Basic Principles of Magnetic Resonance

Transcription

1 Basic Principles of Magnetic Resonance Contents: Jorge Jovicich I) Historical Background II) An MR experiment - Overview - Can we scan the subject? - The subject goes into the magnet - Brief RF pulses are applied - The MR signal - Summary

2 Subject Safety screening Magnetic field Overview of a MRI procedure Tissue protons align with magnetic field (equilibrium state) RF pulses Relaxation processes Protons absorb RF energy (excited state) Relaxation processes Spatial encoding using magnetic field gradients Protons emit RF energy (return to equilibrium state) NMR signal detection Repeat RAW DATA MATRIX Fourier transform IMAGE

3 Can we scan the subject? Safety Issues Not everybody can undergo a MR examination Screening is mandatory to ensure safety / quality during the MR examination

4 A typical MRI scanner The main magnetic field: is VERY strong ( 3T ~ 30,000 times the earth s magnetic field) is A L W A Y S O N!! (superconducting currents) it s strength decays ~ 1 / r 3 (r is the distance from the center)

5 Can we scan the subject? Safety Issues Risks: - Ferromagnetic materials (unsafe) - will be subject to force / torque in the main magnetic field - risks associated with motion / displacements - active biomedical implants may not function properly From:

6 Can we scan the subject? Safety Issues Risks: - Ferromagnetic materials (unsafe) - Non ferromagnetic materials (safe but give image distortions) Sagitall MRI of a normal female subject With hair rubber band* Without hair rubber band * The two ends of the rubber band are joined by a ~ 2 mm cooper clamp.

7 Can we scan the subject? Safety Issues Risks: - Ferromagnetic materials (unsafe) - Non ferromagnetic materials (safe but give image distortions) - Claustrophobia (subject unhappy image distortions)

8 Can we scan the subject? Safety Issues Risks: - Ferromagnetic materials (unsafe) - Non ferromagnetic materials (safe but give image distortions) - Claustrophobia (subject unhappy image distortions) - Movement during examination (potential problem for dynamic studies) - Acoustic protection (mandatory)

9 Overview of a MRI procedure Subject Safety screening Magnetic field We will introduce the following concepts: equilibrium magnetization dynamics of the magnetization rotating coordinate system

10 The subject goes into the magnet... B o Single nucleus H O H Water molecules M o Hydrogen nucleus: magnetic moment r Y B o Anti-parallel Parallel Two energy states: E = E 1 E 0 r r B 0 M 0 : uniform static magnetic field : static macroscopic magnetization High energy state Low energy state (E 1 ) (E 0 ) E = h 0 Precession frequency: o = B o

11 The subject goes into the magnet (continued) B o A group of protons B o Energy states M o E 1 E o E = h 0 ω o = γ B o Y Net magnetization Mo M o Spin states distribution N 1 = exp h B 0 N 0 kt Equilibrium magnetization Mo: - M z aligned with Bo - M xy = 0 N 1 = # of protons in state E 1 N 0 = # of protons in state E 0 k : Boltzmann s constant T : temperature

12 Reminder of three main steps in MRI 0) Equilibrium (M o along B o ) 1) RF excitation (tip M o away from equil.) 2) Precession of M xy induces signal (dephasing for a time TE) Dynamics of magnetization 3) Return to equilibrium (recovery time TR)

13 Dynamics of the magnetization Equation of motion of r M Classical mechanics formalism First, model a single nucleus Then, add up for sample in external r B ext Finally, consider relaxation (Bloch equations)

14 Equation of motion for a single nucleus: Mechanical moment angular momentum (spin) r T = dr L dt Magnetic moment spin r r = L Magnetic moment and magnetic field interaction r T = r r B ext r B ext d r (t ) dt = r (t ) r B ext(t ) Precession of r r about B ext with frequency = B ext

15 Equation of motion for the magnetization vector: Assuming no interaction between nuclei r M = r 0 + r 1 + r r = (spin excess) i And since for each nuclei d r i(t ) dt = r i (t ) r B ext(t ) d r M (t ) dt = r M (t ) r B ext(t) Precession r r of M about B ext with frequency r M B ext = B ext

16 To describe the magnetization we need to choose a coordinate systems Laboratory coordinate system Rotating coordinate system z B o z = z ω o = γ B o B o ω o = γ B o M(t) M (t) x with: B ext (t) = B 0 + B 1 (t) d r M (t ) dt y = r M (t ) r B ext(t) x d r M ' (t ) dt y with: B eff (t) = B 1 (t) = r M ' (t ) r B eff (t ) Example: On-resonance spins: Off-resonance spins: ω o ω o + ω static ω

17 The NMR signal At equilibrium no signal: - static longitudinal magnetization M o B o M xy We need net transverse magnetization: - precession of M xy about B 0 - rotating magnetic field - induces current in a coil: MR signal

18 The NMR signal (continuation) With an RF pulse on resonance we can rotate M 0 B o Rotating frame: dm r Dynamics: ' (t ) = M r ' (t ) B r eff (t ) dt B 1 (t): B 1 constant and to B 0 B 1 B eff (t) = B 1 (t) M precesses about B 1 with ω 1 = γ B 1 Flip angle θ: θ ' = γb 1 t Signal relaxation, system goes back to equilibrium M z M o (T 1 relaxation) M xy 0 (signal loss, T 2 & T 2 * relaxation) Relaxation mechanisms give tissue contrast

19 The NMR signal (continuation) Schematic representation: Radio-frequency pulse (oscillating B 1 (t) rotating at ω 0 ) NMR signal (transverse magnetization decay) Free Induction Decay T 2 * decay

20 Relaxation mechanisms T 1 or spin-lattice relaxation (longitudinal magnetization) Mz defined by spin excess population between two energy states Mz recovery transitions between spin states transitions fluctuating transverse field on resonance molecular motion exponential recovery (T ms, longer for higher B o ) B o M z M o TR time Mz=0 after 90 o RF pulse Mz=Mo at equilibrium dm z dt = M o M z T 1 Repetition time (TR): time allowed for recovery, defines T 1 contrast

21 Relaxation mechanisms (continued) T 2 or spin-spin relaxation (transverse magnetization) incoherent exchange of energy between spins molecular motion fluctuations in local B z resonance frequency variations dephasing of transverse magnetization signal decay exponential decay (T ms) M xy NMR signal M xy M o sinθ TE time M xy max after 90 o RF pulse spins dephase M xy =0 at equilibrium dm dt xy = M T 2 xy Echo time (TE): time allowed for dephasing, defines T 2 contrast

22 Relaxation mechanisms (continued) T 2 * relaxation dephasing of transverse magnetization due to both: - microscopic molecular interactions (T 2 ) - spatial variations of the external main field B (tissue/air, tissue/bone interfaces) exponential decay (T 2 * ms, shorter for higher B o ) M xy M o sin B = µ µ 0 H Boundary conditions Field distortions ( B) T 2 T2* tissue TE time 1 T 2 * = 1 T 2 + Β 2 air

23 Bloch Equations Dynamics of the magnetization + Relaxation effects: d r M (t ) dt = r M (t ) r B ext(t) (M x ˆ i + M y ˆ j ) T 2 * (M z M 0 ) T 1 ˆ k Geometrical description: damped precession (SUMMARY) B 0 M 0 RF NMR signal Equilibrium time Equilibrium