Spinning Nucleus Produces Magnetic Moment A moving electric charge produces a magnetic field. An atomic nucleus can be thought of as a spinning charged body, which acts like a tiny magnet. p  nuclear magnetic moment =p p = angular momentum I = nuclear spin (quantum number) = gyromagnetic ratio  is collinear with p Magnetism is a property of matter that is a result of the orbiting of the electrons in atoms. The orbiting electrons cause the atoms to have a magnetic moment associated with an intrinsic angular momentum called "spin". Normally, the direction that these tiny magnets point in is randomly distributed.

Macroscopic Alignment with B-field Bo A spinning nucleus placed within a large external magnetic field (B0) will align with the external field. M = MBo  In the magnetic field of an MRI scanner at room temperature, there is approximately the same number of proton nuclei aligned with the main magnetic field Bo as counter-aligned. The aligned position is slightly favored, as the nucleus is at a lower energy in this position. For every one-million nuclei, there is about one extra nucleus aligned with the Bo field as opposed to the field. This results in a net or macroscopic magnetization pointing in the direction of the main magnetic field. I = 1/2 case cM: magnetic susceptibility For protons: cM~10-6

Precession at “Resonance” Frequency The magnetic field exerts a torque on the spinning proton, causing it to precess, similar to a spinning top. The magnetic moment precesses around the applied field at a rate proportional to the applied static field: the Larmor frequency. Bo = 1 Tesla H-1 : 42.58 MHz (o/2) Na-23 : 11.26 MHz P-31 : 17.24 MHz The Lamor frequency for conventional MRI lies in the radio frequency range.

Excitation = Tip Magnetization into Transverse Plane An additional magnetic field B1, perpendicular to the static field B0, can be added to tip the spins into the transverse plane. B1 is most efficient when its frequency matches the Lamor frequency: resonance condition. Z Bo B1 a X Y Rotation frequency B1 Flip angle  = g B1 t M

Relaxation  T1 and T2 Mz Mx,y Longitudinal Transverse “Relaxation” = Return to equilibrium magnetization Bo B1 a Mx,y Mz Longitudinal Transverse

T1 Recovery and T2 Decay T1 Recovery Mxy T2 Decay Mz M0 exp(-t/T2) time time T1 and T2 are independent processes, T2≤T1 Transverse magnetization, Mxy, is the detected signal T2 = T1 T2 = 0.5T1 T2 = 0.25T1

B0 T1 T2

T2 is Dephasing of Transverse Signal Spins precess in XY plane about B0. Variation in B0 causes faster and slower precession rates. z Bo B0 B0 Mxy y x z T1 recovery of Mz Bo MZ MRI signal is “net” vector Mxy Mxy y x

Terminology T1 is the time constant of Mz to return to equilibrium. T2 and T2* are time constants of loss of Mxy T2 signal loss is “entropic” -- it cannot be recovered. T2* signal loss is reversable (sometimes) with a spin-echo. TR, Repetition Time Tissue with shorter T1 recovers Mz faster. TE, Echo Time (signal acquisition time) Tissue with shorter T2 (or T2*) loses Mxy faster.

The Spin Echo 90o pulse spins dephase 180o pulse spins re-align spin echo Spin echo refocuses dephasing from static field inhomogeneity, i.e T2*. T2 dephasing is not refocused. Gradient echo creates an artificial, gradient-induced echo. No refocusing of T2 or T2*.

Contrast Contrast: Difference in signal intensity Spatial contrast (e.g. tissue types) Temporal contrast (changing properties, T1 or T2) BOLD is a T2* (or T2) contrast T1 Contrast T2 Contrast T1 Contrast T2 Contrast TR (s) TE (ms)

T1 Contrast Example White Matter Gray Matter CSF 100 200 300 CSF GM WM T1 Contrast Example White Matter Gray Matter CSF 5 4 3 2 1 TR (s) WM GM CSF