1.4 Existing RF Pulse Designs that Address B 1 + Inhomogeneity
1.4.2 Existing spectral-spatial pulse designs
flexible in allowing for excitation, inversion, and refocusing, frequency spectra exhibit erratic behavior thus making the pulses unsuitable for slice-selective imaging. Very recently, a group at Stanford University headed by John Pauli found that using the BIR-4 modulation patterns as an envelope for a series of spectrally selective sub- pulses can result in a slice-selective waveform with similar B+1-insensitive properties to those of the parent BIR-4 (1). This formulation will certainly prove practical in many contexts, with the main drawback being the requisite fulfillment of the adia- batic condition. As mentioned previously, this requirement can prove prohibitive in high-field human applications.
In this thesis, work is presented in which hyperbolic secant and BIR-4 waveforms are numerically optimized to produce the desired insensitivities to field variations (Chapter VI). These efforts differ from those previously described in that the resulting magnetization flip angle is the subject of optimizations rather than fulfillment of the adiabatic condition. Additionally, Appendix C describes adiabatic pulses in more detail than is presented above, including the specific forms of the hyperbolic secant and BIR-4 modulation functions.
(i.e., with a single amplifier) or with a transmission coil for which individual ele- ments are driven independently. The latter technology is typically referred to as parallel transmission or multi-transmit and has emerged in the last five years as the industry-adopted standard by which RF field inhomogeneities are addressed on high- field human scanners.
Single-channel transmission
Spectral-spatial RF pulses typically employ a series of sub-pulses in tandem with an oscillating gradient waveform. Early such designs relied upon the timing of sub- pulses relative to the oscillating gradient lobes to produce frequency selectivity, with spatial selectivity arising in the usual manner of finite bandwidth waveforms executed in the presence of a linear field gradient (57). These original studies were oriented toward targeting specific resonance frequencies in the context of a slice-selective imag- ing. For example, pulses were designed to excite fat within the imaging slice while minimizing signal from water or vice versa (50; 27). The incorporation of transverse gradients (i.e., field gradients imposed perpendicularly to the direction of slice selec- tion) during or between the applied RF sub-pulses allowed for a focused magnetization response within predetermined regions of the imaging slice (65; 67). Eventually, these capabilities were recognized as a means of achieving uniform flip angles in the presence of B1+ inhomogeneities (68). This task can be accomplished through magnetization response being spatially allotted in accordance with the spatial distribution of theB1+ field. Spectral-spatial pulses in which relatively few discrete sub-pulses are interleaved
with transverse field gradients have come to be known as sparse spokes (or simply spokes) designs, and it is this form of spectral-spatial pulses that is most commonly employed to address issues of RF field nonuniformity. Figure 6 illustrates the capa- bility of a spokes design in compensating for the B1+ field variations observed in the human brain at 7 T. Clearly, the strategy is effective. Another application of spokes pulses involves limiting magnetization response to a confined region of the imaging field of view so as to allow for reduced scan times or practical, high-resolution imag- ing of specific anatomy. Regardless of the objective, spokes pulses are implementable on single-channel transmission systems with the potential disadvantage of long total pulse durations (with respect to T2 and T2∗) which may be required to achieve the desired effects. Additionally, the time-consuming subject-specific field mapping and RF calibrations that must be performed prior to implementation of spokes pulses for B1+ mitigation may prove prohibitive, especially in a clinical setting.
Parallel transmission
On a parallel transmission system, independent RF modulations can be executed simultaneously on each RF coil element. Knowledge of theB+1 fields associated with each coil element can be exploited through the design of channel-specific RF wave- forms to counteract the unwanted effects of RF field variations. These RF strategies typically involve numerical optimization of the phase and amplitudes (and sometimes frequency) modulations to be transmitted on each channel. When only the physical separation of the coil elements (along with the optimized RF modulations) is em-
Figure 6: Simulation of a spokes experiment at 7 T showing an actual B1+ field mea- surement (left), the designed excitation pattern from a 25-spoke pulse (middle), and the net excitation pattern when the spokes pulse is executed in the presence of the nonuniform RF field (right). With a traditional RF pulse, the magnetization response would scale with theB1+field such that a map of the resulting flip angles would reflect inhomogeneities in the B1+ distribution. Spokes pulses can be designed to circumvent this problem by concentrating RF effects in a pattern determined by the inverse of the B+1 field. Images reproduced with the permission of Marcin Jankiewicz (34).
ployed to achieve a spatially-varying magnetization response, the process is referred to asRF shimming (37; 48; 84; 49). With this technique, a single pulse is executed on each channel, and, most commonly, all pulses have the same form (e.g., Gaussian or sinc) with only constant phase and amplitude offsets. RF shimming has been shown
effective in moderating B1+-related variations in magnetization phase and flip-angle, with efficacy generally corresponding to the number of RF channels. In practice, the number of independent channels is limited, and the performance of RF shimming is restricted due to the fixed locations of the transceiver elements.
When the spatially varying magnetization responses from RF shimming are inad- equate, spokes pulses may be implemented for parallel transmission. The advantage of a parallel implementation of spokes pulses (as opposed to a single-channel imple- mentation) is that fewer sub-pulses are necessary on each channel, thus resulting in
total pulse duration times that are ∼ N times shorter where N is the number of channels. This increased efficiency relative to the single-channel implementation is due to an optimization in which the spatial separation of the transmitting elements is advantageous. Almost complete mitigation of B1+ inhomogeneities has been demon- strated in the human brain at 7 T using as few as 3 sub-pulses on each channel of an 8-channel system (71; 89).
MR systems equipped with multiple independent transmission channels are be- coming increasingly widespread. The primary motivation is the same as for the use of single-channel spokes pulses—to produce uniform flip angles in the presence of severe B1+ variations. Multi-transmit pulse designs, however, are capable of achieving the desired magnetization responses in far less time, a critical factor given the shorterT2∗ values observed at high field. Despite the impressive performance of multi-transmit systems, there are some inherent limitations. Firstly, the requisite RF amplifiers are expensive, and compromise must be made between the number of channels and accepted performance levels. Also, while B+1-mitigation performance increases with the number of channels, so does the time needed to make the necessary field mea- surements, as separate field maps are required for each channel. Furthermore, the interactions of RF waves from independent coil elements can produce locally high SAR values in the imaging volume. These effects are a function of the coil geometry, the geometry of the imaging volume, and the set of RF waveforms (the latter two of which vary from subject to subject and from slice to slice), so SAR levels can potentially vary greatly from scan to scan, raising the question of whether subject-specific SAR
modeling should be integrated with the pulse optimization process. Such measures, although perhaps justified, would add another step to an increasingly complicated subject-specific workflow—a factor that is not insurmountable but one that will have to be reconciled with clinical practicality in the face of rising healthcare costs.
As described in Section 1.4.1, the pulse designs presented in this thesis fall into the category of B1+-insensitive designs, rather than spectral-spatial designs, and are, in their current forms, intended for single-channel transmission.