In magnetic resonance imaging (MRI), imaging objects are stimulated using radio frequency (RF) pulses to generate signals. To obtain a magnetic resonance (MR) image of an object, the object is placed in a uniform magnetic field. As a result, the object's hydrogen nuclei align with the magnetic field and create a net magnetic moment. A RF pulse is applied. The pulse causes the magnetization to change. Once the RF signal is removed, the nuclei realign themselves such that the net magnetic moment returns. The return to equilibrium is referred to as relaxation. During relaxation, the nuclei lose energy by emitting a RF signal. The signal is measured by a conductive field coil placed around or on the object being imaged. The measurement is processed or reconstructed to obtain MR images.
RF pulses may be designed to generate different reactions under different scenarios or different tissues. The challenge of pulse design is to determine a RF pulse that excites a desired magnetization profile (signal). The change in magnetization and gradient fields may be solved by Bloch equations, for which no analytic inversion exists with respect to the change in magnetization. As such, the “forward problem” of calculating the signal generated by a given RF pulse may be solved by a Bloch simulation, while the “backward problem” of designing the RF pulse that may generate a desired signal is difficult, given the non-linearity of the system.
Designing an RF pulse is even more challenging when requirements such as narrow transition band (spatially, spectrally, and etc.), short RF duration, restricted energy deposition, and insensitivity to system imperfection are attached.