page_title: Adiabatic MRI Pulses
section_title: Adiabatic Passage
hierarchical_section_title: Adiabatic MRI Pulses / Analysis - Adiabatic Excitation Principles / Adiabatic Passage
caption_attribution_description: English: Sweep diagram for on-resonance spins in the case of the hyperbolic secant adiabatic pulse, for different RF peak powers. The direction of Beffective is relatively independent of RF peak power. Solid arrows are the final effective fields for AFP; dotted arrows are the final effective fields for AHP.
context_page_description: Adiabatic radio frequency pulses are used in magnetic resonance imaging to achieve excitation that is insensitive to spatial inhomogeneities in the excitation field or off-resonances in the sampled object.
  Nuclear magnetic resonance experiments are often performed with surface transceiver coils that have desirable sensitivity, but have the disadvantage of producing an inhomogeneous excitation field. This inhomogeneous field causes spatial variations in spin flip angles, which, in turn, causes errors and degrades the receiver’s sensitivity. RF pulses can be designed to create low-variation flip-angles or uniform magnetization inversion across a sample, even in the presence of inhomogeneities such as B1-variation and off-resonance.
context_section_description: In general, the RF magnetic field can be written with a time-varying phase and time-varying amplitude, so that, 
  And Beffective in the frame rotating at  can be written as:
  In an “adiabatic passage” process, the parameters A and ω can be varied gradually. Magnetic spin components that are in parallel with Beffective in the rotating frame will “track” Beffective as it changes, provided that Beffective changes “slowly enough.” Similarly, components that are perpendicular to Beffective will remain perpendicular to Beffective as it gradually changes direction. Figure 1 shows how spins track Beffective in an adiabatic passage transition.
  The “gradualness” of the changing Beffective is defined as the “adiabaticity,” K, of the pulse, which is given by:
  where  is defined as the angle of Beffective with the z-axis in the rotating frame of reference. 
  The term K can be understood by examining the ratio by which it is defined: the precession frequency of a spin about Beffective is proportional to the strength of the effective field, and the angle of the field, phi, must change slower than the precession frequency so that the spin can “track” the effective field as it changes direction. This means that in order for a pulse to be considered adiabatic, the K-factor, or adiabaticity, must be greater than 1 for the entire duration of the excitation sequence.  
  Figure 2 shows the magnitude and angle of Beffective for a commonly-used type of adiabatic sweep modulation function where A(t) and (t) are given by:
  It is common to examine the so-called “sweep-diagram” for adiabatic pulses. Sweep-diagrams plot the trajectory of the effective field for a spin with a particular resonance frequency. Figure 3 shows the sweep diagram for two on-resonance spins: blue sweep trajectory for a spin experiencing a B₁ field strength without error, and red sweep trajectory for a spin experiencing a B₁ field strength with significant deviation. Since the direction of Beffective is largely independent of B₁ strength, adiabatic pulses are considered insensitive to B₁ inhomogeneities. 
  For off-resonance spins, the Beffective sweep diagram is shifted up or down by the amount of off-resonance. Another interpretation: the frequency excursion of the adiabatic pulse is always centered at the presumed Larmor frequency. If we have a spin which is not at the Larmor frequency, the relative frequency excursion of the adiabatic RF pulse will not be centered at that spin’s resonance.
caption: Figure 3. Sweep diagram for on-resonance spins in the case of the hyperbolic secant adiabatic pulse, for different RF peak powers. The direction of Beffective is relatively independent of RF peak power. Solid arrows are the final effective fields for AFP; dotted arrows are the final effective fields for AHP.
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