Motion of Magnetization

Gradient Echo Sequences - One pulse

Gradient Echo Sequences - Two pulses

Gradient Echo Sequences - More pulses

GE Sequences - Approach to steady state

GE Sequences - The steady state

GE Sequences - RF-spoiled steady state

GE Sequences - Balanced sequences

CPMG - One refocusing pulse

CPMG - Mone refocusing pulses

CPMG - CPMG static pseudo steady state

Hyperechos - with CPMG sequences

Hyperechoes with gradient echo sequences

RF Pulses - Sinc pulse

The measurable, macroscopic magnetization **M** is composed of nuclear magnetic moments. The macroscopic magnetization **M** can be modified or changed by magnetic fields (B0 or B1 field) and by relaxation processes (also driven by magnetic fields). The equation of motion of **M(t)** can be described by the Bloch equation:

The series below depicts the motion (precession) of **M** for constant **B** = (√2,0,√2). The precession frequency of **M** is proportional to the magnitude of **B**. The magnetic field **B** is shown in white, the magnetization **M** is yellow.

Circularly polarized RF-fields produce a rotating magnetic field **B1(t)** within the transverse x-y plane. In most cases motion of magnetization is described in the rotating frame that rotates with the Larmor frequency ω=-γB0. If the frequency of the RF-field is equal to the Larmor frequency ω **B1(t)** is a constant vector within the x-y plane. The direction of **B1(t)** is given by the phase of the RF-field. If the frequency of **B1(t)** is not equal to the Larmor frequency **B1(t)** will have an additional component along z direction (in the rotating frame). This case is visualized in the part RF pulses.

The series below depicts the motion of**M** during an RF-pulse along x direction (**B** = (1,0,0), initial **M** = (0,0,1), rotating frame).

The series below depicts the motion of

In the rotating frame the magnetization **M** does not precess without additional magnetic fields. Magnetic gradient fields produce an additional magnetic field oriented along z direction. The magnitude of these gradient fields varies linearly along x, y, or z direction. Deviation of the local magnetic field from the main B0 field leads to a precession of the magnetization **M** around the z axis.

The series below depicts the motion of**M** for an additional B0 field along z direction (**B** = (0,0,1), initial **M** = (1,0,0), rotating frame)

The series below depicts the motion of

T1 relaxation leads to an exponential relaxation of the z component of the magnetization *M* towards its equilibrium value Mz=M0. T2 relaxation gives an exponential decay of the transverse component Mxy towards zero.

In most cases T1 is larger that T2 (except for tetrachlorocyclopropene at –89°C, see Anet et.al. Chem.Phys.Lett 1990;171:401-405) to guaranty that |*M(t)*| ≤ M0.

Motion of*M* during T1 and T2 relaxation (initial *M* = (1,0,0), T1 = 2T2, rotating frame)

In most cases T1 is larger that T2 (except for tetrachlorocyclopropene at –89°C, see Anet et.al. Chem.Phys.Lett 1990;171:401-405) to guaranty that |

Motion of

Last updated: Monday, 18.04.2011