magnetization: precession Motion of Magnetization B d d d ( B) dt d B dt 16 Biomedical Magnetic Resonance: 3 Motion of Magnetization
17 Motion of Magnetization Motion of magnetization: precession d ( B) dt d B dt 17 Biomedical Magnetic Resonance: 3 Motion of Magnetization
18 Motion of Magnetization d Motion of magnetization: precession ( B) dt d B dt 18 Biomedical Magnetic Resonance: 3 Motion of Magnetization
19 Excitation and Reception Hi B x (t) = 2B 1 cos( t) B 0 B 0 B 0 19 Biomedical Magnetic Resonance: 4 Excitation and Reception
20 Excitation and Reception Hi FID: free induction decay precession of magnetization B 0 a) on-resonance, b) off-resonance, c) spectrum 20 Biomedical Magnetic Resonance: 4 Excitation and Reception
21 Magnetic Resonance Imaging Imaging = spatial discrimination Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging 21
22 Magnetic Resonance Imaging 22 Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
23 Bloch equation Magnetic Resonance Imaging dm dt ( M B) = B Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging Larmor equation 23
24 Magnetic Field Gradients Magnetic Resonance Imaging Sample in a homogenous magnetic field B 0 B 0 = B 0 B 0 x 24 Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
25 Magnetic Field Gradients Magnetic Resonance Imaging Sample in a magnetic gradient field B 0 + B B (x) = B 0 + x G x B 0 x Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging 25 am
26 Magnetic Resonance Imaging B Magnetic field y x Iso-Flux Graph Problem: 2D or higher - Frequencies ambiguous Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging x 26 y
27 Radiologische Physik Magnetic Resonance Imaging Magnetic Field Gradients Swichable, linear magnetic field gradients independently in x, y and z direction 27 Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
28 Magnetic Resonance Imaging Spatially resolved reception Gradient x2 x1 28 Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
29 Magnetic Resonance Imaging Spatially resolved reception Spatial encoding: the Fourier Transform 29 Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
30 Magnetic Resonance Imaging Spatially resolved reception RF excitation z gradient x gradient MR signal Gradient FT x2 x1 30 Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
31 Magnetic Resonance Imaging Spatially resolved reception Back projection: imaging sequence RF excitation recon z gradient x gradient y gradient Signal acquisition sinogram FT Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging k 31
32 Magnetic Resonance Imaging Imaging in k-space k-space image 2DFT -i 2 kx (x) S(k) e dk S(k) = S(k(t)) = S(t) 32 i2 kx S(k) (x) e dx Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
33 Magnetic Resonance Imaging Properties of k-space k y k x 33 Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
34 Magnetic Resonance Imaging Properties of k-space 512 x x 8 34 Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
35 Magnetic Resonance Imaging Imaging in k-space k-space RF excitation z gradient x gradient y gradient Signal acquisition i2 kx S(k) (x) e dx S(k) = S(k(t)) = S(t) Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging 1 t kt () G(t)dt
36 Magnetic Resonance Imaging Imaging in k-space: gradient echo (GE) sequence k-space RF excitation z gradient x gradient y gradient Signal acquisition i2 kx S(k) (x) e dx S(k) = S(k(t)) = S(t) Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging 1 t kt () G(t)dt
37 Magnetic Resonance Imaging Imaging in k-space: gradient echo (GE) sequence (EPI) k-space RF excitation z gradient x gradient y gradient Signal acquisition i2 kx S(k) (x) e dx S(k) = S(k(t)) = S(t) Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging 1 t kt () G(t)dt
38 Magnetic Resonance Imaging Imaging in k-space: gradient echo (GE) sequence (spiral EPI) k-space RF excitation z gradient x gradient y gradient Signal acquisition i2 kx S(k) (x) e dx S(k) = S(k(t)) = S(t) Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging 1 t kt () G(t)dt
39 Magnetic Resonance Imaging Imaging in k-space: spin echo (SE) sequence k-space RF excitation 90 z gradient x gradient y gradient Signal acquisition i2 kx S(k) (x) e dx S(k) = S(k(t)) = S(t) Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging 1 t kt () G(t)dt
40 Magnetic Resonance Imaging Imaging in k-space: spin echo (SE) sequence k-space RF excitation z gradient x gradient y gradient Signal acquisition i2 kx S(k) (x) e dx S(k) = S(k(t)) = S(t) Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging 1 t kt () G(t)dt
41 Magnetic Resonance Imaging Imaging in k-space: spin echo (SE) sequence k-space RF excitation z gradient x gradient y gradient Signal acquisition i2 kx S(k) (x) e dx S(k) = S(k(t)) = S(t) Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging 1 t kt () G(t)dt
42 Contrast 42 Biomedical Magnetic Resonance: 6 Contrast
43 Relaxation in living tissue T 1 : recovery of longitudinal magnetization M M x y tt / 2 tt / 2 Contrast tt / 1 M ( M M ) e M z M e xi M e yi zi 0 0 T 2 * : loss of phase coherence of transverse magnetization T 2 * static dephasing random dephasing z T 2` T 2 M T 1 T 2 * Biomedical Magnetic Resonance: 6 Contrast 43 x
44 Spin Echoes Hi 44 Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
45 Contrast Relaxation in living tissue 45 Biomedical Magnetic Resonance: 6 Contrast
46 Contrast Contrast of imaging sequences k-space RF excitation z gradient x gradient y gradient Signal acquisition Repeat hundreds of times 46 Biomedical Magnetic Resonance: 6 Contrast
47 Contrast Contrast of imaging sequences:tr~t1>t2 RF (flip angle ) M 0 Mz Mt M 0 cos M 0 sin Biomedical Magnetic Resonance: 6 Contrast t 47
48 TR TE Contrast Biomedical Magnetic Resonance: 6 Contrast
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