Physics of Imaging Systems Basic Principles of Magnetic Resonance Imaging II

Transcription

1 1 3/14/2019 Page 1 Master s Program in Medical Physics Physics of Imaging Systems Basic Principles of Magnetic Resonance Imaging II Chair in Faculty of Medicine Mannheim University of Heidelberg Theodor-Kutzer-Ufer 1-3 D Mannheim, Germany Lothar.Schad@MedMa.Uni-Heidelberg.de 3/14/2019 Page 2 Literature I Dance et al.: Diagnostic Radiology Physics Publisher: International Atomic Energy Agency PDF/Pub1564webNew pdf Free download!!! Seite 1

2 2 3/14/2019 Page 3 Literature II Reiser and Semmler: Magnetresonanztomographie Chapter 2, /14/2019 Page 4 Literature III Vlaardingerbroek and den Boer: Magnetic Resonance Imaging Theory and Practice, 2003 Seite 2

3 3 3/14/2019 Page 5 Physics: Nuclei Physics: Nuclei 3/14/2019 Page 6 Proton nuclear magnetic moment mechanic moment (spin) rotation charge Seite 3

4 4 3/14/2019 Page 7 Spin Quantum Mechanics I I z = m norm of nuclear spin I with h = Js Planck s constant with m the magnetic quantum number and discrete energy levels -I, -I+1,..., I-1, I in total 2I+1 possibilities m B z 1 2 I = 1 2 E m - m = 1 2 B z Zeeman effect m = /14/2019 Page 8 Spin Quantum Mechanics II magnetic moment µ is defined by nuclear spin I: γ gyromagnetic ratio proton: γ/2π = 42.6 MHz/T only nuclei with I 0 are visible by MRI!! analogy of nuclear magnetism Seite 4

5 5 3/14/2019 Page 9 NMR Nuclei nucleus spin I gyromagnetic ratio γ [10 8 rad s -1 T -1 ] natural abundance of isotope in % sensitivity for B 0 = const. in % (rel. to 1 H) 1 H 1/2 2,675 99,98 100,00 MRI: 110 mol 19 F 1/2 2, ,00 83,40 23 Na 3/2 0, ,00 9,27 31 P 1/2 1, ,00 6,65 2 H 1 0,410 0,01 9, C 0-98,89-13 C 1/2 0,673 1,11 1, N 1 0,193 99,63 1, O 0-99,76-17 O 5/2-0,363 0,04 1, Cl 3/2 0,262 75,77 3, K 3/2 0,125 93,26 4, Mg 5/2-0,164 10,00 2, Ca 7/2-0,180 0,14 8, S 3/2 0,205 0,75 1, (MRS: MRI: MRS: < 10-3 mmol) 50 mmol 40 mmol 3/14/2019 Page 10 Nuclei in an External Magnetic Field Zeeman energy levels of nuclei with I = 3/2 - potential energy in external B 0 : - external RF can induce transition between energy levels if m = ± 1: ω 0 : Larmor frequency = 64 MHz for protons at 1.5 T γ : gyromagnetic ratio = 42.6 MHz/T for protons Seite 5

6 6 3/14/2019 Page 11 NMR History: Discovery Germany - Columbia 1938 Isidor Rabi rebuilt a molecular beam apparatus (Otto Stern) detected nuclear resonance in a stream of Lithium Chloride molecules E -1/2 +1/2 Nobel prize for physics in 1944 B Harvard 1946 Edward Purcell, Torrey and Pound applied radar technology in investigating magnetic resonance achieved the first resonance in a practical sample, a block of paraffin E -1/2 ν +1/2 B Yves De Deene. University of Gent, Belgium B 3/14/2019 Page 12 Semi Classic Description mechanic spinner atomic spinner double precession cone for proton with I =1/2 problem of semi classic description: - mechanic precession = reaction of spinner to external force G - atomic precession = intrinsic properties of proton resulting from QM problem solved by macroscopic quantity: M 0 magnetization Seite 6

7 7 3/14/2019 Page 13 Movie: Summary Plewes DB, Plewes B, Kucharczyk W. The Animated Physics of MRI, University Toronto, Canada 3/14/2019 Page 14 Magnetization M 0 for Spin 1/2 B = 0 M 0 S B = B 0 Σ = N Seite 7

8 8 3/14/2019 Page 15 Boltzmann Statistic M 0 Boltzmann statistic protons: M 0 N +1/2 / N -1/2 = exp( E / kt) = exp(γhb 0 / kt) k : Boltzmann constant = J/K N +1/2 : number of spins parallel to B 0 lower energy level N -1/2 : number of spins anti-parallel to B 0 higher energy level since γhb 0 << kt Taylor series: N +1/2 / N -1/2 = 1 + γhb 0 / kt = = 6.6 ppm at B 0 = 1.0 T and T = 37 C = 310 K. M 0 = (N +1/2 N -1/2 ) <µ z > / volume = (N/V)(γ 2 h 2 /4kT)B 0 3/14/2019 Page 16 Energy Level Ratio source: Lissner and Seiderer. Klinische Kernspintomographie 1987 Seite 8

9 9 3/14/2019 Page 17 Zeeman Effect Curie s law: M 0 = ρ I(I+1) γ 2 h 2 B 0 3kT B 0 m = -1/2 M 0 m = +1/2 B = 0 B = B 0 splitting of energy levels (Zeeman effect) 3/14/2019 Page 18 Magnetic Field B 0 static magnetic field B 0 field strength homogeneity Tesla < 1.0 ppm nitrogen 77 K helium 4.2 K vacuum M 0 copper wires with niobium-titanium-fibers super conducting coil NbTi, Nb 3 Sn cryostat cooling liquid He, (N 2 ) Seite 9

10 10 3/14/2019 Page 19 Magnetic Field B 0 : Construction courtesy: Overweg, Philips 3/14/2019 Page 20 Comparison: CT - MRI CT = transmission tomography MRI = direct tomography X-ray tube detector detector electronics M 0 high voltage projection data Seite 10

11 11 3/14/2019 Page 21 Correspondence Principle in 1 mm 3 water about 6x10 19 protons (6x10 23 protons / mol Avogadro number) 10 ppm (10-5 ) energy level ratio at 1.5 T 6x10 14 parallel spins in M 0 Bohr s correspondence principle lim QM classical physics n 8 Proton M 0 3/14/2019 Page 22 Summary: Proton Bulk source: Schlegel and Mahr. 3D Conformal Radiation Therapy: A Multimedia Introduction to Methods and Techniques" 2007 Seite 11

12 12 3/14/2019 Page 23 Quantum Mechanic Classical Mechanic quantum mechanic classical mechanic Schrödinger equation: Bloch equation notice: M is a macroscopic quantity, all nutation angles are allowed CM µ is a microscopic quantity, only +1/2 and -1/2 are allowed QM Slichter. Principles of Magnetic Resonance /14/2019 Page 24 Leipzig - Stanford 1946 NMR History: Theory Felix Bloch achieved the same in a sample of water provided the mathematical characterization of the nuclear magnetic resonance phenomenon Nobel Prize for physics (Bloch & Purcell) in 1952 the Bloch equations B M x B M dm dt = γ (M x B) - G L L x G L = I ω Yves De Deene. University of Gent, Belgium Seite 12

13 13 3/14/2019 Page 25 Radiofrequency: Resonance N M R Nuclear Magnetic Resonance calculation of RF wave length: c H2O = c/ ε H2O ~ c/7 λ = c/ν λ ~ 67 cm at 1.5 T ( 64 MHz) λ ~ 14 cm at 7.0 T (298 MHz) 3/14/2019 Page 26 Electromagnetic Spectrum frequency [Hz] wave length [m] photon energy [ev] radiation molecular impact x- and γ-ray DNA break UV-radiation visible light IR-radiation e - -excitation (orbital) oscillation rotation UKW KW MW MRI LW source: Lissner and Seiderer. Klinische Kernspintomographie 1987 Seite 13

14 14 3/14/2019 Page 27 Resonance: Basic Principle swing tuning fork - energy transfer between A and B is only possible if both systems are resonant - RF system has to work at 64 MHz at 1.5 T 3/14/2019 Page 28 Radiofrequency: Rotating Frame y y in a rotating coordinate system the x y plane is rotating synchronous with a circular polarized RF-field B 1 -vector is not moving in this system! ω RF x rotating M 0 -vector only sees B 1! B 1 x radiofrequency RF: ω RF = γ B 0 Seite 14

15 15 3/14/2019 Page 29 Movie: Rotating Frame Plewes DB, Plewes B, Kucharczyk W. The Animated Physics of MRI, University Toronto, Canada 3/14/2019 Page 30 Magnetization Dynamic rotating system laboratory system in the rotating frame the M 0 -vector starts to precede with ω 1 = γ B 1 around the direction of B 1 in the laboratory frame the M 0 -vector is moving spirally in the direction of the x,y plane flip angle: α = ω 1 t p = γ B 1 t p B 0 >> B 1 ω 0 >> ω 1 Seite 15

16 16 3/14/2019 Page 31 RF-Pulse Characteristics since t p is a finite quantity the frequency distribution of the excited spins after Fourier transformation does have a frequency shape and bandwidth called sinc-pulse for t p : frequency spectrum gets monochromatically 3/14/2019 Page and Pulses 90 -pulse (π/2-pulse) in the laboratory and rotating coordinate system N -1/2 = N +1/2 to : 3x10 14 spins per 1 mm 3 at 1.5 T 180 -pulse (π-pulse) in the laboratory and rotating coordinate system N -1/2 > N +1/2 = -M 0 to : 6x10 14 spins per 1 mm 3 at 1.5 T source: Lissner and Seiderer. Klinische Kernspintomographie 1987 Seite 16

17 17 3/14/2019 Page 33 Movie: Spin Excitation Plewes DB, Plewes B, Kucharczyk W. The Animated Physics of MRI, University Toronto, Canada 3/14/2019 Page 34 NMR Experiment: Signal Detection object is located in a homogeneous static magnetic field B 0 RF-coil creates a magnetic field B 1 perpendicular to B 0 transmitter after excitation the received signal of the object is transferred by the receiving electronic to the computer receiver Seite 17

18 18 3/14/2019 Page 35 Movie: Free Induction Decay FID free induction decay: FID M xy signal intensity time Plewes DB, Plewes B, Kucharczyk W. The Animated Physics of MRI, University Toronto, Canada 3/14/2019 Page 36 NMR Excitation and Signal Detection B 0 B 0 M magnetic field RF transmit coil with ν = ω 0 M RF receive coil excitation detection RF receive coil Seite 18

19 19 3/14/2019 Page 37 FID Signal and Frequency Spectrum RF receive coil FID-signal (free induction decay) damped oscillation B 0 NMR frequency spectrum ω 0 = -γ B 0 M xy precession Larmor frequency ω 0 3/14/2019 Page 38 Faraday Induction bicycle dynamo loop with rotating magnet rotating magnetic moments z N S x M y y M xy signal intensity free induction decay: FID time Seite 19

20 20 3/14/2019 Page 39 Signal Detection Based on: - Faraday law of electromagnetic induction and - principal of reciprocity Electromagnetic Induction: a temporally variable magnetic flux in a loop (receiver coil) induces a charge in this loop which is proportional to the rate of change of the magnetic flux in the loop Principal of Reciprocity: the sensitivity for detecting a rotating magnetic moment in space is directly proportional to a corresponding electric current in the coil which is necessary for generating the same magnetic field at this point in space 3/14/2019 Page 40 Principal of Reciprocity correspondence between field strength and induced voltage no change of magnetic flux no induced voltage Hoult. Encyclopedia of Nuclear Magnetic Resonance 1996 Seite 20

21 21 3/14/2019 Page 41 Coil Signal magnetic flux through the coil: sensitivity of receiving coil Faraday induction: 3/14/2019 Page 42 Radio Frequency Coils: Volume Resonators Seite 21

22 22 3/14/2019 Page 43 Radio Frequency Coils: Coil Arrays I Hardy et al. MRM 2006 Zhu et al. MRM /14/2019 Page 44 Radio Frequency Coils: Coil Arrays II 102 seamlessly integrated coil elements at 32 receiving channels matrix coils: head neck stem leg courtesy: Siemens AG, Erlangen Seite 22

23 23 3/14/2019 Page 45 Radio Frequency Coils: Coil Sensitivity surface coils inhomogeneity correction phased array coils image combination parallel imaging: SMASH / SENSE array body combination coil 3/14/2019 Page 46 MRI Components: Schema magnet RF-unit (receiver) input/output-panel gradient system RF-unit (transmitter) computer Seite 23

24 24 3/14/2019 Page 47 MRI Components: Physical Parameters radio- gradients G xyz static field B 0 frequency RF shim coils gradient shim transmitter receiver technical component physical parameter static field B 0 M 0 radiofreq. RF signal control panel computer 350 MHz 350 MHz image processor gradients G xyz image Seite 24