Principles of Magnetic Resonance Imaging Alessandro Sbrizzi UMC Utrecht

1. Principles of Magnetic Resonance ImagingAlessandro SbrizziUMC Utrecht

2. A recent history • 1946 Felix Bloch and Edward Purcell independently discover the magnetic resonance phenomena (Nobel Prize in 1952) • 1971 Raymond Damadian: nuclear magnetic relaxation times of tissues and tumors differed→Clinical Application • 1973/1974 Paul C. Lauterbur and Peter Mansfield: spatial localization through Gradient Fields →Imaging (Nobel Prize in 2003)

3. MRI in 1980

4. The present About 100 million MRI scans per year (worldwide): • Tumors • Multiple Sclerosis • Epilepsy • Neuro-degenerative diseases • Ischemic Stroke • Stenosis or aneurysms (MR Angiography) • Cardiac • Brain Functioning (fMRI) • MR guided surgery (MRI-Linac) • ...

6. Brain vessels smaller than 1 mm are visualized

7. Basic physical principles I • Nuclei can be seen as small tiny rotating magnets • Represented by magnetic moment vector • In the presence of external magnetic field B0aligned along the z-axis they precess around it at the Larmor frequency ω = γ |B0|. • Same effect as a spinning top (only much faster) • γis a constant (gyromagnetic ratio) • Governing equation (by F. Bloch): See also: https://www.imaios.com/en/e-Courses/e-MRI/NMR

8. Basic physical principles II • The transverse component of μis randomly distributed over a small volume V (net sum over V = 0) • Only the longitudinalcomponent of μ is slightly different than 0, but it can not be measured. • To measure the magnetic moments, we need them to acquire a net transverse magnetization which differs from 0 See also: https://www.imaios.com/en/e-Courses/e-MRI/NMR

9. Basic physical principles III • Idea: apply an additional external field, BRF in the xy plane which rotates μ around it. • Since μis still precessing, consider a rotating reference frame with the same rotating rate ω = γ |B0|. • In the rotating frame, μrotis frozen, no longer precessing. • We apply BRF such that in this rotating frame it appears to be static too: BRF = (A cos ωt, A sin ωt, 0) thus Brot= (A,0,0). • Since ω is in the radio-frequency range, BRF is called a radio-frequency field. • This condition is called resonance. See also: https://www.imaios.com/en/e-Courses/e-MRI/NMR

10. Basic physical principles IV • Bloch equation in the rotating frame: • Effect in the rotating frame: μrotprecesses around the x axis as long as the RF field is ON. • Effect in the laboratory frame: μ quickly precesses around B0 and slowlyprecesses around BRF See also: https://www.imaios.com/en/e-Courses/e-MRI/NMR

11. Basic physical principles V • Macroscopic view: Net effect on μover a small volume V is described by the net magnetization vector M = (Mx, My , Mz): • When only static B0 is present: M is aligned along it (no transverse component). • When also RF field is on: M is tilted and acquires a transverse component which can be measured. See also: https://www.imaios.com/en/e-Courses/e-MRI/NMR

12. Basic physical principles VI • Once M has a transverse component, signal can be collected: • G is a third type of (time-dependent) magnetic field which is needed in order to spatially encode the signal from the spins (more on this later on…) • Since we are interested in the value of Mx+i Myover the spatial coordinates (i.e. image), we need to solve this equation for Mx+i My.

13. Basic physical principles VII • The MRI scanner: • The main, static magnetic field B0 (to align the spins) • The Radio Frequency field BRF (to tilt the spins) • The Gradient field, G (spatial localization)