TARGET AUDIENCE

Scientists interested in understanding adiabatic, spatial-spectral, and spatially multi-dimensional RF pulses.

OBJECTIVES

Participants should (i) be aware of basic properties and types of RF pulses, (ii) know approaches for RF pulse design, (iii) understand the principles and basic properties of adiabatic, spatial-spectral, and spatially multi-dimensional RF pulses, and (iv) see how the latter could help to realize tailored measurement volumes in MRS.

CONTENT

RF pulses are essential for every MR experiment because they are required to generate transverse magnetization, the source of the acquired signal. Furthermore, they are an important tool to manipulate the magnetization during the experiment, e.g. by reducing the dephasing effect of field inhomogeneities (refocussing), selecting or saturating contributions with a particular chemical shift (spectral editing, water suppression) or at certain spatial positions (slice selection, regional saturation), or enhancing relaxation effects (inversion recovery).
Important parameters of an RF pulse are the complex envelope, usually expressed as magnitude and phase or frequency as a function of time, the duration, and the peak transmitter voltage that define the pulse properties, the most relevant being the energy, the frequency spectrum, often characterized by the bandwidth, and the flip angle which, in general, may vary across the frequency spectrum.
Depending on the purpose of the RF pulse (excitation, saturation, inversion or refocussing), the desired properties, e.g. pulse duration, bandwidth and flip angle, and the boundary conditions, .e.g. maximum transmitter voltage, different RF pulse envelopes may be advantageous. However, to find the best RF pulse envelope for a particular purpose is usually not straightforward, mainly because the desired RF pulse features may require conflicting properties, the Bloch equations cannot be solved analytically for most problems, and physical effects like relaxation and technical or experimental imperfections like inhomogeneities of the transmit RF field (B₁) may degrade the RF pulse performance significantly. These issues have led to the development of methods and tools for RF pulse design and a variety of RF pulse types and envelopes of which a few will be considered in more detail: (i) RF solutions for B1 inhomogeneities, composite and adiabatic RF pulses, (ii) spatial-spectral RF pulses that combine spatial and spectral selectivity, and (iii) spatially multi-dimensional RF pulses that could be used for tailored MRS measurement volumes.
For standard RF pulses the flip angle depends on the B₁ peak amplitude that may vary across the target region, in particular at higher field strengths or when using surface coils for RF transmission. Such inhomogeneities reduce the signal intensity or saturation and labelling efficiency which can hamper applications considerably. To ameliorate these effects, composite RF pulses can be used that consist of several RF sub-pulses with different flip angles and phases. In total, they have the same flip angle as a standard, single RF pulse for an ideal B₁ field but if the B₁ amplitude deviates the flip angle differences of the sub-pulses partially compensate yielding a flip angle much closer to the desired one than for a single RF pulse. A prominent example is the 90°_x-180°_y-90°_x composite RF pulses for the inversion of longitudinal magnetization.
More elaborated are frequency-modulated RF pulses that provide a fixed flip angle for any B₁ peak amplitude exceeding a certain threshold. These so-called adiabatic RF pulses use a variable frequency to obtain an effective flux density in the rotating frame that changes its orientation during the RF pulse, e.g. from longitudinal to transverse, and can “guide” the magnetization parallel to it to the desired orientation. This requires appropriate frequency and amplitude modulation functions and a sufficiently slow change of the effective flux density (adiabatic condition). While adiabatic 90°-excitation and 180°-inversion pulses are rather easy to realize, adiabatic refocussing RF pulses and excitation pulses with arbitrary flip angles are more complex and a composite of basic adiabatic RF pulses.
Spatial-spectral RF pulses that combine spatial and spectral selectivity, are usually composite RF pulses that consist of equidistant, slice-selective RF excitations with different flip angles. Thereby, the temporal distance of the pulses defines the spectral “pass” and “stop” bands: for a phase shift of an even multiple of 180° during the temporal distance, the flip direction is identical for all sub-pulses and their flip angles “add up” to the desired flip angle; for phase shifts that are an odd multiple of 180°, the flip directions alternate between sub-pulses yielding an effective flip angle of 0° if the relative flip angles are chosen according to binomial coefficients. Thus, spectral-spatial RF pulses can be used to excite or saturate water or fat/lipids slice-selective.
The basics of spatially multi-dimensional RF pulses can be sketched when considering the small-flip-angle approximation of the Bloch equations and the so-called excitation K-space: in this case the spatial excitation profile is the Fourier transform of the product of B₁ as a function of K, scaled with the K-space velocity, and the sampling function that defines the gradient trajectory in K-space. This means, for instance, that an appropriate B₁ envelope applied along a 2D, e.g. spiral or blipped-planar, trajectory can excite arbitrarily shaped, two-dimensional profiles which could be used to adapt the MRS measurement volume to the specific shape of the target volume, e.g. to minimize partial volume effects. Thereby, side excitation, periodic copies of the desired excitation profile, occur in the direction of discrete sampling (radial for spiral, blip direction for blipped-planar trajectories) and must be suppressed or positioned outside of the object to avoid unwanted signal contributions.
To achieve a good profile sharpness with such multi-dimensional RF pulses, long trajectories are needed yielding RF pulses with a low bandwidth that are sensitive to frequency offsets like chemical shifts which is a significant problem for MRS applications. However, these effect can be ameliorated or avoided by shorting the effective RF pulseduration, e.g. with parallel transmission technqiues or segmentation, i.e. applying only a segment of the trajectory in each shot and averaging the complex signals obtained for all segments, and/or applying intermediate refocussing RF pulses that avoid the accumulation of phase evolutions along the full RF pulse or the applied segment.

Acknowledgements

No acknowledgement found.