Principles of Magnetic Resonance Imaging Alessandro Sbrizzi UMC Utrecht

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)

MRI in 1980

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) ...

Brain vessels smaller than 1 mm are visualized

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 B0 aligned along the z-axis they precess around it at the Larmor frequency ω = γ |B0|. Same effect as a spinning top (only much faster) γ is a constant (gyromagnetic ratio) Governing equation (by F. Bloch): See also: https://www.imaios.com/en/e-Courses/e-MRI/NMR

Basic physical principles II The transverse component of μ is randomly distributed over a small volume V (net sum over V = 0) Only the longitudinal component 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

Basic physical principles III Idea: apply an additional external field, BRF in the xy plane which rotates μ around it. Since μ is still precessing, consider a rotating reference frame with the same rotating rate ω = γ |B0|. In the rotating frame, μrot is 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

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

Basic physical principles V Macroscopic view: Net effect on μ over 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

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 My over the spatial coordinates (i.e. image), we need to solve this equation for Mx+i My .

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)