p Spinning Nucleus Produces Magnetic Moment • Amovingelectriccharge produces a magnetic field. • An atomic nucleus can be thought of as a spinning charged body, • which acts like a tiny magnet. • nuclear magnetic moment =p • p = angular momentum • I = nuclear spin (quantum number) • = gyromagnetic ratio • is collinear with p • Normally, the direction that these tiny magnets point in is randomly distributed.
Bo Macroscopic Alignment with B-field • A spinning nucleus placed within a large external magnetic field (B0) will align with the external field. M = MBo 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.
Bo a B1 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 X Y Rotation frequency B1 Flip angle = g B1 t M
Bo Mz a B1 Mx,y Relaxation T1 and T2 “Relaxation” = Return to equilibrium magnetization Longitudinal Transverse
Mxy Mz T1 Recovery and T2 Decay T1 Recovery T2 Decay M0 exp(-t/T2) M0 [1-exp(-t/T1)] 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)
300 200 100 0 0 1 2 3 4 5 CSF GM WM T1 Contrast Example White Matter Gray Matter CSF TR (s) WM GM CSF